%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET582+3 : 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 : n011.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 02:14:24 PM UTC 2026
% Result : Theorem 197.88s 29.35s
% Output : CNFRefutation 197.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 159 ( 80 unt; 0 def)
% Number of atoms : 298 ( 46 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 217 ( 78 ~; 109 |; 15 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 299 ( 46 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(prove_th25,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( ~ member(X4,X1)
<=> ( member(X4,X2)
<=> member(X4,X3) ) )
=> X1 = symmetric_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th25) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_8,plain,
! [X11,X12,X13] :
( ( member(X13,difference(X11,X12))
| member(X13,X12)
| ~ member(X13,X11) )
& ( ~ member(X13,difference(X11,X12))
| ~ member(X13,X12) )
& ( ~ member(X13,difference(X11,X12))
| member(X13,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X29,X30,X31,X32,X33] :
( ( subset(X32,X33)
| ~ member(esk3_2(X32,X33),X33) )
& ( subset(X32,X33)
| member(esk3_2(X32,X33),X32) )
& ( member(X31,X30)
| ~ member(X31,X29)
| ~ subset(X29,X30) ) ),
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_defn])])])])])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( ~ member(X4,X1)
<=> ( member(X4,X2)
<=> member(X4,X3) ) )
=> X1 = symmetric_difference(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th25]) ).
cnf(c_0_11,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( ~ member(X4,X1)
<=> ( member(X4,X2)
<=> member(X4,X3) ) )
=> X1 = symmetric_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X16,X17] :
( ( X16 = X17
| ~ subset(X17,X16)
| ~ subset(X16,X17) )
& ( X16 != X17
| subset(X17,X16) )
& ( X16 != X17
| subset(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_15,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_18,negated_conjecture,
! [X39] :
( esk4_0 != symmetric_difference(esk5_0,esk6_0)
& ( ~ member(X39,esk4_0)
| member(X39,esk6_0)
| member(X39,esk5_0) )
& ( ~ member(X39,esk4_0)
| ~ member(X39,esk6_0)
| ~ member(X39,esk5_0) )
& ( member(X39,esk4_0)
| member(X39,esk5_0)
| ~ member(X39,esk6_0) )
& ( member(X39,esk4_0)
| member(X39,esk6_0)
| ~ member(X39,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
fof(c_0_19,plain,
! [X8,X9,X10] :
( ( member(X10,union(X8,X9))
| ~ member(X10,X9) )
& ( member(X10,union(X8,X9))
| ~ member(X10,X8) )
& ( member(X10,X9)
| member(X10,X8)
| ~ member(X10,union(X8,X9)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_20,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(esk3_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(X1,esk5_0)
| member(X1,esk4_0)
| member(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk6_0)
| member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ subset(X1,difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_29,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(esk3_2(X1,esk4_0),esk5_0)
| member(esk3_2(X1,esk4_0),esk6_0)
| subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_31,plain,
( ~ member(esk3_2(X1,difference(X2,X3)),X2)
| member(esk3_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_32,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( member(esk3_2(esk4_0,X1),esk6_0)
| member(esk3_2(esk4_0,X1),esk5_0)
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_35,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( ~ member(X1,difference(X3,X3))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(esk3_2(difference(X1,esk6_0),esk4_0),esk5_0)
| subset(difference(X1,esk6_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_38,plain,
( member(esk3_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,esk6_0)
| member(X1,esk4_0)
| member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( member(esk3_2(esk4_0,union(X1,esk6_0)),esk5_0)
| subset(esk4_0,union(X1,esk6_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_36]) ).
cnf(c_0_44,plain,
( member(esk3_2(difference(difference(X1,X2),X3),X4),X1)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_45,negated_conjecture,
subset(difference(esk5_0,esk6_0),esk4_0),
inference(spm,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_46,plain,
( ~ member(esk3_2(X1,difference(X1,difference(X2,X3))),X3)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(esk3_2(X1,esk4_0),esk6_0)
| member(esk3_2(X1,esk4_0),esk5_0)
| subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
subset(esk4_0,union(esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( member(esk3_2(difference(esk4_0,X1),X2),esk6_0)
| member(esk3_2(difference(esk4_0,X1),X2),esk5_0)
| subset(difference(esk4_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_50,plain,
( member(esk3_2(union(X1,X2),X3),X1)
| member(esk3_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_12]) ).
