%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU217+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 : n017.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 05:11:06 PM UTC 2026
% Result : Theorem 0.57s 1.67s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_215)
% 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(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(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(t35_funct_1,conjecture,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
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(d8_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(t43_subset_1,lemma,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(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(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(t54_subset_1,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(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(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(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(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(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(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(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(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(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(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(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(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(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_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_204,plain,
! [X698,X699] : ordered_pair(X698,X699) = unordered_pair(unordered_pair(X698,X699),singleton(X698)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_205,lemma,
! [X1031] : unordered_pair(X1031,X1031) = singleton(X1031),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(i_0_206,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_207,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_208,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_209,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_210,lemma,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
fof(i_0_211,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(i_0_212,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_213,plain,
! [X711,X712,X713,X714,X715,X717,X718,X719,X722] :
( ( in(ordered_pair(X714,esk47_5(X711,X712,X713,X714,X715)),X711)
| ~ in(ordered_pair(X714,X715),X713)
| X713 != relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) )
& ( in(ordered_pair(esk47_5(X711,X712,X713,X714,X715),X715),X712)
| ~ in(ordered_pair(X714,X715),X713)
| X713 != relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) )
& ( ~ in(ordered_pair(X717,X719),X711)
| ~ in(ordered_pair(X719,X718),X712)
| in(ordered_pair(X717,X718),X713)
| X713 != relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) )
& ( ~ in(ordered_pair(esk48_3(X711,X712,X713),esk49_3(X711,X712,X713)),X713)
| ~ in(ordered_pair(esk48_3(X711,X712,X713),X722),X711)
| ~ in(ordered_pair(X722,esk49_3(X711,X712,X713)),X712)
| X713 = relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) )
& ( in(ordered_pair(esk48_3(X711,X712,X713),esk50_3(X711,X712,X713)),X711)
| in(ordered_pair(esk48_3(X711,X712,X713),esk49_3(X711,X712,X713)),X713)
| X713 = relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) )
& ( in(ordered_pair(esk50_3(X711,X712,X713),esk49_3(X711,X712,X713)),X712)
| in(ordered_pair(esk48_3(X711,X712,X713),esk49_3(X711,X712,X713)),X713)
| X713 = relation_composition(X711,X712)
| ~ relation(X713)
| ~ relation(X712)
| ~ relation(X711) ) ),
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_214,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_204]) ).
cnf(i_0_215,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[i_0_205]) ).
fof(i_0_216,plain,
! [X523,X524,X525,X526,X528,X529,X530,X531,X533] :
( ( in(ordered_pair(esk7_4(X523,X524,X525,X526),X526),X523)
| ~ in(X526,X525)
| X525 != relation_image(X523,X524)
| ~ relation(X523) )
& ( in(esk7_4(X523,X524,X525,X526),X524)
| ~ in(X526,X525)
| X525 != relation_image(X523,X524)
| ~ relation(X523) )
& ( ~ in(ordered_pair(X529,X528),X523)
