%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU172+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 05:10:56 PM UTC 2026
% Result : Theorem 0.49s 1.62s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_109)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t65_zfmisc_1,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(t33_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(t26_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(t50_subset_1,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(t6_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t9_tarski,axiom,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(l25_zfmisc_1,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(t39_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t37_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t136_zfmisc_1,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t46_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(t54_subset_1,conjecture,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(t43_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(t119_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(t118_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t38_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(l3_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(t45_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t63_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t10_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t60_xboole_1,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(t92_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t37_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_101,plain,
! [X353,X354] : ordered_pair(X353,X354) = unordered_pair(unordered_pair(X353,X354),singleton(X353)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_102,lemma,
! [X510] : unordered_pair(X510,X510) = singleton(X510),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_103,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_104,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_105,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_106,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_107,plain,
! [X299,X300,X301,X302,X305,X306,X307,X308,X309,X310,X312,X313] :
( ( in(esk6_4(X299,X300,X301,X302),X299)
| ~ in(X302,X301)
| X301 != cartesian_product2(X299,X300) )
& ( in(esk7_4(X299,X300,X301,X302),X300)
| ~ in(X302,X301)
| X301 != cartesian_product2(X299,X300) )
& ( X302 = ordered_pair(esk6_4(X299,X300,X301,X302),esk7_4(X299,X300,X301,X302))
| ~ in(X302,X301)
| X301 != cartesian_product2(X299,X300) )
& ( ~ in(X306,X299)
| ~ in(X307,X300)
| X305 != ordered_pair(X306,X307)
| in(X305,X301)
| X301 != cartesian_product2(X299,X300) )
& ( ~ in(esk8_3(X308,X309,X310),X310)
| ~ in(X312,X308)
| ~ in(X313,X309)
| esk8_3(X308,X309,X310) != ordered_pair(X312,X313)
| X310 = cartesian_product2(X308,X309) )
& ( in(esk9_3(X308,X309,X310),X308)
| in(esk8_3(X308,X309,X310),X310)
| X310 = cartesian_product2(X308,X309) )
& ( in(esk10_3(X308,X309,X310),X309)
| in(esk8_3(X308,X309,X310),X310)
| X310 = cartesian_product2(X308,X309) )
& ( esk8_3(X308,X309,X310) = ordered_pair(esk9_3(X308,X309,X310),esk10_3(X308,X309,X310))
| in(esk8_3(X308,X309,X310),X310)
| X310 = cartesian_product2(X308,X309) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])]) ).
cnf(i_0_108,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_101]) ).
cnf(i_0_109,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_102]) ).
fof(i_0_110,plain,
! [X322,X323,X324,X325,X326,X327,X328,X329] :
( ( in(X325,X322)
| ~ in(X325,X324)
| X324 != set_intersection2(X322,X323) )
& ( in(X325,X323)
| ~ in(X325,X324)
| X324 != set_intersection2(X322,X323) )
& ( ~ in(X326,X322)
| ~ in(X326,X323)
| in(X326,X324)
| X324 != set_intersection2(X322,X323) )
& ( ~ in(esk12_3(X327,X328,X329),X329)
| ~ in(esk12_3(X327,X328,X329),X327)
| ~ in(esk12_3(X327,X328,X329),X328)
| X329 = set_intersection2(X327,X328) )
& ( in(esk12_3(X327,X328,X329),X327)
| in(esk12_3(X327,X328,X329),X329)
| X329 = set_intersection2(X327,X328) )
& ( in(esk12_3(X327,X328,X329),X328)
| in(esk12_3(X327,X328,X329),X329)
| X329 = set_intersection2(X327,X328) ) ),
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_111,lemma,
! [X488,X489] : set_difference(X488,set_difference(X488,X489)) = set_intersection2(X488,X489),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_112,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_113,lemma,
! [X409,X410,X411,X412] :
( ( in(X409,X411)
| ~ in(ordered_pair(X409,X410),cartesian_product2(X411,X412)) )
& ( in(X410,X412)
| ~ in(ordered_pair(X409,X410),cartesian_product2(X411,X412)) )
& ( ~ in(X409,X411)
| ~ in(X410,X412)
| in(ordered_pair(X409,X410),cartesian_product2(X411,X412)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(i_0_114,lemma,
! [X396,X397,X398,X399] :
( ( in(X396,X398)
| ~ in(ordered_pair(X396,X397),cartesian_product2(X398,X399)) )
& ( in(X397,X399)
| ~ in(ordered_pair(X396,X397),cartesian_product2(X398,X399)) )
& ( ~ in(X396,X398)
| ~ in(X397,X399)
| in(ordered_pair(X396,X397),cartesian_product2(X398,X399)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_115,plain,
! [X364,X365] : ~ empty(ordered_pair(X364,X365)),
inference(variable_rename,[status(thm)],[i_0_103]) ).
fof(i_0_116,lemma,
! [X454,X455,X456,X457] :
( ( X454 = X456
| ordered_pair(X454,X455) != ordered_pair(X456,X457) )
& ( X455 = X457
| ordered_pair(X454,X455) != ordered_pair(X456,X457) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_117,lemma,
! [X441,X442,X443] :
( ~ subset(X441,X442)
| subset(set_intersection2(X441,X443),set_intersection2(X442,X443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_118,lemma,
! [X491,X492,X494,X495,X496] :
( ( disjoint(X491,X492)
| in(esk25_2(X491,X492),set_intersection2(X491,X492)) )
& ( ~ in(X496,set_intersection2(X494,X495))
| ~ disjoint(X494,X495) ) ),
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_104])])])])]) ).
fof(i_0_119,lemma,
! [X434,X435,X436] :
( ~ subset(X434,X435)
| ~ subset(X434,X436)
| subset(X434,set_intersection2(X435,X436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_120,lemma,
! [X389,X390,X391] :
( ~ subset(X389,X390)
| in(X391,X389)
| subset(X389,set_difference(X390,singleton(X391))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_121,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t50_subset_1]) ).
fof(i_0_122,lemma,
! [X512,X513] :
( ~ subset(singleton(X512),singleton(X513))
| X512 = X513 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_123,plain,
! [X261,X262,X263,X264,X265,X266] :
( ( ~ in(X263,X262)
| X263 = X261
| X262 != singleton(X261) )
& ( X264 != X261
| in(X264,X262)
| X262 != singleton(X261) )
& ( ~ in(esk1_2(X265,X266),X266)
| esk1_2(X265,X266) != X265
| X266 = singleton(X265) )
& ( in(esk1_2(X265,X266),X266)
| esk1_2(X265,X266) = X265
| X266 = singleton(X265) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).
fof(i_0_124,plain,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& ! [X5] :
( subset(X5,X3)
=> in(X5,X4) ) ) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[t9_tarski]) ).
fof(i_0_125,lemma,
! [X432,X433] : subset(set_intersection2(X432,X433),X432),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_126,lemma,
! [X508,X509] :
( ( set_difference(X508,singleton(X509)) != X508
| ~ in(X509,X508) )
& ( in(X509,X508)
| set_difference(X508,singleton(X509)) = X508 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_105])]) ).
fof(i_0_127,lemma,
! [X378,X379] :
( ~ disjoint(singleton(X378),X379)
| ~ in(X378,X379) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_128,lemma,
! [X469,X470] :
( ( ~ subset(X469,singleton(X470))
| X469 = empty_set
| X469 = singleton(X470) )
& ( X469 != empty_set
| subset(X469,singleton(X470)) )
& ( X469 != singleton(X470)
| subset(X469,singleton(X470)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_129,lemma,
! [X392,X393] :
( ( ~ subset(X392,singleton(X393))
| X392 = empty_set
| X392 = singleton(X393) )
& ( X392 != empty_set
| subset(X392,singleton(X393)) )
& ( X392 != singleton(X393)
| subset(X392,singleton(X393)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_130,plain,
! [X257,X258] : set_intersection2(X257,X258) = set_intersection2(X258,X257),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_131,lemma,
! [X462,X463] :
( ( ~ subset(singleton(X462),X463)
| in(X462,X463) )
& ( ~ in(X462,X463)
| subset(singleton(X462),X463) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_132,lemma,
! [X382,X383] :
( ( ~ subset(singleton(X382),X383)
| in(X382,X383) )
& ( ~ in(X382,X383)
| subset(singleton(X382),X383) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_133,plain,
! [X355,X356] :
( ( ~ disjoint(X355,X356)
| set_intersection2(X355,X356) = empty_set )
& ( set_intersection2(X355,X356) != empty_set
| disjoint(X355,X356) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_134,lemma,
! [X1] :
? [X2] :
( in(X1,X2)
& ! [X3,X4] :
( ( in(X3,X2)
& subset(X4,X3) )
=> in(X4,X2) )
& ! [X3] :
( in(X3,X2)
=> in(powerset(X3),X2) )
& ! [X3] :
~ ( subset(X3,X2)
& ~ are_equipotent(X3,X2)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[t136_zfmisc_1]) ).
