%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU163+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 : n006.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 0.31s 1.61s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_91)
% 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(t65_zfmisc_1,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
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(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(t46_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
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(t92_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
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_83,plain,
! [X296,X297] : ordered_pair(X296,X297) = unordered_pair(unordered_pair(X296,X297),singleton(X296)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_84,lemma,
! [X413] : unordered_pair(X413,X413) = singleton(X413),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_85,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_86,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_87,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_88,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_89,plain,
! [X244,X245,X246,X247,X250,X251,X252,X253,X254,X255,X257,X258] :
( ( in(esk6_4(X244,X245,X246,X247),X244)
| ~ in(X247,X246)
| X246 != cartesian_product2(X244,X245) )
& ( in(esk7_4(X244,X245,X246,X247),X245)
| ~ in(X247,X246)
| X246 != cartesian_product2(X244,X245) )
& ( X247 = ordered_pair(esk6_4(X244,X245,X246,X247),esk7_4(X244,X245,X246,X247))
| ~ in(X247,X246)
| X246 != cartesian_product2(X244,X245) )
& ( ~ in(X251,X244)
| ~ in(X252,X245)
| X250 != ordered_pair(X251,X252)
| in(X250,X246)
| X246 != cartesian_product2(X244,X245) )
& ( ~ in(esk8_3(X253,X254,X255),X255)
| ~ in(X257,X253)
| ~ in(X258,X254)
| esk8_3(X253,X254,X255) != ordered_pair(X257,X258)
| X255 = cartesian_product2(X253,X254) )
& ( in(esk9_3(X253,X254,X255),X253)
| in(esk8_3(X253,X254,X255),X255)
| X255 = cartesian_product2(X253,X254) )
& ( in(esk10_3(X253,X254,X255),X254)
| in(esk8_3(X253,X254,X255),X255)
| X255 = cartesian_product2(X253,X254) )
& ( esk8_3(X253,X254,X255) = ordered_pair(esk9_3(X253,X254,X255),esk10_3(X253,X254,X255))
| in(esk8_3(X253,X254,X255),X255)
| X255 = cartesian_product2(X253,X254) ) ),
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_90,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_83]) ).
cnf(i_0_91,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_84]) ).
fof(i_0_92,plain,
! [X267,X268,X269,X270,X271,X272,X273,X274] :
( ( in(X270,X267)
| ~ in(X270,X269)
| X269 != set_intersection2(X267,X268) )
& ( in(X270,X268)
| ~ in(X270,X269)
| X269 != set_intersection2(X267,X268) )
& ( ~ in(X271,X267)
| ~ in(X271,X268)
| in(X271,X269)
| X269 != set_intersection2(X267,X268) )
& ( ~ in(esk12_3(X272,X273,X274),X274)
| ~ in(esk12_3(X272,X273,X274),X272)
| ~ in(esk12_3(X272,X273,X274),X273)
| X274 = set_intersection2(X272,X273) )
& ( in(esk12_3(X272,X273,X274),X272)
| in(esk12_3(X272,X273,X274),X274)
| X274 = set_intersection2(X272,X273) )
& ( in(esk12_3(X272,X273,X274),X273)
| in(esk12_3(X272,X273,X274),X274)
| X274 = set_intersection2(X272,X273) ) ),
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_93,lemma,
! [X397,X398] : set_difference(X397,set_difference(X397,X398)) = set_intersection2(X397,X398),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_94,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_95,lemma,
! [X329,X330,X331,X332] :
( ( in(X329,X331)
| ~ in(ordered_pair(X329,X330),cartesian_product2(X331,X332)) )
& ( in(X330,X332)
| ~ in(ordered_pair(X329,X330),cartesian_product2(X331,X332)) )
& ( ~ in(X329,X331)
| ~ in(X330,X332)
| in(ordered_pair(X329,X330),cartesian_product2(X331,X332)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_96,plain,
! [X302,X303] : ~ empty(ordered_pair(X302,X303)),
inference(variable_rename,[status(thm)],[i_0_85]) ).
