%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU148+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 05:10:47 PM UTC 2026
% Result : Theorem 0.16s 1.59s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_94)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t6_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t26_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t60_xboole_1,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_64,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_65,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t6_zfmisc_1]) ).
fof(i_0_66,plain,
! [X195,X196,X197,X198,X199,X200,X201,X202] :
( ( in(X198,X195)
| ~ in(X198,X197)
| X197 != set_intersection2(X195,X196) )
& ( in(X198,X196)
| ~ in(X198,X197)
| X197 != set_intersection2(X195,X196) )
& ( ~ in(X199,X195)
| ~ in(X199,X196)
| in(X199,X197)
| X197 != set_intersection2(X195,X196) )
& ( ~ in(esk7_3(X200,X201,X202),X202)
| ~ in(esk7_3(X200,X201,X202),X200)
| ~ in(esk7_3(X200,X201,X202),X201)
| X202 = set_intersection2(X200,X201) )
& ( in(esk7_3(X200,X201,X202),X200)
| in(esk7_3(X200,X201,X202),X202)
| X202 = set_intersection2(X200,X201) )
& ( in(esk7_3(X200,X201,X202),X201)
| in(esk7_3(X200,X201,X202),X202)
| X202 = set_intersection2(X200,X201) ) ),
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_67,lemma,
! [X281,X282] : set_difference(X281,set_difference(X281,X282)) = set_intersection2(X281,X282),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_68,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_69,lemma,
! [X250,X251,X252] :
( ~ subset(X250,X251)
| subset(set_intersection2(X250,X252),set_intersection2(X251,X252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_70,lemma,
! [X284,X285,X287,X288,X289] :
( ( disjoint(X284,X285)
| in(esk13_2(X284,X285),set_intersection2(X284,X285)) )
& ( ~ in(X289,set_intersection2(X287,X288))
| ~ disjoint(X287,X288) ) ),
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_64])])])])]) ).
fof(i_0_71,lemma,
! [X243,X244,X245] :
( ~ subset(X243,X244)
| ~ subset(X243,X245)
| subset(X243,set_intersection2(X244,X245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_72,lemma,
! [X229,X230,X231] :
( ~ subset(X229,X230)
| in(X231,X229)
| subset(X229,set_difference(X230,singleton(X231))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_73,lemma,
! [X295] : unordered_pair(X295,X295) = singleton(X295),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_74,plain,
! [X153,X154,X155,X156,X157,X158] :
( ( ~ in(X155,X154)
| X155 = X153
| X154 != singleton(X153) )
& ( X156 != X153
| in(X156,X154)
| X154 != singleton(X153) )
& ( ~ in(esk1_2(X157,X158),X158)
| esk1_2(X157,X158) != X157
| X158 = singleton(X157) )
& ( in(esk1_2(X157,X158),X158)
| esk1_2(X157,X158) = X157
| X158 = singleton(X157) ) ),
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_75,lemma,
! [X241,X242] : subset(set_intersection2(X241,X242),X241),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_76,lemma,
! [X232,X233] :
( ( ~ subset(X232,singleton(X233))
| X232 = empty_set
| X232 = singleton(X233) )
& ( X232 != empty_set
| subset(X232,singleton(X233)) )
& ( X232 != singleton(X233)
| subset(X232,singleton(X233)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_77,plain,
! [X149,X150] : set_intersection2(X149,X150) = set_intersection2(X150,X149),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_78,lemma,
! [X225,X226] :
( ( ~ subset(singleton(X225),X226)
| in(X225,X226) )
& ( ~ in(X225,X226)
| subset(singleton(X225),X226) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_79,plain,
! [X213,X214] :
( ( ~ disjoint(X213,X214)
| set_intersection2(X213,X214) = empty_set )
& ( set_intersection2(X213,X214) != empty_set
| disjoint(X213,X214) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_80,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_81,lemma,
! [X253,X254] :
( ~ subset(X253,X254)
| set_intersection2(X253,X254) = X253 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_82,negated_conjecture,
( subset(singleton(esk14_0),singleton(esk15_0))
& esk14_0 != esk15_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_65])])]) ).
fof(i_0_83,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_84,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_85,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_86,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_87,plain,
! [X222] : set_intersection2(X222,X222) = X222,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_88,plain,
! [X255] : set_intersection2(X255,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_89,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_90,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_91,lemma,
! [X224] : singleton(X224) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_92,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_93,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk7_3(X1,X2,X3),X3)
| ~ in(esk7_3(X1,X2,X3),X1)
| ~ in(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_94,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_67]) ).
