%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU161+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 : n023.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 05:10:52 PM UTC 2026
% Result : Theorem 0.34s 1.62s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_89)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(t46_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_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(l55_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(t33_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
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(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(l25_zfmisc_1,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(t39_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_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(t37_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_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(t38_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_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(l50_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_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_81,plain,
! [X292,X293] : ordered_pair(X292,X293) = unordered_pair(unordered_pair(X292,X293),singleton(X292)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_82,lemma,
! [X407] : unordered_pair(X407,X407) = singleton(X407),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_83,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_84,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_85,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_86,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t46_zfmisc_1]) ).
fof(i_0_87,plain,
! [X240,X241,X242,X243,X246,X247,X248,X249,X250,X251,X253,X254] :
( ( in(esk6_4(X240,X241,X242,X243),X240)
| ~ in(X243,X242)
| X242 != cartesian_product2(X240,X241) )
& ( in(esk7_4(X240,X241,X242,X243),X241)
| ~ in(X243,X242)
| X242 != cartesian_product2(X240,X241) )
& ( X243 = ordered_pair(esk6_4(X240,X241,X242,X243),esk7_4(X240,X241,X242,X243))
| ~ in(X243,X242)
| X242 != cartesian_product2(X240,X241) )
& ( ~ in(X247,X240)
| ~ in(X248,X241)
| X246 != ordered_pair(X247,X248)
| in(X246,X242)
| X242 != cartesian_product2(X240,X241) )
& ( ~ in(esk8_3(X249,X250,X251),X251)
| ~ in(X253,X249)
| ~ in(X254,X250)
| esk8_3(X249,X250,X251) != ordered_pair(X253,X254)
| X251 = cartesian_product2(X249,X250) )
& ( in(esk9_3(X249,X250,X251),X249)
| in(esk8_3(X249,X250,X251),X251)
| X251 = cartesian_product2(X249,X250) )
& ( in(esk10_3(X249,X250,X251),X250)
| in(esk8_3(X249,X250,X251),X251)
| X251 = cartesian_product2(X249,X250) )
& ( esk8_3(X249,X250,X251) = ordered_pair(esk9_3(X249,X250,X251),esk10_3(X249,X250,X251))
| in(esk8_3(X249,X250,X251),X251)
| X251 = cartesian_product2(X249,X250) ) ),
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_zfmisc_1])])])])])]) ).
cnf(i_0_88,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
cnf(i_0_89,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
fof(i_0_90,plain,
! [X263,X264,X265,X266,X267,X268,X269,X270] :
( ( in(X266,X263)
| ~ in(X266,X265)
| X265 != set_intersection2(X263,X264) )
& ( in(X266,X264)
| ~ in(X266,X265)
| X265 != set_intersection2(X263,X264) )
& ( ~ in(X267,X263)
| ~ in(X267,X264)
| in(X267,X265)
| X265 != set_intersection2(X263,X264) )
& ( ~ in(esk12_3(X268,X269,X270),X270)
| ~ in(esk12_3(X268,X269,X270),X268)
| ~ in(esk12_3(X268,X269,X270),X269)
| X270 = set_intersection2(X268,X269) )
& ( in(esk12_3(X268,X269,X270),X268)
| in(esk12_3(X268,X269,X270),X270)
| X270 = set_intersection2(X268,X269) )
& ( in(esk12_3(X268,X269,X270),X269)
| in(esk12_3(X268,X269,X270),X270)
| X270 = set_intersection2(X268,X269) ) ),
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_91,lemma,
! [X393,X394] : set_difference(X393,set_difference(X393,X394)) = set_intersection2(X393,X394),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_92,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_93,lemma,
! [X325,X326,X327,X328] :
( ( in(X325,X327)
| ~ in(ordered_pair(X325,X326),cartesian_product2(X327,X328)) )
& ( in(X326,X328)
| ~ in(ordered_pair(X325,X326),cartesian_product2(X327,X328)) )
& ( ~ in(X325,X327)
| ~ in(X326,X328)
| in(ordered_pair(X325,X326),cartesian_product2(X327,X328)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_94,plain,
! [X298,X299] : ~ empty(ordered_pair(X298,X299)),
inference(variable_rename,[status(thm)],[i_0_83]) ).