fof(i_0_97,lemma,
! [X366,X367,X368,X369] :
( ( X366 = X368
| ordered_pair(X366,X367) != ordered_pair(X368,X369) )
& ( X367 = X369
| ordered_pair(X366,X367) != ordered_pair(X368,X369) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_98,lemma,
! [X353,X354,X355] :
( ~ subset(X353,X354)
| subset(set_intersection2(X353,X355),set_intersection2(X354,X355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_99,lemma,
! [X400,X401,X403,X404,X405] :
( ( disjoint(X400,X401)
| in(esk21_2(X400,X401),set_intersection2(X400,X401)) )
& ( ~ in(X405,set_intersection2(X403,X404))
| ~ disjoint(X403,X404) ) ),
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])])])])]) ).
fof(i_0_100,lemma,
! [X346,X347,X348] :
( ~ subset(X346,X347)
| ~ subset(X346,X348)
| subset(X346,set_intersection2(X347,X348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_101,lemma,
! [X322,X323,X324] :
( ~ subset(X322,X323)
| in(X324,X322)
| subset(X322,set_difference(X323,singleton(X324))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_102,lemma,
! [X415,X416] :
( ~ subset(singleton(X415),singleton(X416))
| X415 = X416 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_103,plain,
! [X208,X209,X210,X211,X212,X213] :
( ( ~ in(X210,X209)
| X210 = X208
| X209 != singleton(X208) )
& ( X211 != X208
| in(X211,X209)
| X209 != singleton(X208) )
& ( ~ in(esk1_2(X212,X213),X213)
| esk1_2(X212,X213) != X212
| X213 = singleton(X212) )
& ( in(esk1_2(X212,X213),X213)
| esk1_2(X212,X213) = X212
| X213 = singleton(X212) ) ),
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_104,lemma,
! [X344,X345] : subset(set_intersection2(X344,X345),X344),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_105,lemma,
! [X411,X412] :
( ( set_difference(X411,singleton(X412)) != X411
| ~ in(X412,X411) )
& ( in(X412,X411)
| set_difference(X411,singleton(X412)) = X411 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_87])]) ).
fof(i_0_106,lemma,
! [X314,X315] :
( ~ disjoint(singleton(X314),X315)
| ~ in(X314,X315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_107,lemma,
! [X381,X382] :
( ( ~ subset(X381,singleton(X382))
| X381 = empty_set
| X381 = singleton(X382) )
& ( X381 != empty_set
| subset(X381,singleton(X382)) )
& ( X381 != singleton(X382)
| subset(X381,singleton(X382)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_108,lemma,
! [X325,X326] :
( ( ~ subset(X325,singleton(X326))
| X325 = empty_set
| X325 = singleton(X326) )
& ( X325 != empty_set
| subset(X325,singleton(X326)) )
& ( X325 != singleton(X326)
| subset(X325,singleton(X326)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_109,plain,
! [X204,X205] : set_intersection2(X204,X205) = set_intersection2(X205,X204),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_110,lemma,
! [X374,X375] :
( ( ~ subset(singleton(X374),X375)
| in(X374,X375) )
& ( ~ in(X374,X375)
| subset(singleton(X374),X375) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_111,lemma,
! [X318,X319] :
( ( ~ subset(singleton(X318),X319)
| in(X318,X319) )
& ( ~ in(X318,X319)
| subset(singleton(X318),X319) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_112,plain,
! [X298,X299] :
( ( ~ disjoint(X298,X299)
| set_intersection2(X298,X299) = empty_set )
& ( set_intersection2(X298,X299) != empty_set
| disjoint(X298,X299) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_113,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_114,lemma,
! [X395,X396] :
( ~ in(X395,X396)
| set_union2(singleton(X395),X396) = X396 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_115,lemma,
! [X312,X313] :
( ~ in(X312,X313)
| set_union2(singleton(X312),X313) = X313 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_116,lemma,
! [X356,X357] :
( ~ subset(X356,X357)
| set_intersection2(X356,X357) = X356 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_117,lemma,
! [X316,X317] :
( in(X316,X317)
| disjoint(singleton(X316),X317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_88])]) ).
