%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU177+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 05:10:57 PM UTC 2026
% Result : Theorem 1.99s 2.62s
% Output : CNFRefutation 3.68s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_138)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t20_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(t47_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(t48_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(t6_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(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/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(l25_zfmisc_1,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t37_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(fc3_subset_1,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [X1,X2] : ~ proper_subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d8_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(d1_setfam_1,axiom,
! [X1,X2] :
( ( X1 != empty_set
=> ( X2 = set_meet(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ! [X4] :
( in(X4,X1)
=> in(X3,X4) ) ) ) )
& ( X1 = empty_set
=> ( X2 = set_meet(X1)
<=> X2 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(t54_subset_1,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t46_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(l3_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t10_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t60_xboole_1,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(t92_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t37_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_128,plain,
! [X451,X452] : ordered_pair(X451,X452) = unordered_pair(unordered_pair(X451,X452),singleton(X451)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_129,lemma,
! [X660] : unordered_pair(X660,X660) = singleton(X660),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_130,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_131,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_132,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t20_relat_1]) ).
fof(i_0_133,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_134,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_135,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_136,plain,
! [X376,X377,X378,X379,X382,X383,X384,X385,X386,X387,X389,X390] :
( ( in(esk9_4(X376,X377,X378,X379),X376)
| ~ in(X379,X378)
| X378 != cartesian_product2(X376,X377) )
& ( in(esk10_4(X376,X377,X378,X379),X377)
| ~ in(X379,X378)
| X378 != cartesian_product2(X376,X377) )
& ( X379 = ordered_pair(esk9_4(X376,X377,X378,X379),esk10_4(X376,X377,X378,X379))
| ~ in(X379,X378)
| X378 != cartesian_product2(X376,X377) )
& ( ~ in(X383,X376)
| ~ in(X384,X377)
| X382 != ordered_pair(X383,X384)
| in(X382,X378)
| X378 != cartesian_product2(X376,X377) )
& ( ~ in(esk11_3(X385,X386,X387),X387)
| ~ in(X389,X385)
| ~ in(X390,X386)
| esk11_3(X385,X386,X387) != ordered_pair(X389,X390)
| X387 = cartesian_product2(X385,X386) )
& ( in(esk12_3(X385,X386,X387),X385)
| in(esk11_3(X385,X386,X387),X387)
| X387 = cartesian_product2(X385,X386) )
& ( in(esk13_3(X385,X386,X387),X386)
| in(esk11_3(X385,X386,X387),X387)
| X387 = cartesian_product2(X385,X386) )
& ( esk11_3(X385,X386,X387) = ordered_pair(esk12_3(X385,X386,X387),esk13_3(X385,X386,X387))
| in(esk11_3(X385,X386,X387),X387)
| X387 = cartesian_product2(X385,X386) ) ),
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_137,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_128]) ).
cnf(i_0_138,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_129]) ).
fof(i_0_139,plain,
! [X439,X440,X441,X443,X444,X445,X447] :
( ( ~ in(X441,X440)
| in(ordered_pair(esk23_3(X439,X440,X441),X441),X439)
| X440 != relation_rng(X439)
| ~ relation(X439) )
& ( ~ in(ordered_pair(X444,X443),X439)
| in(X443,X440)
| X440 != relation_rng(X439)
| ~ relation(X439) )
& ( ~ in(esk24_2(X439,X445),X445)
| ~ in(ordered_pair(X447,esk24_2(X439,X445)),X439)
| X445 = relation_rng(X439)
| ~ relation(X439) )
& ( in(esk24_2(X439,X445),X445)
| in(ordered_pair(esk25_2(X439,X445),esk24_2(X439,X445)),X439)
| X445 = relation_rng(X439)
| ~ relation(X439) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(i_0_140,plain,
! [X408,X409,X410,X412,X413,X414,X416] :
( ( ~ in(X410,X409)
| in(ordered_pair(X410,esk16_3(X408,X409,X410)),X408)
| X409 != relation_dom(X408)
| ~ relation(X408) )
& ( ~ in(ordered_pair(X412,X413),X408)
| in(X412,X409)
| X409 != relation_dom(X408)
| ~ relation(X408) )
& ( ~ in(esk17_2(X408,X414),X414)
| ~ in(ordered_pair(esk17_2(X408,X414),X416),X408)
| X414 = relation_dom(X408)
| ~ relation(X408) )
& ( in(esk17_2(X408,X414),X414)
| in(ordered_pair(esk17_2(X408,X414),esk18_2(X408,X414)),X408)
| X414 = relation_dom(X408)
| ~ relation(X408) ) ),
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_relat_1])])])])])]) ).
fof(i_0_141,plain,
! [X399,X400,X401,X402,X403,X404,X405,X406] :
( ( in(X402,X399)
| ~ in(X402,X401)
| X401 != set_intersection2(X399,X400) )
& ( in(X402,X400)
| ~ in(X402,X401)
| X401 != set_intersection2(X399,X400) )
& ( ~ in(X403,X399)
| ~ in(X403,X400)
| in(X403,X401)
| X401 != set_intersection2(X399,X400) )
& ( ~ in(esk15_3(X404,X405,X406),X406)
| ~ in(esk15_3(X404,X405,X406),X404)
| ~ in(esk15_3(X404,X405,X406),X405)
| X406 = set_intersection2(X404,X405) )
& ( in(esk15_3(X404,X405,X406),X404)
| in(esk15_3(X404,X405,X406),X406)
| X406 = set_intersection2(X404,X405) )
& ( in(esk15_3(X404,X405,X406),X405)
| in(esk15_3(X404,X405,X406),X406)
| X406 = set_intersection2(X404,X405) ) ),
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_142,lemma,
! [X632,X633] : set_difference(X632,set_difference(X632,X633)) = set_intersection2(X632,X633),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_143,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_144,lemma,
! [X538,X539,X540,X541] :
( ( in(X538,X540)
| ~ in(ordered_pair(X538,X539),cartesian_product2(X540,X541)) )
& ( in(X539,X541)
| ~ in(ordered_pair(X538,X539),cartesian_product2(X540,X541)) )
& ( ~ in(X538,X540)
| ~ in(X539,X541)
| in(ordered_pair(X538,X539),cartesian_product2(X540,X541)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(i_0_145,lemma,
! [X514,X515,X516,X517] :
( ( in(X514,X516)
| ~ in(ordered_pair(X514,X515),cartesian_product2(X516,X517)) )
& ( in(X515,X517)
| ~ in(ordered_pair(X514,X515),cartesian_product2(X516,X517)) )
& ( ~ in(X514,X516)
| ~ in(X515,X517)
| in(ordered_pair(X514,X515),cartesian_product2(X516,X517)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_146,plain,
! [X477,X478] : ~ empty(ordered_pair(X477,X478)),
inference(variable_rename,[status(thm)],[i_0_130]) ).
fof(i_0_147,lemma,
! [X590,X591,X592,X593] :
( ( X590 = X592
| ordered_pair(X590,X591) != ordered_pair(X592,X593) )
& ( X591 = X593
| ordered_pair(X590,X591) != ordered_pair(X592,X593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_148,lemma,
! [X575,X576,X577] :
( ~ subset(X575,X576)
| subset(set_intersection2(X575,X577),set_intersection2(X576,X577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_149,lemma,
! [X628,X629] :
( ~ element(X629,powerset(powerset(X628)))
| X629 = empty_set
| subset_difference(X628,cast_to_subset(X628),union_of_subsets(X628,X629)) = meet_of_subsets(X628,complements_of_subsets(X628,X629)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).
fof(i_0_150,plain,
! [X418] : cast_to_subset(X418) = X418,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(i_0_151,lemma,
! [X630,X631] :
( ~ element(X631,powerset(powerset(X630)))
| X631 = empty_set
| union_of_subsets(X630,complements_of_subsets(X630,X631)) = subset_difference(X630,cast_to_subset(X630),meet_of_subsets(X630,X631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(i_0_152,lemma,
! [X638,X639,X641,X642,X643] :
( ( disjoint(X638,X639)
| in(esk40_2(X638,X639),set_intersection2(X638,X639)) )
& ( ~ in(X643,set_intersection2(X641,X642))
| ~ disjoint(X641,X642) ) ),
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_131])])])])]) ).
fof(i_0_153,lemma,
! [X563,X564,X565] :
( ~ subset(X563,X564)
| ~ subset(X563,X565)
| subset(X563,set_intersection2(X564,X565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_154,lemma,
! [X507,X508,X509] :
( ~ subset(X507,X508)
| in(X509,X507)
| subset(X507,set_difference(X508,singleton(X509))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_155,negated_conjecture,
( relation(esk37_0)
& in(ordered_pair(esk35_0,esk36_0),esk37_0)
& ( ~ in(esk35_0,relation_dom(esk37_0))
| ~ in(esk36_0,relation_rng(esk37_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_132])])]) ).
fof(i_0_156,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_157,lemma,
! [X662,X663] :
( ~ subset(singleton(X662),singleton(X663))
| X662 = X663 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_158,plain,
! [X338,X339,X340,X341,X342,X343] :
( ( ~ in(X340,X339)
| X340 = X338
| X339 != singleton(X338) )
& ( X341 != X338
| in(X341,X339)
| X339 != singleton(X338) )
& ( ~ in(esk4_2(X342,X343),X343)
| esk4_2(X342,X343) != X342
| X343 = singleton(X342) )
& ( in(esk4_2(X342,X343),X343)
| esk4_2(X342,X343) = X342
| X343 = singleton(X342) ) ),
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_159,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_160,lemma,
! [X561,X562] : subset(set_intersection2(X561,X562),X561),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_161,lemma,
! [X658,X659] :
( ( set_difference(X658,singleton(X659)) != X658
| ~ in(X659,X658) )
& ( in(X659,X658)
| set_difference(X658,singleton(X659)) = X658 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_133])]) ).
