# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18_F1_AE_CS_SP_PS_S0V
# and selection function PSelectComplexExceptRRHorn.
#
# Preprocessing time       : 0.023 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(fc2_ring_4, axiom, ![X1]:((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v2_ring_4(k12_polynom3(X1),X1))), file('e_trans2/e_trans2__l79_e_trans2', fc2_ring_4)).
fof(fc1_ring_4, axiom, ![X1, X2]:(((((~(v2_struct_0(X1))&l2_struct_0(X1))&~(v2_struct_0(X2)))&v2_ring_4(X2,X1))&l1_struct_0(X2))=>v1_ring_4(u1_struct_0(X2),X1)), file('e_trans2/e_trans2__l79_e_trans2', fc1_ring_4)).
fof(dt_k11_gaussint, axiom, ((~(v2_struct_0(k11_gaussint))&v36_algstr_0(k11_gaussint))&l6_algstr_0(k11_gaussint)), file('e_trans2/e_trans2__l79_e_trans2', dt_k11_gaussint)).
fof(fc30_gaussint, axiom, ((((((((((((~(v2_struct_0(k11_gaussint))&~(v6_struct_0(k11_gaussint)))&v13_algstr_0(k11_gaussint))&v33_algstr_0(k11_gaussint))&v36_algstr_0(k11_gaussint))&v3_group_1(k11_gaussint))&v5_group_1(k11_gaussint))&v2_rlvect_1(k11_gaussint))&v3_rlvect_1(k11_gaussint))&v4_rlvect_1(k11_gaussint))&v3_vectsp_1(k11_gaussint))&v5_vectsp_1(k11_gaussint))&v6_vectsp_1(k11_gaussint)), file('e_trans2/e_trans2__l79_e_trans2', fc30_gaussint)).
fof(redefinition_m1_ring_4, axiom, ![X1, X2]:((((~(v2_struct_0(X1))&l2_struct_0(X1))&~(v1_xboole_0(X2)))&v1_ring_4(X2,X1))=>![X3]:(m1_ring_4(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('e_trans2/e_trans2__l79_e_trans2', redefinition_m1_ring_4)).
fof(l79_e_trans2, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(m1_ring_4(X2,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>k5_binom(k12_polynom3(k11_gaussint),X2,X1)=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),k2_basel_2(k11_gaussint,X2)))), file('e_trans2/e_trans2__l79_e_trans2', l79_e_trans2)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('e_trans2/e_trans2__l79_e_trans2', dt_l2_algstr_0)).
fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('e_trans2/e_trans2__l79_e_trans2', dt_l6_algstr_0)).
fof(dt_l1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>l1_struct_0(X1)), file('e_trans2/e_trans2__l79_e_trans2', dt_l1_algstr_0)).
fof(dt_k12_polynom3, axiom, ![X1]:((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&l6_algstr_0(k12_polynom3(X1)))), file('e_trans2/e_trans2__l79_e_trans2', dt_k12_polynom3)).
fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('e_trans2/e_trans2__l79_e_trans2', fc2_struct_0)).
fof(d2_basel_2, axiom, ![X1]:((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))=>k2_basel_2(X1,X2)=X2)), file('e_trans2/e_trans2__l79_e_trans2', d2_basel_2)).
fof(dt_k2_basel_2, axiom, ![X1, X2]:(((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(k12_polynom3(X1))))=>(((v1_funct_1(k2_basel_2(X1,X2))&v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(k2_basel_2(X1,X2),X1))&m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), file('e_trans2/e_trans2__l79_e_trans2', dt_k2_basel_2)).
fof(t2_field_8, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((v1_funct_1(X2)&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>r2_funct_2(k4_ordinal1,u1_struct_0(X1),k4_polynom5(X1,X2,X3),k10_polynom3(X1,k2_ring_4(X1,X3),X2))))), file('e_trans2/e_trans2__l79_e_trans2', t2_field_8)).
fof(dt_k4_polynom5, axiom, ![X1, X2, X3]:((((((~(v2_struct_0(X1))&l3_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&m1_subset_1(X3,u1_struct_0(X1)))=>((v1_funct_1(k4_polynom5(X1,X2,X3))&v1_funct_2(k4_polynom5(X1,X2,X3),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k4_polynom5(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), file('e_trans2/e_trans2__l79_e_trans2', dt_k4_polynom5)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('e_trans2/e_trans2__l79_e_trans2', dt_l5_algstr_0)).
fof(dt_k2_ring_4, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l2_struct_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>((v1_funct_1(k2_ring_4(X1,X2))&v1_funct_2(k2_ring_4(X1,X2),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k2_ring_4(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), file('e_trans2/e_trans2__l79_e_trans2', dt_k2_ring_4)).
fof(fc31_gaussint, axiom, ((~(v2_struct_0(k11_gaussint))&v36_algstr_0(k11_gaussint))&v4_vectsp_1(k11_gaussint)), file('e_trans2/e_trans2__l79_e_trans2', fc31_gaussint)).
fof(dt_l4_algstr_0, axiom, ![X1]:(l4_algstr_0(X1)=>(l3_struct_0(X1)&l3_algstr_0(X1))), file('e_trans2/e_trans2__l79_e_trans2', dt_l4_algstr_0)).
