%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU170+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:24:06 PM UTC 2026
% Result : Theorem 4.59s 1.36s
% Output : CNFRefutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 116 ( 57 unt; 0 def)
% Number of atoms : 229 ( 69 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 191 ( 78 ~; 64 |; 22 &)
% ( 12 <=>; 15 =>; 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 : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 184 ( 8 sgn 112 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_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(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_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(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
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(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
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(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(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
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(t63_xboole_1,lemma,
! [X1,X2,X3] :
( ( disjoint(X2,X3)
& subset(X1,X2) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
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(d2_subset_1,axiom,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
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(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(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,
! [X109,X110] :
( subset_complement(X109,X110) = set_difference(X109,X110)
| ~ element(X110,powerset(X109)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
fof(c_0_26,negated_conjecture,
( ( subset(esk26_0,subset_complement(esk25_0,esk27_0))
| disjoint(esk26_0,esk27_0) )
& ( ~ subset(esk26_0,subset_complement(esk25_0,esk27_0))
| ~ disjoint(esk26_0,esk27_0) )
& element(esk27_0,powerset(esk25_0))
& element(esk26_0,powerset(esk25_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_27,plain,
! [X117,X118] :
( element(subset_complement(X117,X118),powerset(X117))
| ~ element(X118,powerset(X117)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])])]) ).
cnf(c_0_28,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
element(esk27_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,plain,
! [X130,X131] :
( subset_complement(X130,subset_complement(X130,X131)) = X131
| ~ element(X131,powerset(X130)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
fof(c_0_31,plain,
! [X15,X16] : set_intersection2(X15,X16) = set_intersection2(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_32,lemma,
! [X246,X247] : set_difference(X246,set_difference(X246,X247)) = set_intersection2(X246,X247),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_33,lemma,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
& ~ disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_34,plain,
! [X204] : set_intersection2(X204,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_35,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_36,lemma,
! [X225,X226] : set_union2(X225,set_difference(X226,X225)) = set_union2(X225,X226),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_37,lemma,
! [X182,X183] :
( set_union2(X182,X183) = X183
| ~ subset(X182,X183) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
cnf(c_0_38,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,negated_conjecture,
subset_complement(esk25_0,esk27_0) = set_difference(esk25_0,esk27_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_40,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,subset_complement(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,lemma,
! [X249,X250,X252,X253,X254] :
( ( ~ disjoint(X252,X253)
| ~ in(X254,set_intersection2(X252,X253)) )
& ( in(esk28_2(X249,X250),set_intersection2(X249,X250))
| disjoint(X249,X250) ) ),
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)],[c_0_33])])])])])]) ).
cnf(c_0_44,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_45,plain,
! [X229] : set_difference(X229,empty_set) = X229,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_46,plain,
! [X26,X27,X28] :
( ( X28 = empty_set
| in(esk2_1(X28),X28) )
& ( ~ in(X27,X26)
| X26 != empty_set ) ),
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)],[c_0_35])])])])])]) ).
fof(c_0_47,lemma,
! [X237,X238] : set_difference(set_union2(X237,X238),X238) = set_difference(X237,X238),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_48,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,lemma,
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,negated_conjecture,
element(set_difference(esk25_0,esk27_0),powerset(esk25_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29])]) ).
cnf(c_0_51,negated_conjecture,
subset_complement(esk25_0,set_difference(esk25_0,esk27_0)) = esk27_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_39]),c_0_29])]) ).
cnf(c_0_52,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
fof(c_0_53,plain,
! [X13,X14] : set_union2(X13,X14) = set_union2(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_54,lemma,
! [X216,X217] : subset(set_difference(X216,X217),X216),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_55,lemma,
( in(esk28_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_57,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,lemma,
( ~ subset(X1,set_difference(X2,X1))
| set_union2(X1,X2) = set_difference(X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_61,negated_conjecture,
set_difference(esk27_0,set_difference(esk27_0,esk25_0)) = esk27_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_62,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_64,plain,
! [X165,X166] :
( disjoint(X166,X165)
| ~ disjoint(X165,X166) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
cnf(c_0_65,lemma,
( in(esk28_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rw,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_66,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_68,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_69,lemma,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_59,c_0_48]) ).
