%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU152+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 : n014.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 05:10:49 PM UTC 2026
% Result : Theorem 0.30s 1.61s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_101)
% Comments :
%------------------------------------------------------------------------------
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(l23_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_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(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t26_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t6_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_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(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_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(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_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(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
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(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
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(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t45_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_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(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_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(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(t10_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t60_xboole_1,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_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(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
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(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(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(t37_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_68,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(i_0_69,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[l23_zfmisc_1]) ).
fof(i_0_70,plain,
! [X207,X208,X209,X210,X211,X212,X213,X214] :
( ( in(X210,X207)
| ~ in(X210,X209)
| X209 != set_intersection2(X207,X208) )
& ( in(X210,X208)
| ~ in(X210,X209)
| X209 != set_intersection2(X207,X208) )
& ( ~ in(X211,X207)
| ~ in(X211,X208)
| in(X211,X209)
| X209 != set_intersection2(X207,X208) )
& ( ~ in(esk7_3(X212,X213,X214),X214)
| ~ in(esk7_3(X212,X213,X214),X212)
| ~ in(esk7_3(X212,X213,X214),X213)
| X214 = set_intersection2(X212,X213) )
& ( in(esk7_3(X212,X213,X214),X212)
| in(esk7_3(X212,X213,X214),X214)
| X214 = set_intersection2(X212,X213) )
& ( in(esk7_3(X212,X213,X214),X213)
| in(esk7_3(X212,X213,X214),X214)
| X214 = set_intersection2(X212,X213) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(i_0_71,lemma,
! [X299,X300] : set_difference(X299,set_difference(X299,X300)) = set_intersection2(X299,X300),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_72,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(i_0_73,lemma,
! [X268,X269,X270] :
( ~ subset(X268,X269)
| subset(set_intersection2(X268,X270),set_intersection2(X269,X270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_74,lemma,
! [X302,X303,X305,X306,X307] :
( ( disjoint(X302,X303)
| in(esk15_2(X302,X303),set_intersection2(X302,X303)) )
& ( ~ in(X307,set_intersection2(X305,X306))
| ~ disjoint(X305,X306) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_68])])])])]) ).
fof(i_0_75,lemma,
! [X261,X262,X263] :
( ~ subset(X261,X262)
| ~ subset(X261,X263)
| subset(X261,set_intersection2(X262,X263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_76,lemma,
! [X243,X244,X245] :
( ~ subset(X243,X244)
| in(X245,X243)
| subset(X243,set_difference(X244,singleton(X245))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_77,lemma,
! [X313] : unordered_pair(X313,X313) = singleton(X313),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_78,lemma,
! [X315,X316] :
( ~ subset(singleton(X315),singleton(X316))
| X315 = X316 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_79,plain,
! [X165,X166,X167,X168,X169,X170] :
( ( ~ in(X167,X166)
| X167 = X165
| X166 != singleton(X165) )
& ( X168 != X165
| in(X168,X166)
| X166 != singleton(X165) )
& ( ~ in(esk1_2(X169,X170),X170)
| esk1_2(X169,X170) != X169
| X170 = singleton(X169) )
& ( in(esk1_2(X169,X170),X170)
| esk1_2(X169,X170) = X169
| X170 = singleton(X169) ) ),
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_tarski])])])])])]) ).
fof(i_0_80,lemma,
! [X259,X260] : subset(set_intersection2(X259,X260),X259),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_81,lemma,
! [X246,X247] :
( ( ~ subset(X246,singleton(X247))
| X246 = empty_set
| X246 = singleton(X247) )
& ( X246 != empty_set
| subset(X246,singleton(X247)) )
& ( X246 != singleton(X247)
| subset(X246,singleton(X247)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_82,plain,
! [X161,X162] : set_intersection2(X161,X162) = set_intersection2(X162,X161),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_83,lemma,
! [X239,X240] :
( ( ~ subset(singleton(X239),X240)
| in(X239,X240) )
& ( ~ in(X239,X240)
| subset(singleton(X239),X240) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_84,plain,
! [X225,X226] :
( ( ~ disjoint(X225,X226)
| set_intersection2(X225,X226) = empty_set )
& ( set_intersection2(X225,X226) != empty_set
| disjoint(X225,X226) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_85,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(i_0_86,lemma,
! [X271,X272] :
( ~ subset(X271,X272)
| set_intersection2(X271,X272) = X271 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_87,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_88,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_89,negated_conjecture,
( in(esk9_0,esk10_0)
& set_union2(singleton(esk9_0),esk10_0) != esk10_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_69])])]) ).
