%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU153+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 : n007.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 0.26s 1.58s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_103)
% 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(l25_zfmisc_1,conjecture,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_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(l23_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
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_69,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_70,negated_conjecture,
~ ! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
inference(assume_negation,[status(cth)],[l25_zfmisc_1]) ).
fof(i_0_71,plain,
! [X209,X210,X211,X212,X213,X214,X215,X216] :
( ( in(X212,X209)
| ~ in(X212,X211)
| X211 != set_intersection2(X209,X210) )
& ( in(X212,X210)
| ~ in(X212,X211)
| X211 != set_intersection2(X209,X210) )
& ( ~ in(X213,X209)
| ~ in(X213,X210)
| in(X213,X211)
| X211 != set_intersection2(X209,X210) )
& ( ~ in(esk7_3(X214,X215,X216),X216)
| ~ in(esk7_3(X214,X215,X216),X214)
| ~ in(esk7_3(X214,X215,X216),X215)
| X216 = set_intersection2(X214,X215) )
& ( in(esk7_3(X214,X215,X216),X214)
| in(esk7_3(X214,X215,X216),X216)
| X216 = set_intersection2(X214,X215) )
& ( in(esk7_3(X214,X215,X216),X215)
| in(esk7_3(X214,X215,X216),X216)
| X216 = set_intersection2(X214,X215) ) ),
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_72,lemma,
! [X303,X304] : set_difference(X303,set_difference(X303,X304)) = set_intersection2(X303,X304),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_73,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_74,lemma,
! [X272,X273,X274] :
( ~ subset(X272,X273)
| subset(set_intersection2(X272,X274),set_intersection2(X273,X274)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_75,lemma,
! [X306,X307,X309,X310,X311] :
( ( disjoint(X306,X307)
| in(esk15_2(X306,X307),set_intersection2(X306,X307)) )
& ( ~ in(X311,set_intersection2(X309,X310))
| ~ disjoint(X309,X310) ) ),
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_69])])])])]) ).
fof(i_0_76,lemma,
! [X265,X266,X267] :
( ~ subset(X265,X266)
| ~ subset(X265,X267)
| subset(X265,set_intersection2(X266,X267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_77,lemma,
! [X247,X248,X249] :
( ~ subset(X247,X248)
| in(X249,X247)
| subset(X247,set_difference(X248,singleton(X249))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_78,lemma,
! [X317] : unordered_pair(X317,X317) = singleton(X317),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_79,lemma,
! [X319,X320] :
( ~ subset(singleton(X319),singleton(X320))
| X319 = X320 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_80,plain,
! [X167,X168,X169,X170,X171,X172] :
( ( ~ in(X169,X168)
| X169 = X167
| X168 != singleton(X167) )
& ( X170 != X167
| in(X170,X168)
| X168 != singleton(X167) )
& ( ~ in(esk1_2(X171,X172),X172)
| esk1_2(X171,X172) != X171
| X172 = singleton(X171) )
& ( in(esk1_2(X171,X172),X172)
| esk1_2(X171,X172) = X171
| X172 = singleton(X171) ) ),
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_81,lemma,
! [X263,X264] : subset(set_intersection2(X263,X264),X263),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_82,lemma,
! [X250,X251] :
( ( ~ subset(X250,singleton(X251))
| X250 = empty_set
| X250 = singleton(X251) )
& ( X250 != empty_set
| subset(X250,singleton(X251)) )
& ( X250 != singleton(X251)
| subset(X250,singleton(X251)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_83,plain,
! [X163,X164] : set_intersection2(X163,X164) = set_intersection2(X164,X163),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_84,lemma,
! [X243,X244] :
( ( ~ subset(singleton(X243),X244)
| in(X243,X244) )
& ( ~ in(X243,X244)
| subset(singleton(X243),X244) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_85,plain,
! [X227,X228] :
( ( ~ disjoint(X227,X228)
| set_intersection2(X227,X228) = empty_set )
& ( set_intersection2(X227,X228) != empty_set
| disjoint(X227,X228) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_86,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_87,lemma,
! [X239,X240] :
( ~ in(X239,X240)
| set_union2(singleton(X239),X240) = X240 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_88,lemma,
! [X275,X276] :
( ~ subset(X275,X276)
| set_intersection2(X275,X276) = X275 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_89,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_90,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_91,lemma,
! [X332,X333,X334] :
( singleton(X332) != unordered_pair(X333,X334)
| X332 = X333 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_92,lemma,
! [X335,X336,X337] :
( singleton(X335) != unordered_pair(X336,X337)
| X336 = X337 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_93,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_94,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_95,plain,
! [X236] : set_intersection2(X236,X236) = X236,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_96,plain,
! [X277] : set_intersection2(X277,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_97,negated_conjecture,
( disjoint(singleton(esk9_0),esk10_0)
& in(esk9_0,esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_70])])]) ).
