# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___302_C18_F1_URBAN_RG_S04BN
# and selection function PSelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.023 s

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
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_trans1/e_trans1__l24_e_trans1', redefinition_m1_ring_4)).
fof(l24_e_trans1, conjecture, ![X1]:(m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>![X2]:(v7_ordinal1(X2)=>(r2_tarski(X2,k4_finseq_1(k4_e_trans1(X1)))=>(r2_tarski(k1_funct_1(k4_e_trans1(X1),X2),k4_ordinal1)&k1_funct_1(k4_e_trans1(X1),X2)!=k5_numbers)))), file('e_trans1/e_trans1__l24_e_trans1', l24_e_trans1)).
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_trans1/e_trans1__l24_e_trans1', fc2_ring_4)).
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_trans1/e_trans1__l24_e_trans1', dt_k12_polynom3)).
fof(dt_k11_gaussint, axiom, ((~(v2_struct_0(k11_gaussint))&v36_algstr_0(k11_gaussint))&l6_algstr_0(k11_gaussint)), file('e_trans1/e_trans1__l24_e_trans1', dt_k11_gaussint)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('e_trans1/e_trans1__l24_e_trans1', 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_trans1/e_trans1__l24_e_trans1', dt_l6_algstr_0)).
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_trans1/e_trans1__l24_e_trans1', fc1_ring_4)).
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_trans1/e_trans1__l24_e_trans1', fc30_gaussint)).
fof(dt_l1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>l1_struct_0(X1)), file('e_trans1/e_trans1__l24_e_trans1', dt_l1_algstr_0)).
fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('e_trans1/e_trans1__l24_e_trans1', fc2_struct_0)).
fof(dt_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)=>(((v1_funct_1(X3)&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X3,X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))))), file('e_trans1/e_trans1__l24_e_trans1', dt_m1_ring_4)).
fof(dt_k4_e_trans1, axiom, ![X1]:(m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))=>(~(v1_xboole_0(k4_e_trans1(X1)))&m2_finseq_1(k4_e_trans1(X1),k4_ordinal1))), file('e_trans1/e_trans1__l24_e_trans1', dt_k4_e_trans1)).
fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('e_trans1/e_trans1__l24_e_trans1', cc1_relset_1)).
fof(dt_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)=>((v1_funct_1(X2)&v1_finseq_1(X2))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,X1))))), file('e_trans1/e_trans1__l24_e_trans1', dt_m2_finseq_1)).
fof(d12_ordinal1, axiom, ![X1]:(v7_ordinal1(X1)<=>r2_hidden(X1,k4_ordinal1)), file('e_trans1/e_trans1__l24_e_trans1', d12_ordinal1)).
fof(fc66_valued_0, axiom, ![X1, X2]:(((v1_relat_1(X1)&v1_funct_1(X1))&v6_valued_0(X1))=>v7_ordinal1(k1_funct_1(X1,X2))), file('e_trans1/e_trans1__l24_e_trans1', fc66_valued_0)).
fof(cc17_finseq_1, axiom, ![X1]:(m1_finseq_1(X1,k4_ordinal1)=>v6_valued_0(X1)), file('e_trans1/e_trans1__l24_e_trans1', cc17_finseq_1)).
fof(redefinition_r2_tarski, axiom, ![X1, X2]:(r2_tarski(X1,X2)<=>r2_hidden(X1,X2)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_r2_tarski)).
fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_m2_finseq_1)).
fof(cc4_nat_1, axiom, ![X1]:((v7_ordinal1(X1)&v8_ordinal1(X1))=>(v7_ordinal1(X1)&~(v2_xxreal_0(X1)))), file('e_trans1/e_trans1__l24_e_trans1', cc4_nat_1)).
fof(redefinition_k4_finseq_1, axiom, ![X1]:(((v1_relat_1(X1)&v1_funct_1(X1))&v1_finseq_1(X1))=>k4_finseq_1(X1)=k9_xtuple_0(X1)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_k4_finseq_1)).
fof(dt_k20_finseq_1, axiom, ![X1]:(v1_finset_1(X1)=>m2_finseq_1(k20_finseq_1(X1),X1)), file('e_trans1/e_trans1__l24_e_trans1', dt_k20_finseq_1)).
fof(fc7_rat_1, axiom, ![X1]:(v1_rat_1(X1)=>(v7_ordinal1(k1_rat_1(X1))&v2_xxreal_0(k1_rat_1(X1)))), file('e_trans1/e_trans1__l24_e_trans1', fc7_rat_1)).
fof(d4_diophan2, axiom, ![X1]:(((v1_funct_1(X1)&v1_funct_2(X1,k3_numbers,k4_ordinal1))&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1))))=>(X1=k4_diophan2<=>![X2]:(v1_rat_1(X2)=>k1_funct_1(X1,X2)=k1_rat_1(X2)))), file('e_trans1/e_trans1__l24_e_trans1', d4_diophan2)).
fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('e_trans1/e_trans1__l24_e_trans1', cc2_relset_1)).
fof(t3_funct_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>(r2_hidden(X1,k9_xtuple_0(X2))=>r2_tarski(k1_funct_1(X2,X1),k10_xtuple_0(X2)))), file('e_trans1/e_trans1__l24_e_trans1', t3_funct_1)).
fof(redefinition_k20_finseq_1, axiom, ![X1]:(v1_finset_1(X1)=>k20_finseq_1(X1)=k19_finseq_1(X1)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_k20_finseq_1)).
fof(dt_k4_diophan2, axiom, ((v1_funct_1(k4_diophan2)&v1_funct_2(k4_diophan2,k3_numbers,k4_ordinal1))&m1_subset_1(k4_diophan2,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1)))), file('e_trans1/e_trans1__l24_e_trans1', dt_k4_diophan2)).
fof(t4_subset, axiom, ![X1, X2, X3]:((r2_tarski(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('e_trans1/e_trans1__l24_e_trans1', t4_subset)).