fof(i_0_118,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_119,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_120,lemma,
! [X428,X429,X430] :
( singleton(X428) != unordered_pair(X429,X430)
| X428 = X429 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_121,lemma,
! [X433,X434,X435] :
( singleton(X433) != unordered_pair(X434,X435)
| X434 = X435 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_122,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_123,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_124,plain,
! [X309] : set_intersection2(X309,X309) = X309,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_125,plain,
! [X358] : set_intersection2(X358,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_126,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_127,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
inference(assume_negation,[status(cth)],[t92_zfmisc_1]) ).
fof(i_0_128,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_129,lemma,
! [X311] : singleton(X311) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_130,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_131,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_89]) ).
cnf(i_0_132,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_90,c_0_91]) ).
cnf(i_0_133,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_89]) ).
cnf(i_0_134,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_92]) ).
cnf(i_0_135,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_93]) ).
fof(i_0_136,plain,
! [X287,X288,X289,X290,X291,X292,X293,X294] :
( ( in(X290,X287)
| ~ in(X290,X289)
| X289 != set_difference(X287,X288) )
& ( ~ in(X290,X288)
| ~ in(X290,X289)
| X289 != set_difference(X287,X288) )
& ( ~ in(X291,X287)
| in(X291,X288)
| in(X291,X289)
| X289 != set_difference(X287,X288) )
& ( ~ in(esk16_3(X292,X293,X294),X294)
| ~ in(esk16_3(X292,X293,X294),X292)
| in(esk16_3(X292,X293,X294),X293)
| X294 = set_difference(X292,X293) )
& ( in(esk16_3(X292,X293,X294),X292)
| in(esk16_3(X292,X293,X294),X294)
| X294 = set_difference(X292,X293) )
& ( ~ in(esk16_3(X292,X293,X294),X293)
| in(esk16_3(X292,X293,X294),X294)
| X294 = set_difference(X292,X293) ) ),
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_94])])])])])]) ).
cnf(i_0_137,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_89]) ).
fof(i_0_138,plain,
! [X235,X236,X237,X238,X239,X240,X241,X242] :
( ( ~ in(X238,X237)
| in(X238,X235)
| in(X238,X236)
| X237 != set_union2(X235,X236) )
& ( ~ in(X239,X235)
| in(X239,X237)
| X237 != set_union2(X235,X236) )
& ( ~ in(X239,X236)
| in(X239,X237)
| X237 != set_union2(X235,X236) )
& ( ~ in(esk5_3(X240,X241,X242),X240)
| ~ in(esk5_3(X240,X241,X242),X242)
| X242 = set_union2(X240,X241) )
& ( ~ in(esk5_3(X240,X241,X242),X241)
| ~ in(esk5_3(X240,X241,X242),X242)
| X242 = set_union2(X240,X241) )
& ( in(esk5_3(X240,X241,X242),X242)
| in(esk5_3(X240,X241,X242),X240)
| in(esk5_3(X240,X241,X242),X241)
| X242 = set_union2(X240,X241) ) ),
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_139,plain,
! [X226,X227,X228,X229,X230,X231,X232,X233] :
( ( ~ in(X229,X228)
| X229 = X226
| X229 = X227
| X228 != unordered_pair(X226,X227) )
& ( X230 != X226
| in(X230,X228)
| X228 != unordered_pair(X226,X227) )
& ( X230 != X227
| in(X230,X228)
| X228 != unordered_pair(X226,X227) )
& ( esk4_3(X231,X232,X233) != X231
| ~ in(esk4_3(X231,X232,X233),X233)
| X233 = unordered_pair(X231,X232) )
& ( esk4_3(X231,X232,X233) != X232
| ~ in(esk4_3(X231,X232,X233),X233)
| X233 = unordered_pair(X231,X232) )
& ( in(esk4_3(X231,X232,X233),X233)
| esk4_3(X231,X232,X233) = X231
| esk4_3(X231,X232,X233) = X232
| X233 = unordered_pair(X231,X232) ) ),
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_140,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_92]) ).
