# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
# and selection function SelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.021 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t3_radix_1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>![X3]:(v7_ordinal1(X3)=>(X2!=k5_numbers=>k4_nat_d(k4_nat_d(X1,k3_xcmplx_0(X2,X3)),X3)=k4_nat_d(X1,X3))))), file('newton06/newton06__t50_newton06', t3_radix_1)).
fof(t50_newton06, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>![X3]:((v7_ordinal1(X3)&~(v8_ordinal1(X3)))=>![X4]:((v7_ordinal1(X4)&~(v8_ordinal1(X4)))=>(k4_nat_d(X1,k3_xcmplx_0(X3,X4))=k4_nat_d(X2,k3_xcmplx_0(X3,X4))=>k4_nat_d(X1,X3)=k4_nat_d(X2,X3)))))), file('newton06/newton06__t50_newton06', t50_newton06)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('newton06/newton06__t50_newton06', redefinition_k5_numbers)).
fof(commutativity_k3_xcmplx_0, axiom, ![X1, X2]:((v1_xcmplx_0(X1)&v1_xcmplx_0(X2))=>k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)), file('newton06/newton06__t50_newton06', commutativity_k3_xcmplx_0)).
fof(cc1_xcmplx_0, axiom, ![X1]:(v7_ordinal1(X1)=>v1_xcmplx_0(X1)), file('newton06/newton06__t50_newton06', cc1_xcmplx_0)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1), file('newton06/newton06__t50_newton06', fc9_ordinal1)).
fof(c_0_6, plain, ![X22, X23, X24]:(~v7_ordinal1(X22)|(~v7_ordinal1(X23)|(~v7_ordinal1(X24)|(X23=k5_numbers|k4_nat_d(k4_nat_d(X22,k3_xcmplx_0(X23,X24)),X24)=k4_nat_d(X22,X24))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_radix_1])])])).
fof(c_0_7, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>![X3]:((v7_ordinal1(X3)&~v8_ordinal1(X3))=>![X4]:((v7_ordinal1(X4)&~v8_ordinal1(X4))=>(k4_nat_d(X1,k3_xcmplx_0(X3,X4))=k4_nat_d(X2,k3_xcmplx_0(X3,X4))=>k4_nat_d(X1,X3)=k4_nat_d(X2,X3))))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_newton06])])).
cnf(c_0_8, plain, (X2=k5_numbers|k4_nat_d(k4_nat_d(X1,k3_xcmplx_0(X2,X3)),X3)=k4_nat_d(X1,X3)|~v7_ordinal1(X1)|~v7_ordinal1(X2)|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_6])).
cnf(c_0_9, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
fof(c_0_10, negated_conjecture, (v7_ordinal1(esk1_0)&(v7_ordinal1(esk2_0)&((v7_ordinal1(esk3_0)&~v8_ordinal1(esk3_0))&((v7_ordinal1(esk4_0)&~v8_ordinal1(esk4_0))&(k4_nat_d(esk1_0,k3_xcmplx_0(esk3_0,esk4_0))=k4_nat_d(esk2_0,k3_xcmplx_0(esk3_0,esk4_0))&k4_nat_d(esk1_0,esk3_0)!=k4_nat_d(esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])).
cnf(c_0_11, plain, (k4_nat_d(k4_nat_d(X1,k3_xcmplx_0(X2,X3)),X3)=k4_nat_d(X1,X3)|X2=k5_ordinal1|~v7_ordinal1(X3)|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(rw,[status(thm)],[c_0_8, c_0_9])).
cnf(c_0_12, negated_conjecture, (v7_ordinal1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
fof(c_0_13, plain, ![X20, X21]:(~v1_xcmplx_0(X20)|~v1_xcmplx_0(X21)|k3_xcmplx_0(X20,X21)=k3_xcmplx_0(X21,X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k3_xcmplx_0])])).
fof(c_0_14, plain, ![X19]:(~v7_ordinal1(X19)|v1_xcmplx_0(X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xcmplx_0])])).
cnf(c_0_15, negated_conjecture, (k4_nat_d(k4_nat_d(X1,k3_xcmplx_0(X2,esk3_0)),esk3_0)=k4_nat_d(X1,esk3_0)|X2=k5_ordinal1|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_11, c_0_12])).