fof(i_0_98,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_99,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_100,lemma,
! [X238] : singleton(X238) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_101,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_102,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_71]) ).
cnf(i_0_103,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_72]) ).
fof(i_0_104,plain,
! [X218,X219,X220,X221,X222,X223,X224,X225] :
( ( in(X221,X218)
| ~ in(X221,X220)
| X220 != set_difference(X218,X219) )
& ( ~ in(X221,X219)
| ~ in(X221,X220)
| X220 != set_difference(X218,X219) )
& ( ~ in(X222,X218)
| in(X222,X219)
| in(X222,X220)
| X220 != set_difference(X218,X219) )
& ( ~ in(esk8_3(X223,X224,X225),X225)
| ~ in(esk8_3(X223,X224,X225),X223)
| in(esk8_3(X223,X224,X225),X224)
| X225 = set_difference(X223,X224) )
& ( in(esk8_3(X223,X224,X225),X223)
| in(esk8_3(X223,X224,X225),X225)
| X225 = set_difference(X223,X224) )
& ( ~ in(esk8_3(X223,X224,X225),X224)
| in(esk8_3(X223,X224,X225),X225)
| X225 = set_difference(X223,X224) ) ),
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_73])])])])])]) ).
fof(i_0_105,plain,
! [X194,X195,X196,X197,X198,X199,X200,X201] :
( ( ~ in(X197,X196)
| in(X197,X194)
| in(X197,X195)
| X196 != set_union2(X194,X195) )
& ( ~ in(X198,X194)
| in(X198,X196)
| X196 != set_union2(X194,X195) )
& ( ~ in(X198,X195)
| in(X198,X196)
| X196 != set_union2(X194,X195) )
& ( ~ in(esk5_3(X199,X200,X201),X199)
| ~ in(esk5_3(X199,X200,X201),X201)
| X201 = set_union2(X199,X200) )
& ( ~ in(esk5_3(X199,X200,X201),X200)
| ~ in(esk5_3(X199,X200,X201),X201)
| X201 = set_union2(X199,X200) )
& ( in(esk5_3(X199,X200,X201),X201)
| in(esk5_3(X199,X200,X201),X199)
| in(esk5_3(X199,X200,X201),X200)
| X201 = set_union2(X199,X200) ) ),
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_106,plain,
! [X185,X186,X187,X188,X189,X190,X191,X192] :
( ( ~ in(X188,X187)
| X188 = X185
| X188 = X186
| X187 != unordered_pair(X185,X186) )
& ( X189 != X185
| in(X189,X187)
| X187 != unordered_pair(X185,X186) )
& ( X189 != X186
| in(X189,X187)
| X187 != unordered_pair(X185,X186) )
& ( esk4_3(X190,X191,X192) != X190
| ~ in(esk4_3(X190,X191,X192),X192)
| X192 = unordered_pair(X190,X191) )
& ( esk4_3(X190,X191,X192) != X191
| ~ in(esk4_3(X190,X191,X192),X192)
| X192 = unordered_pair(X190,X191) )
& ( in(esk4_3(X190,X191,X192),X192)
| esk4_3(X190,X191,X192) = X190
| esk4_3(X190,X191,X192) = X191
| X192 = unordered_pair(X190,X191) ) ),
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_107,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_71]) ).
