%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU230+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 : n001.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 05:11:10 PM UTC 2026
% Result : Theorem 0.56s 1.66s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_249)
% 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(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t56_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
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(fc1_ordinal1,axiom,
! [X1] : ~ empty(succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(t10_ordinal1,conjecture,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
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(d8_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(d12_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(d11_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_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(d14_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(d7_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(d2_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X1 = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
<=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(t143_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_dom(X3))
& in(ordered_pair(X4,X1),X3)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_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(d10_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = identity_relation(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(d3_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_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(t166_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_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(t68_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_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(t74_relat_1,lemma,
! [X1,X2,X3,X4] :
( relation(X4)
=> ( in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X4))
<=> ( in(X1,X3)
& in(ordered_pair(X1,X2),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(d1_relat_1,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
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(t8_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(t30_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(t20_relat_1,lemma,
! [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(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(t145_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_image(X2,X1) = relation_image(X2,set_intersection2(relation_dom(X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_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(fc1_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(t119_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(t90_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
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(fc4_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_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(fc6_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_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(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(d1_enumset1,axiom,
! [X1,X2,X3,X4] :
( X4 = unordered_triple(X1,X2,X3)
<=> ! [X5] :
( in(X5,X4)
<=> ~ ( X5 != X1
& X5 != X2
& X5 != X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
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(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_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(t54_funct_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
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(t22_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
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(t21_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_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(t70_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_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(l82_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
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(t115_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(t86_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(t23_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_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(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_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(t146_funct_1,lemma,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_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(t34_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_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(t7_tarski,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
fof(t57_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t145_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_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(t178_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( subset(X1,X2)
=> subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(t45_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
fof(t44_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_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(t72_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t47_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(t46_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_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(t147_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(t140_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> relation_dom_restriction(relation_rng_restriction(X1,X3),X2) = relation_rng_restriction(X1,relation_dom_restriction(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_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(t118_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(t99_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_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(t116_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_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(t21_relat_1,lemma,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_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(t3_ordinal1,lemma,
! [X1,X2,X3] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(t160_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_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(t25_relat_1,lemma,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(t174_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_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(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_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(t167_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(t144_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_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(t117_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(t88_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom_restriction(X2,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
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(fc13_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation_empty_yielding(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& relation_empty_yielding(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc9_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(fc10_relat_1,axiom,
! [X1,X2] :
( ( empty(X1)
& relation(X2) )
=> ( empty(relation_composition(X2,X1))
& relation(relation_composition(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(fc2_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(t35_funct_1,lemma,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_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(t94_relat_1,lemma,
! [X1,X2] :
( relation(X2)
=> relation_dom_restriction(X2,X1) = relation_composition(identity_relation(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_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(t55_funct_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(t62_funct_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(fc3_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1)
& one_to_one(X1) )
=> ( relation(relation_inverse(X1))
& function(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(t146_relat_1,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(d9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
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(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_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(t37_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t65_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(dt_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(fc11_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_inverse(X1))
& relation(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(t64_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
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(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t71_relat_1,lemma,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t60_relat_1,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(i_0_235,plain,
! [X811,X812] : ordered_pair(X811,X812) = unordered_pair(unordered_pair(X811,X812),singleton(X811)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_236,lemma,
! [X1193] : unordered_pair(X1193,X1193) = singleton(X1193),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_237,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(i_0_238,lemma,
! [X1] :
( relation(X1)
=> ( ! [X2,X3] : ~ in(ordered_pair(X2,X3),X1)
=> X1 = empty_set ) ),
inference(fof_simplification,[status(thm)],[t56_relat_1]) ).
fof(i_0_239,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_240,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_241,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[fc1_ordinal1]) ).
fof(i_0_242,plain,
! [X649] : succ(X649) = set_union2(X649,singleton(X649)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(i_0_243,negated_conjecture,
~ ! [X1] : in(X1,succ(X1)),
inference(assume_negation,[status(cth)],[t10_ordinal1]) ).
fof(i_0_244,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_245,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_246,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_247,plain,
! [X829,X830,X831,X832,X833,X835,X836,X837,X840] :
( ( in(ordered_pair(X832,esk57_5(X829,X830,X831,X832,X833)),X829)
| ~ in(ordered_pair(X832,X833),X831)
| X831 != relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) )
& ( in(ordered_pair(esk57_5(X829,X830,X831,X832,X833),X833),X830)
| ~ in(ordered_pair(X832,X833),X831)
| X831 != relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) )
& ( ~ in(ordered_pair(X835,X837),X829)
| ~ in(ordered_pair(X837,X836),X830)
| in(ordered_pair(X835,X836),X831)
| X831 != relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) )
& ( ~ in(ordered_pair(esk58_3(X829,X830,X831),esk59_3(X829,X830,X831)),X831)
| ~ in(ordered_pair(esk58_3(X829,X830,X831),X840),X829)
| ~ in(ordered_pair(X840,esk59_3(X829,X830,X831)),X830)
| X831 = relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) )
& ( in(ordered_pair(esk58_3(X829,X830,X831),esk60_3(X829,X830,X831)),X829)
| in(ordered_pair(esk58_3(X829,X830,X831),esk59_3(X829,X830,X831)),X831)
| X831 = relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) )
& ( in(ordered_pair(esk60_3(X829,X830,X831),esk59_3(X829,X830,X831)),X830)
| in(ordered_pair(esk58_3(X829,X830,X831),esk59_3(X829,X830,X831)),X831)
| X831 = relation_composition(X829,X830)
| ~ relation(X831)
| ~ relation(X830)
| ~ relation(X829) ) ),
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)],[d8_relat_1])])])])])]) ).
cnf(i_0_248,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_235]) ).
cnf(i_0_249,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_236]) ).
fof(i_0_250,plain,
! [X614,X615,X616,X617,X619,X620,X621,X622,X624] :
( ( in(ordered_pair(esk11_4(X614,X615,X616,X617),X617),X614)
| ~ in(X617,X616)
| X616 != relation_image(X614,X615)
| ~ relation(X614) )
& ( in(esk11_4(X614,X615,X616,X617),X615)
| ~ in(X617,X616)
| X616 != relation_image(X614,X615)
| ~ relation(X614) )
& ( ~ in(ordered_pair(X620,X619),X614)
| ~ in(X620,X615)
| in(X619,X616)
| X616 != relation_image(X614,X615)
| ~ relation(X614) )
& ( ~ in(esk12_3(X614,X621,X622),X622)
| ~ in(ordered_pair(X624,esk12_3(X614,X621,X622)),X614)
| ~ in(X624,X621)
| X622 = relation_image(X614,X621)
| ~ relation(X614) )
& ( in(ordered_pair(esk13_3(X614,X621,X622),esk12_3(X614,X621,X622)),X614)
| in(esk12_3(X614,X621,X622),X622)
| X622 = relation_image(X614,X621)
| ~ relation(X614) )
& ( in(esk13_3(X614,X621,X622),X621)
| in(esk12_3(X614,X621,X622),X622)
| X622 = relation_image(X614,X621)
| ~ relation(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)],[d13_relat_1])])])])])]) ).
fof(i_0_251,plain,
! [X597,X598,X599,X600,X601,X602,X603] :
( ( in(X601,X597)
| ~ in(ordered_pair(X600,X601),X599)
| X599 != relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) )
& ( in(ordered_pair(X600,X601),X598)
| ~ in(ordered_pair(X600,X601),X599)
| X599 != relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) )
& ( ~ in(X603,X597)
| ~ in(ordered_pair(X602,X603),X598)
| in(ordered_pair(X602,X603),X599)
| X599 != relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) )
& ( ~ in(ordered_pair(esk8_3(X597,X598,X599),esk9_3(X597,X598,X599)),X599)
| ~ in(esk9_3(X597,X598,X599),X597)
| ~ in(ordered_pair(esk8_3(X597,X598,X599),esk9_3(X597,X598,X599)),X598)
| X599 = relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) )
& ( in(esk9_3(X597,X598,X599),X597)
| in(ordered_pair(esk8_3(X597,X598,X599),esk9_3(X597,X598,X599)),X599)
| X599 = relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) )
& ( in(ordered_pair(esk8_3(X597,X598,X599),esk9_3(X597,X598,X599)),X598)
| in(ordered_pair(esk8_3(X597,X598,X599),esk9_3(X597,X598,X599)),X599)
| X599 = relation_rng_restriction(X597,X598)
| ~ relation(X599)
| ~ relation(X598) ) ),
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)],[d12_relat_1])])])])])]) ).
fof(i_0_252,plain,
! [X576,X577,X578,X579,X580,X581,X582] :
( ( in(X579,X577)
| ~ in(ordered_pair(X579,X580),X578)
| X578 != relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) )
& ( in(ordered_pair(X579,X580),X576)
| ~ in(ordered_pair(X579,X580),X578)
| X578 != relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) )
& ( ~ in(X581,X577)
| ~ in(ordered_pair(X581,X582),X576)
| in(ordered_pair(X581,X582),X578)
| X578 != relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) )
& ( ~ in(ordered_pair(esk3_3(X576,X577,X578),esk4_3(X576,X577,X578)),X578)
| ~ in(esk3_3(X576,X577,X578),X577)
| ~ in(ordered_pair(esk3_3(X576,X577,X578),esk4_3(X576,X577,X578)),X576)
| X578 = relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) )
& ( in(esk3_3(X576,X577,X578),X577)
| in(ordered_pair(esk3_3(X576,X577,X578),esk4_3(X576,X577,X578)),X578)
| X578 = relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) )
& ( in(ordered_pair(esk3_3(X576,X577,X578),esk4_3(X576,X577,X578)),X576)
| in(ordered_pair(esk3_3(X576,X577,X578),esk4_3(X576,X577,X578)),X578)
| X578 = relation_dom_restriction(X576,X577)
| ~ relation(X578)
| ~ relation(X576) ) ),
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)],[d11_relat_1])])])])])]) ).
fof(i_0_253,plain,
! [X717,X718,X719,X720,X723,X724,X725,X726,X727,X728,X730,X731] :
( ( in(esk31_4(X717,X718,X719,X720),X717)
| ~ in(X720,X719)
| X719 != cartesian_product2(X717,X718) )
& ( in(esk32_4(X717,X718,X719,X720),X718)
| ~ in(X720,X719)
| X719 != cartesian_product2(X717,X718) )
& ( X720 = ordered_pair(esk31_4(X717,X718,X719,X720),esk32_4(X717,X718,X719,X720))
| ~ in(X720,X719)
| X719 != cartesian_product2(X717,X718) )
& ( ~ in(X724,X717)
| ~ in(X725,X718)
| X723 != ordered_pair(X724,X725)
| in(X723,X719)
| X719 != cartesian_product2(X717,X718) )
& ( ~ in(esk33_3(X726,X727,X728),X728)
| ~ in(X730,X726)
| ~ in(X731,X727)
| esk33_3(X726,X727,X728) != ordered_pair(X730,X731)
| X728 = cartesian_product2(X726,X727) )
& ( in(esk34_3(X726,X727,X728),X726)
| in(esk33_3(X726,X727,X728),X728)
| X728 = cartesian_product2(X726,X727) )
& ( in(esk35_3(X726,X727,X728),X727)
| in(esk33_3(X726,X727,X728),X728)
| X728 = cartesian_product2(X726,X727) )
& ( esk33_3(X726,X727,X728) = ordered_pair(esk34_3(X726,X727,X728),esk35_3(X726,X727,X728))
| in(esk33_3(X726,X727,X728),X728)
| X728 = cartesian_product2(X726,X727) ) ),
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])])])])])]) ).
fof(i_0_254,plain,
! [X626,X627,X628,X629,X631,X632,X633,X634,X636] :
( ( in(ordered_pair(X629,esk14_4(X626,X627,X628,X629)),X626)
| ~ in(X629,X628)
| X628 != relation_inverse_image(X626,X627)
| ~ relation(X626) )
& ( in(esk14_4(X626,X627,X628,X629),X627)
| ~ in(X629,X628)
| X628 != relation_inverse_image(X626,X627)
| ~ relation(X626) )
& ( ~ in(ordered_pair(X631,X632),X626)
| ~ in(X632,X627)
| in(X631,X628)
| X628 != relation_inverse_image(X626,X627)
| ~ relation(X626) )
& ( ~ in(esk15_3(X626,X633,X634),X634)
| ~ in(ordered_pair(esk15_3(X626,X633,X634),X636),X626)
| ~ in(X636,X633)
| X634 = relation_inverse_image(X626,X633)
| ~ relation(X626) )
& ( in(ordered_pair(esk15_3(X626,X633,X634),esk16_3(X626,X633,X634)),X626)
| in(esk15_3(X626,X633,X634),X634)
| X634 = relation_inverse_image(X626,X633)
| ~ relation(X626) )
& ( in(esk16_3(X626,X633,X634),X633)
| in(esk15_3(X626,X633,X634),X634)
| X634 = relation_inverse_image(X626,X633)
| ~ relation(X626) ) ),
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)],[d14_relat_1])])])])])]) ).
fof(i_0_255,plain,
! [X814,X815,X816,X817,X818,X819] :
( ( ~ in(ordered_pair(X816,X817),X815)
| in(ordered_pair(X817,X816),X814)
| X815 != relation_inverse(X814)
| ~ relation(X815)
| ~ relation(X814) )
& ( ~ in(ordered_pair(X819,X818),X814)
| in(ordered_pair(X818,X819),X815)
| X815 != relation_inverse(X814)
| ~ relation(X815)
| ~ relation(X814) )
& ( ~ in(ordered_pair(esk53_2(X814,X815),esk54_2(X814,X815)),X815)
| ~ in(ordered_pair(esk54_2(X814,X815),esk53_2(X814,X815)),X814)
| X815 = relation_inverse(X814)
| ~ relation(X815)
| ~ relation(X814) )
& ( in(ordered_pair(esk53_2(X814,X815),esk54_2(X814,X815)),X815)
| in(ordered_pair(esk54_2(X814,X815),esk53_2(X814,X815)),X814)
| X815 = relation_inverse(X814)
| ~ relation(X815)
| ~ relation(X814) ) ),
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)],[d7_relat_1])])])])])]) ).
fof(i_0_256,plain,
! [X689,X690,X691,X692,X693,X694] :
( ( ~ in(ordered_pair(X691,X692),X689)
| in(ordered_pair(X691,X692),X690)
| X689 != X690
| ~ relation(X690)
| ~ relation(X689) )
& ( ~ in(ordered_pair(X693,X694),X690)
| in(ordered_pair(X693,X694),X689)
| X689 != X690
| ~ relation(X690)
| ~ relation(X689) )
& ( ~ in(ordered_pair(esk27_2(X689,X690),esk28_2(X689,X690)),X689)
| ~ in(ordered_pair(esk27_2(X689,X690),esk28_2(X689,X690)),X690)
| X689 = X690
| ~ relation(X690)
| ~ relation(X689) )
& ( in(ordered_pair(esk27_2(X689,X690),esk28_2(X689,X690)),X689)
| in(ordered_pair(esk27_2(X689,X690),esk28_2(X689,X690)),X690)
| X689 = X690
| ~ relation(X690)
| ~ relation(X689) ) ),
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_relat_1])])])])])]) ).
fof(i_0_257,lemma,
! [X1007,X1008,X1009,X1011] :
( ( in(esk77_3(X1007,X1008,X1009),relation_dom(X1009))
| ~ in(X1007,relation_image(X1009,X1008))
| ~ relation(X1009) )
& ( in(ordered_pair(esk77_3(X1007,X1008,X1009),X1007),X1009)
| ~ in(X1007,relation_image(X1009,X1008))
| ~ relation(X1009) )
& ( in(esk77_3(X1007,X1008,X1009),X1008)
| ~ in(X1007,relation_image(X1009,X1008))
| ~ relation(X1009) )
& ( ~ in(X1011,relation_dom(X1009))
| ~ in(ordered_pair(X1011,X1007),X1009)
| ~ in(X1011,X1008)
| in(X1007,relation_image(X1009,X1008))
| ~ relation(X1009) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t143_relat_1])])])])]) ).
fof(i_0_258,plain,
! [X799,X800,X801,X803,X804,X805,X807] :
( ( ~ in(X801,X800)
| in(ordered_pair(esk50_3(X799,X800,X801),X801),X799)
| X800 != relation_rng(X799)
| ~ relation(X799) )
& ( ~ in(ordered_pair(X804,X803),X799)
| in(X803,X800)
| X800 != relation_rng(X799)
| ~ relation(X799) )
& ( ~ in(esk51_2(X799,X805),X805)
| ~ in(ordered_pair(X807,esk51_2(X799,X805)),X799)
| X805 = relation_rng(X799)
| ~ relation(X799) )
& ( in(esk51_2(X799,X805),X805)
| in(ordered_pair(esk52_2(X799,X805),esk51_2(X799,X805)),X799)
| X805 = relation_rng(X799)
| ~ relation(X799) ) ),
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_259,plain,
! [X566,X567,X568,X569,X570,X571] :
( ( in(X568,X566)
| ~ in(ordered_pair(X568,X569),X567)
| X567 != identity_relation(X566)
| ~ relation(X567) )
& ( X568 = X569
| ~ in(ordered_pair(X568,X569),X567)
| X567 != identity_relation(X566)
| ~ relation(X567) )
& ( ~ in(X570,X566)
| X570 != X571
| in(ordered_pair(X570,X571),X567)
| X567 != identity_relation(X566)
| ~ relation(X567) )
& ( ~ in(ordered_pair(esk1_2(X566,X567),esk2_2(X566,X567)),X567)
| ~ in(esk1_2(X566,X567),X566)
| esk1_2(X566,X567) != esk2_2(X566,X567)
| X567 = identity_relation(X566)
| ~ relation(X567) )
& ( in(esk1_2(X566,X567),X566)
| in(ordered_pair(esk1_2(X566,X567),esk2_2(X566,X567)),X567)
| X567 = identity_relation(X566)
| ~ relation(X567) )
& ( esk1_2(X566,X567) = esk2_2(X566,X567)
| in(ordered_pair(esk1_2(X566,X567),esk2_2(X566,X567)),X567)
| X567 = identity_relation(X566)
| ~ relation(X567) ) ),
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)],[d10_relat_1])])])])])]) ).
fof(i_0_260,plain,
! [X734,X735,X736,X737] :
( ( ~ subset(X734,X735)
| ~ in(ordered_pair(X736,X737),X734)
| in(ordered_pair(X736,X737),X735)
| ~ relation(X735)
| ~ relation(X734) )
& ( in(ordered_pair(esk36_2(X734,X735),esk37_2(X734,X735)),X734)
| subset(X734,X735)
| ~ relation(X735)
| ~ relation(X734) )
& ( ~ in(ordered_pair(esk36_2(X734,X735),esk37_2(X734,X735)),X735)
| subset(X734,X735)
| ~ relation(X735)
| ~ relation(X734) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relat_1])])])])]) ).
fof(i_0_261,plain,
! [X758,X759,X760,X762,X763,X764,X766] :
( ( ~ in(X760,X759)
| in(ordered_pair(X760,esk40_3(X758,X759,X760)),X758)
| X759 != relation_dom(X758)
| ~ relation(X758) )
& ( ~ in(ordered_pair(X762,X763),X758)
| in(X762,X759)
| X759 != relation_dom(X758)
| ~ relation(X758) )
& ( ~ in(esk41_2(X758,X764),X764)
| ~ in(ordered_pair(esk41_2(X758,X764),X766),X758)
| X764 = relation_dom(X758)
| ~ relation(X758) )
& ( in(esk41_2(X758,X764),X764)
| in(ordered_pair(esk41_2(X758,X764),esk42_2(X758,X764)),X758)
| X764 = relation_dom(X758)
| ~ relation(X758) ) ),
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_262,lemma,
! [X1025,X1026,X1027,X1029] :
( ( in(esk78_3(X1025,X1026,X1027),relation_rng(X1027))
| ~ in(X1025,relation_inverse_image(X1027,X1026))
| ~ relation(X1027) )
& ( in(ordered_pair(X1025,esk78_3(X1025,X1026,X1027)),X1027)
| ~ in(X1025,relation_inverse_image(X1027,X1026))
| ~ relation(X1027) )
& ( in(esk78_3(X1025,X1026,X1027),X1026)
| ~ in(X1025,relation_inverse_image(X1027,X1026))
| ~ relation(X1027) )
& ( ~ in(X1029,relation_rng(X1027))
| ~ in(ordered_pair(X1025,X1029),X1027)
| ~ in(X1029,X1026)
| in(X1025,relation_inverse_image(X1027,X1026))
| ~ relation(X1027) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t166_relat_1])])])])]) ).
