# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S068N
# and selection function PSelectNewComplexAHP.
#
# Preprocessing time       : 0.024 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(cc4_nat_1, axiom, ![X1]:((v7_ordinal1(X1)&v8_ordinal1(X1))=>(v7_ordinal1(X1)&~(v2_xxreal_0(X1)))), file('newton06/newton06__t31_newton06', cc4_nat_1)).
fof(t4_real, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>~(((r1_xxreal_0(X1,X2)&~(v2_xxreal_0(X2)))&v2_xxreal_0(X1))))), file('newton06/newton06__t31_newton06', t4_real)).
fof(t31_newton06, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(r1_int_2(X1,X2)=>![X3]:((~(v1_zfmisc_1(X3))&v7_ordinal1(X3))=>~(r1_xxreal_0(k4_xxreal_0(k4_nat_d(X1,X3),k4_nat_d(X2,X3)),k5_numbers)))))), file('newton06/newton06__t31_newton06', t31_newton06)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1), file('newton06/newton06__t31_newton06', fc9_ordinal1)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('newton06/newton06__t31_newton06', redefinition_k5_numbers)).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1), file('newton06/newton06__t31_newton06', fc8_ordinal1)).
fof(fc8_newton03, axiom, ![X1, X2]:(((~(v8_ordinal1(X1))&v1_int_1(X1))&v1_int_1(X2))=>(v7_ordinal1(k3_int_2(X1,X2))&v2_xxreal_0(k3_int_2(X1,X2)))), file('newton06/newton06__t31_newton06', fc8_newton03)).
fof(cc13_ordinal1, axiom, ![X1]:(~(v1_zfmisc_1(X1))=>~(v8_ordinal1(X1))), file('newton06/newton06__t31_newton06', cc13_ordinal1)).
fof(rd4_newton02, axiom, ![X1]:(v7_ordinal1(X1)=>k3_int_2(X1,k5_numbers)=X1), file('newton06/newton06__t31_newton06', rd4_newton02)).
fof(cc2_int_1, axiom, ![X1]:(v7_ordinal1(X1)=>v1_int_1(X1)), file('newton06/newton06__t31_newton06', cc2_int_1)).
fof(cc2_xreal_0, axiom, ![X1]:(v7_ordinal1(X1)=>v1_xreal_0(X1)), file('newton06/newton06__t31_newton06', cc2_xreal_0)).
fof(d1_nat_2, axiom, ![X1]:(v7_ordinal1(X1)=>(v1_zfmisc_1(X1)<=>(X1=k5_numbers|X1=np__1))), file('newton06/newton06__t31_newton06', d1_nat_2)).
fof(fc124_complex3, axiom, ![X1, X2]:(((v2_xxreal_0(X1)&v1_xreal_0(X1))&v1_xreal_0(X2))=>(v1_xxreal_0(k4_xxreal_0(X1,X2))&v2_xxreal_0(k4_xxreal_0(X1,X2)))), file('newton06/newton06__t31_newton06', fc124_complex3)).
fof(fc36_xreal_0, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>(v1_xxreal_0(k4_xxreal_0(X1,X2))&v1_xreal_0(k4_xxreal_0(X1,X2)))), file('newton06/newton06__t31_newton06', fc36_xreal_0)).
fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('newton06/newton06__t31_newton06', cc8_ordinal1)).
fof(dt_k4_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>m1_subset_1(k4_nat_d(X1,X2),k4_ordinal1)), file('newton06/newton06__t31_newton06', dt_k4_nat_d)).
fof(spc1_numerals, axiom, (v2_xxreal_0(np__1)&m1_subset_1(np__1,k4_ordinal1)), file('newton06/newton06__t31_newton06', spc1_numerals)).
fof(commutativity_k4_xxreal_0, axiom, ![X1, X2]:((v1_xxreal_0(X1)&v1_xxreal_0(X2))=>k4_xxreal_0(X1,X2)=k4_xxreal_0(X2,X1)), file('newton06/newton06__t31_newton06', commutativity_k4_xxreal_0)).
fof(cc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xxreal_0(X1)), file('newton06/newton06__t31_newton06', cc4_xreal_0)).