fof(dt_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>m1_subset_1(k2_relset_1(X1,X2),k1_zfmisc_1(X1))), file('e_trans1/e_trans1__l24_e_trans1', dt_k2_relset_1)).
fof(d3_e_trans1, axiom, ![X1]:(m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>k3_e_trans1(X1)=k7_relset_1(k3_numbers,k4_ordinal1,k4_diophan2,k2_relset_1(u1_struct_0(k11_gaussint),X1))), file('e_trans1/e_trans1__l24_e_trans1', d3_e_trans1)).
fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_k2_relset_1)).
fof(redefinition_k7_relset_1, axiom, ![X1, X2, X3, X4]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>k7_relset_1(X1,X2,X3,X4)=k7_relat_1(X3,X4)), file('e_trans1/e_trans1__l24_e_trans1', redefinition_k7_relset_1)).
fof(d3_funct_2, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>(v2_funct_2(X2,X1)<=>k2_relset_1(X1,X2)=X1)), file('e_trans1/e_trans1__l24_e_trans1', d3_funct_2)).
fof(fc40_finseq_1, axiom, ![X1]:(v1_finset_1(X1)=>(v2_funct_1(k19_finseq_1(X1))&v2_funct_2(k19_finseq_1(X1),X1))), file('e_trans1/e_trans1__l24_e_trans1', fc40_finseq_1)).
fof(d4_e_trans1, axiom, ![X1]:(m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>k4_e_trans1(X1)=k20_finseq_1(k3_e_trans1(X1))), file('e_trans1/e_trans1__l24_e_trans1', d4_e_trans1)).
fof(d6_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2, X3]:(X3=k7_relat_1(X1,X2)<=>![X4]:(r2_hidden(X4,X3)<=>?[X5]:((r2_hidden(X5,k9_xtuple_0(X1))&r2_hidden(X5,X2))&X4=k1_funct_1(X1,X5))))), file('e_trans1/e_trans1__l24_e_trans1', d6_funct_1)).
fof(cc4_gaussint, axiom, ![X1]:(m1_subset_1(X1,u1_struct_0(k11_gaussint))=>v1_rat_1(X1)), file('e_trans1/e_trans1__l24_e_trans1', cc4_gaussint)).
fof(dt_k3_e_trans1, axiom, ![X1]:(m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))=>((~(v1_xboole_0(k3_e_trans1(X1)))&v1_finset_1(k3_e_trans1(X1)))&m1_subset_1(k3_e_trans1(X1),k1_zfmisc_1(k4_ordinal1)))), file('e_trans1/e_trans1__l24_e_trans1', dt_k3_e_trans1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1), file('e_trans1/e_trans1__l24_e_trans1', fc9_ordinal1)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('e_trans1/e_trans1__l24_e_trans1', redefinition_k5_numbers)).
fof(c_0_42, 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_43, negated_conjecture, ~(![X1]:(m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))=>![X2]:(v7_ordinal1(X2)=>(r2_tarski(X2,k4_finseq_1(k4_e_trans1(X1)))=>(r2_tarski(k1_funct_1(k4_e_trans1(X1),X2),k4_ordinal1)&k1_funct_1(k4_e_trans1(X1),X2)!=k5_numbers))))), inference(assume_negation,[status(cth)],[l24_e_trans1])).
fof(c_0_44, 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_45, 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_46, plain, ![X132, X133, X134]:((~m1_ring_4(X134,X132,X133)|m1_subset_1(X134,X133)|(v2_struct_0(X132)|~l2_struct_0(X132)|v1_xboole_0(X133)|~v1_ring_4(X133,X132)))&(~m1_subset_1(X134,X133)|m1_ring_4(X134,X132,X133)|(v2_struct_0(X132)|~l2_struct_0(X132)|v1_xboole_0(X133)|~v1_ring_4(X133,X132)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])).
fof(c_0_47, negated_conjecture, (m1_ring_4(esk1_0,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))&(v7_ordinal1(esk2_0)&(r2_tarski(esk2_0,k4_finseq_1(k4_e_trans1(esk1_0)))&(~r2_tarski(k1_funct_1(k4_e_trans1(esk1_0),esk2_0),k4_ordinal1)|k1_funct_1(k4_e_trans1(esk1_0),esk2_0)=k5_numbers)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])).
fof(c_0_48, 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_49, plain, ![X109]:((l2_struct_0(X109)|~l2_algstr_0(X109))&(l1_algstr_0(X109)|~l2_algstr_0(X109))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
fof(c_0_50, plain, ![X110]:((l2_algstr_0(X110)|~l6_algstr_0(X110))&(l5_algstr_0(X110)|~l6_algstr_0(X110))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_51, 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_52, plain, ![X118]:(((~v2_struct_0(k12_polynom3(X118))|(v2_struct_0(X118)|~v13_algstr_0(X118)|~v3_rlvect_1(X118)|~v4_rlvect_1(X118)|~v5_vectsp_1(X118)|~l6_algstr_0(X118)))&(v36_algstr_0(k12_polynom3(X118))|(v2_struct_0(X118)|~v13_algstr_0(X118)|~v3_rlvect_1(X118)|~v4_rlvect_1(X118)|~v5_vectsp_1(X118)|~l6_algstr_0(X118))))&(v2_ring_4(k12_polynom3(X118),X118)|(v2_struct_0(X118)|~v13_algstr_0(X118)|~v3_rlvect_1(X118)|~v4_rlvect_1(X118)|~v5_vectsp_1(X118)|~l6_algstr_0(X118)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])).
fof(c_0_53, 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_54, plain, ![X102]:(((~v2_struct_0(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~l6_algstr_0(X102)))&(v36_algstr_0(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~l6_algstr_0(X102))))&(l6_algstr_0(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~l6_algstr_0(X102)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])).
cnf(c_0_55, 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_46])).