cnf(c_0_51,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_52,plain,
( ~ subset(X1,difference(X2,X2))
| X1 = difference(X2,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_53,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,difference(esk5_0,esk6_0))
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_55,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_12]) ).
cnf(c_0_56,negated_conjecture,
( member(esk3_2(difference(esk6_0,X1),esk4_0),esk5_0)
| subset(difference(esk6_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,union(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_58,plain,
( member(esk3_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4)
| subset(difference(difference(X1,X2),X3),difference(X1,X4)) ),
inference(spm,[status(thm)],[c_0_31,c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( member(esk3_2(difference(esk4_0,esk6_0),X1),esk5_0)
| subset(difference(esk4_0,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_60,plain,
( member(esk3_2(union(difference(X1,X1),X2),X3),X2)
| subset(union(difference(X1,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_61,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_51]),c_0_21])]) ).
cnf(c_0_62,plain,
difference(difference(X1,X2),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( member(esk3_2(difference(difference(esk5_0,esk6_0),X1),X2),esk4_0)
| subset(difference(difference(esk5_0,esk6_0),X1),X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_16]) ).
cnf(c_0_64,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_55]),c_0_21])]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_66,negated_conjecture,
subset(difference(esk6_0,esk5_0),esk4_0),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
( member(esk3_2(difference(esk5_0,esk6_0),X1),esk4_0)
| subset(difference(esk5_0,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_12]) ).
cnf(c_0_68,negated_conjecture,
( ~ member(esk3_2(difference(X1,union(esk5_0,esk6_0)),X2),esk4_0)
| subset(difference(X1,union(esk5_0,esk6_0)),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_69,plain,
subset(difference(X1,X2),union(X3,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_70,plain,
subset(difference(difference(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_58]) ).
cnf(c_0_71,negated_conjecture,
subset(difference(esk4_0,esk6_0),difference(difference(esk4_0,esk6_0),difference(X1,esk5_0))),
inference(spm,[status(thm)],[c_0_46,c_0_59]) ).
fof(c_0_72,plain,
! [X18,X19] : union(X18,X19) = union(X19,X18),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_73,plain,
subset(union(difference(X1,X1),X2),X2),
inference(spm,[status(thm)],[c_0_15,c_0_60]) ).
cnf(c_0_74,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_75,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_76,negated_conjecture,
subset(difference(difference(esk5_0,esk6_0),esk4_0),X1),
inference(spm,[status(thm)],[c_0_22,c_0_63]) ).
cnf(c_0_77,plain,
( ~ member(esk3_2(X1,X2),difference(X3,X1))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_64]) ).
cnf(c_0_78,plain,
( member(esk3_2(X1,difference(X1,difference(X2,X3))),X2)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_38]) ).
cnf(c_0_79,negated_conjecture,
( ~ member(esk3_2(difference(esk4_0,X1),X2),esk6_0)
| ~ member(esk3_2(difference(esk4_0,X1),X2),esk5_0)
| subset(difference(esk4_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_16]) ).
cnf(c_0_80,plain,
( member(esk3_2(difference(X1,X2),difference(X1,X3)),X3)
| subset(difference(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_81,plain,
( ~ member(esk3_2(difference(X1,difference(X2,X3)),X4),X2)
| member(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| subset(difference(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(X1,difference(esk6_0,esk5_0))
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
subset(difference(esk5_0,esk6_0),union(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_33,c_0_67]) ).
cnf(c_0_84,negated_conjecture,
subset(difference(esk4_0,union(esk5_0,esk6_0)),X1),
inference(spm,[status(thm)],[c_0_68,c_0_16]) ).
cnf(c_0_85,plain,
( ~ member(X1,difference(X3,X4))
| member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_69]) ).
