# 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       : 0.018 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t24_nat_d, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(~(r1_xxreal_0(X2,X1))=>k2_nat_d(X1,X2)=X1))), file('number15/number15__l3_number15', t24_nat_d)).
fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('number15/number15__l3_number15', cc8_ordinal1)).
fof(spc4_numerals, axiom, (v2_xxreal_0(np__4)&m1_subset_1(np__4,k4_ordinal1)), file('number15/number15__l3_number15', spc4_numerals)).
fof(spc1_numerals, axiom, (v2_xxreal_0(np__1)&m1_subset_1(np__1,k4_ordinal1)), file('number15/number15__l3_number15', spc1_numerals)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r1, axiom, ~(r1_xxreal_0(np__4,np__1)), file('number15/number15__l3_number15', rqLessOrEqual__r1_xxreal_0__r4_r1)).
fof(redefinition_k2_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>k2_nat_d(X1,X2)=k5_int_1(X1,X2)), file('number15/number15__l3_number15', redefinition_k2_nat_d)).
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('number15/number15__l3_number15', redefinition_k4_nat_d)).
fof(l3_number15, conjecture, k4_nat_d(np__1,np__4)=np__1, file('number15/number15__l3_number15', l3_number15)).
fof(c_0_8, plain, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(~r1_xxreal_0(X2,X1)=>k2_nat_d(X1,X2)=X1))), inference(fof_simplification,[status(thm)],[t24_nat_d])).
fof(c_0_9, plain, ![X10]:(~m1_subset_1(X10,k4_ordinal1)|v7_ordinal1(X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])).
fof(c_0_10, plain, ![X15, X16]:(~v7_ordinal1(X15)|(~v7_ordinal1(X16)|(r1_xxreal_0(X16,X15)|k2_nat_d(X15,X16)=X15))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])).
cnf(c_0_11, plain, (v7_ordinal1(X1)|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_12, plain, (m1_subset_1(np__4,k4_ordinal1)), inference(split_conjunct,[status(thm)],[spc4_numerals])).
cnf(c_0_13, plain, (r1_xxreal_0(X2,X1)|k2_nat_d(X1,X2)=X1|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_10])).
cnf(c_0_14, plain, (v7_ordinal1(np__4)), inference(spm,[status(thm)],[c_0_11, c_0_12])).
cnf(c_0_15, plain, (m1_subset_1(np__1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[spc1_numerals])).
fof(c_0_16, plain, ~r1_xxreal_0(np__4,np__1), inference(fof_simplification,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r4_r1])).
fof(c_0_17, plain, ![X11, X12]:(~v7_ordinal1(X11)|~v7_ordinal1(X12)|k2_nat_d(X11,X12)=k5_int_1(X11,X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_nat_d])])).
cnf(c_0_18, plain, (k2_nat_d(X1,np__4)=X1|r1_xxreal_0(np__4,X1)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_13, c_0_14])).
cnf(c_0_19, plain, (v7_ordinal1(np__1)), inference(spm,[status(thm)],[c_0_11, c_0_15])).
cnf(c_0_20, plain, (~r1_xxreal_0(np__4,np__1)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_21, plain, ![X13, X14]:(~v7_ordinal1(X13)|~v7_ordinal1(X14)|k4_nat_d(X13,X14)=k5_int_1(X13,X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_nat_d])])).
cnf(c_0_22, plain, (k2_nat_d(X1,X2)=k5_int_1(X1,X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_23, plain, (k2_nat_d(np__1,np__4)=np__1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20])).
fof(c_0_24, negated_conjecture, k4_nat_d(np__1,np__4)!=np__1, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l3_number15])])).
cnf(c_0_25, plain, (k4_nat_d(X1,X2)=k5_int_1(X1,X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_26, plain, (k5_int_1(np__1,np__4)=np__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_14]), c_0_19])])).
cnf(c_0_27, negated_conjecture, (k4_nat_d(np__1,np__4)!=np__1), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_28, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_14]), c_0_19])]), c_0_27]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 29
# Proof object clause steps            : 14
# Proof object formula steps           : 15
# Proof object conjectures             : 3
# Proof object clause conjectures      : 1
# Proof object formula conjectures     : 2
# Proof object initial clauses used    : 8
# Proof object initial formulas used   : 8
# Proof object generating inferences   : 6
# Proof object simplifying inferences  : 8
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 8
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 10
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 10
# Processed clauses                    : 25
# ...of these trivial                  : 0
# ...subsumed                          : 0
# ...remaining for further processing  : 25
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 0
# Backward-rewritten                   : 0
# Generated clauses                    : 8
# ...of the previous two non-trivial   : 7
# Contextual simplify-reflections      : 0
# Paramodulations                      : 8
# 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  : 15
#    Positive orientable unit clauses  : 8
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 2
#    Non-unit-clauses                  : 5
# Current number of unprocessed clauses: 2
# ...number of literals in the above   : 5
# Current number of archived formulas  : 0
# Current number of archived clauses   : 10
# Clause-clause subsumption calls (NU) : 12
# Rec. Clause-clause subsumption calls : 8
# Non-unit clause-clause subsumptions  : 0
# Unit Clause-clause subsumption calls : 0
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 0
# BW rewrite match successes           : 0
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 700

# -------------------------------------------------
# User time                : 0.020 s
# System time              : 0.001 s
# Total time               : 0.021 s
# Maximum resident set size: 3080 pages