fof(i_0_263,plain,
! [X746,X747,X748,X749,X750,X751,X752,X753] :
( ( in(X749,X746)
| ~ in(X749,X748)
| X748 != set_intersection2(X746,X747) )
& ( in(X749,X747)
| ~ in(X749,X748)
| X748 != set_intersection2(X746,X747) )
& ( ~ in(X750,X746)
| ~ in(X750,X747)
| in(X750,X748)
| X748 != set_intersection2(X746,X747) )
& ( ~ in(esk39_3(X751,X752,X753),X753)
| ~ in(esk39_3(X751,X752,X753),X751)
| ~ in(esk39_3(X751,X752,X753),X752)
| X753 = set_intersection2(X751,X752) )
& ( in(esk39_3(X751,X752,X753),X751)
| in(esk39_3(X751,X752,X753),X753)
| X753 = set_intersection2(X751,X752) )
& ( in(esk39_3(X751,X752,X753),X752)
| in(esk39_3(X751,X752,X753),X753)
| X753 = set_intersection2(X751,X752) ) ),
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_264,lemma,
! [X1141,X1142] : set_difference(X1141,set_difference(X1141,X1142)) = set_intersection2(X1141,X1142),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_265,lemma,
! [X1188,X1189,X1190,X1191] :
( ( relation_dom(X1189) = set_intersection2(relation_dom(X1190),X1188)
| X1189 != relation_dom_restriction(X1190,X1188)
| ~ relation(X1190)
| ~ function(X1190)
| ~ relation(X1189)
| ~ function(X1189) )
& ( ~ in(X1191,relation_dom(X1189))
| apply(X1189,X1191) = apply(X1190,X1191)
| X1189 != relation_dom_restriction(X1190,X1188)
| ~ relation(X1190)
| ~ function(X1190)
| ~ relation(X1189)
| ~ function(X1189) )
& ( in(esk89_3(X1188,X1189,X1190),relation_dom(X1189))
| relation_dom(X1189) != set_intersection2(relation_dom(X1190),X1188)
| X1189 = relation_dom_restriction(X1190,X1188)
| ~ relation(X1190)
| ~ function(X1190)
| ~ relation(X1189)
| ~ function(X1189) )
& ( apply(X1189,esk89_3(X1188,X1189,X1190)) != apply(X1190,esk89_3(X1188,X1189,X1190))
| relation_dom(X1189) != set_intersection2(relation_dom(X1190),X1188)
| X1189 = relation_dom_restriction(X1190,X1188)
| ~ relation(X1190)
| ~ function(X1190)
| ~ relation(X1189)
| ~ function(X1189) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
fof(i_0_266,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_267,lemma,
! [X1204,X1205,X1206,X1207] :
( ( in(X1204,X1206)
| ~ in(ordered_pair(X1204,X1205),relation_composition(identity_relation(X1206),X1207))
| ~ relation(X1207) )
& ( in(ordered_pair(X1204,X1205),X1207)
| ~ in(ordered_pair(X1204,X1205),relation_composition(identity_relation(X1206),X1207))
| ~ relation(X1207) )
& ( ~ in(X1204,X1206)
| ~ in(ordered_pair(X1204,X1205),X1207)
| in(ordered_pair(X1204,X1205),relation_composition(identity_relation(X1206),X1207))
| ~ relation(X1207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t74_relat_1])])]) ).
fof(i_0_268,plain,
! [X650,X651,X654,X656,X657] :
( ( ~ relation(X650)
| ~ in(X651,X650)
| X651 = ordered_pair(esk18_2(X650,X651),esk19_2(X650,X651)) )
& ( in(esk20_1(X654),X654)
| relation(X654) )
& ( esk20_1(X654) != ordered_pair(X656,X657)
| relation(X654) ) ),
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_relat_1])])])])])]) ).
fof(i_0_269,plain,
! [X755,X756,X757] :
( ( X757 != apply(X755,X756)
| in(ordered_pair(X756,X757),X755)
| ~ in(X756,relation_dom(X755))
| ~ relation(X755)
| ~ function(X755) )
& ( ~ in(ordered_pair(X756,X757),X755)
| X757 = apply(X755,X756)
| ~ in(X756,relation_dom(X755))
| ~ relation(X755)
| ~ function(X755) )
& ( X757 != apply(X755,X756)
| X757 = empty_set
| in(X756,relation_dom(X755))
| ~ relation(X755)
| ~ function(X755) )
& ( X757 != empty_set
| X757 = apply(X755,X756)
| in(X756,relation_dom(X755))
| ~ relation(X755)
| ~ function(X755) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_237])])])]) ).
fof(i_0_270,lemma,
! [X969,X970,X971,X972] :
( ( in(X969,X971)
| ~ in(ordered_pair(X969,X970),cartesian_product2(X971,X972)) )
& ( in(X970,X972)
| ~ in(ordered_pair(X969,X970),cartesian_product2(X971,X972)) )
& ( ~ in(X969,X971)
| ~ in(X970,X972)
| in(ordered_pair(X969,X970),cartesian_product2(X971,X972)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(i_0_271,lemma,
! [X936,X937,X938,X939] :
( ( in(X936,X938)
| ~ in(ordered_pair(X936,X937),cartesian_product2(X938,X939)) )
& ( in(X937,X939)
| ~ in(ordered_pair(X936,X937),cartesian_product2(X938,X939)) )
& ( ~ in(X936,X938)
| ~ in(X937,X939)
| in(ordered_pair(X936,X937),cartesian_product2(X938,X939)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_272,lemma,
! [X1225,X1226,X1227] :
( ( in(X1225,relation_dom(X1227))
| ~ in(ordered_pair(X1225,X1226),X1227)
| ~ relation(X1227)
| ~ function(X1227) )
& ( X1226 = apply(X1227,X1225)
| ~ in(ordered_pair(X1225,X1226),X1227)
| ~ relation(X1227)
| ~ function(X1227) )
& ( ~ in(X1225,relation_dom(X1227))
| X1226 != apply(X1227,X1225)
| in(ordered_pair(X1225,X1226),X1227)
| ~ relation(X1227)
| ~ function(X1227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])]) ).
fof(i_0_273,lemma,
! [X1075,X1076,X1077] :
( ( in(X1075,relation_field(X1077))
| ~ in(ordered_pair(X1075,X1076),X1077)
| ~ relation(X1077) )
& ( in(X1076,relation_field(X1077))
| ~ in(ordered_pair(X1075,X1076),X1077)
| ~ relation(X1077) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_relat_1])])]) ).
fof(i_0_274,lemma,
! [X1048,X1049,X1050] :
( ( in(X1048,relation_dom(X1050))
| ~ in(ordered_pair(X1048,X1049),X1050)
| ~ relation(X1050) )
& ( in(X1049,relation_rng(X1050))
| ~ in(ordered_pair(X1048,X1049),X1050)
| ~ relation(X1050) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
fof(i_0_275,lemma,
! [X1170] :
( ~ relation(X1170)
| in(ordered_pair(esk87_1(X1170),esk88_1(X1170)),X1170)
| X1170 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_238])])]) ).
fof(i_0_276,plain,
! [X884,X885] : ~ empty(ordered_pair(X884,X885)),
inference(variable_rename,[status(thm)],[i_0_239]) ).
fof(i_0_277,lemma,
! [X1081,X1082,X1083,X1084] :
( ( X1081 = X1083
| ordered_pair(X1081,X1082) != ordered_pair(X1083,X1084) )
& ( X1082 = X1084
| ordered_pair(X1081,X1082) != ordered_pair(X1083,X1084) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_278,lemma,
! [X1063,X1064,X1065] :
( ~ subset(X1063,X1064)
| subset(set_intersection2(X1063,X1065),set_intersection2(X1064,X1065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_279,lemma,
! [X1137,X1138] :
( ~ element(X1138,powerset(powerset(X1137)))
| X1138 = empty_set
| subset_difference(X1137,cast_to_subset(X1137),union_of_subsets(X1137,X1138)) = meet_of_subsets(X1137,complements_of_subsets(X1137,X1138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).
fof(i_0_280,plain,
! [X768] : cast_to_subset(X768) = X768,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(i_0_281,lemma,
! [X1139,X1140] :
( ~ element(X1140,powerset(powerset(X1139)))
| X1140 = empty_set
| union_of_subsets(X1139,complements_of_subsets(X1139,X1140)) = subset_difference(X1139,cast_to_subset(X1139),meet_of_subsets(X1139,X1140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(i_0_282,lemma,
! [X1147,X1148,X1150,X1151,X1152] :
( ( disjoint(X1147,X1148)
| in(esk82_2(X1147,X1148),set_intersection2(X1147,X1148)) )
& ( ~ in(X1152,set_intersection2(X1150,X1151))
| ~ disjoint(X1150,X1151) ) ),
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_240])])])])]) ).
fof(i_0_283,lemma,
! [X1016,X1017] :
( ~ relation(X1017)
| relation_image(X1017,X1016) = relation_image(X1017,set_intersection2(relation_dom(X1017),X1016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_relat_1])]) ).
fof(i_0_284,lemma,
! [X1039,X1040,X1041] :
( ~ subset(X1039,X1040)
| ~ subset(X1039,X1041)
| subset(X1039,set_intersection2(X1040,X1041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_285,lemma,
! [X929,X930,X931] :
( ~ subset(X929,X930)
| in(X931,X929)
| subset(X929,set_difference(X930,singleton(X931))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_286,plain,
! [X880] : ~ empty(succ(X880)),
inference(variable_rename,[status(thm)],[i_0_241]) ).
cnf(i_0_287,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_242]) ).
fof(i_0_288,negated_conjecture,
~ in(esk75_0,succ(esk75_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_243])])]) ).
fof(i_0_289,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_290,lemma,
! [X1195,X1196] :
( ~ subset(singleton(X1195),singleton(X1196))
| X1195 = X1196 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_291,plain,
! [X671,X672,X673,X674,X675,X676] :
( ( ~ in(X673,X672)
| X673 = X671
| X672 != singleton(X671) )
& ( X674 != X671
| in(X674,X672)
| X672 != singleton(X671) )
& ( ~ in(esk24_2(X675,X676),X676)
| esk24_2(X675,X676) != X675
| X676 = singleton(X675) )
& ( in(esk24_2(X675,X676),X676)
| esk24_2(X675,X676) = X675
| X676 = singleton(X675) ) ),
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_292,plain,
! [X881,X882] :
( ~ relation(X881)
| ~ relation(X882)
| relation(set_intersection2(X881,X882)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_relat_1])]) ).
fof(i_0_293,lemma,
! [X990,X991] :
( ~ relation(X991)
| relation_rng(relation_rng_restriction(X990,X991)) = set_intersection2(relation_rng(X991),X990) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_relat_1])]) ).
fof(i_0_294,lemma,
! [X1234,X1235] :
( ~ relation(X1235)
| relation_dom(relation_dom_restriction(X1235,X1234)) = set_intersection2(relation_dom(X1235),X1234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_relat_1])]) ).
fof(i_0_295,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_296,lemma,
! [X1037,X1038] : subset(set_intersection2(X1037,X1038),X1037),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_297,lemma,
! [X1186,X1187] :
( ( set_difference(X1186,singleton(X1187)) != X1186
| ~ in(X1187,X1186) )
& ( in(X1187,X1186)
| set_difference(X1186,singleton(X1187)) = X1186 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_244])]) ).
fof(i_0_298,lemma,
! [X918,X919] :
( ~ disjoint(singleton(X918),X919)
| ~ in(X918,X919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_299,lemma,
! [X1103,X1104] :
( ( ~ subset(X1103,singleton(X1104))
| X1103 = empty_set
| X1103 = singleton(X1104) )
& ( X1103 != empty_set
| subset(X1103,singleton(X1104)) )
& ( X1103 != singleton(X1104)
| subset(X1103,singleton(X1104)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_300,lemma,
! [X932,X933] :
( ( ~ subset(X932,singleton(X933))
| X932 = empty_set
| X932 = singleton(X933) )
& ( X932 != empty_set
| subset(X932,singleton(X933)) )
& ( X932 != singleton(X933)
| subset(X932,singleton(X933)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_301,plain,
! [X564,X565] : set_intersection2(X564,X565) = set_intersection2(X565,X564),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_302,lemma,
! [X1096,X1097] :
( ( ~ subset(singleton(X1096),X1097)
| in(X1096,X1097) )
& ( ~ in(X1096,X1097)
| subset(singleton(X1096),X1097) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_303,lemma,
! [X922,X923] :
( ( ~ subset(singleton(X922),X923)
| in(X922,X923) )
& ( ~ in(X922,X923)
| subset(singleton(X922),X923) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_304,plain,
! [X822,X823] :
( ( ~ disjoint(X822,X823)
| set_intersection2(X822,X823) = empty_set )
& ( set_intersection2(X822,X823) != empty_set
| disjoint(X822,X823) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_305,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_306,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_307,lemma,
! [X1133,X1134] :
( ~ in(X1133,X1134)
| set_union2(singleton(X1133),X1134) = X1134 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_308,lemma,
! [X916,X917] :
( ~ in(X916,X917)
| set_union2(singleton(X916),X917) = X917 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_309,lemma,
! [X1066,X1067] :
( ~ subset(X1066,X1067)
| set_intersection2(X1066,X1067) = X1066 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_310,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_311,lemma,
! [X920,X921] :
( in(X920,X921)
| disjoint(singleton(X920),X921) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_245])]) ).
fof(i_0_312,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_313,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_314,plain,
! [X889] : ~ empty(singleton(X889)),
inference(variable_rename,[status(thm)],[i_0_246]) ).
fof(i_0_315,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_316,lemma,
! [X1231,X1232,X1233] :
( singleton(X1231) != unordered_pair(X1232,X1233)
| X1231 = X1232 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_317,lemma,
! [X1251,X1252,X1253] :
( singleton(X1251) != unordered_pair(X1252,X1253)
| X1252 = X1253 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_318,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_319,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_320,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_321,plain,
! [X908] : set_intersection2(X908,X908) = X908,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_322,plain,
! [X1068] : set_intersection2(X1068,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_323,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_324,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
fof(i_0_325,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_326,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_327,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_328,lemma,
! [X915] : singleton(X915) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_329,plain,
! [X851] : element(cast_to_subset(X851),powerset(X851)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(i_0_330,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_331,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_332,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
cnf(i_0_333,plain,
( in(ordered_pair(esk57_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_334,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_248,c_0_249]) ).
cnf(i_0_335,plain,
( in(ordered_pair(X1,esk57_5(X2,X3,X4,X1,X5)),X2)
| ~ in(ordered_pair(X1,X5),X4)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_336,plain,
( in(ordered_pair(esk11_4(X1,X2,X3,X4),X4),X1)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]) ).
cnf(i_0_337,plain,
( X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(esk58_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,esk59_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_338,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| ~ in(esk9_3(X1,X2,X3),X1)
| ~ in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_339,plain,
( X3 = relation_dom_restriction(X1,X2)
| ~ in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_340,plain,
( X1 = ordered_pair(esk31_4(X2,X3,X4,X1),esk32_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
cnf(i_0_341,plain,
( in(ordered_pair(esk60_3(X1,X2,X3),esk59_3(X1,X2,X3)),X2)
| in(ordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_342,plain,
( in(ordered_pair(esk58_3(X1,X2,X3),esk60_3(X1,X2,X3)),X1)
| in(ordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_343,plain,
( in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X2)
| in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_344,plain,
( in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X1)
| in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_345,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk15_3(X1,X2,X3),X3)
| ~ in(ordered_pair(esk15_3(X1,X2,X3),X4),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_254]) ).
cnf(i_0_346,plain,
( in(ordered_pair(X1,esk14_4(X2,X3,X4,X1)),X2)
| ~ in(X1,X4)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_254]) ).
cnf(i_0_347,plain,
( in(esk9_3(X1,X2,X3),X1)
| in(ordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_348,plain,
( in(esk3_3(X1,X2,X3),X2)
| in(ordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),X3)
| X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_349,plain,
( in(ordered_pair(esk15_3(X1,X2,X3),esk16_3(X1,X2,X3)),X1)
| in(esk15_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_254]) ).
cnf(i_0_350,plain,
( in(ordered_pair(esk13_3(X1,X2,X3),esk12_3(X1,X2,X3)),X1)
| in(esk12_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]) ).
cnf(i_0_351,plain,
( X2 = relation_inverse(X1)
| ~ in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X2)
| ~ in(ordered_pair(esk54_2(X1,X2),esk53_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_255]) ).
cnf(i_0_352,plain,
( X1 = X2
| ~ in(ordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),X1)
| ~ in(ordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_256]) ).
cnf(i_0_353,lemma,
( in(ordered_pair(esk77_3(X1,X2,X3),X1),X3)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_257]) ).
cnf(i_0_354,plain,
( in(ordered_pair(esk50_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_258]) ).
fof(i_0_355,plain,
! [X638,X639,X640,X641,X642,X643,X644,X645,X646,X647] :
( ( ~ in(X642,X641)
| X642 = X638
| X642 = X639
| X642 = X640
| X641 != unordered_triple(X638,X639,X640) )
& ( X643 != X638
| in(X643,X641)
| X641 != unordered_triple(X638,X639,X640) )
& ( X643 != X639
| in(X643,X641)
| X641 != unordered_triple(X638,X639,X640) )
& ( X643 != X640
| in(X643,X641)
| X641 != unordered_triple(X638,X639,X640) )
& ( esk17_4(X644,X645,X646,X647) != X644
| ~ in(esk17_4(X644,X645,X646,X647),X647)
| X647 = unordered_triple(X644,X645,X646) )
& ( esk17_4(X644,X645,X646,X647) != X645
| ~ in(esk17_4(X644,X645,X646,X647),X647)
| X647 = unordered_triple(X644,X645,X646) )
& ( esk17_4(X644,X645,X646,X647) != X646
| ~ in(esk17_4(X644,X645,X646,X647),X647)
| X647 = unordered_triple(X644,X645,X646) )
& ( in(esk17_4(X644,X645,X646,X647),X647)
| esk17_4(X644,X645,X646,X647) = X644
| esk17_4(X644,X645,X646,X647) = X645
| esk17_4(X644,X645,X646,X647) = X646
| X647 = unordered_triple(X644,X645,X646) ) ),
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_enumset1])])])])])]) ).
cnf(i_0_356,plain,
( in(ordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),X2)
| in(ordered_pair(esk54_2(X1,X2),esk53_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_255]) ).
cnf(i_0_357,plain,
( in(ordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),X1)
| in(ordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_256]) ).
cnf(i_0_358,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(ordered_pair(X4,esk12_3(X1,X2,X3)),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]) ).
cnf(i_0_359,plain,
( esk33_3(X1,X2,X3) = ordered_pair(esk34_3(X1,X2,X3),esk35_3(X1,X2,X3))
| in(esk33_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
cnf(i_0_360,plain,
( X2 = identity_relation(X1)
| ~ in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| ~ in(esk1_2(X1,X2),X1)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
cnf(i_0_361,plain,
( subset(X1,X2)
| ~ in(ordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_260]) ).
fof(i_0_362,plain,
! [X606,X607,X608,X609,X610,X611,X612] :
( ( in(X609,relation_dom(X606))
| ~ in(X609,X608)
| X608 != relation_inverse_image(X606,X607)
| ~ relation(X606)
| ~ function(X606) )
& ( in(apply(X606,X609),X607)
| ~ in(X609,X608)
| X608 != relation_inverse_image(X606,X607)
| ~ relation(X606)
| ~ function(X606) )
& ( ~ in(X610,relation_dom(X606))
| ~ in(apply(X606,X610),X607)
| in(X610,X608)
| X608 != relation_inverse_image(X606,X607)
| ~ relation(X606)
| ~ function(X606) )
& ( ~ in(esk10_3(X606,X611,X612),X612)
| ~ in(esk10_3(X606,X611,X612),relation_dom(X606))
| ~ in(apply(X606,esk10_3(X606,X611,X612)),X611)
| X612 = relation_inverse_image(X606,X611)
| ~ relation(X606)
| ~ function(X606) )
& ( in(esk10_3(X606,X611,X612),relation_dom(X606))
| in(esk10_3(X606,X611,X612),X612)
| X612 = relation_inverse_image(X606,X611)
| ~ relation(X606)
| ~ function(X606) )
& ( in(apply(X606,esk10_3(X606,X611,X612)),X611)
| in(esk10_3(X606,X611,X612),X612)
| X612 = relation_inverse_image(X606,X611)
| ~ relation(X606)
| ~ function(X606) ) ),
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)],[d13_funct_1])])])])])]) ).
cnf(i_0_363,plain,
( X2 = relation_dom(X1)
| ~ in(esk41_2(X1,X2),X2)
| ~ in(ordered_pair(esk41_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
fof(i_0_364,plain,
! [X842,X843,X844,X845] :
( ( ~ in(X845,X844)
| in(subset_complement(X842,X845),X843)
| ~ element(X845,powerset(X842))
| X844 != complements_of_subsets(X842,X843)
| ~ element(X844,powerset(powerset(X842)))
| ~ element(X843,powerset(powerset(X842))) )
& ( ~ in(subset_complement(X842,X845),X843)
| in(X845,X844)
| ~ element(X845,powerset(X842))
| X844 != complements_of_subsets(X842,X843)
| ~ element(X844,powerset(powerset(X842)))
| ~ element(X843,powerset(powerset(X842))) )
& ( element(esk61_3(X842,X843,X844),powerset(X842))
| X844 = complements_of_subsets(X842,X843)
| ~ element(X844,powerset(powerset(X842)))
| ~ element(X843,powerset(powerset(X842))) )
& ( ~ in(esk61_3(X842,X843,X844),X844)
| ~ in(subset_complement(X842,esk61_3(X842,X843,X844)),X843)
| X844 = complements_of_subsets(X842,X843)
| ~ element(X844,powerset(powerset(X842)))
| ~ element(X843,powerset(powerset(X842))) )
& ( in(esk61_3(X842,X843,X844),X844)
| in(subset_complement(X842,esk61_3(X842,X843,X844)),X843)
| X844 = complements_of_subsets(X842,X843)
| ~ element(X844,powerset(powerset(X842)))
| ~ element(X843,powerset(powerset(X842))) ) ),
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_365,plain,
( in(ordered_pair(X1,X4),X6)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X2,X4),X5)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
cnf(i_0_366,lemma,
( in(ordered_pair(X1,esk78_3(X1,X2,X3)),X3)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_262]) ).