fof(i_0_135,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_136,lemma,
! [X486,X487] :
( ~ in(X486,X487)
| set_union2(singleton(X486),X487) = X487 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_137,lemma,
! [X376,X377] :
( ~ in(X376,X377)
| set_union2(singleton(X376),X377) = X377 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_138,lemma,
! [X444,X445] :
( ~ subset(X444,X445)
| set_intersection2(X444,X445) = X444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_139,lemma,
! [X380,X381] :
( in(X380,X381)
| disjoint(singleton(X380),X381) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_106])]) ).
fof(i_0_140,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_141,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_142,lemma,
! [X525,X526,X527] :
( singleton(X525) != unordered_pair(X526,X527)
| X525 = X526 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_143,lemma,
! [X539,X540,X541] :
( singleton(X539) != unordered_pair(X540,X541)
| X540 = X541 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_144,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_145,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_146,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(i_0_147,plain,
! [X371] : set_intersection2(X371,X371) = X371,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_148,plain,
! [X446] : set_intersection2(X446,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_149,negated_conjecture,
~ ! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t54_subset_1]) ).
fof(i_0_150,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_151,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_152,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_153,lemma,
! [X375] : singleton(X375) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_154,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_155,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_156,plain,
( X1 = ordered_pair(esk6_4(X2,X3,X4,X1),esk7_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_157,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_108,c_0_109]) ).
cnf(i_0_158,plain,
( esk8_3(X1,X2,X3) = ordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3))
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_159,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X1)
| ~ in(esk12_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_160,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_111]) ).
fof(i_0_161,plain,
! [X342,X343,X344,X345,X346,X347,X348,X349] :
( ( in(X345,X342)
| ~ in(X345,X344)
| X344 != set_difference(X342,X343) )
& ( ~ in(X345,X343)
| ~ in(X345,X344)
| X344 != set_difference(X342,X343) )
& ( ~ in(X346,X342)
| in(X346,X343)
| in(X346,X344)
| X344 != set_difference(X342,X343) )
& ( ~ in(esk16_3(X347,X348,X349),X349)
| ~ in(esk16_3(X347,X348,X349),X347)
| in(esk16_3(X347,X348,X349),X348)
| X349 = set_difference(X347,X348) )
& ( in(esk16_3(X347,X348,X349),X347)
| in(esk16_3(X347,X348,X349),X349)
| X349 = set_difference(X347,X348) )
& ( ~ in(esk16_3(X347,X348,X349),X348)
| in(esk16_3(X347,X348,X349),X349)
| X349 = set_difference(X347,X348) ) ),
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_112])])])])])]) ).
cnf(i_0_162,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk8_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
fof(i_0_163,plain,
! [X290,X291,X292,X293,X294,X295,X296,X297] :
( ( ~ in(X293,X292)
| in(X293,X290)
| in(X293,X291)
| X292 != set_union2(X290,X291) )
& ( ~ in(X294,X290)
| in(X294,X292)
| X292 != set_union2(X290,X291) )
& ( ~ in(X294,X291)
| in(X294,X292)
| X292 != set_union2(X290,X291) )
& ( ~ in(esk5_3(X295,X296,X297),X295)
| ~ in(esk5_3(X295,X296,X297),X297)
| X297 = set_union2(X295,X296) )
& ( ~ in(esk5_3(X295,X296,X297),X296)
| ~ in(esk5_3(X295,X296,X297),X297)
| X297 = set_union2(X295,X296) )
& ( in(esk5_3(X295,X296,X297),X297)
| in(esk5_3(X295,X296,X297),X295)
| in(esk5_3(X295,X296,X297),X296)
| X297 = set_union2(X295,X296) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
fof(i_0_164,plain,
! [X281,X282,X283,X284,X285,X286,X287,X288] :
( ( ~ in(X284,X283)
| X284 = X281
| X284 = X282
| X283 != unordered_pair(X281,X282) )
& ( X285 != X281
| in(X285,X283)
| X283 != unordered_pair(X281,X282) )
& ( X285 != X282
| in(X285,X283)
| X283 != unordered_pair(X281,X282) )
& ( esk4_3(X286,X287,X288) != X286
| ~ in(esk4_3(X286,X287,X288),X288)
| X288 = unordered_pair(X286,X287) )
& ( esk4_3(X286,X287,X288) != X287
| ~ in(esk4_3(X286,X287,X288),X288)
| X288 = unordered_pair(X286,X287) )
& ( in(esk4_3(X286,X287,X288),X288)
| esk4_3(X286,X287,X288) = X286
| esk4_3(X286,X287,X288) = X287
| X288 = unordered_pair(X286,X287) ) ),
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_165,plain,
( in(esk12_3(X1,X2,X3),X1)
| in(esk12_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_166,plain,
( in(esk12_3(X1,X2,X3),X2)
| in(esk12_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_167,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_113]) ).
cnf(i_0_168,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_114]) ).
cnf(i_0_169,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_113]) ).
cnf(i_0_170,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_114]) ).
cnf(i_0_171,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_113]) ).
cnf(i_0_172,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_114]) ).
cnf(i_0_173,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_115]) ).
cnf(i_0_174,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_116]) ).
cnf(i_0_175,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]) ).
cnf(i_0_176,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]) ).
cnf(i_0_177,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_107]) ).
cnf(i_0_178,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_118]) ).
fof(i_0_179,plain,
! [X331,X332,X333,X335,X336,X337,X338,X340] :
( ( in(X333,esk13_3(X331,X332,X333))
| ~ in(X333,X332)
| X332 != union(X331) )
& ( in(esk13_3(X331,X332,X333),X331)
| ~ in(X333,X332)
| X332 != union(X331) )
& ( ~ in(X335,X336)
| ~ in(X336,X331)
| in(X335,X332)
| X332 != union(X331) )
& ( ~ in(esk14_2(X337,X338),X338)
| ~ in(esk14_2(X337,X338),X340)
| ~ in(X340,X337)
| X338 = union(X337) )
& ( in(esk14_2(X337,X338),esk15_2(X337,X338))
| in(esk14_2(X337,X338),X338)
| X338 = union(X337) )
& ( in(esk15_2(X337,X338),X337)
| in(esk14_2(X337,X338),X338)
| X338 = union(X337) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_tarski])])])])])]) ).
fof(i_0_180,lemma,
! [X481,X482,X483] :
( ( ~ disjoint(X482,X483)
| subset(X482,subset_complement(X481,X483))
| ~ element(X483,powerset(X481))
| ~ element(X482,powerset(X481)) )
& ( ~ subset(X482,subset_complement(X481,X483))
| disjoint(X482,X483)
| ~ element(X483,powerset(X481))
| ~ element(X482,powerset(X481)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_subset_1])])])]) ).
cnf(i_0_181,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_119]) ).
cnf(i_0_182,lemma,
( disjoint(X1,X2)
| in(esk25_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_118]) ).
fof(i_0_183,plain,
! [X272,X273,X274,X275,X276,X277] :
( ( ~ in(X274,X273)
| subset(X274,X272)
| X273 != powerset(X272) )
& ( ~ subset(X275,X272)
| in(X275,X273)
| X273 != powerset(X272) )
& ( ~ in(esk3_2(X276,X277),X277)
| ~ subset(esk3_2(X276,X277),X276)
| X277 = powerset(X276) )
& ( in(esk3_2(X276,X277),X277)
| subset(esk3_2(X276,X277),X276)
| X277 = powerset(X276) ) ),
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_184,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_120]) ).
fof(i_0_185,plain,
! [X447,X448] :
( ( ~ in(esk23_2(X447,X448),X447)
| ~ in(esk23_2(X447,X448),X448)
| X447 = X448 )
& ( in(esk23_2(X447,X448),X447)
| in(esk23_2(X447,X448),X448)
| X447 = X448 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_186,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
fof(i_0_187,lemma,
! [X420,X421,X422,X423] :
( ~ subset(X420,X421)
| ~ subset(X422,X423)
| subset(cartesian_product2(X420,X422),cartesian_product2(X421,X423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(i_0_188,lemma,
! [X497,X498,X499] :
( X497 = empty_set
| ~ element(X498,powerset(X497))
| ~ element(X499,X497)
| in(X499,X498)
| in(X499,subset_complement(X497,X498)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_121])])]) ).
cnf(i_0_189,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_122]) ).
cnf(i_0_190,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_123]) ).