fof(i_0_95,lemma,
! [X362,X363,X364,X365] :
( ( X362 = X364
| ordered_pair(X362,X363) != ordered_pair(X364,X365) )
& ( X363 = X365
| ordered_pair(X362,X363) != ordered_pair(X364,X365) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_96,lemma,
! [X349,X350,X351] :
( ~ subset(X349,X350)
| subset(set_intersection2(X349,X351),set_intersection2(X350,X351)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_97,lemma,
! [X396,X397,X399,X400,X401] :
( ( disjoint(X396,X397)
| in(esk23_2(X396,X397),set_intersection2(X396,X397)) )
& ( ~ in(X401,set_intersection2(X399,X400))
| ~ disjoint(X399,X400) ) ),
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_84])])])])]) ).
fof(i_0_98,lemma,
! [X342,X343,X344] :
( ~ subset(X342,X343)
| ~ subset(X342,X344)
| subset(X342,set_intersection2(X343,X344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_99,lemma,
! [X318,X319,X320] :
( ~ subset(X318,X319)
| in(X320,X318)
| subset(X318,set_difference(X319,singleton(X320))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_100,lemma,
! [X409,X410] :
( ~ subset(singleton(X409),singleton(X410))
| X409 = X410 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_101,plain,
! [X204,X205,X206,X207,X208,X209] :
( ( ~ in(X206,X205)
| X206 = X204
| X205 != singleton(X204) )
& ( X207 != X204
| in(X207,X205)
| X205 != singleton(X204) )
& ( ~ in(esk1_2(X208,X209),X209)
| esk1_2(X208,X209) != X208
| X209 = singleton(X208) )
& ( in(esk1_2(X208,X209),X209)
| esk1_2(X208,X209) = X208
| X209 = singleton(X208) ) ),
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_102,lemma,
! [X340,X341] : subset(set_intersection2(X340,X341),X340),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_103,lemma,
! [X310,X311] :
( ~ disjoint(singleton(X310),X311)
| ~ in(X310,X311) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_104,lemma,
! [X377,X378] :
( ( ~ subset(X377,singleton(X378))
| X377 = empty_set
| X377 = singleton(X378) )
& ( X377 != empty_set
| subset(X377,singleton(X378)) )
& ( X377 != singleton(X378)
| subset(X377,singleton(X378)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_105,lemma,
! [X321,X322] :
( ( ~ subset(X321,singleton(X322))
| X321 = empty_set
| X321 = singleton(X322) )
& ( X321 != empty_set
| subset(X321,singleton(X322)) )
& ( X321 != singleton(X322)
| subset(X321,singleton(X322)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_106,plain,
! [X200,X201] : set_intersection2(X200,X201) = set_intersection2(X201,X200),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_107,lemma,
! [X370,X371] :
( ( ~ subset(singleton(X370),X371)
| in(X370,X371) )
& ( ~ in(X370,X371)
| subset(singleton(X370),X371) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_108,lemma,
! [X314,X315] :
( ( ~ subset(singleton(X314),X315)
| in(X314,X315) )
& ( ~ in(X314,X315)
| subset(singleton(X314),X315) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_109,plain,
! [X294,X295] :
( ( ~ disjoint(X294,X295)
| set_intersection2(X294,X295) = empty_set )
& ( set_intersection2(X294,X295) != empty_set
| disjoint(X294,X295) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_110,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_111,lemma,
! [X308,X309] :
( ~ in(X308,X309)
| set_union2(singleton(X308),X309) = X309 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_112,lemma,
! [X352,X353] :
( ~ subset(X352,X353)
| set_intersection2(X352,X353) = X352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_113,lemma,
! [X312,X313] :
( in(X312,X313)
| disjoint(singleton(X312),X313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_85])]) ).
fof(i_0_114,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_115,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_116,negated_conjecture,
( in(esk21_0,esk22_0)
& set_union2(singleton(esk21_0),esk22_0) != esk22_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_86])])]) ).