fof(i_0_162,lemma,
! [X496,X497] :
( ~ disjoint(singleton(X496),X497)
| ~ in(X496,X497) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_163,lemma,
! [X605,X606] :
( ( ~ subset(X605,singleton(X606))
| X605 = empty_set
| X605 = singleton(X606) )
& ( X605 != empty_set
| subset(X605,singleton(X606)) )
& ( X605 != singleton(X606)
| subset(X605,singleton(X606)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_164,lemma,
! [X510,X511] :
( ( ~ subset(X510,singleton(X511))
| X510 = empty_set
| X510 = singleton(X511) )
& ( X510 != empty_set
| subset(X510,singleton(X511)) )
& ( X510 != singleton(X511)
| subset(X510,singleton(X511)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_165,plain,
! [X321,X322] : set_intersection2(X321,X322) = set_intersection2(X322,X321),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_166,lemma,
! [X598,X599] :
( ( ~ subset(singleton(X598),X599)
| in(X598,X599) )
& ( ~ in(X598,X599)
| subset(singleton(X598),X599) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_167,lemma,
! [X500,X501] :
( ( ~ subset(singleton(X500),X501)
| in(X500,X501) )
& ( ~ in(X500,X501)
| subset(singleton(X500),X501) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_168,plain,
! [X453,X454] :
( ( ~ disjoint(X453,X454)
| set_intersection2(X453,X454) = empty_set )
& ( set_intersection2(X453,X454) != empty_set
| disjoint(X453,X454) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_169,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_170,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_171,lemma,
! [X626,X627] :
( ~ in(X626,X627)
| set_union2(singleton(X626),X627) = X627 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_172,lemma,
! [X494,X495] :
( ~ in(X494,X495)
| set_union2(singleton(X494),X495) = X495 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_173,lemma,
! [X578,X579] :
( ~ subset(X578,X579)
| set_intersection2(X578,X579) = X578 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_174,lemma,
! [X498,X499] :
( in(X498,X499)
| disjoint(singleton(X498),X499) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_134])]) ).
fof(i_0_175,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_176,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_177,plain,
! [X479] : ~ empty(singleton(X479)),
inference(variable_rename,[status(thm)],[i_0_135]) ).
fof(i_0_178,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_179,lemma,
! [X675,X676,X677] :
( singleton(X675) != unordered_pair(X676,X677)
| X675 = X676 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_180,lemma,
! [X689,X690,X691] :
( singleton(X689) != unordered_pair(X690,X691)
| X690 = X691 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_181,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_182,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_183,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_184,plain,
! [X487] : set_intersection2(X487,X487) = X487,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_185,plain,
! [X580] : set_intersection2(X580,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_186,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_187,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_188,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_189,lemma,
! [X493] : singleton(X493) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_190,plain,
! [X462] : element(cast_to_subset(X462),powerset(X462)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(i_0_191,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_192,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_193,plain,
( X1 = ordered_pair(esk9_4(X2,X3,X4,X1),esk10_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_136]) ).
cnf(i_0_194,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_137,c_0_138]) ).
cnf(i_0_195,plain,
( in(ordered_pair(esk23_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_139]) ).
cnf(i_0_196,plain,
( esk11_3(X1,X2,X3) = ordered_pair(esk12_3(X1,X2,X3),esk13_3(X1,X2,X3))
| in(esk11_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]) ).
cnf(i_0_197,plain,
( X2 = relation_dom(X1)
| ~ in(esk17_2(X1,X2),X2)
| ~ in(ordered_pair(esk17_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_140]) ).
fof(i_0_198,plain,
! [X455,X456,X457,X458] :
( ( ~ in(X458,X457)
| in(subset_complement(X455,X458),X456)
| ~ element(X458,powerset(X455))
| X457 != complements_of_subsets(X455,X456)
| ~ element(X457,powerset(powerset(X455)))
| ~ element(X456,powerset(powerset(X455))) )
& ( ~ in(subset_complement(X455,X458),X456)
| in(X458,X457)
| ~ element(X458,powerset(X455))
| X457 != complements_of_subsets(X455,X456)
| ~ element(X457,powerset(powerset(X455)))
| ~ element(X456,powerset(powerset(X455))) )
& ( element(esk26_3(X455,X456,X457),powerset(X455))
| X457 = complements_of_subsets(X455,X456)
| ~ element(X457,powerset(powerset(X455)))
| ~ element(X456,powerset(powerset(X455))) )
& ( ~ in(esk26_3(X455,X456,X457),X457)
| ~ in(subset_complement(X455,esk26_3(X455,X456,X457)),X456)
| X457 = complements_of_subsets(X455,X456)
| ~ element(X457,powerset(powerset(X455)))
| ~ element(X456,powerset(powerset(X455))) )
& ( in(esk26_3(X455,X456,X457),X457)
| in(subset_complement(X455,esk26_3(X455,X456,X457)),X456)
| X457 = complements_of_subsets(X455,X456)
| ~ element(X457,powerset(powerset(X455)))
| ~ element(X456,powerset(powerset(X455))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_setfam_1])])])])]) ).
cnf(i_0_199,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk15_3(X1,X2,X3),X3)
| ~ in(esk15_3(X1,X2,X3),X1)
| ~ in(esk15_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
cnf(i_0_200,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_142]) ).
cnf(i_0_201,plain,
( in(esk24_2(X1,X2),X2)
| in(ordered_pair(esk25_2(X1,X2),esk24_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_139]) ).
cnf(i_0_202,plain,
( in(esk17_2(X1,X2),X2)
| in(ordered_pair(esk17_2(X1,X2),esk18_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_140]) ).
cnf(i_0_203,plain,
( in(ordered_pair(X1,esk16_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_140]) ).
fof(i_0_204,plain,
! [X430,X431,X432,X433,X434,X435,X436,X437] :
( ( in(X433,X430)
| ~ in(X433,X432)
| X432 != set_difference(X430,X431) )
& ( ~ in(X433,X431)
| ~ in(X433,X432)
| X432 != set_difference(X430,X431) )
& ( ~ in(X434,X430)
| in(X434,X431)
| in(X434,X432)
| X432 != set_difference(X430,X431) )
& ( ~ in(esk22_3(X435,X436,X437),X437)
| ~ in(esk22_3(X435,X436,X437),X435)
| in(esk22_3(X435,X436,X437),X436)
| X437 = set_difference(X435,X436) )
& ( in(esk22_3(X435,X436,X437),X435)
| in(esk22_3(X435,X436,X437),X437)
| X437 = set_difference(X435,X436) )
& ( ~ in(esk22_3(X435,X436,X437),X436)
| in(esk22_3(X435,X436,X437),X437)
| X437 = set_difference(X435,X436) ) ),
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_143])])])])])]) ).
cnf(i_0_205,plain,
( X2 = relation_rng(X1)
| ~ in(esk24_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk24_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_139]) ).
cnf(i_0_206,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk11_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk11_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_136]) ).
fof(i_0_207,plain,
! [X367,X368,X369,X370,X371,X372,X373,X374] :
( ( ~ in(X370,X369)
| in(X370,X367)
| in(X370,X368)
| X369 != set_union2(X367,X368) )
& ( ~ in(X371,X367)
| in(X371,X369)
| X369 != set_union2(X367,X368) )
& ( ~ in(X371,X368)
| in(X371,X369)
| X369 != set_union2(X367,X368) )
& ( ~ in(esk8_3(X372,X373,X374),X372)
| ~ in(esk8_3(X372,X373,X374),X374)
| X374 = set_union2(X372,X373) )
& ( ~ in(esk8_3(X372,X373,X374),X373)
| ~ in(esk8_3(X372,X373,X374),X374)
| X374 = set_union2(X372,X373) )
& ( in(esk8_3(X372,X373,X374),X374)
| in(esk8_3(X372,X373,X374),X372)
| in(esk8_3(X372,X373,X374),X373)
| X374 = set_union2(X372,X373) ) ),
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_208,plain,
! [X358,X359,X360,X361,X362,X363,X364,X365] :
( ( ~ in(X361,X360)
| X361 = X358
| X361 = X359
| X360 != unordered_pair(X358,X359) )
& ( X362 != X358
| in(X362,X360)
| X360 != unordered_pair(X358,X359) )
& ( X362 != X359
| in(X362,X360)
| X360 != unordered_pair(X358,X359) )
& ( esk7_3(X363,X364,X365) != X363
| ~ in(esk7_3(X363,X364,X365),X365)
| X365 = unordered_pair(X363,X364) )
& ( esk7_3(X363,X364,X365) != X364
| ~ in(esk7_3(X363,X364,X365),X365)
| X365 = unordered_pair(X363,X364) )
& ( in(esk7_3(X363,X364,X365),X365)
| esk7_3(X363,X364,X365) = X363
| esk7_3(X363,X364,X365) = X364
| X365 = unordered_pair(X363,X364) ) ),
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_209,plain,
( in(esk15_3(X1,X2,X3),X1)
| in(esk15_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
cnf(i_0_210,plain,
( in(esk15_3(X1,X2,X3),X2)
| in(esk15_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
cnf(i_0_211,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_144]) ).
cnf(i_0_212,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_145]) ).
cnf(i_0_213,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_144]) ).
cnf(i_0_214,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_145]) ).
cnf(i_0_215,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_140]) ).
cnf(i_0_216,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_139]) ).
cnf(i_0_217,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_144]) ).
cnf(i_0_218,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_145]) ).
fof(i_0_219,plain,
! [X325,X326,X327,X328,X329,X331,X334,X335,X336,X337] :
( ( ~ in(X327,X326)
| ~ in(X328,X325)
| in(X327,X328)
| X326 != set_meet(X325)
| X325 = empty_set )
& ( in(esk1_3(X325,X326,X329),X325)
| in(X329,X326)
| X326 != set_meet(X325)
| X325 = empty_set )
& ( ~ in(X329,esk1_3(X325,X326,X329))
| in(X329,X326)
| X326 != set_meet(X325)
| X325 = empty_set )
& ( in(esk3_2(X325,X331),X325)
| ~ in(esk2_2(X325,X331),X331)
| X331 = set_meet(X325)
| X325 = empty_set )
& ( ~ in(esk2_2(X325,X331),esk3_2(X325,X331))
| ~ in(esk2_2(X325,X331),X331)
| X331 = set_meet(X325)
| X325 = empty_set )
& ( in(esk2_2(X325,X331),X331)
| ~ in(X334,X325)
| in(esk2_2(X325,X331),X334)
| X331 = set_meet(X325)
| X325 = empty_set )
& ( X336 != set_meet(X335)
| X336 = empty_set
| X335 != empty_set )
& ( X337 != empty_set
| X337 = set_meet(X335)
| X335 != empty_set ) ),
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_setfam_1])])])])])]) ).
cnf(i_0_220,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_146]) ).
cnf(i_0_221,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_147]) ).
cnf(i_0_222,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_147]) ).
cnf(i_0_223,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_148]) ).
fof(i_0_224,plain,
! [X469,X470,X471] :
( ~ element(X470,powerset(X469))
| ~ element(X471,powerset(X469))
| element(subset_difference(X469,X470,X471),powerset(X469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
cnf(i_0_225,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_136]) ).
cnf(i_0_226,lemma,
( X1 = empty_set
| subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_149]) ).
cnf(i_0_227,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_150]) ).
cnf(i_0_228,lemma,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,cast_to_subset(X2),meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_151]) ).
cnf(i_0_229,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_152]) ).