cnf(i_0_141,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_92]) ).
cnf(i_0_142,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_95]) ).
cnf(i_0_143,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_95]) ).
cnf(i_0_144,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_95]) ).
cnf(i_0_145,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_96]) ).
cnf(i_0_146,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_97]) ).
cnf(i_0_147,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_97]) ).
cnf(i_0_148,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_98]) ).
cnf(i_0_149,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_89]) ).
cnf(i_0_150,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_99]) ).
fof(i_0_151,plain,
! [X276,X277,X278,X280,X281,X282,X283,X285] :
( ( in(X278,esk13_3(X276,X277,X278))
| ~ in(X278,X277)
| X277 != union(X276) )
& ( in(esk13_3(X276,X277,X278),X276)
| ~ in(X278,X277)
| X277 != union(X276) )
& ( ~ in(X280,X281)
| ~ in(X281,X276)
| in(X280,X277)
| X277 != union(X276) )
& ( ~ in(esk14_2(X282,X283),X283)
| ~ in(esk14_2(X282,X283),X285)
| ~ in(X285,X282)
| X283 = union(X282) )
& ( in(esk14_2(X282,X283),esk15_2(X282,X283))
| in(esk14_2(X282,X283),X283)
| X283 = union(X282) )
& ( in(esk15_2(X282,X283),X282)
| in(esk14_2(X282,X283),X283)
| X283 = union(X282) ) ),
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_152,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_100]) ).
cnf(i_0_153,lemma,
( disjoint(X1,X2)
| in(esk21_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_99]) ).
fof(i_0_154,plain,
! [X219,X220,X221,X222,X223,X224] :
( ( ~ in(X221,X220)
| subset(X221,X219)
| X220 != powerset(X219) )
& ( ~ subset(X222,X219)
| in(X222,X220)
| X220 != powerset(X219) )
& ( ~ in(esk3_2(X223,X224),X224)
| ~ subset(esk3_2(X223,X224),X223)
| X224 = powerset(X223) )
& ( in(esk3_2(X223,X224),X224)
| subset(esk3_2(X223,X224),X223)
| X224 = powerset(X223) ) ),
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_155,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
fof(i_0_156,plain,
! [X359,X360] :
( ( ~ in(esk19_2(X359,X360),X359)
| ~ in(esk19_2(X359,X360),X360)
| X359 = X360 )
& ( in(esk19_2(X359,X360),X359)
| in(esk19_2(X359,X360),X360)
| X359 = X360 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_157,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
cnf(i_0_158,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_102]) ).
cnf(i_0_159,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_103]) ).
cnf(i_0_160,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
cnf(i_0_161,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
cnf(i_0_162,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_104]) ).
fof(i_0_163,lemma,
! [X363,X364,X365] :
( ~ subset(X363,X364)
| subset(set_difference(X363,X365),set_difference(X364,X365)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
cnf(i_0_164,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]) ).
cnf(i_0_165,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_106]) ).
fof(i_0_166,lemma,
! [X425,X426,X427] :
( ~ subset(X425,X426)
| ~ subset(X427,X426)
| subset(set_union2(X425,X427),X426) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_167,lemma,
! [X376,X377,X378] :
( ( in(X376,X378)
| ~ subset(unordered_pair(X376,X377),X378) )
& ( in(X377,X378)
| ~ subset(unordered_pair(X376,X377),X378) )
& ( ~ in(X376,X378)
| ~ in(X377,X378)
| subset(unordered_pair(X376,X377),X378) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
cnf(i_0_168,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_169,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_108]) ).
cnf(i_0_170,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_109]) ).
fof(i_0_171,plain,
! [X261,X262,X263,X264,X265] :
( ( ~ subset(X261,X262)
| ~ in(X263,X261)
| in(X263,X262) )
& ( in(esk11_2(X264,X265),X264)
| subset(X264,X265) )
& ( ~ in(esk11_2(X264,X265),X265)
| subset(X264,X265) ) ),
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_172,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_173,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]) ).