fof(i_0_117,lemma,
! [X422,X423,X424] :
( singleton(X422) != unordered_pair(X423,X424)
| X422 = X423 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_118,lemma,
! [X425,X426,X427] :
( singleton(X425) != unordered_pair(X426,X427)
| X426 = X427 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_119,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_120,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_121,plain,
! [X305] : set_intersection2(X305,X305) = X305,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_122,plain,
! [X354] : set_intersection2(X354,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_123,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_124,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_125,lemma,
! [X307] : singleton(X307) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_126,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_127,plain,
( X1 = ordered_pair(esk6_4(X2,X3,X4,X1),esk7_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_87]) ).
cnf(i_0_128,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_88,c_0_89]) ).
cnf(i_0_129,plain,
( esk8_3(X1,X2,X3) = ordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3))
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]) ).
cnf(i_0_130,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X1)
| ~ in(esk12_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_131,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_91]) ).
fof(i_0_132,plain,
! [X283,X284,X285,X286,X287,X288,X289,X290] :
( ( in(X286,X283)
| ~ in(X286,X285)
| X285 != set_difference(X283,X284) )
& ( ~ in(X286,X284)
| ~ in(X286,X285)
| X285 != set_difference(X283,X284) )
& ( ~ in(X287,X283)
| in(X287,X284)
| in(X287,X285)
| X285 != set_difference(X283,X284) )
& ( ~ in(esk16_3(X288,X289,X290),X290)
| ~ in(esk16_3(X288,X289,X290),X288)
| in(esk16_3(X288,X289,X290),X289)
| X290 = set_difference(X288,X289) )
& ( in(esk16_3(X288,X289,X290),X288)
| in(esk16_3(X288,X289,X290),X290)
| X290 = set_difference(X288,X289) )
& ( ~ in(esk16_3(X288,X289,X290),X289)
| in(esk16_3(X288,X289,X290),X290)
| X290 = set_difference(X288,X289) ) ),
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_92])])])])])]) ).
cnf(i_0_133,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk8_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_87]) ).
fof(i_0_134,plain,
! [X231,X232,X233,X234,X235,X236,X237,X238] :
( ( ~ in(X234,X233)
| in(X234,X231)
| in(X234,X232)
| X233 != set_union2(X231,X232) )
& ( ~ in(X235,X231)
| in(X235,X233)
| X233 != set_union2(X231,X232) )
& ( ~ in(X235,X232)
| in(X235,X233)
| X233 != set_union2(X231,X232) )
& ( ~ in(esk5_3(X236,X237,X238),X236)
| ~ in(esk5_3(X236,X237,X238),X238)
| X238 = set_union2(X236,X237) )
& ( ~ in(esk5_3(X236,X237,X238),X237)
| ~ in(esk5_3(X236,X237,X238),X238)
| X238 = set_union2(X236,X237) )
& ( in(esk5_3(X236,X237,X238),X238)
| in(esk5_3(X236,X237,X238),X236)
| in(esk5_3(X236,X237,X238),X237)
| X238 = set_union2(X236,X237) ) ),
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_135,plain,
! [X222,X223,X224,X225,X226,X227,X228,X229] :
( ( ~ in(X225,X224)
| X225 = X222
| X225 = X223
| X224 != unordered_pair(X222,X223) )
& ( X226 != X222
| in(X226,X224)
| X224 != unordered_pair(X222,X223) )
& ( X226 != X223
| in(X226,X224)
| X224 != unordered_pair(X222,X223) )
& ( esk4_3(X227,X228,X229) != X227
| ~ in(esk4_3(X227,X228,X229),X229)
| X229 = unordered_pair(X227,X228) )
& ( esk4_3(X227,X228,X229) != X228
| ~ in(esk4_3(X227,X228,X229),X229)
| X229 = unordered_pair(X227,X228) )
& ( in(esk4_3(X227,X228,X229),X229)
| esk4_3(X227,X228,X229) = X227
| esk4_3(X227,X228,X229) = X228
| X229 = unordered_pair(X227,X228) ) ),
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_136,plain,
( in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_137,plain,
( in(esk12_3(X1,X2,X3),X2)
| in(esk12_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_138,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_93]) ).