cnf(i_0_191,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
cnf(i_0_192,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]) ).
fof(i_0_193,plain,
! [X531,X533,X534,X535,X537,X538] :
( in(X531,esk29_1(X531))
& ( ~ in(X533,esk29_1(X531))
| ~ subset(X534,X533)
| in(X534,esk29_1(X531)) )
& ( in(esk30_2(X531,X535),esk29_1(X531))
| ~ in(X535,esk29_1(X531)) )
& ( ~ subset(X537,X535)
| in(X537,esk30_2(X531,X535))
| ~ in(X535,esk29_1(X531)) )
& ( ~ subset(X538,esk29_1(X531))
| are_equipotent(X538,esk29_1(X531))
| in(X538,esk29_1(X531)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_124])])])])]) ).
cnf(i_0_194,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_125]) ).
fof(i_0_195,lemma,
! [X451,X452,X453] :
( ~ subset(X451,X452)
| subset(set_difference(X451,X453),set_difference(X452,X453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_196,lemma,
! [X417,X418,X419] :
( ( subset(cartesian_product2(X417,X419),cartesian_product2(X418,X419))
| ~ subset(X417,X418) )
& ( subset(cartesian_product2(X419,X417),cartesian_product2(X419,X418))
| ~ subset(X417,X418) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
cnf(i_0_197,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_126]) ).
cnf(i_0_198,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_127]) ).
fof(i_0_199,lemma,
! [X522,X523,X524] :
( ~ subset(X522,X523)
| ~ subset(X524,X523)
| subset(set_union2(X522,X524),X523) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_200,lemma,
! [X464,X465,X466] :
( ( in(X464,X466)
| ~ subset(unordered_pair(X464,X465),X466) )
& ( in(X465,X466)
| ~ subset(unordered_pair(X464,X465),X466) )
& ( ~ in(X464,X466)
| ~ in(X465,X466)
| subset(unordered_pair(X464,X465),X466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
cnf(i_0_201,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_128]) ).
cnf(i_0_202,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_129]) ).
cnf(i_0_203,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_130]) ).
fof(i_0_204,plain,
! [X359,X360] :
( ~ element(X360,powerset(X359))
| element(subset_complement(X359,X360),powerset(X359)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_205,plain,
! [X316,X317,X318,X319,X320] :
( ( ~ subset(X316,X317)
| ~ in(X318,X316)
| in(X318,X317) )
& ( in(esk11_2(X319,X320),X319)
| subset(X319,X320) )
& ( ~ in(esk11_2(X319,X320),X320)
| subset(X319,X320) ) ),
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_206,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]) ).
cnf(i_0_207,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]) ).
cnf(i_0_208,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_133]) ).
fof(i_0_209,lemma,
! [X426,X428,X429,X430,X431] :
( in(X426,esk22_1(X426))
& ( ~ in(X428,esk22_1(X426))
| ~ subset(X429,X428)
| in(X429,esk22_1(X426)) )
& ( ~ in(X430,esk22_1(X426))
| in(powerset(X430),esk22_1(X426)) )
& ( ~ subset(X431,esk22_1(X426))
| are_equipotent(X431,esk22_1(X426))
| in(X431,esk22_1(X426)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_134])])])]) ).
fof(i_0_210,plain,
! [X372,X373] :
( ~ element(X373,powerset(X372))
| subset_complement(X372,subset_complement(X372,X373)) = X373 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(i_0_211,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_123]) ).
fof(i_0_212,lemma,
! [X386,X387,X388] :
( ~ element(X387,powerset(X386))
| ~ in(X388,X387)
| in(X388,X386) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
fof(i_0_213,lemma,
! [X472,X473,X475,X476,X477] :
( ( in(esk24_2(X472,X473),X472)
| disjoint(X472,X473) )
& ( in(esk24_2(X472,X473),X473)
| disjoint(X472,X473) )
& ( ~ in(X477,X475)
| ~ in(X477,X476)
| ~ disjoint(X475,X476) ) ),
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_135])])])])])]) ).
cnf(i_0_214,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_128]) ).
cnf(i_0_215,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_129]) ).
cnf(i_0_216,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]) ).
cnf(i_0_217,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_137]) ).
cnf(i_0_218,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_138]) ).
fof(i_0_219,lemma,
! [X484,X485] :
( ~ subset(X484,X485)
| X485 = set_union2(X484,set_difference(X485,X484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_220,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]) ).
cnf(i_0_221,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]) ).
cnf(i_0_222,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_133]) ).
fof(i_0_223,plain,
! [X351,X352] :
( ~ element(X352,powerset(X351))
| subset_complement(X351,X352) = set_difference(X351,X352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_224,lemma,
! [X505,X506,X507] :
( ~ subset(X505,X506)
| ~ disjoint(X506,X507)
| disjoint(X505,X507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_225,lemma,
! [X438,X439,X440] :
( ~ subset(X438,X439)
| ~ subset(X439,X440)
| subset(X438,X440) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(i_0_226,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_126]) ).
cnf(i_0_227,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_139]) ).
fof(i_0_228,lemma,
! [X479,X480] : set_difference(set_union2(X479,X480),X480) = set_difference(X479,X480),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_229,lemma,
! [X467,X468] : set_union2(X467,set_difference(X468,X467)) = set_union2(X467,X468),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_230,plain,
! [X366,X367] :
( empty(X366)
| ~ empty(set_union2(X366,X367)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_140])]) ).
fof(i_0_231,plain,
! [X368,X369] :
( empty(X368)
| ~ empty(set_union2(X369,X368)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_141])]) ).
cnf(i_0_232,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_123]) ).
fof(i_0_233,lemma,
! [X413,X414,X415,X416] :
( unordered_pair(X413,X414) != unordered_pair(X415,X416)
| X413 = X415
| X413 = X416 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
fof(i_0_234,plain,
! [X259,X260] :
( ( subset(X259,X260)
| X259 != X260 )
& ( subset(X260,X259)
| X259 != X260 )
& ( ~ subset(X259,X260)
| ~ subset(X260,X259)
| X259 = X260 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(i_0_235,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_142]) ).
cnf(i_0_236,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_143]) ).
fof(i_0_237,lemma,
! [X503,X504] :
( ~ subset(X503,X504)
| ~ proper_subset(X504,X503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_238,plain,
! [X251,X252] :
( ~ proper_subset(X251,X252)
| ~ proper_subset(X252,X251) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_144])]) ).
fof(i_0_239,plain,
! [X249,X250] :
( ~ in(X249,X250)
| ~ in(X250,X249) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_145])]) ).
fof(i_0_240,lemma,
! [X528,X529] :
( ~ in(X528,X529)
| subset(X528,union(X529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
fof(i_0_241,lemma,
! [X394,X395] :
( ~ in(X394,X395)
| subset(X394,union(X395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_242,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_128]) ).
cnf(i_0_243,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_129]) ).
cnf(i_0_244,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_123]) ).
fof(i_0_245,plain,
! [X279,X280] :
( ( ~ element(X280,X279)
| in(X280,X279)
| empty(X279) )
& ( ~ in(X280,X279)
| element(X280,X279)
| empty(X279) )
& ( ~ element(X280,X279)
| empty(X280)
| ~ empty(X279) )
& ( ~ empty(X280)
| element(X280,X279)
| ~ empty(X279) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_146])])]) ).
cnf(i_0_246,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_147]) ).
fof(i_0_247,lemma,
! [X458,X459] : subset(set_difference(X458,X459),X458),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_248,lemma,
! [X516,X517] : subset(X516,set_union2(X516,X517)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_249,plain,
! [X357,X358] :
( ( subset(X357,X358)
| ~ proper_subset(X357,X358) )
& ( X357 != X358
| ~ proper_subset(X357,X358) )
& ( ~ subset(X357,X358)
| X357 = X358
| proper_subset(X357,X358) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_250,lemma,
! [X518,X519] :
( ( ~ disjoint(X518,X519)
| set_difference(X518,X519) = X518 )
& ( set_difference(X518,X519) != X518
| disjoint(X518,X519) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_251,lemma,
! [X424,X425] :
( ~ subset(X424,X425)
| set_union2(X424,X425) = X425 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_252,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_148]) ).
fof(i_0_253,plain,
! [X407,X408] :
( ~ disjoint(X407,X408)
| disjoint(X408,X407) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_254,lemma,
! [X460,X461] :
( ( set_difference(X460,X461) != empty_set
| subset(X460,X461) )
& ( ~ subset(X460,X461)
| set_difference(X460,X461) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_255,lemma,
! [X384,X385] :
( ( set_difference(X384,X385) != empty_set
| subset(X384,X385) )
& ( ~ subset(X384,X385)
| set_difference(X384,X385) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_256,negated_conjecture,
( element(esk28_0,powerset(esk26_0))
& in(esk27_0,subset_complement(esk26_0,esk28_0))
& in(esk27_0,esk28_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_149])])]) ).