fof(i_0_230,plain,
! [X419,X420,X421,X423,X424,X425,X426,X428] :
( ( in(X421,esk19_3(X419,X420,X421))
| ~ in(X421,X420)
| X420 != union(X419) )
& ( in(esk19_3(X419,X420,X421),X419)
| ~ in(X421,X420)
| X420 != union(X419) )
& ( ~ in(X423,X424)
| ~ in(X424,X419)
| in(X423,X420)
| X420 != union(X419) )
& ( ~ in(esk20_2(X425,X426),X426)
| ~ in(esk20_2(X425,X426),X428)
| ~ in(X428,X425)
| X426 = union(X425) )
& ( in(esk20_2(X425,X426),esk21_2(X425,X426))
| in(esk20_2(X425,X426),X426)
| X426 = union(X425) )
& ( in(esk21_2(X425,X426),X425)
| in(esk20_2(X425,X426),X426)
| X426 = union(X425) ) ),
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_231,lemma,
! [X619,X620,X621] :
( ( ~ disjoint(X620,X621)
| subset(X620,subset_complement(X619,X621))
| ~ element(X621,powerset(X619))
| ~ element(X620,powerset(X619)) )
& ( ~ subset(X620,subset_complement(X619,X621))
| disjoint(X620,X621)
| ~ element(X621,powerset(X619))
| ~ element(X620,powerset(X619)) ) ),
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_232,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_153]) ).
fof(i_0_233,plain,
! [X532,X533,X534] :
( ~ element(X533,powerset(X532))
| ~ element(X534,powerset(X532))
| subset_difference(X532,X533,X534) = set_difference(X533,X534) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(i_0_234,lemma,
( disjoint(X1,X2)
| in(esk40_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_152]) ).
fof(i_0_235,plain,
! [X349,X350,X351,X352,X353,X354] :
( ( ~ in(X351,X350)
| subset(X351,X349)
| X350 != powerset(X349) )
& ( ~ subset(X352,X349)
| in(X352,X350)
| X350 != powerset(X349) )
& ( ~ in(esk6_2(X353,X354),X354)
| ~ subset(esk6_2(X353,X354),X353)
| X354 = powerset(X353) )
& ( in(esk6_2(X353,X354),X354)
| subset(esk6_2(X353,X354),X353)
| X354 = powerset(X353) ) ),
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_236,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_154]) ).
fof(i_0_237,plain,
! [X583,X584] :
( ( ~ in(esk38_2(X583,X584),X583)
| ~ in(esk38_2(X583,X584),X584)
| X583 = X584 )
& ( in(esk38_2(X583,X584),X583)
| in(esk38_2(X583,X584),X584)
| X583 = X584 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_238,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
fof(i_0_239,lemma,
! [X647,X648,X649] :
( ~ element(X649,powerset(X647))
| ~ in(X648,subset_complement(X647,X649))
| ~ in(X648,X649) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).
cnf(i_0_240,negated_conjecture,
in(ordered_pair(esk35_0,esk36_0),esk37_0),
inference(split_conjunct,[status(thm)],[i_0_155]) ).
fof(i_0_241,lemma,
! [X549,X550,X551,X552] :
( ~ subset(X549,X550)
| ~ subset(X551,X552)
| subset(cartesian_product2(X549,X551),cartesian_product2(X550,X552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(i_0_242,lemma,
! [X644,X645,X646] :
( X644 = empty_set
| ~ element(X645,powerset(X644))
| ~ element(X646,X644)
| in(X646,X645)
| in(X646,subset_complement(X644,X645)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_156])])]) ).
fof(i_0_243,plain,
! [X472,X473] :
( ~ element(X473,powerset(powerset(X472)))
| element(complements_of_subsets(X472,X473),powerset(powerset(X472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
cnf(i_0_244,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_157]) ).
cnf(i_0_245,plain,
( X2 = singleton(X1)
| ~ in(esk4_2(X1,X2),X2)
| esk4_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_158]) ).
cnf(i_0_246,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
cnf(i_0_247,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_141]) ).
fof(i_0_248,plain,
! [X467,X468] :
( ~ element(X468,powerset(powerset(X467)))
| element(meet_of_subsets(X467,X468),powerset(X467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(i_0_249,plain,
! [X465,X466] :
( ~ element(X466,powerset(powerset(X465)))
| element(union_of_subsets(X465,X466),powerset(X465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
fof(i_0_250,plain,
! [X681,X683,X684,X685,X687,X688] :
( in(X681,esk41_1(X681))
& ( ~ in(X683,esk41_1(X681))
| ~ subset(X684,X683)
| in(X684,esk41_1(X681)) )
& ( in(esk42_2(X681,X685),esk41_1(X681))
| ~ in(X685,esk41_1(X681)) )
& ( ~ subset(X687,X685)
| in(X687,esk42_2(X681,X685))
| ~ in(X685,esk41_1(X681)) )
& ( ~ subset(X688,esk41_1(X681))
| are_equipotent(X688,esk41_1(X681))
| in(X688,esk41_1(X681)) ) ),
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_159])])])])]) ).
fof(i_0_251,plain,
! [X490,X491] :
( ~ element(X491,powerset(powerset(X490)))
| complements_of_subsets(X490,complements_of_subsets(X490,X491)) = X491 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(i_0_252,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_160]) ).
fof(i_0_253,lemma,
! [X587,X588,X589] :
( ~ subset(X587,X588)
| subset(set_difference(X587,X589),set_difference(X588,X589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_254,lemma,
! [X546,X547,X548] :
( ( subset(cartesian_product2(X546,X548),cartesian_product2(X547,X548))
| ~ subset(X546,X547) )
& ( subset(cartesian_product2(X548,X546),cartesian_product2(X548,X547))
| ~ subset(X546,X547) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
cnf(i_0_255,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_161]) ).
cnf(i_0_256,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_162]) ).
fof(i_0_257,lemma,
! [X672,X673,X674] :
( ~ subset(X672,X673)
| ~ subset(X674,X673)
| subset(set_union2(X672,X674),X673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_258,lemma,
! [X600,X601,X602] :
( ( in(X600,X602)
| ~ subset(unordered_pair(X600,X601),X602) )
& ( in(X601,X602)
| ~ subset(unordered_pair(X600,X601),X602) )
& ( ~ in(X600,X602)
| ~ in(X601,X602)
| subset(unordered_pair(X600,X601),X602) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(i_0_259,lemma,
! [X518,X519] :
( ( in(esk28_2(X518,X519),X518)
| element(X518,powerset(X519)) )
& ( ~ in(esk28_2(X518,X519),X519)
| element(X518,powerset(X519)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
cnf(i_0_260,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_163]) ).
cnf(i_0_261,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_164]) ).
cnf(i_0_262,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_165]) ).
fof(i_0_263,plain,
! [X463,X464] :
( ~ element(X464,powerset(X463))
| element(subset_complement(X463,X464),powerset(X463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_264,plain,
! [X393,X394,X395,X396,X397] :
( ( ~ subset(X393,X394)
| ~ in(X395,X393)
| in(X395,X394) )
& ( in(esk14_2(X396,X397),X396)
| subset(X396,X397) )
& ( ~ in(esk14_2(X396,X397),X397)
| subset(X396,X397) ) ),
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_265,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_166]) ).
cnf(i_0_266,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_167]) ).
cnf(i_0_267,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_168]) ).
fof(i_0_268,lemma,
! [X624,X625] :
( ~ element(X625,powerset(powerset(X624)))
| X625 = empty_set
| complements_of_subsets(X624,X625) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(i_0_269,lemma,
! [X555,X557,X558,X559,X560] :
( in(X555,esk34_1(X555))
& ( ~ in(X557,esk34_1(X555))
| ~ subset(X558,X557)
| in(X558,esk34_1(X555)) )
& ( ~ in(X559,esk34_1(X555))
| in(powerset(X559),esk34_1(X555)) )
& ( ~ subset(X560,esk34_1(X555))
| are_equipotent(X560,esk34_1(X555))
| in(X560,esk34_1(X555)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_169])])])]) ).
fof(i_0_270,plain,
! [X488,X489] :
( ~ element(X489,powerset(X488))
| subset_complement(X488,subset_complement(X488,X489)) = X489 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(i_0_271,plain,
( in(esk4_2(X1,X2),X2)
| esk4_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]) ).
fof(i_0_272,plain,
! [X530,X531] :
( ~ element(X531,powerset(powerset(X530)))
| meet_of_subsets(X530,X531) = set_meet(X531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])]) ).
fof(i_0_273,plain,
! [X528,X529] :
( ~ element(X529,powerset(powerset(X528)))
| union_of_subsets(X528,X529) = union(X529) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(i_0_274,plain,
! [X635,X636,X637] :
( ~ in(X635,X636)
| ~ element(X636,powerset(X637))
| element(X635,X637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_275,lemma,
! [X504,X505,X506] :
( ~ element(X505,powerset(X504))
| ~ in(X506,X505)
| in(X506,X504) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
fof(i_0_276,lemma,
! [X610,X611,X613,X614,X615] :
( ( in(esk39_2(X610,X611),X610)
| disjoint(X610,X611) )
& ( in(esk39_2(X610,X611),X611)
| disjoint(X610,X611) )
& ( ~ in(X615,X613)
| ~ in(X615,X614)
| ~ disjoint(X613,X614) ) ),
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_170])])])])])]) ).
cnf(i_0_277,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_163]) ).
cnf(i_0_278,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_164]) ).
cnf(i_0_279,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_171]) ).
cnf(i_0_280,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_172]) ).
cnf(i_0_281,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_173]) ).
fof(i_0_282,lemma,
! [X622,X623] :
( ~ subset(X622,X623)
| X623 = set_union2(X622,set_difference(X623,X622)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
cnf(i_0_283,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_166]) ).
cnf(i_0_284,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_167]) ).
cnf(i_0_285,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_168]) ).
fof(i_0_286,plain,
! [X650,X651,X652] :
( ~ in(X650,X651)
| ~ element(X651,powerset(X652))
| ~ empty(X652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_287,plain,
! [X449,X450] :
( ~ element(X450,powerset(X449))
| subset_complement(X449,X450) = set_difference(X449,X450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_288,lemma,
! [X655,X656,X657] :
( ~ subset(X655,X656)
| ~ disjoint(X656,X657)
| disjoint(X655,X657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_289,lemma,
! [X569,X570,X571] :
( ~ subset(X569,X570)
| ~ subset(X570,X571)
| subset(X569,X571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(i_0_290,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_161]) ).
cnf(i_0_291,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_174]) ).
fof(i_0_292,lemma,
! [X617,X618] : set_difference(set_union2(X617,X618),X618) = set_difference(X617,X618),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_293,lemma,
! [X603,X604] : set_union2(X603,set_difference(X604,X603)) = set_union2(X603,X604),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_294,plain,
! [X480,X481] :
( empty(X480)
| ~ empty(set_union2(X480,X481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_175])]) ).
fof(i_0_295,plain,
! [X484,X485] :
( empty(X484)
| ~ empty(set_union2(X485,X484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_176])]) ).
cnf(i_0_296,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_158]) ).