cnf(i_0_367,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk39_3(X1,X2,X3),X3)
| ~ in(esk39_3(X1,X2,X3),X1)
| ~ in(esk39_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
cnf(i_0_368,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_264]) ).
cnf(i_0_369,plain,
( in(esk51_2(X1,X2),X2)
| in(ordered_pair(esk52_2(X1,X2),esk51_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_258]) ).
cnf(i_0_370,plain,
( in(esk41_2(X1,X2),X2)
| in(ordered_pair(esk41_2(X1,X2),esk42_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_371,plain,
( in(esk1_2(X1,X2),X1)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
cnf(i_0_372,plain,
( in(ordered_pair(X1,esk40_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_373,plain,
( esk1_2(X1,X2) = esk2_2(X1,X2)
| in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X2 = identity_relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
cnf(i_0_374,plain,
( in(ordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_260]) ).
fof(i_0_375,plain,
! [X585,X586,X587,X588,X590,X591,X592,X593,X595] :
( ( in(esk5_4(X585,X586,X587,X588),relation_dom(X585))
| ~ in(X588,X587)
| X587 != relation_image(X585,X586)
| ~ relation(X585)
| ~ function(X585) )
& ( in(esk5_4(X585,X586,X587,X588),X586)
| ~ in(X588,X587)
| X587 != relation_image(X585,X586)
| ~ relation(X585)
| ~ function(X585) )
& ( X588 = apply(X585,esk5_4(X585,X586,X587,X588))
| ~ in(X588,X587)
| X587 != relation_image(X585,X586)
| ~ relation(X585)
| ~ function(X585) )
& ( ~ in(X591,relation_dom(X585))
| ~ in(X591,X586)
| X590 != apply(X585,X591)
| in(X590,X587)
| X587 != relation_image(X585,X586)
| ~ relation(X585)
| ~ function(X585) )
& ( ~ in(esk6_3(X585,X592,X593),X593)
| ~ in(X595,relation_dom(X585))
| ~ in(X595,X592)
| esk6_3(X585,X592,X593) != apply(X585,X595)
| X593 = relation_image(X585,X592)
| ~ relation(X585)
| ~ function(X585) )
& ( in(esk7_3(X585,X592,X593),relation_dom(X585))
| in(esk6_3(X585,X592,X593),X593)
| X593 = relation_image(X585,X592)
| ~ relation(X585)
| ~ function(X585) )
& ( in(esk7_3(X585,X592,X593),X592)
| in(esk6_3(X585,X592,X593),X593)
| X593 = relation_image(X585,X592)
| ~ relation(X585)
| ~ function(X585) )
& ( esk6_3(X585,X592,X593) = apply(X585,esk7_3(X585,X592,X593))
| in(esk6_3(X585,X592,X593),X593)
| X593 = relation_image(X585,X592)
| ~ relation(X585)
| ~ function(X585) ) ),
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)],[d12_funct_1])])])])])]) ).
cnf(i_0_376,lemma,
( X1 = relation_dom_restriction(X3,X2)
| apply(X1,esk89_3(X2,X1,X3)) != apply(X3,esk89_3(X2,X1,X3))
| relation_dom(X1) != set_intersection2(relation_dom(X3),X2)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_265]) ).
fof(i_0_377,plain,
! [X780,X781,X782,X783,X784,X785,X786,X787] :
( ( in(X783,X780)
| ~ in(X783,X782)
| X782 != set_difference(X780,X781) )
& ( ~ in(X783,X781)
| ~ in(X783,X782)
| X782 != set_difference(X780,X781) )
& ( ~ in(X784,X780)
| in(X784,X781)
| in(X784,X782)
| X782 != set_difference(X780,X781) )
& ( ~ in(esk46_3(X785,X786,X787),X787)
| ~ in(esk46_3(X785,X786,X787),X785)
| in(esk46_3(X785,X786,X787),X786)
| X787 = set_difference(X785,X786) )
& ( in(esk46_3(X785,X786,X787),X785)
| in(esk46_3(X785,X786,X787),X787)
| X787 = set_difference(X785,X786) )
& ( ~ in(esk46_3(X785,X786,X787),X786)
| in(esk46_3(X785,X786,X787),X787)
| X787 = set_difference(X785,X786) ) ),
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_266])])])])])]) ).
cnf(i_0_378,plain,
( X2 = relation_rng(X1)
| ~ in(esk51_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk51_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_258]) ).
cnf(i_0_379,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk33_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk33_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
cnf(i_0_380,lemma,
( in(ordered_pair(X1,X3),relation_composition(identity_relation(X2),X4))
| ~ in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_267]) ).
cnf(i_0_381,lemma,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),relation_composition(identity_relation(X4),X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_267]) ).
cnf(i_0_382,plain,
( in(ordered_pair(X1,X3),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_383,plain,
( in(ordered_pair(X3,X1),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_384,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_385,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_386,plain,
( in(ordered_pair(X3,X4),X2)
| ~ subset(X1,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_260]) ).
fof(i_0_387,plain,
! [X708,X709,X710,X711,X712,X713,X714,X715] :
( ( ~ in(X711,X710)
| in(X711,X708)
| in(X711,X709)
| X710 != set_union2(X708,X709) )
& ( ~ in(X712,X708)
| in(X712,X710)
| X710 != set_union2(X708,X709) )
& ( ~ in(X712,X709)
| in(X712,X710)
| X710 != set_union2(X708,X709) )
& ( ~ in(esk30_3(X713,X714,X715),X713)
| ~ in(esk30_3(X713,X714,X715),X715)
| X715 = set_union2(X713,X714) )
& ( ~ in(esk30_3(X713,X714,X715),X714)
| ~ in(esk30_3(X713,X714,X715),X715)
| X715 = set_union2(X713,X714) )
& ( in(esk30_3(X713,X714,X715),X715)
| in(esk30_3(X713,X714,X715),X713)
| in(esk30_3(X713,X714,X715),X714)
| X715 = set_union2(X713,X714) ) ),
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])])])])])]) ).
cnf(i_0_388,plain,
( in(ordered_pair(X2,X1),X4)
| ~ in(ordered_pair(X1,X2),X3)
| X3 != relation_inverse(X4)
| ~ relation(X3)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_255]) ).
cnf(i_0_389,plain,
( in(ordered_pair(X2,X1),X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_255]) ).
fof(i_0_390,lemma,
! [X1156,X1157,X1158,X1159,X1160,X1161] :
( ( relation_dom(X1157) = relation_rng(X1156)
| X1157 != function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( in(X1159,relation_dom(X1156))
| ~ in(X1158,relation_rng(X1156))
| X1159 != apply(X1157,X1158)
| X1157 != function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( X1158 = apply(X1156,X1159)
| ~ in(X1158,relation_rng(X1156))
| X1159 != apply(X1157,X1158)
| X1157 != function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( in(X1160,relation_rng(X1156))
| ~ in(X1161,relation_dom(X1156))
| X1160 != apply(X1156,X1161)
| X1157 != function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( X1161 = apply(X1157,X1160)
| ~ in(X1161,relation_dom(X1156))
| X1160 != apply(X1156,X1161)
| X1157 != function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( in(esk86_2(X1156,X1157),relation_dom(X1156))
| in(esk83_2(X1156,X1157),relation_rng(X1156))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( esk85_2(X1156,X1157) = apply(X1156,esk86_2(X1156,X1157))
| in(esk83_2(X1156,X1157),relation_rng(X1156))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( ~ in(esk85_2(X1156,X1157),relation_rng(X1156))
| esk86_2(X1156,X1157) != apply(X1157,esk85_2(X1156,X1157))
| in(esk83_2(X1156,X1157),relation_rng(X1156))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( in(esk86_2(X1156,X1157),relation_dom(X1156))
| esk84_2(X1156,X1157) = apply(X1157,esk83_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( esk85_2(X1156,X1157) = apply(X1156,esk86_2(X1156,X1157))
| esk84_2(X1156,X1157) = apply(X1157,esk83_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( ~ in(esk85_2(X1156,X1157),relation_rng(X1156))
| esk86_2(X1156,X1157) != apply(X1157,esk85_2(X1156,X1157))
| esk84_2(X1156,X1157) = apply(X1157,esk83_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( in(esk86_2(X1156,X1157),relation_dom(X1156))
| ~ in(esk84_2(X1156,X1157),relation_dom(X1156))
| esk83_2(X1156,X1157) != apply(X1156,esk84_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( esk85_2(X1156,X1157) = apply(X1156,esk86_2(X1156,X1157))
| ~ in(esk84_2(X1156,X1157),relation_dom(X1156))
| esk83_2(X1156,X1157) != apply(X1156,esk84_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) )
& ( ~ in(esk85_2(X1156,X1157),relation_rng(X1156))
| esk86_2(X1156,X1157) != apply(X1157,esk85_2(X1156,X1157))
| ~ in(esk84_2(X1156,X1157),relation_dom(X1156))
| esk83_2(X1156,X1157) != apply(X1156,esk84_2(X1156,X1157))
| relation_dom(X1157) != relation_rng(X1156)
| X1157 = function_inverse(X1156)
| ~ relation(X1157)
| ~ function(X1157)
| ~ one_to_one(X1156)
| ~ relation(X1156)
| ~ function(X1156) ) ),
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)],[t54_funct_1])])])])])]) ).
cnf(i_0_391,lemma,
( in(X3,relation_inverse_image(X2,X4))
| ~ in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_262]) ).
cnf(i_0_392,lemma,
( in(X3,relation_image(X2,X4))
| ~ in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_257]) ).
cnf(i_0_393,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),relation_composition(identity_relation(X2),X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_267]) ).
cnf(i_0_394,plain,
( X2 = ordered_pair(esk18_2(X1,X2),esk19_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_268]) ).
cnf(i_0_395,plain,
( in(X1,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X2,X4)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_254]) ).
cnf(i_0_396,plain,
( in(X2,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X5 != relation_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_250]) ).
fof(i_0_397,plain,
! [X699,X700,X701,X702,X703,X704,X705,X706] :
( ( ~ in(X702,X701)
| X702 = X699
| X702 = X700
| X701 != unordered_pair(X699,X700) )
& ( X703 != X699
| in(X703,X701)
| X701 != unordered_pair(X699,X700) )
& ( X703 != X700
| in(X703,X701)
| X701 != unordered_pair(X699,X700) )
& ( esk29_3(X704,X705,X706) != X704
| ~ in(esk29_3(X704,X705,X706),X706)
| X706 = unordered_pair(X704,X705) )
& ( esk29_3(X704,X705,X706) != X705
| ~ in(esk29_3(X704,X705,X706),X706)
| X706 = unordered_pair(X704,X705) )
& ( in(esk29_3(X704,X705,X706),X706)
| esk29_3(X704,X705,X706) = X704
| esk29_3(X704,X705,X706) = X705
| X706 = unordered_pair(X704,X705) ) ),
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_398,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_269]) ).
cnf(i_0_399,plain,
( in(esk39_3(X1,X2,X3),X1)
| in(esk39_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
cnf(i_0_400,plain,
( in(esk39_3(X1,X2,X3),X2)
| in(esk39_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
cnf(i_0_401,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_270]) ).
cnf(i_0_402,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_271]) ).
cnf(i_0_403,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_270]) ).
cnf(i_0_404,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_271]) ).
cnf(i_0_405,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[i_0_251]) ).
cnf(i_0_406,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_407,lemma,
( in(esk89_3(X1,X2,X3),relation_dom(X2))
| X2 = relation_dom_restriction(X3,X1)
| relation_dom(X2) != set_intersection2(relation_dom(X3),X1)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_265]) ).
cnf(i_0_408,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_272]) ).
cnf(i_0_409,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
cnf(i_0_410,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_411,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_258]) ).
cnf(i_0_412,lemma,
( X1 = apply(X2,X3)
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_272]) ).
cnf(i_0_413,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_273]) ).
cnf(i_0_414,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_273]) ).
cnf(i_0_415,lemma,
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_274]) ).
cnf(i_0_416,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_274]) ).
cnf(i_0_417,lemma,
( in(ordered_pair(esk87_1(X1),esk88_1(X1)),X1)
| X1 = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_275]) ).
cnf(i_0_418,plain,
( X1 = X2
| ~ in(ordered_pair(X1,X2),X3)
| X3 != identity_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
fof(i_0_419,lemma,
! [X1055,X1056,X1057] :
( ~ relation(X1056)
| ~ function(X1056)
| ~ relation(X1057)
| ~ function(X1057)
| ~ in(X1055,relation_dom(relation_composition(X1057,X1056)))
| apply(relation_composition(X1057,X1056),X1055) = apply(X1056,apply(X1057,X1055)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(i_0_420,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_270]) ).
cnf(i_0_421,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_271]) ).
fof(i_0_422,plain,
! [X658,X659,X660,X661,X662,X664,X667,X668,X669,X670] :
( ( ~ in(X660,X659)
| ~ in(X661,X658)
| in(X660,X661)
| X659 != set_meet(X658)
| X658 = empty_set )
& ( in(esk21_3(X658,X659,X662),X658)
| in(X662,X659)
| X659 != set_meet(X658)
| X658 = empty_set )
& ( ~ in(X662,esk21_3(X658,X659,X662))
| in(X662,X659)
| X659 != set_meet(X658)
| X658 = empty_set )
& ( in(esk23_2(X658,X664),X658)
| ~ in(esk22_2(X658,X664),X664)
| X664 = set_meet(X658)
| X658 = empty_set )
& ( ~ in(esk22_2(X658,X664),esk23_2(X658,X664))
| ~ in(esk22_2(X658,X664),X664)
| X664 = set_meet(X658)
| X658 = empty_set )
& ( in(esk22_2(X658,X664),X664)
| ~ in(X667,X658)
| in(esk22_2(X658,X664),X667)
| X664 = set_meet(X658)
| X658 = empty_set )
& ( X669 != set_meet(X668)
| X669 = empty_set
| X668 != empty_set )
& ( X670 != empty_set
| X670 = set_meet(X668)
| X668 != 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_423,lemma,
( in(ordered_pair(X1,X3),X2)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_272]) ).
cnf(i_0_424,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_269]) ).
cnf(i_0_425,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_276]) ).
cnf(i_0_426,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_277]) ).
cnf(i_0_427,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_277]) ).
fof(i_0_428,lemma,
! [X1051,X1052,X1053] :
( ( in(X1051,relation_dom(X1053))
| ~ in(X1051,relation_dom(relation_composition(X1053,X1052)))
| ~ relation(X1053)
| ~ function(X1053)
| ~ relation(X1052)
| ~ function(X1052) )
& ( in(apply(X1053,X1051),relation_dom(X1052))
| ~ in(X1051,relation_dom(relation_composition(X1053,X1052)))
| ~ relation(X1053)
| ~ function(X1053)
| ~ relation(X1052)
| ~ function(X1052) )
& ( ~ in(X1051,relation_dom(X1053))
| ~ in(apply(X1053,X1051),relation_dom(X1052))
| in(X1051,relation_dom(relation_composition(X1053,X1052)))
| ~ relation(X1053)
| ~ function(X1053)
| ~ relation(X1052)
| ~ function(X1052) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
cnf(i_0_429,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_278]) ).
fof(i_0_430,plain,
! [X862,X863,X864] :
( ~ element(X863,powerset(X862))
| ~ element(X864,powerset(X862))
| element(subset_difference(X862,X863,X864),powerset(X862)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
cnf(i_0_431,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_253]) ).
cnf(i_0_432,plain,
( in(ordered_pair(X1,X3),X4)
| ~ in(X1,X2)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
fof(i_0_433,lemma,
! [X1197,X1198,X1199] :
( ~ relation(X1199)
| ~ function(X1199)
| ~ in(X1198,relation_dom(relation_dom_restriction(X1199,X1197)))
| apply(relation_dom_restriction(X1199,X1197),X1198) = apply(X1199,X1198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])]) ).
cnf(i_0_434,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_279]) ).
cnf(i_0_435,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_280]) ).
cnf(i_0_436,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_281]) ).
fof(i_0_437,plain,
! [X789,X790,X791,X793,X794,X795,X797] :
( ( in(esk47_3(X789,X790,X791),relation_dom(X789))
| ~ in(X791,X790)
| X790 != relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) )
& ( X791 = apply(X789,esk47_3(X789,X790,X791))
| ~ in(X791,X790)
| X790 != relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) )
& ( ~ in(X794,relation_dom(X789))
| X793 != apply(X789,X794)
| in(X793,X790)
| X790 != relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) )
& ( ~ in(esk48_2(X789,X795),X795)
| ~ in(X797,relation_dom(X789))
| esk48_2(X789,X795) != apply(X789,X797)
| X795 = relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) )
& ( in(esk49_2(X789,X795),relation_dom(X789))
| in(esk48_2(X789,X795),X795)
| X795 = relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) )
& ( esk48_2(X789,X795) = apply(X789,esk49_2(X789,X795))
| in(esk48_2(X789,X795),X795)
| X795 = relation_rng(X789)
| ~ relation(X789)
| ~ function(X789) ) ),
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_funct_1])])])])])]) ).
cnf(i_0_438,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_282]) ).
fof(i_0_439,plain,
! [X769,X770,X771,X773,X774,X775,X776,X778] :
( ( in(X771,esk43_3(X769,X770,X771))
| ~ in(X771,X770)
| X770 != union(X769) )
& ( in(esk43_3(X769,X770,X771),X769)
| ~ in(X771,X770)
| X770 != union(X769) )
& ( ~ in(X773,X774)
| ~ in(X774,X769)
| in(X773,X770)
| X770 != union(X769) )
& ( ~ in(esk44_2(X775,X776),X776)
| ~ in(esk44_2(X775,X776),X778)
| ~ in(X778,X775)
| X776 = union(X775) )
& ( in(esk44_2(X775,X776),esk45_2(X775,X776))
| in(esk44_2(X775,X776),X776)
| X776 = union(X775) )
& ( in(esk45_2(X775,X776),X775)
| in(esk44_2(X775,X776),X776)
| X776 = union(X775) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_tarski])])])])])]) ).
cnf(i_0_440,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_283]) ).
fof(i_0_441,lemma,
! [X943,X944,X945] :
( ( in(X944,relation_dom(X945))
| ~ in(X944,relation_dom(relation_dom_restriction(X945,X943)))
| ~ relation(X945)
| ~ function(X945) )
& ( in(X944,X943)
| ~ in(X944,relation_dom(relation_dom_restriction(X945,X943)))
| ~ relation(X945)
| ~ function(X945) )
& ( ~ in(X944,relation_dom(X945))
| ~ in(X944,X943)
| in(X944,relation_dom(relation_dom_restriction(X945,X943)))
| ~ relation(X945)
| ~ function(X945) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).
fof(i_0_442,lemma,
! [X1120,X1121,X1122] :
( ( ~ disjoint(X1121,X1122)
| subset(X1121,subset_complement(X1120,X1122))
| ~ element(X1122,powerset(X1120))
| ~ element(X1121,powerset(X1120)) )
& ( ~ subset(X1121,subset_complement(X1120,X1122))
| disjoint(X1121,X1122)
| ~ element(X1122,powerset(X1120))
| ~ element(X1121,powerset(X1120)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_subset_1])])])]) ).
fof(i_0_443,lemma,
! [X978,X979,X980] :
( ( in(X978,X979)
| ~ in(X978,relation_rng(relation_rng_restriction(X979,X980)))
| ~ relation(X980) )
& ( in(X978,relation_rng(X980))
| ~ in(X978,relation_rng(relation_rng_restriction(X979,X980)))
| ~ relation(X980) )
& ( ~ in(X978,X979)
| ~ in(X978,relation_rng(X980))
| in(X978,relation_rng(relation_rng_restriction(X979,X980)))
| ~ relation(X980) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t115_relat_1])])]) ).
fof(i_0_444,lemma,
! [X1218,X1219,X1220] :
( ( in(X1218,X1219)
| ~ in(X1218,relation_dom(relation_dom_restriction(X1220,X1219)))
| ~ relation(X1220) )
& ( in(X1218,relation_dom(X1220))
| ~ in(X1218,relation_dom(relation_dom_restriction(X1220,X1219)))
| ~ relation(X1220) )
& ( ~ in(X1218,X1219)
| ~ in(X1218,relation_dom(X1220))
| in(X1218,relation_dom(relation_dom_restriction(X1220,X1219)))
| ~ relation(X1220) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])]) ).
