%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU143+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 : n020.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 05:10:46 PM UTC 2026
% Result : Theorem 0.35s 1.62s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_84)
% 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(l1_zfmisc_1,conjecture,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_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(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(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(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(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_58,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_59,negated_conjecture,
~ ! [X1] : singleton(X1) != empty_set,
inference(assume_negation,[status(cth)],[l1_zfmisc_1]) ).
fof(i_0_60,plain,
! [X176,X177,X178,X179,X180,X181,X182,X183] :
( ( in(X179,X176)
| ~ in(X179,X178)
| X178 != set_intersection2(X176,X177) )
& ( in(X179,X177)
| ~ in(X179,X178)
| X178 != set_intersection2(X176,X177) )
& ( ~ in(X180,X176)
| ~ in(X180,X177)
| in(X180,X178)
| X178 != set_intersection2(X176,X177) )
& ( ~ in(esk6_3(X181,X182,X183),X183)
| ~ in(esk6_3(X181,X182,X183),X181)
| ~ in(esk6_3(X181,X182,X183),X182)
| X183 = set_intersection2(X181,X182) )
& ( in(esk6_3(X181,X182,X183),X181)
| in(esk6_3(X181,X182,X183),X183)
| X183 = set_intersection2(X181,X182) )
& ( in(esk6_3(X181,X182,X183),X182)
| in(esk6_3(X181,X182,X183),X183)
| X183 = set_intersection2(X181,X182) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(i_0_61,lemma,
! [X255,X256] : set_difference(X255,set_difference(X255,X256)) = set_intersection2(X255,X256),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_62,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_63,lemma,
! [X224,X225,X226] :
( ~ subset(X224,X225)
| subset(set_intersection2(X224,X226),set_intersection2(X225,X226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_64,lemma,
! [X258,X259,X261,X262,X263] :
( ( disjoint(X258,X259)
| in(esk13_2(X258,X259),set_intersection2(X258,X259)) )
& ( ~ in(X263,set_intersection2(X261,X262))
| ~ disjoint(X261,X262) ) ),
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_58])])])])]) ).
fof(i_0_65,lemma,
! [X217,X218,X219] :
( ~ subset(X217,X218)
| ~ subset(X217,X219)
| subset(X217,set_intersection2(X218,X219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_66,plain,
! [X141,X142,X143,X144,X145,X146] :
( ( ~ in(X143,X142)
| X143 = X141
| X142 != singleton(X141) )
& ( X144 != X141
| in(X144,X142)
| X142 != singleton(X141) )
& ( ~ in(esk1_2(X145,X146),X146)
| esk1_2(X145,X146) != X145
| X146 = singleton(X145) )
& ( in(esk1_2(X145,X146),X146)
| esk1_2(X145,X146) = X145
| X146 = singleton(X145) ) ),
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_67,lemma,
! [X269] : unordered_pair(X269,X269) = singleton(X269),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_68,lemma,
! [X215,X216] : subset(set_intersection2(X215,X216),X215),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_69,plain,
! [X137,X138] : set_intersection2(X137,X138) = set_intersection2(X138,X137),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_70,plain,
! [X194,X195] :
( ( ~ disjoint(X194,X195)
| set_intersection2(X194,X195) = empty_set )
& ( set_intersection2(X194,X195) != empty_set
| disjoint(X194,X195) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_71,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_72,lemma,
! [X227,X228] :
( ~ subset(X227,X228)
| set_intersection2(X227,X228) = X227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_73,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_74,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_75,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_76,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_77,plain,
! [X203] : set_intersection2(X203,X203) = X203,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_78,plain,
! [X229] : set_intersection2(X229,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_79,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_80,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_81,negated_conjecture,
singleton(esk8_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_59])])]) ).
fof(i_0_82,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_83,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk6_3(X1,X2,X3),X3)
| ~ in(esk6_3(X1,X2,X3),X1)
| ~ in(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_84,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_61]) ).