cnf(c_0_86,plain,
( ~ member(esk3_2(X1,union(difference(X2,X3),X4)),X2)
| member(esk3_2(X1,union(difference(X2,X3),X4)),X3)
| subset(X1,union(difference(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_87,plain,
( member(esk3_2(union(X1,X2),union(X3,X1)),X2)
| subset(union(X1,X2),union(X3,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_88,plain,
subset(difference(X1,X2),difference(X1,difference(X3,difference(X1,X2)))),
inference(spm,[status(thm)],[c_0_70,c_0_64]) ).
cnf(c_0_89,negated_conjecture,
difference(difference(esk4_0,esk6_0),difference(X1,esk5_0)) = difference(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_71]),c_0_21])]) ).
cnf(c_0_90,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_91,plain,
union(difference(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_73]),c_0_74])]) ).
cnf(c_0_92,plain,
difference(X1,difference(difference(difference(X2,X3),X2),X4)) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_75]) ).
cnf(c_0_93,negated_conjecture,
difference(difference(esk5_0,esk6_0),esk4_0) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_52,c_0_76]) ).
cnf(c_0_94,plain,
subset(X1,difference(X1,difference(difference(X2,X1),X3))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_95,negated_conjecture,
( ~ member(esk3_2(difference(esk4_0,X1),difference(esk4_0,esk6_0)),esk5_0)
| subset(difference(esk4_0,X1),difference(esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_96,plain,
( member(esk3_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_81,c_0_16]) ).
cnf(c_0_97,negated_conjecture,
( member(esk3_2(difference(esk6_0,esk5_0),X1),esk4_0)
| subset(difference(esk6_0,esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_12]) ).
cnf(c_0_98,negated_conjecture,
( ~ member(X1,difference(esk5_0,esk6_0))
| member(X1,union(X2,esk4_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_83]) ).
cnf(c_0_99,negated_conjecture,
difference(esk4_0,union(esk5_0,esk6_0)) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_52,c_0_84]) ).
cnf(c_0_100,plain,
( member(esk3_2(difference(X1,X2),X3),union(X4,X1))
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_85,c_0_12]) ).
cnf(c_0_101,plain,
( member(esk3_2(union(X1,X2),union(difference(X2,X3),X1)),X3)
| subset(union(X1,X2),union(difference(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_102,negated_conjecture,
subset(difference(X1,esk5_0),difference(X1,difference(esk4_0,esk6_0))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_103,plain,
union(X1,difference(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_104,negated_conjecture,
difference(X1,difference(difference(esk5_0,esk6_0),esk4_0)) = X1,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_94]),c_0_21])]) ).
cnf(c_0_106,negated_conjecture,
subset(difference(esk4_0,difference(esk4_0,esk5_0)),difference(esk4_0,esk6_0)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_107,negated_conjecture,
subset(difference(esk4_0,esk6_0),difference(esk4_0,difference(X1,esk5_0))),
inference(spm,[status(thm)],[c_0_70,c_0_89]) ).
cnf(c_0_108,negated_conjecture,
subset(difference(esk6_0,esk5_0),union(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_97]) ).
cnf(c_0_109,negated_conjecture,
( ~ member(esk3_2(X1,union(X2,esk4_0)),difference(esk5_0,esk6_0))
| subset(X1,union(X2,esk4_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_98]) ).
cnf(c_0_110,negated_conjecture,
difference(X1,difference(esk4_0,union(esk5_0,esk6_0))) = X1,
inference(spm,[status(thm)],[c_0_92,c_0_99]) ).
cnf(c_0_111,plain,
( ~ member(esk3_2(X1,union(X2,difference(X3,X4))),X3)
| member(esk3_2(X1,union(X2,difference(X3,X4))),X4)
| subset(X1,union(X2,difference(X3,X4))) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_112,plain,
( member(esk3_2(difference(X1,X2),difference(union(X3,X1),X4)),X4)
| subset(difference(X1,X2),difference(union(X3,X1),X4)) ),
inference(spm,[status(thm)],[c_0_31,c_0_100]) ).
cnf(c_0_113,plain,
subset(difference(X1,X2),difference(difference(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_114,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_101]),c_0_90]) ).