fof(i_0_95,plain,
! [X204,X205,X206,X207,X208,X209,X210,X211] :
( ( in(X207,X204)
| ~ in(X207,X206)
| X206 != set_difference(X204,X205) )
& ( ~ in(X207,X205)
| ~ in(X207,X206)
| X206 != set_difference(X204,X205) )
& ( ~ in(X208,X204)
| in(X208,X205)
| in(X208,X206)
| X206 != set_difference(X204,X205) )
& ( ~ in(esk8_3(X209,X210,X211),X211)
| ~ in(esk8_3(X209,X210,X211),X209)
| in(esk8_3(X209,X210,X211),X210)
| X211 = set_difference(X209,X210) )
& ( in(esk8_3(X209,X210,X211),X209)
| in(esk8_3(X209,X210,X211),X211)
| X211 = set_difference(X209,X210) )
& ( ~ in(esk8_3(X209,X210,X211),X210)
| in(esk8_3(X209,X210,X211),X211)
| X211 = set_difference(X209,X210) ) ),
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_68])])])])])]) ).
fof(i_0_96,plain,
! [X180,X181,X182,X183,X184,X185,X186,X187] :
( ( ~ in(X183,X182)
| in(X183,X180)
| in(X183,X181)
| X182 != set_union2(X180,X181) )
& ( ~ in(X184,X180)
| in(X184,X182)
| X182 != set_union2(X180,X181) )
& ( ~ in(X184,X181)
| in(X184,X182)
| X182 != set_union2(X180,X181) )
& ( ~ in(esk5_3(X185,X186,X187),X185)
| ~ in(esk5_3(X185,X186,X187),X187)
| X187 = set_union2(X185,X186) )
& ( ~ in(esk5_3(X185,X186,X187),X186)
| ~ in(esk5_3(X185,X186,X187),X187)
| X187 = set_union2(X185,X186) )
& ( in(esk5_3(X185,X186,X187),X187)
| in(esk5_3(X185,X186,X187),X185)
| in(esk5_3(X185,X186,X187),X186)
| X187 = set_union2(X185,X186) ) ),
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_97,plain,
! [X171,X172,X173,X174,X175,X176,X177,X178] :
( ( ~ in(X174,X173)
| X174 = X171
| X174 = X172
| X173 != unordered_pair(X171,X172) )
& ( X175 != X171
| in(X175,X173)
| X173 != unordered_pair(X171,X172) )
& ( X175 != X172
| in(X175,X173)
| X173 != unordered_pair(X171,X172) )
& ( esk4_3(X176,X177,X178) != X176
| ~ in(esk4_3(X176,X177,X178),X178)
| X178 = unordered_pair(X176,X177) )
& ( esk4_3(X176,X177,X178) != X177
| ~ in(esk4_3(X176,X177,X178),X178)
| X178 = unordered_pair(X176,X177) )
& ( in(esk4_3(X176,X177,X178),X178)
| esk4_3(X176,X177,X178) = X176
| esk4_3(X176,X177,X178) = X177
| X178 = unordered_pair(X176,X177) ) ),
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_98,plain,
( in(esk7_3(X1,X2,X3),X1)
| in(esk7_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_99,plain,
( in(esk7_3(X1,X2,X3),X2)
| in(esk7_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_100,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]) ).
cnf(i_0_101,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_102,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_71]) ).
cnf(i_0_103,lemma,
( disjoint(X1,X2)
| in(esk13_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
fof(i_0_104,plain,
! [X164,X165,X166,X167,X168,X169] :
( ( ~ in(X166,X165)
| subset(X166,X164)
| X165 != powerset(X164) )
& ( ~ subset(X167,X164)
| in(X167,X165)
| X165 != powerset(X164) )
& ( ~ in(esk3_2(X168,X169),X169)
| ~ subset(esk3_2(X168,X169),X168)
| X169 = powerset(X168) )
& ( in(esk3_2(X168,X169),X169)
| subset(esk3_2(X168,X169),X168)
| X169 = powerset(X168) ) ),
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_105,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]) ).
cnf(i_0_106,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_73]) ).