fof(i_0_257,plain,
! [X400] :
( ( element(esk18_1(X400),powerset(X400))
| empty(X400) )
& ( ~ empty(esk18_1(X400))
| empty(X400) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_150])])])]) ).
fof(i_0_258,plain,
! [X514,X515] :
( ~ in(X514,X515)
| ~ empty(X515) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_259,plain,
! [X255,X256] : set_union2(X255,X256) = set_union2(X256,X255),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_260,plain,
! [X253,X254] : unordered_pair(X253,X254) = unordered_pair(X254,X253),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_261,plain,
! [X403] :
( element(esk20_1(X403),powerset(X403))
& empty(esk20_1(X403)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_262,plain,
! [X268,X269,X270] :
( ( X268 != empty_set
| ~ in(X269,X268) )
& ( in(esk2_1(X270),X270)
| X270 = 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_151])])])])]) ).
fof(i_0_263,plain,
! [X374] : ~ proper_subset(X374,X374),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_152])]) ).
cnf(i_0_264,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_153]) ).
fof(i_0_265,lemma,
! [X478] :
( ~ subset(X478,empty_set)
| X478 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_266,plain,
! [X361] : element(esk17_1(X361),X361),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_267,plain,
! [X363] : ~ empty(powerset(X363)),
inference(variable_rename,[status(thm)],[i_0_154]) ).
fof(i_0_268,plain,
! [X520,X521] :
( ~ empty(X520)
| X520 = X521
| ~ empty(X521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_269,plain,
! [X370] : set_union2(X370,X370) = X370,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_270,plain,
! [X406] : subset(X406,X406),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_271,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_272,plain,
! [X471] : set_difference(X471,empty_set) = X471,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_273,plain,
! [X437] : set_union2(X437,empty_set) = X437,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_274,lemma,
! [X450] : subset(empty_set,X450),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_275,plain,
! [X490] : set_difference(empty_set,X490) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_276,lemma,
! [X530] : union(powerset(X530)) = X530,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(i_0_277,plain,
! [X511] :
( ~ empty(X511)
| X511 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_278,plain,
~ empty(esk21_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_155])]) ).
fof(i_0_279,plain,
empty(esk19_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_280,plain,
( X1 = unordered_pair(unordered_pair(esk6_4(X2,X3,X4,X1),esk7_4(X2,X3,X4,X1)),unordered_pair(esk6_4(X2,X3,X4,X1),esk6_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_156,c_0_157]),
[final] ).
cnf(i_0_281,plain,
( X3 = cartesian_product2(X1,X2)
| esk8_3(X1,X2,X3) = unordered_pair(unordered_pair(esk9_3(X1,X2,X3),esk10_3(X1,X2,X3)),unordered_pair(esk9_3(X1,X2,X3),esk9_3(X1,X2,X3)))
| in(esk8_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_158,c_0_157]),
[final] ).
cnf(i_0_282,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(esk12_3(X1,X2,X3),X2)
| ~ in(esk12_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_159,c_0_160]),
[final] ).
cnf(i_0_283,plain,
( in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_284,plain,
( in(esk6_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_285,plain,
( in(esk16_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk16_3(X1,X2,X3),X3)
| ~ in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_286,plain,
( X3 = cartesian_product2(X1,X2)
| esk8_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk8_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_162,c_0_157]),
[final] ).
cnf(i_0_287,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_163]),
[final] ).
cnf(i_0_288,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_163]),
[final] ).
cnf(i_0_289,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_163]),
[final] ).
cnf(i_0_290,plain,
( in(esk16_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk16_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_291,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_164]),
[final] ).
cnf(i_0_292,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_164]),
[final] ).
cnf(i_0_293,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk12_3(X1,X2,X3),X3)
| in(esk12_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_165,c_0_160]),
[final] ).
cnf(i_0_294,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk12_3(X1,X2,X3),X3)
| in(esk12_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_166,c_0_160]),
[final] ).
cnf(i_0_295,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_167,c_0_157]),
[final] ).
cnf(i_0_296,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_168,c_0_157]),
[final] ).
cnf(i_0_297,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_169,c_0_157]),
[final] ).
cnf(i_0_298,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_170,c_0_157]),
[final] ).
cnf(i_0_299,plain,
( in(esk16_3(X1,X2,X3),X1)
| in(esk16_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_300,plain,
( in(esk10_3(X1,X2,X3),X2)
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_301,plain,
( in(esk9_3(X1,X2,X3),X1)
| in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_302,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_164]),
[final] ).
cnf(i_0_303,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_171,c_0_157]),
[final] ).
cnf(i_0_304,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_172,c_0_157]),
[final] ).
cnf(i_0_305,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_173,c_0_157]),
[final] ).
cnf(i_0_306,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_174,c_0_157]),c_0_157]),
[final] ).
cnf(i_0_307,lemma,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)) != unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_175,c_0_157]),c_0_157]),
[final] ).
cnf(i_0_308,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_176,c_0_160]),c_0_160]),
[final] ).
cnf(i_0_309,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_177,c_0_157]),
[final] ).
cnf(i_0_310,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_178,c_0_160]),
[final] ).
cnf(i_0_311,plain,
( X2 = union(X1)
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_312,plain,
( in(esk13_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_313,plain,
( in(X1,esk13_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_314,lemma,
( disjoint(X1,X3)
| ~ subset(X1,subset_complement(X2,X3))
| ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_315,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_181,c_0_160]),
[final] ).
cnf(i_0_316,lemma,
( disjoint(X1,X2)
| in(esk25_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_182,c_0_160]),
[final] ).
cnf(i_0_317,plain,
( X2 = powerset(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ subset(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_318,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_184,c_0_109]),
[final] ).
cnf(i_0_319,plain,
( X1 = X2
| ~ in(esk23_2(X1,X2),X1)
| ~ in(esk23_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_320,lemma,
( subset(X1,subset_complement(X3,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X3))
| ~ element(X1,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_321,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_186,c_0_160]),
[final] ).
cnf(i_0_322,plain,
( in(esk14_2(X1,X2),esk15_2(X1,X2))
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_323,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_324,lemma,
( X1 = empty_set
| in(X3,X2)
| in(X3,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_325,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_189,c_0_109]),c_0_109]),
[final] ).
cnf(i_0_326,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_190,c_0_109]),
[final] ).
cnf(i_0_327,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_191,c_0_160]),
[final] ).
cnf(i_0_328,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_192,c_0_160]),
[final] ).
cnf(i_0_329,plain,
( in(X1,esk30_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk29_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_330,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_194,c_0_160]),
[final] ).
cnf(i_0_331,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_332,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_333,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_334,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_197,c_0_109]),
[final] ).
cnf(i_0_335,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_198,c_0_109]),
[final] ).
cnf(i_0_336,plain,
( in(esk15_2(X1,X2),X1)
| in(esk14_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_337,plain,
( in(esk3_2(X1,X2),X2)
| subset(esk3_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_338,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_339,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_340,plain,
( in(esk23_2(X1,X2),X1)
| in(esk23_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_341,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_201,c_0_109]),c_0_109]),
[final] ).
cnf(i_0_342,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_202,c_0_109]),c_0_109]),
[final] ).
cnf(i_0_343,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_203,c_0_160]),c_0_160]),
[final] ).
cnf(i_0_344,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_345,plain,
( in(esk30_2(X1,X2),esk29_1(X1))
| ~ in(X2,esk29_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_346,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_347,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_206,c_0_109]),
[final] ).
cnf(i_0_348,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_207,c_0_109]),
[final] ).
cnf(i_0_349,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_350,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_351,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_208,c_0_160]),
[final] ).
cnf(i_0_352,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_353,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_354,plain,
( in(X3,esk29_1(X2))
| ~ in(X1,esk29_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_355,lemma,
( in(X3,esk22_1(X2))
| ~ in(X1,esk22_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_356,plain,
( are_equipotent(X1,esk29_1(X2))
| in(X1,esk29_1(X2))
| ~ subset(X1,esk29_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_357,lemma,
( are_equipotent(X1,esk22_1(X2))
| in(X1,esk22_1(X2))
| ~ subset(X1,esk22_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_358,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_210]),
[final] ).
cnf(i_0_359,plain,
( X2 = unordered_pair(X1,X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_211,c_0_109]),
[final] ).
cnf(i_0_360,lemma,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_212]),
[final] ).
cnf(i_0_361,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_362,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_363,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_364,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_214,c_0_109]),c_0_109]),
[final] ).