cnf(i_0_108,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_71]) ).
cnf(i_0_109,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
cnf(i_0_110,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_75]) ).
cnf(i_0_111,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_76]) ).
cnf(i_0_112,lemma,
( disjoint(X1,X2)
| in(esk15_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_75]) ).
fof(i_0_113,plain,
! [X178,X179,X180,X181,X182,X183] :
( ( ~ in(X180,X179)
| subset(X180,X178)
| X179 != powerset(X178) )
& ( ~ subset(X181,X178)
| in(X181,X179)
| X179 != powerset(X178) )
& ( ~ in(esk3_2(X182,X183),X183)
| ~ subset(esk3_2(X182,X183),X182)
| X183 = powerset(X182) )
& ( in(esk3_2(X182,X183),X183)
| subset(esk3_2(X182,X183),X182)
| X183 = powerset(X182) ) ),
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_114,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_77]) ).
cnf(i_0_115,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_78]) ).
fof(i_0_116,plain,
! [X278,X279] :
( ( ~ in(esk13_2(X278,X279),X278)
| ~ in(esk13_2(X278,X279),X279)
| X278 = X279 )
& ( in(esk13_2(X278,X279),X278)
| in(esk13_2(X278,X279),X279)
| X278 = X279 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_117,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_71]) ).
cnf(i_0_118,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
cnf(i_0_119,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_80]) ).
cnf(i_0_120,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_71]) ).
cnf(i_0_121,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]) ).
cnf(i_0_122,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
fof(i_0_123,lemma,
! [X282,X283,X284] :
( ~ subset(X282,X283)
| subset(set_difference(X282,X284),set_difference(X283,X284)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_124,lemma,
! [X329,X330,X331] :
( ~ subset(X329,X330)
| ~ subset(X331,X330)
| subset(set_union2(X329,X331),X330) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(i_0_125,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
cnf(i_0_126,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_83]) ).
fof(i_0_127,plain,
! [X203,X204,X205,X206,X207] :
( ( ~ subset(X203,X204)
| ~ in(X205,X203)
| in(X205,X204) )
& ( in(esk6_2(X206,X207),X206)
| subset(X206,X207) )
& ( ~ in(esk6_2(X206,X207),X207)
| subset(X206,X207) ) ),
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_128,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]) ).
cnf(i_0_129,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_85]) ).
cnf(i_0_130,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]) ).
fof(i_0_131,lemma,
! [X292,X293,X295,X296,X297] :
( ( in(esk14_2(X292,X293),X292)
| disjoint(X292,X293) )
& ( in(esk14_2(X292,X293),X293)
| disjoint(X292,X293) )
& ( ~ in(X297,X295)
| ~ in(X297,X296)
| ~ disjoint(X295,X296) ) ),
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_86])])])])])]) ).
cnf(i_0_132,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
cnf(i_0_133,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]) ).
cnf(i_0_134,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]) ).
fof(i_0_135,lemma,
! [X301,X302] :
( ~ subset(X301,X302)
| X302 = set_union2(X301,set_difference(X302,X301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_136,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]) ).
cnf(i_0_137,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]) ).
fof(i_0_138,lemma,
! [X314,X315,X316] :
( ~ subset(X314,X315)
| ~ disjoint(X315,X316)
| disjoint(X314,X316) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_139,lemma,
! [X269,X270,X271] :
( ~ subset(X269,X270)
| ~ subset(X270,X271)
| subset(X269,X271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_140,lemma,
! [X299,X300] : set_difference(set_union2(X299,X300),X300) = set_difference(X299,X300),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_141,lemma,
! [X289,X290] : set_union2(X289,set_difference(X290,X289)) = set_union2(X289,X290),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_142,plain,
! [X231,X232] :
( empty(X231)
| ~ empty(set_union2(X231,X232)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_89])]) ).