fof(i_0_107,plain,
! [X256,X257] :
( ( ~ in(esk11_2(X256,X257),X256)
| ~ in(esk11_2(X256,X257),X257)
| X256 = X257 )
& ( in(esk11_2(X256,X257),X256)
| in(esk11_2(X256,X257),X257)
| X256 = X257 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_108,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_109,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
cnf(i_0_110,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_111,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_112,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_75]) ).
fof(i_0_113,lemma,
! [X260,X261,X262] :
( ~ subset(X260,X261)
| subset(set_difference(X260,X262),set_difference(X261,X262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_114,lemma,
! [X307,X308,X309] :
( ~ subset(X307,X308)
| ~ subset(X309,X308)
| subset(set_union2(X307,X309),X308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(i_0_115,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_76]) ).
cnf(i_0_116,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_77]) ).
fof(i_0_117,plain,
! [X189,X190,X191,X192,X193] :
( ( ~ subset(X189,X190)
| ~ in(X191,X189)
| in(X191,X190) )
& ( in(esk6_2(X192,X193),X192)
| subset(X192,X193) )
& ( ~ in(esk6_2(X192,X193),X193)
| subset(X192,X193) ) ),
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_118,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]) ).
cnf(i_0_119,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
cnf(i_0_120,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
fof(i_0_121,lemma,
! [X270,X271,X273,X274,X275] :
( ( in(esk12_2(X270,X271),X270)
| disjoint(X270,X271) )
& ( in(esk12_2(X270,X271),X271)
| disjoint(X270,X271) )
& ( ~ in(X275,X273)
| ~ in(X275,X274)
| ~ disjoint(X273,X274) ) ),
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_80])])])])])]) ).
cnf(i_0_122,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_76]) ).
cnf(i_0_123,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]) ).
fof(i_0_124,lemma,
! [X279,X280] :
( ~ subset(X279,X280)
| X280 = set_union2(X279,set_difference(X280,X279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_125,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]) ).
cnf(i_0_126,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]) ).
fof(i_0_127,lemma,
! [X292,X293,X294] :
( ~ subset(X292,X293)
| ~ disjoint(X293,X294)
| disjoint(X292,X294) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_128,lemma,
! [X247,X248,X249] :
( ~ subset(X247,X248)
| ~ subset(X248,X249)
| subset(X247,X249) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(i_0_129,negated_conjecture,
subset(singleton(esk14_0),singleton(esk15_0)),
inference(split_conjunct,[status(thm)],[i_0_82]) ).
fof(i_0_130,lemma,
! [X277,X278] : set_difference(set_union2(X277,X278),X278) = set_difference(X277,X278),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_131,lemma,
! [X267,X268] : set_union2(X267,set_difference(X268,X267)) = set_union2(X267,X268),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_132,plain,
! [X217,X218] :
( empty(X217)
| ~ empty(set_union2(X217,X218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_83])]) ).
fof(i_0_133,plain,
! [X219,X220] :
( empty(X219)
| ~ empty(set_union2(X220,X219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_84])]) ).
cnf(i_0_134,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
fof(i_0_135,plain,
! [X151,X152] :
( ( subset(X151,X152)
| X151 != X152 )
& ( subset(X152,X151)
| X151 != X152 )
& ( ~ subset(X151,X152)
| ~ subset(X152,X151)
| X151 = X152 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_136,lemma,
! [X290,X291] :
( ~ subset(X290,X291)
| ~ proper_subset(X291,X290) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_137,plain,
! [X143,X144] :
( ~ proper_subset(X143,X144)
| ~ proper_subset(X144,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_85])]) ).
fof(i_0_138,plain,
! [X141,X142] :
( ~ in(X141,X142)
| ~ in(X142,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_86])]) ).
cnf(i_0_139,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_76]) ).
cnf(i_0_140,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]) ).
cnf(i_0_141,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_87]) ).
fof(i_0_142,lemma,
! [X263,X264] : subset(set_difference(X263,X264),X263),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_143,lemma,
! [X301,X302] : subset(X301,set_union2(X301,X302)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_144,plain,
! [X215,X216] :
( ( subset(X215,X216)
| ~ proper_subset(X215,X216) )
& ( X215 != X216
| ~ proper_subset(X215,X216) )
& ( ~ subset(X215,X216)
| X215 = X216
| proper_subset(X215,X216) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_145,lemma,
! [X303,X304] :
( ( ~ disjoint(X303,X304)
| set_difference(X303,X304) = X303 )
& ( set_difference(X303,X304) != X303
| disjoint(X303,X304) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_146,lemma,
! [X239,X240] :
( ~ subset(X239,X240)
| set_union2(X239,X240) = X240 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_147,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_88]) ).