fof(i_0_85,plain,
! [X185,X186,X187,X188,X189,X190,X191,X192] :
( ( in(X188,X185)
| ~ in(X188,X187)
| X187 != set_difference(X185,X186) )
& ( ~ in(X188,X186)
| ~ in(X188,X187)
| X187 != set_difference(X185,X186) )
& ( ~ in(X189,X185)
| in(X189,X186)
| in(X189,X187)
| X187 != set_difference(X185,X186) )
& ( ~ in(esk7_3(X190,X191,X192),X192)
| ~ in(esk7_3(X190,X191,X192),X190)
| in(esk7_3(X190,X191,X192),X191)
| X192 = set_difference(X190,X191) )
& ( in(esk7_3(X190,X191,X192),X190)
| in(esk7_3(X190,X191,X192),X192)
| X192 = set_difference(X190,X191) )
& ( ~ in(esk7_3(X190,X191,X192),X191)
| in(esk7_3(X190,X191,X192),X192)
| X192 = set_difference(X190,X191) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_62])])])])])]) ).
fof(i_0_86,plain,
! [X161,X162,X163,X164,X165,X166,X167,X168] :
( ( ~ in(X164,X163)
| in(X164,X161)
| in(X164,X162)
| X163 != set_union2(X161,X162) )
& ( ~ in(X165,X161)
| in(X165,X163)
| X163 != set_union2(X161,X162) )
& ( ~ in(X165,X162)
| in(X165,X163)
| X163 != set_union2(X161,X162) )
& ( ~ in(esk4_3(X166,X167,X168),X166)
| ~ in(esk4_3(X166,X167,X168),X168)
| X168 = set_union2(X166,X167) )
& ( ~ in(esk4_3(X166,X167,X168),X167)
| ~ in(esk4_3(X166,X167,X168),X168)
| X168 = set_union2(X166,X167) )
& ( in(esk4_3(X166,X167,X168),X168)
| in(esk4_3(X166,X167,X168),X166)
| in(esk4_3(X166,X167,X168),X167)
| X168 = set_union2(X166,X167) ) ),
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_87,plain,
! [X152,X153,X154,X155,X156,X157,X158,X159] :
( ( ~ in(X155,X154)
| X155 = X152
| X155 = X153
| X154 != unordered_pair(X152,X153) )
& ( X156 != X152
| in(X156,X154)
| X154 != unordered_pair(X152,X153) )
& ( X156 != X153
| in(X156,X154)
| X154 != unordered_pair(X152,X153) )
& ( esk3_3(X157,X158,X159) != X157
| ~ in(esk3_3(X157,X158,X159),X159)
| X159 = unordered_pair(X157,X158) )
& ( esk3_3(X157,X158,X159) != X158
| ~ in(esk3_3(X157,X158,X159),X159)
| X159 = unordered_pair(X157,X158) )
& ( in(esk3_3(X157,X158,X159),X159)
| esk3_3(X157,X158,X159) = X157
| esk3_3(X157,X158,X159) = X158
| X159 = unordered_pair(X157,X158) ) ),
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_88,plain,
( in(esk6_3(X1,X2,X3),X1)
| in(esk6_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_89,plain,
( in(esk6_3(X1,X2,X3),X2)
| in(esk6_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_90,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_63]) ).
cnf(i_0_91,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_64]) ).
cnf(i_0_92,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_65]) ).
cnf(i_0_93,lemma,
( disjoint(X1,X2)
| in(esk13_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_64]) ).
fof(i_0_94,plain,
! [X230,X231] :
( ( ~ in(esk11_2(X230,X231),X230)
| ~ in(esk11_2(X230,X231),X231)
| X230 = X231 )
& ( in(esk11_2(X230,X231),X230)
| in(esk11_2(X230,X231),X231)
| X230 = X231 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_95,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_96,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_97,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_67]) ).
cnf(i_0_98,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_99,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]) ).
cnf(i_0_100,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_68]) ).
fof(i_0_101,lemma,
! [X234,X235,X236] :
( ~ subset(X234,X235)
| subset(set_difference(X234,X236),set_difference(X235,X236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_102,lemma,
! [X279,X280,X281] :
( ~ subset(X279,X280)
| ~ subset(X281,X280)
| subset(set_union2(X279,X281),X280) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(i_0_103,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_69]) ).