cnf(i_0_139,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_93]) ).
cnf(i_0_140,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_93]) ).
cnf(i_0_141,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_94]) ).
cnf(i_0_142,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_95]) ).
cnf(i_0_143,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]) ).
cnf(i_0_144,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_96]) ).
cnf(i_0_145,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_87]) ).
cnf(i_0_146,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_97]) ).
fof(i_0_147,plain,
! [X272,X273,X274,X276,X277,X278,X279,X281] :
( ( in(X274,esk13_3(X272,X273,X274))
| ~ in(X274,X273)
| X273 != union(X272) )
& ( in(esk13_3(X272,X273,X274),X272)
| ~ in(X274,X273)
| X273 != union(X272) )
& ( ~ in(X276,X277)
| ~ in(X277,X272)
| in(X276,X273)
| X273 != union(X272) )
& ( ~ in(esk14_2(X278,X279),X279)
| ~ in(esk14_2(X278,X279),X281)
| ~ in(X281,X278)
| X279 = union(X278) )
& ( in(esk14_2(X278,X279),esk15_2(X278,X279))
| in(esk14_2(X278,X279),X279)
| X279 = union(X278) )
& ( in(esk15_2(X278,X279),X278)
| in(esk14_2(X278,X279),X279)
| X279 = union(X278) ) ),
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)],[d4_tarski])])])])])]) ).
cnf(i_0_148,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_98]) ).
cnf(i_0_149,lemma,
( disjoint(X1,X2)
| in(esk23_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_97]) ).
fof(i_0_150,plain,
! [X215,X216,X217,X218,X219,X220] :
( ( ~ in(X217,X216)
| subset(X217,X215)
| X216 != powerset(X215) )
& ( ~ subset(X218,X215)
| in(X218,X216)
| X216 != powerset(X215) )
& ( ~ in(esk3_2(X219,X220),X220)
| ~ subset(esk3_2(X219,X220),X219)
| X220 = powerset(X219) )
& ( in(esk3_2(X219,X220),X220)
| subset(esk3_2(X219,X220),X219)
| X220 = powerset(X219) ) ),
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_151,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_99]) ).
fof(i_0_152,plain,
! [X355,X356] :
( ( ~ in(esk19_2(X355,X356),X355)
| ~ in(esk19_2(X355,X356),X356)
| X355 = X356 )
& ( in(esk19_2(X355,X356),X355)
| in(esk19_2(X355,X356),X356)
| X355 = X356 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_153,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_154,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_100]) ).
cnf(i_0_155,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
cnf(i_0_156,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_157,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_158,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_102]) ).
fof(i_0_159,lemma,
! [X359,X360,X361] :
( ~ subset(X359,X360)
| subset(set_difference(X359,X361),set_difference(X360,X361)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
cnf(i_0_160,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_103]) ).
fof(i_0_161,lemma,
! [X419,X420,X421] :
( ~ subset(X419,X420)
| ~ subset(X421,X420)
| subset(set_union2(X419,X421),X420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_162,lemma,
! [X372,X373,X374] :
( ( in(X372,X374)
| ~ subset(unordered_pair(X372,X373),X374) )
& ( in(X373,X374)
| ~ subset(unordered_pair(X372,X373),X374) )
& ( ~ in(X372,X374)
| ~ in(X373,X374)
| subset(unordered_pair(X372,X373),X374) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
cnf(i_0_163,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_104]) ).
cnf(i_0_164,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_105]) ).
cnf(i_0_165,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_106]) ).
fof(i_0_166,plain,
! [X257,X258,X259,X260,X261] :
( ( ~ subset(X257,X258)
| ~ in(X259,X257)
| in(X259,X258) )
& ( in(esk11_2(X260,X261),X260)
| subset(X260,X261) )
& ( ~ in(esk11_2(X260,X261),X261)
| subset(X260,X261) ) ),
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_167,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_168,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]) ).
cnf(i_0_169,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_109]) ).