fof(t62_int_1, axiom, ![X1]:(v1_int_1(X1)=>(~(r1_xxreal_0(X1,k5_numbers))=>![X2]:(v1_int_1(X2)=>(k5_int_1(X2,X1)=k5_numbers<=>r1_int_1(X1,X2))))), file('newton06/newton06__t31_newton06', t62_int_1)).
fof(redefinition_k4_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>k4_nat_d(X1,X2)=k5_int_1(X1,X2)), file('newton06/newton06__t31_newton06', redefinition_k4_nat_d)).
fof(redefinition_r1_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>(r1_nat_d(X1,X2)<=>r1_int_1(X1,X2))), file('newton06/newton06__t31_newton06', redefinition_r1_nat_d)).
fof(d1_pythtrip, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(r1_int_2(X1,X2)<=>![X3]:(v7_ordinal1(X3)=>((r1_nat_d(X3,X1)&r1_nat_d(X3,X2))=>X3=np__1))))), file('newton06/newton06__t31_newton06', d1_pythtrip)).
fof(c_0_23, plain, ![X1]:((v7_ordinal1(X1)&v8_ordinal1(X1))=>(v7_ordinal1(X1)&~v2_xxreal_0(X1))), inference(fof_simplification,[status(thm)],[cc4_nat_1])).
fof(c_0_24, plain, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>~(((r1_xxreal_0(X1,X2)&~v2_xxreal_0(X2))&v2_xxreal_0(X1))))), inference(fof_simplification,[status(thm)],[t4_real])).
fof(c_0_25, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(r1_int_2(X1,X2)=>![X3]:((~v1_zfmisc_1(X3)&v7_ordinal1(X3))=>~r1_xxreal_0(k4_xxreal_0(k4_nat_d(X1,X3),k4_nat_d(X2,X3)),k5_numbers)))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_newton06])])).
fof(c_0_26, plain, ![X46]:((v7_ordinal1(X46)|(~v7_ordinal1(X46)|~v8_ordinal1(X46)))&(~v2_xxreal_0(X46)|(~v7_ordinal1(X46)|~v8_ordinal1(X46)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])).
cnf(c_0_27, plain, (v8_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc9_ordinal1])).
cnf(c_0_28, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
cnf(c_0_29, plain, (v7_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc8_ordinal1])).
fof(c_0_30, plain, ![X1, X2]:(((~v8_ordinal1(X1)&v1_int_1(X1))&v1_int_1(X2))=>(v7_ordinal1(k3_int_2(X1,X2))&v2_xxreal_0(k3_int_2(X1,X2)))), inference(fof_simplification,[status(thm)],[fc8_newton03])).
fof(c_0_31, plain, ![X69, X70]:(~v1_xreal_0(X69)|(~v1_xreal_0(X70)|(~r1_xxreal_0(X69,X70)|v2_xxreal_0(X70)|~v2_xxreal_0(X69)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])).
fof(c_0_32, negated_conjecture, (v7_ordinal1(esk1_0)&(v7_ordinal1(esk2_0)&(r1_int_2(esk1_0,esk2_0)&((~v1_zfmisc_1(esk3_0)&v7_ordinal1(esk3_0))&r1_xxreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)),k5_numbers))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])).
cnf(c_0_33, plain, (~v2_xxreal_0(X1)|~v7_ordinal1(X1)|~v8_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_26])).
cnf(c_0_34, plain, (v8_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_27, c_0_28])).
cnf(c_0_35, plain, (v7_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_29, c_0_28])).
fof(c_0_36, plain, ![X1]:(~v1_zfmisc_1(X1)=>~v8_ordinal1(X1)), inference(fof_simplification,[status(thm)],[cc13_ordinal1])).
fof(c_0_37, plain, ![X62, X63]:((v7_ordinal1(k3_int_2(X62,X63))|(v8_ordinal1(X62)|~v1_int_1(X62)|~v1_int_1(X63)))&(v2_xxreal_0(k3_int_2(X62,X63))|(v8_ordinal1(X62)|~v1_int_1(X62)|~v1_int_1(X63)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])).
fof(c_0_38, plain, ![X64]:(~v7_ordinal1(X64)|k3_int_2(X64,k5_numbers)=X64), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rd4_newton02])])).
fof(c_0_39, plain, ![X43]:(~v7_ordinal1(X43)|v1_int_1(X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_int_1])])).