cnf(c_0_56, negated_conjecture, (m1_ring_4(esk1_0,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_57, plain, (~v2_struct_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_58, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_59, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
fof(c_0_60, plain, ![X116, X117]:(v2_struct_0(X116)|~l2_struct_0(X116)|v2_struct_0(X117)|~v2_ring_4(X117,X116)|~l1_struct_0(X117)|v1_ring_4(u1_struct_0(X117),X116)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])).
cnf(c_0_61, 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_52])).
cnf(c_0_62, plain, (v5_vectsp_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_63, plain, (v4_rlvect_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_64, plain, (v3_rlvect_1(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_65, plain, (v13_algstr_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_66, plain, (l6_algstr_0(k11_gaussint)), inference(split_conjunct,[status(thm)],[c_0_48])).
cnf(c_0_67, 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_54])).
cnf(c_0_68, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_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_55, c_0_56]), c_0_57])).
cnf(c_0_69, plain, (l2_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_58, c_0_59])).
cnf(c_0_70, 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_60])).
cnf(c_0_71, 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_61, c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66])]), c_0_57])).
cnf(c_0_72, plain, (~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(spm,[status(thm)],[c_0_67, c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66])]), c_0_57])).
cnf(c_0_73, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_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_68, c_0_69]), c_0_66])])).
cnf(c_0_74, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k11_gaussint)),k11_gaussint)|~l2_struct_0(k11_gaussint)|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_57]), c_0_72])).
fof(c_0_75, plain, ![X108]:(~l1_algstr_0(X108)|l1_struct_0(X108)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_algstr_0])])).
cnf(c_0_76, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~l2_struct_0(k11_gaussint)|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_73, c_0_74])).
cnf(c_0_77, plain, (l1_struct_0(X1)|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_75])).
cnf(c_0_78, plain, (l1_algstr_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])).
fof(c_0_79, 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_80, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,u1_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_76, c_0_69]), c_0_66])])).
cnf(c_0_81, plain, (l1_struct_0(X1)|~l2_algstr_0(X1)), inference(spm,[status(thm)],[c_0_77, c_0_78])).
cnf(c_0_82, 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_54])).
fof(c_0_83, 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)=>(((v1_funct_1(X3)&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X3,X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))))), inference(fof_simplification,[status(thm)],[dt_m1_ring_4])).
fof(c_0_84, plain, ![X1]:(m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))=>(~v1_xboole_0(k4_e_trans1(X1))&m2_finseq_1(k4_e_trans1(X1),k4_ordinal1))), inference(fof_simplification,[status(thm)],[dt_k4_e_trans1])).
fof(c_0_85, plain, ![X74, X75, X76]:(~m1_subset_1(X76,k1_zfmisc_1(k2_zfmisc_1(X74,X75)))|v1_relat_1(X76)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])).
fof(c_0_86, plain, ![X114, X115]:(((v1_funct_1(X115)|~m2_finseq_1(X115,X114))&(v1_finseq_1(X115)|~m2_finseq_1(X115,X114)))&(m1_subset_1(X115,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,X114)))|~m2_finseq_1(X115,X114))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_finseq_1])])])).
fof(c_0_87, plain, ![X119]:(v2_struct_0(X119)|~l1_struct_0(X119)|~v1_xboole_0(u1_struct_0(X119))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])).
cnf(c_0_88, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~l2_algstr_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_80, c_0_81])).
cnf(c_0_89, 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_82, c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66])]), c_0_57])).
fof(c_0_90, plain, ![X111, X112, X113]:((((v1_funct_1(X113)|~m1_ring_4(X113,X111,X112)|(v2_struct_0(X111)|~l2_struct_0(X111)|v1_xboole_0(X112)|~v1_ring_4(X112,X111)))&(v1_funct_2(X113,k4_ordinal1,u1_struct_0(X111))|~m1_ring_4(X113,X111,X112)|(v2_struct_0(X111)|~l2_struct_0(X111)|v1_xboole_0(X112)|~v1_ring_4(X112,X111))))&(v1_polynom1(X113,X111)|~m1_ring_4(X113,X111,X112)|(v2_struct_0(X111)|~l2_struct_0(X111)|v1_xboole_0(X112)|~v1_ring_4(X112,X111))))&(m1_subset_1(X113,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X111))))|~m1_ring_4(X113,X111,X112)|(v2_struct_0(X111)|~l2_struct_0(X111)|v1_xboole_0(X112)|~v1_ring_4(X112,X111)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])])).
fof(c_0_91, plain, ![X82]:((~v7_ordinal1(X82)|r2_hidden(X82,k4_ordinal1))&(~r2_hidden(X82,k4_ordinal1)|v7_ordinal1(X82))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_ordinal1])])).
fof(c_0_92, plain, ![X121, X122]:(~v1_relat_1(X121)|~v1_funct_1(X121)|~v6_valued_0(X121)|v7_ordinal1(k1_funct_1(X121,X122))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc66_valued_0])])).
fof(c_0_93, plain, ![X107]:((~v1_xboole_0(k4_e_trans1(X107))|~m1_subset_1(X107,u1_struct_0(k12_polynom3(k11_gaussint))))&(m2_finseq_1(k4_e_trans1(X107),k4_ordinal1)|~m1_subset_1(X107,u1_struct_0(k12_polynom3(k11_gaussint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])).
cnf(c_0_94, plain, (v1_relat_1(X1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_95, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,X2)))|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_96, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_97, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_59]), c_0_89])])).
cnf(c_0_98, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X2))))|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_90])).
cnf(c_0_99, plain, (r2_hidden(X1,k4_ordinal1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_91])).
cnf(c_0_100, plain, (v7_ordinal1(k1_funct_1(X1,X2))|~v1_relat_1(X1)|~v1_funct_1(X1)|~v6_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_92])).
cnf(c_0_101, plain, (v1_funct_1(X1)|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86])).
cnf(c_0_102, plain, (m2_finseq_1(k4_e_trans1(X1),k4_ordinal1)|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_93])).