fof(i_0_445,lemma,
! [X1058,X1059,X1060] :
( ~ relation(X1059)
| ~ function(X1059)
| ~ relation(X1060)
| ~ function(X1060)
| ~ in(X1058,relation_dom(X1059))
| apply(relation_composition(X1059,X1060),X1058) = apply(X1060,apply(X1059,X1058)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(i_0_446,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_284]) ).
fof(i_0_447,plain,
! [X963,X964,X965] :
( ~ element(X964,powerset(X963))
| ~ element(X965,powerset(X963))
| subset_difference(X963,X964,X965) = set_difference(X964,X965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(i_0_448,plain,
! [X824,X825,X826] :
( ( ~ one_to_one(X824)
| ~ in(X825,relation_dom(X824))
| ~ in(X826,relation_dom(X824))
| apply(X824,X825) != apply(X824,X826)
| X825 = X826
| ~ relation(X824)
| ~ function(X824) )
& ( in(esk55_1(X824),relation_dom(X824))
| one_to_one(X824)
| ~ relation(X824)
| ~ function(X824) )
& ( in(esk56_1(X824),relation_dom(X824))
| one_to_one(X824)
| ~ relation(X824)
| ~ function(X824) )
& ( apply(X824,esk55_1(X824)) = apply(X824,esk56_1(X824))
| one_to_one(X824)
| ~ relation(X824)
| ~ function(X824) )
& ( esk55_1(X824) != esk56_1(X824)
| one_to_one(X824)
| ~ relation(X824)
| ~ function(X824) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(i_0_449,lemma,
( disjoint(X1,X2)
| in(esk82_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_282]) ).
fof(i_0_450,plain,
! [X682,X683,X684,X685,X686,X687] :
( ( ~ in(X684,X683)
| subset(X684,X682)
| X683 != powerset(X682) )
& ( ~ subset(X685,X682)
| in(X685,X683)
| X683 != powerset(X682) )
& ( ~ in(esk26_2(X686,X687),X687)
| ~ subset(esk26_2(X686,X687),X686)
| X687 = powerset(X686) )
& ( in(esk26_2(X686,X687),X687)
| subset(esk26_2(X686,X687),X686)
| X687 = powerset(X686) ) ),
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])])])])])]) ).
fof(i_0_451,lemma,
! [X1018,X1019] :
( ~ relation(X1019)
| ~ subset(X1018,relation_dom(X1019))
| subset(X1018,relation_inverse_image(X1019,relation_image(X1019,X1018))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_funct_1])]) ).
cnf(i_0_452,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_285]) ).
cnf(i_0_453,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_286]) ).
cnf(i_0_454,plain,
succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_287,c_0_249]) ).
fof(i_0_455,plain,
! [X1071,X1072] :
( ( ~ in(esk79_2(X1071,X1072),X1071)
| ~ in(esk79_2(X1071,X1072),X1072)
| X1071 = X1072 )
& ( in(esk79_2(X1071,X1072),X1071)
| in(esk79_2(X1071,X1072),X1072)
| X1071 = X1072 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_456,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
fof(i_0_457,lemma,
! [X1166,X1167,X1168] :
( ~ element(X1168,powerset(X1166))
| ~ in(X1167,subset_complement(X1166,X1168))
| ~ in(X1167,X1168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).
cnf(i_0_458,negated_conjecture,
~ in(esk75_0,succ(esk75_0)),
inference(split_conjunct,[status(thm)],[i_0_288]) ).
cnf(i_0_459,lemma,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_265]) ).
cnf(i_0_460,plain,
( relation(X1)
| esk20_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_268]) ).
fof(i_0_461,lemma,
! [X1085,X1086,X1087] :
( ( relation_dom(X1086) = X1085
| X1086 != identity_relation(X1085)
| ~ relation(X1086)
| ~ function(X1086) )
& ( ~ in(X1087,X1085)
| apply(X1086,X1087) = X1087
| X1086 != identity_relation(X1085)
| ~ relation(X1086)
| ~ function(X1086) )
& ( in(esk80_2(X1085,X1086),X1085)
| relation_dom(X1086) != X1085
| X1086 = identity_relation(X1085)
| ~ relation(X1086)
| ~ function(X1086) )
& ( apply(X1086,esk80_2(X1085,X1086)) != esk80_2(X1085,X1086)
| relation_dom(X1086) != X1085
| X1086 = identity_relation(X1085)
| ~ relation(X1086)
| ~ function(X1086) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(i_0_462,lemma,
! [X992,X993,X994,X995] :
( ~ subset(X992,X993)
| ~ subset(X994,X995)
| subset(cartesian_product2(X992,X994),cartesian_product2(X993,X995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(i_0_463,lemma,
! [X1153,X1154,X1155] :
( X1153 = empty_set
| ~ element(X1154,powerset(X1153))
| ~ element(X1155,X1153)
| in(X1155,X1154)
| in(X1155,subset_complement(X1153,X1154)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_289])])]) ).
fof(i_0_464,plain,
! [X867,X868] :
( ~ element(X868,powerset(powerset(X867)))
| element(complements_of_subsets(X867,X868),powerset(powerset(X867))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(i_0_465,plain,
! [X1210,X1211,X1213] :
( ( in(esk90_2(X1210,X1211),X1211)
| ~ in(X1210,X1211) )
& ( ~ in(X1213,X1211)
| ~ in(X1213,esk90_2(X1210,X1211))
| ~ in(X1210,X1211) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_tarski])])])])]) ).
fof(i_0_466,lemma,
! [X1173,X1174] :
( ( X1173 = apply(X1174,apply(function_inverse(X1174),X1173))
| ~ one_to_one(X1174)
| ~ in(X1173,relation_rng(X1174))
| ~ relation(X1174)
| ~ function(X1174) )
& ( X1173 = apply(relation_composition(function_inverse(X1174),X1174),X1173)
| ~ one_to_one(X1174)
| ~ in(X1173,relation_rng(X1174))
| ~ relation(X1174)
| ~ function(X1174) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
fof(i_0_467,lemma,
! [X1014,X1015] :
( ~ relation(X1015)
| ~ function(X1015)
| subset(relation_image(X1015,relation_inverse_image(X1015,X1014)),X1014) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_funct_1])]) ).
cnf(i_0_468,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_290]) ).
cnf(i_0_469,plain,
( X2 = singleton(X1)
| ~ in(esk24_2(X1,X2),X2)
| esk24_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_291]) ).
cnf(i_0_470,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
cnf(i_0_471,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
fof(i_0_472,plain,
! [X860,X861] :
( ~ element(X861,powerset(powerset(X860)))
| element(meet_of_subsets(X860,X861),powerset(X860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(i_0_473,plain,
! [X857,X858] :
( ~ element(X858,powerset(powerset(X857)))
| element(union_of_subsets(X857,X858),powerset(X857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(i_0_474,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_292]) ).
fof(i_0_475,lemma,
! [X1034,X1035,X1036] :
( ~ relation(X1036)
| ~ subset(X1034,X1035)
| subset(relation_inverse_image(X1036,X1034),relation_inverse_image(X1036,X1035)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t178_relat_1])]) ).
cnf(i_0_476,lemma,
( relation_rng(relation_rng_restriction(X2,X1)) = set_intersection2(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_293]) ).
cnf(i_0_477,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_294]) ).
fof(i_0_478,plain,
! [X1243,X1245,X1246,X1247,X1249,X1250] :
( in(X1243,esk91_1(X1243))
& ( ~ in(X1245,esk91_1(X1243))
| ~ subset(X1246,X1245)
| in(X1246,esk91_1(X1243)) )
& ( in(esk92_2(X1243,X1247),esk91_1(X1243))
| ~ in(X1247,esk91_1(X1243)) )
& ( ~ subset(X1249,X1247)
| in(X1249,esk92_2(X1243,X1247))
| ~ in(X1247,esk91_1(X1243)) )
& ( ~ subset(X1250,esk91_1(X1243))
| are_equipotent(X1250,esk91_1(X1243))
| in(X1250,esk91_1(X1243)) ) ),
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_295])])])])]) ).
fof(i_0_479,lemma,
! [X1125,X1126] :
( ~ relation(X1125)
| ~ relation(X1126)
| subset(relation_rng(relation_composition(X1125,X1126)),relation_rng(X1126)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_relat_1])])]) ).
fof(i_0_480,lemma,
! [X1123,X1124] :
( ~ relation(X1123)
| ~ relation(X1124)
| subset(relation_dom(relation_composition(X1123,X1124)),relation_dom(X1123)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_relat_1])])]) ).
fof(i_0_481,plain,
! [X912,X913] :
( ~ element(X913,powerset(powerset(X912)))
| complements_of_subsets(X912,complements_of_subsets(X912,X913)) = X913 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(i_0_482,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_296]) ).
fof(i_0_483,lemma,
! [X1201,X1202,X1203] :
( ~ relation(X1203)
| ~ function(X1203)
| ~ in(X1202,X1201)
| apply(relation_dom_restriction(X1203,X1201),X1202) = apply(X1203,X1202) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t72_funct_1])]) ).
fof(i_0_484,lemma,
! [X1135,X1136] :
( ~ relation(X1135)
| ~ relation(X1136)
| ~ subset(relation_dom(X1135),relation_rng(X1136))
| relation_rng(relation_composition(X1136,X1135)) = relation_rng(X1135) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).
fof(i_0_485,lemma,
! [X1129,X1130] :
( ~ relation(X1129)
| ~ relation(X1130)
| ~ subset(relation_rng(X1129),relation_dom(X1130))
| relation_dom(relation_composition(X1129,X1130)) = relation_dom(X1129) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
fof(i_0_486,lemma,
! [X1078,X1079,X1080] :
( ~ subset(X1078,X1079)
| subset(set_difference(X1078,X1080),set_difference(X1079,X1080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_487,lemma,
! [X987,X988,X989] :
( ( subset(cartesian_product2(X987,X989),cartesian_product2(X988,X989))
| ~ subset(X987,X988) )
& ( subset(cartesian_product2(X989,X987),cartesian_product2(X989,X988))
| ~ subset(X987,X988) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
fof(i_0_488,lemma,
! [X1021,X1022] :
( ~ relation(X1022)
| ~ function(X1022)
| ~ subset(X1021,relation_rng(X1022))
| relation_image(X1022,relation_inverse_image(X1022,X1021)) = X1021 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t147_funct_1])]) ).
cnf(i_0_489,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_297]) ).
fof(i_0_490,lemma,
! [X1004,X1005,X1006] :
( ~ relation(X1006)
| relation_dom_restriction(relation_rng_restriction(X1004,X1006),X1005) = relation_rng_restriction(X1004,relation_dom_restriction(X1006,X1005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t140_relat_1])]) ).
cnf(i_0_491,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_298]) ).
fof(i_0_492,lemma,
! [X1228,X1229,X1230] :
( ~ subset(X1228,X1229)
| ~ subset(X1230,X1229)
| subset(set_union2(X1228,X1230),X1229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_493,lemma,
! [X1098,X1099,X1100] :
( ( in(X1098,X1100)
| ~ subset(unordered_pair(X1098,X1099),X1100) )
& ( in(X1099,X1100)
| ~ subset(unordered_pair(X1098,X1099),X1100) )
& ( ~ in(X1098,X1100)
| ~ in(X1099,X1100)
| subset(unordered_pair(X1098,X1099),X1100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(i_0_494,lemma,
! [X985,X986] :
( ~ relation(X986)
| subset(relation_rng(relation_rng_restriction(X985,X986)),relation_rng(X986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_relat_1])]) ).
fof(i_0_495,lemma,
! [X1240,X1241] :
( ~ relation(X1241)
| subset(relation_rng(relation_dom_restriction(X1241,X1240)),relation_rng(X1241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t99_relat_1])]) ).
fof(i_0_496,lemma,
! [X940,X941] :
( ( in(esk63_2(X940,X941),X940)
| element(X940,powerset(X941)) )
& ( ~ in(esk63_2(X940,X941),X941)
| element(X940,powerset(X941)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
cnf(i_0_497,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_299]) ).
cnf(i_0_498,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_300]) ).
cnf(i_0_499,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_301]) ).
fof(i_0_500,lemma,
! [X981,X982] :
( ~ relation(X982)
| subset(relation_rng(relation_rng_restriction(X981,X982)),X981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t116_relat_1])]) ).
fof(i_0_501,plain,
! [X852,X853] :
( ~ element(X853,powerset(X852))
| element(subset_complement(X852,X853),powerset(X852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_502,plain,
! [X740,X741,X742,X743,X744] :
( ( ~ subset(X740,X741)
| ~ in(X742,X740)
| in(X742,X741) )
& ( in(esk38_2(X743,X744),X743)
| subset(X743,X744) )
& ( ~ in(esk38_2(X743,X744),X744)
| subset(X743,X744) ) ),
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_503,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_302]) ).
cnf(i_0_504,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_303]) ).
cnf(i_0_505,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_304]) ).
fof(i_0_506,lemma,
! [X1131,X1132] :
( ~ element(X1132,powerset(powerset(X1131)))
| X1132 = empty_set
| complements_of_subsets(X1131,X1132) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(i_0_507,lemma,
! [X998,X1000,X1001,X1002,X1003] :
( in(X998,esk76_1(X998))
& ( ~ in(X1000,esk76_1(X998))
| ~ subset(X1001,X1000)
| in(X1001,esk76_1(X998)) )
& ( ~ in(X1002,esk76_1(X998))
| in(powerset(X1002),esk76_1(X998)) )
& ( ~ subset(X1003,esk76_1(X998))
| are_equipotent(X1003,esk76_1(X998))
| in(X1003,esk76_1(X998)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_305])])])]) ).
fof(i_0_508,plain,
! [X909,X910] :
( ~ element(X910,powerset(X909))
| subset_complement(X909,subset_complement(X909,X910)) = X910 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(i_0_509,lemma,
! [X1054] :
( ~ relation(X1054)
| subset(X1054,cartesian_product2(relation_dom(X1054),relation_rng(X1054))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
cnf(i_0_510,plain,
( in(esk24_2(X1,X2),X2)
| esk24_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_291]) ).
fof(i_0_511,plain,
! [X961,X962] :
( ~ element(X962,powerset(powerset(X961)))
| meet_of_subsets(X961,X962) = set_meet(X962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])]) ).
fof(i_0_512,plain,
! [X959,X960] :
( ~ element(X960,powerset(powerset(X959)))
| union_of_subsets(X959,X960) = union(X960) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(i_0_513,plain,
! [X1144,X1145,X1146] :
( ~ in(X1144,X1145)
| ~ element(X1145,powerset(X1146))
| element(X1144,X1146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_514,lemma,
! [X926,X927,X928] :
( ~ element(X927,powerset(X926))
| ~ in(X928,X927)
| in(X928,X926) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
fof(i_0_515,lemma,
! [X1111,X1112,X1114,X1115,X1116] :
( ( in(esk81_2(X1111,X1112),X1111)
| disjoint(X1111,X1112) )
& ( in(esk81_2(X1111,X1112),X1112)
| disjoint(X1111,X1112) )
& ( ~ in(X1116,X1114)
| ~ in(X1116,X1115)
| ~ disjoint(X1114,X1115) ) ),
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_306])])])])])]) ).
fof(i_0_516,lemma,
! [X1106,X1107,X1108] :
( ~ in(X1106,X1107)
| ~ in(X1107,X1108)
| ~ in(X1108,X1106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_ordinal1])]) ).
fof(i_0_517,lemma,
! [X1023,X1024] :
( ~ relation(X1023)
| ~ relation(X1024)
| relation_rng(relation_composition(X1023,X1024)) = relation_image(X1024,relation_rng(X1023)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t160_relat_1])])]) ).
cnf(i_0_518,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_299]) ).
cnf(i_0_519,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_300]) ).
cnf(i_0_520,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_307]) ).
cnf(i_0_521,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_308]) ).
cnf(i_0_522,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_309]) ).
fof(i_0_523,lemma,
! [X1127,X1128] :
( ~ subset(X1127,X1128)
| X1128 = set_union2(X1127,set_difference(X1128,X1127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
fof(i_0_524,lemma,
! [X1061,X1062] :
( ( subset(relation_dom(X1061),relation_dom(X1062))
| ~ subset(X1061,X1062)
| ~ relation(X1062)
| ~ relation(X1061) )
& ( subset(relation_rng(X1061),relation_rng(X1062))
| ~ subset(X1061,X1062)
| ~ relation(X1062)
| ~ relation(X1061) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_relat_1])])])]) ).
fof(i_0_525,lemma,
! [X1032,X1033] :
( ~ relation(X1033)
| X1032 = empty_set
| ~ subset(X1032,relation_rng(X1033))
| relation_inverse_image(X1033,X1032) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t174_relat_1])]) ).
cnf(i_0_526,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_302]) ).
cnf(i_0_527,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_303]) ).
cnf(i_0_528,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_304]) ).
fof(i_0_529,plain,
! [X1175,X1176,X1177] :
( ~ in(X1175,X1176)
| ~ element(X1176,powerset(X1177))
| ~ empty(X1177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_530,plain,
! [X809,X810] :
( ~ element(X810,powerset(X809))
| subset_complement(X809,X810) = set_difference(X809,X810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_531,lemma,
! [X1181,X1182,X1183] :
( ~ subset(X1181,X1182)
| ~ disjoint(X1182,X1183)
| disjoint(X1181,X1183) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_532,lemma,
! [X1045,X1046,X1047] :
( ~ subset(X1045,X1046)
| ~ subset(X1046,X1047)
| subset(X1045,X1047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_533,plain,
! [X878,X879] :
( ( relation(relation_composition(X878,X879))
| ~ relation(X878)
| ~ function(X878)
| ~ relation(X879)
| ~ function(X879) )
& ( function(relation_composition(X878,X879))
| ~ relation(X878)
| ~ function(X878)
| ~ relation(X879)
| ~ function(X879) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(i_0_534,plain,
! [X899,X900] :
( empty(X899)
| empty(X900)
| ~ empty(cartesian_product2(X899,X900)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_310])]) ).
cnf(i_0_535,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_297]) ).
cnf(i_0_536,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_311]) ).
fof(i_0_537,lemma,
! [X1118,X1119] : set_difference(set_union2(X1118,X1119),X1119) = set_difference(X1118,X1119),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_538,lemma,
! [X1101,X1102] : set_union2(X1101,set_difference(X1102,X1101)) = set_union2(X1101,X1102),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_539,lemma,
! [X1030,X1031] :
( ~ relation(X1031)
| subset(relation_inverse_image(X1031,X1030),relation_dom(X1031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t167_relat_1])]) ).
fof(i_0_540,lemma,
! [X1012,X1013] :
( ~ relation(X1013)
| subset(relation_image(X1013,X1012),relation_rng(X1013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_relat_1])]) ).
fof(i_0_541,plain,
! [X890,X891] :
( empty(X890)
| ~ empty(set_union2(X890,X891)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_312])]) ).
fof(i_0_542,plain,
! [X895,X896] :
( empty(X895)
| ~ empty(set_union2(X896,X895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_313])]) ).
cnf(i_0_543,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_291]) ).
fof(i_0_544,lemma,
! [X974,X975,X976,X977] :
( unordered_pair(X974,X975) != unordered_pair(X976,X977)
| X974 = X976
| X974 = X977 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(i_0_545,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_314]) ).
fof(i_0_546,plain,
! [X893,X894] : ~ empty(unordered_pair(X893,X894)),
inference(variable_rename,[status(thm)],[i_0_315]) ).
fof(i_0_547,plain,
! [X574,X575] :
( ( subset(X574,X575)
| X574 != X575 )
& ( subset(X575,X574)
| X574 != X575 )
& ( ~ subset(X574,X575)
| ~ subset(X575,X574)
| X574 = X575 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_548,lemma,
! [X983,X984] :
( ~ relation(X984)
| subset(relation_rng_restriction(X983,X984),X984) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_relat_1])]) ).
fof(i_0_549,lemma,
! [X1221,X1222] :
( ~ relation(X1222)
| subset(relation_dom_restriction(X1222,X1221),X1222) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t88_relat_1])]) ).
fof(i_0_550,plain,
! [X1109,X1110] :
( ( ~ element(X1109,powerset(X1110))
| subset(X1109,X1110) )
& ( ~ subset(X1109,X1110)
| element(X1109,powerset(X1110)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(i_0_551,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_316]) ).
cnf(i_0_552,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_317]) ).
fof(i_0_553,lemma,
! [X1178,X1179] :
( ~ subset(X1178,X1179)
| ~ proper_subset(X1179,X1178) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_554,plain,
! [X555,X556] :
( ~ proper_subset(X555,X556)
| ~ proper_subset(X556,X555) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_318])]) ).
fof(i_0_555,plain,
! [X553,X554] :
( ~ in(X553,X554)
| ~ in(X554,X553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_319])]) ).
fof(i_0_556,plain,
! [X876,X877] :
( ( relation(relation_dom_restriction(X876,X877))
| ~ relation(X876)
| ~ relation_empty_yielding(X876) )
& ( relation_empty_yielding(relation_dom_restriction(X876,X877))
| ~ relation(X876)
| ~ relation_empty_yielding(X876) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_relat_1])])]) ).