cnf(c_0_40, plain, (v2_xxreal_0(X2)|~v1_xreal_0(X1)|~v1_xreal_0(X2)|~r1_xxreal_0(X1,X2)|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_41, negated_conjecture, (r1_xxreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)),k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_42, plain, (~v2_xxreal_0(k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])])).
fof(c_0_43, plain, ![X44]:(~v7_ordinal1(X44)|v1_xreal_0(X44)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_xreal_0])])).
fof(c_0_44, plain, ![X51]:((~v1_zfmisc_1(X51)|(X51=k5_numbers|X51=np__1)|~v7_ordinal1(X51))&((X51!=k5_numbers|v1_zfmisc_1(X51)|~v7_ordinal1(X51))&(X51!=np__1|v1_zfmisc_1(X51)|~v7_ordinal1(X51)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_nat_2])])])).
fof(c_0_45, plain, ![X42]:(v1_zfmisc_1(X42)|~v8_ordinal1(X42)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])).
cnf(c_0_46, plain, (v2_xxreal_0(k3_int_2(X1,X2))|v8_ordinal1(X1)|~v1_int_1(X1)|~v1_int_1(X2)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_47, plain, (k3_int_2(X1,k5_numbers)=X1|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_38])).
cnf(c_0_48, plain, (v1_int_1(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_39])).
cnf(c_0_49, negated_conjecture, (~v2_xxreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)))|~v1_xreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)))|~v1_xreal_0(k5_numbers)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42])).
cnf(c_0_50, plain, (v1_xreal_0(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_43])).
fof(c_0_51, plain, ![X58, X59]:((v1_xxreal_0(k4_xxreal_0(X58,X59))|(~v2_xxreal_0(X58)|~v1_xreal_0(X58)|~v1_xreal_0(X59)))&(v2_xxreal_0(k4_xxreal_0(X58,X59))|(~v2_xxreal_0(X58)|~v1_xreal_0(X58)|~v1_xreal_0(X59)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc124_complex3])])])).
fof(c_0_52, plain, ![X60, X61]:((v1_xxreal_0(k4_xxreal_0(X60,X61))|(~v1_xreal_0(X60)|~v1_xreal_0(X61)))&(v1_xreal_0(k4_xxreal_0(X60,X61))|(~v1_xreal_0(X60)|~v1_xreal_0(X61)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc36_xreal_0])])])).
cnf(c_0_53, plain, (X1=k5_numbers|X1=np__1|~v1_zfmisc_1(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_54, plain, (v1_zfmisc_1(X1)|~v8_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_45])).
cnf(c_0_55, plain, (v2_xxreal_0(X1)|v8_ordinal1(X1)|~v1_int_1(k5_numbers)|~v7_ordinal1(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48])).
cnf(c_0_56, negated_conjecture, (~v2_xxreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)))|~v1_xreal_0(k4_xxreal_0(k4_nat_d(esk1_0,esk3_0),k4_nat_d(esk2_0,esk3_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_35])])).
cnf(c_0_57, plain, (v2_xxreal_0(k4_xxreal_0(X1,X2))|~v2_xxreal_0(X1)|~v1_xreal_0(X1)|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_58, plain, (v1_xreal_0(k4_xxreal_0(X1,X2))|~v1_xreal_0(X1)|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_52])).
cnf(c_0_59, plain, (X1=np__1|X1=k5_numbers|~v8_ordinal1(X1)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_53, c_0_54])).
cnf(c_0_60, plain, (v2_xxreal_0(X1)|v8_ordinal1(X1)|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_48]), c_0_35])])).
cnf(c_0_61, negated_conjecture, (~v2_xxreal_0(k4_nat_d(esk1_0,esk3_0))|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))|~v1_xreal_0(k4_nat_d(esk1_0,esk3_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])).
cnf(c_0_62, plain, (X1=k5_numbers|X1=np__1|v2_xxreal_0(X1)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_59, c_0_60])).
fof(c_0_63, plain, ![X48]:(~m1_subset_1(X48,k4_ordinal1)|v7_ordinal1(X48)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])).
fof(c_0_64, plain, ![X56, X57]:(~v7_ordinal1(X56)|~v7_ordinal1(X57)|m1_subset_1(k4_nat_d(X56,X57),k4_ordinal1)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_nat_d])])).