cnf(i_0_170,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
fof(i_0_171,lemma,
! [X380,X381,X383,X384,X385] :
( ( in(esk20_2(X380,X381),X380)
| disjoint(X380,X381) )
& ( in(esk20_2(X380,X381),X381)
| disjoint(X380,X381) )
& ( ~ in(X385,X383)
| ~ in(X385,X384)
| ~ disjoint(X383,X384) ) ),
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_110])])])])])]) ).
cnf(i_0_172,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]) ).
cnf(i_0_173,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_105]) ).
cnf(i_0_174,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]) ).
cnf(i_0_175,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_112]) ).
fof(i_0_176,lemma,
! [X389,X390] :
( ~ subset(X389,X390)
| X390 = set_union2(X389,set_difference(X390,X389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_177,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_178,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]) ).
cnf(i_0_179,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_109]) ).
fof(i_0_180,lemma,
! [X404,X405,X406] :
( ~ subset(X404,X405)
| ~ disjoint(X405,X406)
| disjoint(X404,X406) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_181,lemma,
! [X346,X347,X348] :
( ~ subset(X346,X347)
| ~ subset(X347,X348)
| subset(X346,X348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(i_0_182,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_113]) ).
fof(i_0_183,lemma,
! [X387,X388] : set_difference(set_union2(X387,X388),X388) = set_difference(X387,X388),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_184,lemma,
! [X375,X376] : set_union2(X375,set_difference(X376,X375)) = set_union2(X375,X376),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_185,plain,
! [X300,X301] :
( empty(X300)
| ~ empty(set_union2(X300,X301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_114])]) ).
fof(i_0_186,plain,
! [X302,X303] :
( empty(X302)
| ~ empty(set_union2(X303,X302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_115])]) ).
cnf(i_0_187,negated_conjecture,
set_union2(singleton(esk21_0),esk22_0) != esk22_0,
inference(split_conjunct,[status(thm)],[i_0_116]) ).
cnf(i_0_188,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
fof(i_0_189,lemma,
! [X334,X335,X336,X337] :
( unordered_pair(X334,X335) != unordered_pair(X336,X337)
| X334 = X336
| X334 = X337 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
fof(i_0_190,plain,
! [X202,X203] :
( ( subset(X202,X203)
| X202 != X203 )
& ( subset(X203,X202)
| X202 != X203 )
& ( ~ subset(X202,X203)
| ~ subset(X203,X202)
| X202 = X203 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(i_0_191,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_117]) ).
cnf(i_0_192,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_118]) ).
fof(i_0_193,lemma,
! [X402,X403] :
( ~ subset(X402,X403)
| ~ proper_subset(X403,X402) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_194,plain,
! [X194,X195] :
( ~ proper_subset(X194,X195)
| ~ proper_subset(X195,X194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_119])]) ).
fof(i_0_195,plain,
! [X192,X193] :
( ~ in(X192,X193)
| ~ in(X193,X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_120])]) ).
fof(i_0_196,lemma,
! [X323,X324] :
( ~ in(X323,X324)
| subset(X323,union(X324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_197,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_104]) ).
cnf(i_0_198,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_105]) ).
cnf(i_0_199,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
cnf(i_0_200,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_121]) ).
fof(i_0_201,lemma,
! [X366,X367] : subset(set_difference(X366,X367),X366),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_202,lemma,
! [X413,X414] : subset(X413,set_union2(X413,X414)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_203,plain,
! [X296,X297] :
( ( subset(X296,X297)
| ~ proper_subset(X296,X297) )
& ( X296 != X297
| ~ proper_subset(X296,X297) )
& ( ~ subset(X296,X297)
| X296 = X297
| proper_subset(X296,X297) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_204,lemma,
! [X415,X416] :
( ( ~ disjoint(X415,X416)
| set_difference(X415,X416) = X415 )
& ( set_difference(X415,X416) != X415
| disjoint(X415,X416) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_205,lemma,
! [X338,X339] :
( ~ subset(X338,X339)
| set_union2(X338,X339) = X339 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_206,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_122]) ).
