# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___008_C18_F1_PI_SE_CS_SP_CO_S4S
# and selection function SelectNewComplexAHPNS.
#
# Preprocessing time       : 0.022 s

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(dt_k6_group_1, axiom, ![X1, X2]:(((((~(v2_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k6_group_1(X1,X2),k4_ordinal1)), file('group_24/group_24__t82_group_24', dt_k6_group_1)).
fof(t82_group_24, conjecture, ![X1]:(((((~(v2_struct_0(X1))&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(~(r1_xxreal_0(k6_group_1(X1,X2),k5_numbers))&r1_xxreal_0(k6_group_1(X1,X2),k7_group_1(X1))))), file('group_24/group_24__t82_group_24', t82_group_24)).
fof(t8_gr_cy_1, axiom, ![X1]:(((((~(v2_struct_0(X1))&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>r1_nat_d(k6_group_1(X1,X2),k7_group_1(X1)))), file('group_24/group_24__t82_group_24', t8_gr_cy_1)).
fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('group_24/group_24__t82_group_24', cc8_ordinal1)).
fof(fc18_struct_0, axiom, ![X1]:(((~(v2_struct_0(X1))&v8_struct_0(X1))&l1_struct_0(X1))=>(v7_ordinal1(k7_struct_0(X1))&~(v8_ordinal1(k7_struct_0(X1))))), file('group_24/group_24__t82_group_24', fc18_struct_0)).
fof(t7_nat_d, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(r1_nat_d(X1,X2)=>(r1_xxreal_0(X2,k5_numbers)|r1_xxreal_0(X1,X2))))), file('group_24/group_24__t82_group_24', t7_nat_d)).
fof(redefinition_k7_group_1, axiom, ![X1]:((v8_struct_0(X1)&l1_struct_0(X1))=>k7_group_1(X1)=k7_struct_0(X1)), file('group_24/group_24__t82_group_24', redefinition_k7_group_1)).
fof(dt_l3_algstr_0, axiom, ![X1]:(l3_algstr_0(X1)=>l1_struct_0(X1)), file('group_24/group_24__t82_group_24', dt_l3_algstr_0)).
fof(t6_real, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>(r1_xxreal_0(X1,X2)=>(v8_ordinal1(X1)|v2_xxreal_0(X2)|v3_xxreal_0(X1))))), file('group_24/group_24__t82_group_24', t6_real)).
fof(cc2_xreal_0, axiom, ![X1]:(v7_ordinal1(X1)=>v1_xreal_0(X1)), file('group_24/group_24__t82_group_24', cc2_xreal_0)).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1), file('group_24/group_24__t82_group_24', fc8_ordinal1)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('group_24/group_24__t82_group_24', redefinition_k5_numbers)).
fof(cc2_nat_1, axiom, ![X1]:(v7_ordinal1(X1)=>(v7_ordinal1(X1)&~(v3_xxreal_0(X1)))), file('group_24/group_24__t82_group_24', cc2_nat_1)).
fof(cc4_nat_1, axiom, ![X1]:((v7_ordinal1(X1)&v8_ordinal1(X1))=>(v7_ordinal1(X1)&~(v2_xxreal_0(X1)))), file('group_24/group_24__t82_group_24', cc4_nat_1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1), file('group_24/group_24__t82_group_24', fc9_ordinal1)).
fof(fc4_card_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>(~(v8_ordinal1(k1_card_1(X1)))&v1_card_1(k1_card_1(X1)))), file('group_24/group_24__t82_group_24', fc4_card_1)).
fof(rd1_card_1, axiom, ![X1]:(v1_card_1(X1)=>k1_card_1(X1)=X1), file('group_24/group_24__t82_group_24', rd1_card_1)).
fof(cc3_card_1, axiom, ![X1]:(v7_ordinal1(X1)=>v1_card_1(X1)), file('group_24/group_24__t82_group_24', cc3_card_1)).
fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('group_24/group_24__t82_group_24', t6_boole)).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0, file('group_24/group_24__t82_group_24', d13_ordinal1)).