fof(i_0_297,lemma,
! [X542,X543,X544,X545] :
( unordered_pair(X542,X543) != unordered_pair(X544,X545)
| X542 = X544
| X542 = X545 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(i_0_298,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_177]) ).
fof(i_0_299,plain,
! [X482,X483] : ~ empty(unordered_pair(X482,X483)),
inference(variable_rename,[status(thm)],[i_0_178]) ).
fof(i_0_300,plain,
! [X323,X324] :
( ( subset(X323,X324)
| X323 != X324 )
& ( subset(X324,X323)
| X323 != X324 )
& ( ~ subset(X323,X324)
| ~ subset(X324,X323)
| X323 = X324 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_301,plain,
! [X608,X609] :
( ( ~ element(X608,powerset(X609))
| subset(X608,X609) )
& ( ~ subset(X608,X609)
| element(X608,powerset(X609)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(i_0_302,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_179]) ).
cnf(i_0_303,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_180]) ).
fof(i_0_304,lemma,
! [X653,X654] :
( ~ subset(X653,X654)
| ~ proper_subset(X654,X653) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_305,plain,
! [X315,X316] :
( ~ proper_subset(X315,X316)
| ~ proper_subset(X316,X315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_181])]) ).
fof(i_0_306,plain,
! [X313,X314] :
( ~ in(X313,X314)
| ~ in(X314,X313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_182])]) ).
fof(i_0_307,lemma,
! [X678,X679] :
( ~ in(X678,X679)
| subset(X678,union(X679)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
fof(i_0_308,lemma,
! [X512,X513] :
( ~ in(X512,X513)
| subset(X512,union(X513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_309,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_163]) ).
cnf(i_0_310,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_164]) ).
cnf(i_0_311,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_158]) ).
fof(i_0_312,plain,
! [X356,X357] :
( ( ~ element(X357,X356)
| in(X357,X356)
| empty(X356) )
& ( ~ in(X357,X356)
| element(X357,X356)
| empty(X356) )
& ( ~ element(X357,X356)
| empty(X357)
| ~ empty(X356) )
& ( ~ empty(X357)
| element(X357,X356)
| ~ empty(X356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_183])])]) ).
fof(i_0_313,plain,
! [X581,X582] :
( ~ element(X581,X582)
| empty(X582)
| in(X581,X582) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(i_0_314,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_184]) ).
fof(i_0_315,lemma,
! [X594,X595] : subset(set_difference(X594,X595),X594),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_316,lemma,
! [X666,X667] : subset(X666,set_union2(X666,X667)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_317,plain,
! [X460,X461] :
( ( subset(X460,X461)
| ~ proper_subset(X460,X461) )
& ( X460 != X461
| ~ proper_subset(X460,X461) )
& ( ~ subset(X460,X461)
| X460 = X461
| proper_subset(X460,X461) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_318,lemma,
! [X668,X669] :
( ( ~ disjoint(X668,X669)
| set_difference(X668,X669) = X668 )
& ( set_difference(X668,X669) != X668
| disjoint(X668,X669) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_319,lemma,
! [X553,X554] :
( ~ subset(X553,X554)
| set_union2(X553,X554) = X554 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(i_0_320,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_185]) ).
fof(i_0_321,plain,
! [X536,X537] :
( ~ disjoint(X536,X537)
| disjoint(X537,X536) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_322,plain,
! [X567,X568] :
( ~ in(X567,X568)
| element(X567,X568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_323,lemma,
! [X596,X597] :
( ( set_difference(X596,X597) != empty_set
| subset(X596,X597) )
& ( ~ subset(X596,X597)
| set_difference(X596,X597) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_324,lemma,
! [X502,X503] :
( ( set_difference(X502,X503) != empty_set
| subset(X502,X503) )
& ( ~ subset(X502,X503)
| set_difference(X502,X503) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_325,plain,
! [X522] :
( ( element(esk30_1(X522),powerset(X522))
| empty(X522) )
& ( ~ empty(esk30_1(X522))
| empty(X522) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_186])])])]) ).
fof(i_0_326,plain,
! [X664,X665] :
( ~ in(X664,X665)
| ~ empty(X665) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_327,plain,
! [X319,X320] : set_union2(X319,X320) = set_union2(X320,X319),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_328,plain,
! [X317,X318] : unordered_pair(X317,X318) = unordered_pair(X318,X317),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_329,plain,
! [X525] :
( element(esk32_1(X525),powerset(X525))
& empty(esk32_1(X525)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_330,plain,
! [X345,X346,X347] :
( ( X345 != empty_set
| ~ in(X346,X345) )
& ( in(esk5_1(X347),X347)
| X347 = 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_187])])])])]) ).
fof(i_0_331,plain,
! [X492] : ~ proper_subset(X492,X492),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_188])]) ).
cnf(i_0_332,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_189]) ).
fof(i_0_333,lemma,
! [X616] :
( ~ subset(X616,empty_set)
| X616 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_334,plain,
! [X474] : element(esk27_1(X474),X474),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(i_0_335,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_190]) ).
fof(i_0_336,plain,
! [X476] : ~ empty(powerset(X476)),
inference(variable_rename,[status(thm)],[i_0_191]) ).
fof(i_0_337,plain,
! [X670,X671] :
( ~ empty(X670)
| X670 = X671
| ~ empty(X671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_338,plain,
! [X486] : set_union2(X486,X486) = X486,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_339,plain,
! [X535] : subset(X535,X535),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_340,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_341,plain,
! [X607] : set_difference(X607,empty_set) = X607,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_342,plain,
! [X566] : set_union2(X566,empty_set) = X566,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_343,lemma,
! [X586] : subset(empty_set,X586),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_344,plain,
! [X634] : set_difference(empty_set,X634) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_345,lemma,
! [X680] : union(powerset(X680)) = X680,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(i_0_346,plain,
! [X661] :
( ~ empty(X661)
| X661 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_347,plain,
~ empty(esk33_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_192])]) ).
fof(i_0_348,plain,
( empty(esk29_0)
& relation(esk29_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_349,plain,
empty(esk31_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_350,plain,
( X1 = unordered_pair(unordered_pair(esk9_4(X2,X3,X4,X1),esk10_4(X2,X3,X4,X1)),unordered_pair(esk9_4(X2,X3,X4,X1),esk9_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_193,c_0_194]),
[final] ).
cnf(i_0_351,plain,
( in(unordered_pair(unordered_pair(esk23_3(X3,X2,X1),X1),unordered_pair(esk23_3(X3,X2,X1),esk23_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_195,c_0_194]),
[final] ).
cnf(i_0_352,plain,
( X3 = cartesian_product2(X1,X2)
| esk11_3(X1,X2,X3) = unordered_pair(unordered_pair(esk12_3(X1,X2,X3),esk13_3(X1,X2,X3)),unordered_pair(esk12_3(X1,X2,X3),esk12_3(X1,X2,X3)))
| in(esk11_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_196,c_0_194]),
[final] ).
cnf(i_0_353,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk17_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk17_2(X1,X2),X3),unordered_pair(esk17_2(X1,X2),esk17_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_197,c_0_194]),
[final] ).
cnf(i_0_354,plain,
( X3 = complements_of_subsets(X1,X2)
| ~ in(esk26_3(X1,X2,X3),X3)
| ~ in(subset_complement(X1,esk26_3(X1,X2,X3)),X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_355,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk15_3(X1,X2,X3),X3)
| ~ in(esk15_3(X1,X2,X3),X2)
| ~ in(esk15_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_199,c_0_200]),
[final] ).
cnf(i_0_356,plain,
( X2 = relation_rng(X1)
| in(esk24_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk25_2(X1,X2),esk24_2(X1,X2)),unordered_pair(esk25_2(X1,X2),esk25_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_201,c_0_194]),
[final] ).
cnf(i_0_357,plain,
( X2 = relation_dom(X1)
| in(esk17_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk17_2(X1,X2),esk18_2(X1,X2)),unordered_pair(esk17_2(X1,X2),esk17_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_202,c_0_194]),
[final] ).
cnf(i_0_358,plain,
( in(unordered_pair(unordered_pair(X1,esk16_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_203,c_0_194]),
[final] ).
cnf(i_0_359,plain,
( in(esk10_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_360,plain,
( in(esk9_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_361,plain,
( in(esk22_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk22_3(X1,X2,X3),X3)
| ~ in(esk22_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_362,plain,
( in(esk26_3(X1,X2,X3),X3)
| in(subset_complement(X1,esk26_3(X1,X2,X3)),X2)
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_363,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk24_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk24_2(X1,X2)),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[i_0_205,c_0_194]),
[final] ).
cnf(i_0_364,plain,
( X3 = cartesian_product2(X1,X2)
| esk11_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk11_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_206,c_0_194]),
[final] ).
cnf(i_0_365,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X1)
| ~ in(esk8_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_366,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X2)
| ~ in(esk8_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_367,plain,
( in(esk8_3(X1,X2,X3),X3)
| in(esk8_3(X1,X2,X3),X1)
| in(esk8_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_368,plain,
( in(esk22_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk22_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_369,plain,
( X3 = unordered_pair(X1,X2)
| esk7_3(X1,X2,X3) != X1
| ~ in(esk7_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_370,plain,
( X3 = unordered_pair(X1,X2)
| esk7_3(X1,X2,X3) != X2
| ~ in(esk7_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_371,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk15_3(X1,X2,X3),X3)
| in(esk15_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_209,c_0_200]),
[final] ).
cnf(i_0_372,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk15_3(X1,X2,X3),X3)
| in(esk15_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_210,c_0_200]),
[final] ).
cnf(i_0_373,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_211,c_0_194]),
[final] ).
cnf(i_0_374,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_212,c_0_194]),
[final] ).
cnf(i_0_375,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_213,c_0_194]),
[final] ).
cnf(i_0_376,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_214,c_0_194]),
[final] ).
cnf(i_0_377,plain,
( in(esk22_3(X1,X2,X3),X1)
| in(esk22_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_378,plain,
( in(esk13_3(X1,X2,X3),X2)
| in(esk11_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_379,plain,
( in(esk12_3(X1,X2,X3),X1)
| in(esk11_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_380,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_215,c_0_194]),
[final] ).
cnf(i_0_381,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_216,c_0_194]),
[final] ).
cnf(i_0_382,plain,
( in(esk7_3(X1,X2,X3),X3)
| esk7_3(X1,X2,X3) = X1
| esk7_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_383,plain,
( element(esk26_3(X1,X2,X3),powerset(X1))
| X3 = complements_of_subsets(X1,X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_384,plain,
( in(X2,X4)
| ~ in(subset_complement(X1,X2),X3)
| ~ element(X2,powerset(X1))
| X4 != complements_of_subsets(X1,X3)
| ~ element(X4,powerset(powerset(X1)))
| ~ element(X3,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_385,plain,
( in(subset_complement(X3,X1),X4)
| ~ in(X1,X2)
| ~ element(X1,powerset(X3))
| X2 != complements_of_subsets(X3,X4)
| ~ element(X2,powerset(powerset(X3)))
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_386,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_217,c_0_194]),
[final] ).