fof(i_0_90,lemma,
! [X328,X329,X330] :
( singleton(X328) != unordered_pair(X329,X330)
| X328 = X329 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_91,lemma,
! [X331,X332,X333] :
( singleton(X331) != unordered_pair(X332,X333)
| X332 = X333 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_92,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_93,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_94,plain,
! [X234] : set_intersection2(X234,X234) = X234,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_95,plain,
! [X273] : set_intersection2(X273,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_96,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_97,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_98,lemma,
! [X236] : singleton(X236) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_99,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_100,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk7_3(X1,X2,X3),X3)
| ~ in(esk7_3(X1,X2,X3),X1)
| ~ in(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_101,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_71]) ).
fof(i_0_102,plain,
! [X216,X217,X218,X219,X220,X221,X222,X223] :
( ( in(X219,X216)
| ~ in(X219,X218)
| X218 != set_difference(X216,X217) )
& ( ~ in(X219,X217)
| ~ in(X219,X218)
| X218 != set_difference(X216,X217) )
& ( ~ in(X220,X216)
| in(X220,X217)
| in(X220,X218)
| X218 != set_difference(X216,X217) )
& ( ~ in(esk8_3(X221,X222,X223),X223)
| ~ in(esk8_3(X221,X222,X223),X221)
| in(esk8_3(X221,X222,X223),X222)
| X223 = set_difference(X221,X222) )
& ( in(esk8_3(X221,X222,X223),X221)
| in(esk8_3(X221,X222,X223),X223)
| X223 = set_difference(X221,X222) )
& ( ~ in(esk8_3(X221,X222,X223),X222)
| in(esk8_3(X221,X222,X223),X223)
| X223 = set_difference(X221,X222) ) ),
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)],[i_0_72])])])])])]) ).
fof(i_0_103,plain,
! [X192,X193,X194,X195,X196,X197,X198,X199] :
( ( ~ in(X195,X194)
| in(X195,X192)
| in(X195,X193)
| X194 != set_union2(X192,X193) )
& ( ~ in(X196,X192)
| in(X196,X194)
| X194 != set_union2(X192,X193) )
& ( ~ in(X196,X193)
| in(X196,X194)
| X194 != set_union2(X192,X193) )
& ( ~ in(esk5_3(X197,X198,X199),X197)
| ~ in(esk5_3(X197,X198,X199),X199)
| X199 = set_union2(X197,X198) )
& ( ~ in(esk5_3(X197,X198,X199),X198)
| ~ in(esk5_3(X197,X198,X199),X199)
| X199 = set_union2(X197,X198) )
& ( in(esk5_3(X197,X198,X199),X199)
| in(esk5_3(X197,X198,X199),X197)
| in(esk5_3(X197,X198,X199),X198)
| X199 = set_union2(X197,X198) ) ),
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)],[d2_xboole_0])])])])])]) ).
fof(i_0_104,plain,
! [X183,X184,X185,X186,X187,X188,X189,X190] :
( ( ~ in(X186,X185)
| X186 = X183
| X186 = X184
| X185 != unordered_pair(X183,X184) )
& ( X187 != X183
| in(X187,X185)
| X185 != unordered_pair(X183,X184) )
& ( X187 != X184
| in(X187,X185)
| X185 != unordered_pair(X183,X184) )
& ( esk4_3(X188,X189,X190) != X188
| ~ in(esk4_3(X188,X189,X190),X190)
| X190 = unordered_pair(X188,X189) )
& ( esk4_3(X188,X189,X190) != X189
| ~ in(esk4_3(X188,X189,X190),X190)
| X190 = unordered_pair(X188,X189) )
& ( in(esk4_3(X188,X189,X190),X190)
| esk4_3(X188,X189,X190) = X188
| esk4_3(X188,X189,X190) = X189
| X190 = unordered_pair(X188,X189) ) ),
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)],[d2_tarski])])])])])]) ).
