%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:15:02 PM UTC 2026
% Result : Theorem 0.66s 0.58s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 72 ( 13 unt; 0 def)
% Number of atoms : 177 ( 44 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 167 ( 62 ~; 87 |; 11 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 8 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI41,conjecture,
! [X1,X2] : equal_set(union(singleton(X1),singleton(X2)),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI41) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X2
| X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] : equal_set(union(singleton(X1),singleton(X2)),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[thI41]) ).
fof(c_0_8,negated_conjecture,
~ equal_set(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X12,X13] :
( ( equal_set(X12,X13)
| ~ subset(X13,X12)
| ~ subset(X12,X13) )
& ( ~ equal_set(X12,X13)
| subset(X13,X12) )
& ( ~ equal_set(X12,X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_10,negated_conjecture,
~ equal_set(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk1_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk1_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ subset(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0))
| ~ subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X19,X20,X21] :
( ( member(X19,union(X20,X21))
| ~ member(X19,X21) )
& ( member(X19,union(X20,X21))
| ~ member(X19,X20) )
& ( member(X19,X21)
| member(X19,X20)
| ~ member(X19,union(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,plain,
! [X26,X27] :
( ( member(X26,singleton(X27))
| X26 != X27 )
& ( X26 = X27
| ~ member(X26,singleton(X27)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])]) ).
cnf(c_0_18,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk5_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( X1 != X2
| member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_24,plain,
! [X28,X29,X30] :
( ( member(X28,unordered_pair(X29,X30))
| X28 != X30 )
& ( member(X28,unordered_pair(X29,X30))
| X28 != X29 )
& ( X28 = X30
| X28 = X29
| ~ member(X28,unordered_pair(X29,X30)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])])]) ).
cnf(c_0_25,negated_conjecture,
( member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0))
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0)))
| ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_29,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0))
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_31,plain,
( X1 != X2
| member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( ~ subset(singleton(X1),X2)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X14,X15] :
( ( member(X14,power_set(X15))
| ~ subset(X14,X15) )
& ( subset(X14,X15)
| ~ member(X14,power_set(X15)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0))
| member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),unordered_pair(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( X1 != X2
| member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,plain,
( ~ member(esk1_2(singleton(X1),X2),X2)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_39,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_41,plain,
( ~ subset(X1,X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_29]) ).
cnf(c_0_43,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( ~ member(esk1_2(singleton(X1),union(X2,X3)),X3)
| member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( member(X1,X2)
| member(esk1_2(singleton(X1),X2),singleton(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk5_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_47,plain,
( ~ member(esk1_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_48,negated_conjecture,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_43])]),c_0_29]) ).
cnf(c_0_49,plain,
member(X1,union(X2,singleton(X1))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),singleton(esk4_0))
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_51,plain,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_52,negated_conjecture,
( member(unordered_pair(esk4_0,esk5_0),power_set(union(singleton(esk4_0),singleton(esk5_0))))
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( subset(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0)))
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),singleton(esk5_0))
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( ~ subset(union(singleton(esk4_0),singleton(esk5_0)),X1)
| ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0))
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_27])]) ).
cnf(c_0_59,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),X1),X1)
| ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0)))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_23]) ).
cnf(c_0_61,negated_conjecture,
( esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_36])]) ).
cnf(c_0_62,plain,
( ~ member(esk1_2(singleton(X1),union(X2,X3)),X2)
| member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),X1),X1)
| ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),singleton(esk4_0))
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_61]),c_0_43])]) ).
cnf(c_0_65,plain,
member(X1,union(singleton(X1),X2)),
inference(spm,[status(thm)],[c_0_62,c_0_45]) ).
cnf(c_0_66,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0))
| ~ member(esk1_2(unordered_pair(esk4_0,esk5_0),union(singleton(esk4_0),singleton(esk5_0))),union(singleton(esk4_0),singleton(esk5_0))) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),X1),X1)
| member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_27])]) ).
cnf(c_0_68,negated_conjecture,
( esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk5_0
| esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_64]),c_0_65])]) ).
cnf(c_0_69,negated_conjecture,
~ member(esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)),unordered_pair(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_64]),c_0_65])]) ).
cnf(c_0_70,negated_conjecture,
esk1_2(union(singleton(esk4_0),singleton(esk5_0)),unordered_pair(esk4_0,esk5_0)) = esk4_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_36])]),c_0_69]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:33:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.58 % Version: 3.5.1
% 0.66/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.66/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.66/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.66/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.66/0.58 % Starting sh5l with 300s (1) cores
% 0.66/0.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 950255 completed with status 0
% 0.66/0.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.66/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.66/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.66/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.66/0.58 % No SInE strategy applied
% 0.66/0.58 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.66/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.66/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.66/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.66/0.58 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.66/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.66/0.58 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 0.66/0.58 % G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with pid 950266 completed with status 0
% 0.66/0.58 % Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N
% 0.66/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.66/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.66/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.66/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.66/0.58 % No SInE strategy applied
% 0.66/0.58 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.66/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.66/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.66/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.66/0.58 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.66/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.66/0.58 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S033N with 136s (1) cores
% 0.66/0.58 % Preprocessing time : 0.001 s
% 0.66/0.58 % Presaturation interreduction done
% 0.66/0.58
% 0.66/0.58 % Proof found!