fof(d11_group_1, axiom, ![X1]:((((~(v2_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,k4_ordinal1)=>((v4_group_1(X2,X1)=>(X3=k6_group_1(X1,X2)<=>X3=k5_numbers))&(~(v4_group_1(X2,X1))=>(X3=k6_group_1(X1,X2)<=>((k5_group_1(X1,X2,X3)=k1_group_1(X1)&X3!=k5_numbers)&![X4]:(v7_ordinal1(X4)=>(k5_group_1(X1,X2,X4)=k1_group_1(X1)=>(X4=k5_numbers|r1_xxreal_0(X3,X4))))))))))), file('group_24/group_24__t82_group_24', d11_group_1)).
fof(t6_gr_cy_1, axiom, ![X1]:(((((~(v2_struct_0(X1))&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>~(v4_group_1(X2,X1)))), file('group_24/group_24__t82_group_24', t6_gr_cy_1)).
fof(c_0_22, plain, ![X1, X2]:(((((~v2_struct_0(X1)&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k6_group_1(X1,X2),k4_ordinal1)), inference(fof_simplification,[status(thm)],[dt_k6_group_1])).
fof(c_0_23, negated_conjecture, ~(![X1]:(((((~v2_struct_0(X1)&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(~r1_xxreal_0(k6_group_1(X1,X2),k5_numbers)&r1_xxreal_0(k6_group_1(X1,X2),k7_group_1(X1)))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t82_group_24])])).
fof(c_0_24, plain, ![X1]:(((((~v2_struct_0(X1)&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>r1_nat_d(k6_group_1(X1,X2),k7_group_1(X1)))), inference(fof_simplification,[status(thm)],[t8_gr_cy_1])).
fof(c_0_25, plain, ![X41, X42]:(v2_struct_0(X41)|~v2_group_1(X41)|~v3_group_1(X41)|~l3_algstr_0(X41)|~m1_subset_1(X42,u1_struct_0(X41))|m1_subset_1(k6_group_1(X41,X42),k4_ordinal1)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])).
fof(c_0_26, negated_conjecture, (((((~v2_struct_0(esk1_0)&v8_struct_0(esk1_0))&v2_group_1(esk1_0))&v3_group_1(esk1_0))&l3_algstr_0(esk1_0))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])).
fof(c_0_27, plain, ![X55, X56]:(v2_struct_0(X55)|~v8_struct_0(X55)|~v2_group_1(X55)|~v3_group_1(X55)|~l3_algstr_0(X55)|(~m1_subset_1(X56,u1_struct_0(X55))|r1_nat_d(k6_group_1(X55,X56),k7_group_1(X55)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])).
fof(c_0_28, plain, ![X38]:(~m1_subset_1(X38,k4_ordinal1)|v7_ordinal1(X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])).
cnf(c_0_29, plain, (v2_struct_0(X1)|m1_subset_1(k6_group_1(X1,X2),k4_ordinal1)|~v2_group_1(X1)|~v3_group_1(X1)|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_25])).
cnf(c_0_30, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_31, negated_conjecture, (l3_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_32, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_33, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_34, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])).
fof(c_0_35, plain, ![X1]:(((~v2_struct_0(X1)&v8_struct_0(X1))&l1_struct_0(X1))=>(v7_ordinal1(k7_struct_0(X1))&~v8_ordinal1(k7_struct_0(X1)))), inference(fof_simplification,[status(thm)],[fc18_struct_0])).
fof(c_0_36, plain, ![X53, X54]:(~v7_ordinal1(X53)|(~v7_ordinal1(X54)|(~r1_nat_d(X53,X54)|(r1_xxreal_0(X54,k5_numbers)|r1_xxreal_0(X53,X54))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_nat_d])])])).
cnf(c_0_37, plain, (v2_struct_0(X1)|r1_nat_d(k6_group_1(X1,X2),k7_group_1(X1))|~v8_struct_0(X1)|~v2_group_1(X1)|~v3_group_1(X1)|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_27])).
cnf(c_0_38, negated_conjecture, (v8_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_39, plain, (v7_ordinal1(X1)|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_40, negated_conjecture, (m1_subset_1(k6_group_1(esk1_0,esk2_0),k4_ordinal1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])).