cnf(c_0_70,negated_conjecture,
set_union2(esk27_0,set_difference(esk27_0,esk25_0)) = esk27_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63])]) ).
cnf(c_0_71,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,lemma,
disjoint(esk27_0,set_difference(esk27_0,esk25_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_61]),c_0_66]),c_0_67]) ).
cnf(c_0_73,lemma,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| ~ disjoint(X2,X3) ),
inference(rw,[status(thm)],[c_0_68,c_0_42]) ).
cnf(c_0_74,negated_conjecture,
set_difference(set_difference(esk27_0,esk25_0),esk27_0) = empty_set,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_61]),c_0_62]),c_0_70]),c_0_66]) ).
cnf(c_0_75,lemma,
disjoint(set_difference(esk27_0,esk25_0),esk27_0),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,lemma,
~ in(X1,set_difference(esk27_0,esk25_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_57])]) ).
cnf(c_0_77,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_78,plain,
! [X195] : set_union2(X195,empty_set) = X195,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(c_0_79,plain,
! [X113,X114] :
( ( disjoint(X113,X114)
| set_intersection2(X113,X114) != empty_set )
& ( set_intersection2(X113,X114) = empty_set
| ~ disjoint(X113,X114) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])]) ).
cnf(c_0_80,lemma,
set_difference(esk27_0,esk25_0) = empty_set,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,plain,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,lemma,
set_union2(esk27_0,esk25_0) = esk25_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_80]),c_0_81]),c_0_62]) ).
cnf(c_0_84,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rw,[status(thm)],[c_0_82,c_0_42]) ).
cnf(c_0_85,lemma,
set_difference(esk27_0,set_difference(esk25_0,esk27_0)) = esk27_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_83]),c_0_52]),c_0_80]),c_0_57]) ).
fof(c_0_86,lemma,
! [X257,X258,X259] :
( disjoint(X257,X259)
| ~ disjoint(X258,X259)
| ~ subset(X257,X258) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])])]) ).
cnf(c_0_87,lemma,
disjoint(esk27_0,set_difference(esk25_0,esk27_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_66])]) ).
fof(c_0_88,lemma,
! [X270,X271] :
( ( disjoint(X270,X271)
| set_difference(X270,X271) != X270 )
& ( set_difference(X270,X271) = X270
| ~ disjoint(X270,X271) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])])]) ).
cnf(c_0_89,negated_conjecture,
( subset(esk26_0,subset_complement(esk25_0,esk27_0))
| disjoint(esk26_0,esk27_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_90,negated_conjecture,
( ~ subset(esk26_0,subset_complement(esk25_0,esk27_0))
| ~ disjoint(esk26_0,esk27_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_91,lemma,
( ~ disjoint(X2,X3)
| ~ subset(X1,X2)
| disjoint(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,lemma,
disjoint(set_difference(esk25_0,esk27_0),esk27_0),
inference(spm,[status(thm)],[c_0_71,c_0_87]) ).
fof(c_0_93,plain,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_94,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_95,lemma,
( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( subset(esk26_0,set_difference(esk25_0,esk27_0))
| disjoint(esk26_0,esk27_0) ),
inference(rw,[status(thm)],[c_0_89,c_0_39]) ).
cnf(c_0_97,negated_conjecture,
( ~ subset(esk26_0,set_difference(esk25_0,esk27_0))
| ~ disjoint(esk26_0,esk27_0) ),
inference(rw,[status(thm)],[c_0_90,c_0_39]) ).
