%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU170+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:10:55 PM UTC 2026
% Result : Theorem 143.86s 95.90s
% Output : CNFRefutation 144.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 110 ( 54 unt; 0 def)
% Number of atoms : 218 ( 71 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 178 ( 70 ~; 66 |; 18 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 167 ( 8 sgn 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(t43_subset_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t63_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(c_0_22,plain,
! [X266,X267,X268,X269,X270,X271] :
( ( ~ in(X268,X267)
| subset(X268,X266)
| X267 != powerset(X266) )
& ( ~ subset(X269,X266)
| in(X269,X267)
| X267 != powerset(X266) )
& ( ~ in(esk3_2(X270,X271),X271)
| ~ subset(esk3_2(X270,X271),X270)
| X271 = powerset(X270) )
& ( in(esk3_2(X270,X271),X271)
| subset(esk3_2(X270,X271),X270)
| X271 = powerset(X270) ) ),
inference(distribute,[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)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
inference(assume_negation,[status(cth)],[t43_subset_1]) ).
fof(c_0_25,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_26,lemma,
! [X378,X379] :
( ( set_difference(X378,X379) != empty_set
| subset(X378,X379) )
& ( ~ subset(X378,X379)
| set_difference(X378,X379) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_27,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X273,X274] :
( ( ~ element(X274,X273)
| in(X274,X273)
| empty(X273) )
& ( ~ in(X274,X273)
| element(X274,X273)
| empty(X273) )
& ( ~ element(X274,X273)
| empty(X274)
| ~ empty(X273) )
& ( ~ empty(X274)
| element(X274,X273)
| ~ empty(X273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_29,negated_conjecture,
( element(esk26_0,powerset(esk25_0))
& element(esk27_0,powerset(esk25_0))
& ( ~ disjoint(esk26_0,esk27_0)
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) )
& ( disjoint(esk26_0,esk27_0)
| subset(esk26_0,subset_complement(esk25_0,esk27_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_30,plain,
! [X357] : ~ empty(powerset(X357)),
inference(variable_rename,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X345,X346] :
( ~ element(X346,powerset(X345))
| subset_complement(X345,X346) = set_difference(X345,X346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
cnf(c_0_32,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
element(esk27_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,plain,
! [X502,X503] :
( ~ in(X502,X503)
| ~ empty(X503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_38,lemma,
! [X506,X507] :
( ( ~ disjoint(X506,X507)
| set_difference(X506,X507) = X506 )
& ( set_difference(X506,X507) != X506
| disjoint(X506,X507) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(c_0_39,lemma,
! [X461,X462] : set_union2(X461,set_difference(X462,X461)) = set_union2(X461,X462),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_40,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,lemma,
( set_difference(X1,X2) = empty_set
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
in(esk27_0,powerset(esk25_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
fof(c_0_43,plain,
! [X431] : set_union2(X431,empty_set) = X431,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_44,plain,
! [X249,X250] : set_union2(X249,X250) = set_union2(X250,X249),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_45,plain,
! [X499] :
( ~ empty(X499)
| X499 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_46,plain,
! [X397] :
( element(esk20_1(X397),powerset(X397))
& empty(esk20_1(X397)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_47,plain,
! [X349,X350] :
( ( ~ disjoint(X349,X350)
| set_intersection2(X349,X350) = empty_set )
& ( set_intersection2(X349,X350) != empty_set
| disjoint(X349,X350) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(c_0_48,lemma,
! [X482,X483] : set_difference(X482,set_difference(X482,X483)) = set_intersection2(X482,X483),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_49,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_50,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_52,lemma,
! [X452,X453] : subset(set_difference(X452,X453),X452),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_53,lemma,
! [X493,X494,X495] :
( ~ subset(X493,X494)
| ~ disjoint(X494,X495)
| disjoint(X493,X495) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
cnf(c_0_54,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,negated_conjecture,
( disjoint(esk26_0,esk27_0)
| subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_56,lemma,
! [X473,X474] : set_difference(set_union2(X473,X474),X474) = set_difference(X473,X474),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_57,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_58,negated_conjecture,
set_difference(esk25_0,esk27_0) = subset_complement(esk25_0,esk27_0),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_59,negated_conjecture,
set_difference(esk27_0,esk25_0) = empty_set,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_60,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_61,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_62,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_63,plain,
empty(esk20_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,negated_conjecture,
element(esk26_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_65,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_66,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_68,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_69,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_70,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_71,negated_conjecture,
( set_difference(esk26_0,esk27_0) = esk26_0
| subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_72,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,lemma,
set_union2(esk27_0,subset_complement(esk25_0,esk27_0)) = set_union2(esk27_0,esk25_0),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_74,lemma,
set_union2(esk27_0,esk25_0) = esk25_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_59]),c_0_60]),c_0_61]) ).