fof(c_0_41, plain, ![X44]:((v7_ordinal1(k7_struct_0(X44))|(v2_struct_0(X44)|~v8_struct_0(X44)|~l1_struct_0(X44)))&(~v8_ordinal1(k7_struct_0(X44))|(v2_struct_0(X44)|~v8_struct_0(X44)|~l1_struct_0(X44)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])).
fof(c_0_42, plain, ![X47]:(~v8_struct_0(X47)|~l1_struct_0(X47)|k7_group_1(X47)=k7_struct_0(X47)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_group_1])])).
cnf(c_0_43, plain, (r1_xxreal_0(X2,k5_numbers)|r1_xxreal_0(X1,X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)|~r1_nat_d(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_44, negated_conjecture, (r1_nat_d(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_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(spm,[status(thm)],[c_0_37, c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_38])]), c_0_34])).
cnf(c_0_45, negated_conjecture, (v7_ordinal1(k6_group_1(esk1_0,esk2_0))), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_46, plain, (v7_ordinal1(k7_struct_0(X1))|v2_struct_0(X1)|~v8_struct_0(X1)|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_47, plain, (k7_group_1(X1)=k7_struct_0(X1)|~v8_struct_0(X1)|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_48, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_0))|r1_xxreal_0(k7_group_1(esk1_0),k5_numbers)|~v7_ordinal1(k7_group_1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45])])).
cnf(c_0_49, plain, (v7_ordinal1(k7_group_1(X1))|v2_struct_0(X1)|~l1_struct_0(X1)|~v8_struct_0(X1)), inference(spm,[status(thm)],[c_0_46, c_0_47])).
fof(c_0_50, plain, ![X43]:(~l3_algstr_0(X43)|l1_struct_0(X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_algstr_0])])).
cnf(c_0_51, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_0))|r1_xxreal_0(k7_group_1(esk1_0),k5_numbers)|~l1_struct_0(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_38])]), c_0_34])).
cnf(c_0_52, plain, (l1_struct_0(X1)|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
fof(c_0_53, plain, ![X51, X52]:(~v1_xreal_0(X51)|(~v1_xreal_0(X52)|(~r1_xxreal_0(X51,X52)|(v8_ordinal1(X51)|v2_xxreal_0(X52)|v3_xxreal_0(X51))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_real])])])).
cnf(c_0_54, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_55, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k7_group_1(esk1_0))|r1_xxreal_0(k7_group_1(esk1_0),k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_31])])).
cnf(c_0_56, plain, (v8_ordinal1(X1)|v2_xxreal_0(X2)|v3_xxreal_0(X1)|~v1_xreal_0(X1)|~v1_xreal_0(X2)|~r1_xxreal_0(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_57, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|r1_xxreal_0(k7_group_1(esk1_0),k5_numbers)), inference(spm,[status(thm)],[c_0_54, c_0_55])).
fof(c_0_58, plain, ![X35]:(~v7_ordinal1(X35)|v1_xreal_0(X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_xreal_0])])).
cnf(c_0_59, plain, (v7_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc8_ordinal1])).
cnf(c_0_60, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
fof(c_0_61, plain, ![X1]:(v7_ordinal1(X1)=>(v7_ordinal1(X1)&~v3_xxreal_0(X1))), inference(fof_simplification,[status(thm)],[cc2_nat_1])).
cnf(c_0_62, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k7_group_1(esk1_0))|v3_xxreal_0(k7_group_1(esk1_0))|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~v1_xreal_0(k7_group_1(esk1_0))|~v1_xreal_0(k5_numbers)), inference(spm,[status(thm)],[c_0_56, c_0_57])).
cnf(c_0_63, plain, (v1_xreal_0(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_58])).
cnf(c_0_64, plain, (v7_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_59, c_0_60])).
fof(c_0_65, plain, ![X34]:((v7_ordinal1(X34)|~v7_ordinal1(X34))&(~v3_xxreal_0(X34)|~v7_ordinal1(X34))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])).