cnf(c_0_115,negated_conjecture,
difference(difference(esk4_0,esk6_0),esk5_0) = difference(difference(esk5_0,esk6_0),esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_102]),c_0_93]) ).
cnf(c_0_116,negated_conjecture,
union(X1,difference(difference(esk5_0,esk6_0),esk4_0)) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_117,plain,
( member(esk3_2(difference(X1,difference(X2,X3)),difference(X1,X2)),X3)
| subset(difference(X1,difference(X2,X3)),difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_80]) ).
cnf(c_0_118,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_105,c_0_64]) ).
cnf(c_0_119,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_15,c_0_96]) ).
cnf(c_0_120,negated_conjecture,
difference(esk4_0,difference(esk4_0,esk5_0)) = difference(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_106]),c_0_107])]) ).
cnf(c_0_121,negated_conjecture,
( ~ member(X1,difference(esk6_0,esk5_0))
| member(X1,union(esk4_0,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_108]) ).
cnf(c_0_122,negated_conjecture,
subset(union(esk4_0,difference(esk5_0,esk6_0)),union(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_109,c_0_87]) ).
cnf(c_0_123,negated_conjecture,
union(difference(esk4_0,union(esk5_0,esk6_0)),X1) = X1,
inference(spm,[status(thm)],[c_0_91,c_0_110]) ).
cnf(c_0_124,plain,
( member(esk3_2(difference(X1,X2),union(X3,difference(X1,X4))),X4)
| subset(difference(X1,X2),union(X3,difference(X1,X4))) ),
inference(spm,[status(thm)],[c_0_111,c_0_16]) ).
cnf(c_0_125,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_112]) ).
cnf(c_0_126,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_113]),c_0_21])]) ).
cnf(c_0_127,negated_conjecture,
subset(union(esk5_0,difference(esk4_0,esk6_0)),esk5_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_128,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_74,c_0_90]) ).
cnf(c_0_129,negated_conjecture,
( member(esk3_2(difference(esk6_0,esk5_0),difference(esk4_0,X1)),X1)
| subset(difference(esk6_0,esk5_0),difference(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_97]) ).
cnf(c_0_130,negated_conjecture,
subset(difference(esk4_0,difference(esk6_0,esk5_0)),difference(esk4_0,esk6_0)),
inference(spm,[status(thm)],[c_0_95,c_0_117]) ).
cnf(c_0_131,plain,
subset(difference(X1,X2),difference(X1,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_70,c_0_118]) ).
cnf(c_0_132,negated_conjecture,
subset(difference(esk4_0,difference(esk4_0,esk6_0)),difference(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_133,negated_conjecture,
( ~ member(esk3_2(X1,union(esk4_0,X2)),difference(esk6_0,esk5_0))
| subset(X1,union(esk4_0,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_121]) ).
cnf(c_0_134,negated_conjecture,
subset(union(esk4_0,difference(esk5_0,esk6_0)),esk4_0),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
fof(c_0_135,plain,
! [X14,X15] : symmetric_difference(X14,X15) = union(difference(X14,X15),difference(X15,X14)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_136,plain,
subset(difference(X1,X2),union(X3,difference(X1,X3))),
inference(spm,[status(thm)],[c_0_40,c_0_124]) ).
cnf(c_0_137,plain,
subset(difference(X1,X2),difference(union(X3,difference(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_138,negated_conjecture,
union(esk5_0,difference(esk4_0,esk6_0)) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_127]),c_0_128])]) ).
cnf(c_0_139,negated_conjecture,
( member(esk3_2(difference(esk5_0,esk6_0),difference(esk4_0,X1)),X1)
| subset(difference(esk5_0,esk6_0),difference(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_67]) ).
cnf(c_0_140,negated_conjecture,
subset(difference(esk6_0,esk5_0),difference(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_22,c_0_129]) ).
cnf(c_0_141,negated_conjecture,
difference(esk4_0,difference(esk6_0,esk5_0)) = difference(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_130]),c_0_131])]) ).
cnf(c_0_142,negated_conjecture,
difference(esk4_0,difference(esk4_0,esk6_0)) = difference(esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_132]),c_0_102])]) ).