cnf(i_0_365,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_215,c_0_109]),c_0_109]),
[final] ).
cnf(i_0_366,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_216,c_0_109]),
[final] ).
cnf(i_0_367,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_217,c_0_109]),
[final] ).
cnf(i_0_368,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_218,c_0_160]),
[final] ).
cnf(i_0_369,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_370,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_220,c_0_109]),
[final] ).
cnf(i_0_371,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_221,c_0_109]),
[final] ).
cnf(i_0_372,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_222,c_0_160]),
[final] ).
cnf(i_0_373,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_374,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_375,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_376,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_377,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_378,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_225]),
[final] ).
cnf(i_0_379,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_380,lemma,
( in(powerset(X1),esk22_1(X2))
| ~ in(X1,esk22_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_381,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_226,c_0_109]),
[final] ).
cnf(i_0_382,lemma,
( in(esk24_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_383,lemma,
( in(esk24_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_213]),
[final] ).
cnf(i_0_384,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_385,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_227,c_0_109]),
[final] ).
cnf(i_0_386,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_387,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_229]),
[final] ).
cnf(i_0_388,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_389,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_231]),
[final] ).
cnf(i_0_390,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_391,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_232,c_0_109]),
[final] ).
cnf(i_0_392,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_393,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_394,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_235,c_0_109]),
[final] ).
cnf(i_0_395,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_236,c_0_109]),
[final] ).
cnf(i_0_396,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_397,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_398,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_399,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_238]),
[final] ).
cnf(i_0_400,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_239]),
[final] ).
cnf(i_0_401,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_240]),
[final] ).
cnf(i_0_402,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_241]),
[final] ).
cnf(i_0_403,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_242,c_0_109]),
[final] ).
cnf(i_0_404,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_243,c_0_109]),
[final] ).
cnf(i_0_405,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_244,c_0_109]),
[final] ).
cnf(i_0_406,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_407,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_408,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_409,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_410,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_246,c_0_160]),
[final] ).
cnf(i_0_411,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_247]),
[final] ).
cnf(i_0_412,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_248]),
[final] ).
cnf(i_0_413,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_249]),
[final] ).
cnf(i_0_414,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_415,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_416,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_251]),
[final] ).
cnf(i_0_417,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_252,c_0_160]),
[final] ).
cnf(i_0_418,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_419,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_249]),
[final] ).
cnf(i_0_420,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_421,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_255]),
[final] ).
cnf(i_0_422,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_423,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_255]),
[final] ).
cnf(i_0_424,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_425,negated_conjecture,
in(esk27_0,subset_complement(esk26_0,esk28_0)),
inference(split_conjunct,[status(thm)],[i_0_256]),
[final] ).
cnf(i_0_426,plain,
( element(esk18_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_257]),
[final] ).
cnf(i_0_427,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_258]),
[final] ).
cnf(i_0_428,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_245]),
[final] ).
cnf(i_0_429,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_259]),
[final] ).
cnf(i_0_430,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_260]),
[final] ).
cnf(i_0_431,plain,
element(esk20_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_261]),
[final] ).
cnf(i_0_432,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_249]),
[final] ).
cnf(i_0_433,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_262]),
[final] ).
cnf(i_0_434,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_263]),
[final] ).
cnf(i_0_435,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_264,c_0_109]),
[final] ).
cnf(i_0_436,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_262]),
[final] ).
cnf(i_0_437,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_265]),
[final] ).
cnf(i_0_438,plain,
( empty(X1)
| ~ empty(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_257]),
[final] ).
cnf(i_0_439,plain,
element(esk17_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_266]),
[final] ).
cnf(i_0_440,plain,
in(X1,esk29_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_441,lemma,
in(X1,esk22_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_442,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_443,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_444,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_267]),
[final] ).
cnf(i_0_445,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_268]),
[final] ).
cnf(i_0_446,negated_conjecture,
element(esk28_0,powerset(esk26_0)),
inference(split_conjunct,[status(thm)],[i_0_256]),
[final] ).
cnf(i_0_447,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_448,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_270]),
[final] ).
cnf(i_0_449,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_271,c_0_109]),
[final] ).
cnf(i_0_450,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_272]),
[final] ).
cnf(i_0_451,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_273]),
[final] ).
cnf(i_0_452,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_274]),
[final] ).
cnf(i_0_453,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_275]),
[final] ).
cnf(i_0_454,negated_conjecture,
in(esk27_0,esk28_0),
inference(split_conjunct,[status(thm)],[i_0_256]),
[final] ).
cnf(i_0_455,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_276]),
[final] ).
cnf(i_0_456,plain,
empty(esk20_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_261]),
[final] ).
cnf(i_0_457,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_277]),
[final] ).
cnf(i_0_458,plain,
~ empty(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_278]),
[final] ).
cnf(i_0_459,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_279]),
[final] ).
cnf(i_0_460,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_461,axiom,
X1 = X1 ).
cnf(i_0_462,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_463,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_464,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_465,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_466,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_467,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_468,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_469,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_470,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_471,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_472,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_473,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_474,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_475,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_476,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_477,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_478,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_479,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_480,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_481,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_482,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_483,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_484,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_485,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_486,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_487,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_488,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_489,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_490,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_491,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_492,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_493,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_494,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_495,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_496,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_461_001,axiom,
X1 = X1 ).
cnf(i_0_462_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_463_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_464_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_465_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_466_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_467_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_468_008,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_469_009,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_470_010,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_471_011,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_472_012,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_473_013,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_474_014,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_475_015,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_476_016,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_477_017,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_478_018,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_479_019,axiom,
( X1 != X2
| esk8_3(X1,X3,X4) = esk8_3(X2,X3,X4) ) ).
cnf(i_0_480_020,axiom,
( X1 != X2
| esk8_3(X3,X1,X4) = esk8_3(X3,X2,X4) ) ).
cnf(i_0_481_021,axiom,
( X1 != X2
| esk8_3(X3,X4,X1) = esk8_3(X3,X4,X2) ) ).
cnf(i_0_482_022,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_483_023,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_484_024,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_485_025,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_486_026,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_487_027,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_488_028,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_489_029,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_490_030,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_491_031,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_492_032,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_493_033,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_494_034,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_495_035,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_496_036,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_497,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),esk7_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),esk6_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[280]) ).
cnf(i_0_498,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk7_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[283]) ).
cnf(i_0_499,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk6_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[284]) ).
cnf(i_0_500,plain,
X1 = X1,
inference(equality_inference,[],[306]) ).
cnf(i_0_501,plain,
X1 = X1,
inference(equality_inference,[],[307]) ).
cnf(i_0_502,plain,
( ~ in(X1,union(X2))
| in(esk13_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[312]) ).
cnf(i_0_503,plain,
( ~ in(X1,union(X2))
| in(X1,esk13_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[313]) ).
cnf(i_0_504,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[321]) ).
cnf(i_0_505,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[328]) ).
cnf(i_0_506,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[352]) ).
cnf(i_0_507,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[353]) ).
cnf(i_0_508,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[361]) ).
cnf(i_0_509,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[362]) ).
cnf(i_0_510,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[373]) ).
cnf(i_0_511,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[374]) ).
cnf(i_0_512,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[375]) ).
cnf(i_0_513,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[390]) ).
cnf(i_0_514,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[391]) ).
cnf(i_0_515,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[392]) ).
cnf(i_0_516,plain,
X1 = X1,
inference(equality_inference,[],[394]) ).
cnf(i_0_517,plain,
X1 = X1,
inference(equality_inference,[],[395]) ).
cnf(i_0_518,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[396]) ).
cnf(i_0_519,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[397]) ).
cnf(i_0_520,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[404]) ).
cnf(i_0_521,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[432]) ).
cnf(i_0_522,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[433]) ).
cnf(i_0_523,plain,
subset(X1,X1),
inference(equality_inference,[],[442]) ).
cnf(i_0_524,plain,
subset(X1,X1),
inference(equality_inference,[],[443]) ).
cnf(i_0_525,plain,
element(subset_complement(esk26_0,esk28_0),powerset(esk26_0)),
inference(scs_inference,[],[i_0_446,i_0_344]) ).
cnf(i_0_526,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_344]) ).
cnf(i_0_527,plain,
subset_complement(esk26_0,esk28_0) = set_difference(esk26_0,esk28_0),
inference(scs_inference,[],[i_0_446,i_0_344,i_0_376]) ).
cnf(i_0_528,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_376]) ).
cnf(i_0_529,plain,
~ in(subset_complement(esk26_0,esk28_0),esk27_0),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_344,i_0_376,i_0_400]) ).
cnf(i_0_530,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_531,plain,
~ in(X1,esk19_0),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427]) ).