fof(i_0_148,plain,
! [X237,X238] :
( ~ disjoint(X237,X238)
| disjoint(X238,X237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_149,lemma,
! [X265,X266] :
( ( set_difference(X265,X266) != empty_set
| subset(X265,X266) )
& ( ~ subset(X265,X266)
| set_difference(X265,X266) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_150,lemma,
! [X227,X228] :
( ( set_difference(X227,X228) != empty_set
| subset(X227,X228) )
& ( ~ subset(X227,X228)
| set_difference(X227,X228) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_151,plain,
! [X299,X300] :
( ~ in(X299,X300)
| ~ empty(X300) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_152,plain,
! [X147,X148] : set_union2(X147,X148) = set_union2(X148,X147),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_153,plain,
! [X145,X146] : unordered_pair(X145,X146) = unordered_pair(X146,X145),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_154,plain,
! [X160,X161,X162] :
( ( X160 != empty_set
| ~ in(X161,X160) )
& ( in(esk2_1(X162),X162)
| X162 = 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_89])])])])]) ).
fof(i_0_155,plain,
! [X223] : ~ proper_subset(X223,X223),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_90])]) ).
cnf(i_0_156,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_91]) ).
fof(i_0_157,lemma,
! [X276] :
( ~ subset(X276,empty_set)
| X276 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_158,plain,
! [X305,X306] :
( ~ empty(X305)
| X305 = X306
| ~ empty(X306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_159,plain,
! [X221] : set_union2(X221,X221) = X221,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_160,plain,
! [X236] : subset(X236,X236),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_161,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_162,plain,
! [X269] : set_difference(X269,empty_set) = X269,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_163,plain,
! [X246] : set_union2(X246,empty_set) = X246,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_164,lemma,
! [X259] : subset(empty_set,X259),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_165,plain,
! [X283] : set_difference(empty_set,X283) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_166,plain,
! [X296] :
( ~ empty(X296)
| X296 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_167,plain,
~ empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_92])]) ).
fof(i_0_168,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_169,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk7_3(X1,X2,X3),X3)
| ~ in(esk7_3(X1,X2,X3),X2)
| ~ in(esk7_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_93,c_0_94]),
[final] ).
cnf(i_0_170,plain,
( in(esk8_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(esk8_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_171,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_96]),
[final] ).
cnf(i_0_172,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_96]),
[final] ).
cnf(i_0_173,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_96]),
[final] ).
cnf(i_0_174,plain,
( in(esk8_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_175,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_97]),
[final] ).
cnf(i_0_176,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_97]),
[final] ).
cnf(i_0_177,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk7_3(X1,X2,X3),X3)
| in(esk7_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_98,c_0_94]),
[final] ).
cnf(i_0_178,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk7_3(X1,X2,X3),X3)
| in(esk7_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_99,c_0_94]),
[final] ).
cnf(i_0_179,plain,
( in(esk8_3(X1,X2,X3),X1)
| in(esk8_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_180,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_97]),
[final] ).
cnf(i_0_181,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_100,c_0_94]),c_0_94]),
[final] ).
cnf(i_0_182,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_101,c_0_94]),
[final] ).
cnf(i_0_183,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_102,c_0_94]),
[final] ).
cnf(i_0_184,lemma,
( disjoint(X1,X2)
| in(esk13_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_103,c_0_94]),
[final] ).
cnf(i_0_185,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_186,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_105,c_0_106]),
[final] ).
cnf(i_0_187,plain,
( X1 = X2
| ~ in(esk11_2(X1,X2),X1)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_188,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_108,c_0_94]),
[final] ).
cnf(i_0_189,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_109,c_0_106]),
[final] ).
cnf(i_0_190,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_110,c_0_94]),
[final] ).
cnf(i_0_191,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_111,c_0_94]),
[final] ).
cnf(i_0_192,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_112,c_0_94]),
[final] ).
cnf(i_0_193,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_194,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_195,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_196,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_197,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_115,c_0_106]),c_0_106]),
[final] ).
cnf(i_0_198,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_116,c_0_94]),c_0_94]),
[final] ).
cnf(i_0_199,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_200,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_118,c_0_106]),
[final] ).
cnf(i_0_201,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_119,c_0_94]),
[final] ).