cnf(c_0_98,lemma,
( ~ subset(X1,set_difference(esk25_0,esk27_0))
| disjoint(X1,esk27_0) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
fof(c_0_99,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( X35 = powerset(X34)
| subset(esk3_2(X34,X35),X34)
| in(esk3_2(X34,X35),X35) )
& ( X35 = powerset(X34)
| ~ subset(esk3_2(X34,X35),X34)
| ~ in(esk3_2(X34,X35),X35) )
& ( X31 != powerset(X30)
| in(X33,X31)
| ~ subset(X33,X30) )
& ( X31 != powerset(X30)
| subset(X32,X30)
| ~ in(X32,X31) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_100,plain,
! [X37,X38] :
( ( ~ empty(X37)
| element(X38,X37)
| ~ empty(X38) )
& ( ~ empty(X37)
| empty(X38)
| ~ element(X38,X37) )
& ( empty(X37)
| element(X38,X37)
| ~ in(X38,X37) )
& ( empty(X37)
| in(X38,X37)
| ~ element(X38,X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])]) ).
fof(c_0_101,plain,
! [X121] : ~ empty(powerset(X121)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_94])]) ).
fof(c_0_102,lemma,
! [X209,X210,X211] :
( subset(set_difference(X209,X211),set_difference(X210,X211))
| ~ subset(X209,X210) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])])]) ).
cnf(c_0_103,lemma,
( subset(esk26_0,set_difference(esk25_0,esk27_0))
| set_difference(esk26_0,esk27_0) = esk26_0 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_104,negated_conjecture,
~ subset(esk26_0,set_difference(esk25_0,esk27_0)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_106,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,negated_conjecture,
element(esk26_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_108,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_109,lemma,
( ~ subset(X1,X2)
| subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_110,lemma,
set_difference(esk26_0,esk27_0) = esk26_0,
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_112,negated_conjecture,
in(esk26_0,powerset(esk25_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_113,lemma,
( ~ subset(esk26_0,X1)
| subset(esk26_0,set_difference(X1,esk27_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,negated_conjecture,
subset(esk26_0,esk25_0),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_115,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_113]),c_0_114])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU170+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:54:40 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 4.59/1.36 % Version: 3.5.1
% 4.59/1.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.59/1.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.59/1.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.59/1.36 % Starting new_bool_3 with 300s (1) cores
% 4.59/1.36 % Starting new_bool_1 with 300s (1) cores
% 4.59/1.36 % Starting sh5l with 300s (1) cores
% 4.59/1.36 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 162874 completed with status 0
% 4.59/1.36 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.59/1.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.59/1.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.59/1.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.59/1.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.59/1.36 % No SInE strategy applied
% 4.59/1.36 % Search class: FGHSM-FSLM32-MFFFFFNN
% 4.59/1.36 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 4.59/1.36 % Starting SubtermCWHack with 136s (1) cores
% 4.59/1.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.59/1.36 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 4.59/1.36 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 4.59/1.36 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 4.59/1.36 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 162885 completed with status 0
% 4.59/1.36 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 4.59/1.36 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.59/1.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.59/1.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.59/1.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.59/1.36 % No SInE strategy applied
% 4.59/1.36 % Search class: FGHSM-FSLM32-MFFFFFNN
% 4.59/1.36 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 4.59/1.36 % Starting SubtermCWHack with 136s (1) cores
% 4.59/1.36 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.59/1.36 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 4.59/1.36 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 4.59/1.36 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 4.59/1.36 % Preprocessing time : 0.005 s
% 4.59/1.36 % Presaturation interreduction done
% 4.59/1.36
% 4.59/1.36 % Proof found!