fof(i_0_557,plain,
! [X855,X856] :
( ~ relation(X855)
| ~ relation(X856)
| relation(relation_composition(X855,X856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(i_0_558,plain,
! [X905,X906] :
( ( empty(relation_composition(X905,X906))
| ~ empty(X905)
| ~ relation(X906) )
& ( relation(relation_composition(X905,X906))
| ~ empty(X905)
| ~ relation(X906) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_relat_1])])]) ).
fof(i_0_559,plain,
! [X873,X874] :
( ( empty(relation_composition(X874,X873))
| ~ empty(X873)
| ~ relation(X874) )
& ( relation(relation_composition(X874,X873))
| ~ empty(X873)
| ~ relation(X874) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_relat_1])])]) ).
fof(i_0_560,plain,
! [X897,X898] :
( ( relation(relation_dom_restriction(X897,X898))
| ~ relation(X897)
| ~ function(X897) )
& ( function(relation_dom_restriction(X897,X898))
| ~ relation(X897)
| ~ function(X897) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(i_0_561,plain,
! [X887,X888] :
( ~ relation(X887)
| ~ relation(X888)
| relation(set_union2(X887,X888)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_562,lemma,
! [X1089,X1090] :
( ~ in(X1090,X1089)
| apply(identity_relation(X1089),X1090) = X1090 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])]) ).
fof(i_0_563,lemma,
! [X1236,X1237] :
( ~ in(X1236,X1237)
| subset(X1236,union(X1237)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
fof(i_0_564,lemma,
! [X934,X935] :
( ~ in(X934,X935)
| subset(X934,union(X935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_565,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_299]) ).
cnf(i_0_566,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_300]) ).
cnf(i_0_567,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_291]) ).
fof(i_0_568,plain,
! [X697,X698] :
( ( ~ element(X698,X697)
| in(X698,X697)
| empty(X697) )
& ( ~ in(X698,X697)
| element(X698,X697)
| empty(X697) )
& ( ~ element(X698,X697)
| empty(X698)
| ~ empty(X697) )
& ( ~ empty(X698)
| element(X698,X697)
| ~ empty(X697) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_320])])]) ).
fof(i_0_569,plain,
! [X1069,X1070] :
( ~ element(X1069,X1070)
| empty(X1070)
| in(X1069,X1070) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_570,lemma,
! [X1238,X1239] :
( ~ relation(X1239)
| relation_dom_restriction(X1239,X1238) = relation_composition(identity_relation(X1238),X1239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t94_relat_1])]) ).
cnf(i_0_571,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_321]) ).
fof(i_0_572,lemma,
! [X1091,X1092] : subset(set_difference(X1091,X1092),X1091),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_573,lemma,
! [X1214,X1215] : subset(X1214,set_union2(X1214,X1215)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_574,plain,
! [X847,X848] :
( ( subset(X847,X848)
| ~ proper_subset(X847,X848) )
& ( X847 != X848
| ~ proper_subset(X847,X848) )
& ( ~ subset(X847,X848)
| X847 = X848
| proper_subset(X847,X848) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_575,lemma,
! [X1216,X1217] :
( ( ~ disjoint(X1216,X1217)
| set_difference(X1216,X1217) = X1216 )
& ( set_difference(X1216,X1217) != X1216
| disjoint(X1216,X1217) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_576,lemma,
! [X996,X997] :
( ~ subset(X996,X997)
| set_union2(X996,X997) = X997 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(i_0_577,plain,
! [X813] :
( ~ relation(X813)
| relation_field(X813) = set_union2(relation_dom(X813),relation_rng(X813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(i_0_578,plain,
! [X869,X870] :
( ~ relation(X870)
| relation(relation_rng_restriction(X869,X870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(i_0_579,plain,
! [X865,X866] :
( ~ relation(X865)
| relation(relation_dom_restriction(X865,X866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
cnf(i_0_580,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_322]) ).
fof(i_0_581,plain,
! [X967,X968] :
( ~ disjoint(X967,X968)
| disjoint(X968,X967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_582,plain,
! [X1043,X1044] :
( ~ in(X1043,X1044)
| element(X1043,X1044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_583,lemma,
! [X1094,X1095] :
( ( set_difference(X1094,X1095) != empty_set
| subset(X1094,X1095) )
& ( ~ subset(X1094,X1095)
| set_difference(X1094,X1095) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_584,lemma,
! [X924,X925] :
( ( set_difference(X924,X925) != empty_set
| subset(X924,X925) )
& ( ~ subset(X924,X925)
| set_difference(X924,X925) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_585,lemma,
! [X1169] :
( ( relation_rng(X1169) = relation_dom(function_inverse(X1169))
| ~ one_to_one(X1169)
| ~ relation(X1169)
| ~ function(X1169) )
& ( relation_dom(X1169) = relation_rng(function_inverse(X1169))
| ~ one_to_one(X1169)
| ~ relation(X1169)
| ~ function(X1169) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(i_0_586,lemma,
! [X1180] :
( ~ relation(X1180)
| ~ function(X1180)
| ~ one_to_one(X1180)
| one_to_one(function_inverse(X1180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t62_funct_1])]) ).
fof(i_0_587,plain,
! [X892] :
( ( relation(relation_inverse(X892))
| ~ relation(X892)
| ~ function(X892)
| ~ one_to_one(X892) )
& ( function(relation_inverse(X892))
| ~ relation(X892)
| ~ function(X892)
| ~ one_to_one(X892) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_funct_1])])]) ).
fof(i_0_588,lemma,
! [X1020] :
( ~ relation(X1020)
| relation_image(X1020,relation_dom(X1020)) = relation_rng(X1020) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_relat_1])]) ).
fof(i_0_589,plain,
! [X948] :
( ( element(esk66_1(X948),powerset(X948))
| empty(X948) )
& ( ~ empty(esk66_1(X948))
| empty(X948) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_323])])])]) ).
fof(i_0_590,plain,
! [X1208,X1209] :
( ~ in(X1208,X1209)
| ~ empty(X1209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_591,plain,
! [X849] :
( ~ relation(X849)
| ~ function(X849)
| ~ one_to_one(X849)
| function_inverse(X849) = relation_inverse(X849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_funct_1])]) ).
fof(i_0_592,plain,
! [X902] :
( empty(X902)
| ~ relation(X902)
| ~ empty(relation_rng(X902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_324])]) ).
fof(i_0_593,plain,
! [X901] :
( empty(X901)
| ~ relation(X901)
| ~ empty(relation_dom(X901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_325])]) ).
fof(i_0_594,plain,
! [X562,X563] : set_union2(X562,X563) = set_union2(X563,X562),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_595,plain,
! [X560,X561] : unordered_pair(X560,X561) = unordered_pair(X561,X560),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_596,plain,
! [X953] :
( element(esk70_1(X953),powerset(X953))
& empty(esk70_1(X953)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_597,plain,
! [X559] :
( ( relation(X559)
| ~ relation(X559)
| ~ empty(X559)
| ~ function(X559) )
& ( function(X559)
| ~ relation(X559)
| ~ empty(X559)
| ~ function(X559) )
& ( one_to_one(X559)
| ~ relation(X559)
| ~ empty(X559)
| ~ function(X559) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_598,plain,
! [X678,X679,X680] :
( ( X678 != empty_set
| ~ in(X679,X678) )
& ( in(esk25_1(X680),X680)
| X680 = 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_326])])])])]) ).
fof(i_0_599,plain,
! [X850] :
( ( relation(function_inverse(X850))
| ~ relation(X850)
| ~ function(X850) )
& ( function(function_inverse(X850))
| ~ relation(X850)
| ~ function(X850) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(i_0_600,plain,
! [X914] : ~ proper_subset(X914,X914),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_327])]) ).
cnf(i_0_601,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_328]) ).
fof(i_0_602,lemma,
! [X1117] :
( ~ subset(X1117,empty_set)
| X1117 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_603,lemma,
! [X1093] :
( ( relation_rng(X1093) = relation_dom(relation_inverse(X1093))
| ~ relation(X1093) )
& ( relation_dom(X1093) = relation_rng(relation_inverse(X1093))
| ~ relation(X1093) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
fof(i_0_604,plain,
! [X871] : element(esk62_1(X871),X871),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(i_0_605,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_329]) ).
fof(i_0_606,lemma,
! [X1185] :
( ( relation_dom(X1185) != empty_set
| relation_rng(X1185) = empty_set
| ~ relation(X1185) )
& ( relation_rng(X1185) != empty_set
| relation_dom(X1185) = empty_set
| ~ relation(X1185) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])]) ).
fof(i_0_607,plain,
! [X911] :
( ~ relation(X911)
| relation_inverse(relation_inverse(X911)) = X911 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
fof(i_0_608,plain,
! [X854] :
( ~ relation(X854)
| relation(relation_inverse(X854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relat_1])]) ).
fof(i_0_609,plain,
! [X875] :
( ( empty(relation_inverse(X875))
| ~ empty(X875) )
& ( relation(relation_inverse(X875))
| ~ empty(X875) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc11_relat_1])])]) ).
fof(i_0_610,plain,
! [X904] :
( ( empty(relation_rng(X904))
| ~ empty(X904) )
& ( relation(relation_rng(X904))
| ~ empty(X904) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(i_0_611,plain,
! [X903] :
( ( empty(relation_dom(X903))
| ~ empty(X903) )
& ( relation(relation_dom(X903))
| ~ empty(X903) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_612,plain,
! [X883] : ~ empty(powerset(X883)),
inference(variable_rename,[status(thm)],[i_0_330]) ).
fof(i_0_613,plain,
! [X1223,X1224] :
( ~ empty(X1223)
| X1223 = X1224
| ~ empty(X1224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_614,lemma,
! [X1184] :
( ( relation_dom(X1184) != empty_set
| X1184 = empty_set
| ~ relation(X1184) )
& ( relation_rng(X1184) != empty_set
| X1184 = empty_set
| ~ relation(X1184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).
fof(i_0_615,plain,
! [X907] : set_union2(X907,X907) = X907,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_616,plain,
! [X966] : subset(X966,X966),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_617,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_618,plain,
! [X1105] : set_difference(X1105,empty_set) = X1105,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_619,plain,
! [X1042] : set_union2(X1042,empty_set) = X1042,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_620,lemma,
! [X1074] : subset(empty_set,X1074),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_621,plain,
! [X1143] : set_difference(empty_set,X1143) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_622,plain,
! [X558] :
( ~ empty(X558)
| relation(X558) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_623,plain,
! [X557] :
( ~ empty(X557)
| function(X557) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_624,lemma,
! [X1200] :
( relation_dom(identity_relation(X1200)) = X1200
& relation_rng(identity_relation(X1200)) = X1200 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(i_0_625,lemma,
! [X1242] : union(powerset(X1242)) = X1242,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(i_0_626,plain,
! [X886] :
( relation(identity_relation(X886))
& function(identity_relation(X886)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(i_0_627,plain,
! [X859] : relation(identity_relation(X859)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(i_0_628,plain,
! [X1194] :
( ~ empty(X1194)
| X1194 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_629,plain,
~ empty(esk71_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_331])]) ).
fof(i_0_630,plain,
( ~ empty(esk69_0)
& relation(esk69_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_332])]) ).
fof(i_0_631,plain,
( relation(esk74_0)
& relation_empty_yielding(esk74_0)
& function(esk74_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_632,plain,
( relation(esk73_0)
& relation_empty_yielding(esk73_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_633,plain,
( relation(esk72_0)
& function(esk72_0)
& one_to_one(esk72_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_634,plain,
( relation(esk68_0)
& empty(esk68_0)
& function(esk68_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_635,plain,
( empty(esk65_0)
& relation(esk65_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_636,plain,
( relation(esk64_0)
& function(esk64_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_637,plain,
empty(esk67_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_638,plain,
( in(unordered_pair(unordered_pair(esk57_5(X1,X2,X3,X4,X5),X5),unordered_pair(esk57_5(X1,X2,X3,X4,X5),esk57_5(X1,X2,X3,X4,X5))),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_333,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_639,plain,
( in(unordered_pair(unordered_pair(X1,esk57_5(X2,X3,X4,X1,X5)),unordered_pair(X1,X1)),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_335,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_640,plain,
( in(unordered_pair(unordered_pair(esk11_4(X1,X2,X3,X4),X4),unordered_pair(esk11_4(X1,X2,X3,X4),esk11_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[i_0_336,c_0_334]),
[final] ).
cnf(i_0_641,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,esk59_3(X1,X2,X3)),unordered_pair(X4,X4)),X2)
| ~ in(unordered_pair(unordered_pair(esk58_3(X1,X2,X3),X4),unordered_pair(esk58_3(X1,X2,X3),esk58_3(X1,X2,X3))),X1)
| ~ in(unordered_pair(unordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),unordered_pair(esk58_3(X1,X2,X3),esk58_3(X1,X2,X3))),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_337,c_0_334]),c_0_334]),c_0_334]),
[final] ).
cnf(i_0_642,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(esk9_3(X1,X2,X3),X1)
| ~ in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_338,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_643,plain,
( X3 = relation_dom_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_339,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_644,plain,
( X1 = unordered_pair(unordered_pair(esk31_4(X2,X3,X4,X1),esk32_4(X2,X3,X4,X1)),unordered_pair(esk31_4(X2,X3,X4,X1),esk31_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_340,c_0_334]),
[final] ).
cnf(i_0_645,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),unordered_pair(esk58_3(X1,X2,X3),esk58_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk60_3(X1,X2,X3),esk59_3(X1,X2,X3)),unordered_pair(esk60_3(X1,X2,X3),esk60_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_341,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_646,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk58_3(X1,X2,X3),esk59_3(X1,X2,X3)),unordered_pair(esk58_3(X1,X2,X3),esk58_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk58_3(X1,X2,X3),esk60_3(X1,X2,X3)),unordered_pair(esk58_3(X1,X2,X3),esk58_3(X1,X2,X3))),X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_342,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_647,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_343,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_648,plain,
( X3 = relation_dom_restriction(X1,X2)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_344,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_649,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk15_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(esk15_3(X1,X2,X3),X4),unordered_pair(esk15_3(X1,X2,X3),esk15_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[i_0_345,c_0_334]),
[final] ).
cnf(i_0_650,plain,
( in(unordered_pair(unordered_pair(X1,esk14_4(X2,X3,X4,X1)),unordered_pair(X1,X1)),X2)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_346,c_0_334]),
[final] ).
cnf(i_0_651,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(esk9_3(X1,X2,X3),X1)
| in(unordered_pair(unordered_pair(esk8_3(X1,X2,X3),esk9_3(X1,X2,X3)),unordered_pair(esk8_3(X1,X2,X3),esk8_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_347,c_0_334]),
[final] ).
cnf(i_0_652,plain,
( X3 = relation_dom_restriction(X1,X2)
| in(esk3_3(X1,X2,X3),X2)
| in(unordered_pair(unordered_pair(esk3_3(X1,X2,X3),esk4_3(X1,X2,X3)),unordered_pair(esk3_3(X1,X2,X3),esk3_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_348,c_0_334]),
[final] ).
cnf(i_0_653,plain,
( X3 = relation_inverse_image(X1,X2)
| in(esk15_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk15_3(X1,X2,X3),esk16_3(X1,X2,X3)),unordered_pair(esk15_3(X1,X2,X3),esk15_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_349,c_0_334]),
[final] ).
cnf(i_0_654,plain,
( X3 = relation_image(X1,X2)
| in(esk12_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk13_3(X1,X2,X3),esk12_3(X1,X2,X3)),unordered_pair(esk13_3(X1,X2,X3),esk13_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_350,c_0_334]),
[final] ).
cnf(i_0_655,plain,
( X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),unordered_pair(esk53_2(X1,X2),esk53_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk54_2(X1,X2),esk53_2(X1,X2)),unordered_pair(esk54_2(X1,X2),esk54_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_351,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_656,plain,
( X1 = X2
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_352,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_657,lemma,
( in(unordered_pair(unordered_pair(esk77_3(X1,X2,X3),X1),unordered_pair(esk77_3(X1,X2,X3),esk77_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ in(X1,relation_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_353,c_0_334]),
[final] ).
cnf(i_0_658,plain,
( in(unordered_pair(unordered_pair(esk50_3(X3,X2,X1),X1),unordered_pair(esk50_3(X3,X2,X1),esk50_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_354,c_0_334]),
[final] ).
cnf(i_0_659,plain,
( in(esk17_4(X1,X2,X3,X4),X4)
| esk17_4(X1,X2,X3,X4) = X1
| esk17_4(X1,X2,X3,X4) = X2
| esk17_4(X1,X2,X3,X4) = X3
| X4 = unordered_triple(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_660,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk17_4(X1,X2,X3,X4) != X1
| ~ in(esk17_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_661,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk17_4(X1,X2,X3,X4) != X2
| ~ in(esk17_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_662,plain,
( X4 = unordered_triple(X1,X2,X3)
| esk17_4(X1,X2,X3,X4) != X3
| ~ in(esk17_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_663,plain,
( X2 = relation_inverse(X1)
| in(unordered_pair(unordered_pair(esk53_2(X1,X2),esk54_2(X1,X2)),unordered_pair(esk53_2(X1,X2),esk53_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk54_2(X1,X2),esk53_2(X1,X2)),unordered_pair(esk54_2(X1,X2),esk54_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_356,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_664,plain,
( X1 = X2
| in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_357,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_665,plain,
( X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk12_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk12_3(X1,X2,X3)),unordered_pair(X4,X4)),X1) ),
inference(rw,[status(thm)],[i_0_358,c_0_334]),
[final] ).
cnf(i_0_666,plain,
( X3 = cartesian_product2(X1,X2)
| esk33_3(X1,X2,X3) = unordered_pair(unordered_pair(esk34_3(X1,X2,X3),esk35_3(X1,X2,X3)),unordered_pair(esk34_3(X1,X2,X3),esk34_3(X1,X2,X3)))
| in(esk33_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_359,c_0_334]),
[final] ).
cnf(i_0_667,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) != esk1_2(X1,X2)
| ~ relation(X2)
| ~ in(esk1_2(X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_360,c_0_334]),
[final] ).
cnf(i_0_668,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),unordered_pair(esk36_2(X1,X2),esk36_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_361,c_0_334]),
[final] ).
cnf(i_0_669,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk10_3(X1,X2,X3),X3)
| ~ in(esk10_3(X1,X2,X3),relation_dom(X1))
| ~ in(apply(X1,esk10_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_670,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk41_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk41_2(X1,X2),X3),unordered_pair(esk41_2(X1,X2),esk41_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_363,c_0_334]),
[final] ).
cnf(i_0_671,plain,
( X3 = complements_of_subsets(X1,X2)
| ~ in(esk61_3(X1,X2,X3),X3)
| ~ in(subset_complement(X1,esk61_3(X1,X2,X3)),X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_364]),
[final] ).
cnf(i_0_672,plain,
( in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X6)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X5)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_365,c_0_334]),c_0_334]),c_0_334]),
[final] ).
cnf(i_0_673,lemma,
( in(unordered_pair(unordered_pair(X1,esk78_3(X1,X2,X3)),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(X1,relation_inverse_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_366,c_0_334]),
[final] ).
cnf(i_0_674,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk39_3(X1,X2,X3),X3)
| ~ in(esk39_3(X1,X2,X3),X2)
| ~ in(esk39_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_367,c_0_368]),
[final] ).
cnf(i_0_675,plain,
( X2 = relation_rng(X1)
| in(esk51_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk52_2(X1,X2),esk51_2(X1,X2)),unordered_pair(esk52_2(X1,X2),esk52_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_369,c_0_334]),
[final] ).
cnf(i_0_676,plain,
( X2 = relation_dom(X1)
| in(esk41_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk41_2(X1,X2),esk42_2(X1,X2)),unordered_pair(esk41_2(X1,X2),esk41_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_370,c_0_334]),
[final] ).
cnf(i_0_677,plain,
( X2 = identity_relation(X1)
| in(esk1_2(X1,X2),X1)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_371,c_0_334]),
[final] ).
cnf(i_0_678,plain,
( in(unordered_pair(unordered_pair(X1,esk40_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_372,c_0_334]),
[final] ).
cnf(i_0_679,plain,
( X2 = identity_relation(X1)
| esk2_2(X1,X2) = esk1_2(X1,X2)
| in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_373,c_0_334]),
[final] ).
cnf(i_0_680,plain,
( subset(X1,X2)
| in(unordered_pair(unordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),unordered_pair(esk36_2(X1,X2),esk36_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_374,c_0_334]),
[final] ).
cnf(i_0_681,plain,
( in(esk5_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_682,plain,
( X1 = apply(X2,esk5_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_683,plain,
( in(esk5_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_684,plain,
( in(esk14_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_685,plain,
( in(esk11_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_686,plain,
( in(esk32_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_687,plain,
( in(esk31_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_688,lemma,
( X1 = relation_dom_restriction(X3,X2)
| relation_dom(X1) != set_difference(relation_dom(X3),set_difference(relation_dom(X3),X2))
| apply(X1,esk89_3(X2,X1,X3)) != apply(X3,esk89_3(X2,X1,X3))
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_376,c_0_368]),
[final] ).
cnf(i_0_689,plain,
( in(esk46_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk46_3(X1,X2,X3),X3)
| ~ in(esk46_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_690,plain,
( in(esk61_3(X1,X2,X3),X3)
| in(subset_complement(X1,esk61_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_364]),
[final] ).