cnf(c_0_143,negated_conjecture,
subset(union(X1,difference(esk6_0,esk5_0)),union(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_133,c_0_87]) ).
cnf(c_0_144,negated_conjecture,
union(esk4_0,difference(esk5_0,esk6_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_134]),c_0_128])]) ).
cnf(c_0_145,negated_conjecture,
esk4_0 != symmetric_difference(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_146,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_147,negated_conjecture,
subset(X1,union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_136,c_0_110]) ).
cnf(c_0_148,negated_conjecture,
subset(difference(esk4_0,esk6_0),difference(esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_149,negated_conjecture,
subset(difference(esk5_0,esk6_0),difference(esk4_0,esk6_0)),
inference(spm,[status(thm)],[c_0_22,c_0_139]) ).
cnf(c_0_150,negated_conjecture,
( ~ subset(difference(esk4_0,esk5_0),difference(esk6_0,esk5_0))
| difference(esk4_0,esk5_0) = difference(esk6_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_140]) ).
cnf(c_0_151,negated_conjecture,
subset(difference(esk4_0,esk5_0),difference(esk6_0,esk5_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_141]),c_0_142]) ).
cnf(c_0_152,negated_conjecture,
subset(union(difference(esk5_0,esk6_0),difference(esk6_0,esk5_0)),esk4_0),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_153,negated_conjecture,
esk4_0 != union(difference(esk5_0,esk6_0),difference(esk6_0,esk5_0)),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_154,negated_conjecture,
subset(esk4_0,union(difference(esk4_0,esk5_0),difference(esk4_0,esk6_0))),
inference(spm,[status(thm)],[c_0_147,c_0_120]) ).
cnf(c_0_155,negated_conjecture,
difference(esk4_0,esk6_0) = difference(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_148]),c_0_149])]) ).
cnf(c_0_156,negated_conjecture,
difference(esk4_0,esk5_0) = difference(esk6_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
cnf(c_0_157,negated_conjecture,
~ subset(esk4_0,union(difference(esk5_0,esk6_0),difference(esk6_0,esk5_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_152]),c_0_153]) ).
cnf(c_0_158,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]),c_0_90]),c_0_157]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET582+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:27:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 197.88/29.35 % Version: 3.5.1
% 197.88/29.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 197.88/29.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.88/29.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 197.88/29.35 % Starting new_bool_3 with 300s (1) cores
% 197.88/29.35 % Starting new_bool_1 with 300s (1) cores
% 197.88/29.35 % Starting sh5l with 300s (1) cores
% 197.88/29.35 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1055088 completed with status 0
% 197.88/29.35 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 197.88/29.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 197.88/29.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.88/29.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 197.88/29.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 197.88/29.35 % No SInE strategy applied
% 197.88/29.35 % Search class: FGHSS-FFMF22-SFFFFFNN
% 197.88/29.35 % partial match(1): FGHSS-FFMF32-SFFFFFNN
% 197.88/29.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 197.88/29.35 % Starting SubtermCWHack with 136s (1) cores
% 197.88/29.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 197.88/29.35 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 197.88/29.35 % Starting new_bool_3 with 248s (1) cores
% 197.88/29.35 % Starting new_bool_1 with 241s (1) cores
% 197.88/29.35 % SubtermCWHack with pid 1055095 completed with status 0
% 197.88/29.35 % Result found by SubtermCWHack
% 197.88/29.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 197.88/29.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.88/29.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 197.88/29.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 197.88/29.35 % No SInE strategy applied
% 197.88/29.35 % Search class: FGHSS-FFMF22-SFFFFFNN
% 197.88/29.35 % partial match(1): FGHSS-FFMF32-SFFFFFNN
% 197.88/29.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 197.88/29.35 % Starting SubtermCWHack with 136s (1) cores
% 197.88/29.35 % Preprocessing time : 0.001 s
% 197.88/29.35
% 197.88/29.35 % Proof found!