fof(i_0_143,plain,
! [X233,X234] :
( empty(X233)
| ~ empty(set_union2(X234,X233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_90])]) ).
cnf(i_0_144,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_80]) ).
fof(i_0_145,lemma,
! [X257,X258,X259,X260] :
( unordered_pair(X257,X258) != unordered_pair(X259,X260)
| X257 = X259
| X257 = X260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
fof(i_0_146,plain,
! [X165,X166] :
( ( subset(X165,X166)
| X165 != X166 )
& ( subset(X166,X165)
| X165 != X166 )
& ( ~ subset(X165,X166)
| ~ subset(X166,X165)
| X165 = X166 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(i_0_147,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_91]) ).
cnf(i_0_148,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
fof(i_0_149,lemma,
! [X312,X313] :
( ~ subset(X312,X313)
| ~ proper_subset(X313,X312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_150,plain,
! [X157,X158] :
( ~ proper_subset(X157,X158)
| ~ proper_subset(X158,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_93])]) ).
fof(i_0_151,plain,
! [X155,X156] :
( ~ in(X155,X156)
| ~ in(X156,X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_94])]) ).
cnf(i_0_152,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
cnf(i_0_153,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]) ).
cnf(i_0_154,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_95]) ).
fof(i_0_155,lemma,
! [X285,X286] : subset(set_difference(X285,X286),X285),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_156,lemma,
! [X323,X324] : subset(X323,set_union2(X323,X324)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_157,plain,
! [X229,X230] :
( ( subset(X229,X230)
| ~ proper_subset(X229,X230) )
& ( X229 != X230
| ~ proper_subset(X229,X230) )
& ( ~ subset(X229,X230)
| X229 = X230
| proper_subset(X229,X230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_158,lemma,
! [X325,X326] :
( ( ~ disjoint(X325,X326)
| set_difference(X325,X326) = X325 )
& ( set_difference(X325,X326) != X325
| disjoint(X325,X326) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_159,lemma,
! [X261,X262] :
( ~ subset(X261,X262)
| set_union2(X261,X262) = X262 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_160,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_96]) ).
fof(i_0_161,plain,
! [X255,X256] :
( ~ disjoint(X255,X256)
| disjoint(X256,X255) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_162,lemma,
! [X287,X288] :
( ( set_difference(X287,X288) != empty_set
| subset(X287,X288) )
& ( ~ subset(X287,X288)
| set_difference(X287,X288) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_163,lemma,
! [X245,X246] :
( ( set_difference(X245,X246) != empty_set
| subset(X245,X246) )
& ( ~ subset(X245,X246)
| set_difference(X245,X246) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(i_0_164,negated_conjecture,
disjoint(singleton(esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[i_0_97]) ).
fof(i_0_165,plain,
! [X321,X322] :
( ~ in(X321,X322)
| ~ empty(X322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_166,plain,
! [X161,X162] : set_union2(X161,X162) = set_union2(X162,X161),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_167,plain,
! [X159,X160] : unordered_pair(X159,X160) = unordered_pair(X160,X159),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_168,plain,
! [X174,X175,X176] :
( ( X174 != empty_set
| ~ in(X175,X174) )
& ( in(esk2_1(X176),X176)
| X176 = 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_98])])])])]) ).
fof(i_0_169,plain,
! [X237] : ~ proper_subset(X237,X237),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_99])]) ).
cnf(i_0_170,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_100]) ).