cnf(i_0_691,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk51_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk51_2(X1,X2)),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[i_0_378,c_0_334]),
[final] ).
cnf(i_0_692,plain,
( X3 = cartesian_product2(X1,X2)
| esk33_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk33_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_379,c_0_334]),
[final] ).
cnf(i_0_693,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X4))
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_380,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_694,lemma,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X4),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_381,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_695,plain,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X5)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_382,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_696,plain,
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X5)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_383,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_697,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_384,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_698,plain,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_385,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_699,plain,
( in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_386,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_700,plain,
( in(apply(X1,esk10_3(X1,X2,X3)),X2)
| in(esk10_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_701,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk30_3(X1,X2,X3),X1)
| ~ in(esk30_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_702,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk30_3(X1,X2,X3),X2)
| ~ in(esk30_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_703,plain,
( in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X3 != relation_inverse(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_388,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_704,plain,
( in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X4)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_389,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_705,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk6_3(X1,X2,X3),X3)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,X2)
| esk6_3(X1,X2,X3) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_706,plain,
( in(esk30_3(X1,X2,X3),X3)
| in(esk30_3(X1,X2,X3),X1)
| in(esk30_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_707,lemma,
( X2 = function_inverse(X1)
| ~ in(esk85_2(X1,X2),relation_rng(X1))
| esk86_2(X1,X2) != apply(X2,esk85_2(X1,X2))
| ~ in(esk84_2(X1,X2),relation_dom(X1))
| esk83_2(X1,X2) != apply(X1,esk84_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_708,lemma,
( in(X3,relation_inverse_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_391,c_0_334]),
[final] ).
cnf(i_0_709,lemma,
( in(X3,relation_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_392,c_0_334]),
[final] ).
cnf(i_0_710,plain,
( in(esk46_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk46_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_711,plain,
( esk6_3(X1,X2,X3) = apply(X1,esk7_3(X1,X2,X3))
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_712,lemma,
( in(X1,X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X4)) ),
inference(rw,[status(thm)],[i_0_393,c_0_334]),
[final] ).
cnf(i_0_713,plain,
( X2 = unordered_pair(unordered_pair(esk18_2(X1,X2),esk19_2(X1,X2)),unordered_pair(esk18_2(X1,X2),esk18_2(X1,X2)))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_394,c_0_334]),
[final] ).
cnf(i_0_714,plain,
( in(X1,X5)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_395,c_0_334]),
[final] ).
cnf(i_0_715,plain,
( in(X2,X5)
| X5 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_396,c_0_334]),
[final] ).
cnf(i_0_716,plain,
( X3 = unordered_pair(X1,X2)
| esk29_3(X1,X2,X3) != X1
| ~ in(esk29_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_717,plain,
( X3 = unordered_pair(X1,X2)
| esk29_3(X1,X2,X3) != X2
| ~ in(esk29_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_718,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_398,c_0_334]),
[final] ).
cnf(i_0_719,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk39_3(X1,X2,X3),X3)
| in(esk39_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_399,c_0_368]),
[final] ).
cnf(i_0_720,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk39_3(X1,X2,X3),X3)
| in(esk39_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_400,c_0_368]),
[final] ).
cnf(i_0_721,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_401,c_0_334]),
[final] ).
cnf(i_0_722,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_402,c_0_334]),
[final] ).
cnf(i_0_723,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_403,c_0_334]),
[final] ).
cnf(i_0_724,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_404,c_0_334]),
[final] ).
cnf(i_0_725,plain,
( in(X1,X2)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X4) ),
inference(rw,[status(thm)],[i_0_405,c_0_334]),
[final] ).
cnf(i_0_726,plain,
( in(X1,X2)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[i_0_406,c_0_334]),
[final] ).
cnf(i_0_727,plain,
( in(esk10_3(X1,X2,X3),relation_dom(X1))
| in(esk10_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_728,plain,
( in(esk7_3(X1,X2,X3),relation_dom(X1))
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_729,plain,
( in(esk7_3(X1,X2,X3),X2)
| in(esk6_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_730,lemma,
( X2 = relation_dom_restriction(X3,X1)
| in(esk89_3(X1,X2,X3),relation_dom(X2))
| relation_dom(X2) != set_difference(relation_dom(X3),set_difference(relation_dom(X3),X1))
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_407,c_0_368]),
[final] ).
cnf(i_0_731,lemma,
( esk85_2(X1,X2) = apply(X1,esk86_2(X1,X2))
| X2 = function_inverse(X1)
| ~ in(esk84_2(X1,X2),relation_dom(X1))
| esk83_2(X1,X2) != apply(X1,esk84_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_732,lemma,
( esk84_2(X1,X2) = apply(X2,esk83_2(X1,X2))
| X2 = function_inverse(X1)
| ~ in(esk85_2(X1,X2),relation_rng(X1))
| esk86_2(X1,X2) != apply(X2,esk85_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_733,plain,
( in(esk16_3(X1,X2,X3),X2)
| in(esk15_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_254]),
[final] ).
cnf(i_0_734,plain,
( in(esk13_3(X1,X2,X3),X2)
| in(esk12_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_250]),
[final] ).
cnf(i_0_735,lemma,
( in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_408,c_0_334]),
[final] ).
cnf(i_0_736,lemma,
( in(esk86_2(X1,X2),relation_dom(X1))
| X2 = function_inverse(X1)
| ~ in(esk84_2(X1,X2),relation_dom(X1))
| esk83_2(X1,X2) != apply(X1,esk84_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_737,lemma,
( in(esk83_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| ~ in(esk85_2(X1,X2),relation_rng(X1))
| esk86_2(X1,X2) != apply(X2,esk85_2(X1,X2))
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_738,plain,
( in(esk46_3(X1,X2,X3),X1)
| in(esk46_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_739,plain,
( in(esk35_3(X1,X2,X3),X2)
| in(esk33_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_740,plain,
( in(esk34_3(X1,X2,X3),X1)
| in(esk33_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]),
[final] ).
cnf(i_0_741,plain,
( in(X1,X2)
| X4 != identity_relation(X2)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4) ),
inference(rw,[status(thm)],[i_0_409,c_0_334]),
[final] ).
cnf(i_0_742,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_410,c_0_334]),
[final] ).
cnf(i_0_743,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_411,c_0_334]),
[final] ).
cnf(i_0_744,lemma,
( X1 = apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_412,c_0_334]),
[final] ).
cnf(i_0_745,lemma,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_413,c_0_334]),
[final] ).
cnf(i_0_746,lemma,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_414,c_0_334]),
[final] ).
cnf(i_0_747,lemma,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[i_0_415,c_0_334]),
[final] ).
cnf(i_0_748,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[i_0_416,c_0_334]),
[final] ).
cnf(i_0_749,lemma,
( X1 = empty_set
| in(unordered_pair(unordered_pair(esk87_1(X1),esk88_1(X1)),unordered_pair(esk87_1(X1),esk87_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_417,c_0_334]),
[final] ).
cnf(i_0_750,plain,
( in(esk29_3(X1,X2,X3),X3)
| esk29_3(X1,X2,X3) = X1
| esk29_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_751,plain,
( element(esk61_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_364]),
[final] ).
cnf(i_0_752,plain,
( X1 = X2
| X3 != identity_relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[i_0_418,c_0_334]),
[final] ).
cnf(i_0_753,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_364]),
[final] ).
cnf(i_0_754,lemma,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_419]),
[final] ).
cnf(i_0_755,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_364]),
[final] ).
cnf(i_0_756,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_420,c_0_334]),
[final] ).
cnf(i_0_757,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_421,c_0_334]),
[final] ).
cnf(i_0_758,plain,
( in(X1,X3)
| X2 = empty_set
| ~ in(X1,esk21_3(X2,X3,X1))
| X3 != set_meet(X2) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_759,lemma,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| X3 != apply(X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[i_0_423,c_0_334]),
[final] ).
cnf(i_0_760,plain,
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[i_0_424,c_0_334]),
[final] ).
cnf(i_0_761,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_425,c_0_334]),
[final] ).
cnf(i_0_762,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_426,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_763,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_427,c_0_334]),c_0_334]),
[final] ).
cnf(i_0_764,lemma,
( in(X1,relation_dom(relation_composition(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_428]),
[final] ).
cnf(i_0_765,lemma,
( in(esk78_3(X1,X2,X3),relation_rng(X3))
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_262]),
[final] ).
cnf(i_0_766,lemma,
( in(esk77_3(X1,X2,X3),relation_dom(X3))
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_257]),
[final] ).
cnf(i_0_767,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_429,c_0_368]),c_0_368]),
[final] ).
cnf(i_0_768,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_430]),
[final] ).
cnf(i_0_769,lemma,
( in(esk78_3(X1,X2,X3),X2)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_262]),
[final] ).
cnf(i_0_770,lemma,
( in(esk77_3(X1,X2,X3),X2)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_257]),
[final] ).
cnf(i_0_771,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_431,c_0_334]),
[final] ).
cnf(i_0_772,lemma,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_428]),
[final] ).
cnf(i_0_773,plain,
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| X1 != X3
| X4 != identity_relation(X2)
| ~ relation(X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_432,c_0_334]),
[final] ).
cnf(i_0_774,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_433]),
[final] ).
cnf(i_0_775,plain,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk22_2(X1,X2),esk23_2(X1,X2))
| ~ in(esk22_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_776,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_434,c_0_435]),
[final] ).
cnf(i_0_777,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_436,c_0_435]),
[final] ).
cnf(i_0_778,plain,
( in(esk47_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_779,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_438,c_0_368]),
[final] ).
cnf(i_0_780,plain,
( X1 = apply(X2,esk47_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_781,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,X3)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_428]),
[final] ).
cnf(i_0_782,lemma,
( esk85_2(X1,X2) = apply(X1,esk86_2(X1,X2))
| esk84_2(X1,X2) = apply(X2,esk83_2(X1,X2))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_783,plain,
( X2 = relation_rng(X1)
| ~ in(esk48_2(X1,X2),X2)
| ~ in(X3,relation_dom(X1))
| esk48_2(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_784,lemma,
( esk85_2(X1,X2) = apply(X1,esk86_2(X1,X2))
| in(esk83_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_785,lemma,
( in(esk86_2(X1,X2),relation_dom(X1))
| esk84_2(X1,X2) = apply(X2,esk83_2(X1,X2))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_786,plain,
( X2 = union(X1)
| ~ in(esk44_2(X1,X2),X2)
| ~ in(esk44_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_787,plain,
( in(esk43_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_788,plain,
( in(X1,esk43_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_789,lemma,
( relation_image(X1,X2) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_440,c_0_368]),
[final] ).
cnf(i_0_790,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_441]),
[final] ).
cnf(i_0_791,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_792,lemma,
( in(esk86_2(X1,X2),relation_dom(X1))
| in(esk83_2(X1,X2),relation_rng(X1))
| X2 = function_inverse(X1)
| relation_dom(X2) != relation_rng(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_793,plain,
( in(esk21_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_794,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_442]),
[final] ).
cnf(i_0_795,lemma,
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_441]),
[final] ).
cnf(i_0_796,lemma,
( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_441]),
[final] ).
cnf(i_0_797,lemma,
( in(X1,relation_rng(X2))
| ~ in(X1,relation_rng(relation_rng_restriction(X3,X2)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_443]),
[final] ).
cnf(i_0_798,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_444]),
[final] ).
cnf(i_0_799,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_445]),
[final] ).
cnf(i_0_800,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_446,c_0_368]),
[final] ).
cnf(i_0_801,lemma,
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X3)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_443]),
[final] ).
cnf(i_0_802,lemma,
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_444]),
[final] ).
cnf(i_0_803,lemma,
( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_443]),
[final] ).
cnf(i_0_804,lemma,
( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ in(X1,X2)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_444]),
[final] ).
cnf(i_0_805,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_447]),
[final] ).
cnf(i_0_806,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_448]),
[final] ).
cnf(i_0_807,lemma,
( disjoint(X1,X2)
| in(esk82_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_449,c_0_368]),
[final] ).
cnf(i_0_808,plain,
( X2 = powerset(X1)
| ~ in(esk26_2(X1,X2),X2)
| ~ subset(esk26_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_809,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_375]),
[final] ).
cnf(i_0_810,lemma,
( subset(X2,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ relation(X1)
| ~ subset(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_451]),
[final] ).
cnf(i_0_811,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_452,c_0_249]),
[final] ).
cnf(i_0_812,plain,
~ empty(set_union2(X1,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_453,c_0_454]),
[final] ).
cnf(i_0_813,plain,
( X1 = X2
| ~ in(esk79_2(X1,X2),X1)
| ~ in(esk79_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_455]),
[final] ).
cnf(i_0_814,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_442]),
[final] ).
cnf(i_0_815,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_456,c_0_368]),
[final] ).
cnf(i_0_816,lemma,
( in(X1,relation_rng(X2))
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_817,lemma,
( in(X1,relation_dom(X2))
| ~ in(X3,relation_rng(X2))
| X1 != apply(X4,X3)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_818,lemma,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_457]),
[final] ).
cnf(i_0_819,negated_conjecture,
~ in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0))),
inference(rw,[status(thm)],[i_0_458,c_0_454]),
[final] ).
cnf(i_0_820,plain,
( X1 = X3
| X1 = X4
| X1 = X5
| ~ in(X1,X2)
| X2 != unordered_triple(X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_821,lemma,
( X1 = apply(X2,X3)
| ~ in(X1,relation_dom(X4))
| X3 != apply(X4,X1)
| X2 != function_inverse(X4)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_822,lemma,
( X1 = apply(X2,X3)
| ~ in(X1,relation_rng(X2))
| X3 != apply(X4,X1)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_823,lemma,
( relation_dom(X1) = set_difference(relation_dom(X2),set_difference(relation_dom(X2),X3))
| X1 != relation_dom_restriction(X2,X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_459,c_0_368]),
[final] ).
cnf(i_0_824,plain,
( relation(X1)
| esk20_1(X1) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[i_0_460,c_0_334]),
[final] ).
cnf(i_0_825,plain,
( esk48_2(X1,X2) = apply(X1,esk49_2(X1,X2))
| in(esk48_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_826,lemma,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_dom_restriction(X3,X4)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_265]),
[final] ).
cnf(i_0_827,lemma,
( X1 = identity_relation(X2)
| apply(X1,esk80_2(X2,X1)) != esk80_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_461]),
[final] ).
cnf(i_0_828,plain,
( in(esk44_2(X1,X2),esk45_2(X1,X2))
| in(esk44_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_829,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_462]),
[final] ).
cnf(i_0_830,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_463]),
[final] ).
cnf(i_0_831,plain,
( in(esk23_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk22_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_832,plain,
( in(esk22_2(X1,X2),X2)
| in(esk22_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_833,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_464]),
[final] ).
cnf(i_0_834,plain,
( ~ in(X1,X2)
| ~ in(X1,esk90_2(X3,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_465]),
[final] ).
cnf(i_0_835,lemma,
( X1 = apply(relation_composition(function_inverse(X2),X2),X1)
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_466]),
[final] ).
cnf(i_0_836,lemma,
( X1 = apply(X2,apply(function_inverse(X2),X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_466]),
[final] ).
cnf(i_0_837,plain,
( in(esk49_2(X1,X2),relation_dom(X1))
| in(esk48_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_838,lemma,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_467]),
[final] ).
cnf(i_0_839,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_468,c_0_249]),c_0_249]),
[final] ).
cnf(i_0_840,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_841,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X4,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_842,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_triple(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_843,plain,
( X2 = unordered_pair(X1,X1)
| esk24_2(X1,X2) != X1
| ~ in(esk24_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_469,c_0_249]),
[final] ).
cnf(i_0_844,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_470,c_0_368]),
[final] ).
cnf(i_0_845,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_471,c_0_368]),
[final] ).
cnf(i_0_846,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_847,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_472]),
[final] ).
cnf(i_0_848,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_473]),
[final] ).
cnf(i_0_849,plain,
( relation(set_difference(X1,set_difference(X1,X2)))
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_474,c_0_368]),
[final] ).
cnf(i_0_850,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_475]),
[final] ).
cnf(i_0_851,lemma,
( relation_rng(relation_rng_restriction(X2,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X2))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_476,c_0_368]),
[final] ).
cnf(i_0_852,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_477,c_0_368]),
[final] ).
cnf(i_0_853,plain,
( in(X1,esk92_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk91_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_478]),
[final] ).
cnf(i_0_854,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_855,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_479]),
[final] ).
cnf(i_0_856,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_480]),
[final] ).
cnf(i_0_857,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_481]),
[final] ).
cnf(i_0_858,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_482,c_0_368]),
[final] ).
cnf(i_0_859,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_483]),
[final] ).
cnf(i_0_860,lemma,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_484]),
[final] ).
cnf(i_0_861,lemma,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_485]),
[final] ).
cnf(i_0_862,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_486]),
[final] ).
cnf(i_0_863,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_487]),
[final] ).
cnf(i_0_864,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_487]),
[final] ).
cnf(i_0_865,lemma,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ subset(X2,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_488]),
[final] ).
cnf(i_0_866,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_489,c_0_249]),
[final] ).
cnf(i_0_867,lemma,
( relation_dom_restriction(relation_rng_restriction(X2,X1),X3) = relation_rng_restriction(X2,relation_dom_restriction(X1,X3))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_490]),
[final] ).
cnf(i_0_868,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_491,c_0_249]),
[final] ).
cnf(i_0_869,plain,
( in(esk45_2(X1,X2),X1)
| in(esk44_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_870,plain,
( in(esk26_2(X1,X2),X2)
| subset(esk26_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_871,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_492]),
[final] ).
cnf(i_0_872,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_493]),
[final] ).
cnf(i_0_873,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_494]),
[final] ).
cnf(i_0_874,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_495]),
[final] ).
cnf(i_0_875,lemma,
( element(X1,powerset(X2))
| ~ in(esk63_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_496]),
[final] ).
cnf(i_0_876,plain,
( in(esk79_2(X1,X2),X1)
| in(esk79_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_455]),
[final] ).
cnf(i_0_877,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_362]),
[final] ).
cnf(i_0_878,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_497,c_0_249]),c_0_249]),
[final] ).
cnf(i_0_879,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_498,c_0_249]),c_0_249]),
[final] ).
cnf(i_0_880,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_499,c_0_368]),c_0_368]),
[final] ).
cnf(i_0_881,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_500]),
[final] ).
cnf(i_0_882,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_501]),
[final] ).
cnf(i_0_883,plain,
( in(esk92_2(X1,X2),esk91_1(X1))
| ~ in(X2,esk91_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_478]),
[final] ).
cnf(i_0_884,plain,
( subset(X1,X2)
| ~ in(esk38_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_502]),
[final] ).
cnf(i_0_885,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_503,c_0_249]),
[final] ).
cnf(i_0_886,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_504,c_0_249]),
[final] ).
cnf(i_0_887,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_493]),
[final] ).
cnf(i_0_888,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_493]),
[final] ).
cnf(i_0_889,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_505,c_0_368]),
[final] ).
cnf(i_0_890,lemma,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_506]),
[final] ).
cnf(i_0_891,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_892,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_893,plain,
( in(X3,esk91_1(X2))
| ~ in(X1,esk91_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_478]),
[final] ).
cnf(i_0_894,lemma,
( in(X3,esk76_1(X2))
| ~ in(X1,esk76_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_895,plain,
( are_equipotent(X1,esk91_1(X2))
| in(X1,esk91_1(X2))
| ~ subset(X1,esk91_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_478]),
[final] ).
cnf(i_0_896,lemma,
( are_equipotent(X1,esk76_1(X2))
| in(X1,esk76_1(X2))
| ~ subset(X1,esk76_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_897,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_508]),
[final] ).
cnf(i_0_898,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_509]),
[final] ).
cnf(i_0_899,plain,
( X2 = unordered_pair(X1,X1)
| esk24_2(X1,X2) = X1
| in(esk24_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_510,c_0_249]),
[final] ).
cnf(i_0_900,plain,
( in(X1,X3)
| X4 = empty_set
| ~ in(X1,X2)
| ~ in(X3,X4)
| X2 != set_meet(X4) ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_901,plain,
( meet_of_subsets(X2,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_511]),
[final] ).
cnf(i_0_902,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_512]),
[final] ).
cnf(i_0_903,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_513]),
[final] ).
cnf(i_0_904,lemma,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_514]),
[final] ).
cnf(i_0_905,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_906,lemma,
( in(esk80_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_461]),
[final] ).
cnf(i_0_907,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_908,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_515]),
[final] ).
cnf(i_0_909,lemma,
( ~ in(X1,X2)
| ~ in(X2,X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_516]),
[final] ).
cnf(i_0_910,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_517]),
[final] ).
cnf(i_0_911,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_518,c_0_249]),c_0_249]),
[final] ).
cnf(i_0_912,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_519,c_0_249]),c_0_249]),
[final] ).
cnf(i_0_913,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_520,c_0_249]),
[final] ).
cnf(i_0_914,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_521,c_0_249]),
[final] ).
cnf(i_0_915,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_522,c_0_368]),
[final] ).
cnf(i_0_916,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_523]),
[final] ).
cnf(i_0_917,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_524]),
[final] ).
cnf(i_0_918,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_524]),
[final] ).