cnf(c_0_103, plain, (v1_relat_1(X1)|~m2_finseq_1(X1,X2)), inference(spm,[status(thm)],[c_0_94, c_0_95])).
cnf(c_0_104, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_72])).
cnf(c_0_105, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(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_98, c_0_56]), c_0_57])).
cnf(c_0_106, plain, (r2_hidden(k1_funct_1(X1,X2),k4_ordinal1)|~v1_funct_1(X1)|~v1_relat_1(X1)|~v6_valued_0(X1)), inference(spm,[status(thm)],[c_0_99, c_0_100])).
cnf(c_0_107, plain, (v1_funct_1(k4_e_trans1(X1))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_101, c_0_102])).
cnf(c_0_108, plain, (v1_relat_1(k4_e_trans1(X1))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_103, c_0_102])).
cnf(c_0_109, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))|~l2_algstr_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_104, c_0_81])).
cnf(c_0_110, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(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_105, c_0_69]), c_0_66])])).
cnf(c_0_111, plain, (r2_hidden(k1_funct_1(k4_e_trans1(X1),X2),k4_ordinal1)|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))|~v6_valued_0(k4_e_trans1(X1))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107]), c_0_108])).
cnf(c_0_112, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_59]), c_0_89])])).
fof(c_0_113, plain, ![X73]:(~m1_finseq_1(X73,k4_ordinal1)|v6_valued_0(X73)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_finseq_1])])).
cnf(c_0_114, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|~l2_struct_0(k11_gaussint)|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_110, c_0_74])).
fof(c_0_115, plain, ![X137, X138]:((~r2_tarski(X137,X138)|r2_hidden(X137,X138))&(~r2_hidden(X137,X138)|r2_tarski(X137,X138))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_tarski])])).
cnf(c_0_116, negated_conjecture, (r2_hidden(k1_funct_1(k4_e_trans1(esk1_0),X1),k4_ordinal1)|~v6_valued_0(k4_e_trans1(esk1_0))), inference(spm,[status(thm)],[c_0_111, c_0_112])).
cnf(c_0_117, plain, (v6_valued_0(X1)|~m1_finseq_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_113])).
fof(c_0_118, plain, ![X135, X136]:((~m2_finseq_1(X136,X135)|m1_finseq_1(X136,X135))&(~m1_finseq_1(X136,X135)|m2_finseq_1(X136,X135))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])).
fof(c_0_119, plain, ![X1]:((v7_ordinal1(X1)&v8_ordinal1(X1))=>(v7_ordinal1(X1)&~v2_xxreal_0(X1))), inference(fof_simplification,[status(thm)],[cc4_nat_1])).
cnf(c_0_120, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_69]), c_0_66])])).
cnf(c_0_121, negated_conjecture, (k1_funct_1(k4_e_trans1(esk1_0),esk2_0)=k5_numbers|~r2_tarski(k1_funct_1(k4_e_trans1(esk1_0),esk2_0),k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_122, plain, (r2_tarski(X1,X2)|~r2_hidden(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_115])).
cnf(c_0_123, negated_conjecture, (r2_hidden(k1_funct_1(k4_e_trans1(esk1_0),X1),k4_ordinal1)|~m1_finseq_1(k4_e_trans1(esk1_0),k4_ordinal1)), inference(spm,[status(thm)],[c_0_116, c_0_117])).
cnf(c_0_124, plain, (m1_finseq_1(X1,X2)|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_118])).
fof(c_0_125, plain, ![X127]:(~v1_relat_1(X127)|~v1_funct_1(X127)|~v1_finseq_1(X127)|k4_finseq_1(X127)=k9_xtuple_0(X127)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_finseq_1])])).
cnf(c_0_126, plain, (v1_finseq_1(X1)|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_86])).
fof(c_0_127, plain, ![X103]:(~v1_finset_1(X103)|m2_finseq_1(k20_finseq_1(X103),X103)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k20_finseq_1])])).
fof(c_0_128, plain, ![X81]:((v7_ordinal1(X81)|(~v7_ordinal1(X81)|~v8_ordinal1(X81)))&(~v2_xxreal_0(X81)|(~v7_ordinal1(X81)|~v8_ordinal1(X81)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])).
fof(c_0_129, plain, ![X123]:((v7_ordinal1(k1_rat_1(X123))|~v1_rat_1(X123))&(v2_xxreal_0(k1_rat_1(X123))|~v1_rat_1(X123))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_rat_1])])])).
fof(c_0_130, plain, ![X86, X87]:((X86!=k4_diophan2|(~v1_rat_1(X87)|k1_funct_1(X86,X87)=k1_rat_1(X87))|(~v1_funct_1(X86)|~v1_funct_2(X86,k3_numbers,k4_ordinal1)|~m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1)))))&((v1_rat_1(esk3_1(X86))|X86=k4_diophan2|(~v1_funct_1(X86)|~v1_funct_2(X86,k3_numbers,k4_ordinal1)|~m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1)))))&(k1_funct_1(X86,esk3_1(X86))!=k1_rat_1(esk3_1(X86))|X86=k4_diophan2|(~v1_funct_1(X86)|~v1_funct_2(X86,k3_numbers,k4_ordinal1)|~m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_diophan2])])])])])).
fof(c_0_131, plain, ![X77, X78, X79]:((v4_relat_1(X79,X77)|~m1_subset_1(X79,k1_zfmisc_1(k2_zfmisc_1(X77,X78))))&(v5_relat_1(X79,X78)|~m1_subset_1(X79,k1_zfmisc_1(k2_zfmisc_1(X77,X78))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])).
cnf(c_0_132, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))|~l2_algstr_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_120, c_0_81])).
fof(c_0_133, plain, ![X139, X140]:(~v1_relat_1(X140)|~v1_funct_1(X140)|(~r2_hidden(X139,k9_xtuple_0(X140))|r2_tarski(k1_funct_1(X140,X139),k10_xtuple_0(X140)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_funct_1])])).