cnf(c_0_66, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k7_group_1(esk1_0))|v3_xxreal_0(k7_group_1(esk1_0))|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~v1_xreal_0(k7_group_1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])).
cnf(c_0_67, plain, (~v3_xxreal_0(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_68, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k7_group_1(esk1_0))|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~v7_ordinal1(k7_group_1(esk1_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_63]), c_0_67])).
cnf(c_0_69, plain, (v2_struct_0(X1)|~v8_ordinal1(k7_struct_0(X1))|~v8_struct_0(X1)|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_70, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k7_group_1(esk1_0))|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~l1_struct_0(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_49]), c_0_38])]), c_0_34])).
fof(c_0_71, 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_72, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v8_ordinal1(k7_group_1(X1))|~v8_struct_0(X1)), inference(spm,[status(thm)],[c_0_69, c_0_47])).
cnf(c_0_73, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k7_group_1(esk1_0))|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_52]), c_0_31])])).
fof(c_0_74, plain, ![X37]:((v7_ordinal1(X37)|(~v7_ordinal1(X37)|~v8_ordinal1(X37)))&(~v2_xxreal_0(X37)|(~v7_ordinal1(X37)|~v8_ordinal1(X37)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])).
cnf(c_0_75, negated_conjecture, (v2_xxreal_0(k5_numbers)|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)|~l1_struct_0(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_38])]), c_0_34])).
cnf(c_0_76, plain, (v8_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc9_ordinal1])).
cnf(c_0_77, plain, (~v2_xxreal_0(X1)|~v7_ordinal1(X1)|~v8_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_74])).
cnf(c_0_78, negated_conjecture, (v2_xxreal_0(k5_numbers)|r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_52]), c_0_31])])).
cnf(c_0_79, plain, (v8_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_76, c_0_60])).
cnf(c_0_80, negated_conjecture, (r1_xxreal_0(k6_group_1(esk1_0,esk2_0),k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), c_0_64])])).
fof(c_0_81, plain, ![X1]:(~v1_xboole_0(X1)=>(~v8_ordinal1(k1_card_1(X1))&v1_card_1(k1_card_1(X1)))), inference(fof_simplification,[status(thm)],[fc4_card_1])).
fof(c_0_82, plain, ![X46]:(~v1_card_1(X46)|k1_card_1(X46)=X46), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rd1_card_1])])).
fof(c_0_83, plain, ![X36]:(~v7_ordinal1(X36)|v1_card_1(X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_card_1])])).
cnf(c_0_84, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k6_group_1(esk1_0,esk2_0))|v3_xxreal_0(k6_group_1(esk1_0,esk2_0))|~v1_xreal_0(k6_group_1(esk1_0,esk2_0))|~v1_xreal_0(k5_numbers)), inference(spm,[status(thm)],[c_0_56, c_0_80])).
fof(c_0_85, plain, ![X48]:(~v1_xboole_0(X48)|X48=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])).
cnf(c_0_86, plain, (k5_ordinal1=k1_xboole_0), inference(split_conjunct,[status(thm)],[d13_ordinal1])).
fof(c_0_87, plain, ![X45]:((~v8_ordinal1(k1_card_1(X45))|v1_xboole_0(X45))&(v1_card_1(k1_card_1(X45))|v1_xboole_0(X45))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])])])).
cnf(c_0_88, plain, (k1_card_1(X1)=X1|~v1_card_1(X1)), inference(split_conjunct,[status(thm)],[c_0_82])).
cnf(c_0_89, plain, (v1_card_1(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_90, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k6_group_1(esk1_0,esk2_0))|v3_xxreal_0(k6_group_1(esk1_0,esk2_0))|~v1_xreal_0(k6_group_1(esk1_0,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_63]), c_0_64])])).
