%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET698+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 : n007.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 02:15:01 PM UTC 2026
% Result : Theorem 0.10s 0.52s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 82 ( 8 unt; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 242 ( 106 ~; 108 |; 17 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 4 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI32,conjecture,
! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> equal_set(union(difference(X4,X1),X2),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI32) ).
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(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(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(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> equal_set(union(difference(X4,X1),X2),X4) ) ),
inference(assume_negation,[status(cth)],[thI32]) ).
fof(c_0_7,negated_conjecture,
( ( equal_set(union(difference(esk6_0,esk4_0),esk5_0),esk6_0)
| subset(esk4_0,esk5_0) )
& ( ~ equal_set(union(difference(esk6_0,esk4_0),esk5_0),esk6_0)
| ~ subset(esk4_0,esk5_0) )
& subset(esk5_0,esk6_0)
& subset(esk4_0,esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,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_9,negated_conjecture,
( ~ equal_set(union(difference(esk6_0,esk4_0),esk5_0),esk6_0)
| ~ subset(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,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_12,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(union(difference(esk6_0,esk4_0),esk5_0),esk6_0)
| ~ subset(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
( ~ equal_set(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( equal_set(union(difference(esk6_0,esk4_0),esk5_0),esk6_0)
| subset(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk6_0,union(difference(esk6_0,esk4_0),esk5_0))
| ~ member(union(difference(esk6_0,esk4_0),esk5_0),power_set(esk6_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,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_19,plain,
( ~ subset(X1,X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(union(difference(esk6_0,esk4_0),esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| ~ member(union(difference(esk6_0,esk4_0),esk5_0),power_set(esk6_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk4_0,esk5_0)
| member(union(difference(esk6_0,esk4_0),esk5_0),power_set(esk6_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( subset(esk4_0,esk5_0)
| member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| ~ member(union(difference(esk6_0,esk4_0),esk5_0),power_set(esk6_0))
| member(esk1_2(esk4_0,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(union(difference(esk6_0,esk4_0),esk5_0),power_set(esk6_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(X1,esk6_0)
| subset(esk4_0,esk5_0)
| member(X1,union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(esk1_2(esk4_0,esk5_0),esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
fof(c_0_34,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_35,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_36,negated_conjecture,
( ~ member(X1,esk6_0)
| member(esk4_0,power_set(esk5_0))
| member(X1,union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(esk1_2(esk4_0,esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_39,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk6_0,union(difference(esk6_0,esk4_0),esk5_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
fof(c_0_40,plain,
! [X23,X24,X25] :
( ( member(X23,difference(X25,X24))
| member(X23,X24)
| ~ member(X23,X25) )
& ( ~ member(X23,difference(X25,X24))
| ~ member(X23,X24) )
& ( ~ member(X23,difference(X25,X24))
| member(X23,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_41,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(esk1_2(esk4_0,esk5_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( ~ member(esk1_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_45,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| member(esk1_2(esk4_0,esk5_0),difference(esk6_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,plain,
( member(X1,power_set(X2))
| member(esk1_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_48,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(esk6_0,union(difference(esk6_0,esk4_0),esk5_0))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_13]) ).
cnf(c_0_50,negated_conjecture,
member(esk4_0,power_set(esk5_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0)
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0)
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_13]) ).
cnf(c_0_54,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),union(difference(esk6_0,esk4_0),esk5_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk5_0)
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),difference(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0)
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),difference(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_59,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_60,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),difference(esk6_0,esk4_0))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk5_0)
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),difference(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(X1,esk5_0)
| member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0)
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),difference(esk6_0,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_50])]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk5_0)
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_59,c_0_13]) ).
cnf(c_0_66,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_13]) ).
cnf(c_0_67,plain,
( ~ member(X1,X3)
| ~ member(X3,power_set(X2))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_68,negated_conjecture,
~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),difference(esk6_0,esk4_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]) ).
cnf(c_0_69,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_70,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk5_0)
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk5_0)
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),difference(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_58]) ).
cnf(c_0_71,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk5_0)
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_50])]) ).
cnf(c_0_72,negated_conjecture,
( ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),union(difference(esk6_0,esk4_0),esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_50])]) ).
cnf(c_0_73,negated_conjecture,
( ~ member(esk4_0,power_set(esk5_0))
| ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_13]) ).
cnf(c_0_74,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_50]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk6_0)
| member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk5_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_62]),c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk5_0)
| member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),difference(esk6_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( ~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0)))
| ~ member(esk1_2(union(difference(esk6_0,esk4_0),esk5_0),esk6_0),esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_50])]) ).
cnf(c_0_79,negated_conjecture,
~ member(esk1_2(esk6_0,union(difference(esk6_0,esk4_0),esk5_0)),esk6_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_80,negated_conjecture,
~ member(esk6_0,power_set(union(difference(esk6_0,esk4_0),esk5_0))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_77]),c_0_62]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_47]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET698+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:30:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.52 % Version: 3.5.1
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.52 % Starting sh5l with 300s (1) cores
% 0.10/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 274395 completed with status 0
% 0.10/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.52 % No SInE strategy applied
% 0.10/0.52 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.10/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.52 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.10/0.52 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.10/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.52 % 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 274409 completed with status 0
% 0.10/0.52 % Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.52 % No SInE strategy applied
% 0.10/0.52 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.10/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.52 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.10/0.52 % Preprocessing time : 0.002 s
% 0.10/0.52 % Presaturation interreduction done
% 0.10/0.52
% 0.10/0.52 % Proof found!