fof(dt_k9_struct_0, axiom, ![X1, X2]:(l1_struct_0(X2)=>m1_subset_1(k9_struct_0(X1,X2),u1_struct_0(X2))), file('e_trans2/e_trans2__l79_e_trans2', dt_k9_struct_0)).
fof(dt_k11_polynom3, axiom, ![X1, X2, X3]:((((((((((((~(v2_struct_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&v1_funct_1(X3))&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((v1_funct_1(k11_polynom3(X1,X2,X3))&v1_funct_2(k11_polynom3(X1,X2,X3),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k11_polynom3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), file('e_trans2/e_trans2__l79_e_trans2', dt_k11_polynom3)).
fof(redefinition_k11_polynom3, axiom, ![X1, X2, X3]:((((((((((((~(v2_struct_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&v1_funct_1(X3))&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>k11_polynom3(X1,X2,X3)=k10_polynom3(X1,X2,X3)), file('e_trans2/e_trans2__l79_e_trans2', redefinition_k11_polynom3)).
fof(t6_e_trans1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(m1_ring_4(X2,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>k5_binom(k12_polynom3(k11_gaussint),X2,X1)=k4_polynom5(k11_gaussint,X2,k9_struct_0(X1,k11_gaussint)))), file('e_trans2/e_trans2__l79_e_trans2', t6_e_trans1)).
fof(redefinition_r2_funct_2, axiom, ![X1, X2, X3, X4]:((((((v1_funct_1(X3)&v1_funct_2(X3,X1,X2))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&v1_funct_1(X4))&v1_funct_2(X4,X1,X2))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_funct_2(X1,X2,X3,X4)<=>X3=X4)), file('e_trans2/e_trans2__l79_e_trans2', redefinition_r2_funct_2)).
fof(c_0_24, plain, ![X1]:((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v2_ring_4(k12_polynom3(X1),X1))), inference(fof_simplification,[status(thm)],[fc2_ring_4])).
fof(c_0_25, plain, ![X1, X2]:(((((~v2_struct_0(X1)&l2_struct_0(X1))&~v2_struct_0(X2))&v2_ring_4(X2,X1))&l1_struct_0(X2))=>v1_ring_4(u1_struct_0(X2),X1)), inference(fof_simplification,[status(thm)],[fc1_ring_4])).
fof(c_0_26, plain, ![X72]:(((~v2_struct_0(k12_polynom3(X72))|(v2_struct_0(X72)|~v13_algstr_0(X72)|~v3_rlvect_1(X72)|~v4_rlvect_1(X72)|~v5_vectsp_1(X72)|~l6_algstr_0(X72)))&(v36_algstr_0(k12_polynom3(X72))|(v2_struct_0(X72)|~v13_algstr_0(X72)|~v3_rlvect_1(X72)|~v4_rlvect_1(X72)|~v5_vectsp_1(X72)|~l6_algstr_0(X72))))&(v2_ring_4(k12_polynom3(X72),X72)|(v2_struct_0(X72)|~v13_algstr_0(X72)|~v3_rlvect_1(X72)|~v4_rlvect_1(X72)|~v5_vectsp_1(X72)|~l6_algstr_0(X72)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])).
fof(c_0_27, plain, ((~v2_struct_0(k11_gaussint)&v36_algstr_0(k11_gaussint))&l6_algstr_0(k11_gaussint)), inference(fof_simplification,[status(thm)],[dt_k11_gaussint])).
fof(c_0_28, plain, ((((((((((((~v2_struct_0(k11_gaussint)&~v6_struct_0(k11_gaussint))&v13_algstr_0(k11_gaussint))&v33_algstr_0(k11_gaussint))&v36_algstr_0(k11_gaussint))&v3_group_1(k11_gaussint))&v5_group_1(k11_gaussint))&v2_rlvect_1(k11_gaussint))&v3_rlvect_1(k11_gaussint))&v4_rlvect_1(k11_gaussint))&v3_vectsp_1(k11_gaussint))&v5_vectsp_1(k11_gaussint))&v6_vectsp_1(k11_gaussint)), inference(fof_simplification,[status(thm)],[fc30_gaussint])).
fof(c_0_29, plain, ![X1, X2]:((((~v2_struct_0(X1)&l2_struct_0(X1))&~v1_xboole_0(X2))&v1_ring_4(X2,X1))=>![X3]:(m1_ring_4(X3,X1,X2)<=>m1_subset_1(X3,X2))), inference(fof_simplification,[status(thm)],[redefinition_m1_ring_4])).
fof(c_0_30, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(m1_ring_4(X2,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>k5_binom(k12_polynom3(k11_gaussint),X2,X1)=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),k2_basel_2(k11_gaussint,X2))))), inference(assume_negation,[status(cth)],[l79_e_trans2])).
fof(c_0_31, plain, ![X70, X71]:(v2_struct_0(X70)|~l2_struct_0(X70)|v2_struct_0(X71)|~v2_ring_4(X71,X70)|~l1_struct_0(X71)|v1_ring_4(u1_struct_0(X71),X70)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])).