cnf(i_0_919,lemma,
( X2 = empty_set
| ~ relation(X1)
| ~ subset(X2,relation_rng(X1))
| relation_inverse_image(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_525]),
[final] ).
cnf(i_0_920,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_526,c_0_249]),
[final] ).
cnf(i_0_921,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_527,c_0_249]),
[final] ).
cnf(i_0_922,plain,
( in(esk90_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_465]),
[final] ).
cnf(i_0_923,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_528,c_0_368]),
[final] ).
cnf(i_0_924,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_529]),
[final] ).
cnf(i_0_925,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_377]),
[final] ).
cnf(i_0_926,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_927,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_928,lemma,
( in(esk63_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_496]),
[final] ).
cnf(i_0_929,lemma,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_461]),
[final] ).
cnf(i_0_930,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_530]),
[final] ).
cnf(i_0_931,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_932,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_531]),
[final] ).
cnf(i_0_933,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_532]),
[final] ).
cnf(i_0_934,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_502]),
[final] ).
cnf(i_0_935,plain,
( apply(X1,esk55_1(X1)) = apply(X1,esk56_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_448]),
[final] ).
cnf(i_0_936,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_533]),
[final] ).
cnf(i_0_937,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_533]),
[final] ).
cnf(i_0_938,lemma,
( in(powerset(X1),esk76_1(X2))
| ~ in(X1,esk76_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_939,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_534]),
[final] ).
cnf(i_0_940,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_535,c_0_249]),
[final] ).
cnf(i_0_941,lemma,
( in(esk81_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_515]),
[final] ).
cnf(i_0_942,lemma,
( in(esk81_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_515]),
[final] ).
cnf(i_0_943,plain,
( in(esk38_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_502]),
[final] ).
cnf(i_0_944,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_536,c_0_249]),
[final] ).
cnf(i_0_945,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_537]),
[final] ).
cnf(i_0_946,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_538]),
[final] ).
cnf(i_0_947,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_539]),
[final] ).
cnf(i_0_948,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_540]),
[final] ).
cnf(i_0_949,lemma,
( relation_dom(X1) = relation_rng(X2)
| X1 != function_inverse(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_390]),
[final] ).
cnf(i_0_950,plain,
( X1 = apply(X2,X3)
| in(X3,relation_dom(X2))
| X1 != empty_set
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_269]),
[final] ).
cnf(i_0_951,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_541]),
[final] ).
cnf(i_0_952,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_542]),
[final] ).
cnf(i_0_953,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_954,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_543,c_0_249]),
[final] ).
cnf(i_0_955,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_544]),
[final] ).
cnf(i_0_956,plain,
~ empty(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_545,c_0_249]),
[final] ).
cnf(i_0_957,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_546]),
[final] ).
cnf(i_0_958,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_547]),
[final] ).
cnf(i_0_959,lemma,
( subset(relation_rng_restriction(X2,X1),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_548]),
[final] ).
cnf(i_0_960,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_549]),
[final] ).
cnf(i_0_961,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_550]),
[final] ).
cnf(i_0_962,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_551,c_0_249]),
[final] ).
cnf(i_0_963,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_552,c_0_249]),
[final] ).
cnf(i_0_964,plain,
( in(esk56_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_448]),
[final] ).
cnf(i_0_965,plain,
( in(esk55_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_448]),
[final] ).
cnf(i_0_966,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_967,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_968,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_553]),
[final] ).
cnf(i_0_969,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_554]),
[final] ).
cnf(i_0_970,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_555]),
[final] ).
cnf(i_0_971,plain,
( relation_empty_yielding(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation_empty_yielding(X1) ),
inference(split_conjunct,[status(thm)],[i_0_556]),
[final] ).
cnf(i_0_972,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_557]),
[final] ).
cnf(i_0_973,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_558]),
[final] ).
cnf(i_0_974,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_559]),
[final] ).
cnf(i_0_975,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation_empty_yielding(X1) ),
inference(split_conjunct,[status(thm)],[i_0_556]),
[final] ).
cnf(i_0_976,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_560]),
[final] ).
cnf(i_0_977,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_561]),
[final] ).
cnf(i_0_978,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_560]),
[final] ).
cnf(i_0_979,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_558]),
[final] ).
cnf(i_0_980,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_559]),
[final] ).
cnf(i_0_981,lemma,
( apply(identity_relation(X2),X1) = X1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_562]),
[final] ).
cnf(i_0_982,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_550]),
[final] ).
cnf(i_0_983,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_563]),
[final] ).
cnf(i_0_984,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_564]),
[final] ).
cnf(i_0_985,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_565,c_0_249]),
[final] ).
cnf(i_0_986,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_566,c_0_249]),
[final] ).
cnf(i_0_987,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_567,c_0_249]),
[final] ).
cnf(i_0_988,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_989,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_990,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_568]),
[final] ).
cnf(i_0_991,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_569]),
[final] ).
cnf(i_0_992,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_568]),
[final] ).
cnf(i_0_993,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_570]),
[final] ).
cnf(i_0_994,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_571,c_0_368]),
[final] ).
cnf(i_0_995,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_572]),
[final] ).
cnf(i_0_996,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_573]),
[final] ).
cnf(i_0_997,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_574]),
[final] ).
cnf(i_0_998,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_575]),
[final] ).
cnf(i_0_999,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_575]),
[final] ).
cnf(i_0_1000,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_576]),
[final] ).
cnf(i_0_1001,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_577]),
[final] ).
cnf(i_0_1002,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_578]),
[final] ).
cnf(i_0_1003,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_579]),
[final] ).
cnf(i_0_1004,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_580,c_0_368]),
[final] ).
cnf(i_0_1005,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_581]),
[final] ).
cnf(i_0_1006,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_582]),
[final] ).
cnf(i_0_1007,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_574]),
[final] ).
cnf(i_0_1008,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_583]),
[final] ).
cnf(i_0_1009,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1010,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_583]),
[final] ).
cnf(i_0_1011,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1012,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[final] ).
cnf(i_0_1013,lemma,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[final] ).
cnf(i_0_1014,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_568]),
[final] ).
cnf(i_0_1015,lemma,
( one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_586]),
[final] ).
cnf(i_0_1016,plain,
( relation(relation_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_1017,plain,
( function(relation_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_1018,plain,
( one_to_one(X1)
| esk55_1(X1) != esk56_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_448]),
[final] ).
cnf(i_0_1019,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1020,plain,
( element(esk66_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1021,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1022,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1023,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_568]),
[final] ).
cnf(i_0_1024,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1025,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1026,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1027,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1028,lemma,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_461]),
[final] ).
cnf(i_0_1029,plain,
element(esk70_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1030,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_574]),
[final] ).
cnf(i_0_1031,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1032,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1033,plain,
( in(esk20_1(X1),X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_268]),
[final] ).
cnf(i_0_1034,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1035,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1036,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1037,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_601,c_0_249]),
[final] ).
cnf(i_0_1038,plain,
( in(esk25_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1039,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1040,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1041,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1042,plain,
( empty(X1)
| ~ empty(esk66_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1043,plain,
element(esk62_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1044,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[i_0_605,c_0_435]),
[final] ).
cnf(i_0_1045,plain,
in(X1,esk91_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_478]),
[final] ).
cnf(i_0_1046,lemma,
in(X1,esk76_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_1047,lemma,
( relation_rng(X1) = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1048,lemma,
( relation_dom(X1) = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1049,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1050,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_547]),
[final] ).
cnf(i_0_1051,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_547]),
[final] ).
cnf(i_0_1052,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1053,plain,
( relation(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1054,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1055,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1056,plain,
( empty(relation_inverse(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1057,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1058,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1059,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1060,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1061,lemma,
( X1 = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1062,lemma,
( X1 = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1063,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1064,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1065,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_617,c_0_249]),
[final] ).
cnf(i_0_1066,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1067,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1068,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1069,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1070,plain,
( X1 = empty_set
| X1 != set_meet(X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_1071,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1072,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1073,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1074,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1075,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1076,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1077,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1078,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1079,plain,
empty(esk70_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1080,plain,
( X1 = set_meet(X2)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_422]),
[final] ).
cnf(i_0_1081,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1082,plain,
~ empty(esk71_0),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1083,plain,
~ empty(esk69_0),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1084,plain,
relation_empty_yielding(esk74_0),
inference(split_conjunct,[status(thm)],[i_0_631]),
[final] ).
cnf(i_0_1085,plain,
relation_empty_yielding(esk73_0),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1086,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_1087,plain,
one_to_one(esk72_0),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1088,plain,
relation(esk74_0),
inference(split_conjunct,[status(thm)],[i_0_631]),
[final] ).
cnf(i_0_1089,plain,
relation(esk73_0),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1090,plain,
relation(esk72_0),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1091,plain,
relation(esk69_0),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1092,plain,
relation(esk68_0),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1093,plain,
relation(esk65_0),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1094,plain,
relation(esk64_0),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1095,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_1096,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_1097,plain,
function(esk74_0),
inference(split_conjunct,[status(thm)],[i_0_631]),
[final] ).
cnf(i_0_1098,plain,
function(esk72_0),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1099,plain,
function(esk68_0),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1100,plain,
function(esk64_0),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1101,plain,
empty(esk68_0),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1102,plain,
empty(esk67_0),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1103,plain,
empty(esk65_0),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1104,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_1105,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_1106,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_1107,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_1108,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_1109,axiom,
X1 = X1 ).
cnf(i_0_1110,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1111,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1112,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_1113,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_1114,axiom,
( X1 != X2
| esk55_1(X1) = esk55_1(X2) ) ).
cnf(i_0_1115,axiom,
( X1 != X2
| esk56_1(X1) = esk56_1(X2) ) ).
cnf(i_0_1116,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_1117,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_1118,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_1119,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_1120,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_1121,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_1122,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_1123,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_1124,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_1125,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_1126,axiom,
( X1 != X2
| esk17_4(X1,X3,X4,X5) = esk17_4(X2,X3,X4,X5) ) ).
cnf(i_0_1127,axiom,
( X1 != X2
| esk17_4(X3,X1,X4,X5) = esk17_4(X3,X2,X4,X5) ) ).
cnf(i_0_1128,axiom,
( X1 != X2
| esk17_4(X3,X4,X1,X5) = esk17_4(X3,X4,X2,X5) ) ).
cnf(i_0_1129,axiom,
( X1 != X2
| esk17_4(X3,X4,X5,X1) = esk17_4(X3,X4,X5,X2) ) ).
cnf(i_0_1130,axiom,
( X1 != X2
| unordered_triple(X1,X3,X4) = unordered_triple(X2,X3,X4) ) ).
cnf(i_0_1131,axiom,
( X1 != X2
| unordered_triple(X3,X1,X4) = unordered_triple(X3,X2,X4) ) ).
cnf(i_0_1132,axiom,
( X1 != X2
| unordered_triple(X3,X4,X1) = unordered_triple(X3,X4,X2) ) ).
cnf(i_0_1133,axiom,
( X1 != X2
| esk33_3(X1,X3,X4) = esk33_3(X2,X3,X4) ) ).
cnf(i_0_1134,axiom,
( X1 != X2
| esk33_3(X3,X1,X4) = esk33_3(X3,X2,X4) ) ).
cnf(i_0_1135,axiom,
( X1 != X2
| esk33_3(X3,X4,X1) = esk33_3(X3,X4,X2) ) ).
cnf(i_0_1136,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_1137,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_1138,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_1139,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_1140,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_1141,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_1142,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_1143,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_1144,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_1145,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_1146,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_1147,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_1148,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_1149,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_1150,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_1151,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_1152,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_1153,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_1154,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_1155,axiom,
( X1 != X2
| esk6_3(X1,X3,X4) = esk6_3(X2,X3,X4) ) ).
cnf(i_0_1156,axiom,
( X1 != X2
| esk6_3(X3,X1,X4) = esk6_3(X3,X2,X4) ) ).
cnf(i_0_1157,axiom,
( X1 != X2
| esk6_3(X3,X4,X1) = esk6_3(X3,X4,X2) ) ).
cnf(i_0_1158,axiom,
( X1 != X2
| function_inverse(X1) = function_inverse(X2) ) ).
cnf(i_0_1159,axiom,
( X1 != X2
| esk85_2(X1,X3) = esk85_2(X2,X3) ) ).
cnf(i_0_1160,axiom,
( X1 != X2
| esk85_2(X3,X1) = esk85_2(X3,X2) ) ).
cnf(i_0_1161,axiom,
( X1 != X2
| esk86_2(X1,X3) = esk86_2(X2,X3) ) ).
cnf(i_0_1162,axiom,
( X1 != X2
| esk86_2(X3,X1) = esk86_2(X3,X2) ) ).
cnf(i_0_1163,axiom,
( X1 != X2
| esk84_2(X1,X3) = esk84_2(X2,X3) ) ).
cnf(i_0_1164,axiom,
( X1 != X2
| esk84_2(X3,X1) = esk84_2(X3,X2) ) ).
cnf(i_0_1165,axiom,
( X1 != X2
| esk83_2(X1,X3) = esk83_2(X2,X3) ) ).
cnf(i_0_1166,axiom,
( X1 != X2
| esk83_2(X3,X1) = esk83_2(X3,X2) ) ).
cnf(i_0_1167,axiom,
( X1 != X2
| esk29_3(X1,X3,X4) = esk29_3(X2,X3,X4) ) ).
cnf(i_0_1168,axiom,
( X1 != X2
| esk29_3(X3,X1,X4) = esk29_3(X3,X2,X4) ) ).
cnf(i_0_1169,axiom,
( X1 != X2
| esk29_3(X3,X4,X1) = esk29_3(X3,X4,X2) ) ).
cnf(i_0_1170,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_1171,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_1172,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_1173,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_1174,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_1175,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_1176,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_1177,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_1178,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_1179,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_1180,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_1181,axiom,
( X1 != X2
| esk48_2(X1,X3) = esk48_2(X2,X3) ) ).
cnf(i_0_1182,axiom,
( X1 != X2
| esk48_2(X3,X1) = esk48_2(X3,X2) ) ).
cnf(i_0_1183,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_1184,axiom,
( X1 != X2
| esk20_1(X1) = esk20_1(X2) ) ).
cnf(i_0_1185,axiom,
( X1 != X2
| esk80_2(X1,X3) = esk80_2(X2,X3) ) ).
cnf(i_0_1186,axiom,
( X1 != X2
| esk80_2(X3,X1) = esk80_2(X3,X2) ) ).
cnf(i_0_1187,axiom,
( X1 != X2
| esk24_2(X1,X3) = esk24_2(X2,X3) ) ).
cnf(i_0_1188,axiom,
( X1 != X2
| esk24_2(X3,X1) = esk24_2(X3,X2) ) ).
cnf(i_0_1189,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_1190,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_1191,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_1192,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_1193,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_1194,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_1195,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_1196,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_1197,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_1198,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_1199,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_1200,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_1201,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_1202,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_1203,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_1204,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_1205,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_1109_001,axiom,
X1 = X1 ).
cnf(i_0_1110_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1111_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1112_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_1113_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_1114_006,axiom,
( X1 != X2
| esk55_1(X1) = esk55_1(X2) ) ).
cnf(i_0_1115_007,axiom,
( X1 != X2
| esk56_1(X1) = esk56_1(X2) ) ).
cnf(i_0_1116_008,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_1117_009,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_1118_010,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_1119_011,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_1120_012,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_1121_013,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_1122_014,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_1123_015,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_1124_016,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_1125_017,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_1126_018,axiom,
( X1 != X2
| esk17_4(X1,X3,X4,X5) = esk17_4(X2,X3,X4,X5) ) ).
cnf(i_0_1127_019,axiom,
( X1 != X2
| esk17_4(X3,X1,X4,X5) = esk17_4(X3,X2,X4,X5) ) ).
cnf(i_0_1128_020,axiom,
( X1 != X2
| esk17_4(X3,X4,X1,X5) = esk17_4(X3,X4,X2,X5) ) ).
cnf(i_0_1129_021,axiom,
( X1 != X2
| esk17_4(X3,X4,X5,X1) = esk17_4(X3,X4,X5,X2) ) ).
cnf(i_0_1130_022,axiom,
( X1 != X2
| unordered_triple(X1,X3,X4) = unordered_triple(X2,X3,X4) ) ).
cnf(i_0_1131_023,axiom,
( X1 != X2
| unordered_triple(X3,X1,X4) = unordered_triple(X3,X2,X4) ) ).
cnf(i_0_1132_024,axiom,
( X1 != X2
| unordered_triple(X3,X4,X1) = unordered_triple(X3,X4,X2) ) ).
cnf(i_0_1133_025,axiom,
( X1 != X2
| esk33_3(X1,X3,X4) = esk33_3(X2,X3,X4) ) ).
cnf(i_0_1134_026,axiom,
( X1 != X2
| esk33_3(X3,X1,X4) = esk33_3(X3,X2,X4) ) ).
cnf(i_0_1135_027,axiom,
( X1 != X2
| esk33_3(X3,X4,X1) = esk33_3(X3,X4,X2) ) ).
cnf(i_0_1136_028,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_1137_029,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_1138_030,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_1139_031,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_1140_032,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_1141_033,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_1142_034,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_1143_035,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_1144_036,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_1145_037,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_1146_038,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_1147_039,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_1148_040,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_1149_041,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_1150_042,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_1151_043,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_1152_044,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_1153_045,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_1154_046,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_1155_047,axiom,
( X1 != X2
| esk6_3(X1,X3,X4) = esk6_3(X2,X3,X4) ) ).
cnf(i_0_1156_048,axiom,
( X1 != X2
| esk6_3(X3,X1,X4) = esk6_3(X3,X2,X4) ) ).
cnf(i_0_1157_049,axiom,
( X1 != X2
| esk6_3(X3,X4,X1) = esk6_3(X3,X4,X2) ) ).
cnf(i_0_1158_050,axiom,
( X1 != X2
| function_inverse(X1) = function_inverse(X2) ) ).
cnf(i_0_1159_051,axiom,
( X1 != X2
| esk85_2(X1,X3) = esk85_2(X2,X3) ) ).
cnf(i_0_1160_052,axiom,
( X1 != X2
| esk85_2(X3,X1) = esk85_2(X3,X2) ) ).
cnf(i_0_1161_053,axiom,
( X1 != X2
| esk86_2(X1,X3) = esk86_2(X2,X3) ) ).
cnf(i_0_1162_054,axiom,
( X1 != X2
| esk86_2(X3,X1) = esk86_2(X3,X2) ) ).
cnf(i_0_1163_055,axiom,
( X1 != X2
| esk84_2(X1,X3) = esk84_2(X2,X3) ) ).
cnf(i_0_1164_056,axiom,
( X1 != X2
| esk84_2(X3,X1) = esk84_2(X3,X2) ) ).
cnf(i_0_1165_057,axiom,
( X1 != X2
| esk83_2(X1,X3) = esk83_2(X2,X3) ) ).
cnf(i_0_1166_058,axiom,
( X1 != X2
| esk83_2(X3,X1) = esk83_2(X3,X2) ) ).
cnf(i_0_1167_059,axiom,
( X1 != X2
| esk29_3(X1,X3,X4) = esk29_3(X2,X3,X4) ) ).
cnf(i_0_1168_060,axiom,
( X1 != X2
| esk29_3(X3,X1,X4) = esk29_3(X3,X2,X4) ) ).
cnf(i_0_1169_061,axiom,
( X1 != X2
| esk29_3(X3,X4,X1) = esk29_3(X3,X4,X2) ) ).
cnf(i_0_1170_062,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_1171_063,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_1172_064,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_1173_065,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_1174_066,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_1175_067,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_1176_068,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_1177_069,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_1178_070,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_1179_071,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_1180_072,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_1181_073,axiom,
( X1 != X2
| esk48_2(X1,X3) = esk48_2(X2,X3) ) ).
cnf(i_0_1182_074,axiom,
( X1 != X2
| esk48_2(X3,X1) = esk48_2(X3,X2) ) ).
cnf(i_0_1183_075,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_1184_076,axiom,
( X1 != X2
| esk20_1(X1) = esk20_1(X2) ) ).
cnf(i_0_1185_077,axiom,
( X1 != X2
| esk80_2(X1,X3) = esk80_2(X2,X3) ) ).
cnf(i_0_1186_078,axiom,
( X1 != X2
| esk80_2(X3,X1) = esk80_2(X3,X2) ) ).
cnf(i_0_1187_079,axiom,
( X1 != X2
| esk24_2(X1,X3) = esk24_2(X2,X3) ) ).
cnf(i_0_1188_080,axiom,
( X1 != X2
| esk24_2(X3,X1) = esk24_2(X3,X2) ) ).
cnf(i_0_1189_081,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_1190_082,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_1191_083,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_1192_084,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_1193_085,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_1194_086,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_1195_087,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_1196_088,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_1197_089,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_1198_090,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_1199_091,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_1200_092,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_1201_093,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_1202_094,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_1203_095,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_1204_096,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_1205_097,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_1206,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_composition(X1,X2))
| in(unordered_pair(unordered_pair(esk57_5(X1,X2,relation_composition(X1,X2),X3,X4),X4),unordered_pair(esk57_5(X1,X2,relation_composition(X1,X2),X3,X4),esk57_5(X1,X2,relation_composition(X1,X2),X3,X4))),X2) ),
inference(equality_inference,[],[638]) ).