fof(i_0_171,lemma,
! [X298] :
( ~ subset(X298,empty_set)
| X298 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_172,plain,
! [X327,X328] :
( ~ empty(X327)
| X327 = X328
| ~ empty(X328) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_173,plain,
! [X235] : set_union2(X235,X235) = X235,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_174,plain,
! [X254] : subset(X254,X254),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_175,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_176,plain,
! [X291] : set_difference(X291,empty_set) = X291,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_177,plain,
! [X268] : set_union2(X268,empty_set) = X268,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_178,lemma,
! [X281] : subset(empty_set,X281),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_179,plain,
! [X305] : set_difference(empty_set,X305) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_180,plain,
! [X318] :
( ~ empty(X318)
| X318 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_181,plain,
~ empty(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_101])]) ).
fof(i_0_182,plain,
empty(esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_183,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_102,c_0_103]),
[final] ).
cnf(i_0_184,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_104]),
[final] ).
cnf(i_0_185,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_105]),
[final] ).
cnf(i_0_186,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_105]),
[final] ).
cnf(i_0_187,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_105]),
[final] ).
cnf(i_0_188,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_104]),
[final] ).
cnf(i_0_189,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_106]),
[final] ).
cnf(i_0_190,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_106]),
[final] ).
cnf(i_0_191,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_107,c_0_103]),
[final] ).
cnf(i_0_192,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_108,c_0_103]),
[final] ).
cnf(i_0_193,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_104]),
[final] ).
cnf(i_0_194,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_106]),
[final] ).
cnf(i_0_195,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_109,c_0_103]),c_0_103]),
[final] ).
cnf(i_0_196,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_110,c_0_103]),
[final] ).
cnf(i_0_197,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_111,c_0_103]),
[final] ).
cnf(i_0_198,lemma,
( disjoint(X1,X2)
| in(esk15_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_112,c_0_103]),
[final] ).
cnf(i_0_199,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_200,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_114,c_0_115]),
[final] ).
cnf(i_0_201,plain,
( X1 = X2
| ~ in(esk13_2(X1,X2),X1)
| ~ in(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_202,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_117,c_0_103]),
[final] ).
cnf(i_0_203,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_118,c_0_115]),c_0_115]),
[final] ).
cnf(i_0_204,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_119,c_0_115]),
[final] ).
cnf(i_0_205,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_120,c_0_103]),
[final] ).
cnf(i_0_206,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_121,c_0_103]),
[final] ).
cnf(i_0_207,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_122,c_0_103]),
[final] ).
cnf(i_0_208,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_209,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_210,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_211,plain,
( in(esk13_2(X1,X2),X1)
| in(esk13_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_212,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_125,c_0_115]),c_0_115]),
[final] ).
cnf(i_0_213,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_126,c_0_103]),c_0_103]),
[final] ).
cnf(i_0_214,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_215,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_128,c_0_115]),
[final] ).
cnf(i_0_216,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_129,c_0_103]),
[final] ).
cnf(i_0_217,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_218,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_219,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_130,c_0_115]),
[final] ).
cnf(i_0_220,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_221,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_222,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_132,c_0_115]),c_0_115]),
[final] ).
cnf(i_0_223,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_133,c_0_115]),
[final] ).
cnf(i_0_224,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_134,c_0_103]),
[final] ).
cnf(i_0_225,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_226,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_136,c_0_115]),
[final] ).
cnf(i_0_227,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_137,c_0_103]),
[final] ).
cnf(i_0_228,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_229,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_230,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_231,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_232,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_233,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_234,lemma,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_235,lemma,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_236,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_237,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_140]),
[final] ).
cnf(i_0_238,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_239,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_240,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_143]),
[final] ).
cnf(i_0_241,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_242,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_144,c_0_115]),
[final] ).
cnf(i_0_243,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_244,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_245,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_147,c_0_115]),
[final] ).
cnf(i_0_246,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_148,c_0_115]),
[final] ).
cnf(i_0_247,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_248,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_249,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_250,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_251,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_252,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_152,c_0_115]),
[final] ).
cnf(i_0_253,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_153,c_0_115]),
[final] ).
cnf(i_0_254,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_255,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_256,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_154,c_0_103]),
[final] ).