cnf(c_0_32, plain, (v2_ring_4(k12_polynom3(X1),X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_33, plain, (l6_algstr_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_34, plain, (v5_vectsp_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_35, plain, (v4_rlvect_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_36, plain, (v3_rlvect_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_37, plain, (v13_algstr_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_38, plain, (~v2_struct_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_27])).
fof(c_0_39, plain, ![X66]:((l2_struct_0(X66)|~l2_algstr_0(X66))&(l1_algstr_0(X66)|~l2_algstr_0(X66))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
fof(c_0_40, plain, ![X69]:((l2_algstr_0(X69)|~l6_algstr_0(X69))&(l5_algstr_0(X69)|~l6_algstr_0(X69))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_41, plain, ![X65]:(~l1_algstr_0(X65)|l1_struct_0(X65)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_algstr_0])])).
fof(c_0_42, plain, ![X1]:((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&l6_algstr_0(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[dt_k12_polynom3])).
fof(c_0_43, plain, ![X79, X80, X81]:((~m1_ring_4(X81,X79,X80)|m1_subset_1(X81,X80)|(v2_struct_0(X79)|~l2_struct_0(X79)|v1_xboole_0(X80)|~v1_ring_4(X80,X79)))&(~m1_subset_1(X81,X80)|m1_ring_4(X81,X79,X80)|(v2_struct_0(X79)|~l2_struct_0(X79)|v1_xboole_0(X80)|~v1_ring_4(X80,X79)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])).
fof(c_0_44, negated_conjecture, (v7_ordinal1(esk1_0)&(m1_ring_4(esk2_0,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))&k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0)!=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(esk1_0,k11_gaussint)),k2_basel_2(k11_gaussint,esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])).
cnf(c_0_45, plain, (v2_struct_0(X1)|v2_struct_0(X2)|v1_ring_4(u1_struct_0(X2),X1)|~l2_struct_0(X1)|~v2_ring_4(X2,X1)|~l1_struct_0(X2)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_46, plain, (v2_ring_4(k12_polynom3(k11_gaussint),k11_gaussint)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_47, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_39])).
cnf(c_0_48, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])).
cnf(c_0_49, plain, (l1_struct_0(X1)|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_50, plain, (l1_algstr_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_39])).
fof(c_0_51, plain, ![X55]:(((~v2_struct_0(k12_polynom3(X55))|(v2_struct_0(X55)|~v13_algstr_0(X55)|~v3_rlvect_1(X55)|~v4_rlvect_1(X55)|~v5_vectsp_1(X55)|~l6_algstr_0(X55)))&(v36_algstr_0(k12_polynom3(X55))|(v2_struct_0(X55)|~v13_algstr_0(X55)|~v3_rlvect_1(X55)|~v4_rlvect_1(X55)|~v5_vectsp_1(X55)|~l6_algstr_0(X55))))&(l6_algstr_0(k12_polynom3(X55))|(v2_struct_0(X55)|~v13_algstr_0(X55)|~v3_rlvect_1(X55)|~v4_rlvect_1(X55)|~v5_vectsp_1(X55)|~l6_algstr_0(X55)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])).
cnf(c_0_52, plain, (m1_subset_1(X1,X3)|v2_struct_0(X2)|v1_xboole_0(X3)|~m1_ring_4(X1,X2,X3)|~l2_struct_0(X2)|~v1_ring_4(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_43])).
cnf(c_0_53, negated_conjecture, (m1_ring_4(esk2_0,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_54, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k12_polynom3(k11_gaussint))|~l2_struct_0(k11_gaussint)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_38])).
cnf(c_0_55, plain, (l2_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_47, c_0_48])).
cnf(c_0_56, plain, (l1_struct_0(X1)|~l2_algstr_0(X1)), inference(spm,[status(thm)],[c_0_49, c_0_50])).
cnf(c_0_57, plain, (l6_algstr_0(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_51])).
fof(c_0_58, plain, ![X1]:((~v2_struct_0(X1)&l1_struct_0(X1))=>~v1_xboole_0(u1_struct_0(X1))), inference(fof_simplification,[status(thm)],[fc2_struct_0])).
cnf(c_0_59, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk2_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)|~l2_struct_0(k11_gaussint)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_38])).
cnf(c_0_60, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_33])])).
cnf(c_0_61, plain, (l1_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_56, c_0_48])).
cnf(c_0_62, plain, (l6_algstr_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
fof(c_0_63, plain, ![X73]:(v2_struct_0(X73)|~l1_struct_0(X73)|~v1_xboole_0(u1_struct_0(X73))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])).
cnf(c_0_64, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk2_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_55]), c_0_33])])).
cnf(c_0_65, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_62])])).
fof(c_0_66, plain, ![X1]:((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))=>k2_basel_2(X1,X2)=X2)), inference(fof_simplification,[status(thm)],[d2_basel_2])).
cnf(c_0_67, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_68, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk2_0,u1_struct_0(k12_polynom3(k11_gaussint)))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_64, c_0_65])).
fof(c_0_69, plain, ![X1, X2]:(((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(k12_polynom3(X1))))=>(((v1_funct_1(k2_basel_2(X1,X2))&v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(k2_basel_2(X1,X2),X1))&m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k2_basel_2])).