fof(i_0_104,plain,
! [X170,X171,X172,X173,X174] :
( ( ~ subset(X170,X171)
| ~ in(X172,X170)
| in(X172,X171) )
& ( in(esk5_2(X173,X174),X173)
| subset(X173,X174) )
& ( ~ in(esk5_2(X173,X174),X174)
| subset(X173,X174) ) ),
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_105,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
cnf(i_0_106,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
fof(i_0_107,lemma,
! [X244,X245,X247,X248,X249] :
( ( in(esk12_2(X244,X245),X244)
| disjoint(X244,X245) )
& ( in(esk12_2(X244,X245),X245)
| disjoint(X244,X245) )
& ( ~ in(X249,X247)
| ~ in(X249,X248)
| ~ disjoint(X247,X248) ) ),
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_71])])])])])]) ).
cnf(i_0_108,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]) ).
fof(i_0_109,lemma,
! [X253,X254] :
( ~ subset(X253,X254)
| X254 = set_union2(X253,set_difference(X254,X253)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_110,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]) ).
fof(i_0_111,lemma,
! [X266,X267,X268] :
( ~ subset(X266,X267)
| ~ disjoint(X267,X268)
| disjoint(X266,X268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_112,lemma,
! [X221,X222,X223] :
( ~ subset(X221,X222)
| ~ subset(X222,X223)
| subset(X221,X223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_113,lemma,
! [X251,X252] : set_difference(set_union2(X251,X252),X252) = set_difference(X251,X252),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_114,lemma,
! [X241,X242] : set_union2(X241,set_difference(X242,X241)) = set_union2(X241,X242),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_115,plain,
! [X198,X199] :
( empty(X198)
| ~ empty(set_union2(X198,X199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_73])]) ).
fof(i_0_116,plain,
! [X200,X201] :
( empty(X200)
| ~ empty(set_union2(X201,X200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_74])]) ).
cnf(i_0_117,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
fof(i_0_118,plain,
! [X139,X140] :
( ( subset(X139,X140)
| X139 != X140 )
& ( subset(X140,X139)
| X139 != X140 )
& ( ~ subset(X139,X140)
| ~ subset(X140,X139)
| X139 = X140 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_119,lemma,
! [X264,X265] :
( ~ subset(X264,X265)
| ~ proper_subset(X265,X264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_120,plain,
! [X131,X132] :
( ~ proper_subset(X131,X132)
| ~ proper_subset(X132,X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_75])]) ).
fof(i_0_121,plain,
! [X129,X130] :
( ~ in(X129,X130)
| ~ in(X130,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_76])]) ).
cnf(i_0_122,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_123,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_77]) ).
fof(i_0_124,lemma,
! [X237,X238] : subset(set_difference(X237,X238),X237),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_125,lemma,
! [X273,X274] : subset(X273,set_union2(X273,X274)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_126,plain,
! [X196,X197] :
( ( subset(X196,X197)
| ~ proper_subset(X196,X197) )
& ( X196 != X197
| ~ proper_subset(X196,X197) )
& ( ~ subset(X196,X197)
| X196 = X197
| proper_subset(X196,X197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_127,lemma,
! [X275,X276] :
( ( ~ disjoint(X275,X276)
| set_difference(X275,X276) = X275 )
& ( set_difference(X275,X276) != X275
| disjoint(X275,X276) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_128,lemma,
! [X213,X214] :
( ~ subset(X213,X214)
| set_union2(X213,X214) = X214 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_129,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_78]) ).
fof(i_0_130,plain,
! [X211,X212] :
( ~ disjoint(X211,X212)
| disjoint(X212,X211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_131,lemma,
! [X239,X240] :
( ( set_difference(X239,X240) != empty_set
| subset(X239,X240) )
& ( ~ subset(X239,X240)
| set_difference(X239,X240) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_132,lemma,
! [X206,X207] :
( ( set_difference(X206,X207) != empty_set
| subset(X206,X207) )
& ( ~ subset(X206,X207)
| set_difference(X206,X207) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_133,plain,
! [X271,X272] :
( ~ in(X271,X272)
| ~ empty(X272) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_134,plain,
! [X135,X136] : set_union2(X135,X136) = set_union2(X136,X135),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_135,plain,
! [X133,X134] : unordered_pair(X133,X134) = unordered_pair(X134,X133),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_136,plain,
! [X148,X149,X150] :
( ( X148 != empty_set
| ~ in(X149,X148) )
& ( in(esk2_1(X150),X150)
| X150 = 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_79])])])])]) ).