fof(i_0_207,plain,
! [X332,X333] :
( ~ disjoint(X332,X333)
| disjoint(X333,X332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_208,lemma,
! [X368,X369] :
( ( set_difference(X368,X369) != empty_set
| subset(X368,X369) )
& ( ~ subset(X368,X369)
| set_difference(X368,X369) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_209,lemma,
! [X316,X317] :
( ( set_difference(X316,X317) != empty_set
| subset(X316,X317) )
& ( ~ subset(X316,X317)
| set_difference(X316,X317) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_210,plain,
! [X411,X412] :
( ~ in(X411,X412)
| ~ empty(X412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_211,plain,
! [X198,X199] : set_union2(X198,X199) = set_union2(X199,X198),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_212,plain,
! [X196,X197] : unordered_pair(X196,X197) = unordered_pair(X197,X196),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_213,plain,
! [X211,X212,X213] :
( ( X211 != empty_set
| ~ in(X212,X211) )
& ( in(esk2_1(X213),X213)
| X213 = 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_123])])])])]) ).
fof(i_0_214,plain,
! [X306] : ~ proper_subset(X306,X306),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_124])]) ).
cnf(i_0_215,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_125]) ).
fof(i_0_216,lemma,
! [X386] :
( ~ subset(X386,empty_set)
| X386 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_217,plain,
! [X417,X418] :
( ~ empty(X417)
| X417 = X418
| ~ empty(X418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_218,plain,
! [X304] : set_union2(X304,X304) = X304,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_219,plain,
! [X331] : subset(X331,X331),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_220,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_221,plain,
! [X379] : set_difference(X379,empty_set) = X379,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_222,plain,
! [X345] : set_union2(X345,empty_set) = X345,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_223,lemma,
! [X358] : subset(empty_set,X358),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_224,plain,
! [X395] : set_difference(empty_set,X395) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_225,plain,
! [X408] :
( ~ empty(X408)
| X408 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_226,plain,
~ empty(esk18_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_126])]) ).
fof(i_0_227,plain,
empty(esk17_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_228,plain,
( X1 = unordered_pair(unordered_pair(esk6_4(X2,X3,X4,X1),esk7_4(X2,X3,X4,X1)),unordered_pair(esk6_4(X2,X3,X4,X1),esk6_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_127,c_0_128]),
[final] ).
cnf(i_0_229,plain,
( X3 = cartesian_product2(X1,X2)
| esk8_3(X1,X2,X3) = unordered_pair(unordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3)),unordered_pair(esk9_3(X1,X2,X3),esk9_3(X1,X2,X3)))
| in(esk8_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_129,c_0_128]),
[final] ).
cnf(i_0_230,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X2)
| ~ in(esk12_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_130,c_0_131]),
[final] ).
cnf(i_0_231,plain,
( in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_232,plain,
( in(esk6_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_233,plain,
( in(esk16_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk16_3(X1,X2,X3),X3)
| ~ in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_234,plain,
( X3 = cartesian_product2(X1,X2)
| esk8_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk8_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_133,c_0_128]),
[final] ).
cnf(i_0_235,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_134]),
[final] ).
cnf(i_0_236,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_134]),
[final] ).
cnf(i_0_237,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_134]),
[final] ).
cnf(i_0_238,plain,
( in(esk16_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk16_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_239,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_135]),
[final] ).
cnf(i_0_240,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_135]),
[final] ).
cnf(i_0_241,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk12_3(X1,X2,X3),X3)
| in(esk12_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_136,c_0_131]),
[final] ).
cnf(i_0_242,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk12_3(X1,X2,X3),X3)
| in(esk12_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_137,c_0_131]),
[final] ).
cnf(i_0_243,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_138,c_0_128]),
[final] ).
cnf(i_0_244,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_139,c_0_128]),
[final] ).
cnf(i_0_245,plain,
( in(esk16_3(X1,X2,X3),X1)
| in(esk16_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_246,plain,
( in(esk10_3(X1,X2,X3),X2)
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_247,plain,
( in(esk9_3(X1,X2,X3),X1)
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_248,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_135]),
[final] ).