% 0.66/0.58 % SZS status Theorem
% 0.66/0.58 % SZS output start CNFRefutation
% See solution above
% 0.66/0.58 % Parsed axioms : 12
% 0.66/0.58 % Removed by relevancy pruning/SinE : 0
% 0.66/0.58 % Initial clauses : 30
% 0.66/0.58 % Removed in clause preprocessing : 0
% 0.66/0.58 % Initial clauses in saturation : 30
% 0.66/0.58 % Processed clauses : 785
% 0.66/0.58 % ...of these trivial : 28
% 0.66/0.58 % ...subsumed : 282
% 0.66/0.58 % ...remaining for further processing : 475
% 0.66/0.58 % Other redundant clauses eliminated : 5
% 0.66/0.58 % Clauses deleted for lack of memory : 0
% 0.66/0.58 % Backward-subsumed : 29
% 0.66/0.58 % Backward-rewritten : 32
% 0.66/0.58 % Generated clauses : 10139
% 0.66/0.58 % ...of the previous two non-redundant : 5769
% 0.66/0.58 % ...aggressively subsumed : 0
% 0.66/0.58 % Contextual simplify-reflections : 3
% 0.66/0.58 % Paramodulations : 10116
% 0.66/0.58 % Factorizations : 18
% 0.66/0.58 % NegExts : 0
% 0.66/0.58 % Equation resolutions : 5
% 0.66/0.58 % Disequality decompositions : 0
% 0.66/0.58 % Total rewrite steps : 4524
% 0.66/0.58 % ...of those cached : 4085
% 0.66/0.58 % Propositional unsat checks : 0
% 0.66/0.58 % Propositional check models : 0
% 0.66/0.58 % Propositional check unsatisfiable : 0
% 0.66/0.58 % Propositional clauses : 0
% 0.66/0.58 % Propositional clauses after purity: 0
% 0.66/0.58 % Propositional unsat core size : 0
% 0.66/0.58 % Propositional preprocessing time : 0.000
% 0.66/0.58 % Propositional encoding time : 0.000
% 0.66/0.58 % Propositional solver time : 0.000
% 0.66/0.58 % Success case prop preproc time : 0.000
% 0.66/0.58 % Success case prop encoding time : 0.000
% 0.66/0.58 % Success case prop solver time : 0.000
% 0.66/0.58 % Current number of processed clauses : 381
% 0.66/0.58 % Positive orientable unit clauses : 144
% 0.66/0.58 % Positive unorientable unit clauses: 0
% 0.66/0.58 % Negative unit clauses : 4
% 0.66/0.58 % Non-unit-clauses : 233
% 0.66/0.58 % Current number of unprocessed clauses: 4998
% 0.66/0.58 % ...number of literals in the above : 9846
% 0.66/0.58 % Current number of archived formulas : 0
% 0.66/0.58 % Current number of archived clauses : 91
% 0.66/0.58 % Clause-clause subsumption calls (NU) : 19504
% 0.66/0.58 % Rec. Clause-clause subsumption calls : 14543
% 0.66/0.58 % Non-unit clause-clause subsumptions : 294
% 0.66/0.58 % Unit Clause-clause subsumption calls : 954
% 0.66/0.58 % Rewrite failures with RHS unbound : 0
% 0.66/0.58 % BW rewrite match attempts : 322
% 0.66/0.58 % BW rewrite match successes : 4
% 0.66/0.58 % Condensation attempts : 0
% 0.66/0.58 % Condensation successes : 0
% 0.66/0.58 % Termbank termtop insertions : 116644
% 0.66/0.58 % Search garbage collected termcells : 448
% 0.66/0.58
% 0.66/0.58 % -------------------------------------------------
% 0.66/0.58 % User time : 0.138 s
% 0.66/0.58 % System time : 0.012 s
% 0.66/0.58 % Total time : 0.150 s
% 0.66/0.58 % Maximum resident set size: 3596 pages
% 0.66/0.58
% 0.66/0.58 % -------------------------------------------------
% 0.66/0.58 % User time : 0.665 s
% 0.66/0.58 % System time : 0.071 s
% 0.66/0.58 % Total time : 0.736 s
% 0.66/0.58 % Maximum resident set size: 4864 pages
% 0.66/0.58 % E exiting
%------------------------------------------------------------------------------