cnf(i_0_387,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_218,c_0_194]),
[final] ).
cnf(i_0_388,plain,
( in(X1,X3)
| X2 = empty_set
| ~ in(X1,esk1_3(X2,X3,X1))
| X3 != set_meet(X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_389,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_220,c_0_194]),
[final] ).
cnf(i_0_390,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_221,c_0_194]),c_0_194]),
[final] ).
cnf(i_0_391,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_222,c_0_194]),c_0_194]),
[final] ).
cnf(i_0_392,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_223,c_0_200]),c_0_200]),
[final] ).
cnf(i_0_393,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_224]),
[final] ).
cnf(i_0_394,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_225,c_0_194]),
[final] ).
cnf(i_0_395,plain,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk2_2(X1,X2),esk3_2(X1,X2))
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_396,lemma,
( X1 = empty_set
| subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[i_0_226,c_0_227]),
[final] ).
cnf(i_0_397,lemma,
( X1 = empty_set
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,X2,meet_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[i_0_228,c_0_227]),
[final] ).
cnf(i_0_398,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_229,c_0_200]),
[final] ).
cnf(i_0_399,plain,
( X2 = union(X1)
| ~ in(esk20_2(X1,X2),X2)
| ~ in(esk20_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_400,plain,
( in(esk19_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_401,plain,
( in(X1,esk19_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_402,plain,
( in(esk1_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_403,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_231]),
[final] ).
cnf(i_0_404,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_232,c_0_200]),
[final] ).
cnf(i_0_405,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_406,lemma,
( disjoint(X1,X2)
| in(esk40_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_234,c_0_200]),
[final] ).
cnf(i_0_407,plain,
( X2 = powerset(X1)
| ~ in(esk6_2(X1,X2),X2)
| ~ subset(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_408,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_236,c_0_138]),
[final] ).
cnf(i_0_409,plain,
( X1 = X2
| ~ in(esk38_2(X1,X2),X1)
| ~ in(esk38_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_410,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_231]),
[final] ).
cnf(i_0_411,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_238,c_0_200]),
[final] ).
cnf(i_0_412,lemma,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_239]),
[final] ).
cnf(i_0_413,negated_conjecture,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),esk37_0),
inference(rw,[status(thm)],[i_0_240,c_0_194]),
[final] ).
cnf(i_0_414,plain,
( in(esk20_2(X1,X2),esk21_2(X1,X2))
| in(esk20_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_415,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_241]),
[final] ).
cnf(i_0_416,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_242]),
[final] ).
cnf(i_0_417,plain,
( in(esk3_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_418,plain,
( in(esk2_2(X1,X2),X2)
| in(esk2_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_419,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_243]),
[final] ).
cnf(i_0_420,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_244,c_0_138]),c_0_138]),
[final] ).
cnf(i_0_421,plain,
( X2 = unordered_pair(X1,X1)
| esk4_2(X1,X2) != X1
| ~ in(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_245,c_0_138]),
[final] ).
cnf(i_0_422,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_246,c_0_200]),
[final] ).
cnf(i_0_423,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_247,c_0_200]),
[final] ).
cnf(i_0_424,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_248]),
[final] ).
cnf(i_0_425,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_249]),
[final] ).
cnf(i_0_426,plain,
( in(X1,esk42_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk41_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_427,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_251]),
[final] ).
cnf(i_0_428,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_252,c_0_200]),
[final] ).
cnf(i_0_429,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_430,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_431,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_432,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_255,c_0_138]),
[final] ).
cnf(i_0_433,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_256,c_0_138]),
[final] ).
cnf(i_0_434,plain,
( in(esk21_2(X1,X2),X1)
| in(esk20_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_435,plain,
( in(esk6_2(X1,X2),X2)
| subset(esk6_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_436,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_257]),
[final] ).
cnf(i_0_437,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_258]),
[final] ).
cnf(i_0_438,lemma,
( element(X1,powerset(X2))
| ~ in(esk28_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_259]),
[final] ).
cnf(i_0_439,plain,
( in(esk38_2(X1,X2),X1)
| in(esk38_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_237]),
[final] ).
cnf(i_0_440,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_260,c_0_138]),c_0_138]),
[final] ).
cnf(i_0_441,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_261,c_0_138]),c_0_138]),
[final] ).
cnf(i_0_442,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_262,c_0_200]),c_0_200]),
[final] ).
cnf(i_0_443,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_263]),
[final] ).
cnf(i_0_444,plain,
( in(esk42_2(X1,X2),esk41_1(X1))
| ~ in(X2,esk41_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_445,plain,
( subset(X1,X2)
| ~ in(esk14_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_264]),
[final] ).
cnf(i_0_446,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_265,c_0_138]),
[final] ).
cnf(i_0_447,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_266,c_0_138]),
[final] ).
cnf(i_0_448,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_258]),
[final] ).
cnf(i_0_449,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_258]),
[final] ).
cnf(i_0_450,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_267,c_0_200]),
[final] ).
cnf(i_0_451,lemma,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_268]),
[final] ).
cnf(i_0_452,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_453,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_454,plain,
( in(X3,esk41_1(X2))
| ~ in(X1,esk41_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_455,lemma,
( in(X3,esk34_1(X2))
| ~ in(X1,esk34_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_456,plain,
( are_equipotent(X1,esk41_1(X2))
| in(X1,esk41_1(X2))
| ~ subset(X1,esk41_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_457,lemma,
( are_equipotent(X1,esk34_1(X2))
| in(X1,esk34_1(X2))
| ~ subset(X1,esk34_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_458,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_270]),
[final] ).
cnf(i_0_459,plain,
( X2 = unordered_pair(X1,X1)
| esk4_2(X1,X2) = X1
| in(esk4_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_271,c_0_138]),
[final] ).
cnf(i_0_460,plain,
( in(X1,X3)
| X4 = empty_set
| ~ in(X1,X2)
| ~ in(X3,X4)
| X2 != set_meet(X4) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_461,plain,
( meet_of_subsets(X2,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_272]),
[final] ).
cnf(i_0_462,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_273]),
[final] ).
cnf(i_0_463,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_274]),
[final] ).
cnf(i_0_464,lemma,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_275]),
[final] ).
cnf(i_0_465,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_466,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_230]),
[final] ).
cnf(i_0_467,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_276]),
[final] ).
cnf(i_0_468,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_277,c_0_138]),c_0_138]),
[final] ).
cnf(i_0_469,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_278,c_0_138]),c_0_138]),
[final] ).
cnf(i_0_470,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_279,c_0_138]),
[final] ).
cnf(i_0_471,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_280,c_0_138]),
[final] ).
cnf(i_0_472,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_281,c_0_200]),
[final] ).
cnf(i_0_473,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_282]),
[final] ).
cnf(i_0_474,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_283,c_0_138]),
[final] ).
cnf(i_0_475,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_284,c_0_138]),
[final] ).
cnf(i_0_476,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_285,c_0_200]),
[final] ).
cnf(i_0_477,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_286]),
[final] ).
cnf(i_0_478,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_479,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_480,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_481,lemma,
( in(esk28_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_259]),
[final] ).
cnf(i_0_482,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_287]),
[final] ).
cnf(i_0_483,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_288]),
[final] ).
cnf(i_0_484,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_289]),
[final] ).
cnf(i_0_485,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_264]),
[final] ).
cnf(i_0_486,lemma,
( in(powerset(X1),esk34_1(X2))
| ~ in(X1,esk34_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_487,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_290,c_0_138]),
[final] ).
cnf(i_0_488,lemma,
( in(esk39_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_276]),
[final] ).
cnf(i_0_489,lemma,
( in(esk39_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_276]),
[final] ).
cnf(i_0_490,plain,
( in(esk14_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_264]),
[final] ).
cnf(i_0_491,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_291,c_0_138]),
[final] ).
cnf(i_0_492,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_292]),
[final] ).
cnf(i_0_493,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_293]),
[final] ).
cnf(i_0_494,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_294]),
[final] ).
cnf(i_0_495,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_295]),
[final] ).
cnf(i_0_496,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_497,negated_conjecture,
( ~ in(esk35_0,relation_dom(esk37_0))
| ~ in(esk36_0,relation_rng(esk37_0)) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_498,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_296,c_0_138]),
[final] ).
cnf(i_0_499,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_297]),
[final] ).
cnf(i_0_500,plain,
~ empty(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_298,c_0_138]),
[final] ).
cnf(i_0_501,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_299]),
[final] ).
cnf(i_0_502,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_300]),
[final] ).
cnf(i_0_503,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_301]),
[final] ).
cnf(i_0_504,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_302,c_0_138]),
[final] ).
cnf(i_0_505,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_303,c_0_138]),
[final] ).
cnf(i_0_506,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_507,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_235]),
[final] ).
cnf(i_0_508,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_304]),
[final] ).
cnf(i_0_509,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_305]),
[final] ).
cnf(i_0_510,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_306]),
[final] ).
cnf(i_0_511,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_301]),
[final] ).
cnf(i_0_512,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_307]),
[final] ).
cnf(i_0_513,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_308]),
[final] ).
cnf(i_0_514,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_309,c_0_138]),
[final] ).
cnf(i_0_515,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_310,c_0_138]),
[final] ).
cnf(i_0_516,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_311,c_0_138]),
[final] ).
cnf(i_0_517,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_518,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_519,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_312]),
[final] ).
cnf(i_0_520,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_313]),
[final] ).
cnf(i_0_521,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_312]),
[final] ).
cnf(i_0_522,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_314,c_0_200]),
[final] ).
cnf(i_0_523,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_315]),
[final] ).
cnf(i_0_524,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_316]),
[final] ).
cnf(i_0_525,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_317]),
[final] ).
cnf(i_0_526,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_318]),
[final] ).
cnf(i_0_527,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_318]),
[final] ).
cnf(i_0_528,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_319]),
[final] ).
cnf(i_0_529,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_320,c_0_200]),
[final] ).
cnf(i_0_530,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_321]),
[final] ).
cnf(i_0_531,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_322]),
[final] ).
cnf(i_0_532,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_317]),
[final] ).
cnf(i_0_533,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_323]),
[final] ).
cnf(i_0_534,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_324]),
[final] ).
cnf(i_0_535,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_323]),
[final] ).
cnf(i_0_536,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_324]),
[final] ).
cnf(i_0_537,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_312]),
[final] ).
cnf(i_0_538,plain,
( element(esk30_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_325]),
[final] ).
cnf(i_0_539,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_326]),
[final] ).