cnf(c_0_134, negated_conjecture, (k1_funct_1(k4_e_trans1(esk1_0),esk2_0)=k5_numbers|~r2_hidden(k1_funct_1(k4_e_trans1(esk1_0),esk2_0),k4_ordinal1)), inference(spm,[status(thm)],[c_0_121, c_0_122])).
cnf(c_0_135, negated_conjecture, (r2_hidden(k1_funct_1(k4_e_trans1(esk1_0),X1),k4_ordinal1)|~m2_finseq_1(k4_e_trans1(esk1_0),k4_ordinal1)), inference(spm,[status(thm)],[c_0_123, c_0_124])).
cnf(c_0_136, plain, (r2_hidden(X1,X2)|~r2_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_115])).
cnf(c_0_137, negated_conjecture, (r2_tarski(esk2_0,k4_finseq_1(k4_e_trans1(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_138, plain, (k4_finseq_1(X1)=k9_xtuple_0(X1)|~v1_relat_1(X1)|~v1_funct_1(X1)|~v1_finseq_1(X1)), inference(split_conjunct,[status(thm)],[c_0_125])).
cnf(c_0_139, plain, (v1_finseq_1(k4_e_trans1(X1))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_126, c_0_102])).
cnf(c_0_140, plain, (m2_finseq_1(k20_finseq_1(X1),X1)|~v1_finset_1(X1)), inference(split_conjunct,[status(thm)],[c_0_127])).
fof(c_0_141, plain, ![X124]:(~v1_finset_1(X124)|k20_finseq_1(X124)=k19_finseq_1(X124)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k20_finseq_1])])).
cnf(c_0_142, plain, (~v2_xxreal_0(X1)|~v7_ordinal1(X1)|~v8_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_128])).
cnf(c_0_143, plain, (v2_xxreal_0(k1_rat_1(X1))|~v1_rat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_129])).
cnf(c_0_144, plain, (v7_ordinal1(k1_rat_1(X1))|~v1_rat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_129])).
cnf(c_0_145, plain, (k1_funct_1(X1,X2)=k1_rat_1(X2)|X1!=k4_diophan2|~v1_rat_1(X2)|~v1_funct_1(X1)|~v1_funct_2(X1,k3_numbers,k4_ordinal1)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1)))), inference(split_conjunct,[status(thm)],[c_0_130])).
cnf(c_0_146, plain, (m1_subset_1(k4_diophan2,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,k4_ordinal1)))), inference(split_conjunct,[status(thm)],[dt_k4_diophan2])).
cnf(c_0_147, plain, (v1_funct_2(k4_diophan2,k3_numbers,k4_ordinal1)), inference(split_conjunct,[status(thm)],[dt_k4_diophan2])).
cnf(c_0_148, plain, (v1_funct_1(k4_diophan2)), inference(split_conjunct,[status(thm)],[dt_k4_diophan2])).
fof(c_0_149, plain, ![X141, X142, X143]:(~r2_tarski(X141,X142)|~m1_subset_1(X142,k1_zfmisc_1(X143))|m1_subset_1(X141,X143)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])).
fof(c_0_150, plain, ![X104, X105]:(~v1_relat_1(X105)|~v5_relat_1(X105,X104)|m1_subset_1(k2_relset_1(X104,X105),k1_zfmisc_1(X104))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_relset_1])])).
fof(c_0_151, plain, ![X83]:(~m1_ring_4(X83,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))|k3_e_trans1(X83)=k7_relset_1(k3_numbers,k4_ordinal1,k4_diophan2,k2_relset_1(u1_struct_0(k11_gaussint),X83))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_e_trans1])])).
fof(c_0_152, plain, ![X125, X126]:(~v1_relat_1(X126)|~v5_relat_1(X126,X125)|k2_relset_1(X125,X126)=k10_xtuple_0(X126)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])).
fof(c_0_153, plain, ![X128, X129, X130, X131]:(~m1_subset_1(X130,k1_zfmisc_1(k2_zfmisc_1(X128,X129)))|k7_relset_1(X128,X129,X130,X131)=k7_relat_1(X130,X131)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_relset_1])])).
cnf(c_0_154, plain, (v5_relat_1(X1,X2)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_131])).
cnf(c_0_155, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_gaussint))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_59]), c_0_89])])).
cnf(c_0_156, plain, (r2_tarski(k1_funct_1(X1,X2),k10_xtuple_0(X1))|~v1_relat_1(X1)|~v1_funct_1(X1)|~r2_hidden(X2,k9_xtuple_0(X1))), inference(split_conjunct,[status(thm)],[c_0_133])).
cnf(c_0_157, negated_conjecture, (k1_funct_1(k4_e_trans1(esk1_0),esk2_0)=k5_numbers|~m2_finseq_1(k4_e_trans1(esk1_0),k4_ordinal1)), inference(spm,[status(thm)],[c_0_134, c_0_135])).
cnf(c_0_158, negated_conjecture, (r2_hidden(esk2_0,k4_finseq_1(k4_e_trans1(esk1_0)))), inference(spm,[status(thm)],[c_0_136, c_0_137])).
cnf(c_0_159, plain, (k4_finseq_1(k4_e_trans1(X1))=k9_xtuple_0(k4_e_trans1(X1))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_139]), c_0_108]), c_0_107])).
fof(c_0_160, plain, ![X84, X85]:((~v2_funct_2(X85,X84)|k2_relset_1(X84,X85)=X84|(~v1_relat_1(X85)|~v5_relat_1(X85,X84)))&(k2_relset_1(X84,X85)!=X84|v2_funct_2(X85,X84)|(~v1_relat_1(X85)|~v5_relat_1(X85,X84)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_funct_2])])])).
fof(c_0_161, plain, ![X120]:((v2_funct_1(k19_finseq_1(X120))|~v1_finset_1(X120))&(v2_funct_2(k19_finseq_1(X120),X120)|~v1_finset_1(X120))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc40_finseq_1])])])).