fof(c_0_70, plain, ![X50, X51]:(v2_struct_0(X50)|~v13_algstr_0(X50)|~v3_rlvect_1(X50)|~v4_rlvect_1(X50)|~v5_vectsp_1(X50)|~l6_algstr_0(X50)|(~m1_subset_1(X51,u1_struct_0(k12_polynom3(X50)))|k2_basel_2(X50,X51)=X51)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])).
cnf(c_0_71, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k12_polynom3(k11_gaussint)))|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
fof(c_0_72, plain, ![X56, X57]:((((v1_funct_1(k2_basel_2(X56,X57))|(v2_struct_0(X56)|~v13_algstr_0(X56)|~v3_rlvect_1(X56)|~v4_rlvect_1(X56)|~v5_vectsp_1(X56)|~l6_algstr_0(X56)|~m1_subset_1(X57,u1_struct_0(k12_polynom3(X56)))))&(v1_funct_2(k2_basel_2(X56,X57),k4_ordinal1,u1_struct_0(X56))|(v2_struct_0(X56)|~v13_algstr_0(X56)|~v3_rlvect_1(X56)|~v4_rlvect_1(X56)|~v5_vectsp_1(X56)|~l6_algstr_0(X56)|~m1_subset_1(X57,u1_struct_0(k12_polynom3(X56))))))&(v1_polynom1(k2_basel_2(X56,X57),X56)|(v2_struct_0(X56)|~v13_algstr_0(X56)|~v3_rlvect_1(X56)|~v4_rlvect_1(X56)|~v5_vectsp_1(X56)|~l6_algstr_0(X56)|~m1_subset_1(X57,u1_struct_0(k12_polynom3(X56))))))&(m1_subset_1(k2_basel_2(X56,X57),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X56))))|(v2_struct_0(X56)|~v13_algstr_0(X56)|~v3_rlvect_1(X56)|~v4_rlvect_1(X56)|~v5_vectsp_1(X56)|~l6_algstr_0(X56)|~m1_subset_1(X57,u1_struct_0(k12_polynom3(X56)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])).
cnf(c_0_73, plain, (v2_struct_0(X1)|k2_basel_2(X1,X2)=X2|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_70])).
cnf(c_0_74, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k12_polynom3(k11_gaussint)))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_61]), c_0_62])])).
cnf(c_0_75, plain, (v1_funct_1(k2_basel_2(X1,X2))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_72])).
fof(c_0_76, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((v1_funct_1(X2)&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>r2_funct_2(k4_ordinal1,u1_struct_0(X1),k4_polynom5(X1,X2,X3),k10_polynom3(X1,k2_ring_4(X1,X3),X2))))), inference(fof_simplification,[status(thm)],[t2_field_8])).
cnf(c_0_77, plain, (m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_72])).
cnf(c_0_78, plain, (v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_72])).
cnf(c_0_79, negated_conjecture, (k2_basel_2(k11_gaussint,esk2_0)=esk2_0|v2_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_80, negated_conjecture, (v1_funct_1(k2_basel_2(k11_gaussint,esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_74]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_81, plain, (v1_polynom1(k2_basel_2(X1,X2),X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_72])).
fof(c_0_82, plain, ![X1, X2, X3]:((((((~v2_struct_0(X1)&l3_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&m1_subset_1(X3,u1_struct_0(X1)))=>((v1_funct_1(k4_polynom5(X1,X2,X3))&v1_funct_2(k4_polynom5(X1,X2,X3),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k4_polynom5(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k4_polynom5])).
fof(c_0_83, plain, ![X68]:((l4_algstr_0(X68)|~l5_algstr_0(X68))&(l4_struct_0(X68)|~l5_algstr_0(X68))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
fof(c_0_84, plain, ![X1, X2]:(((~v2_struct_0(X1)&l2_struct_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>((v1_funct_1(k2_ring_4(X1,X2))&v1_funct_2(k2_ring_4(X1,X2),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k2_ring_4(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k2_ring_4])).
fof(c_0_85, plain, ![X86, X87, X88]:(v2_struct_0(X86)|~v13_algstr_0(X86)|~v2_rlvect_1(X86)|~v3_rlvect_1(X86)|~v4_rlvect_1(X86)|~v4_vectsp_1(X86)|~v5_vectsp_1(X86)|~v3_group_1(X86)|~l6_algstr_0(X86)|(~v1_funct_1(X87)|~v1_funct_2(X87,k4_ordinal1,u1_struct_0(X86))|~v1_polynom1(X87,X86)|~m1_subset_1(X87,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X86))))|(~m1_subset_1(X88,u1_struct_0(X86))|r2_funct_2(k4_ordinal1,u1_struct_0(X86),k4_polynom5(X86,X87,X88),k10_polynom3(X86,k2_ring_4(X86,X88),X87))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])).
cnf(c_0_86, negated_conjecture, (m1_subset_1(k2_basel_2(k11_gaussint,esk2_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_74]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
fof(c_0_87, plain, ((~v2_struct_0(k11_gaussint)&v36_algstr_0(k11_gaussint))&v4_vectsp_1(k11_gaussint)), inference(fof_simplification,[status(thm)],[fc31_gaussint])).
cnf(c_0_88, plain, (v2_struct_0(X1)|~v2_struct_0(k12_polynom3(X1))|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_89, negated_conjecture, (v1_funct_2(esk2_0,k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38]), c_0_74])).