cnf(i_0_249,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_140,c_0_128]),
[final] ).
cnf(i_0_250,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_141,c_0_128]),
[final] ).
cnf(i_0_251,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_142,c_0_128]),c_0_128]),
[final] ).
cnf(i_0_252,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)) != unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_143,c_0_128]),c_0_128]),
[final] ).
cnf(i_0_253,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_144,c_0_131]),c_0_131]),
[final] ).
cnf(i_0_254,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_145,c_0_128]),
[final] ).
cnf(i_0_255,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_146,c_0_131]),
[final] ).
cnf(i_0_256,plain,
( X2 = union(X1)
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_257,plain,
( in(esk13_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_258,plain,
( in(X1,esk13_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_259,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_148,c_0_131]),
[final] ).
cnf(i_0_260,lemma,
( disjoint(X1,X2)
| in(esk23_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_149,c_0_131]),
[final] ).
cnf(i_0_261,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_262,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_151,c_0_89]),
[final] ).
cnf(i_0_263,plain,
( X1 = X2
| ~ in(esk19_2(X1,X2),X1)
| ~ in(esk19_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_264,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_153,c_0_131]),
[final] ).
cnf(i_0_265,plain,
( in(esk14_2(X1,X2),esk15_2(X1,X2))
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_266,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_154,c_0_89]),c_0_89]),
[final] ).
cnf(i_0_267,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_155,c_0_89]),
[final] ).
cnf(i_0_268,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_156,c_0_131]),
[final] ).
cnf(i_0_269,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_157,c_0_131]),
[final] ).
cnf(i_0_270,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_158,c_0_131]),
[final] ).
cnf(i_0_271,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_272,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_160,c_0_89]),
[final] ).
cnf(i_0_273,plain,
( in(esk15_2(X1,X2),X1)
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_274,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_275,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_276,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_277,plain,
( in(esk19_2(X1,X2),X1)
| in(esk19_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_278,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_163,c_0_89]),c_0_89]),
[final] ).
cnf(i_0_279,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_164,c_0_89]),c_0_89]),
[final] ).
cnf(i_0_280,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_165,c_0_131]),c_0_131]),
[final] ).
cnf(i_0_281,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_282,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_167,c_0_89]),
[final] ).
cnf(i_0_283,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_168,c_0_89]),
[final] ).
cnf(i_0_284,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_285,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_286,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_169,c_0_131]),
[final] ).
cnf(i_0_287,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_288,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_289,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_170,c_0_89]),
[final] ).
cnf(i_0_290,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_291,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_292,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_293,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_172,c_0_89]),c_0_89]),
[final] ).
cnf(i_0_294,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_173,c_0_89]),c_0_89]),
[final] ).
cnf(i_0_295,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_174,c_0_89]),
[final] ).
cnf(i_0_296,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_175,c_0_131]),
[final] ).
cnf(i_0_297,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_298,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_177,c_0_89]),
[final] ).
cnf(i_0_299,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_178,c_0_89]),
[final] ).
cnf(i_0_300,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_179,c_0_131]),
[final] ).
cnf(i_0_301,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_302,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_303,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_304,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_305,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_306,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_307,lemma,
( in(esk20_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_308,lemma,
( in(esk20_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_309,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_310,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_182,c_0_89]),
[final] ).
cnf(i_0_311,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_312,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_313,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_314,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_315,negated_conjecture,
set_union2(unordered_pair(esk21_0,esk21_0),esk22_0) != esk22_0,
inference(rw,[status(thm)],[i_0_187,c_0_89]),
[final] ).
cnf(i_0_316,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_317,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_188,c_0_89]),
[final] ).
cnf(i_0_318,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_319,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_320,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_191,c_0_89]),
[final] ).
cnf(i_0_321,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_192,c_0_89]),
[final] ).
cnf(i_0_322,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_323,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_324,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_325,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_194]),
[final] ).
cnf(i_0_326,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_327,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_328,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_197,c_0_89]),
[final] ).
cnf(i_0_329,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_198,c_0_89]),
[final] ).