fof(i_0_137,plain,
! [X204] : ~ proper_subset(X204,X204),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_80])]) ).
fof(i_0_138,lemma,
! [X250] :
( ~ subset(X250,empty_set)
| X250 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_139,plain,
! [X277,X278] :
( ~ empty(X277)
| X277 = X278
| ~ empty(X278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_140,plain,
! [X202] : set_union2(X202,X202) = X202,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_141,plain,
! [X210] : subset(X210,X210),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_142,plain,
! [X243] : set_difference(X243,empty_set) = X243,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_143,plain,
! [X220] : set_union2(X220,empty_set) = X220,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_144,lemma,
! [X233] : subset(empty_set,X233),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_145,plain,
! [X257] : set_difference(empty_set,X257) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(i_0_146,negated_conjecture,
singleton(esk8_0) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_81]) ).
fof(i_0_147,plain,
! [X270] :
( ~ empty(X270)
| X270 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_148,plain,
~ empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_82])]) ).
fof(i_0_149,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_150,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk6_3(X1,X2,X3),X3)
| ~ in(esk6_3(X1,X2,X3),X2)
| ~ in(esk6_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_83,c_0_84]),
[final] ).
cnf(i_0_151,plain,
( in(esk7_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk7_3(X1,X2,X3),X3)
| ~ in(esk7_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_152,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X1)
| ~ in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_153,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X2)
| ~ in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_154,plain,
( in(esk4_3(X1,X2,X3),X3)
| in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_155,plain,
( in(esk7_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_156,plain,
( X3 = unordered_pair(X1,X2)
| esk3_3(X1,X2,X3) != X1
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_157,plain,
( X3 = unordered_pair(X1,X2)
| esk3_3(X1,X2,X3) != X2
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_158,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk6_3(X1,X2,X3),X3)
| in(esk6_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_88,c_0_84]),
[final] ).
cnf(i_0_159,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk6_3(X1,X2,X3),X3)
| in(esk6_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_89,c_0_84]),
[final] ).
cnf(i_0_160,plain,
( in(esk7_3(X1,X2,X3),X1)
| in(esk7_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_161,plain,
( in(esk3_3(X1,X2,X3),X3)
| esk3_3(X1,X2,X3) = X1
| esk3_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_162,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_90,c_0_84]),c_0_84]),
[final] ).
cnf(i_0_163,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_91,c_0_84]),
[final] ).
cnf(i_0_164,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_92,c_0_84]),
[final] ).
cnf(i_0_165,lemma,
( disjoint(X1,X2)
| in(esk13_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_93,c_0_84]),
[final] ).
cnf(i_0_166,plain,
( X1 = X2
| ~ in(esk11_2(X1,X2),X1)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_167,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_95,c_0_84]),
[final] ).
cnf(i_0_168,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_96,c_0_97]),
[final] ).
cnf(i_0_169,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_98,c_0_84]),
[final] ).
cnf(i_0_170,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_99,c_0_84]),
[final] ).
cnf(i_0_171,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_100,c_0_84]),
[final] ).
cnf(i_0_172,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_173,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_174,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_175,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_103,c_0_84]),c_0_84]),
[final] ).
cnf(i_0_176,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_177,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_105,c_0_84]),
[final] ).
cnf(i_0_178,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_179,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_180,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_106,c_0_97]),
[final] ).
cnf(i_0_181,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_182,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_183,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_108,c_0_84]),
[final] ).
cnf(i_0_184,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_185,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_110,c_0_84]),
[final] ).
cnf(i_0_186,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_187,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_188,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_189,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_190,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_191,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_192,lemma,
( in(esk12_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_193,lemma,
( in(esk12_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_194,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_195,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_196,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_197,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_198,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_199,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_200,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_117,c_0_97]),
[final] ).
cnf(i_0_201,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_202,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_203,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_204,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_205,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_122,c_0_97]),
[final] ).