cnf(c_0_90, negated_conjecture, (v1_funct_1(esk2_0)|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_80, c_0_79])).
cnf(c_0_91, negated_conjecture, (v1_polynom1(k2_basel_2(k11_gaussint,esk2_0),k11_gaussint)|v2_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_74]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
fof(c_0_92, plain, ![X60, X61, X62]:(((v1_funct_1(k4_polynom5(X60,X61,X62))|(v2_struct_0(X60)|~l3_algstr_0(X60)|~v1_funct_1(X61)|~v1_funct_2(X61,k4_ordinal1,u1_struct_0(X60))|~m1_subset_1(X61,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X60))))|~m1_subset_1(X62,u1_struct_0(X60))))&(v1_funct_2(k4_polynom5(X60,X61,X62),k4_ordinal1,u1_struct_0(X60))|(v2_struct_0(X60)|~l3_algstr_0(X60)|~v1_funct_1(X61)|~v1_funct_2(X61,k4_ordinal1,u1_struct_0(X60))|~m1_subset_1(X61,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X60))))|~m1_subset_1(X62,u1_struct_0(X60)))))&(m1_subset_1(k4_polynom5(X60,X61,X62),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X60))))|(v2_struct_0(X60)|~l3_algstr_0(X60)|~v1_funct_1(X61)|~v1_funct_2(X61,k4_ordinal1,u1_struct_0(X60))|~m1_subset_1(X61,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X60))))|~m1_subset_1(X62,u1_struct_0(X60))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])).
fof(c_0_93, plain, ![X67]:((l3_struct_0(X67)|~l4_algstr_0(X67))&(l3_algstr_0(X67)|~l4_algstr_0(X67))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l4_algstr_0])])])).
cnf(c_0_94, plain, (l4_algstr_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_95, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])).
fof(c_0_96, plain, ![X58, X59]:(((v1_funct_1(k2_ring_4(X58,X59))|(v2_struct_0(X58)|~l2_struct_0(X58)|~m1_subset_1(X59,u1_struct_0(X58))))&(v1_funct_2(k2_ring_4(X58,X59),k4_ordinal1,u1_struct_0(X58))|(v2_struct_0(X58)|~l2_struct_0(X58)|~m1_subset_1(X59,u1_struct_0(X58)))))&(m1_subset_1(k2_ring_4(X58,X59),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X58))))|(v2_struct_0(X58)|~l2_struct_0(X58)|~m1_subset_1(X59,u1_struct_0(X58))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])).
fof(c_0_97, plain, ![X63, X64]:(~l1_struct_0(X64)|m1_subset_1(k9_struct_0(X63,X64),u1_struct_0(X64))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k9_struct_0])])).
cnf(c_0_98, plain, (v2_struct_0(X1)|r2_funct_2(k4_ordinal1,u1_struct_0(X1),k4_polynom5(X1,X2,X3),k10_polynom3(X1,k2_ring_4(X1,X3),X2))|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~v1_polynom1(X2,X1)|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_99, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_86, c_0_79])).
cnf(c_0_100, plain, (v4_vectsp_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_101, plain, (v3_group_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_102, negated_conjecture, (v1_funct_2(esk2_0,k4_ordinal1,u1_struct_0(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_103, negated_conjecture, (v1_funct_1(esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_90]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_104, plain, (v2_rlvect_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_105, negated_conjecture, (v1_polynom1(esk2_0,k11_gaussint)|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_91, c_0_79])).
cnf(c_0_106, plain, (m1_subset_1(k4_polynom5(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~l3_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_92])).
cnf(c_0_107, plain, (l3_algstr_0(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_108, plain, (l4_algstr_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_94, c_0_95])).
cnf(c_0_109, plain, (v1_funct_1(k4_polynom5(X1,X2,X3))|v2_struct_0(X1)|~l3_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_92])).
cnf(c_0_110, plain, (v1_funct_2(k4_polynom5(X1,X2,X3),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~l3_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_92])).
fof(c_0_111, plain, ![X1, X2, X3]:((((((((((((~v2_struct_0(X1)&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&v1_funct_1(X3))&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((v1_funct_1(k11_polynom3(X1,X2,X3))&v1_funct_2(k11_polynom3(X1,X2,X3),k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(k11_polynom3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k11_polynom3])).
cnf(c_0_112, plain, (m1_subset_1(k2_ring_4(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~l2_struct_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_113, plain, (m1_subset_1(k9_struct_0(X2,X1),u1_struct_0(X1))|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_97])).
cnf(c_0_114, plain, (v1_funct_2(k2_ring_4(X1,X2),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~l2_struct_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_115, plain, (v1_funct_1(k2_ring_4(X1,X2))|v2_struct_0(X1)|~l2_struct_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_96])).
cnf(c_0_116, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k4_polynom5(k11_gaussint,esk2_0,X1),k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,X1),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99]), c_0_100]), c_0_101]), c_0_102]), c_0_103]), c_0_104]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38]), c_0_105])).
fof(c_0_117, plain, ![X1, X2, X3]:((((((((((((~v2_struct_0(X1)&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&v1_funct_1(X3))&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>k11_polynom3(X1,X2,X3)=k10_polynom3(X1,X2,X3)), inference(fof_simplification,[status(thm)],[redefinition_k11_polynom3])).