cnf(c_0_65, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=np__1|k4_nat_d(esk1_0,esk3_0)=k5_numbers|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))|~v7_ordinal1(k4_nat_d(esk1_0,esk3_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_50])).
cnf(c_0_66, plain, (v7_ordinal1(X1)|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_67, plain, (m1_subset_1(k4_nat_d(X1,X2),k4_ordinal1)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_64])).
cnf(c_0_68, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers|k4_nat_d(esk1_0,esk3_0)=np__1|~v7_ordinal1(k4_nat_d(esk1_0,esk3_0))|~v7_ordinal1(k4_nat_d(esk2_0,esk3_0))), inference(spm,[status(thm)],[c_0_65, c_0_50])).
cnf(c_0_69, plain, (v7_ordinal1(k4_nat_d(X1,X2))|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_66, c_0_67])).
cnf(c_0_70, negated_conjecture, (v7_ordinal1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_71, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_72, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=np__1|k4_nat_d(esk1_0,esk3_0)=k5_numbers|~v7_ordinal1(k4_nat_d(esk2_0,esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70]), c_0_71])])).
cnf(c_0_73, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_74, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers|k4_nat_d(esk1_0,esk3_0)=np__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_69]), c_0_70]), c_0_73])])).
cnf(c_0_75, plain, (v2_xxreal_0(np__1)), inference(split_conjunct,[status(thm)],[spc1_numerals])).
cnf(c_0_76, plain, (m1_subset_1(np__1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[spc1_numerals])).
cnf(c_0_77, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))|~v1_xreal_0(np__1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_74]), c_0_75])])).
cnf(c_0_78, plain, (v7_ordinal1(np__1)), inference(spm,[status(thm)],[c_0_66, c_0_76])).
fof(c_0_79, plain, ![X49, X50]:(~v1_xxreal_0(X49)|~v1_xxreal_0(X50)|k4_xxreal_0(X49,X50)=k4_xxreal_0(X50,X49)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k4_xxreal_0])])).
fof(c_0_80, plain, ![X47]:(~v1_xreal_0(X47)|v1_xxreal_0(X47)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_xreal_0])])).
cnf(c_0_81, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_50]), c_0_78])])).
cnf(c_0_82, plain, (k4_xxreal_0(X1,X2)=k4_xxreal_0(X2,X1)|~v1_xxreal_0(X1)|~v1_xxreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_83, plain, (v1_xxreal_0(X1)|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_84, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers|~v7_ordinal1(k4_nat_d(esk2_0,esk3_0))), inference(spm,[status(thm)],[c_0_81, c_0_50])).
cnf(c_0_85, plain, (k4_xxreal_0(X1,X2)=k4_xxreal_0(X2,X1)|~v1_xxreal_0(X2)|~v1_xreal_0(X1)), inference(spm,[status(thm)],[c_0_82, c_0_83])).
cnf(c_0_86, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)=k5_numbers), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_69]), c_0_70]), c_0_73])])).
cnf(c_0_87, plain, (k4_xxreal_0(X1,X2)=k4_xxreal_0(X2,X1)|~v1_xreal_0(X1)|~v1_xreal_0(X2)), inference(spm,[status(thm)],[c_0_85, c_0_83])).
cnf(c_0_88, negated_conjecture, (~v2_xxreal_0(k4_xxreal_0(k5_numbers,k4_nat_d(esk2_0,esk3_0)))|~v1_xreal_0(k4_xxreal_0(k5_numbers,k4_nat_d(esk2_0,esk3_0)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_86]), c_0_86])).
cnf(c_0_89, plain, (v2_xxreal_0(k4_xxreal_0(X1,X2))|~v2_xxreal_0(X2)|~v1_xreal_0(X1)|~v1_xreal_0(X2)), inference(spm,[status(thm)],[c_0_57, c_0_87])).
cnf(c_0_90, negated_conjecture, (~v2_xxreal_0(k4_nat_d(esk2_0,esk3_0))|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))|~v1_xreal_0(k5_numbers)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_58])).
cnf(c_0_91, negated_conjecture, (~v2_xxreal_0(k4_nat_d(esk2_0,esk3_0))|~v1_xreal_0(k4_nat_d(esk2_0,esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_50]), c_0_35])])).