cnf(i_0_206,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_207,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_208,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_123,c_0_84]),
[final] ).
cnf(i_0_209,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_210,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_211,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_212,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_213,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_214,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_215,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_129,c_0_84]),
[final] ).
cnf(i_0_216,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_217,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_218,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_219,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_220,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_221,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_222,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_223,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_224,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_225,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_226,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_227,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_137]),
[final] ).
cnf(i_0_228,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_229,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_230,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_231,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_232,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_233,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_140]),
[final] ).
cnf(i_0_234,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_235,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_236,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_143]),
[final] ).
cnf(i_0_237,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_238,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_239,negated_conjecture,
unordered_pair(esk8_0,esk8_0) = empty_set,
inference(rw,[status(thm)],[i_0_146,c_0_97]),
[final] ).
cnf(i_0_240,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_241,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_242,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_243,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_244,axiom,
X1 = X1 ).
cnf(i_0_245,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_246,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_247,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_248,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_249,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_250,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_251,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_252,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_253,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_254,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_255,axiom,
( X1 != X2
| esk3_3(X1,X3,X4) = esk3_3(X2,X3,X4) ) ).
cnf(i_0_256,axiom,
( X1 != X2
| esk3_3(X3,X1,X4) = esk3_3(X3,X2,X4) ) ).
cnf(i_0_257,axiom,
( X1 != X2
| esk3_3(X3,X4,X1) = esk3_3(X3,X4,X2) ) ).
cnf(i_0_258,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_259,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_260,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_261,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_262,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_263,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_264,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_265,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_266,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_244_001,axiom,
X1 = X1 ).
cnf(i_0_245_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_246_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_247_004,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_248_005,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_249_006,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_250_007,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_251_008,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_252_009,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_253_010,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_254_011,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_255_012,axiom,
( X1 != X2
| esk3_3(X1,X3,X4) = esk3_3(X2,X3,X4) ) ).
cnf(i_0_256_013,axiom,
( X1 != X2
| esk3_3(X3,X1,X4) = esk3_3(X3,X2,X4) ) ).
cnf(i_0_257_014,axiom,
( X1 != X2
| esk3_3(X3,X4,X1) = esk3_3(X3,X4,X2) ) ).
cnf(i_0_258_015,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_259_016,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_260_017,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_261_018,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_262_019,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_263_020,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_264_021,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_265_022,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_266_023,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_267,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[167]) ).
cnf(i_0_268,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[170]) ).
cnf(i_0_269,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[178]) ).
cnf(i_0_270,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[179]) ).
cnf(i_0_271,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[181]) ).
cnf(i_0_272,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[186]) ).
cnf(i_0_273,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[187]) ).
cnf(i_0_274,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[188]) ).
cnf(i_0_275,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[199]) ).
cnf(i_0_276,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[200]) ).
cnf(i_0_277,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[225]) ).
cnf(i_0_278,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[226]) ).
cnf(i_0_279,plain,
subset(X1,X1),
inference(equality_inference,[],[230]) ).
cnf(i_0_280,plain,
subset(X1,X1),
inference(equality_inference,[],[231]) ).
cnf(i_0_281,plain,
~ in(X1,unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_239,i_0_226]) ).
cnf(i_0_282,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_226]) ).
cnf(i_0_283,plain,
subset(unordered_pair(esk8_0,esk8_0),empty_set),
inference(scs_inference,[],[i_0_239,i_0_226,i_0_230]) ).
cnf(i_0_284,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_285,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_239,i_0_223,i_0_226,i_0_230,i_0_231]) ).
cnf(i_0_286,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_231]) ).
cnf(i_0_287,plain,
empty_set = unordered_pair(esk8_0,esk8_0),
inference(scs_inference,[],[i_0_239,i_0_223,i_0_226,i_0_230,i_0_231,i_0_245]) ).
cnf(i_0_288,plain,
disjoint(empty_set,empty_set),
inference(scs_inference,[],[i_0_239,i_0_223,i_0_208,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177]) ).
cnf(i_0_289,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rename_variables,[],[i_0_208]) ).
cnf(i_0_290,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_177]) ).
cnf(i_0_291,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_223,i_0_208,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192]) ).
