# 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       : 0.022 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(d5_surreals, axiom, ![X1]:(v1_xtuple_0(X1)=>![X2, X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(X3=k5_surreals(X1,X2)<=>(k9_xtuple_0(X3)=k4_ordinal1&![X4]:(v7_ordinal1(X4)=>k1_funct_1(X3,X4)=k2_xtuple_0(k1_funct_1(k3_surreals(X1,X2),X4))))))), file('surreals/surreals__t6_surreals', d5_surreals)).
fof(redefinition_k2_surreal0, axiom, ![X1]:k2_surreal0(X1)=k2_xtuple_0(X1), file('surreals/surreals__t6_surreals', redefinition_k2_surreal0)).
fof(dt_k5_surreals, axiom, ![X1, X2]:(v1_xtuple_0(X1)=>(v1_relat_1(k5_surreals(X1,X2))&v1_funct_1(k5_surreals(X1,X2)))), file('surreals/surreals__t6_surreals', dt_k5_surreals)).
fof(d3_surreals, axiom, ![X1]:(v1_xtuple_0(X1)=>![X2, X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(X3=k3_surreals(X1,X2)<=>((k9_xtuple_0(X3)=k4_ordinal1&k1_funct_1(X3,k5_numbers)=X1)&![X4]:(v7_ordinal1(X4)=>((v1_xtuple_0(k1_funct_1(X3,X4))&k1_xtuple_0(k1_funct_1(X3,k1_nat_1(X4,np__1)))=k2_xboole_0(k1_surreal0(k1_funct_1(X3,X4)),k2_surreals(X2,k1_surreal0(k1_funct_1(X3,X4)),k2_surreal0(k1_funct_1(X3,X4)))))&k2_xtuple_0(k1_funct_1(X3,k1_nat_1(X4,np__1)))=k2_xboole_0(k2_xboole_0(k2_surreal0(k1_funct_1(X3,X4)),k2_surreals(X2,k1_surreal0(k1_funct_1(X3,X4)),k1_surreal0(k1_funct_1(X3,X4)))),k2_surreals(X2,k2_surreal0(k1_funct_1(X3,X4)),k2_surreal0(k1_funct_1(X3,X4)))))))))), file('surreals/surreals__t6_surreals', d3_surreals)).
fof(dt_k3_surreals, axiom, ![X1, X2]:(v1_xtuple_0(X1)=>(v1_relat_1(k3_surreals(X1,X2))&v1_funct_1(k3_surreals(X1,X2)))), file('surreals/surreals__t6_surreals', dt_k3_surreals)).
fof(d4_surreals, axiom, ![X1]:(v1_xtuple_0(X1)=>![X2, X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(X3=k4_surreals(X1,X2)<=>(k9_xtuple_0(X3)=k4_ordinal1&![X4]:(v7_ordinal1(X4)=>k1_funct_1(X3,X4)=k1_xtuple_0(k1_funct_1(k3_surreals(X1,X2),X4))))))), file('surreals/surreals__t6_surreals', d4_surreals)).
fof(redefinition_k1_surreal0, axiom, ![X1]:k1_surreal0(X1)=k1_xtuple_0(X1), file('surreals/surreals__t6_surreals', redefinition_k1_surreal0)).
fof(t6_surreals, conjecture, ![X1, X2]:(v1_xtuple_0(X2)=>(k1_funct_1(k4_surreals(X2,X1),k5_numbers)=k1_surreal0(X2)&k1_funct_1(k5_surreals(X2,X1),k5_numbers)=k2_surreal0(X2))), file('surreals/surreals__t6_surreals', t6_surreals)).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1), file('surreals/surreals__t6_surreals', fc8_ordinal1)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('surreals/surreals__t6_surreals', redefinition_k5_numbers)).
fof(dt_k4_surreals, axiom, ![X1, X2]:(v1_xtuple_0(X1)=>(v1_relat_1(k4_surreals(X1,X2))&v1_funct_1(k4_surreals(X1,X2)))), file('surreals/surreals__t6_surreals', dt_k4_surreals)).