fof(c_0_75,plain,
! [X366,X367] :
( ~ element(X367,powerset(X366))
| subset_complement(X366,subset_complement(X366,X367)) = X367 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(c_0_76,plain,
element(esk20_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_77,plain,
esk20_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_78,plain,
! [X465] : set_difference(X465,empty_set) = X465,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_79,negated_conjecture,
in(esk26_0,powerset(esk25_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_64]),c_0_36]) ).
cnf(c_0_80,negated_conjecture,
( ~ disjoint(esk26_0,esk27_0)
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_81,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_82,plain,
( set_difference(X1,X2) = subset_complement(X1,X2)
| ~ in(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_83,lemma,
in(set_difference(X1,X2),powerset(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_84,negated_conjecture,
( set_difference(esk26_0,esk27_0) = esk26_0
| disjoint(esk26_0,X1)
| ~ disjoint(subset_complement(esk25_0,esk27_0),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_85,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_86,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_72,c_0_61]) ).
cnf(c_0_87,lemma,
set_union2(esk27_0,subset_complement(esk25_0,esk27_0)) = esk25_0,
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_88,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_89,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_90,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_91,lemma,
! [X445,X446,X447] :
( ~ subset(X445,X446)
| subset(set_difference(X445,X447),set_difference(X446,X447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(c_0_92,lemma,
! [X504,X505] : subset(X504,set_union2(X504,X505)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_93,negated_conjecture,
set_difference(esk26_0,esk25_0) = empty_set,
inference(spm,[status(thm)],[c_0_41,c_0_79]) ).
cnf(c_0_94,negated_conjecture,
( set_difference(esk26_0,set_difference(esk26_0,esk27_0)) != empty_set
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_95,lemma,
set_difference(X1,set_difference(X1,X2)) = subset_complement(X1,set_difference(X1,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_96,lemma,
( set_difference(esk26_0,esk27_0) = esk26_0
| disjoint(esk26_0,X1)
| set_difference(subset_complement(esk25_0,esk27_0),X1) != subset_complement(esk25_0,esk27_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_97,lemma,
set_difference(subset_complement(esk25_0,esk27_0),esk27_0) = subset_complement(esk25_0,esk27_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_58]) ).
cnf(c_0_98,plain,
subset_complement(X1,subset_complement(X1,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_99,plain,
subset_complement(X1,empty_set) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_89]),c_0_90]) ).
cnf(c_0_100,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,lemma,
set_union2(esk26_0,esk25_0) = esk25_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_93]),c_0_60]),c_0_61]) ).
cnf(c_0_103,negated_conjecture,
( subset_complement(esk26_0,set_difference(esk26_0,esk27_0)) != empty_set
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
set_difference(esk26_0,esk27_0) = esk26_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_96]),c_0_97])]),c_0_71]) ).
cnf(c_0_105,plain,
subset_complement(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( subset(set_difference(X1,esk27_0),subset_complement(esk25_0,esk27_0))
| ~ subset(X1,esk25_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_58]) ).
cnf(c_0_107,lemma,
subset(esk26_0,esk25_0),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
~ subset(esk26_0,subset_complement(esk25_0,esk27_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_104]),c_0_107])]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU170+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.08/0.25 % Computer : n012.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue May 5 02:46:31 EDT 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.26 % start to proof: theBenchmark
% 143.86/95.90 % Version : CSE_E---1.7
% 143.86/95.90 % Problem : theBenchmark.p
% 143.86/95.90 % SZS status Theorem for theBenchmark.p
% 143.86/95.90 % SZS output start CNFRefutation
% See solution above
% 144.25/96.38 % Total time : 77.949s
%------------------------------------------------------------------------------