cnf(i_0_174,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_112]) ).
cnf(i_0_175,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]) ).
fof(i_0_176,lemma,
! [X384,X385,X387,X388,X389] :
( ( in(esk20_2(X384,X385),X384)
| disjoint(X384,X385) )
& ( in(esk20_2(X384,X385),X385)
| disjoint(X384,X385) )
& ( ~ in(X389,X387)
| ~ in(X389,X388)
| ~ disjoint(X387,X388) ) ),
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_113])])])])])]) ).
cnf(i_0_177,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_178,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_108]) ).
cnf(i_0_179,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_114]) ).
cnf(i_0_180,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_115]) ).
cnf(i_0_181,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]) ).
fof(i_0_182,lemma,
! [X393,X394] :
( ~ subset(X393,X394)
| X394 = set_union2(X393,set_difference(X394,X393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_183,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_184,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]) ).
cnf(i_0_185,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_112]) ).
fof(i_0_186,lemma,
! [X408,X409,X410] :
( ~ subset(X408,X409)
| ~ disjoint(X409,X410)
| disjoint(X408,X410) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_187,lemma,
! [X350,X351,X352] :
( ~ subset(X350,X351)
| ~ subset(X351,X352)
| subset(X350,X352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(i_0_188,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_105]) ).
cnf(i_0_189,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]) ).
fof(i_0_190,lemma,
! [X391,X392] : set_difference(set_union2(X391,X392),X392) = set_difference(X391,X392),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_191,lemma,
! [X379,X380] : set_union2(X379,set_difference(X380,X379)) = set_union2(X379,X380),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_192,plain,
! [X304,X305] :
( empty(X304)
| ~ empty(set_union2(X304,X305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_118])]) ).
fof(i_0_193,plain,
! [X306,X307] :
( empty(X306)
| ~ empty(set_union2(X307,X306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_119])]) ).
cnf(i_0_194,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_103]) ).
fof(i_0_195,lemma,
! [X338,X339,X340,X341] :
( unordered_pair(X338,X339) != unordered_pair(X340,X341)
| X338 = X340
| X338 = X341 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
fof(i_0_196,plain,
! [X206,X207] :
( ( subset(X206,X207)
| X206 != X207 )
& ( subset(X207,X206)
| X206 != X207 )
& ( ~ subset(X206,X207)
| ~ subset(X207,X206)
| X206 = X207 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(i_0_197,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_120]) ).
cnf(i_0_198,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_121]) ).
fof(i_0_199,lemma,
! [X406,X407] :
( ~ subset(X406,X407)
| ~ proper_subset(X407,X406) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_200,plain,
! [X198,X199] :
( ~ proper_subset(X198,X199)
| ~ proper_subset(X199,X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_122])]) ).
fof(i_0_201,plain,
! [X196,X197] :
( ~ in(X196,X197)
| ~ in(X197,X196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_123])]) ).
fof(i_0_202,lemma,
! [X327,X328] :
( ~ in(X327,X328)
| subset(X327,union(X328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_203,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_204,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_108]) ).
cnf(i_0_205,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_103]) ).
cnf(i_0_206,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_124]) ).
fof(i_0_207,lemma,
! [X370,X371] : subset(set_difference(X370,X371),X370),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_208,lemma,
! [X419,X420] : subset(X419,set_union2(X419,X420)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_209,plain,
! [X300,X301] :
( ( subset(X300,X301)
| ~ proper_subset(X300,X301) )
& ( X300 != X301
| ~ proper_subset(X300,X301) )
& ( ~ subset(X300,X301)
| X300 = X301
| proper_subset(X300,X301) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_210,lemma,
! [X421,X422] :
( ( ~ disjoint(X421,X422)
| set_difference(X421,X422) = X421 )
& ( set_difference(X421,X422) != X421
| disjoint(X421,X422) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_211,lemma,
! [X342,X343] :
( ~ subset(X342,X343)
| set_union2(X342,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_212,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_125]) ).