cnf(i_0_257,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_258,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_259,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_260,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_261,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_262,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_263,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_160,c_0_103]),
[final] ).
cnf(i_0_264,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_265,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_266,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_267,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_268,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_269,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_270,negated_conjecture,
disjoint(unordered_pair(esk9_0,esk9_0),esk10_0),
inference(rw,[status(thm)],[i_0_164,c_0_115]),
[final] ).
cnf(i_0_271,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_272,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_273,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_274,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_275,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_276,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_277,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_170,c_0_115]),
[final] ).
cnf(i_0_278,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_279,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_280,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_281,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_282,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_283,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_173]),
[final] ).
cnf(i_0_284,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_285,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_175,c_0_115]),
[final] ).
cnf(i_0_286,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_287,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_288,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_289,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_290,negated_conjecture,
in(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_291,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_292,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_293,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_294,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_295,axiom,
X1 = X1 ).
cnf(i_0_296,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_297,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_298,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_300,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_301,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_302,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_303,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_304,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_305,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_306,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_307,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_308,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_309,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_310,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_311,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_312,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_313,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_314,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_315,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_316,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_317,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_318,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_295_001,axiom,
X1 = X1 ).
cnf(i_0_296_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_297_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_298_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_299_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_300_006,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_301_007,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_302_008,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_303_009,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_304_010,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_305_011,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_306_012,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_307_013,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_308_014,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_309_015,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_310_016,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_311_017,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_312_018,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_313_019,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_314_020,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_315_021,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_316_022,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_317_023,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_318_024,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_319,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[202]) ).
cnf(i_0_320,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[206]) ).
cnf(i_0_321,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[217]) ).
cnf(i_0_322,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[218]) ).
cnf(i_0_323,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[220]) ).
cnf(i_0_324,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[228]) ).
cnf(i_0_325,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[229]) ).
cnf(i_0_326,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[230]) ).
cnf(i_0_327,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[241]) ).
cnf(i_0_328,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[242]) ).
cnf(i_0_329,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[243]) ).
cnf(i_0_330,plain,
X1 = X1,
inference(equality_inference,[],[245]) ).
cnf(i_0_331,plain,
X1 = X1,
inference(equality_inference,[],[246]) ).
cnf(i_0_332,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[247]) ).
cnf(i_0_333,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[248]) ).
cnf(i_0_334,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[252]) ).
cnf(i_0_335,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[274]) ).
cnf(i_0_336,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[275]) ).
cnf(i_0_337,plain,
subset(X1,X1),
inference(equality_inference,[],[280]) ).
cnf(i_0_338,plain,
subset(X1,X1),
inference(equality_inference,[],[281]) ).
cnf(i_0_339,plain,
~ in(esk10_0,esk9_0),
inference(scs_inference,[],[i_0_290,i_0_251]) ).
cnf(i_0_340,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_251]) ).
cnf(i_0_341,plain,
disjoint(esk10_0,unordered_pair(esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_251,i_0_264]) ).
cnf(i_0_342,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_264]) ).
cnf(i_0_343,plain,
~ in(X1,esk11_0),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_293,i_0_251,i_0_264,i_0_271]) ).
cnf(i_0_344,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_345,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275]) ).
cnf(i_0_346,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_283]) ).
cnf(i_0_347,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_275]) ).
cnf(i_0_348,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320]) ).
cnf(i_0_349,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_320]) ).
cnf(i_0_350,plain,
~ in(esk9_0,set_difference(X1,esk10_0)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323]) ).
cnf(i_0_351,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_323]) ).
cnf(i_0_352,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324]) ).
cnf(i_0_353,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_324]) ).
cnf(i_0_354,plain,
in(esk9_0,set_union2(esk10_0,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325]) ).
cnf(i_0_355,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_325]) ).
cnf(i_0_356,plain,
in(esk9_0,set_union2(X1,esk10_0)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326]) ).