fof(c_0_11, plain, ![X39, X40, X41, X42]:(((k9_xtuple_0(X41)=k4_ordinal1|X41!=k5_surreals(X39,X40)|(~v1_relat_1(X41)|~v1_funct_1(X41))|~v1_xtuple_0(X39))&(~v7_ordinal1(X42)|k1_funct_1(X41,X42)=k2_xtuple_0(k1_funct_1(k3_surreals(X39,X40),X42))|X41!=k5_surreals(X39,X40)|(~v1_relat_1(X41)|~v1_funct_1(X41))|~v1_xtuple_0(X39)))&((v7_ordinal1(esk5_3(X39,X40,X41))|k9_xtuple_0(X41)!=k4_ordinal1|X41=k5_surreals(X39,X40)|(~v1_relat_1(X41)|~v1_funct_1(X41))|~v1_xtuple_0(X39))&(k1_funct_1(X41,esk5_3(X39,X40,X41))!=k2_xtuple_0(k1_funct_1(k3_surreals(X39,X40),esk5_3(X39,X40,X41)))|k9_xtuple_0(X41)!=k4_ordinal1|X41=k5_surreals(X39,X40)|(~v1_relat_1(X41)|~v1_funct_1(X41))|~v1_xtuple_0(X39)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_surreals])])])])])).
fof(c_0_12, plain, ![X51]:k2_surreal0(X51)=k2_xtuple_0(X51), inference(variable_rename,[status(thm)],[redefinition_k2_surreal0])).
cnf(c_0_13, plain, (k1_funct_1(X2,X1)=k2_xtuple_0(k1_funct_1(k3_surreals(X3,X4),X1))|~v7_ordinal1(X1)|X2!=k5_surreals(X3,X4)|~v1_relat_1(X2)|~v1_funct_1(X2)|~v1_xtuple_0(X3)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_14, plain, (k2_surreal0(X1)=k2_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
fof(c_0_15, plain, ![X48, X49]:((v1_relat_1(k5_surreals(X48,X49))|~v1_xtuple_0(X48))&(v1_funct_1(k5_surreals(X48,X49))|~v1_xtuple_0(X48))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_surreals])])])).
fof(c_0_16, plain, ![X29, X30, X31, X32]:((((k9_xtuple_0(X31)=k4_ordinal1|X31!=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29))&(k1_funct_1(X31,k5_numbers)=X29|X31!=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29)))&(((v1_xtuple_0(k1_funct_1(X31,X32))|~v7_ordinal1(X32)|X31!=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29))&(k1_xtuple_0(k1_funct_1(X31,k1_nat_1(X32,np__1)))=k2_xboole_0(k1_surreal0(k1_funct_1(X31,X32)),k2_surreals(X30,k1_surreal0(k1_funct_1(X31,X32)),k2_surreal0(k1_funct_1(X31,X32))))|~v7_ordinal1(X32)|X31!=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29)))&(k2_xtuple_0(k1_funct_1(X31,k1_nat_1(X32,np__1)))=k2_xboole_0(k2_xboole_0(k2_surreal0(k1_funct_1(X31,X32)),k2_surreals(X30,k1_surreal0(k1_funct_1(X31,X32)),k1_surreal0(k1_funct_1(X31,X32)))),k2_surreals(X30,k2_surreal0(k1_funct_1(X31,X32)),k2_surreal0(k1_funct_1(X31,X32))))|~v7_ordinal1(X32)|X31!=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29))))&((v7_ordinal1(esk3_3(X29,X30,X31))|(k9_xtuple_0(X31)!=k4_ordinal1|k1_funct_1(X31,k5_numbers)!=X29)|X31=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29))&(~v1_xtuple_0(k1_funct_1(X31,esk3_3(X29,X30,X31)))|k1_xtuple_0(k1_funct_1(X31,k1_nat_1(esk3_3(X29,X30,X31),np__1)))!=k2_xboole_0(k1_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))),k2_surreals(X30,k1_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))),k2_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31)))))|k2_xtuple_0(k1_funct_1(X31,k1_nat_1(esk3_3(X29,X30,X31),np__1)))!=k2_xboole_0(k2_xboole_0(k2_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))),k2_surreals(X30,k1_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))),k1_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))))),k2_surreals(X30,k2_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31))),k2_surreal0(k1_funct_1(X31,esk3_3(X29,X30,X31)))))|(k9_xtuple_0(X31)!=k4_ordinal1|k1_funct_1(X31,k5_numbers)!=X29)|X31=k3_surreals(X29,X30)|(~v1_relat_1(X31)|~v1_funct_1(X31))|~v1_xtuple_0(X29)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_surreals])])])])])).