cnf(i_0_202,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_203,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_204,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_120,c_0_106]),
[final] ).
cnf(i_0_205,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_206,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_207,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_122,c_0_106]),c_0_106]),
[final] ).
cnf(i_0_208,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_123,c_0_94]),
[final] ).
cnf(i_0_209,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_210,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_125,c_0_106]),
[final] ).
cnf(i_0_211,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_126,c_0_94]),
[final] ).
cnf(i_0_212,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_213,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_214,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_215,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_216,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_217,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_218,lemma,
( in(esk12_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_219,lemma,
( in(esk12_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_220,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_221,negated_conjecture,
subset(unordered_pair(esk14_0,esk14_0),unordered_pair(esk15_0,esk15_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_129,c_0_106]),c_0_106]),
[final] ).
cnf(i_0_222,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_223,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_224,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_225,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_226,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_227,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_134,c_0_106]),
[final] ).
cnf(i_0_228,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_229,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_230,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_231,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_232,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_137]),
[final] ).
cnf(i_0_233,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_234,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_139,c_0_106]),
[final] ).
cnf(i_0_235,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_140,c_0_106]),
[final] ).
cnf(i_0_236,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_237,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_238,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_141,c_0_94]),
[final] ).
cnf(i_0_239,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_240,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_143]),
[final] ).
cnf(i_0_241,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_242,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_243,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_244,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_245,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_147,c_0_94]),
[final] ).
cnf(i_0_246,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_247,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_248,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_249,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_250,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_251,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_252,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_253,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_254,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_255,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_256,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_257,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_258,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_156,c_0_106]),
[final] ).
cnf(i_0_259,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_260,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_261,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_262,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_263,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_264,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_265,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_266,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_161,c_0_106]),
[final] ).
cnf(i_0_267,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_268,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_269,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_270,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_271,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_272,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_273,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_274,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_275,negated_conjecture,
esk14_0 != esk15_0,
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_276,axiom,
X1 = X1 ).
cnf(i_0_277,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_278,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_279,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_280,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_281,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_282,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_283,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_284,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_285,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_286,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_287,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_288,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_293,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_294,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_298,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_276_001,axiom,
X1 = X1 ).
cnf(i_0_277_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_278_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_279_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_280_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_281_006,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_282_007,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_283_008,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_284_009,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_285_010,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_286_011,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_287_012,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_288_013,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_289_014,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_290_015,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_291_016,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_292_017,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_293_018,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_294_019,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_295_020,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_296_021,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_297_022,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_298_023,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_299_024,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_300,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[188]) ).
cnf(i_0_301,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[191]) ).
cnf(i_0_302,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[202]) ).
cnf(i_0_303,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[203]) ).
cnf(i_0_304,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[205]) ).
cnf(i_0_305,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[212]) ).
cnf(i_0_306,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[213]) ).
cnf(i_0_307,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[214]) ).
cnf(i_0_308,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[226]) ).
cnf(i_0_309,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[227]) ).
cnf(i_0_310,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[229]) ).
cnf(i_0_311,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[230]) ).
cnf(i_0_312,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[234]) ).
cnf(i_0_313,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[255]) ).
cnf(i_0_314,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[256]) ).
cnf(i_0_315,plain,
subset(X1,X1),
inference(equality_inference,[],[261]) ).
cnf(i_0_316,plain,
subset(X1,X1),
inference(equality_inference,[],[262]) ).
cnf(i_0_317,plain,
in(esk14_0,unordered_pair(esk15_0,esk15_0)),
inference(scs_inference,[],[i_0_221,i_0_200]) ).
cnf(i_0_318,plain,
( ~ subset(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_319,plain,
$false,
inference(scs_inference,[],[i_0_221,i_0_275,i_0_200,i_0_309]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SEU148+2 : TPTP v9.2.1. Released v3.3.0.
% 0.05/0.14 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.32 % Computer : n024.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8042.1875MB
% 0.07/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.32 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Mon May 4 21:45:42 EDT 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 % start to proof: theBenchmark
% 0.16/1.59 % Version : CSE_E---1.7
% 0.16/1.59 % Problem : theBenchmark.p
% 0.16/1.59 % SZS status Theorem for theBenchmark.p
% 0.16/1.59 % SZS output start CNFRefutation
% See solution above
% 0.16/1.61 % Total time : 1.261s
%------------------------------------------------------------------------------