cnf(i_0_1207,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_composition(X1,X2))
| in(unordered_pair(unordered_pair(X3,esk57_5(X1,X2,relation_composition(X1,X2),X3,X4)),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[639]) ).
cnf(i_0_1208,plain,
( ~ relation(X1)
| ~ in(X2,relation_image(X1,X3))
| in(unordered_pair(unordered_pair(esk11_4(X1,X3,relation_image(X1,X3),X2),X2),unordered_pair(esk11_4(X1,X3,relation_image(X1,X3),X2),esk11_4(X1,X3,relation_image(X1,X3),X2))),X1) ),
inference(equality_inference,[],[640]) ).
cnf(i_0_1209,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk31_4(X2,X3,cartesian_product2(X2,X3),X1),esk32_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk31_4(X2,X3,cartesian_product2(X2,X3),X1),esk31_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[644]) ).
cnf(i_0_1210,plain,
( ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(unordered_pair(unordered_pair(X2,esk14_4(X1,X3,relation_inverse_image(X1,X3),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[650]) ).
cnf(i_0_1211,plain,
( ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| in(unordered_pair(unordered_pair(esk50_3(X1,relation_rng(X1),X2),X2),unordered_pair(esk50_3(X1,relation_rng(X1),X2),esk50_3(X1,relation_rng(X1),X2))),X1) ),
inference(equality_inference,[],[658]) ).
cnf(i_0_1212,plain,
( ~ relation(relation_composition(X1,X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| in(unordered_pair(unordered_pair(X3,X5),unordered_pair(X3,X3)),relation_composition(X1,X2))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X2) ),
inference(equality_inference,[],[672]) ).
cnf(i_0_1213,plain,
( ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,esk40_3(X1,relation_dom(X1),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[678]) ).
cnf(i_0_1214,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| in(esk5_4(X2,X3,relation_image(X2,X3),X1),relation_dom(X2)) ),
inference(equality_inference,[],[681]) ).
cnf(i_0_1215,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| X1 = apply(X2,esk5_4(X2,X3,relation_image(X2,X3),X1)) ),
inference(equality_inference,[],[682]) ).
cnf(i_0_1216,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| in(esk5_4(X2,X3,relation_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[683]) ).
cnf(i_0_1217,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| in(esk14_4(X2,X3,relation_inverse_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[684]) ).
cnf(i_0_1218,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| in(esk11_4(X2,X3,relation_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[685]) ).
cnf(i_0_1219,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk32_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[686]) ).
cnf(i_0_1220,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk31_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[687]) ).
cnf(i_0_1221,plain,
( ~ relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2)) ),
inference(equality_inference,[],[695]) ).
cnf(i_0_1222,plain,
( ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X2)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),relation_rng_restriction(X1,X2)) ),
inference(equality_inference,[],[696]) ).
cnf(i_0_1223,plain,
( ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_rng_restriction(X1,X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2) ),
inference(equality_inference,[],[697]) ).
cnf(i_0_1224,plain,
( ~ relation(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2))
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[698]) ).
cnf(i_0_1225,plain,
( ~ relation(X1)
| ~ relation(relation_inverse(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),relation_inverse(X1))
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[703]) ).
cnf(i_0_1226,plain,
( ~ relation(relation_inverse(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1)
| in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),relation_inverse(X1)) ),
inference(equality_inference,[],[704]) ).
cnf(i_0_1227,plain,
( ~ relation(X1)
| in(X2,relation_inverse_image(X1,X3))
| ~ in(X4,X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[714]) ).
cnf(i_0_1228,plain,
( ~ relation(X1)
| in(X2,relation_image(X1,X3))
| ~ in(X4,X3)
| ~ in(unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)),X1) ),
inference(equality_inference,[],[715]) ).
cnf(i_0_1229,plain,
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X2,X1))
| in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),relation_rng_restriction(X2,X1)) ),
inference(equality_inference,[],[725]) ).
cnf(i_0_1230,plain,
( ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| in(X3,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),relation_dom_restriction(X1,X2)) ),
inference(equality_inference,[],[726]) ).
cnf(i_0_1231,plain,
( ~ relation(identity_relation(X1))
| in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),identity_relation(X1)) ),
inference(equality_inference,[],[741]) ).
cnf(i_0_1232,plain,
( ~ relation(X1)
| in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[742]) ).
cnf(i_0_1233,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[743]) ).
cnf(i_0_1234,plain,
( ~ relation(identity_relation(X1))
| X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),identity_relation(X1)) ),
inference(equality_inference,[],[752]) ).
cnf(i_0_1235,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,[],[753]) ).
cnf(i_0_1236,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,[],[755]) ).
cnf(i_0_1237,plain,
( in(X1,set_meet(X2))
| ~ in(X1,esk21_3(X2,set_meet(X2),X1))
| X2 = empty_set ),
inference(equality_inference,[],[758]) ).
cnf(i_0_1238,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,apply(X1,X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[760]) ).
cnf(i_0_1239,plain,
X1 = X1,
inference(equality_inference,[],[762]) ).
cnf(i_0_1240,plain,
X1 = X1,
inference(equality_inference,[],[763]) ).
cnf(i_0_1241,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2)
| in(esk47_3(X2,relation_rng(X2),X1),relation_dom(X2)) ),
inference(equality_inference,[],[778]) ).
cnf(i_0_1242,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2)
| X1 = apply(X2,esk47_3(X2,relation_rng(X2),X1)) ),
inference(equality_inference,[],[780]) ).
cnf(i_0_1243,plain,
( ~ in(X1,union(X2))
| in(esk43_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[787]) ).
cnf(i_0_1244,plain,
( ~ in(X1,union(X2))
| in(X1,esk43_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[788]) ).
cnf(i_0_1245,plain,
( ~ relation(X1)
| ~ function(X1)
| in(X2,relation_inverse_image(X1,X3))
| ~ in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[791]) ).
cnf(i_0_1246,plain,
( in(X1,set_meet(X2))
| X2 = empty_set
| in(esk21_3(X2,set_meet(X2),X1),X2) ),
inference(equality_inference,[],[793]) ).
cnf(i_0_1247,plain,
( ~ relation(X1)
| ~ function(X1)
| X2 = X2
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[806]) ).
cnf(i_0_1248,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[815]) ).
cnf(i_0_1249,plain,
( X1 = X2
| X1 = X3
| X1 = X4
| ~ in(X1,unordered_triple(X2,X3,X4)) ),
inference(equality_inference,[],[820]) ).
cnf(i_0_1250,plain,
( ~ function(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| relation_dom(relation_dom_restriction(X1,X2)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) ),
inference(equality_inference,[],[823]) ).
cnf(i_0_1251,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3) ),
inference(equality_inference,[],[826]) ).
cnf(i_0_1252,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[845]) ).
cnf(i_0_1253,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(apply(X1,X2),X3) ),
inference(equality_inference,[],[846]) ).
cnf(i_0_1254,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[877]) ).
cnf(i_0_1255,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[891]) ).
cnf(i_0_1256,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[892]) ).
cnf(i_0_1257,plain,
( ~ in(X1,X2)
| in(X3,X1)
| ~ in(X3,set_meet(X2))
| X2 = empty_set ),
inference(equality_inference,[],[900]) ).
cnf(i_0_1258,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[905]) ).
cnf(i_0_1259,plain,
( ~ relation(X1)
| ~ function(X1)
| X1 = identity_relation(relation_dom(X1))
| in(esk80_2(relation_dom(X1),X1),relation_dom(X1)) ),
inference(equality_inference,[],[906]) ).
cnf(i_0_1260,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[907]) ).
cnf(i_0_1261,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[925]) ).
cnf(i_0_1262,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[926]) ).
cnf(i_0_1263,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[927]) ).
cnf(i_0_1264,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(equality_inference,[],[929]) ).
cnf(i_0_1265,plain,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,X2) = empty_set
| in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[931]) ).
cnf(i_0_1266,plain,
( ~ relation(function_inverse(X1))
| ~ function(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(function_inverse(X1)) = relation_rng(X1) ),
inference(equality_inference,[],[949]) ).
cnf(i_0_1267,plain,
( ~ relation(X1)
| ~ function(X1)
| in(X2,relation_dom(X1))
| empty_set = apply(X1,X2) ),
inference(equality_inference,[],[950]) ).
cnf(i_0_1268,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[953]) ).
cnf(i_0_1269,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[954]) ).
cnf(i_0_1270,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[955]) ).
cnf(i_0_1271,plain,
X1 = X1,
inference(equality_inference,[],[962]) ).
cnf(i_0_1272,plain,
X1 = X1,
inference(equality_inference,[],[963]) ).
cnf(i_0_1273,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[966]) ).
cnf(i_0_1274,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[967]) ).
cnf(i_0_1275,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[986]) ).
cnf(i_0_1276,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| relation_dom(identity_relation(X1)) = X1 ),
inference(equality_inference,[],[1028]) ).
cnf(i_0_1277,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[1030]) ).
cnf(i_0_1278,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[1032]) ).
cnf(i_0_1279,plain,
subset(X1,X1),
inference(equality_inference,[],[1050]) ).
cnf(i_0_1280,plain,
subset(X1,X1),
inference(equality_inference,[],[1051]) ).
cnf(i_0_1281,plain,
in(X1,unordered_pair(X1,X2)),
inference(scs_inference,[],[i_0_1064,i_0_887]) ).
cnf(i_0_1282,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_1064]) ).
cnf(i_0_1283,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_887]) ).
cnf(i_0_1284,plain,
in(X1,unordered_pair(X2,X1)),
inference(scs_inference,[],[i_0_1064,i_0_1282,i_0_887,i_0_888]) ).
cnf(i_0_1285,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_1064]) ).
cnf(i_0_1286,plain,
( ~ subset(unordered_pair(X1,X2),X3)
| in(X2,X3) ),
inference(rename_variables,[],[i_0_888]) ).
cnf(i_0_1287,plain,
~ in(esk75_0,set_difference(X1,set_difference(X1,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0))))),
inference(scs_inference,[],[i_0_819,i_0_1064,i_0_1282,i_0_887,i_0_888,i_0_1252]) ).
cnf(i_0_1288,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(rename_variables,[],[i_0_1252]) ).
cnf(i_0_1289,plain,
~ in(esk75_0,set_difference(set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)),X1)),
inference(scs_inference,[],[i_0_819,i_0_1064,i_0_1282,i_0_887,i_0_888,i_0_1252,i_0_1261]) ).
cnf(i_0_1290,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(rename_variables,[],[i_0_1261]) ).
cnf(i_0_1291,plain,
in(X1,set_union2(esk91_1(X1),X2)),
inference(scs_inference,[],[i_0_819,i_0_1045,i_0_1064,i_0_1282,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262]) ).
cnf(i_0_1292,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_1262]) ).
cnf(i_0_1293,plain,
in(X1,set_union2(X2,esk91_1(X1))),
inference(scs_inference,[],[i_0_819,i_0_1045,i_0_1064,i_0_1282,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263]) ).
cnf(i_0_1294,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_1263]) ).
cnf(i_0_1295,plain,
in(X1,powerset(X1)),
inference(scs_inference,[],[i_0_819,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274]) ).
cnf(i_0_1296,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(rename_variables,[],[i_0_1274]) ).
cnf(i_0_1297,plain,
element(complements_of_subsets(X1,esk70_1(powerset(X1))),powerset(powerset(X1))),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833]) ).
cnf(i_0_1298,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1299,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(rename_variables,[],[i_0_833]) ).
cnf(i_0_1300,plain,
element(meet_of_subsets(X1,esk70_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847]) ).
cnf(i_0_1301,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1302,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(meet_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_847]) ).
cnf(i_0_1303,plain,
element(union_of_subsets(X1,esk70_1(powerset(X1))),powerset(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848]) ).
cnf(i_0_1304,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1305,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(union_of_subsets(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_848]) ).
cnf(i_0_1306,plain,
complements_of_subsets(X1,complements_of_subsets(X1,esk70_1(powerset(X1)))) = esk70_1(powerset(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857]) ).
cnf(i_0_1307,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1308,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(rename_variables,[],[i_0_857]) ).
cnf(i_0_1309,plain,
element(subset_complement(X1,esk70_1(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882]) ).
cnf(i_0_1310,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(rename_variables,[],[i_0_882]) ).
cnf(i_0_1311,plain,
in(esk92_2(X1,X1),esk91_1(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1045,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883]) ).
cnf(i_0_1312,plain,
( ~ in(X1,esk91_1(X2))
| in(esk92_2(X2,X1),esk91_1(X2)) ),
inference(rename_variables,[],[i_0_883]) ).
cnf(i_0_1313,plain,
disjoint(empty_set,empty_set),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889]) ).
cnf(i_0_1314,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rename_variables,[],[i_0_994]) ).
cnf(i_0_1315,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_889]) ).
cnf(i_0_1316,plain,
meet_of_subsets(X1,esk70_1(powerset(X1))) = set_meet(esk70_1(powerset(X1))),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901]) ).
cnf(i_0_1317,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1318,plain,
( ~ element(X1,powerset(powerset(X2)))
| meet_of_subsets(X2,X1) = set_meet(X1) ),
inference(rename_variables,[],[i_0_901]) ).
cnf(i_0_1319,plain,
union_of_subsets(X1,esk70_1(powerset(X1))) = union(esk70_1(powerset(X1))),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902]) ).
cnf(i_0_1320,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1321,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,X1) = union(X1) ),
inference(rename_variables,[],[i_0_902]) ).
cnf(i_0_1322,plain,
subset_complement(X1,esk70_1(X1)) = set_difference(X1,esk70_1(X1)),
inference(scs_inference,[],[i_0_819,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930]) ).
cnf(i_0_1323,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(rename_variables,[],[i_0_930]) ).
cnf(i_0_1324,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941]) ).
cnf(i_0_1325,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_1278]) ).
cnf(i_0_1326,plain,
( in(esk81_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_941]) ).
cnf(i_0_1327,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942]) ).
cnf(i_0_1328,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_1278]) ).
cnf(i_0_1329,plain,
( in(esk81_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_942]) ).
cnf(i_0_1330,plain,
~ in(esk91_1(X1),X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970]) ).
cnf(i_0_1331,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_970]) ).
cnf(i_0_1332,plain,
subset(set_union2(empty_set,empty_set),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986]) ).
cnf(i_0_1333,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1334,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_986]) ).
cnf(i_0_1335,plain,
disjoint(X1,set_difference(X1,X1)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998]) ).
cnf(i_0_1336,plain,
( set_difference(X1,X2) != X1
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_998]) ).
cnf(i_0_1337,plain,
element(X1,esk91_1(X1)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006]) ).
cnf(i_0_1338,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_1006]) ).
cnf(i_0_1339,plain,
subset(X1,set_difference(X1,empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009]) ).
cnf(i_0_1340,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_1009]) ).
cnf(i_0_1341,plain,
~ in(X1,esk68_0),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021]) ).
cnf(i_0_1342,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_1021]) ).
cnf(i_0_1343,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032]) ).
cnf(i_0_1344,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1345,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_1032]) ).
cnf(i_0_1346,plain,
relation(set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033]) ).
cnf(i_0_1347,plain,
( in(esk20_1(X1),X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_1033]) ).
cnf(i_0_1348,plain,
in(esk25_1(unordered_pair(X1,X1)),unordered_pair(X1,X1)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038]) ).
cnf(i_0_1349,plain,
( X1 = empty_set
| in(esk25_1(X1),X1) ),
inference(rename_variables,[],[i_0_1038]) ).
cnf(i_0_1350,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1344,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050]) ).
cnf(i_0_1351,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_1050]) ).
cnf(i_0_1352,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051]) ).
cnf(i_0_1353,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_1051]) ).
cnf(i_0_1354,plain,
relation(esk67_0),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071]) ).
cnf(i_0_1355,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_1071]) ).
cnf(i_0_1356,plain,
~ in(X1,cartesian_product2(X2,empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219]) ).
cnf(i_0_1357,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_1278]) ).
cnf(i_0_1358,plain,
( in(esk32_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_1219]) ).
cnf(i_0_1359,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220]) ).
cnf(i_0_1360,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_1278]) ).
cnf(i_0_1361,plain,
( in(esk31_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(rename_variables,[],[i_0_1220]) ).
cnf(i_0_1362,plain,
~ in(X1,union(empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243]) ).
cnf(i_0_1363,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_1278]) ).
cnf(i_0_1364,plain,
( in(esk43_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(rename_variables,[],[i_0_1243]) ).
cnf(i_0_1365,plain,
~ in(X1,set_difference(X2,esk91_1(X1))),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258]) ).
cnf(i_0_1366,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(rename_variables,[],[i_0_1258]) ).
cnf(i_0_1367,plain,
~ in(unordered_pair(X1,X1),unordered_pair(empty_set,empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269]) ).
cnf(i_0_1368,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(rename_variables,[],[i_0_1269]) ).
cnf(i_0_1369,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110]) ).
cnf(i_0_1370,plain,
subset(esk70_1(X1),X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961]) ).
cnf(i_0_1371,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_961]) ).
cnf(i_0_1372,plain,
disjoint(set_difference(X1,X1),X1),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005]) ).
cnf(i_0_1373,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(rename_variables,[],[i_0_1005]) ).
cnf(i_0_1374,plain,
function(esk67_0),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072]) ).
cnf(i_0_1375,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_1072]) ).
cnf(i_0_1376,plain,
~ in(esk75_0,set_union2(set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)),set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)))),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190]) ).
cnf(i_0_1377,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1378,plain,
esk91_1(set_union2(unordered_triple(X1,X2,X3),unordered_triple(X1,X2,X3))) != X1,
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840]) ).
cnf(i_0_1379,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1380,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X2 ),
inference(rename_variables,[],[i_0_840]) ).
cnf(i_0_1381,plain,
esk91_1(set_union2(unordered_triple(X1,X2,X3),unordered_triple(X1,X2,X3))) != X2,
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841]) ).
cnf(i_0_1382,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1383,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X3 ),
inference(rename_variables,[],[i_0_841]) ).
cnf(i_0_1384,plain,
esk91_1(set_union2(unordered_triple(X1,X2,X3),unordered_triple(X1,X2,X3))) != X3,
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1382,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841,i_0_842]) ).
cnf(i_0_1385,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1386,plain,
( X1 != unordered_triple(X2,X3,X4)
| in(X5,X1)
| X5 != X4 ),
inference(rename_variables,[],[i_0_842]) ).
cnf(i_0_1387,plain,
~ in(esk75_0,esk70_1(set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)))),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1382,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841,i_0_842,i_0_904]) ).
cnf(i_0_1388,plain,
element(esk70_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_1029]) ).
cnf(i_0_1389,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,X1)
| in(X3,X2) ),
inference(rename_variables,[],[i_0_904]) ).
cnf(i_0_1390,plain,
~ in(esk75_0,set_difference(set_difference(set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)),X1),empty_set)),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1382,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1066,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841,i_0_842,i_0_904,i_0_925]) ).
cnf(i_0_1391,plain,
set_difference(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_1066]) ).
cnf(i_0_1392,plain,
( X1 != set_difference(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_925]) ).
cnf(i_0_1393,plain,
~ in(esk75_0,esk75_0),
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1382,i_0_1385,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1066,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841,i_0_842,i_0_904,i_0_925,i_0_926]) ).
cnf(i_0_1394,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_1063]) ).
cnf(i_0_1395,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_926]) ).
cnf(i_0_1396,plain,
$false,
inference(scs_inference,[],[i_0_819,i_0_1278,i_0_1325,i_0_1328,i_0_1357,i_0_1360,i_0_1063,i_0_1333,i_0_1344,i_0_1377,i_0_1379,i_0_1382,i_0_1385,i_0_1394,i_0_1026,i_0_1029,i_0_1298,i_0_1301,i_0_1304,i_0_1307,i_0_1317,i_0_1320,i_0_1045,i_0_1066,i_0_1037,i_0_994,i_0_1314,i_0_1004,i_0_1064,i_0_1282,i_0_1285,i_0_1101,i_0_1102,i_0_887,i_0_888,i_0_1252,i_0_1261,i_0_1262,i_0_1263,i_0_1274,i_0_833,i_0_847,i_0_848,i_0_857,i_0_882,i_0_883,i_0_889,i_0_901,i_0_902,i_0_930,i_0_941,i_0_942,i_0_970,i_0_986,i_0_998,i_0_1006,i_0_1009,i_0_1021,i_0_1032,i_0_1033,i_0_1038,i_0_1050,i_0_1051,i_0_1071,i_0_1219,i_0_1220,i_0_1243,i_0_1258,i_0_1269,i_0_1110,i_0_961,i_0_1005,i_0_1072,i_0_1190,i_0_840,i_0_841,i_0_842,i_0_904,i_0_925,i_0_926,i_0_927]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU230+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n001.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:51:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.56/1.66 % Version : CSE_E---1.7
% 0.56/1.66 % Problem : theBenchmark.p
% 0.56/1.66 % SZS status Theorem for theBenchmark.p
% 0.56/1.66 % SZS output start CNFRefutation
% See solution above
% 1.31/2.42 % Total time : 1.325s
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