cnf(i_0_105,plain,
( in(esk7_3(X1,X2,X3),X1)
| in(esk7_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_106,plain,
( in(esk7_3(X1,X2,X3),X2)
| in(esk7_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_107,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_73]) ).
cnf(i_0_108,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
cnf(i_0_109,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_75]) ).
cnf(i_0_110,lemma,
( disjoint(X1,X2)
| in(esk15_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
fof(i_0_111,plain,
! [X176,X177,X178,X179,X180,X181] :
( ( ~ in(X178,X177)
| subset(X178,X176)
| X177 != powerset(X176) )
& ( ~ subset(X179,X176)
| in(X179,X177)
| X177 != powerset(X176) )
& ( ~ in(esk3_2(X180,X181),X181)
| ~ subset(esk3_2(X180,X181),X180)
| X181 = powerset(X180) )
& ( in(esk3_2(X180,X181),X181)
| subset(esk3_2(X180,X181),X180)
| X181 = powerset(X180) ) ),
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])])])])])]) ).
cnf(i_0_112,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_76]) ).
cnf(i_0_113,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_77]) ).
fof(i_0_114,plain,
! [X274,X275] :
( ( ~ in(esk13_2(X274,X275),X274)
| ~ in(esk13_2(X274,X275),X275)
| X274 = X275 )
& ( in(esk13_2(X274,X275),X274)
| in(esk13_2(X274,X275),X275)
| X274 = X275 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_115,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_116,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_78]) ).
cnf(i_0_117,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
cnf(i_0_118,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_119,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_120,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_80]) ).
fof(i_0_121,lemma,
! [X278,X279,X280] :
( ~ subset(X278,X279)
| subset(set_difference(X278,X280),set_difference(X279,X280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_122,lemma,
! [X325,X326,X327] :
( ~ subset(X325,X326)
| ~ subset(X327,X326)
| subset(set_union2(X325,X327),X326) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(i_0_123,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
cnf(i_0_124,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
fof(i_0_125,plain,
! [X201,X202,X203,X204,X205] :
( ( ~ subset(X201,X202)
| ~ in(X203,X201)
| in(X203,X202) )
& ( in(esk6_2(X204,X205),X204)
| subset(X204,X205) )
& ( ~ in(esk6_2(X204,X205),X205)
| subset(X204,X205) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(i_0_126,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]) ).
cnf(i_0_127,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_84]) ).
cnf(i_0_128,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
fof(i_0_129,lemma,
! [X288,X289,X291,X292,X293] :
( ( in(esk14_2(X288,X289),X288)
| disjoint(X288,X289) )
& ( in(esk14_2(X288,X289),X289)
| disjoint(X288,X289) )
& ( ~ in(X293,X291)
| ~ in(X293,X292)
| ~ disjoint(X291,X292) ) ),
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)],[i_0_85])])])])])]) ).
cnf(i_0_130,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
cnf(i_0_131,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]) ).
fof(i_0_132,lemma,
! [X297,X298] :
( ~ subset(X297,X298)
| X298 = set_union2(X297,set_difference(X298,X297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_133,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]) ).
cnf(i_0_134,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]) ).
fof(i_0_135,lemma,
! [X310,X311,X312] :
( ~ subset(X310,X311)
| ~ disjoint(X311,X312)
| disjoint(X310,X312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_136,lemma,
! [X265,X266,X267] :
( ~ subset(X265,X266)
| ~ subset(X266,X267)
| subset(X265,X267) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_137,lemma,
! [X295,X296] : set_difference(set_union2(X295,X296),X296) = set_difference(X295,X296),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_138,lemma,
! [X285,X286] : set_union2(X285,set_difference(X286,X285)) = set_union2(X285,X286),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_139,plain,
! [X229,X230] :
( empty(X229)
| ~ empty(set_union2(X229,X230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_87])]) ).
fof(i_0_140,plain,
! [X231,X232] :
( empty(X231)
| ~ empty(set_union2(X232,X231)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_88])]) ).
cnf(i_0_141,negated_conjecture,
set_union2(singleton(esk9_0),esk10_0) != esk10_0,
inference(split_conjunct,[status(thm)],[i_0_89]) ).