fof(i_0_213,plain,
! [X336,X337] :
( ~ disjoint(X336,X337)
| disjoint(X337,X336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_214,lemma,
! [X372,X373] :
( ( set_difference(X372,X373) != empty_set
| subset(X372,X373) )
& ( ~ subset(X372,X373)
| set_difference(X372,X373) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_215,lemma,
! [X320,X321] :
( ( set_difference(X320,X321) != empty_set
| subset(X320,X321) )
& ( ~ subset(X320,X321)
| set_difference(X320,X321) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_216,plain,
! [X417,X418] :
( ~ in(X417,X418)
| ~ empty(X418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_217,plain,
! [X202,X203] : set_union2(X202,X203) = set_union2(X203,X202),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_218,plain,
! [X200,X201] : unordered_pair(X200,X201) = unordered_pair(X201,X200),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_219,plain,
! [X215,X216,X217] :
( ( X215 != empty_set
| ~ in(X216,X215) )
& ( in(esk2_1(X217),X217)
| X217 = 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_126])])])])]) ).
fof(i_0_220,negated_conjecture,
( in(esk22_0,esk23_0)
& ~ subset(esk22_0,union(esk23_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_127])])]) ).
fof(i_0_221,plain,
! [X310] : ~ proper_subset(X310,X310),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_128])]) ).
cnf(i_0_222,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_129]) ).
fof(i_0_223,lemma,
! [X390] :
( ~ subset(X390,empty_set)
| X390 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_224,plain,
! [X423,X424] :
( ~ empty(X423)
| X423 = X424
| ~ empty(X424) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_225,plain,
! [X308] : set_union2(X308,X308) = X308,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_226,plain,
! [X335] : subset(X335,X335),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_227,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_228,plain,
! [X383] : set_difference(X383,empty_set) = X383,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_229,plain,
! [X349] : set_union2(X349,empty_set) = X349,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_230,lemma,
! [X362] : subset(empty_set,X362),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_231,plain,
! [X399] : set_difference(empty_set,X399) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_232,plain,
! [X414] :
( ~ empty(X414)
| X414 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_233,plain,
~ empty(esk18_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_130])]) ).
fof(i_0_234,plain,
empty(esk17_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_235,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_131,c_0_132]),
[final] ).
cnf(i_0_236,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_133,c_0_132]),
[final] ).
cnf(i_0_237,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_134,c_0_135]),
[final] ).
cnf(i_0_238,plain,
( in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_239,plain,
( in(esk6_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_240,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_136]),
[final] ).
cnf(i_0_241,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_137,c_0_132]),
[final] ).
cnf(i_0_242,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_138]),
[final] ).
cnf(i_0_243,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_138]),
[final] ).
cnf(i_0_244,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_138]),
[final] ).
cnf(i_0_245,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_136]),
[final] ).
cnf(i_0_246,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_139]),
[final] ).
cnf(i_0_247,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_139]),
[final] ).
cnf(i_0_248,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_140,c_0_135]),
[final] ).
cnf(i_0_249,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_141,c_0_135]),
[final] ).
cnf(i_0_250,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_142,c_0_132]),
[final] ).
cnf(i_0_251,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_143,c_0_132]),
[final] ).
cnf(i_0_252,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_136]),
[final] ).
cnf(i_0_253,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_89]),
[final] ).
cnf(i_0_254,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_89]),
[final] ).
cnf(i_0_255,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_139]),
[final] ).
cnf(i_0_256,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_144,c_0_132]),
[final] ).
cnf(i_0_257,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_145,c_0_132]),
[final] ).
cnf(i_0_258,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_146,c_0_132]),c_0_132]),
[final] ).
cnf(i_0_259,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_147,c_0_132]),c_0_132]),
[final] ).
cnf(i_0_260,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_148,c_0_135]),c_0_135]),
[final] ).
cnf(i_0_261,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_149,c_0_132]),
[final] ).