cnf(i_0_540,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_312]),
[final] ).
cnf(i_0_541,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_327]),
[final] ).
cnf(i_0_542,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_328]),
[final] ).
cnf(i_0_543,plain,
element(esk32_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_329]),
[final] ).
cnf(i_0_544,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_317]),
[final] ).
cnf(i_0_545,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_330]),
[final] ).
cnf(i_0_546,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_331]),
[final] ).
cnf(i_0_547,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_332,c_0_138]),
[final] ).
cnf(i_0_548,plain,
( in(esk5_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_330]),
[final] ).
cnf(i_0_549,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_333]),
[final] ).
cnf(i_0_550,plain,
( empty(X1)
| ~ empty(esk30_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_325]),
[final] ).
cnf(i_0_551,plain,
element(esk27_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_334]),
[final] ).
cnf(i_0_552,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[i_0_335,c_0_227]),
[final] ).
cnf(i_0_553,plain,
in(X1,esk41_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_554,lemma,
in(X1,esk34_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_555,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_300]),
[final] ).
cnf(i_0_556,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_300]),
[final] ).
cnf(i_0_557,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_558,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_337]),
[final] ).
cnf(i_0_559,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_338]),
[final] ).
cnf(i_0_560,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_339]),
[final] ).
cnf(i_0_561,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_340,c_0_138]),
[final] ).
cnf(i_0_562,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_341]),
[final] ).
cnf(i_0_563,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_342]),
[final] ).
cnf(i_0_564,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_343]),
[final] ).
cnf(i_0_565,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_344]),
[final] ).
cnf(i_0_566,plain,
( X1 = empty_set
| X1 != set_meet(X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_567,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_345]),
[final] ).
cnf(i_0_568,plain,
empty(esk32_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_329]),
[final] ).
cnf(i_0_569,plain,
( X1 = set_meet(X2)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_570,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_571,plain,
~ empty(esk33_0),
inference(split_conjunct,[status(thm)],[i_0_347]),
[final] ).
cnf(i_0_572,negated_conjecture,
relation(esk37_0),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_573,plain,
relation(esk29_0),
inference(split_conjunct,[status(thm)],[i_0_348]),
[final] ).
cnf(i_0_574,plain,
empty(esk31_0),
inference(split_conjunct,[status(thm)],[i_0_349]),
[final] ).
cnf(i_0_575,plain,
empty(esk29_0),
inference(split_conjunct,[status(thm)],[i_0_348]),
[final] ).
cnf(i_0_576,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_577,axiom,
X1 = X1 ).
cnf(i_0_578,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_579,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_580,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_581,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_582,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_583,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_584,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_585,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_586,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_587,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_588,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_589,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_590,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_591,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_592,axiom,
( X1 != X2
| esk7_3(X1,X3,X4) = esk7_3(X2,X3,X4) ) ).
cnf(i_0_593,axiom,
( X1 != X2
| esk7_3(X3,X1,X4) = esk7_3(X3,X2,X4) ) ).
cnf(i_0_594,axiom,
( X1 != X2
| esk7_3(X3,X4,X1) = esk7_3(X3,X4,X2) ) ).
cnf(i_0_595,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_596,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_597,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_598,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_599,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_600,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_601,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_602,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_603,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_604,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_605,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_606,axiom,
( X1 != X2
| esk4_2(X1,X3) = esk4_2(X2,X3) ) ).
cnf(i_0_607,axiom,
( X1 != X2
| esk4_2(X3,X1) = esk4_2(X3,X2) ) ).
cnf(i_0_608,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_609,axiom,
( X1 != X2
| esk11_3(X1,X3,X4) = esk11_3(X2,X3,X4) ) ).
cnf(i_0_610,axiom,
( X1 != X2
| esk11_3(X3,X1,X4) = esk11_3(X3,X2,X4) ) ).
cnf(i_0_611,axiom,
( X1 != X2
| esk11_3(X3,X4,X1) = esk11_3(X3,X4,X2) ) ).
cnf(i_0_612,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_613,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_614,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_615,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_616,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_617,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_618,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_619,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_620,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_621,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_622,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_623,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_624,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_625,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_577_001,axiom,
X1 = X1 ).
cnf(i_0_578_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_579_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_580_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_581_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_582_006,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_583_007,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_584_008,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_585_009,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_586_010,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_587_011,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_588_012,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_589_013,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_590_014,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_591_015,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_592_016,axiom,
( X1 != X2
| esk7_3(X1,X3,X4) = esk7_3(X2,X3,X4) ) ).
cnf(i_0_593_017,axiom,
( X1 != X2
| esk7_3(X3,X1,X4) = esk7_3(X3,X2,X4) ) ).
cnf(i_0_594_018,axiom,
( X1 != X2
| esk7_3(X3,X4,X1) = esk7_3(X3,X4,X2) ) ).
cnf(i_0_595_019,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_596_020,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_597_021,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_598_022,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_599_023,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_600_024,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_601_025,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_602_026,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_603_027,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_604_028,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_605_029,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_606_030,axiom,
( X1 != X2
| esk4_2(X1,X3) = esk4_2(X2,X3) ) ).
cnf(i_0_607_031,axiom,
( X1 != X2
| esk4_2(X3,X1) = esk4_2(X3,X2) ) ).
cnf(i_0_608_032,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_609_033,axiom,
( X1 != X2
| esk11_3(X1,X3,X4) = esk11_3(X2,X3,X4) ) ).
cnf(i_0_610_034,axiom,
( X1 != X2
| esk11_3(X3,X1,X4) = esk11_3(X3,X2,X4) ) ).
cnf(i_0_611_035,axiom,
( X1 != X2
| esk11_3(X3,X4,X1) = esk11_3(X3,X4,X2) ) ).
cnf(i_0_612_036,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_613_037,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_614_038,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_615_039,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_616_040,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_617_041,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_618_042,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_619_043,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_620_044,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_621_045,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_622_046,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_623_047,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_624_048,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_625_049,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_626,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk9_4(X2,X3,cartesian_product2(X2,X3),X1),esk10_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk9_4(X2,X3,cartesian_product2(X2,X3),X1),esk9_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[350]) ).
cnf(i_0_627,plain,
( ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| in(unordered_pair(unordered_pair(esk23_3(X1,relation_rng(X1),X2),X2),unordered_pair(esk23_3(X1,relation_rng(X1),X2),esk23_3(X1,relation_rng(X1),X2))),X1) ),
inference(equality_inference,[],[351]) ).
cnf(i_0_628,plain,
( ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,esk16_3(X1,relation_dom(X1),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[358]) ).
cnf(i_0_629,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk10_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[359]) ).
cnf(i_0_630,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk9_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[360]) ).
cnf(i_0_631,plain,
( ~ relation(X1)
| in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[380]) ).
cnf(i_0_632,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[381]) ).
cnf(i_0_633,plain,
( in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| ~ in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[384]) ).
cnf(i_0_634,plain,
( ~ in(X1,complements_of_subsets(X2,X3))
| ~ element(X1,powerset(X2))
| in(subset_complement(X2,X1),X3)
| ~ element(complements_of_subsets(X2,X3),powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(equality_inference,[],[385]) ).
cnf(i_0_635,plain,
( in(X1,set_meet(X2))
| ~ in(X1,esk1_3(X2,set_meet(X2),X1))
| X2 = empty_set ),
inference(equality_inference,[],[388]) ).
cnf(i_0_636,plain,
X1 = X1,
inference(equality_inference,[],[390]) ).
cnf(i_0_637,plain,
X1 = X1,
inference(equality_inference,[],[391]) ).
cnf(i_0_638,plain,
( ~ in(X1,union(X2))
| in(esk19_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[400]) ).
cnf(i_0_639,plain,
( ~ in(X1,union(X2))
| in(X1,esk19_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[401]) ).
cnf(i_0_640,plain,
( in(X1,set_meet(X2))
| X2 = empty_set
| in(esk1_3(X2,set_meet(X2),X1),X2) ),
inference(equality_inference,[],[402]) ).
cnf(i_0_641,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[411]) ).
cnf(i_0_642,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[423]) ).
cnf(i_0_643,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[452]) ).
cnf(i_0_644,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[453]) ).
cnf(i_0_645,plain,
( ~ in(X1,X2)
| in(X3,X1)
| ~ in(X3,set_meet(X2))
| X2 = empty_set ),
inference(equality_inference,[],[460]) ).
cnf(i_0_646,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[465]) ).
cnf(i_0_647,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[466]) ).
cnf(i_0_648,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[478]) ).
cnf(i_0_649,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[479]) ).
cnf(i_0_650,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[480]) ).
cnf(i_0_651,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[496]) ).
cnf(i_0_652,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[498]) ).
cnf(i_0_653,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[499]) ).
cnf(i_0_654,plain,
X1 = X1,
inference(equality_inference,[],[504]) ).
cnf(i_0_655,plain,
X1 = X1,
inference(equality_inference,[],[505]) ).
cnf(i_0_656,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[506]) ).
cnf(i_0_657,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[507]) ).
cnf(i_0_658,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[515]) ).
cnf(i_0_659,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[544]) ).
cnf(i_0_660,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[545]) ).
cnf(i_0_661,plain,
subset(X1,X1),
inference(equality_inference,[],[555]) ).
cnf(i_0_662,plain,
subset(X1,X1),
inference(equality_inference,[],[556]) ).
cnf(i_0_663,plain,
in(X1,unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_560,i_0_448]) ).
cnf(i_0_664,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_560]) ).
cnf(i_0_665,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_448]) ).
cnf(i_0_666,plain,
in(X1,unordered_pair(X2,X1)),
inference(scs_inference,[],[i_0_560,i_0_664,i_0_448,i_0_449]) ).
cnf(i_0_667,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_560]) ).
cnf(i_0_668,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_449]) ).
cnf(i_0_669,plain,
~ in(esk37_0,unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0))),
inference(scs_inference,[],[i_0_413,i_0_560,i_0_664,i_0_448,i_0_449,i_0_510]) ).
cnf(i_0_670,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_510]) ).
cnf(i_0_671,plain,
element(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),esk37_0),
inference(scs_inference,[],[i_0_413,i_0_560,i_0_664,i_0_448,i_0_449,i_0_510,i_0_531]) ).
cnf(i_0_672,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_531]) ).
cnf(i_0_673,plain,
~ in(X1,esk31_0),
inference(scs_inference,[],[i_0_413,i_0_560,i_0_664,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539]) ).
cnf(i_0_674,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_539]) ).
cnf(i_0_675,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545]) ).
cnf(i_0_676,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_677,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_545]) ).
cnf(i_0_678,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629]) ).
cnf(i_0_679,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_680,plain,
( in(esk10_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_629]) ).
cnf(i_0_681,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630]) ).
cnf(i_0_682,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_683,plain,
( in(esk9_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_630]) ).