cnf(i_0_142,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
fof(i_0_143,lemma,
! [X253,X254,X255,X256] :
( unordered_pair(X253,X254) != unordered_pair(X255,X256)
| X253 = X255
| X253 = X256 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
fof(i_0_144,plain,
! [X163,X164] :
( ( subset(X163,X164)
| X163 != X164 )
& ( subset(X164,X163)
| X163 != X164 )
& ( ~ subset(X163,X164)
| ~ subset(X164,X163)
| X163 = X164 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(i_0_145,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_146,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_91]) ).
fof(i_0_147,lemma,
! [X308,X309] :
( ~ subset(X308,X309)
| ~ proper_subset(X309,X308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_148,plain,
! [X155,X156] :
( ~ proper_subset(X155,X156)
| ~ proper_subset(X156,X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_92])]) ).
fof(i_0_149,plain,
! [X153,X154] :
( ~ in(X153,X154)
| ~ in(X154,X153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_93])]) ).
cnf(i_0_150,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
cnf(i_0_151,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
cnf(i_0_152,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_94]) ).
fof(i_0_153,lemma,
! [X281,X282] : subset(set_difference(X281,X282),X281),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_154,lemma,
! [X319,X320] : subset(X319,set_union2(X319,X320)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_155,plain,
! [X227,X228] :
( ( subset(X227,X228)
| ~ proper_subset(X227,X228) )
& ( X227 != X228
| ~ proper_subset(X227,X228) )
& ( ~ subset(X227,X228)
| X227 = X228
| proper_subset(X227,X228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_156,lemma,
! [X321,X322] :
( ( ~ disjoint(X321,X322)
| set_difference(X321,X322) = X321 )
& ( set_difference(X321,X322) != X321
| disjoint(X321,X322) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_157,lemma,
! [X257,X258] :
( ~ subset(X257,X258)
| set_union2(X257,X258) = X258 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_158,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_95]) ).
fof(i_0_159,plain,
! [X251,X252] :
( ~ disjoint(X251,X252)
| disjoint(X252,X251) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_160,lemma,
! [X283,X284] :
( ( set_difference(X283,X284) != empty_set
| subset(X283,X284) )
& ( ~ subset(X283,X284)
| set_difference(X283,X284) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_161,lemma,
! [X241,X242] :
( ( set_difference(X241,X242) != empty_set
| subset(X241,X242) )
& ( ~ subset(X241,X242)
| set_difference(X241,X242) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_162,plain,
! [X317,X318] :
( ~ in(X317,X318)
| ~ empty(X318) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_163,plain,
! [X159,X160] : set_union2(X159,X160) = set_union2(X160,X159),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_164,plain,
! [X157,X158] : unordered_pair(X157,X158) = unordered_pair(X158,X157),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_165,plain,
! [X172,X173,X174] :
( ( X172 != empty_set
| ~ in(X173,X172) )
& ( in(esk2_1(X174),X174)
| X174 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_96])])])])]) ).
fof(i_0_166,plain,
! [X235] : ~ proper_subset(X235,X235),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_97])]) ).
cnf(i_0_167,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_98]) ).
fof(i_0_168,lemma,
! [X294] :
( ~ subset(X294,empty_set)
| X294 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_169,plain,
! [X323,X324] :
( ~ empty(X323)
| X323 = X324
| ~ empty(X324) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_170,plain,
! [X233] : set_union2(X233,X233) = X233,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_171,plain,
! [X250] : subset(X250,X250),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_172,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_173,plain,
! [X287] : set_difference(X287,empty_set) = X287,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_174,plain,
! [X264] : set_union2(X264,empty_set) = X264,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_175,lemma,
! [X277] : subset(empty_set,X277),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_176,plain,
! [X301] : set_difference(empty_set,X301) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_177,plain,
! [X314] :
( ~ empty(X314)
| X314 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_178,plain,
~ empty(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_99])]) ).
fof(i_0_179,plain,
empty(esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_180,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk7_3(X1,X2,X3),X3)
| ~ in(esk7_3(X1,X2,X3),X2)
| ~ in(esk7_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_100,c_0_101]),
[final] ).