cnf(i_0_262,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_150,c_0_135]),
[final] ).
cnf(i_0_263,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_151]),
[final] ).
cnf(i_0_264,plain,
( in(esk13_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_265,plain,
( in(X1,esk13_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_266,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_152,c_0_135]),
[final] ).
cnf(i_0_267,lemma,
( disjoint(X1,X2)
| in(esk21_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_153,c_0_135]),
[final] ).
cnf(i_0_268,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_269,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_155,c_0_91]),
[final] ).
cnf(i_0_270,plain,
( X1 = X2
| ~ in(esk19_2(X1,X2),X1)
| ~ in(esk19_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_271,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_157,c_0_135]),
[final] ).
cnf(i_0_272,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_151]),
[final] ).
cnf(i_0_273,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_158,c_0_91]),c_0_91]),
[final] ).
cnf(i_0_274,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_159,c_0_91]),
[final] ).
cnf(i_0_275,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_160,c_0_135]),
[final] ).
cnf(i_0_276,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_161,c_0_135]),
[final] ).
cnf(i_0_277,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_162,c_0_135]),
[final] ).
cnf(i_0_278,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_279,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_164,c_0_91]),
[final] ).
cnf(i_0_280,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_165,c_0_91]),
[final] ).
cnf(i_0_281,plain,
( in(esk15_2(X1,X2),X1)
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_282,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_283,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_284,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_285,plain,
( in(esk19_2(X1,X2),X1)
| in(esk19_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_286,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_168,c_0_91]),c_0_91]),
[final] ).
cnf(i_0_287,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_169,c_0_91]),c_0_91]),
[final] ).
cnf(i_0_288,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_170,c_0_135]),c_0_135]),
[final] ).
cnf(i_0_289,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_290,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_172,c_0_91]),
[final] ).
cnf(i_0_291,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_173,c_0_91]),
[final] ).
cnf(i_0_292,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_293,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_294,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_174,c_0_135]),
[final] ).
cnf(i_0_295,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_296,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_297,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_175,c_0_91]),
[final] ).
cnf(i_0_298,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_299,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_300,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_301,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_177,c_0_91]),c_0_91]),
[final] ).
cnf(i_0_302,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_178,c_0_91]),c_0_91]),
[final] ).
cnf(i_0_303,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_179,c_0_91]),
[final] ).
cnf(i_0_304,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_180,c_0_91]),
[final] ).
cnf(i_0_305,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_181,c_0_135]),
[final] ).
cnf(i_0_306,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_307,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_183,c_0_91]),
[final] ).
cnf(i_0_308,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_184,c_0_91]),
[final] ).
cnf(i_0_309,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_185,c_0_135]),
[final] ).
cnf(i_0_310,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_311,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_312,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_313,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_314,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_315,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_316,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_188,c_0_91]),
[final] ).
cnf(i_0_317,lemma,
( in(esk20_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_318,lemma,
( in(esk20_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_319,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_320,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_189,c_0_91]),
[final] ).
cnf(i_0_321,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_322,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_191]),
[final] ).
cnf(i_0_323,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_192]),
[final] ).
cnf(i_0_324,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_325,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_326,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_194,c_0_91]),
[final] ).
cnf(i_0_327,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_328,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_329,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_197,c_0_91]),
[final] ).
cnf(i_0_330,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_198,c_0_91]),
[final] ).
cnf(i_0_331,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_332,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_333,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_334,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_335,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_336,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_337,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_203,c_0_91]),
[final] ).
cnf(i_0_338,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_204,c_0_91]),
[final] ).
cnf(i_0_339,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_205,c_0_91]),
[final] ).
cnf(i_0_340,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_341,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_342,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_206,c_0_135]),
[final] ).
cnf(i_0_343,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_344,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_345,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_346,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_347,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_348,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_211]),
[final] ).
cnf(i_0_349,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_212,c_0_135]),
[final] ).
cnf(i_0_350,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_351,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_352,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_353,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_215]),
[final] ).
cnf(i_0_354,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_214]),
[final] ).