cnf(c_0_118, negated_conjecture, (m1_subset_1(k4_polynom5(k11_gaussint,esk2_0,X1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))|~l3_algstr_0(k11_gaussint)|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_99]), c_0_102]), c_0_103])]), c_0_38])).
cnf(c_0_119, plain, (l3_algstr_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_107, c_0_108])).
cnf(c_0_120, negated_conjecture, (v1_funct_1(k4_polynom5(k11_gaussint,esk2_0,X1))|v2_struct_0(k12_polynom3(k11_gaussint))|~l3_algstr_0(k11_gaussint)|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_99]), c_0_102]), c_0_103])]), c_0_38])).
cnf(c_0_121, negated_conjecture, (v1_funct_2(k4_polynom5(k11_gaussint,esk2_0,X1),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))|~l3_algstr_0(k11_gaussint)|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_99]), c_0_102]), c_0_103])]), c_0_38])).
fof(c_0_122, plain, ![X52, X53, X54]:(((v1_funct_1(k11_polynom3(X52,X53,X54))|(v2_struct_0(X52)|~v2_rlvect_1(X52)|~v3_rlvect_1(X52)|~v4_rlvect_1(X52)|~v5_group_1(X52)|~l6_algstr_0(X52)|~v1_funct_1(X53)|~v1_funct_2(X53,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X53,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))|~v1_funct_1(X54)|~v1_funct_2(X54,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))))&(v1_funct_2(k11_polynom3(X52,X53,X54),k4_ordinal1,u1_struct_0(X52))|(v2_struct_0(X52)|~v2_rlvect_1(X52)|~v3_rlvect_1(X52)|~v4_rlvect_1(X52)|~v5_group_1(X52)|~l6_algstr_0(X52)|~v1_funct_1(X53)|~v1_funct_2(X53,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X53,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))|~v1_funct_1(X54)|~v1_funct_2(X54,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52)))))))&(m1_subset_1(k11_polynom3(X52,X53,X54),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))|(v2_struct_0(X52)|~v2_rlvect_1(X52)|~v3_rlvect_1(X52)|~v4_rlvect_1(X52)|~v5_group_1(X52)|~l6_algstr_0(X52)|~v1_funct_1(X53)|~v1_funct_2(X53,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X53,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))|~v1_funct_1(X54)|~v1_funct_2(X54,k4_ordinal1,u1_struct_0(X52))|~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X52))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])])).
cnf(c_0_123, plain, (m1_subset_1(k2_ring_4(X1,k9_struct_0(X2,X1)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~l1_struct_0(X1)|~l2_struct_0(X1)), inference(spm,[status(thm)],[c_0_112, c_0_113])).
cnf(c_0_124, plain, (v1_funct_2(k2_ring_4(X1,k9_struct_0(X2,X1)),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~l1_struct_0(X1)|~l2_struct_0(X1)), inference(spm,[status(thm)],[c_0_114, c_0_113])).
cnf(c_0_125, plain, (v1_funct_1(k2_ring_4(X1,k9_struct_0(X2,X1)))|v2_struct_0(X1)|~l1_struct_0(X1)|~l2_struct_0(X1)), inference(spm,[status(thm)],[c_0_115, c_0_113])).
cnf(c_0_126, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k11_gaussint)), inference(spm,[status(thm)],[c_0_116, c_0_113])).
fof(c_0_127, plain, ![X89, X90]:(~v7_ordinal1(X89)|(~m1_ring_4(X90,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))|k5_binom(k12_polynom3(k11_gaussint),X90,X89)=k4_polynom5(k11_gaussint,X90,k9_struct_0(X89,k11_gaussint)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_e_trans1])])])).
fof(c_0_128, plain, ![X76, X77, X78]:(v2_struct_0(X76)|~v2_rlvect_1(X76)|~v3_rlvect_1(X76)|~v4_rlvect_1(X76)|~v5_group_1(X76)|~l6_algstr_0(X76)|~v1_funct_1(X77)|~v1_funct_2(X77,k4_ordinal1,u1_struct_0(X76))|~m1_subset_1(X77,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X76))))|~v1_funct_1(X78)|~v1_funct_2(X78,k4_ordinal1,u1_struct_0(X76))|~m1_subset_1(X78,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X76))))|k11_polynom3(X76,X77,X78)=k10_polynom3(X76,X77,X78)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_117])])).
cnf(c_0_129, negated_conjecture, (m1_subset_1(k4_polynom5(k11_gaussint,esk2_0,X1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_33])])).
cnf(c_0_130, negated_conjecture, (v1_funct_1(k4_polynom5(k11_gaussint,esk2_0,X1))|v2_struct_0(k12_polynom3(k11_gaussint))|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_119]), c_0_33])])).
cnf(c_0_131, negated_conjecture, (v1_funct_2(k4_polynom5(k11_gaussint,esk2_0,X1),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_119]), c_0_33])])).
cnf(c_0_132, plain, (m1_subset_1(k11_polynom3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~v1_funct_1(X3)|~v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_122])).
cnf(c_0_133, plain, (v5_group_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_134, plain, (m1_subset_1(k2_ring_4(X1,k9_struct_0(X2,X1)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~l6_algstr_0(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_61]), c_0_55])).