cnf(i_0_532,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_533,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433]) ).
cnf(i_0_534,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_535,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_433]) ).
cnf(i_0_536,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498]) ).
cnf(i_0_537,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_538,plain,
( in(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_539,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499]) ).
cnf(i_0_540,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_541,plain,
( in(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_499]) ).
cnf(i_0_542,plain,
~ in(X1,union(empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502]) ).
cnf(i_0_543,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_544,plain,
( in(esk13_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(rename_variables,[],[i_0_502]) ).
cnf(i_0_545,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505]) ).
cnf(i_0_546,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_505]) ).
cnf(i_0_547,plain,
~ in(esk27_0,set_difference(X1,subset_complement(esk26_0,esk28_0))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508]) ).
cnf(i_0_548,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_508]) ).
cnf(i_0_549,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510]) ).
cnf(i_0_550,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_510]) ).
cnf(i_0_551,plain,
in(esk27_0,set_union2(subset_complement(esk26_0,esk28_0),X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511]) ).
cnf(i_0_552,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_511]) ).
cnf(i_0_553,plain,
in(esk27_0,set_union2(X1,subset_complement(esk26_0,esk28_0))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512]) ).
cnf(i_0_554,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_512]) ).
cnf(i_0_555,plain,
~ in(unordered_pair(X1,X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_435,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514]) ).
cnf(i_0_556,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_514]) ).
cnf(i_0_557,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_459,i_0_435,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316]) ).
cnf(i_0_558,plain,
( in(esk25_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_559,plain,
in(esk30_2(X1,X1),esk29_1(X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_447,i_0_440,i_0_459,i_0_435,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345]) ).
cnf(i_0_560,plain,
( ~ in(X1,esk29_1(X2))
| in(esk30_2(X2,X1),esk29_1(X2)) ),
inference(rename_variables,[],[i_0_345]) ).
cnf(i_0_561,plain,
in(X1,unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_447,i_0_440,i_0_459,i_0_435,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349]) ).
cnf(i_0_562,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_448]) ).
cnf(i_0_563,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_349]) ).
cnf(i_0_564,plain,
in(X1,unordered_pair(X2,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_440,i_0_459,i_0_435,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350]) ).
cnf(i_0_565,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_448]) ).
cnf(i_0_566,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_567,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_440,i_0_459,i_0_435,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351]) ).
cnf(i_0_568,plain,
set_difference(empty_set,X1) = empty_set,
inference(rename_variables,[],[i_0_453]) ).
cnf(i_0_569,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_570,plain,
disjoint(esk19_0,X1),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_440,i_0_459,i_0_435,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382]) ).
cnf(i_0_571,plain,
( in(esk24_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_382]) ).
cnf(i_0_572,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_440,i_0_459,i_0_435,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383]) ).
cnf(i_0_573,plain,
( in(esk24_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_383]) ).
cnf(i_0_574,plain,
subset(cartesian_product2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_440,i_0_459,i_0_435,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384]) ).
cnf(i_0_575,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_576,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404]) ).
cnf(i_0_577,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_578,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_404]) ).
cnf(i_0_579,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414]) ).
cnf(i_0_580,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_414]) ).
cnf(i_0_581,plain,
disjoint(X1,esk19_0),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418]) ).
cnf(i_0_582,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_583,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421]) ).
cnf(i_0_584,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_421]) ).
cnf(i_0_585,plain,
in(esk2_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436]) ).
cnf(i_0_586,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(rename_variables,[],[i_0_436]) ).
cnf(i_0_587,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437]) ).
cnf(i_0_588,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_437]) ).
cnf(i_0_589,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_577,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442]) ).
cnf(i_0_590,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_591,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_577,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443]) ).
cnf(i_0_592,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_443]) ).
cnf(i_0_593,plain,
~ empty(unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_447,i_0_534,i_0_577,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457]) ).
cnf(i_0_594,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(rename_variables,[],[i_0_457]) ).
cnf(i_0_595,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519]) ).
cnf(i_0_596,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_519]) ).
cnf(i_0_597,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462]) ).
cnf(i_0_598,plain,
~ in(X1,set_union2(cartesian_product2(X2,cartesian_product2(empty_set,X3)),cartesian_product2(X2,cartesian_product2(empty_set,X3)))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283]) ).
cnf(i_0_599,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_600,plain,
( X1 != cartesian_product2(X2,X3)
| in(esk7_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_283]) ).
cnf(i_0_601,plain,
~ in(X1,set_union2(cartesian_product2(union(empty_set),X2),cartesian_product2(union(empty_set),X2))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284]) ).
cnf(i_0_602,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_603,plain,
( X1 != cartesian_product2(X2,X3)
| in(esk6_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_284]) ).
cnf(i_0_604,plain,
~ in(esk25_2(X1,empty_set),set_union2(set_difference(X2,set_difference(X2,empty_set)),set_difference(X2,set_difference(X2,empty_set)))),
inference(scs_inference,[],[i_0_425,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328]) ).
cnf(i_0_605,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_606,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_607,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_608,plain,
in(esk27_0,esk26_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360]) ).
cnf(i_0_609,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,X1)
| in(X3,X2) ),
inference(rename_variables,[],[i_0_360]) ).
cnf(i_0_610,plain,
~ in(esk27_0,set_union2(set_difference(X1,subset_complement(esk26_0,esk28_0)),set_difference(X1,subset_complement(esk26_0,esk28_0)))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361]) ).
cnf(i_0_611,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_612,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_361]) ).
cnf(i_0_613,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373]) ).
cnf(i_0_614,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_615,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_373]) ).
cnf(i_0_616,plain,
in(esk27_0,set_union2(set_union2(subset_complement(esk26_0,esk28_0),X1),set_union2(subset_complement(esk26_0,esk28_0),X1))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374]) ).
cnf(i_0_617,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_618,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_374]) ).
cnf(i_0_619,plain,
in(esk27_0,set_union2(set_union2(X1,subset_complement(esk26_0,esk28_0)),set_union2(X1,subset_complement(esk26_0,esk28_0)))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375]) ).
cnf(i_0_620,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_621,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_375]) ).
cnf(i_0_622,plain,
~ subset(subset_complement(esk26_0,esk28_0),empty_set),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379]) ).
cnf(i_0_623,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_624,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_379]) ).
cnf(i_0_625,plain,
~ in(unordered_pair(X1,X1),set_union2(unordered_pair(empty_set,empty_set),unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391]) ).
cnf(i_0_626,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_627,plain,
( X1 != unordered_pair(X2,X2)
| ~ in(X3,X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_391]) ).
cnf(i_0_628,plain,
~ in(subset_complement(esk26_0,esk28_0),set_union2(powerset(empty_set),powerset(empty_set))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_440,i_0_459,i_0_435,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396]) ).
cnf(i_0_629,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_630,plain,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_396]) ).
cnf(i_0_631,plain,
element(X1,powerset(X1)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_440,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408]) ).
cnf(i_0_632,plain,
~ empty(powerset(X1)),
inference(rename_variables,[],[i_0_444]) ).
cnf(i_0_633,plain,
( empty(X1)
| ~ in(X2,X1)
| element(X2,X1) ),
inference(rename_variables,[],[i_0_408]) ).
cnf(i_0_634,plain,
in(esk17_1(esk21_0),esk21_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409]) ).
cnf(i_0_635,plain,
element(esk17_1(X1),X1),
inference(rename_variables,[],[i_0_439]) ).
cnf(i_0_636,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_409]) ).
cnf(i_0_637,plain,
~ element(esk21_0,esk19_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424]) ).
cnf(i_0_638,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_424]) ).
cnf(i_0_639,plain,
in(esk27_0,set_difference(subset_complement(esk26_0,esk28_0),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507]) ).
cnf(i_0_640,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_641,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_507]) ).
cnf(i_0_642,plain,
in(esk27_0,union(esk29_1(subset_complement(esk26_0,esk28_0)))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509]) ).
cnf(i_0_643,plain,
in(X1,esk29_1(X1)),
inference(rename_variables,[],[i_0_440]) ).
cnf(i_0_644,plain,
( ~ in(X1,X2)
| in(X3,union(X2))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_509]) ).
cnf(i_0_645,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513]) ).
cnf(i_0_646,plain,
( ~ in(X1,unordered_pair(X2,X3))
| X1 = X2
| X1 = X3 ),
inference(rename_variables,[],[i_0_513]) ).
cnf(i_0_647,plain,
~ in(set_union2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)),esk27_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484]) ).
cnf(i_0_648,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_649,plain,
~ in(subset_complement(esk26_0,esk28_0),set_union2(esk27_0,esk27_0)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485]) ).