cnf(i_0_292,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_293,plain,
( in(esk12_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_294,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_208,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193]) ).
cnf(i_0_295,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_296,plain,
( in(esk12_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_193]) ).
cnf(i_0_297,plain,
subset(unordered_pair(esk8_0,esk8_0),X1),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_208,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194]) ).
cnf(i_0_298,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_299,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_208,i_0_289,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212]) ).
cnf(i_0_300,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_301,plain,
disjoint(set_difference(X1,X1),X1),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_208,i_0_289,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216]) ).
cnf(i_0_302,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_216]) ).
cnf(i_0_303,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219]) ).
cnf(i_0_304,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_219]) ).
cnf(i_0_305,plain,
~ in(X1,esk9_0),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222]) ).
cnf(i_0_306,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_222]) ).
cnf(i_0_307,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268]) ).
cnf(i_0_308,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_268]) ).
cnf(i_0_309,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272]) ).
cnf(i_0_310,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_311,plain,
~ proper_subset(empty_set,unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266]) ).
cnf(i_0_312,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_313,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_233,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206]) ).
cnf(i_0_314,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_315,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_206]) ).
cnf(i_0_316,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(unordered_pair(X1,empty_set),unordered_pair(X1,empty_set))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_233,i_0_314,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207]) ).
cnf(i_0_317,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_318,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_207]) ).
cnf(i_0_319,plain,
set_union2(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk8_0)) = empty_set,
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_233,i_0_314,i_0_317,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246]) ).
cnf(i_0_320,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_321,plain,
~ in(esk5_2(unordered_pair(esk8_0,esk8_0),X1),set_union2(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk8_0))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_233,i_0_314,i_0_317,i_0_320,i_0_223,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259]) ).
cnf(i_0_322,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_323,plain,
esk9_0 != esk10_0,
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_233,i_0_314,i_0_317,i_0_320,i_0_223,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264]) ).
cnf(i_0_324,plain,
~ proper_subset(unordered_pair(esk8_0,esk8_0),empty_set),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_223,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265]) ).
cnf(i_0_325,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_326,plain,
~ in(X1,set_difference(set_difference(X2,set_difference(X2,empty_set)),empty_set)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_223,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170]) ).
cnf(i_0_327,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_328,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_329,plain,
esk9_0 = empty_set,
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_223,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174]) ).
cnf(i_0_330,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_331,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_332,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186]) ).
cnf(i_0_333,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_334,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_186]) ).
cnf(i_0_335,plain,
~ subset(set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1)),empty_set),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191]) ).
cnf(i_0_336,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_337,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_191]) ).
cnf(i_0_338,plain,
~ in(esk9_0,unordered_pair(esk10_0,esk10_0)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_224,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200]) ).
cnf(i_0_339,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_224]) ).
cnf(i_0_340,plain,
( X1 != unordered_pair(X2,X2)
| ~ in(X3,X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_341,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201]) ).
cnf(i_0_342,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_209]) ).
cnf(i_0_343,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_201]) ).
cnf(i_0_344,plain,
in(unordered_pair(esk8_0,esk8_0),unordered_pair(empty_set,X1)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269]) ).
cnf(i_0_345,plain,
( ~ in(X1,set_union2(X2,X3))
| in(X1,X2)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_269]) ).
cnf(i_0_346,plain,
in(unordered_pair(esk8_0,esk8_0),set_difference(set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1)),empty_set)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270]) ).
cnf(i_0_347,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_278]) ).
cnf(i_0_348,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_270]) ).
cnf(i_0_349,plain,
~ subset(set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1)),unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261]) ).
cnf(i_0_350,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178]) ).
cnf(i_0_351,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_352,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_353,plain,
~ in(esk9_0,set_union2(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,esk10_0))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199]) ).
cnf(i_0_354,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_355,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_199]) ).
cnf(i_0_356,plain,
~ in(unordered_pair(esk8_0,esk8_0),set_difference(X1,set_union2(unordered_pair(empty_set,X2),unordered_pair(empty_set,X2)))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271]) ).
cnf(i_0_357,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_358,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1)),X2)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273]) ).
cnf(i_0_359,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_273]) ).