cnf(i_0_355,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_215]),
[final] ).
cnf(i_0_356,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_357,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_217]),
[final] ).
cnf(i_0_358,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_218]),
[final] ).
cnf(i_0_359,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_360,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_361,negated_conjecture,
~ subset(esk22_0,union(esk23_0)),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_362,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_221]),
[final] ).
cnf(i_0_363,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_222,c_0_91]),
[final] ).
cnf(i_0_364,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_365,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_366,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_367,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_368,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_369,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_370,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_226]),
[final] ).
cnf(i_0_371,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_227,c_0_91]),
[final] ).
cnf(i_0_372,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_373,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_229]),
[final] ).
cnf(i_0_374,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_375,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_231]),
[final] ).
cnf(i_0_376,negated_conjecture,
in(esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_377,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_232]),
[final] ).
cnf(i_0_378,plain,
~ empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_379,plain,
empty(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_380,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_381,axiom,
X1 = X1 ).
cnf(i_0_382,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_383,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_384,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_385,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_386,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_387,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_388,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_389,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_390,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_391,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_392,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_393,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_394,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_395,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_396,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_397,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_398,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_399,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_400,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_401,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_402,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_403,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_404,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_405,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_406,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_407,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_408,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_409,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_410,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_381_001,axiom,
X1 = X1 ).
cnf(i_0_382_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_383_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_384_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_385_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_386_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_387_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_388_008,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_389_009,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_390_010,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_391_011,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_392_012,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_393_013,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_394_014,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_395_015,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_396_016,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_397_017,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_398_018,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_399_019,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_400_020,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_401_021,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_402_022,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_403_023,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_404_024,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_405_025,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_406_026,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_407_027,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_408_028,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_409_029,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_410_030,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_411,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,[],[235]) ).
cnf(i_0_412,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk7_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[238]) ).
cnf(i_0_413,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[239]) ).
cnf(i_0_414,plain,
X1 = X1,
inference(equality_inference,[],[258]) ).
cnf(i_0_415,plain,
X1 = X1,
inference(equality_inference,[],[259]) ).
cnf(i_0_416,plain,
( ~ in(X1,union(X2))
| in(esk13_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[264]) ).
cnf(i_0_417,plain,
( ~ in(X1,union(X2))
| in(X1,esk13_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[265]) ).
cnf(i_0_418,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[271]) ).
cnf(i_0_419,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[276]) ).
cnf(i_0_420,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[295]) ).
cnf(i_0_421,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[296]) ).
cnf(i_0_422,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[298]) ).
cnf(i_0_423,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[299]) ).
cnf(i_0_424,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[310]) ).
cnf(i_0_425,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[311]) ).
cnf(i_0_426,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[312]) ).
cnf(i_0_427,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[325]) ).
cnf(i_0_428,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[326]) ).
cnf(i_0_429,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[327]) ).
cnf(i_0_430,plain,
X1 = X1,
inference(equality_inference,[],[329]) ).
cnf(i_0_431,plain,
X1 = X1,
inference(equality_inference,[],[330]) ).
cnf(i_0_432,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[331]) ).
cnf(i_0_433,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[332]) ).
cnf(i_0_434,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[338]) ).
cnf(i_0_435,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[359]) ).
cnf(i_0_436,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[360]) ).
cnf(i_0_437,plain,
subset(X1,X1),
inference(equality_inference,[],[366]) ).
cnf(i_0_438,plain,
subset(X1,X1),
inference(equality_inference,[],[367]) ).
cnf(i_0_439,plain,
$false,
inference(scs_inference,[],[i_0_361,i_0_376,i_0_336]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU163+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
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:46:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.31/1.61 % Version : CSE_E---1.7
% 0.31/1.61 % Problem : theBenchmark.p
% 0.31/1.61 % SZS status Theorem for theBenchmark.p
% 0.31/1.61 % SZS output start CNFRefutation
% See solution above
% 0.31/1.66 % Total time : 1.272s
%------------------------------------------------------------------------------