cnf(i_0_650,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_651,plain,
~ element(set_union2(esk21_0,esk21_0),esk19_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491]) ).
cnf(i_0_652,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_653,plain,
~ element(esk21_0,set_union2(esk19_0,esk19_0)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492]) ).
cnf(i_0_654,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_655,plain,
~ proper_subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_434,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495]) ).
cnf(i_0_656,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_434]) ).
cnf(i_0_657,plain,
~ proper_subset(X1,set_union2(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496]) ).
cnf(i_0_658,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_434]) ).
cnf(i_0_659,plain,
set_union2(cartesian_product2(X1,cartesian_product2(empty_set,X2)),cartesian_product2(X1,cartesian_product2(empty_set,X2))) = cartesian_product2(X3,empty_set),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300]) ).
cnf(i_0_660,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_661,plain,
( in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2)
| in(esk10_3(X1,X2,X3),X2) ),
inference(rename_variables,[],[i_0_300]) ).
cnf(i_0_662,plain,
set_union2(cartesian_product2(union(empty_set),X1),cartesian_product2(union(empty_set),X1)) = cartesian_product2(empty_set,X2),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301]) ).
cnf(i_0_663,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_664,plain,
( in(esk8_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2)
| in(esk9_3(X1,X2,X3),X1) ),
inference(rename_variables,[],[i_0_301]) ).
cnf(i_0_665,plain,
in(X1,esk30_2(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329]) ).
cnf(i_0_666,plain,
in(X1,esk29_1(X1)),
inference(rename_variables,[],[i_0_440]) ).
cnf(i_0_667,plain,
( ~ in(X1,esk29_1(X2))
| in(X3,esk30_2(X2,X1))
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_668,plain,
~ subset(subset_complement(esk26_0,esk28_0),set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378]) ).
cnf(i_0_669,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_411]) ).
cnf(i_0_670,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_378]) ).
cnf(i_0_671,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393]) ).
cnf(i_0_672,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_411]) ).
cnf(i_0_673,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_393]) ).
cnf(i_0_674,plain,
in(X1,set_difference(powerset(X1),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397]) ).
cnf(i_0_675,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_676,plain,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(rename_variables,[],[i_0_397]) ).
cnf(i_0_677,plain,
in(set_union2(X1,X1),set_difference(unordered_pair(X1,X2),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406]) ).
cnf(i_0_678,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_679,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_406]) ).
cnf(i_0_680,plain,
in(set_union2(X1,X1),set_difference(unordered_pair(X2,X1),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407]) ).
cnf(i_0_681,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_682,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_407]) ).
cnf(i_0_683,plain,
element(esk19_0,esk19_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428]) ).
cnf(i_0_684,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_428]) ).
cnf(i_0_685,plain,
unordered_pair(X1,X1) != set_union2(empty_set,empty_set),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463]) ).
cnf(i_0_686,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_687,plain,
esk19_0 != esk21_0,
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486]) ).
cnf(i_0_688,plain,
~ subset(set_union2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)),empty_set),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487]) ).
cnf(i_0_689,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_690,plain,
~ subset(subset_complement(esk26_0,esk28_0),set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488]) ).
cnf(i_0_691,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_692,plain,
in(esk27_0,set_difference(subset_complement(esk26_0,esk28_0),set_difference(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321]) ).
cnf(i_0_693,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rename_variables,[],[i_0_343]) ).
cnf(i_0_694,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X3)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(rename_variables,[],[i_0_321]) ).
cnf(i_0_695,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352]) ).
cnf(i_0_696,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_697,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_352]) ).
cnf(i_0_698,plain,
in(esk27_0,set_difference(set_difference(subset_complement(esk26_0,esk28_0),empty_set),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353]) ).
cnf(i_0_699,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_700,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_701,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_353]) ).
cnf(i_0_702,plain,
~ in(unordered_pair(X1,X1),set_difference(unordered_pair(empty_set,empty_set),empty_set)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390]) ).
cnf(i_0_703,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_704,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_390]) ).
cnf(i_0_705,plain,
in(esk5_3(empty_set,empty_set,unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_429,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289]) ).
cnf(i_0_706,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_707,plain,
( X1 = set_union2(X2,X3)
| in(esk5_3(X2,X3,X1),X1)
| in(esk5_3(X2,X3,X1),X2)
| in(esk5_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_289]) ).
cnf(i_0_708,plain,
in(unordered_pair(unordered_pair(esk27_0,esk27_0),unordered_pair(esk27_0,esk27_0)),set_union2(cartesian_product2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)),cartesian_product2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309]) ).
cnf(i_0_709,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_430]) ).
cnf(i_0_710,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_711,plain,
( X1 != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X4 != cartesian_product2(X5,X6)
| ~ in(X3,X6)
| ~ in(X2,X5)
| in(X1,X4) ),
inference(rename_variables,[],[i_0_309]) ).
cnf(i_0_712,plain,
~ in(X1,set_difference(unordered_pair(X1,X1),unordered_pair(X1,X1))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335]) ).
cnf(i_0_713,plain,
( ~ disjoint(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rename_variables,[],[i_0_335]) ).
cnf(i_0_714,plain,
~ disjoint(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310]) ).
cnf(i_0_715,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| ~ disjoint(X2,X3) ),
inference(rename_variables,[],[i_0_310]) ).
cnf(i_0_716,plain,
~ in(X1,set_union2(union(empty_set),union(empty_set))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312]) ).
cnf(i_0_717,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_718,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_719,plain,
( X1 != union(X2)
| in(esk13_3(X2,X1,X3),X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_312]) ).
cnf(i_0_720,plain,
( ~ in(X1,set_union2(union(X2),union(X2)))
| in(X1,esk13_3(X2,set_union2(union(X2),union(X2)),X1)) ),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313]) ).
cnf(i_0_721,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_722,plain,
( X1 != union(X2)
| in(X3,esk13_3(X2,X1,X3))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_313]) ).
cnf(i_0_723,plain,
in(unordered_pair(unordered_pair(esk27_0,esk27_0),unordered_pair(esk27_0,esk27_0)),cartesian_product2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506]) ).
cnf(i_0_724,plain,
( ~ in(X1,set_union2(X2,X3))
| in(X1,X2)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_506]) ).
cnf(i_0_725,plain,
empty_set = union(set_union2(union(empty_set),union(empty_set))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336]) ).
cnf(i_0_726,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_522]) ).
cnf(i_0_727,plain,
( in(esk14_2(X1,X2),X2)
| X2 = union(X1)
| in(esk15_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_728,plain,
~ subset(subset_complement(esk26_0,esk28_0),esk19_0),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336,i_0_377]) ).
cnf(i_0_729,plain,
( ~ disjoint(X1,X2)
| disjoint(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_377]) ).
cnf(i_0_730,plain,
~ disjoint(set_union2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0)),subset_complement(esk26_0,esk28_0)),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_721,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336,i_0_377,i_0_489]) ).
cnf(i_0_731,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_732,plain,
~ disjoint(subset_complement(esk26_0,esk28_0),set_union2(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,esk28_0))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_721,i_0_731,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336,i_0_377,i_0_489,i_0_490]) ).
cnf(i_0_733,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_447]) ).
cnf(i_0_734,plain,
~ subset(subset_complement(esk26_0,esk28_0),subset_complement(esk26_0,subset_complement(esk26_0,esk28_0))),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_721,i_0_731,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336,i_0_377,i_0_489,i_0_490,i_0_314]) ).
cnf(i_0_735,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| ~ subset(X3,subset_complement(X2,X1))
| disjoint(X3,X1) ),
inference(rename_variables,[],[i_0_314]) ).