fof(c_0_92, plain, ![X1]:(v1_int_1(X1)=>(~r1_xxreal_0(X1,k5_numbers)=>![X2]:(v1_int_1(X2)=>(k5_int_1(X2,X1)=k5_numbers<=>r1_int_1(X1,X2))))), inference(fof_simplification,[status(thm)],[t62_int_1])).
cnf(c_0_93, negated_conjecture, (k4_nat_d(esk2_0,esk3_0)=np__1|k4_nat_d(esk2_0,esk3_0)=k5_numbers|~v7_ordinal1(k4_nat_d(esk2_0,esk3_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_62]), c_0_50])).
fof(c_0_94, plain, ![X71, X72]:((k5_int_1(X72,X71)!=k5_numbers|r1_int_1(X71,X72)|~v1_int_1(X72)|r1_xxreal_0(X71,k5_numbers)|~v1_int_1(X71))&(~r1_int_1(X71,X72)|k5_int_1(X72,X71)=k5_numbers|~v1_int_1(X72)|r1_xxreal_0(X71,k5_numbers)|~v1_int_1(X71))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])])])).
fof(c_0_95, plain, ![X65, X66]:(~v7_ordinal1(X65)|~v7_ordinal1(X66)|k4_nat_d(X65,X66)=k5_int_1(X65,X66)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_nat_d])])).
cnf(c_0_96, negated_conjecture, (k4_nat_d(esk2_0,esk3_0)=k5_numbers|k4_nat_d(esk2_0,esk3_0)=np__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_69]), c_0_70]), c_0_73])])).
cnf(c_0_97, plain, (r1_int_1(X2,X1)|r1_xxreal_0(X2,k5_numbers)|k5_int_1(X1,X2)!=k5_numbers|~v1_int_1(X1)|~v1_int_1(X2)), inference(split_conjunct,[status(thm)],[c_0_94])).
cnf(c_0_98, plain, (k4_nat_d(X1,X2)=k5_int_1(X1,X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_95])).
cnf(c_0_99, negated_conjecture, (k4_nat_d(esk2_0,esk3_0)=k5_numbers|~v1_xreal_0(np__1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_96]), c_0_75])])).
fof(c_0_100, plain, ![X67, X68]:((~r1_nat_d(X67,X68)|r1_int_1(X67,X68)|(~v7_ordinal1(X67)|~v7_ordinal1(X68)))&(~r1_int_1(X67,X68)|r1_nat_d(X67,X68)|(~v7_ordinal1(X67)|~v7_ordinal1(X68)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_nat_d])])])).
cnf(c_0_101, plain, (r1_int_1(X1,X2)|r1_xxreal_0(X1,k5_numbers)|k4_nat_d(X2,X1)!=k5_numbers|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98]), c_0_48]), c_0_48])).
cnf(c_0_102, negated_conjecture, (k4_nat_d(esk2_0,esk3_0)=k5_numbers), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_50]), c_0_78])])).
cnf(c_0_103, negated_conjecture, (~v1_zfmisc_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_104, plain, (r1_nat_d(X1,X2)|~r1_int_1(X1,X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_100])).
cnf(c_0_105, negated_conjecture, (r1_int_1(esk3_0,esk2_0)|r1_xxreal_0(esk3_0,k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_70]), c_0_73])])).
cnf(c_0_106, negated_conjecture, (~v8_ordinal1(esk3_0)), inference(spm,[status(thm)],[c_0_103, c_0_54])).
cnf(c_0_107, negated_conjecture, (r1_nat_d(esk3_0,esk2_0)|r1_xxreal_0(esk3_0,k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_73]), c_0_70])])).
cnf(c_0_108, negated_conjecture, (v2_xxreal_0(esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_60]), c_0_70])])).
cnf(c_0_109, negated_conjecture, (r1_int_1(esk3_0,esk1_0)|r1_xxreal_0(esk3_0,k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_86]), c_0_70]), c_0_71])])).
cnf(c_0_110, negated_conjecture, (r1_nat_d(esk3_0,esk2_0)|~v1_xreal_0(k5_numbers)|~v1_xreal_0(esk3_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_107]), c_0_108])]), c_0_42])).
cnf(c_0_111, negated_conjecture, (r1_nat_d(esk3_0,esk1_0)|r1_xxreal_0(esk3_0,k5_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_109]), c_0_71]), c_0_70])])).