cnf(i_0_181,plain,
( in(esk8_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(esk8_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_182,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_183,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk5_3(X1,X2,X3),X2)
| ~ in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_184,plain,
( in(esk5_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1)
| in(esk5_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_185,plain,
( in(esk8_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_186,plain,
( X3 = unordered_pair(X1,X2)
| esk4_3(X1,X2,X3) != X1
| ~ in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_187,plain,
( X3 = unordered_pair(X1,X2)
| esk4_3(X1,X2,X3) != X2
| ~ in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_188,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk7_3(X1,X2,X3),X3)
| in(esk7_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_105,c_0_101]),
[final] ).
cnf(i_0_189,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk7_3(X1,X2,X3),X3)
| in(esk7_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_106,c_0_101]),
[final] ).
cnf(i_0_190,plain,
( in(esk8_3(X1,X2,X3),X1)
| in(esk8_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_191,plain,
( in(esk4_3(X1,X2,X3),X3)
| esk4_3(X1,X2,X3) = X1
| esk4_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_192,lemma,
( subset(set_difference(X1,set_difference(X1,X3)),set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_107,c_0_101]),c_0_101]),
[final] ).
cnf(i_0_193,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_108,c_0_101]),
[final] ).
cnf(i_0_194,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_109,c_0_101]),
[final] ).
cnf(i_0_195,lemma,
( disjoint(X1,X2)
| in(esk15_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_110,c_0_101]),
[final] ).
cnf(i_0_196,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_197,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_112,c_0_113]),
[final] ).
cnf(i_0_198,plain,
( X1 = X2
| ~ in(esk13_2(X1,X2),X1)
| ~ in(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_199,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_115,c_0_101]),
[final] ).
cnf(i_0_200,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_116,c_0_113]),c_0_113]),
[final] ).
cnf(i_0_201,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_117,c_0_113]),
[final] ).
cnf(i_0_202,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_118,c_0_101]),
[final] ).
cnf(i_0_203,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_119,c_0_101]),
[final] ).
cnf(i_0_204,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_120,c_0_101]),
[final] ).
cnf(i_0_205,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_206,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_207,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_208,plain,
( in(esk13_2(X1,X2),X1)
| in(esk13_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_209,lemma,
( X1 = empty_set
| X1 = unordered_pair(X2,X2)
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_123,c_0_113]),c_0_113]),
[final] ).
cnf(i_0_210,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_124,c_0_101]),c_0_101]),
[final] ).
cnf(i_0_211,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_212,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_126,c_0_113]),
[final] ).
cnf(i_0_213,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_127,c_0_101]),
[final] ).
cnf(i_0_214,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_215,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_216,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_128,c_0_113]),
[final] ).
cnf(i_0_217,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_218,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_219,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_130,c_0_113]),c_0_113]),
[final] ).
cnf(i_0_220,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_131,c_0_101]),
[final] ).
cnf(i_0_221,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_222,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_133,c_0_113]),
[final] ).
cnf(i_0_223,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_134,c_0_101]),
[final] ).
cnf(i_0_224,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_225,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_226,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_227,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_228,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_229,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_230,lemma,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_231,lemma,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_232,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_233,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_137]),
[final] ).
cnf(i_0_234,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_235,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_236,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_140]),
[final] ).
cnf(i_0_237,negated_conjecture,
set_union2(unordered_pair(esk9_0,esk9_0),esk10_0) != esk10_0,
inference(rw,[status(thm)],[i_0_141,c_0_113]),
[final] ).
cnf(i_0_238,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_239,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_142,c_0_113]),
[final] ).
cnf(i_0_240,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_143]),
[final] ).
cnf(i_0_241,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_242,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_145,c_0_113]),
[final] ).
cnf(i_0_243,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_146,c_0_113]),
[final] ).
cnf(i_0_244,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_245,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_246,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_247,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_248,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_249,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_150,c_0_113]),
[final] ).
cnf(i_0_250,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_151,c_0_113]),
[final] ).
cnf(i_0_251,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_252,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_253,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_152,c_0_101]),
[final] ).
cnf(i_0_254,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_255,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_256,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_257,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_258,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_259,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_260,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_158,c_0_101]),
[final] ).
cnf(i_0_261,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_262,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_263,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_264,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_265,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_266,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_267,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_268,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_269,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_270,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_271,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_272,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_273,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_167,c_0_113]),
[final] ).