cnf(i_0_736,plain,
( ~ disjoint(esk28_0,esk28_0)
| subset(esk28_0,subset_complement(esk26_0,esk28_0)) ),
inference(scs_inference,[],[i_0_425,i_0_454,i_0_446,i_0_522,i_0_537,i_0_540,i_0_543,i_0_606,i_0_623,i_0_640,i_0_660,i_0_663,i_0_700,i_0_706,i_0_718,i_0_434,i_0_656,i_0_448,i_0_562,i_0_565,i_0_447,i_0_534,i_0_577,i_0_599,i_0_602,i_0_605,i_0_611,i_0_614,i_0_617,i_0_620,i_0_626,i_0_629,i_0_648,i_0_650,i_0_652,i_0_654,i_0_686,i_0_689,i_0_691,i_0_696,i_0_710,i_0_717,i_0_721,i_0_731,i_0_429,i_0_430,i_0_439,i_0_440,i_0_643,i_0_411,i_0_669,i_0_450,i_0_675,i_0_678,i_0_681,i_0_699,i_0_458,i_0_459,i_0_435,i_0_444,i_0_410,i_0_343,i_0_453,i_0_417,i_0_344,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_505,i_0_508,i_0_510,i_0_511,i_0_512,i_0_514,i_0_316,i_0_345,i_0_349,i_0_350,i_0_351,i_0_382,i_0_383,i_0_384,i_0_404,i_0_414,i_0_418,i_0_421,i_0_436,i_0_437,i_0_442,i_0_443,i_0_457,i_0_519,i_0_462,i_0_283,i_0_284,i_0_328,i_0_360,i_0_361,i_0_373,i_0_374,i_0_375,i_0_379,i_0_391,i_0_396,i_0_408,i_0_409,i_0_424,i_0_507,i_0_509,i_0_513,i_0_484,i_0_485,i_0_491,i_0_492,i_0_495,i_0_496,i_0_300,i_0_301,i_0_329,i_0_378,i_0_393,i_0_397,i_0_406,i_0_407,i_0_428,i_0_463,i_0_486,i_0_487,i_0_488,i_0_321,i_0_352,i_0_353,i_0_390,i_0_289,i_0_309,i_0_335,i_0_310,i_0_312,i_0_313,i_0_506,i_0_336,i_0_377,i_0_489,i_0_490,i_0_314,i_0_320]) ).
cnf(i_0_737,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset(X3,subset_complement(X2,X1))
| ~ disjoint(X3,X1) ),
inference(rename_variables,[],[i_0_320]) ).
cnf(i_0_738,plain,
subset_complement(X1,X1) = set_difference(X1,X1),
inference(scs_inference,[],[i_0_631,i_0_376]) ).
cnf(i_0_739,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_376]) ).
cnf(i_0_740,plain,
~ in(esk28_0,esk27_0),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_376,i_0_400]) ).
cnf(i_0_741,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_742,plain,
~ in(X1,esk20_1(X2)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_456,i_0_376,i_0_400,i_0_427]) ).
cnf(i_0_743,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_744,plain,
~ in(X1,esk2_1(unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433]) ).
cnf(i_0_745,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(rename_variables,[],[i_0_645]) ).
cnf(i_0_746,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_433]) ).
cnf(i_0_747,plain,
~ in(X1,cartesian_product2(X2,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498]) ).
cnf(i_0_748,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_749,plain,
( in(esk7_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_750,plain,
~ in(X1,cartesian_product2(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X2)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499]) ).
cnf(i_0_751,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_752,plain,
( in(esk6_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_499]) ).
cnf(i_0_753,plain,
~ in(X1,union(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502]) ).
cnf(i_0_754,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_755,plain,
( in(esk13_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(rename_variables,[],[i_0_502]) ).
cnf(i_0_756,plain,
~ in(esk27_0,set_difference(X1,esk28_0)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508]) ).
cnf(i_0_757,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_508]) ).
cnf(i_0_758,plain,
~ in(unordered_pair(X1,X1),unordered_pair(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_685,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514]) ).
cnf(i_0_759,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_514]) ).
cnf(i_0_760,plain,
in(esk30_2(X1,esk30_2(X1,X1)),esk29_1(X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_559,i_0_685,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345]) ).
cnf(i_0_761,plain,
( ~ in(X1,esk29_1(X2))
| in(esk30_2(X2,X1),esk29_1(X2)) ),
inference(rename_variables,[],[i_0_345]) ).
cnf(i_0_762,plain,
in(X1,set_difference(unordered_pair(X1,X2),empty_set)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_559,i_0_685,i_0_583,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349]) ).
cnf(i_0_763,plain,
subset(X1,set_difference(X1,empty_set)),
inference(rename_variables,[],[i_0_583]) ).
cnf(i_0_764,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_349]) ).
cnf(i_0_765,plain,
in(X1,set_difference(unordered_pair(X2,X1),empty_set)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350]) ).
cnf(i_0_766,plain,
subset(X1,set_difference(X1,empty_set)),
inference(rename_variables,[],[i_0_583]) ).
cnf(i_0_767,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_768,plain,
subset(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X1),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_695,i_0_748,i_0_751,i_0_754,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384]) ).
cnf(i_0_769,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_770,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_771,plain,
subset(esk2_1(unordered_pair(empty_set,empty_set)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_695,i_0_748,i_0_751,i_0_754,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404]) ).
cnf(i_0_772,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(rename_variables,[],[i_0_645]) ).
cnf(i_0_773,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_404]) ).
cnf(i_0_774,plain,
subset(esk2_1(unordered_pair(X1,X1)),X1),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442]) ).
cnf(i_0_775,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_776,plain,
element(subset_complement(X1,X1),powerset(X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344]) ).
cnf(i_0_777,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_344]) ).
cnf(i_0_778,plain,
~ in(unordered_pair(X1,X1),set_difference(X2,set_difference(X2,unordered_pair(empty_set,empty_set)))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505]) ).
cnf(i_0_779,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_505]) ).
cnf(i_0_780,plain,
in(esk27_0,set_union2(esk28_0,X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511]) ).
cnf(i_0_781,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_511]) ).
cnf(i_0_782,plain,
in(esk27_0,set_union2(X1,esk28_0)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512]) ).
cnf(i_0_783,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_512]) ).
cnf(i_0_784,plain,
set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)) = empty_set,
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437]) ).
cnf(i_0_785,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_437]) ).
cnf(i_0_786,plain,
subset(X1,esk2_1(unordered_pair(X1,X1))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443]) ).
cnf(i_0_787,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_443]) ).
cnf(i_0_788,plain,
in(set_union2(X1,X1),powerset(X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519]) ).
cnf(i_0_789,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_519]) ).
cnf(i_0_790,plain,
~ in(X1,set_difference(set_difference(unordered_pair(X1,X1),unordered_pair(X1,X1)),X2)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_555,i_0_559,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510]) ).
cnf(i_0_791,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_510]) ).
cnf(i_0_792,plain,
disjoint(set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),X1),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_555,i_0_559,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382]) ).
cnf(i_0_793,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_794,plain,
( in(esk24_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_382]) ).
cnf(i_0_795,plain,
disjoint(set_difference(X1,X1),X1),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_555,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418]) ).
cnf(i_0_796,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_797,plain,
disjoint(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_793,i_0_555,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418,i_0_383]) ).
cnf(i_0_798,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_799,plain,
( in(esk24_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_383]) ).
cnf(i_0_800,plain,
X1 = esk2_1(unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_793,i_0_555,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418,i_0_383,i_0_462]) ).
cnf(i_0_801,plain,
set_difference(X1,set_difference(X1,empty_set)) = set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_793,i_0_798,i_0_545,i_0_555,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418,i_0_383,i_0_462,i_0_340]) ).
cnf(i_0_802,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(rename_variables,[],[i_0_545]) ).
cnf(i_0_803,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_695]) ).
cnf(i_0_804,plain,
( in(esk23_2(X1,X2),X1)
| in(esk23_2(X1,X2),X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_340]) ).
cnf(i_0_805,plain,
~ in(X1,subset_complement(set_difference(unordered_pair(X1,X1),unordered_pair(X1,X1)),set_difference(unordered_pair(X1,X1),unordered_pair(X1,X1)))),
inference(scs_inference,[],[i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_793,i_0_798,i_0_545,i_0_555,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418,i_0_383,i_0_462,i_0_340,i_0_360]) ).
cnf(i_0_806,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,X1)
| in(X3,X2) ),
inference(rename_variables,[],[i_0_360]) ).
cnf(i_0_807,plain,
$false,
inference(scs_inference,[],[i_0_425,i_0_454,i_0_631,i_0_712,i_0_645,i_0_745,i_0_772,i_0_695,i_0_748,i_0_751,i_0_754,i_0_769,i_0_793,i_0_798,i_0_545,i_0_555,i_0_527,i_0_559,i_0_579,i_0_589,i_0_685,i_0_583,i_0_763,i_0_456,i_0_376,i_0_400,i_0_427,i_0_433,i_0_498,i_0_499,i_0_502,i_0_508,i_0_514,i_0_345,i_0_349,i_0_350,i_0_384,i_0_404,i_0_442,i_0_344,i_0_505,i_0_511,i_0_512,i_0_437,i_0_443,i_0_519,i_0_510,i_0_382,i_0_418,i_0_383,i_0_462,i_0_340,i_0_360,i_0_361]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU172+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:46:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.49/1.62 % Version : CSE_E---1.7
% 0.49/1.62 % Problem : theBenchmark.p
% 0.49/1.62 % SZS status Theorem for theBenchmark.p
% 0.49/1.62 % SZS output start CNFRefutation
% See solution above
% 2.02/3.16 % Total time : 1.271s
%------------------------------------------------------------------------------