fof(c_0_17, plain, ![X44, X45]:((v1_relat_1(k3_surreals(X44,X45))|~v1_xtuple_0(X44))&(v1_funct_1(k3_surreals(X44,X45))|~v1_xtuple_0(X44))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_surreals])])])).
fof(c_0_18, plain, ![X34, X35, X36, X37]:(((k9_xtuple_0(X36)=k4_ordinal1|X36!=k4_surreals(X34,X35)|(~v1_relat_1(X36)|~v1_funct_1(X36))|~v1_xtuple_0(X34))&(~v7_ordinal1(X37)|k1_funct_1(X36,X37)=k1_xtuple_0(k1_funct_1(k3_surreals(X34,X35),X37))|X36!=k4_surreals(X34,X35)|(~v1_relat_1(X36)|~v1_funct_1(X36))|~v1_xtuple_0(X34)))&((v7_ordinal1(esk4_3(X34,X35,X36))|k9_xtuple_0(X36)!=k4_ordinal1|X36=k4_surreals(X34,X35)|(~v1_relat_1(X36)|~v1_funct_1(X36))|~v1_xtuple_0(X34))&(k1_funct_1(X36,esk4_3(X34,X35,X36))!=k1_xtuple_0(k1_funct_1(k3_surreals(X34,X35),esk4_3(X34,X35,X36)))|k9_xtuple_0(X36)!=k4_ordinal1|X36=k4_surreals(X34,X35)|(~v1_relat_1(X36)|~v1_funct_1(X36))|~v1_xtuple_0(X34)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_surreals])])])])])).
fof(c_0_19, plain, ![X50]:k1_surreal0(X50)=k1_xtuple_0(X50), inference(variable_rename,[status(thm)],[redefinition_k1_surreal0])).
fof(c_0_20, negated_conjecture, ~(![X1, X2]:(v1_xtuple_0(X2)=>(k1_funct_1(k4_surreals(X2,X1),k5_numbers)=k1_surreal0(X2)&k1_funct_1(k5_surreals(X2,X1),k5_numbers)=k2_surreal0(X2)))), inference(assume_negation,[status(cth)],[t6_surreals])).
cnf(c_0_21, plain, (k1_funct_1(X2,X1)=k2_surreal0(k1_funct_1(k3_surreals(X3,X4),X1))|X2!=k5_surreals(X3,X4)|~v1_xtuple_0(X3)|~v1_relat_1(X2)|~v1_funct_1(X2)|~v7_ordinal1(X1)), inference(rw,[status(thm)],[c_0_13, c_0_14])).
cnf(c_0_22, plain, (v1_relat_1(k5_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_23, plain, (v1_funct_1(k5_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_24, plain, (k1_funct_1(X1,k5_numbers)=X2|X1!=k3_surreals(X2,X3)|~v1_relat_1(X1)|~v1_funct_1(X1)|~v1_xtuple_0(X2)), inference(split_conjunct,[status(thm)],[c_0_16])).
cnf(c_0_25, plain, (v1_relat_1(k3_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_26, plain, (v1_funct_1(k3_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_27, plain, (v7_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc8_ordinal1])).
cnf(c_0_28, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
cnf(c_0_29, plain, (k1_funct_1(X2,X1)=k1_xtuple_0(k1_funct_1(k3_surreals(X3,X4),X1))|~v7_ordinal1(X1)|X2!=k4_surreals(X3,X4)|~v1_relat_1(X2)|~v1_funct_1(X2)|~v1_xtuple_0(X3)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_30, plain, (k1_surreal0(X1)=k1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_31, plain, ![X46, X47]:((v1_relat_1(k4_surreals(X46,X47))|~v1_xtuple_0(X46))&(v1_funct_1(k4_surreals(X46,X47))|~v1_xtuple_0(X46))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_surreals])])])).