cnf(c_0_135, plain, (v1_funct_2(k2_ring_4(X1,k9_struct_0(X2,X1)),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~l6_algstr_0(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_61]), c_0_55])).
cnf(c_0_136, plain, (v1_funct_1(k2_ring_4(X1,k9_struct_0(X2,X1)))|v2_struct_0(X1)|~l6_algstr_0(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_61]), c_0_55])).
cnf(c_0_137, plain, (v1_funct_1(k11_polynom3(X1,X2,X3))|v2_struct_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~v1_funct_1(X3)|~v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_122])).
cnf(c_0_138, plain, (v1_funct_2(k11_polynom3(X1,X2,X3),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~v1_funct_1(X3)|~v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_122])).
cnf(c_0_139, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_61]), c_0_33])])).
cnf(c_0_140, plain, (k5_binom(k12_polynom3(k11_gaussint),X2,X1)=k4_polynom5(k11_gaussint,X2,k9_struct_0(X1,k11_gaussint))|~v7_ordinal1(X1)|~m1_ring_4(X2,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_127])).
cnf(c_0_141, plain, (v2_struct_0(X1)|k11_polynom3(X1,X2,X3)=k10_polynom3(X1,X2,X3)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~v1_funct_1(X3)|~v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_128])).
cnf(c_0_142, negated_conjecture, (m1_subset_1(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k11_gaussint)), inference(spm,[status(thm)],[c_0_129, c_0_113])).
cnf(c_0_143, negated_conjecture, (v1_funct_1(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)))|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k11_gaussint)), inference(spm,[status(thm)],[c_0_130, c_0_113])).
cnf(c_0_144, negated_conjecture, (v1_funct_2(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))|~l1_struct_0(k11_gaussint)), inference(spm,[status(thm)],[c_0_131, c_0_113])).
fof(c_0_145, plain, ![X82, X83, X84, X85]:((~r2_funct_2(X82,X83,X84,X85)|X84=X85|(~v1_funct_1(X84)|~v1_funct_2(X84,X82,X83)|~m1_subset_1(X84,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))|~v1_funct_1(X85)|~v1_funct_2(X85,X82,X83)|~m1_subset_1(X85,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))))&(X84!=X85|r2_funct_2(X82,X83,X84,X85)|(~v1_funct_1(X84)|~v1_funct_2(X84,X82,X83)|~m1_subset_1(X84,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))|~v1_funct_1(X85)|~v1_funct_2(X85,X82,X83)|~m1_subset_1(X85,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_funct_2])])])).
cnf(c_0_146, negated_conjecture, (m1_subset_1(k11_polynom3(k11_gaussint,X1,esk2_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))|~v1_funct_2(X1,k4_ordinal1,u1_struct_0(k11_gaussint))|~v1_funct_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_99]), c_0_102]), c_0_103]), c_0_133]), c_0_104]), c_0_33]), c_0_35]), c_0_36])]), c_0_38])).
cnf(c_0_147, plain, (m1_subset_1(k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_33]), c_0_38])).
cnf(c_0_148, plain, (v1_funct_2(k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),k4_ordinal1,u1_struct_0(k11_gaussint))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_33]), c_0_38])).
cnf(c_0_149, plain, (v1_funct_1(k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_33]), c_0_38])).
cnf(c_0_150, negated_conjecture, (v1_funct_1(k11_polynom3(k11_gaussint,X1,esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))|~v1_funct_2(X1,k4_ordinal1,u1_struct_0(k11_gaussint))|~v1_funct_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_99]), c_0_102]), c_0_103]), c_0_133]), c_0_104]), c_0_33]), c_0_35]), c_0_36])]), c_0_38])).
cnf(c_0_151, negated_conjecture, (v1_funct_2(k11_polynom3(k11_gaussint,X1,esk2_0),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))|~v1_funct_2(X1,k4_ordinal1,u1_struct_0(k11_gaussint))|~v1_funct_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_99]), c_0_102]), c_0_103]), c_0_133]), c_0_104]), c_0_33]), c_0_35]), c_0_36])]), c_0_38])).
cnf(c_0_152, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k5_binom(k12_polynom3(k11_gaussint),esk2_0,X1),k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140]), c_0_53])])).
cnf(c_0_153, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_154, negated_conjecture, (k10_polynom3(k11_gaussint,X1,esk2_0)=k11_polynom3(k11_gaussint,X1,esk2_0)|v2_struct_0(k12_polynom3(k11_gaussint))|~v1_funct_2(X1,k4_ordinal1,u1_struct_0(k11_gaussint))|~v1_funct_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_99]), c_0_102]), c_0_103]), c_0_133]), c_0_104]), c_0_33]), c_0_35]), c_0_36])]), c_0_38])).
cnf(c_0_155, negated_conjecture, (m1_subset_1(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_61]), c_0_33])])).
cnf(c_0_156, negated_conjecture, (v1_funct_1(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_61]), c_0_33])])).
cnf(c_0_157, negated_conjecture, (v1_funct_2(k4_polynom5(k11_gaussint,esk2_0,k9_struct_0(X1,k11_gaussint)),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_61]), c_0_33])])).