cnf(i_0_274,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_275,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_276,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_277,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_278,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_279,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_170]),
[final] ).
cnf(i_0_280,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_281,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_172,c_0_113]),
[final] ).
cnf(i_0_282,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_173]),
[final] ).
cnf(i_0_283,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_284,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_175]),
[final] ).
cnf(i_0_285,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_286,negated_conjecture,
in(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_287,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_288,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_289,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_290,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_291,axiom,
X1 = X1 ).
cnf(i_0_292,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_293,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_294,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_298,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_300,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_301,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_302,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_303,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_304,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_305,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_306,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_307,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_308,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_309,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_310,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_311,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_312,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_313,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_314,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_291_001,axiom,
X1 = X1 ).
cnf(i_0_292_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_293_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_294_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_295_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_296_006,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_297_007,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_298_008,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_299_009,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_300_010,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_301_011,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_302_012,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_303_013,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_304_014,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_305_015,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_306_016,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_307_017,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_308_018,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_309_019,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_310_020,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_311_021,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_312_022,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_313_023,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_314_024,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_315,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[199]) ).
cnf(i_0_316,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[203]) ).
cnf(i_0_317,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[214]) ).
cnf(i_0_318,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[215]) ).
cnf(i_0_319,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[217]) ).
cnf(i_0_320,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[224]) ).
cnf(i_0_321,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[225]) ).
cnf(i_0_322,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[226]) ).
cnf(i_0_323,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[238]) ).
cnf(i_0_324,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[239]) ).
cnf(i_0_325,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[240]) ).
cnf(i_0_326,plain,
X1 = X1,
inference(equality_inference,[],[242]) ).
cnf(i_0_327,plain,
X1 = X1,
inference(equality_inference,[],[243]) ).
cnf(i_0_328,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[244]) ).
cnf(i_0_329,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[245]) ).
cnf(i_0_330,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[249]) ).
cnf(i_0_331,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[270]) ).
cnf(i_0_332,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[271]) ).
cnf(i_0_333,plain,
subset(X1,X1),
inference(equality_inference,[],[276]) ).
cnf(i_0_334,plain,
subset(X1,X1),
inference(equality_inference,[],[277]) ).
cnf(i_0_335,plain,
~ in(esk10_0,esk9_0),
inference(scs_inference,[],[i_0_286,i_0_248]) ).
cnf(i_0_336,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_248]) ).
cnf(i_0_337,plain,
~ subset(unordered_pair(esk9_0,esk9_0),esk10_0),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_248,i_0_259]) ).
cnf(i_0_338,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_339,plain,
~ in(X1,esk11_0),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_289,i_0_248,i_0_259,i_0_267]) ).
cnf(i_0_340,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_267]) ).
cnf(i_0_341,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271]) ).
cnf(i_0_342,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_343,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_344,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316]) ).
cnf(i_0_345,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_346,plain,
~ in(esk9_0,set_difference(X1,esk10_0)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319]) ).
cnf(i_0_347,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_348,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320]) ).
cnf(i_0_349,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_320]) ).
cnf(i_0_350,plain,
in(esk9_0,set_union2(esk10_0,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321]) ).
cnf(i_0_351,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_321]) ).
cnf(i_0_352,plain,
in(esk9_0,set_union2(X1,esk10_0)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322]) ).
cnf(i_0_353,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_322]) ).
cnf(i_0_354,plain,
~ in(set_union2(unordered_pair(esk9_0,esk9_0),esk10_0),unordered_pair(esk10_0,esk10_0)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324]) ).
cnf(i_0_355,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_324]) ).
cnf(i_0_356,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_342,i_0_289,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292]) ).
cnf(i_0_357,plain,
disjoint(empty_set,empty_set),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213]) ).
cnf(i_0_358,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rename_variables,[],[i_0_253]) ).
cnf(i_0_359,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_213]) ).
cnf(i_0_360,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249]) ).
cnf(i_0_361,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_362,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_249]) ).
cnf(i_0_363,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329]) ).
cnf(i_0_364,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_365,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195]) ).
cnf(i_0_366,plain,
( in(esk15_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_195]) ).