cnf(i_0_684,plain,
~ in(X1,union(empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638]) ).
cnf(i_0_685,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_686,plain,
( in(esk19_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(rename_variables,[],[i_0_638]) ).
cnf(i_0_687,plain,
~ in(X1,set_difference(X2,set_difference(X2,empty_set))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642]) ).
cnf(i_0_688,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_642]) ).
cnf(i_0_689,plain,
~ in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_difference(X1,esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646]) ).
cnf(i_0_690,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_646]) ).
cnf(i_0_691,plain,
~ in(X1,set_difference(empty_set,X2)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648]) ).
cnf(i_0_692,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_648]) ).
cnf(i_0_693,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(esk37_0,X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649]) ).
cnf(i_0_694,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_649]) ).
cnf(i_0_695,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(X1,esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650]) ).
cnf(i_0_696,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_650]) ).
cnf(i_0_697,plain,
~ in(unordered_pair(X1,X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_559,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652]) ).
cnf(i_0_698,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_652]) ).
cnf(i_0_699,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657]) ).
cnf(i_0_700,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_657]) ).
cnf(i_0_701,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406]) ).
cnf(i_0_702,plain,
( in(esk40_2(X1,X2),set_difference(X1,set_difference(X1,X2)))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_406]) ).
cnf(i_0_703,plain,
element(complements_of_subsets(X1,esk32_1(powerset(X1))),powerset(powerset(X1))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419]) ).
cnf(i_0_704,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_705,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_419]) ).
cnf(i_0_706,plain,
element(meet_of_subsets(X1,esk32_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424]) ).
cnf(i_0_707,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_708,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(meet_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_424]) ).
cnf(i_0_709,plain,
element(union_of_subsets(X1,esk32_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425]) ).
cnf(i_0_710,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_711,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(union_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_425]) ).
cnf(i_0_712,plain,
complements_of_subsets(X1,complements_of_subsets(X1,powerset(X1))) = powerset(X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_552,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427]) ).
cnf(i_0_713,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_552]) ).
cnf(i_0_714,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_715,plain,
element(subset_complement(X1,esk32_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443]) ).
cnf(i_0_716,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_443]) ).
cnf(i_0_717,plain,
in(esk42_2(X1,X1),esk41_1(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_553,i_0_574,i_0_547,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444]) ).
cnf(i_0_718,plain,
( ~ in(X1,esk41_1(X2))
| in(esk42_2(X2,X1),esk41_1(X2)) ),
inference(rename_variables,[],[i_0_444]) ).
cnf(i_0_719,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450]) ).
cnf(i_0_720,plain,
set_difference(empty_set,X1) = empty_set,
inference(rename_variables,[],[i_0_565]) ).
cnf(i_0_721,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_450]) ).
cnf(i_0_722,plain,
meet_of_subsets(X1,powerset(X1)) = set_meet(powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461]) ).
cnf(i_0_723,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_552]) ).
cnf(i_0_724,plain,
( ~ element(X1,powerset(powerset(X2)))
| meet_of_subsets(X2,X1) = set_meet(X1) ),
inference(rename_variables,[],[i_0_461]) ).
cnf(i_0_725,plain,
union_of_subsets(X1,powerset(X1)) = union(powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462]) ).
cnf(i_0_726,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_552]) ).
cnf(i_0_727,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,X1) = union(X1) ),
inference(rename_variables,[],[i_0_462]) ).
cnf(i_0_728,plain,
subset_complement(X1,esk32_1(X1)) = set_difference(X1,esk32_1(X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482]) ).
cnf(i_0_729,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_482]) ).
cnf(i_0_730,plain,
disjoint(esk31_0,X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488]) ).
cnf(i_0_731,plain,
( in(esk39_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_488]) ).
cnf(i_0_732,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489]) ).
cnf(i_0_733,plain,
( in(esk39_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_489]) ).
cnf(i_0_734,plain,
subset(cartesian_product2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490]) ).
cnf(i_0_735,plain,
( in(esk14_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_490]) ).
cnf(i_0_736,plain,
subset(esk32_1(X1),X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503]) ).
cnf(i_0_737,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_503]) ).
cnf(i_0_738,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515]) ).
cnf(i_0_739,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_740,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_515]) ).
cnf(i_0_741,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526]) ).
cnf(i_0_742,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_526]) ).
cnf(i_0_743,plain,
disjoint(X1,esk31_0),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530]) ).
cnf(i_0_744,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_530]) ).
cnf(i_0_745,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534]) ).
cnf(i_0_746,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_534]) ).
cnf(i_0_747,plain,
in(esk5_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548]) ).
cnf(i_0_748,plain,
( X1 = empty_set
| in(esk5_1(X1),X1) ),
inference(rename_variables,[],[i_0_548]) ).
cnf(i_0_749,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549]) ).
cnf(i_0_750,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_549]) ).
cnf(i_0_751,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555]) ).
cnf(i_0_752,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_555]) ).
cnf(i_0_753,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556]) ).
cnf(i_0_754,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_556]) ).
cnf(i_0_755,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578]) ).
cnf(i_0_756,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_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359]) ).
cnf(i_0_757,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_758,plain,
( X1 != cartesian_product2(X2,X3)
| in(esk10_4(X2,X3,X1,X4),X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_359]) ).
cnf(i_0_759,plain,
~ in(X1,set_union2(cartesian_product2(union(empty_set),X2),cartesian_product2(union(empty_set),X2))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360]) ).
cnf(i_0_760,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_761,plain,
( X1 != cartesian_product2(X2,X3)
| in(esk9_4(X2,X3,X1,X4),X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_360]) ).
cnf(i_0_762,plain,
~ in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),subset_complement(esk37_0,esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412]) ).
cnf(i_0_763,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_552]) ).
cnf(i_0_764,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_412]) ).
cnf(i_0_765,plain,
~ in(esk40_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_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423]) ).
cnf(i_0_766,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_767,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_768,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X1)
| in(X4,X3) ),
inference(rename_variables,[],[i_0_423]) ).
cnf(i_0_769,plain,
~ in(X1,esk32_1(empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464]) ).
cnf(i_0_770,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_771,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,X1)
| in(X3,X2) ),
inference(rename_variables,[],[i_0_464]) ).
cnf(i_0_772,plain,
~ in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(set_difference(X1,esk37_0),set_difference(X1,esk37_0))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465]) ).
cnf(i_0_773,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_774,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_465]) ).
cnf(i_0_775,plain,
~ in(X1,esk32_1(esk31_0)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477]) ).
cnf(i_0_776,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_777,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_477]) ).
cnf(i_0_778,plain,
~ in(X1,set_union2(set_difference(empty_set,X2),set_difference(empty_set,X2))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478]) ).
cnf(i_0_779,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_780,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_478]) ).
cnf(i_0_781,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(set_union2(esk37_0,X1),set_union2(esk37_0,X1))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479]) ).
cnf(i_0_782,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_783,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_479]) ).
cnf(i_0_784,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(set_union2(X1,esk37_0),set_union2(X1,esk37_0))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480]) ).
cnf(i_0_785,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_786,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_480]) ).
cnf(i_0_787,plain,
~ subset(esk37_0,empty_set),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485]) ).
cnf(i_0_788,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_789,plain,
( ~ in(X1,X2)
| in(X1,X3)
| ~ subset(X2,X3) ),
inference(rename_variables,[],[i_0_485]) ).
cnf(i_0_790,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_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498]) ).
cnf(i_0_791,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_792,plain,
( X1 != unordered_pair(X2,X2)
| ~ in(X3,X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_793,plain,
~ in(esk37_0,set_union2(powerset(empty_set),powerset(empty_set))),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506]) ).
cnf(i_0_794,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_795,plain,
( X1 != powerset(X2)
| subset(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_506]) ).
cnf(i_0_796,plain,
in(X1,set_difference(powerset(X1),empty_set)),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507]) ).
cnf(i_0_797,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_562]) ).
cnf(i_0_798,plain,
( X1 != powerset(X2)
| in(X3,X1)
| ~ subset(X3,X2) ),
inference(rename_variables,[],[i_0_507]) ).
cnf(i_0_799,plain,
esk37_0 != unordered_pair(esk35_0,esk35_0),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517]) ).
cnf(i_0_800,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_542]) ).
cnf(i_0_801,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_517]) ).
cnf(i_0_802,plain,
esk37_0 != unordered_pair(esk35_0,esk36_0),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518]) ).
cnf(i_0_803,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(rename_variables,[],[i_0_542]) ).
cnf(i_0_804,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_518]) ).
cnf(i_0_805,plain,
in(esk27_1(esk33_0),esk33_0),
inference(scs_inference,[],[i_0_413,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521]) ).
cnf(i_0_806,plain,
element(esk27_1(X1),X1),
inference(rename_variables,[],[i_0_551]) ).
cnf(i_0_807,plain,
( empty(X1)
| ~ element(X2,X1)
| in(X2,X1) ),
inference(rename_variables,[],[i_0_521]) ).
cnf(i_0_808,plain,
in(esk35_0,relation_dom(esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631]) ).
cnf(i_0_809,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| in(X1,relation_dom(X3)) ),
inference(rename_variables,[],[i_0_631]) ).
cnf(i_0_810,plain,
in(esk36_0,relation_rng(esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632]) ).
cnf(i_0_811,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| in(X2,relation_rng(X3)) ),
inference(rename_variables,[],[i_0_632]) ).
cnf(i_0_812,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_difference(esk37_0,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644]) ).
cnf(i_0_813,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_814,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_644]) ).
cnf(i_0_815,plain,
in(unordered_pair(esk35_0,esk36_0),union(esk37_0)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647]) ).
cnf(i_0_816,plain,
( ~ in(X1,X2)
| in(X3,union(X2))
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_647]) ).
cnf(i_0_817,plain,
esk5_1(unordered_pair(X1,X1)) = X1,
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651]) ).
cnf(i_0_818,plain,
( ~ in(X1,unordered_pair(X2,X3))
| X1 = X2
| X1 = X3 ),
inference(rename_variables,[],[i_0_651]) ).
cnf(i_0_819,plain,
~ in(set_union2(esk37_0,esk37_0),unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612]) ).
cnf(i_0_820,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_821,plain,
~ in(esk37_0,set_union2(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613]) ).
cnf(i_0_822,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_823,plain,
~ proper_subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_546,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624]) ).
cnf(i_0_824,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_546]) ).
cnf(i_0_825,plain,
~ proper_subset(X1,set_union2(X1,X1)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625]) ).
cnf(i_0_826,plain,
~ proper_subset(X1,X1),
inference(rename_variables,[],[i_0_546]) ).
cnf(i_0_827,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_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378]) ).
cnf(i_0_828,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_829,plain,
( in(esk11_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2)
| in(esk13_3(X1,X2,X3),X2) ),
inference(rename_variables,[],[i_0_378]) ).