fof(c_0_112, plain, ![X52, X53, X54]:((~r1_int_2(X52,X53)|(~v7_ordinal1(X54)|(~r1_nat_d(X54,X52)|~r1_nat_d(X54,X53)|X54=np__1))|~v7_ordinal1(X53)|~v7_ordinal1(X52))&((v7_ordinal1(esk4_2(X52,X53))|r1_int_2(X52,X53)|~v7_ordinal1(X53)|~v7_ordinal1(X52))&(((r1_nat_d(esk4_2(X52,X53),X52)|r1_int_2(X52,X53)|~v7_ordinal1(X53)|~v7_ordinal1(X52))&(r1_nat_d(esk4_2(X52,X53),X53)|r1_int_2(X52,X53)|~v7_ordinal1(X53)|~v7_ordinal1(X52)))&(esk4_2(X52,X53)!=np__1|r1_int_2(X52,X53)|~v7_ordinal1(X53)|~v7_ordinal1(X52))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_pythtrip])])])])])).
cnf(c_0_113, negated_conjecture, (r1_nat_d(esk3_0,esk2_0)|~v1_xreal_0(esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_50]), c_0_35])])).
cnf(c_0_114, negated_conjecture, (r1_nat_d(esk3_0,esk1_0)|~v1_xreal_0(k5_numbers)|~v1_xreal_0(esk3_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_111]), c_0_108])]), c_0_42])).
cnf(c_0_115, plain, (v1_zfmisc_1(X1)|X1!=np__1|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_116, plain, (X3=np__1|~r1_int_2(X1,X2)|~v7_ordinal1(X3)|~r1_nat_d(X3,X1)|~r1_nat_d(X3,X2)|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_117, negated_conjecture, (r1_nat_d(esk3_0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_50]), c_0_70])])).
cnf(c_0_118, negated_conjecture, (r1_nat_d(esk3_0,esk1_0)|~v1_xreal_0(esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_50]), c_0_35])])).
cnf(c_0_119, plain, (v1_zfmisc_1(np__1)|~v7_ordinal1(np__1)), inference(er,[status(thm)],[c_0_115])).
cnf(c_0_120, negated_conjecture, (np__1=esk3_0|~r1_nat_d(esk3_0,X1)|~r1_int_2(X1,esk2_0)|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_70]), c_0_73])])).
cnf(c_0_121, negated_conjecture, (r1_nat_d(esk3_0,esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_50]), c_0_70])])).
cnf(c_0_122, negated_conjecture, (r1_int_2(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_123, plain, (v1_zfmisc_1(np__1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_78])])).
cnf(c_0_124, negated_conjecture, (np__1=esk3_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121]), c_0_122]), c_0_71])])).
cnf(c_0_125, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_124]), c_0_103]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 126
# Proof object clause steps            : 78
# Proof object formula steps           : 48
# Proof object conjectures             : 41
# Proof object clause conjectures      : 38
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 30
# Proof object initial formulas used   : 23
# Proof object generating inferences   : 42
# Proof object simplifying inferences  : 79
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 25
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 44
# Removed in clause preprocessing      : 2
# Initial clauses in saturation        : 42
# Processed clauses                    : 207
# ...of these trivial                  : 0
# ...subsumed                          : 47
# ...remaining for further processing  : 160
# Other redundant clauses eliminated   : 2
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 30
# Backward-rewritten                   : 27
# Generated clauses                    : 181
# ...of the previous two non-trivial   : 176
# Contextual simplify-reflections      : 11
# Paramodulations                      : 171
# Factorizations                       : 8
# NegExts                              : 0
# Equation resolutions                 : 2
# 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  : 60
#    Positive orientable unit clauses  : 18
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 3
#    Non-unit-clauses                  : 39
# Current number of unprocessed clauses: 31
# ...number of literals in the above   : 168
# Current number of archived formulas  : 0
# Current number of archived clauses   : 98
# Clause-clause subsumption calls (NU) : 1228
# Rec. Clause-clause subsumption calls : 489
# Non-unit clause-clause subsumptions  : 73
# Unit Clause-clause subsumption calls : 38
# 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          : 6227

# -------------------------------------------------
# User time                : 0.024 s
# System time              : 0.010 s
# Total time               : 0.034 s
# Maximum resident set size: 3480 pages