cnf(i_0_330,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_199,c_0_89]),
[final] ).
cnf(i_0_331,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_332,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_333,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_200,c_0_131]),
[final] ).
cnf(i_0_334,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_335,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_336,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_337,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_338,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_339,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_340,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_206,c_0_131]),
[final] ).
cnf(i_0_341,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_342,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_343,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_344,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_345,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_346,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_347,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_348,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_349,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_350,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_351,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_352,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_353,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_215,c_0_89]),
[final] ).
cnf(i_0_354,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_355,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_356,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_357,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_358,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_217]),
[final] ).
cnf(i_0_359,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_360,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_361,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_220,c_0_89]),
[final] ).
cnf(i_0_362,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_363,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_222]),
[final] ).
cnf(i_0_364,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_365,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_366,negated_conjecture,
in(esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_367,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_368,plain,
~ empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_226]),
[final] ).
cnf(i_0_369,plain,
empty(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_227]),
[final] ).
cnf(i_0_370,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_371,axiom,
X1 = X1 ).
cnf(i_0_372,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_373,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_374,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_375,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_376,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_377,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_378,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_379,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_380,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_381,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_382,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_383,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_384,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_385,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_386,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_387,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_388,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_389,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_390,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_391,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_392,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_393,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_394,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_395,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_396,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_397,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_398,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_399,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_400,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_371_001,axiom,
X1 = X1 ).
cnf(i_0_372_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_373_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_374_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_375_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_376_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_377_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_378_008,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_379_009,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_380_010,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_381_011,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_382_012,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_383_013,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_384_014,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_385_015,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_386_016,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_387_017,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_388_018,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_389_019,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_390_020,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_391_021,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_392_022,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_393_023,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_394_024,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_395_025,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_396_026,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_397_027,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_398_028,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_399_029,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_400_030,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_401,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),esk7_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),esk6_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[228]) ).
cnf(i_0_402,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk7_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[231]) ).
cnf(i_0_403,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[232]) ).
cnf(i_0_404,plain,
X1 = X1,
inference(equality_inference,[],[251]) ).
cnf(i_0_405,plain,
X1 = X1,
inference(equality_inference,[],[252]) ).
cnf(i_0_406,plain,
( ~ in(X1,union(X2))
| in(esk13_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[257]) ).
cnf(i_0_407,plain,
( ~ in(X1,union(X2))
| in(X1,esk13_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[258]) ).
cnf(i_0_408,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[264]) ).
cnf(i_0_409,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[269]) ).
cnf(i_0_410,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[287]) ).
cnf(i_0_411,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[288]) ).
cnf(i_0_412,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[290]) ).
cnf(i_0_413,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[291]) ).
cnf(i_0_414,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[301]) ).
cnf(i_0_415,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[302]) ).
cnf(i_0_416,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[303]) ).
cnf(i_0_417,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[316]) ).
cnf(i_0_418,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[317]) ).
cnf(i_0_419,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[318]) ).
cnf(i_0_420,plain,
X1 = X1,
inference(equality_inference,[],[320]) ).
cnf(i_0_421,plain,
X1 = X1,
inference(equality_inference,[],[321]) ).
cnf(i_0_422,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[322]) ).
cnf(i_0_423,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[323]) ).
cnf(i_0_424,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[329]) ).
cnf(i_0_425,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[350]) ).
cnf(i_0_426,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[351]) ).
cnf(i_0_427,plain,
subset(X1,X1),
inference(equality_inference,[],[356]) ).
cnf(i_0_428,plain,
subset(X1,X1),
inference(equality_inference,[],[357]) ).
cnf(i_0_429,plain,
$false,
inference(scs_inference,[],[i_0_315,i_0_366,i_0_295]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU161+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:47:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.34/1.62 % Version : CSE_E---1.7
% 0.34/1.62 % Problem : theBenchmark.p
% 0.34/1.62 % SZS status Theorem for theBenchmark.p
% 0.34/1.62 % SZS output start CNFRefutation
% See solution above
% 0.34/1.66 % Total time : 1.271s
%------------------------------------------------------------------------------