% 0.10/0.52 % SZS status Theorem
% 0.10/0.52 % SZS output start CNFRefutation
% See solution above
% 0.10/0.52 % Parsed axioms : 12
% 0.10/0.52 % Removed by relevancy pruning/SinE : 0
% 0.10/0.52 % Initial clauses : 33
% 0.10/0.52 % Removed in clause preprocessing : 0
% 0.10/0.52 % Initial clauses in saturation : 33
% 0.10/0.52 % Processed clauses : 476
% 0.10/0.52 % ...of these trivial : 46
% 0.10/0.52 % ...subsumed : 66
% 0.10/0.52 % ...remaining for further processing : 364
% 0.10/0.52 % Other redundant clauses eliminated : 3
% 0.10/0.52 % Clauses deleted for lack of memory : 0
% 0.10/0.52 % Backward-subsumed : 56
% 0.10/0.52 % Backward-rewritten : 42
% 0.10/0.52 % Generated clauses : 4024
% 0.10/0.52 % ...of the previous two non-redundant : 3754
% 0.10/0.52 % ...aggressively subsumed : 0
% 0.10/0.52 % Contextual simplify-reflections : 12
% 0.10/0.52 % Paramodulations : 4017
% 0.10/0.52 % Factorizations : 2
% 0.10/0.52 % NegExts : 0
% 0.10/0.52 % Equation resolutions : 3
% 0.10/0.52 % Disequality decompositions : 0
% 0.10/0.52 % Total rewrite steps : 346
% 0.10/0.52 % ...of those cached : 263
% 0.10/0.52 % Propositional unsat checks : 0
% 0.10/0.52 % Propositional check models : 0
% 0.10/0.52 % Propositional check unsatisfiable : 0
% 0.10/0.52 % Propositional clauses : 0
% 0.10/0.52 % Propositional clauses after purity: 0
% 0.10/0.52 % Propositional unsat core size : 0
% 0.10/0.52 % Propositional preprocessing time : 0.000
% 0.10/0.52 % Propositional encoding time : 0.000
% 0.10/0.52 % Propositional solver time : 0.000
% 0.10/0.52 % Success case prop preproc time : 0.000
% 0.10/0.52 % Success case prop encoding time : 0.000
% 0.10/0.52 % Success case prop solver time : 0.000
% 0.10/0.52 % Current number of processed clauses : 228
% 0.10/0.52 % Positive orientable unit clauses : 48
% 0.10/0.52 % Positive unorientable unit clauses: 0
% 0.10/0.52 % Negative unit clauses : 7
% 0.10/0.52 % Non-unit-clauses : 173
% 0.10/0.52 % Current number of unprocessed clauses: 3309
% 0.10/0.52 % ...number of literals in the above : 6905
% 0.10/0.52 % Current number of archived formulas : 0
% 0.10/0.52 % Current number of archived clauses : 133
% 0.10/0.52 % Clause-clause subsumption calls (NU) : 18802
% 0.10/0.52 % Rec. Clause-clause subsumption calls : 16190
% 0.10/0.52 % Non-unit clause-clause subsumptions : 109
% 0.10/0.52 % Unit Clause-clause subsumption calls : 719
% 0.10/0.52 % Rewrite failures with RHS unbound : 0
% 0.10/0.52 % BW rewrite match attempts : 44
% 0.10/0.52 % BW rewrite match successes : 4
% 0.10/0.52 % Condensation attempts : 0
% 0.10/0.52 % Condensation successes : 0
% 0.10/0.52 % Termbank termtop insertions : 55171
% 0.10/0.52 % Search garbage collected termcells : 501
% 0.10/0.52
% 0.10/0.52 % -------------------------------------------------
% 0.10/0.52 % User time : 0.079 s
% 0.10/0.52 % System time : 0.006 s
% 0.10/0.52 % Total time : 0.085 s
% 0.10/0.52 % Maximum resident set size: 3340 pages
% 0.10/0.52
% 0.10/0.52 % -------------------------------------------------
% 0.10/0.52 % User time : 0.344 s
% 0.10/0.52 % System time : 0.036 s
% 0.10/0.52 % Total time : 0.380 s
% 0.10/0.52 % Maximum resident set size: 4608 pages
% 0.10/0.52 % E exiting
%------------------------------------------------------------------------------