cnf(c_0_16, negated_conjecture, (v7_ordinal1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_17, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)|~v1_xcmplx_0(X1)|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_18, plain, (v1_xcmplx_0(X1)|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_19, negated_conjecture, (k4_nat_d(k4_nat_d(X1,k3_xcmplx_0(esk4_0,esk3_0)),esk3_0)=k4_nat_d(X1,esk3_0)|esk4_0=k5_ordinal1|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_15, c_0_16])).
cnf(c_0_20, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_21, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)|~v1_xcmplx_0(X1)|~v7_ordinal1(X2)), inference(spm,[status(thm)],[c_0_17, c_0_18])).
cnf(c_0_22, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_23, negated_conjecture, (k4_nat_d(k4_nat_d(esk2_0,k3_xcmplx_0(esk4_0,esk3_0)),esk3_0)=k4_nat_d(esk2_0,esk3_0)|esk4_0=k5_ordinal1), inference(spm,[status(thm)],[c_0_19, c_0_20])).
cnf(c_0_24, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_21, c_0_18])).
cnf(c_0_25, negated_conjecture, (k4_nat_d(esk1_0,k3_xcmplx_0(esk3_0,esk4_0))=k4_nat_d(esk2_0,k3_xcmplx_0(esk3_0,esk4_0))), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_26, negated_conjecture, (k4_nat_d(k4_nat_d(esk1_0,k3_xcmplx_0(esk4_0,esk3_0)),esk3_0)=k4_nat_d(esk1_0,esk3_0)|esk4_0=k5_ordinal1), inference(spm,[status(thm)],[c_0_19, c_0_22])).
cnf(c_0_27, negated_conjecture, (k4_nat_d(k4_nat_d(esk1_0,k3_xcmplx_0(esk3_0,esk4_0)),esk3_0)=k4_nat_d(esk2_0,esk3_0)|esk4_0=k5_ordinal1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25]), c_0_12]), c_0_16])])).
cnf(c_0_28, negated_conjecture, (k4_nat_d(k4_nat_d(esk1_0,k3_xcmplx_0(esk3_0,esk4_0)),esk3_0)=k4_nat_d(esk1_0,esk3_0)|esk4_0=k5_ordinal1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_24]), c_0_12]), c_0_16])])).
cnf(c_0_29, negated_conjecture, (k4_nat_d(esk1_0,esk3_0)!=k4_nat_d(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_30, negated_conjecture, (~v8_ordinal1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_31, negated_conjecture, (esk4_0=k5_ordinal1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_29])).
cnf(c_0_32, plain, (v8_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc9_ordinal1])).
cnf(c_0_33, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_32])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 34
# Proof object clause steps            : 23
# Proof object formula steps           : 11
# Proof object conjectures             : 18
# Proof object clause conjectures      : 15
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 12
# Proof object initial formulas used   : 6
# Proof object generating inferences   : 9
# Proof object simplifying inferences  : 12
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 6
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 13
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 13
# Processed clauses                    : 145
# ...of these trivial                  : 0
# ...subsumed                          : 19
# ...remaining for further processing  : 126
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 0
# Backward-rewritten                   : 61
# Generated clauses                    : 168
# ...of the previous two non-trivial   : 202
# Contextual simplify-reflections      : 0
# Paramodulations                      : 168
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 0
# 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  : 52
#    Positive orientable unit clauses  : 6
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 2
#    Non-unit-clauses                  : 44
# Current number of unprocessed clauses: 49
# ...number of literals in the above   : 98
# Current number of archived formulas  : 0
# Current number of archived clauses   : 74
# Clause-clause subsumption calls (NU) : 129
# Rec. Clause-clause subsumption calls : 115
# Non-unit clause-clause subsumptions  : 19
# Unit Clause-clause subsumption calls : 2
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 1
# BW rewrite match successes           : 1
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 4328

# -------------------------------------------------
# User time                : 0.028 s
# System time              : 0.000 s
# Total time               : 0.028 s
# Maximum resident set size: 3672 pages