cnf(i_0_360,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(X1,set_union2(unordered_pair(empty_set,X2),unordered_pair(empty_set,X2)))),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273,i_0_274]) ).
cnf(i_0_361,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_274]) ).
cnf(i_0_362,plain,
~ in(set_union2(esk9_0,esk9_0),unordered_pair(esk10_0,esk10_0)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_354,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273,i_0_274,i_0_258]) ).
cnf(i_0_363,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_364,plain,
~ subset(unordered_pair(empty_set,X1),empty_set),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_354,i_0_223,i_0_224,i_0_209,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273,i_0_274,i_0_258,i_0_173]) ).
cnf(i_0_365,plain,
( subset(set_union2(X1,X2),X3)
| ~ subset(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_173]) ).
cnf(i_0_366,plain,
~ subset(set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1)),set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_354,i_0_223,i_0_224,i_0_209,i_0_342,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273,i_0_274,i_0_258,i_0_173,i_0_190]) ).
cnf(i_0_367,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_209]) ).
cnf(i_0_368,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_190]) ).
cnf(i_0_369,plain,
( in(esk11_2(esk9_0,empty_set),set_difference(set_difference(X1,empty_set),set_difference(set_difference(X1,empty_set),X1)))
| ~ in(esk11_2(esk9_0,empty_set),X1) ),
inference(scs_inference,[],[i_0_239,i_0_278,i_0_292,i_0_295,i_0_330,i_0_336,i_0_347,i_0_227,i_0_312,i_0_233,i_0_314,i_0_317,i_0_320,i_0_322,i_0_333,i_0_351,i_0_354,i_0_223,i_0_224,i_0_209,i_0_342,i_0_235,i_0_241,i_0_242,i_0_208,i_0_289,i_0_175,i_0_215,i_0_226,i_0_230,i_0_231,i_0_245,i_0_177,i_0_192,i_0_193,i_0_194,i_0_212,i_0_216,i_0_219,i_0_222,i_0_268,i_0_272,i_0_266,i_0_206,i_0_207,i_0_246,i_0_259,i_0_264,i_0_265,i_0_170,i_0_174,i_0_186,i_0_191,i_0_200,i_0_201,i_0_269,i_0_270,i_0_261,i_0_178,i_0_199,i_0_271,i_0_273,i_0_274,i_0_258,i_0_173,i_0_190,i_0_179]) ).
cnf(i_0_370,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rename_variables,[],[i_0_175]) ).
cnf(i_0_371,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_179]) ).
cnf(i_0_372,plain,
~ in(X1,set_union2(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk8_0))),
inference(scs_inference,[],[i_0_319,i_0_226]) ).
cnf(i_0_373,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_226]) ).
cnf(i_0_374,plain,
~ in(X1,set_difference(X2,set_difference(X2,unordered_pair(esk8_0,esk8_0)))),
inference(scs_inference,[],[i_0_281,i_0_319,i_0_226,i_0_268]) ).
cnf(i_0_375,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_268]) ).
cnf(i_0_376,plain,
~ in(unordered_pair(esk8_0,esk8_0),set_difference(X1,set_union2(unordered_pair(X2,empty_set),unordered_pair(X2,empty_set)))),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_226,i_0_268,i_0_271]) ).
cnf(i_0_377,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_378,plain,
~ in(X1,set_difference(unordered_pair(esk8_0,esk8_0),X2)),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_226,i_0_268,i_0_271,i_0_272]) ).
cnf(i_0_379,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_380,plain,
subset(set_union2(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk8_0)),empty_set),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230]) ).
cnf(i_0_381,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_382,plain,
subset(set_difference(X1,X2),set_difference(set_union2(X1,X2),X2)),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231]) ).
cnf(i_0_383,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_231]) ).
cnf(i_0_384,plain,
disjoint(X1,unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193]) ).
cnf(i_0_385,plain,
~ in(X1,unordered_pair(esk8_0,esk8_0)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_386,plain,
( in(esk12_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_193]) ).
cnf(i_0_387,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(set_union2(unordered_pair(X1,empty_set),unordered_pair(X1,empty_set)),X2)),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273]) ).
cnf(i_0_388,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_273]) ).