fof(c_0_32, negated_conjecture, (v1_xtuple_0(esk2_0)&(k1_funct_1(k4_surreals(esk2_0,esk1_0),k5_numbers)!=k1_surreal0(esk2_0)|k1_funct_1(k5_surreals(esk2_0,esk1_0),k5_numbers)!=k2_surreal0(esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])).
cnf(c_0_33, plain, (k2_surreal0(k1_funct_1(k3_surreals(X1,X2),X3))=k1_funct_1(k5_surreals(X1,X2),X3)|~v7_ordinal1(X3)|~v1_xtuple_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]), c_0_22]), c_0_23])).
cnf(c_0_34, plain, (k1_funct_1(k3_surreals(X1,X2),k5_numbers)=X1|~v1_xtuple_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]), c_0_25]), c_0_26])).
cnf(c_0_35, plain, (v7_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_27, c_0_28])).
cnf(c_0_36, plain, (k1_funct_1(X2,X1)=k1_surreal0(k1_funct_1(k3_surreals(X3,X4),X1))|X2!=k4_surreals(X3,X4)|~v1_xtuple_0(X3)|~v1_relat_1(X2)|~v1_funct_1(X2)|~v7_ordinal1(X1)), inference(rw,[status(thm)],[c_0_29, c_0_30])).
cnf(c_0_37, plain, (v1_relat_1(k4_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_38, plain, (v1_funct_1(k4_surreals(X1,X2))|~v1_xtuple_0(X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_39, negated_conjecture, (k1_funct_1(k4_surreals(esk2_0,esk1_0),k5_numbers)!=k1_surreal0(esk2_0)|k1_funct_1(k5_surreals(esk2_0,esk1_0),k5_numbers)!=k2_surreal0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_40, plain, (k1_funct_1(k5_surreals(X1,X2),k5_numbers)=k2_surreal0(X1)|~v1_xtuple_0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])])).
cnf(c_0_41, negated_conjecture, (v1_xtuple_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_42, plain, (k1_surreal0(k1_funct_1(k3_surreals(X1,X2),X3))=k1_funct_1(k4_surreals(X1,X2),X3)|~v7_ordinal1(X3)|~v1_xtuple_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_36]), c_0_37]), c_0_38])).
cnf(c_0_43, negated_conjecture, (k1_funct_1(k4_surreals(esk2_0,esk1_0),k5_numbers)!=k1_surreal0(esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41])])).
cnf(c_0_44, plain, (k1_funct_1(k4_surreals(X1,X2),k5_numbers)=k1_surreal0(X1)|~v1_xtuple_0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_34]), c_0_35])])).
cnf(c_0_45, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_41])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 46
# Proof object clause steps            : 25
# Proof object formula steps           : 21
# Proof object conjectures             : 7
# Proof object clause conjectures      : 4
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 15
# Proof object initial formulas used   : 11
# Proof object generating inferences   : 4
# Proof object simplifying inferences  : 20
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 11
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 27
# Removed in clause preprocessing      : 2
# Initial clauses in saturation        : 25
# Processed clauses                    : 63
# ...of these trivial                  : 0
# ...subsumed                          : 0
# ...remaining for further processing  : 63
# Other redundant clauses eliminated   : 11
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 0
# Backward-rewritten                   : 0
# Generated clauses                    : 38
# ...of the previous two non-trivial   : 36
# Contextual simplify-reflections      : 18
# Paramodulations                      : 27
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 11
# 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  : 27
#    Positive orientable unit clauses  : 3
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 1
#    Non-unit-clauses                  : 23
# Current number of unprocessed clauses: 23
# ...number of literals in the above   : 116
# Current number of archived formulas  : 0
# Current number of archived clauses   : 27
# Clause-clause subsumption calls (NU) : 1674
# Rec. Clause-clause subsumption calls : 349
# Non-unit clause-clause subsumptions  : 18
# Unit Clause-clause subsumption calls : 1
# 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          : 3777

# -------------------------------------------------
# User time                : 0.025 s
# System time              : 0.002 s
# Total time               : 0.027 s
# Maximum resident set size: 3492 pages