cnf(i_0_830,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_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379]) ).
cnf(i_0_831,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_832,plain,
( in(esk11_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2)
| in(esk12_3(X1,X2,X3),X1) ),
inference(rename_variables,[],[i_0_379]) ).
cnf(i_0_833,plain,
element(subset_difference(X1,esk32_1(X1),esk32_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393]) ).
cnf(i_0_834,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| element(subset_difference(X2,X1,X3),powerset(X2)) ),
inference(rename_variables,[],[i_0_393]) ).
cnf(i_0_835,plain,
subset_difference(X1,esk32_1(X1),esk32_1(X1)) = set_difference(esk32_1(X1),esk32_1(X1)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405]) ).
cnf(i_0_836,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset_difference(X2,X1,X3) = set_difference(X1,X3) ),
inference(rename_variables,[],[i_0_405]) ).
cnf(i_0_837,plain,
in(X1,esk42_2(X1,X1)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426]) ).
cnf(i_0_838,plain,
in(X1,esk41_1(X1)),
inference(rename_variables,[],[i_0_553]) ).
cnf(i_0_839,plain,
( ~ in(X1,esk41_1(X2))
| in(X3,esk42_2(X2,X1))
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_426]) ).
cnf(i_0_840,plain,
empty_set = union(esk32_1(esk31_0)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434]) ).
cnf(i_0_841,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_842,plain,
( in(esk20_2(X1,X2),X2)
| X2 = union(X1)
| in(esk21_2(X1,X2),X1) ),
inference(rename_variables,[],[i_0_434]) ).
cnf(i_0_843,plain,
~ subset(esk37_0,set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484]) ).
cnf(i_0_844,plain,
subset(set_difference(X1,X2),X1),
inference(rename_variables,[],[i_0_523]) ).
cnf(i_0_845,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_846,plain,
esk32_1(empty_set) = empty_set,
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502]) ).
cnf(i_0_847,plain,
subset(empty_set,X1),
inference(rename_variables,[],[i_0_564]) ).
cnf(i_0_848,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_502]) ).
cnf(i_0_849,plain,
~ element(esk33_0,esk31_0),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537]) ).
cnf(i_0_850,plain,
( ~ empty(X1)
| empty(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_537]) ).
cnf(i_0_851,plain,
element(esk31_0,esk31_0),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540]) ).
cnf(i_0_852,plain,
( ~ empty(X1)
| ~ empty(X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_540]) ).
cnf(i_0_853,plain,
unordered_pair(X1,X1) != set_meet(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566]) ).
cnf(i_0_854,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_855,plain,
( X1 != empty_set
| X2 = empty_set
| X2 != set_meet(X1) ),
inference(rename_variables,[],[i_0_566]) ).
cnf(i_0_856,plain,
set_union2(empty_set,empty_set) = set_meet(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569]) ).
cnf(i_0_857,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_858,plain,
( X1 != empty_set
| X2 != empty_set
| X1 = set_meet(X2) ),
inference(rename_variables,[],[i_0_569]) ).
cnf(i_0_859,plain,
unordered_pair(X1,X1) != set_union2(empty_set,empty_set),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579]) ).
cnf(i_0_860,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_861,plain,
~ element(set_union2(esk33_0,esk33_0),esk31_0),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615]) ).
cnf(i_0_862,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_863,plain,
~ element(esk33_0,set_union2(esk31_0,esk31_0)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616]) ).
cnf(i_0_864,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_865,plain,
esk31_0 != esk33_0,
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617]) ).
cnf(i_0_866,plain,
~ subset(set_union2(esk37_0,esk37_0),empty_set),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618]) ).
cnf(i_0_867,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_868,plain,
~ subset(esk37_0,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619]) ).
cnf(i_0_869,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_870,plain,
in(esk35_0,set_union2(relation_dom(esk37_0),relation_dom(esk37_0))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380]) ).
cnf(i_0_871,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_872,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_dom(X3)
| ~ relation(X3)
| in(X1,X4) ),
inference(rename_variables,[],[i_0_380]) ).
cnf(i_0_873,plain,
in(esk36_0,set_union2(relation_rng(esk37_0),relation_rng(esk37_0))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381]) ).
cnf(i_0_874,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_875,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_rng(X3)
| ~ relation(X3)
| in(X2,X4) ),
inference(rename_variables,[],[i_0_381]) ).
cnf(i_0_876,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(set_difference(esk37_0,set_difference(esk37_0,esk37_0)),set_difference(esk37_0,set_difference(esk37_0,esk37_0)))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411]) ).
cnf(i_0_877,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_878,plain,
( X1 != set_difference(X2,set_difference(X2,X3))
| ~ in(X4,X3)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(rename_variables,[],[i_0_411]) ).
cnf(i_0_879,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452]) ).
cnf(i_0_880,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_881,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_452]) ).
cnf(i_0_882,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_difference(set_difference(esk37_0,empty_set),empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_523,i_0_562,i_0_797,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453]) ).
cnf(i_0_883,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_562]) ).
cnf(i_0_884,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_885,plain,
( X1 != set_difference(X2,X3)
| in(X4,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_453]) ).
cnf(i_0_886,plain,
in(unordered_pair(unordered_pair(esk35_0,esk36_0),unordered_pair(esk35_0,esk35_0)),set_union2(union(esk41_1(esk37_0)),union(esk41_1(esk37_0)))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466]) ).
cnf(i_0_887,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_888,plain,
in(X1,esk41_1(X1)),
inference(rename_variables,[],[i_0_553]) ).
cnf(i_0_889,plain,
( X1 != union(X2)
| in(X3,X1)
| ~ in(X3,X4)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_466]) ).
cnf(i_0_890,plain,
~ in(unordered_pair(X1,X1),set_difference(unordered_pair(empty_set,empty_set),empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496]) ).
cnf(i_0_891,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_562]) ).
cnf(i_0_892,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_496]) ).
cnf(i_0_893,plain,
~ in(X1,set_meet(unordered_pair(empty_set,empty_set))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_884,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496,i_0_645]) ).
cnf(i_0_894,plain,
unordered_pair(X1,X1) != empty_set,
inference(rename_variables,[],[i_0_547]) ).
cnf(i_0_895,plain,
( X1 = empty_set
| ~ in(X2,set_meet(X1))
| ~ in(X3,X1)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_645]) ).
cnf(i_0_896,plain,
in(esk8_3(empty_set,empty_set,unordered_pair(empty_set,empty_set)),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_884,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496,i_0_645,i_0_367]) ).
cnf(i_0_897,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_660]) ).
cnf(i_0_898,plain,
( X1 = set_union2(X2,X3)
| in(esk8_3(X2,X3,X1),X1)
| in(esk8_3(X2,X3,X1),X2)
| in(esk8_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_899,plain,
subset(esk32_1(empty_set),subset_complement(empty_set,empty_set)),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_884,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_763,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496,i_0_645,i_0_367,i_0_410]) ).
cnf(i_0_900,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_552]) ).
cnf(i_0_901,plain,
element(esk32_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_543]) ).
cnf(i_0_902,plain,
( ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2))
| subset(X3,subset_complement(X2,X1))
| ~ disjoint(X3,X1) ),
inference(rename_variables,[],[i_0_410]) ).
cnf(i_0_903,plain,
~ in(X1,set_union2(set_meet(unordered_pair(empty_set,empty_set)),set_meet(unordered_pair(empty_set,empty_set)))),
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_884,i_0_897,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_887,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_763,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_894,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496,i_0_645,i_0_367,i_0_410,i_0_460]) ).
cnf(i_0_904,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_559]) ).
cnf(i_0_905,plain,
unordered_pair(X1,X1) != empty_set,
inference(rename_variables,[],[i_0_547]) ).
cnf(i_0_906,plain,
( X1 != set_meet(X2)
| X2 = empty_set
| ~ in(X3,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_460]) ).
cnf(i_0_907,plain,
$false,
inference(scs_inference,[],[i_0_413,i_0_572,i_0_660,i_0_679,i_0_682,i_0_685,i_0_767,i_0_788,i_0_813,i_0_828,i_0_831,i_0_841,i_0_884,i_0_897,i_0_546,i_0_824,i_0_560,i_0_664,i_0_667,i_0_564,i_0_559,i_0_676,i_0_739,i_0_757,i_0_760,i_0_766,i_0_773,i_0_779,i_0_782,i_0_785,i_0_791,i_0_794,i_0_820,i_0_822,i_0_854,i_0_857,i_0_860,i_0_862,i_0_864,i_0_867,i_0_869,i_0_871,i_0_874,i_0_877,i_0_880,i_0_887,i_0_541,i_0_542,i_0_800,i_0_543,i_0_704,i_0_707,i_0_710,i_0_770,i_0_776,i_0_551,i_0_552,i_0_713,i_0_723,i_0_726,i_0_763,i_0_553,i_0_838,i_0_523,i_0_562,i_0_797,i_0_883,i_0_571,i_0_574,i_0_547,i_0_894,i_0_522,i_0_565,i_0_529,i_0_448,i_0_449,i_0_510,i_0_531,i_0_539,i_0_545,i_0_629,i_0_630,i_0_638,i_0_642,i_0_646,i_0_648,i_0_649,i_0_650,i_0_652,i_0_657,i_0_406,i_0_419,i_0_424,i_0_425,i_0_427,i_0_443,i_0_444,i_0_450,i_0_461,i_0_462,i_0_482,i_0_488,i_0_489,i_0_490,i_0_503,i_0_515,i_0_526,i_0_530,i_0_534,i_0_548,i_0_549,i_0_555,i_0_556,i_0_578,i_0_359,i_0_360,i_0_412,i_0_423,i_0_464,i_0_465,i_0_477,i_0_478,i_0_479,i_0_480,i_0_485,i_0_498,i_0_506,i_0_507,i_0_517,i_0_518,i_0_521,i_0_631,i_0_632,i_0_644,i_0_647,i_0_651,i_0_612,i_0_613,i_0_624,i_0_625,i_0_378,i_0_379,i_0_393,i_0_405,i_0_426,i_0_434,i_0_484,i_0_502,i_0_537,i_0_540,i_0_566,i_0_569,i_0_579,i_0_615,i_0_616,i_0_617,i_0_618,i_0_619,i_0_380,i_0_381,i_0_411,i_0_452,i_0_453,i_0_466,i_0_496,i_0_645,i_0_367,i_0_410,i_0_460,i_0_497]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU177+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:46:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.99/2.62 % Version : CSE_E---1.7
% 1.99/2.62 % Problem : theBenchmark.p
% 1.99/2.62 % SZS status Theorem for theBenchmark.p
% 1.99/2.62 % SZS output start CNFRefutation
% See solution above
% 3.68/4.36 % Total time : 2.273s
%------------------------------------------------------------------------------