cnf(i_0_367,plain,
in(X1,unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212]) ).
cnf(i_0_368,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_369,plain,
( ~ subset(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_370,plain,
disjoint(esk11_0,X1),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230]) ).
cnf(i_0_371,plain,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_372,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231]) ).
cnf(i_0_373,plain,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_231]) ).
cnf(i_0_374,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_358,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257]) ).
cnf(i_0_375,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_257]) ).
cnf(i_0_376,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_358,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261]) ).
cnf(i_0_377,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_261]) ).
cnf(i_0_378,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264]) ).
cnf(i_0_379,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_264]) ).
cnf(i_0_380,plain,
in(esk2_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274]) ).
cnf(i_0_381,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(rename_variables,[],[i_0_274]) ).
cnf(i_0_382,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_361,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276]) ).
cnf(i_0_383,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_276]) ).
cnf(i_0_384,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_361,i_0_268,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277]) ).
cnf(i_0_385,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_277]) ).
cnf(i_0_386,plain,
~ empty(unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_361,i_0_268,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287]) ).
cnf(i_0_387,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_287]) ).
cnf(i_0_388,plain,
~ in(esk15_2(X1,empty_set),set_difference(set_difference(X2,set_difference(X2,empty_set)),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_361,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203]) ).
cnf(i_0_389,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_390,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_391,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_203]) ).
cnf(i_0_392,plain,
~ in(esk9_0,set_union2(set_difference(X1,esk10_0),set_difference(X1,esk10_0))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_280,i_0_279,i_0_342,i_0_361,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217]) ).
cnf(i_0_393,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_394,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_217]) ).
cnf(i_0_395,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224]) ).
cnf(i_0_396,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_397,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_224]) ).
cnf(i_0_398,plain,
in(esk9_0,set_union2(set_union2(esk10_0,X1),set_union2(esk10_0,X1))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225]) ).
cnf(i_0_399,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_400,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_225]) ).
cnf(i_0_401,plain,
in(esk9_0,set_union2(set_union2(X1,esk10_0),set_union2(X1,esk10_0))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226]) ).
cnf(i_0_402,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_403,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_226]) ).
cnf(i_0_404,plain,
~ subset(esk10_0,empty_set),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229]) ).
cnf(i_0_405,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_406,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_407,plain,
~ in(set_union2(unordered_pair(esk9_0,esk9_0),esk10_0),set_union2(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,esk10_0))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_268,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239]) ).
cnf(i_0_408,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_409,plain,
( X1 != unordered_pair(X2,X2)
| ~ in(X3,X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_410,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241]) ).
cnf(i_0_411,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_254]) ).
cnf(i_0_412,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_241]) ).
cnf(i_0_413,plain,
~ in(unordered_pair(esk9_0,esk9_0),set_union2(powerset(esk10_0),powerset(esk10_0))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244]) ).
cnf(i_0_414,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_415,plain,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_244]) ).
cnf(i_0_416,plain,
in(esk9_0,set_difference(esk10_0,empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318]) ).
cnf(i_0_417,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_418,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_318]) ).
cnf(i_0_419,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323]) ).
cnf(i_0_420,plain,
( ~ in(X1,unordered_pair(X2,X3))
| X1 = X2
| X1 = X3 ),
inference(rename_variables,[],[i_0_323]) ).
cnf(i_0_421,plain,
set_union2(unordered_pair(esk9_0,esk9_0),esk10_0) != set_union2(esk10_0,esk10_0),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293]) ).
cnf(i_0_422,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_423,plain,
~ in(set_union2(esk10_0,esk10_0),esk9_0),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306]) ).
cnf(i_0_424,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_425,plain,
~ in(esk10_0,set_union2(esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_268,i_0_254,i_0_282,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307]) ).
cnf(i_0_426,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_427,plain,
in(X1,set_difference(powerset(X1),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_368,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_268,i_0_254,i_0_282,i_0_389,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245]) ).
cnf(i_0_428,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_429,plain,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(rename_variables,[],[i_0_245]) ).
cnf(i_0_430,plain,
esk11_0 != esk12_0,
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_280,i_0_368,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_268,i_0_254,i_0_282,i_0_389,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312]) ).
cnf(i_0_431,plain,
~ proper_subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_280,i_0_368,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313]) ).