% 197.88/29.35 % SZS status Theorem
% 197.88/29.35 % SZS output start CNFRefutation
% See solution above
% 197.88/29.35 % Parsed axioms : 11
% 197.88/29.35 % Removed by relevancy pruning/SinE : 0
% 197.88/29.35 % Initial clauses : 27
% 197.88/29.35 % Removed in clause preprocessing : 3
% 197.88/29.35 % Initial clauses in saturation : 24
% 197.88/29.35 % Processed clauses : 65968
% 197.88/29.35 % ...of these trivial : 7802
% 197.88/29.35 % ...subsumed : 52412
% 197.88/29.35 % ...remaining for further processing : 5754
% 197.88/29.35 % Other redundant clauses eliminated : 2
% 197.88/29.35 % Clauses deleted for lack of memory : 0
% 197.88/29.35 % Backward-subsumed : 43
% 197.88/29.35 % Backward-rewritten : 592
% 197.88/29.35 % Generated clauses : 2202509
% 197.88/29.35 % ...of the previous two non-redundant : 1619874
% 197.88/29.35 % ...aggressively subsumed : 0
% 197.88/29.35 % Contextual simplify-reflections : 27
% 197.88/29.35 % Paramodulations : 2199177
% 197.88/29.35 % Factorizations : 3330
% 197.88/29.35 % NegExts : 0
% 197.88/29.35 % Equation resolutions : 2
% 197.88/29.35 % Disequality decompositions : 0
% 197.88/29.35 % Total rewrite steps : 1757872
% 197.88/29.35 % ...of those cached : 1663309
% 197.88/29.35 % Propositional unsat checks : 0
% 197.88/29.35 % Propositional check models : 0
% 197.88/29.35 % Propositional check unsatisfiable : 0
% 197.88/29.35 % Propositional clauses : 0
% 197.88/29.35 % Propositional clauses after purity: 0
% 197.88/29.35 % Propositional unsat core size : 0
% 197.88/29.35 % Propositional preprocessing time : 0.000
% 197.88/29.35 % Propositional encoding time : 0.000
% 197.88/29.35 % Propositional solver time : 0.000
% 197.88/29.35 % Success case prop preproc time : 0.000
% 197.88/29.35 % Success case prop encoding time : 0.000
% 197.88/29.35 % Success case prop solver time : 0.000
% 197.88/29.35 % Current number of processed clauses : 5117
% 197.88/29.35 % Positive orientable unit clauses : 2217
% 197.88/29.35 % Positive unorientable unit clauses: 39
% 197.88/29.35 % Negative unit clauses : 110
% 197.88/29.35 % Non-unit-clauses : 2751
% 197.88/29.35 % Current number of unprocessed clauses: 1546309
% 197.88/29.35 % ...number of literals in the above : 4371562
% 197.88/29.35 % Current number of archived formulas : 0
% 197.88/29.35 % Current number of archived clauses : 636
% 197.88/29.35 % Clause-clause subsumption calls (NU) : 1429160
% 197.88/29.35 % Rec. Clause-clause subsumption calls : 637109
% 197.88/29.35 % Non-unit clause-clause subsumptions : 19441
% 197.88/29.35 % Unit Clause-clause subsumption calls : 727023
% 197.88/29.35 % Rewrite failures with RHS unbound : 3477
% 197.88/29.35 % BW rewrite match attempts : 99893
% 197.88/29.35 % BW rewrite match successes : 736
% 197.88/29.35 % Condensation attempts : 0
% 197.88/29.35 % Condensation successes : 0
% 197.88/29.35 % Termbank termtop insertions : 41222241
% 197.88/29.35 % Search garbage collected termcells : 478
% 197.88/29.35
% 197.88/29.35 % -------------------------------------------------
% 197.88/29.35 % User time : 26.839 s
% 197.88/29.35 % System time : 1.134 s
% 197.88/29.35 % Total time : 27.972 s
% 197.88/29.35 % Maximum resident set size: 3636 pages
% 197.88/29.35
% 197.88/29.35 % -------------------------------------------------
% 197.88/29.35 % User time : 134.780 s
% 197.88/29.35 % System time : 5.521 s
% 197.88/29.35 % Total time : 140.301 s
% 197.88/29.35 % Maximum resident set size: 4864 pages
% 197.88/29.35 % E exiting
%------------------------------------------------------------------------------