cnf(c_0_162, plain, (v1_relat_1(k20_finseq_1(X1))|~v1_finset_1(X1)), inference(spm,[status(thm)],[c_0_103, c_0_140])).
cnf(c_0_163, plain, (k20_finseq_1(X1)=k19_finseq_1(X1)|~v1_finset_1(X1)), inference(split_conjunct,[status(thm)],[c_0_141])).
fof(c_0_164, plain, ![X89]:(~m1_ring_4(X89,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))|k4_e_trans1(X89)=k20_finseq_1(k3_e_trans1(X89))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_e_trans1])])).
cnf(c_0_165, plain, (~v8_ordinal1(k1_rat_1(X1))|~v1_rat_1(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143]), c_0_144])).
cnf(c_0_166, plain, (k1_rat_1(X1)=k1_funct_1(k4_diophan2,X1)|~v1_rat_1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_147]), c_0_148])])).
fof(c_0_167, plain, ![X90, X91, X92, X93, X95, X96, X97, X98, X100]:(((((r2_hidden(esk4_4(X90,X91,X92,X93),k9_xtuple_0(X90))|~r2_hidden(X93,X92)|X92!=k7_relat_1(X90,X91)|(~v1_relat_1(X90)|~v1_funct_1(X90)))&(r2_hidden(esk4_4(X90,X91,X92,X93),X91)|~r2_hidden(X93,X92)|X92!=k7_relat_1(X90,X91)|(~v1_relat_1(X90)|~v1_funct_1(X90))))&(X93=k1_funct_1(X90,esk4_4(X90,X91,X92,X93))|~r2_hidden(X93,X92)|X92!=k7_relat_1(X90,X91)|(~v1_relat_1(X90)|~v1_funct_1(X90))))&(~r2_hidden(X96,k9_xtuple_0(X90))|~r2_hidden(X96,X91)|X95!=k1_funct_1(X90,X96)|r2_hidden(X95,X92)|X92!=k7_relat_1(X90,X91)|(~v1_relat_1(X90)|~v1_funct_1(X90))))&((~r2_hidden(esk5_3(X90,X97,X98),X98)|(~r2_hidden(X100,k9_xtuple_0(X90))|~r2_hidden(X100,X97)|esk5_3(X90,X97,X98)!=k1_funct_1(X90,X100))|X98=k7_relat_1(X90,X97)|(~v1_relat_1(X90)|~v1_funct_1(X90)))&(((r2_hidden(esk6_3(X90,X97,X98),k9_xtuple_0(X90))|r2_hidden(esk5_3(X90,X97,X98),X98)|X98=k7_relat_1(X90,X97)|(~v1_relat_1(X90)|~v1_funct_1(X90)))&(r2_hidden(esk6_3(X90,X97,X98),X97)|r2_hidden(esk5_3(X90,X97,X98),X98)|X98=k7_relat_1(X90,X97)|(~v1_relat_1(X90)|~v1_funct_1(X90))))&(esk5_3(X90,X97,X98)=k1_funct_1(X90,esk6_3(X90,X97,X98))|r2_hidden(esk5_3(X90,X97,X98),X98)|X98=k7_relat_1(X90,X97)|(~v1_relat_1(X90)|~v1_funct_1(X90)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_funct_1])])])])])])).
cnf(c_0_168, plain, (m1_subset_1(X1,X3)|~r2_tarski(X1,X2)|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_149])).
cnf(c_0_169, plain, (m1_subset_1(k2_relset_1(X2,X1),k1_zfmisc_1(X2))|~v1_relat_1(X1)|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_150])).
cnf(c_0_170, plain, (k3_e_trans1(X1)=k7_relset_1(k3_numbers,k4_ordinal1,k4_diophan2,k2_relset_1(u1_struct_0(k11_gaussint),X1))|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_151])).
cnf(c_0_171, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)|~v1_relat_1(X1)|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_152])).
cnf(c_0_172, plain, (k7_relset_1(X2,X3,X1,X4)=k7_relat_1(X1,X4)|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_153])).
cnf(c_0_173, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|v5_relat_1(esk1_0,u1_struct_0(k11_gaussint))), inference(spm,[status(thm)],[c_0_154, c_0_155])).
cnf(c_0_174, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k11_gaussint)))|v1_relat_1(esk1_0)), inference(spm,[status(thm)],[c_0_94, c_0_155])).
cnf(c_0_175, plain, (r2_hidden(k1_funct_1(X1,X2),k10_xtuple_0(X1))|~v1_funct_1(X1)|~r2_hidden(X2,k9_xtuple_0(X1))|~v1_relat_1(X1)), inference(spm,[status(thm)],[c_0_136, c_0_156])).
cnf(c_0_176, negated_conjecture, (k1_funct_1(k4_e_trans1(esk1_0),esk2_0)=k5_numbers), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_102]), c_0_112])])).
cnf(c_0_177, negated_conjecture, (r2_hidden(esk2_0,k9_xtuple_0(k4_e_trans1(esk1_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_112])])).
cnf(c_0_178, plain, (k2_relset_1(X2,X1)=X2|~v2_funct_2(X1,X2)|~v1_relat_1(X1)|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_160])).
cnf(c_0_179, plain, (v2_funct_2(k19_finseq_1(X1),X1)|~v1_finset_1(X1)), inference(split_conjunct,[status(thm)],[c_0_161])).
cnf(c_0_180, plain, (v1_relat_1(k19_finseq_1(X1))|~v1_finset_1(X1)), inference(spm,[status(thm)],[c_0_162, c_0_163])).
cnf(c_0_181, plain, (k4_e_trans1(X1)=k20_finseq_1(k3_e_trans1(X1))|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_164])).
cnf(c_0_182, plain, (~v8_ordinal1(k1_funct_1(k4_diophan2,X1))|~v1_rat_1(X1)), inference(spm,[status(thm)],[c_0_165, c_0_166])).