cnf(i_0_357,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_326]) ).
cnf(i_0_358,plain,
~ in(unordered_pair(X1,X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_283,i_0_293,i_0_277,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328]) ).
cnf(i_0_359,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_360,plain,
in(X1,unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_284,i_0_283,i_0_293,i_0_277,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215]) ).
cnf(i_0_361,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_284]) ).
cnf(i_0_362,plain,
( ~ subset(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_215]) ).
cnf(i_0_363,plain,
disjoint(empty_set,empty_set),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_284,i_0_283,i_0_293,i_0_277,i_0_256,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216]) ).
cnf(i_0_364,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rename_variables,[],[i_0_256]) ).
cnf(i_0_365,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_216]) ).
cnf(i_0_366,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_284,i_0_283,i_0_293,i_0_277,i_0_256,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234]) ).
cnf(i_0_367,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_368,plain,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_234]) ).
cnf(i_0_369,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_293,i_0_277,i_0_256,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235]) ).
cnf(i_0_370,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_371,plain,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_372,plain,
subset(esk11_0,X1),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_293,i_0_277,i_0_256,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236]) ).
cnf(i_0_373,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_236]) ).
cnf(i_0_374,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252]) ).
cnf(i_0_375,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_283]) ).
cnf(i_0_376,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_252]) ).
cnf(i_0_377,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_364,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260]) ).
cnf(i_0_378,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_379,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267]) ).
cnf(i_0_380,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_267]) ).
cnf(i_0_381,plain,
in(esk2_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278]) ).
cnf(i_0_382,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_383,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333]) ).
cnf(i_0_384,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_333]) ).
cnf(i_0_385,plain,
esk11_0 = empty_set,
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279]) ).
cnf(i_0_386,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_387,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280]) ).
cnf(i_0_388,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_389,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281]) ).
cnf(i_0_390,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_391,plain,
~ empty(unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281,i_0_291]) ).
cnf(i_0_392,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_291]) ).
cnf(i_0_393,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281,i_0_291,i_0_296]) ).
cnf(i_0_394,plain,
~ in(X1,set_difference(set_difference(X2,set_difference(X2,empty_set)),empty_set)),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_370,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_286,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281,i_0_291,i_0_296,i_0_206]) ).
cnf(i_0_395,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_286]) ).
cnf(i_0_396,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_206]) ).
cnf(i_0_397,plain,
~ in(esk9_0,set_union2(set_difference(X1,esk10_0),set_difference(X1,esk10_0))),
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_370,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_286,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281,i_0_291,i_0_296,i_0_206,i_0_220]) ).
cnf(i_0_398,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_283]) ).
cnf(i_0_399,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_220]) ).
cnf(i_0_400,plain,
$false,
inference(scs_inference,[],[i_0_270,i_0_290,i_0_336,i_0_367,i_0_370,i_0_284,i_0_361,i_0_283,i_0_346,i_0_375,i_0_272,i_0_286,i_0_293,i_0_277,i_0_256,i_0_364,i_0_263,i_0_251,i_0_264,i_0_271,i_0_275,i_0_320,i_0_323,i_0_324,i_0_325,i_0_326,i_0_328,i_0_215,i_0_216,i_0_234,i_0_235,i_0_236,i_0_252,i_0_260,i_0_267,i_0_278,i_0_333,i_0_279,i_0_280,i_0_281,i_0_291,i_0_296,i_0_206,i_0_220,i_0_221]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU153+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.09 % 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
% 0.10/0.30 % Computer : n007.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 5 02:44:38 EDT 2026
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % start to proof: theBenchmark
% 0.26/1.58 % Version : CSE_E---1.7
% 0.26/1.58 % Problem : theBenchmark.p
% 0.26/1.58 % SZS status Theorem for theBenchmark.p
% 0.26/1.58 % SZS output start CNFRefutation
% See solution above
% 0.60/1.91 % Total time : 1.269s
%------------------------------------------------------------------------------