cnf(i_0_389,plain,
in(unordered_pair(esk8_0,esk8_0),set_union2(X1,set_union2(unordered_pair(X2,empty_set),unordered_pair(X2,empty_set)))),
inference(scs_inference,[],[i_0_281,i_0_316,i_0_319,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274]) ).
cnf(i_0_390,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_274]) ).
cnf(i_0_391,plain,
disjoint(unordered_pair(esk8_0,esk8_0),X1),
inference(scs_inference,[],[i_0_281,i_0_385,i_0_316,i_0_319,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192]) ).
cnf(i_0_392,plain,
~ in(X1,unordered_pair(esk8_0,esk8_0)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_393,plain,
( in(esk12_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_394,plain,
subset(set_difference(X1,set_difference(X1,empty_set)),X2),
inference(scs_inference,[],[i_0_281,i_0_385,i_0_316,i_0_319,i_0_307,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194]) ).
cnf(i_0_395,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(rename_variables,[],[i_0_307]) ).
cnf(i_0_396,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_397,plain,
empty_set = set_union2(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_281,i_0_385,i_0_316,i_0_319,i_0_307,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245]) ).
cnf(i_0_398,plain,
~ subset(set_union2(unordered_pair(empty_set,X1),empty_set),empty_set),
inference(scs_inference,[],[i_0_281,i_0_385,i_0_316,i_0_319,i_0_307,i_0_236,i_0_364,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245,i_0_260]) ).
cnf(i_0_399,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_236]) ).
cnf(i_0_400,plain,
disjoint(set_union2(X1,X2),set_difference(set_union2(X2,X1),set_union2(X2,X1))),
inference(scs_inference,[],[i_0_285,i_0_281,i_0_385,i_0_316,i_0_319,i_0_299,i_0_307,i_0_236,i_0_364,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245,i_0_260,i_0_189]) ).
cnf(i_0_401,plain,
disjoint(X1,set_difference(X1,X1)),
inference(rename_variables,[],[i_0_299]) ).
cnf(i_0_402,plain,
( ~ disjoint(X1,X2)
| disjoint(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_189]) ).
cnf(i_0_403,plain,
set_difference(X1,set_difference(X1,empty_set)) = unordered_pair(esk8_0,esk8_0),
inference(scs_inference,[],[i_0_285,i_0_281,i_0_385,i_0_392,i_0_316,i_0_319,i_0_299,i_0_307,i_0_395,i_0_236,i_0_364,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245,i_0_260,i_0_189,i_0_174]) ).
cnf(i_0_404,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(rename_variables,[],[i_0_307]) ).
cnf(i_0_405,plain,
~ in(X1,unordered_pair(esk8_0,esk8_0)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_406,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_407,plain,
~ subset(set_union2(unordered_pair(X1,empty_set),unordered_pair(X1,empty_set)),unordered_pair(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_285,i_0_281,i_0_385,i_0_392,i_0_405,i_0_316,i_0_319,i_0_299,i_0_307,i_0_395,i_0_236,i_0_364,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245,i_0_260,i_0_189,i_0_174,i_0_191]) ).
cnf(i_0_408,plain,
~ in(X1,unordered_pair(esk8_0,esk8_0)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_409,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_191]) ).
cnf(i_0_410,plain,
$false,
inference(scs_inference,[],[i_0_285,i_0_287,i_0_281,i_0_385,i_0_392,i_0_405,i_0_316,i_0_319,i_0_278,i_0_299,i_0_307,i_0_395,i_0_236,i_0_399,i_0_364,i_0_195,i_0_226,i_0_268,i_0_271,i_0_272,i_0_230,i_0_231,i_0_193,i_0_273,i_0_274,i_0_192,i_0_194,i_0_245,i_0_260,i_0_189,i_0_174,i_0_191,i_0_206]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU143+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:45:20 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.35/1.62 % Version : CSE_E---1.7
% 0.35/1.62 % Problem : theBenchmark.p
% 0.35/1.62 % SZS status Theorem for theBenchmark.p
% 0.35/1.62 % SZS output start CNFRefutation
% See solution above
% 0.78/2.09 % Total time : 1.273s
%------------------------------------------------------------------------------