cnf(c_0_183, plain, (X1=k1_funct_1(X2,esk4_4(X2,X3,X4,X1))|~r2_hidden(X1,X4)|X4!=k7_relat_1(X2,X3)|~v1_relat_1(X2)|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_167])).
cnf(c_0_184, plain, (v1_relat_1(k4_diophan2)), inference(spm,[status(thm)],[c_0_94, c_0_146])).
fof(c_0_185, plain, ![X80]:(~m1_subset_1(X80,u1_struct_0(k11_gaussint))|v1_rat_1(X80)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_gaussint])])).
cnf(c_0_186, plain, (m1_subset_1(X1,X2)|~v5_relat_1(X3,X2)|~v1_relat_1(X3)|~r2_tarski(X1,k2_relset_1(X2,X3))), inference(spm,[status(thm)],[c_0_168, c_0_169])).
cnf(c_0_187, plain, (k7_relset_1(k3_numbers,k4_ordinal1,k4_diophan2,k10_xtuple_0(X1))=k3_e_trans1(X1)|~v5_relat_1(X1,u1_struct_0(k11_gaussint))|~v1_relat_1(X1)|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_170, c_0_171])).
cnf(c_0_188, plain, (k7_relset_1(k3_numbers,k4_ordinal1,k4_diophan2,X1)=k7_relat_1(k4_diophan2,X1)), inference(spm,[status(thm)],[c_0_172, c_0_146])).
cnf(c_0_189, negated_conjecture, (v5_relat_1(esk1_0,u1_struct_0(k11_gaussint))|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_173]), c_0_72])).
cnf(c_0_190, negated_conjecture, (v1_relat_1(esk1_0)|~l1_struct_0(k12_polynom3(k11_gaussint))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_174]), c_0_72])).
cnf(c_0_191, negated_conjecture, (r2_hidden(k5_numbers,k10_xtuple_0(k4_e_trans1(esk1_0)))|~v1_funct_1(k4_e_trans1(esk1_0))|~v1_relat_1(k4_e_trans1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_177])])).
cnf(c_0_192, plain, (k2_relset_1(X1,k19_finseq_1(X1))=X1|~v1_finset_1(X1)|~v5_relat_1(k19_finseq_1(X1),X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178, c_0_179]), c_0_180])).
cnf(c_0_193, plain, (k19_finseq_1(k3_e_trans1(X1))=k4_e_trans1(X1)|~v1_finset_1(k3_e_trans1(X1))|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_163, c_0_181])).
cnf(c_0_194, plain, (X1!=k7_relat_1(k4_diophan2,X2)|~r2_hidden(X3,X1)|~v8_ordinal1(X3)|~v1_rat_1(esk4_4(k4_diophan2,X2,X1,X3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182, c_0_183]), c_0_148]), c_0_184])])).
cnf(c_0_195, plain, (v1_rat_1(X1)|~m1_subset_1(X1,u1_struct_0(k11_gaussint))), inference(split_conjunct,[status(thm)],[c_0_185])).
cnf(c_0_196, plain, (m1_subset_1(X1,X2)|~r2_hidden(X1,k2_relset_1(X2,X3))|~v5_relat_1(X3,X2)|~v1_relat_1(X3)), inference(spm,[status(thm)],[c_0_186, c_0_122])).
cnf(c_0_197, plain, (r2_hidden(esk4_4(X1,X2,X3,X4),X2)|~r2_hidden(X4,X3)|X3!=k7_relat_1(X1,X2)|~v1_relat_1(X1)|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_167])).
cnf(c_0_198, plain, (k7_relat_1(k4_diophan2,k10_xtuple_0(X1))=k3_e_trans1(X1)|~v5_relat_1(X1,u1_struct_0(k11_gaussint))|~v1_relat_1(X1)|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(rw,[status(thm)],[c_0_187, c_0_188])).
cnf(c_0_199, negated_conjecture, (v5_relat_1(esk1_0,u1_struct_0(k11_gaussint))|~l2_algstr_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_189, c_0_81])).
cnf(c_0_200, negated_conjecture, (v1_relat_1(esk1_0)|~l2_algstr_0(k12_polynom3(k11_gaussint))), inference(spm,[status(thm)],[c_0_190, c_0_81])).
cnf(c_0_201, negated_conjecture, (r2_hidden(k5_numbers,k2_relset_1(X1,k4_e_trans1(esk1_0)))|~v1_funct_1(k4_e_trans1(esk1_0))|~v5_relat_1(k4_e_trans1(esk1_0),X1)|~v1_relat_1(k4_e_trans1(esk1_0))), inference(spm,[status(thm)],[c_0_191, c_0_171])).
cnf(c_0_202, plain, (k2_relset_1(k3_e_trans1(X1),k4_e_trans1(X1))=k3_e_trans1(X1)|~v1_finset_1(k3_e_trans1(X1))|~v5_relat_1(k4_e_trans1(X1),k3_e_trans1(X1))|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_192, c_0_193])).
cnf(c_0_203, plain, (X1!=k7_relat_1(k4_diophan2,X2)|~r2_hidden(X3,X1)|~v8_ordinal1(X3)|~m1_subset_1(esk4_4(k4_diophan2,X2,X1,X3),u1_struct_0(k11_gaussint))), inference(spm,[status(thm)],[c_0_194, c_0_195])).
cnf(c_0_204, plain, (m1_subset_1(esk4_4(X1,k2_relset_1(X2,X3),X4,X5),X2)|X4!=k7_relat_1(X1,k2_relset_1(X2,X3))|~v1_funct_1(X1)|~r2_hidden(X5,X4)|~v5_relat_1(X3,X2)|~v1_relat_1(X3)|~v1_relat_1(X1)), inference(spm,[status(thm)],[c_0_196, c_0_197])).
cnf(c_0_205, plain, (k7_relat_1(k4_diophan2,k2_relset_1(X1,X2))=k3_e_trans1(X2)|~v5_relat_1(X2,u1_struct_0(k11_gaussint))|~v5_relat_1(X2,X1)|~v1_relat_1(X2)|~m1_ring_4(X2,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_198, c_0_171])).