% 4.59/1.36 % SZS status Theorem
% 4.59/1.36 % SZS output start CNFRefutation
% See solution above
% 4.59/1.36 % Parsed axioms : 110
% 4.59/1.36 % Removed by relevancy pruning/SinE : 0
% 4.59/1.36 % Initial clauses : 193
% 4.59/1.36 % Removed in clause preprocessing : 14
% 4.59/1.36 % Initial clauses in saturation : 179
% 4.59/1.36 % Processed clauses : 4176
% 4.59/1.36 % ...of these trivial : 53
% 4.59/1.36 % ...subsumed : 2909
% 4.59/1.36 % ...remaining for further processing : 1214
% 4.59/1.36 % Other redundant clauses eliminated : 173
% 4.59/1.36 % Clauses deleted for lack of memory : 0
% 4.59/1.36 % Backward-subsumed : 121
% 4.59/1.36 % Backward-rewritten : 45
% 4.59/1.36 % Generated clauses : 19564
% 4.59/1.36 % ...of the previous two non-redundant : 17106
% 4.59/1.36 % ...aggressively subsumed : 0
% 4.59/1.36 % Contextual simplify-reflections : 7
% 4.59/1.36 % Paramodulations : 19354
% 4.59/1.36 % Factorizations : 31
% 4.59/1.36 % NegExts : 0
% 4.59/1.36 % Equation resolutions : 180
% 4.59/1.36 % Disequality decompositions : 0
% 4.59/1.36 % Total rewrite steps : 7217
% 4.59/1.36 % ...of those cached : 6641
% 4.59/1.36 % Propositional unsat checks : 0
% 4.59/1.36 % Propositional check models : 0
% 4.59/1.36 % Propositional check unsatisfiable : 0
% 4.59/1.36 % Propositional clauses : 0
% 4.59/1.36 % Propositional clauses after purity: 0
% 4.59/1.36 % Propositional unsat core size : 0
% 4.59/1.36 % Propositional preprocessing time : 0.000
% 4.59/1.36 % Propositional encoding time : 0.000
% 4.59/1.36 % Propositional solver time : 0.000
% 4.59/1.36 % Success case prop preproc time : 0.000
% 4.59/1.36 % Success case prop encoding time : 0.000
% 4.59/1.36 % Success case prop solver time : 0.000
% 4.59/1.36 % Current number of processed clauses : 859
% 4.59/1.36 % Positive orientable unit clauses : 97
% 4.59/1.36 % Positive unorientable unit clauses: 4
% 4.59/1.36 % Negative unit clauses : 263
% 4.59/1.36 % Non-unit-clauses : 495
% 4.59/1.36 % Current number of unprocessed clauses: 12970
% 4.59/1.36 % ...number of literals in the above : 38543
% 4.59/1.36 % Current number of archived formulas : 0
% 4.59/1.36 % Current number of archived clauses : 327
% 4.59/1.36 % Clause-clause subsumption calls (NU) : 49666
% 4.59/1.36 % Rec. Clause-clause subsumption calls : 36513
% 4.59/1.36 % Non-unit clause-clause subsumptions : 770
% 4.59/1.36 % Unit Clause-clause subsumption calls : 21253
% 4.59/1.36 % Rewrite failures with RHS unbound : 0
% 4.59/1.36 % BW rewrite match attempts : 136
% 4.59/1.36 % BW rewrite match successes : 81
% 4.59/1.36 % Condensation attempts : 0
% 4.59/1.36 % Condensation successes : 0
% 4.59/1.36 % Termbank termtop insertions : 212487
% 4.59/1.36 % Search garbage collected termcells : 2742
% 4.59/1.36
% 4.59/1.36 % -------------------------------------------------
% 4.59/1.36 % User time : 0.639 s
% 4.59/1.36 % System time : 0.031 s
% 4.59/1.36 % Total time : 0.670 s
% 4.59/1.36 % Maximum resident set size: 4208 pages
% 4.59/1.36
% 4.59/1.36 % -------------------------------------------------
% 4.59/1.36 % User time : 2.541 s
% 4.59/1.36 % System time : 0.115 s
% 4.59/1.36 % Total time : 2.656 s
% 4.59/1.36 % Maximum resident set size: 4864 pages
% 4.59/1.36 % E exiting
%------------------------------------------------------------------------------