cnf(c_0_158, plain, (X3=X4|~r2_funct_2(X1,X2,X3,X4)|~v1_funct_1(X3)|~v1_funct_2(X3,X1,X2)|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))|~v1_funct_1(X4)|~v1_funct_2(X4,X1,X2)|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_145])).
cnf(c_0_159, negated_conjecture, (m1_subset_1(k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_147]), c_0_148]), c_0_149])])).
cnf(c_0_160, negated_conjecture, (v1_funct_1(k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_147]), c_0_148]), c_0_149])])).
cnf(c_0_161, negated_conjecture, (v1_funct_2(k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_147]), c_0_148]), c_0_149])])).
cnf(c_0_162, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0),k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(esk1_0,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_152, c_0_153])).
cnf(c_0_163, negated_conjecture, (k10_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0)=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X1,k11_gaussint)),esk2_0)|v2_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_147]), c_0_148]), c_0_149])])).
cnf(c_0_164, negated_conjecture, (m1_subset_1(k5_binom(k12_polynom3(k11_gaussint),esk2_0,X1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_140]), c_0_53])])).
cnf(c_0_165, negated_conjecture, (v1_funct_1(k5_binom(k12_polynom3(k11_gaussint),esk2_0,X1))|v2_struct_0(k12_polynom3(k11_gaussint))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_140]), c_0_53])])).
cnf(c_0_166, negated_conjecture, (v1_funct_2(k5_binom(k12_polynom3(k11_gaussint),esk2_0,X1),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_140]), c_0_53])])).
cnf(c_0_167, negated_conjecture, (k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0)!=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(esk1_0,k11_gaussint)),k2_basel_2(k11_gaussint,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_168, negated_conjecture, (X1=k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X2,k11_gaussint)),esk2_0)|v2_struct_0(k12_polynom3(k11_gaussint))|~r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),X1,k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(X2,k11_gaussint)),esk2_0))|~v1_funct_2(X1,k4_ordinal1,u1_struct_0(k11_gaussint))|~v1_funct_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_160]), c_0_161])).
cnf(c_0_169, negated_conjecture, (r2_funct_2(k4_ordinal1,u1_struct_0(k11_gaussint),k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0),k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(esk1_0,k11_gaussint)),esk2_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_162, c_0_163])).
cnf(c_0_170, negated_conjecture, (m1_subset_1(k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_164, c_0_153])).
cnf(c_0_171, negated_conjecture, (v1_funct_1(k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_165, c_0_153])).
cnf(c_0_172, negated_conjecture, (v1_funct_2(k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0),k4_ordinal1,u1_struct_0(k11_gaussint))|v2_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_166, c_0_153])).
cnf(c_0_173, negated_conjecture, (v2_struct_0(k12_polynom3(k11_gaussint))|k11_polynom3(k11_gaussint,k2_ring_4(k11_gaussint,k9_struct_0(esk1_0,k11_gaussint)),esk2_0)!=k5_binom(k12_polynom3(k11_gaussint),esk2_0,esk1_0)), inference(spm,[status(thm)],[c_0_167, c_0_79])).
cnf(c_0_174, negated_conjecture, (v2_struct_0(k12_polynom3(k11_gaussint))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_170]), c_0_171]), c_0_172]), c_0_173])).
cnf(c_0_175, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_174]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 176
# Proof object clause steps            : 115
# Proof object formula steps           : 61
# Proof object conjectures             : 57
# Proof object clause conjectures      : 54
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 45
# Proof object initial formulas used   : 24
# Proof object generating inferences   : 70
# Proof object simplifying inferences  : 186
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 25
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 64
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 64
# Processed clauses                    : 4595
# ...of these trivial                  : 7
# ...subsumed                          : 1893
# ...remaining for further processing  : 2695
# Other redundant clauses eliminated   : 1
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 340
# Backward-rewritten                   : 2152
# Generated clauses                    : 22642
# ...of the previous two non-trivial   : 22643
# Contextual simplify-reflections      : 2721
# Paramodulations                      : 22641
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 1
# Propositional unsat checks           : 0
#    Propositional check models        : 0
#    Propositional check unsatisfiable : 0
#    Propositional clauses             : 0
#    Propositional clauses after purity: 0
#    Propositional unsat core size     : 0
#    Propositional preprocessing time  : 0.000
#    Propositional encoding time       : 0.000
#    Propositional solver time         : 0.000
#    Success case prop preproc time    : 0.000
#    Success case prop encoding time   : 0.000
#    Success case prop solver time     : 0.000
# Current number of processed clauses  : 146
#    Positive orientable unit clauses  : 30
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 3
#    Non-unit-clauses                  : 113
# Current number of unprocessed clauses: 18066
# ...number of literals in the above   : 84357
# Current number of archived formulas  : 0
# Current number of archived clauses   : 2548
# Clause-clause subsumption calls (NU) : 3497789
# Rec. Clause-clause subsumption calls : 1286446
# Non-unit clause-clause subsumptions  : 4940
# Unit Clause-clause subsumption calls : 1507
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 8
# BW rewrite match successes           : 8
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 1477528

# -------------------------------------------------
# User time                : 1.117 s
# System time              : 0.032 s
# Total time               : 1.149 s
# Maximum resident set size: 3460 pages