fof(c_0_91, plain, ![X2, X1]:(epred1_2(X1,X2)<=>![X3]:(m1_subset_1(X3,k4_ordinal1)=>((v4_group_1(X2,X1)=>(X3=k6_group_1(X1,X2)<=>X3=k5_numbers))&(~v4_group_1(X2,X1)=>(X3=k6_group_1(X1,X2)<=>((k5_group_1(X1,X2,X3)=k1_group_1(X1)&X3!=k5_numbers)&![X4]:(v7_ordinal1(X4)=>(k5_group_1(X1,X2,X4)=k1_group_1(X1)=>(X4=k5_numbers|r1_xxreal_0(X3,X4)))))))))), introduced(definition)).
cnf(c_0_92, plain, (X1=k1_xboole_0|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_85])).
cnf(c_0_93, plain, (k1_xboole_0=k5_numbers), inference(rw,[status(thm)],[c_0_86, c_0_60])).
cnf(c_0_94, plain, (v1_xboole_0(X1)|~v8_ordinal1(k1_card_1(X1))), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_95, plain, (k1_card_1(X1)=X1|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_88, c_0_89])).
cnf(c_0_96, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k6_group_1(esk1_0,esk2_0))|v3_xxreal_0(k6_group_1(esk1_0,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_63]), c_0_45])])).
fof(c_0_97, plain, ![X2, X1]:(epred1_2(X1,X2)=>![X3]:(m1_subset_1(X3,k4_ordinal1)=>((v4_group_1(X2,X1)=>(X3=k6_group_1(X1,X2)<=>X3=k5_numbers))&(~v4_group_1(X2,X1)=>(X3=k6_group_1(X1,X2)<=>((k5_group_1(X1,X2,X3)=k1_group_1(X1)&X3!=k5_numbers)&![X4]:(v7_ordinal1(X4)=>(k5_group_1(X1,X2,X4)=k1_group_1(X1)=>(X4=k5_numbers|r1_xxreal_0(X3,X4)))))))))), inference(split_equiv,[status(thm)],[c_0_91])).
fof(c_0_98, plain, ![X1]:((((~v2_struct_0(X1)&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>epred1_2(X1,X2))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d11_group_1]), c_0_91])).
cnf(c_0_99, plain, (X1=k5_numbers|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_92, c_0_93])).
cnf(c_0_100, plain, (v1_xboole_0(X1)|~v8_ordinal1(X1)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_94, c_0_95])).
cnf(c_0_101, negated_conjecture, (v2_xxreal_0(k5_numbers)|v8_ordinal1(k6_group_1(esk1_0,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_96]), c_0_45])])).
fof(c_0_102, plain, ![X1]:(((((~v2_struct_0(X1)&v8_struct_0(X1))&v2_group_1(X1))&v3_group_1(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>~v4_group_1(X2,X1))), inference(fof_simplification,[status(thm)],[t6_gr_cy_1])).
fof(c_0_103, plain, ![X57, X58, X59, X60]:(((X59!=k6_group_1(X58,X57)|X59=k5_numbers|~v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))&(X59!=k5_numbers|X59=k6_group_1(X58,X57)|~v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57)))&((((k5_group_1(X58,X57,X59)=k1_group_1(X58)|X59!=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))&(X59!=k5_numbers|X59!=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57)))&(~v7_ordinal1(X60)|(k5_group_1(X58,X57,X60)!=k1_group_1(X58)|(X60=k5_numbers|r1_xxreal_0(X59,X60)))|X59!=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57)))&((v7_ordinal1(esk3_3(X57,X58,X59))|(k5_group_1(X58,X57,X59)!=k1_group_1(X58)|X59=k5_numbers)|X59=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))&((k5_group_1(X58,X57,esk3_3(X57,X58,X59))=k1_group_1(X58)|(k5_group_1(X58,X57,X59)!=k1_group_1(X58)|X59=k5_numbers)|X59=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))&((esk3_3(X57,X58,X59)!=k5_numbers|(k5_group_1(X58,X57,X59)!=k1_group_1(X58)|X59=k5_numbers)|X59=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))&(~r1_xxreal_0(X59,esk3_3(X57,X58,X59))|(k5_group_1(X58,X57,X59)!=k1_group_1(X58)|X59=k5_numbers)|X59=k6_group_1(X58,X57)|v4_group_1(X57,X58)|~m1_subset_1(X59,k4_ordinal1)|~epred1_2(X58,X57))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])])])])).