cnf(i_0_432,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_433,plain,
~ proper_subset(X1,set_union2(X1,X1)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314]) ).
cnf(i_0_434,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_435,plain,
~ subset(unordered_pair(esk9_0,esk9_0),empty_set),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228]) ).
cnf(i_0_436,plain,
subset(empty_set,X1),
inference(rename_variables,[],[i_0_284]) ).
cnf(i_0_437,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_228]) ).
cnf(i_0_438,plain,
in(set_union2(X1,X1),set_difference(unordered_pair(X1,X2),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251]) ).
cnf(i_0_439,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_440,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_251]) ).
cnf(i_0_441,plain,
in(set_union2(X1,X1),set_difference(unordered_pair(X2,X1),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252]) ).
cnf(i_0_442,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_443,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_252]) ).
cnf(i_0_444,plain,
~ subset(set_union2(unordered_pair(esk9_0,esk9_0),unordered_pair(esk9_0,esk9_0)),esk10_0),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308]) ).
cnf(i_0_445,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_446,plain,
~ subset(unordered_pair(esk9_0,esk9_0),set_union2(esk10_0,esk10_0)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309]) ).
cnf(i_0_447,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_448,plain,
in(esk9_0,set_difference(set_difference(esk10_0,set_difference(esk10_0,esk10_0)),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_442,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309,i_0_199]) ).
cnf(i_0_449,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_450,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X3)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(rename_variables,[],[i_0_199]) ).
cnf(i_0_451,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_417,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_447,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_442,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309,i_0_199,i_0_214]) ).
cnf(i_0_452,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_453,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_214]) ).
cnf(i_0_454,plain,
in(esk9_0,set_difference(set_difference(esk10_0,empty_set),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_417,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_447,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_442,i_0_449,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309,i_0_199,i_0_214,i_0_215]) ).
cnf(i_0_455,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_456,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_457,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_215]) ).
cnf(i_0_458,plain,
~ in(set_union2(unordered_pair(esk9_0,esk9_0),esk10_0),set_difference(unordered_pair(esk10_0,esk10_0),empty_set)),
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_417,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_447,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_442,i_0_449,i_0_455,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309,i_0_199,i_0_214,i_0_215,i_0_238]) ).
cnf(i_0_459,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_282]) ).
cnf(i_0_460,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_238]) ).
cnf(i_0_461,plain,
$false,
inference(scs_inference,[],[i_0_237,i_0_286,i_0_332,i_0_390,i_0_405,i_0_417,i_0_272,i_0_432,i_0_280,i_0_368,i_0_284,i_0_279,i_0_342,i_0_361,i_0_393,i_0_396,i_0_399,i_0_402,i_0_408,i_0_414,i_0_422,i_0_424,i_0_426,i_0_445,i_0_447,i_0_268,i_0_254,i_0_282,i_0_389,i_0_428,i_0_439,i_0_442,i_0_449,i_0_455,i_0_288,i_0_289,i_0_273,i_0_253,i_0_358,i_0_260,i_0_248,i_0_259,i_0_267,i_0_271,i_0_316,i_0_319,i_0_320,i_0_321,i_0_322,i_0_324,i_0_292,i_0_213,i_0_249,i_0_329,i_0_195,i_0_212,i_0_230,i_0_231,i_0_257,i_0_261,i_0_264,i_0_274,i_0_276,i_0_277,i_0_287,i_0_203,i_0_217,i_0_224,i_0_225,i_0_226,i_0_229,i_0_239,i_0_241,i_0_244,i_0_318,i_0_323,i_0_293,i_0_306,i_0_307,i_0_245,i_0_312,i_0_313,i_0_314,i_0_228,i_0_251,i_0_252,i_0_308,i_0_309,i_0_199,i_0_214,i_0_215,i_0_238,i_0_222]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU152+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:45:36 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.30/1.61 % Version : CSE_E---1.7
% 0.30/1.61 % Problem : theBenchmark.p
% 0.30/1.61 % SZS status Theorem for theBenchmark.p
% 0.30/1.61 % SZS output start CNFRefutation
% See solution above
% 0.91/2.27 % Total time : 1.271s
%------------------------------------------------------------------------------