cnf(c_0_206, negated_conjecture, (v5_relat_1(esk1_0,u1_struct_0(k11_gaussint))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_59]), c_0_89])])).
cnf(c_0_207, negated_conjecture, (v1_relat_1(esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_59]), c_0_89])])).
cnf(c_0_208, negated_conjecture, (r2_hidden(k5_numbers,k3_e_trans1(esk1_0))|~v1_finset_1(k3_e_trans1(esk1_0))|~v1_funct_1(k4_e_trans1(esk1_0))|~v5_relat_1(k4_e_trans1(esk1_0),k3_e_trans1(esk1_0))|~v1_relat_1(k4_e_trans1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_202]), c_0_56])])).
cnf(c_0_209, plain, (v5_relat_1(X1,X2)|~m2_finseq_1(X1,X2)), inference(spm,[status(thm)],[c_0_154, c_0_95])).
fof(c_0_210, plain, ![X1]:(m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))=>((~v1_xboole_0(k3_e_trans1(X1))&v1_finset_1(k3_e_trans1(X1)))&m1_subset_1(k3_e_trans1(X1),k1_zfmisc_1(k4_ordinal1)))), inference(fof_simplification,[status(thm)],[dt_k3_e_trans1])).
cnf(c_0_211, plain, (X1!=k7_relat_1(k4_diophan2,k2_relset_1(u1_struct_0(k11_gaussint),X2))|~r2_hidden(X3,X1)|~v8_ordinal1(X3)|~v5_relat_1(X2,u1_struct_0(k11_gaussint))|~v1_relat_1(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203, c_0_204]), c_0_148]), c_0_184])])).
cnf(c_0_212, negated_conjecture, (k7_relat_1(k4_diophan2,k2_relset_1(X1,esk1_0))=k3_e_trans1(esk1_0)|~v5_relat_1(esk1_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205, c_0_56]), c_0_206]), c_0_207])])).
cnf(c_0_213, negated_conjecture, (r2_hidden(k5_numbers,k3_e_trans1(esk1_0))|~m2_finseq_1(k4_e_trans1(esk1_0),k3_e_trans1(esk1_0))|~v1_finset_1(k3_e_trans1(esk1_0))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_208, c_0_209]), c_0_103]), c_0_101])).
cnf(c_0_214, plain, (m2_finseq_1(k4_e_trans1(X1),k3_e_trans1(X1))|~v1_finset_1(k3_e_trans1(X1))|~m1_ring_4(X1,k11_gaussint,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(spm,[status(thm)],[c_0_140, c_0_181])).
fof(c_0_215, plain, ![X106]:(((~v1_xboole_0(k3_e_trans1(X106))|~m1_subset_1(X106,u1_struct_0(k12_polynom3(k11_gaussint))))&(v1_finset_1(k3_e_trans1(X106))|~m1_subset_1(X106,u1_struct_0(k12_polynom3(k11_gaussint)))))&(m1_subset_1(k3_e_trans1(X106),k1_zfmisc_1(k4_ordinal1))|~m1_subset_1(X106,u1_struct_0(k12_polynom3(k11_gaussint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_210])])])).
cnf(c_0_216, negated_conjecture, (X1!=k3_e_trans1(esk1_0)|~r2_hidden(X2,X1)|~v8_ordinal1(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211, c_0_212]), c_0_206]), c_0_207])])).
cnf(c_0_217, negated_conjecture, (r2_hidden(k5_numbers,k3_e_trans1(esk1_0))|~v1_finset_1(k3_e_trans1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213, c_0_214]), c_0_56])])).
cnf(c_0_218, plain, (v1_finset_1(k3_e_trans1(X1))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(k11_gaussint)))), inference(split_conjunct,[status(thm)],[c_0_215])).
cnf(c_0_219, plain, (v8_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc9_ordinal1])).
cnf(c_0_220, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
cnf(c_0_221, negated_conjecture, (~r2_hidden(X1,k3_e_trans1(esk1_0))|~v8_ordinal1(X1)), inference(er,[status(thm)],[c_0_216])).
cnf(c_0_222, negated_conjecture, (r2_hidden(k5_numbers,k3_e_trans1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217, c_0_218]), c_0_112])])).
cnf(c_0_223, plain, (v8_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_219, c_0_220])).
cnf(c_0_224, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_222]), c_0_223])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 225
# Proof object clause steps            : 134
# Proof object formula steps           : 91
# Proof object conjectures             : 47
# Proof object clause conjectures      : 44
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 57
# Proof object initial formulas used   : 42
# Proof object generating inferences   : 75
# Proof object simplifying inferences  : 81
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 42
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 93
# Removed in clause preprocessing      : 1
# Initial clauses in saturation        : 92
# Processed clauses                    : 1434
# ...of these trivial                  : 4
# ...subsumed                          : 429
# ...remaining for further processing  : 1001
# Other redundant clauses eliminated   : 2
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 128
# Backward-rewritten                   : 40
# Generated clauses                    : 3396
# ...of the previous two non-trivial   : 3370
# Contextual simplify-reflections      : 99
# Paramodulations                      : 3338
# Factorizations                       : 30
# NegExts                              : 0
# Equation resolutions                 : 28
# 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  : 833
#    Positive orientable unit clauses  : 46
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 3
#    Non-unit-clauses                  : 784
# Current number of unprocessed clauses: 1978
# ...number of literals in the above   : 10437
# Current number of archived formulas  : 0
# Current number of archived clauses   : 168
# Clause-clause subsumption calls (NU) : 206301
# Rec. Clause-clause subsumption calls : 63226
# Non-unit clause-clause subsumptions  : 654
# Unit Clause-clause subsumption calls : 1659
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 17
# BW rewrite match successes           : 17
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 88688

# -------------------------------------------------
# User time                : 0.214 s
# System time              : 0.008 s
# Total time               : 0.222 s
# Maximum resident set size: 3300 pages