fof(c_0_104, plain, ![X39, X40]:(v2_struct_0(X39)|~v2_group_1(X39)|~v3_group_1(X39)|~l3_algstr_0(X39)|(~m1_subset_1(X40,u1_struct_0(X39))|epred1_2(X39,X40))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])])).
cnf(c_0_105, plain, (X1=k5_numbers|~v8_ordinal1(X1)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_99, c_0_100])).
cnf(c_0_106, negated_conjecture, (v8_ordinal1(k6_group_1(esk1_0,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_101]), c_0_79]), c_0_64])])).
fof(c_0_107, plain, ![X49, X50]:(v2_struct_0(X49)|~v8_struct_0(X49)|~v2_group_1(X49)|~v3_group_1(X49)|~l3_algstr_0(X49)|(~m1_subset_1(X50,u1_struct_0(X49))|~v4_group_1(X50,X49))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])])).
cnf(c_0_108, plain, (v4_group_1(X3,X2)|X1!=k5_numbers|X1!=k6_group_1(X2,X3)|~m1_subset_1(X1,k4_ordinal1)|~epred1_2(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_103])).
cnf(c_0_109, plain, (v2_struct_0(X1)|epred1_2(X1,X2)|~v2_group_1(X1)|~v3_group_1(X1)|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_110, negated_conjecture, (k6_group_1(esk1_0,esk2_0)=k5_numbers), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_45])])).
cnf(c_0_111, plain, (v2_struct_0(X1)|~v8_struct_0(X1)|~v2_group_1(X1)|~v3_group_1(X1)|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~v4_group_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_107])).
cnf(c_0_112, plain, (v4_group_1(X1,X2)|k6_group_1(X2,X1)!=k5_numbers|~epred1_2(X2,X1)|~m1_subset_1(k6_group_1(X2,X1),k4_ordinal1)), inference(er,[status(thm)],[c_0_108])).
cnf(c_0_113, negated_conjecture, (epred1_2(esk1_0,esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])).
cnf(c_0_114, negated_conjecture, (m1_subset_1(k5_numbers,k4_ordinal1)), inference(rw,[status(thm)],[c_0_40, c_0_110])).
cnf(c_0_115, negated_conjecture, (~v4_group_1(esk2_0,esk1_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(spm,[status(thm)],[c_0_111, c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_38])]), c_0_34])).
cnf(c_0_116, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_110]), c_0_113]), c_0_114])]), c_0_115]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 117
# Proof object clause steps            : 65
# Proof object formula steps           : 52
# Proof object conjectures             : 35
# Proof object clause conjectures      : 32
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 30
# Proof object initial formulas used   : 22
# Proof object generating inferences   : 29
# Proof object simplifying inferences  : 66
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 22
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 41
# Removed in clause preprocessing      : 2
# Initial clauses in saturation        : 39
# Processed clauses                    : 77
# ...of these trivial                  : 0
# ...subsumed                          : 3
# ...remaining for further processing  : 74
# Other redundant clauses eliminated   : 5
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 11
# Backward-rewritten                   : 10
# Generated clauses                    : 51
# ...of the previous two non-trivial   : 52
# Contextual simplify-reflections      : 1
# Paramodulations                      : 46
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 5
# 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  : 48
#    Positive orientable unit clauses  : 14
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 2
#    Non-unit-clauses                  : 32
# Current number of unprocessed clauses: 13
# ...number of literals in the above   : 63
# Current number of archived formulas  : 0
# Current number of archived clauses   : 21
# Clause-clause subsumption calls (NU) : 814
# Rec. Clause-clause subsumption calls : 260
# Non-unit clause-clause subsumptions  : 14
# Unit Clause-clause subsumption calls : 34
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 3
# BW rewrite match successes           : 3
# Condensation attempts                : 77
# Condensation successes               : 0
# Termbank termtop insertions          : 4483

# -------------------------------------------------
# User time                : 0.026 s
# System time              : 0.003 s
# Total time               : 0.029 s
# Maximum resident set size: 3464 pages