| ~ in(X529,X524)
| in(X528,X525)
| X525 != relation_image(X523,X524)
| ~ relation(X523) )
& ( ~ in(esk8_3(X523,X530,X531),X531)
| ~ in(ordered_pair(X533,esk8_3(X523,X530,X531)),X523)
| ~ in(X533,X530)
| X531 = relation_image(X523,X530)
| ~ relation(X523) )
& ( in(ordered_pair(esk9_3(X523,X530,X531),esk8_3(X523,X530,X531)),X523)
| in(esk8_3(X523,X530,X531),X531)
| X531 = relation_image(X523,X530)
| ~ relation(X523) )
& ( in(esk9_3(X523,X530,X531),X530)
| in(esk8_3(X523,X530,X531),X531)
| X531 = relation_image(X523,X530)
| ~ relation(X523) ) ),
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_217,plain,
! [X514,X515,X516,X517,X518,X519,X520] :
( ( in(X518,X514)
| ~ in(ordered_pair(X517,X518),X516)
| X516 != relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) )
& ( in(ordered_pair(X517,X518),X515)
| ~ in(ordered_pair(X517,X518),X516)
| X516 != relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) )
& ( ~ in(X520,X514)
| ~ in(ordered_pair(X519,X520),X515)
| in(ordered_pair(X519,X520),X516)
| X516 != relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) )
& ( ~ in(ordered_pair(esk5_3(X514,X515,X516),esk6_3(X514,X515,X516)),X516)
| ~ in(esk6_3(X514,X515,X516),X514)
| ~ in(ordered_pair(esk5_3(X514,X515,X516),esk6_3(X514,X515,X516)),X515)
| X516 = relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) )
& ( in(esk6_3(X514,X515,X516),X514)
| in(ordered_pair(esk5_3(X514,X515,X516),esk6_3(X514,X515,X516)),X516)
| X516 = relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) )
& ( in(ordered_pair(esk5_3(X514,X515,X516),esk6_3(X514,X515,X516)),X515)
| in(ordered_pair(esk5_3(X514,X515,X516),esk6_3(X514,X515,X516)),X516)
| X516 = relation_rng_restriction(X514,X515)
| ~ relation(X516)
| ~ relation(X515) ) ),
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_218,plain,
! [X505,X506,X507,X508,X509,X510,X511] :
( ( in(X508,X506)
| ~ in(ordered_pair(X508,X509),X507)
| X507 != relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) )
& ( in(ordered_pair(X508,X509),X505)
| ~ in(ordered_pair(X508,X509),X507)
| X507 != relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) )
& ( ~ in(X510,X506)
| ~ in(ordered_pair(X510,X511),X505)
| in(ordered_pair(X510,X511),X507)
| X507 != relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) )
& ( ~ in(ordered_pair(esk3_3(X505,X506,X507),esk4_3(X505,X506,X507)),X507)
| ~ in(esk3_3(X505,X506,X507),X506)
| ~ in(ordered_pair(esk3_3(X505,X506,X507),esk4_3(X505,X506,X507)),X505)
| X507 = relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) )
& ( in(esk3_3(X505,X506,X507),X506)
| in(ordered_pair(esk3_3(X505,X506,X507),esk4_3(X505,X506,X507)),X507)
| X507 = relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) )
& ( in(ordered_pair(esk3_3(X505,X506,X507),esk4_3(X505,X506,X507)),X505)
| in(ordered_pair(esk3_3(X505,X506,X507),esk4_3(X505,X506,X507)),X507)
| X507 = relation_dom_restriction(X505,X506)
| ~ relation(X507)
| ~ relation(X505) ) ),
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_219,plain,
! [X614,X615,X616,X617,X620,X621,X622,X623,X624,X625,X627,X628] :
( ( in(esk26_4(X614,X615,X616,X617),X614)
| ~ in(X617,X616)
| X616 != cartesian_product2(X614,X615) )
& ( in(esk27_4(X614,X615,X616,X617),X615)
| ~ in(X617,X616)
| X616 != cartesian_product2(X614,X615) )
& ( X617 = ordered_pair(esk26_4(X614,X615,X616,X617),esk27_4(X614,X615,X616,X617))
| ~ in(X617,X616)
| X616 != cartesian_product2(X614,X615) )
& ( ~ in(X621,X614)
| ~ in(X622,X615)
| X620 != ordered_pair(X621,X622)
| in(X620,X616)
| X616 != cartesian_product2(X614,X615) )
& ( ~ in(esk28_3(X623,X624,X625),X625)
| ~ in(X627,X623)
| ~ in(X628,X624)
| esk28_3(X623,X624,X625) != ordered_pair(X627,X628)
| X625 = cartesian_product2(X623,X624) )
& ( in(esk29_3(X623,X624,X625),X623)
| in(esk28_3(X623,X624,X625),X625)
| X625 = cartesian_product2(X623,X624) )
& ( in(esk30_3(X623,X624,X625),X624)
| in(esk28_3(X623,X624,X625),X625)
| X625 = cartesian_product2(X623,X624) )
& ( esk28_3(X623,X624,X625) = ordered_pair(esk29_3(X623,X624,X625),esk30_3(X623,X624,X625))
| in(esk28_3(X623,X624,X625),X625)
| X625 = cartesian_product2(X623,X624) ) ),
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_220,plain,
! [X535,X536,X537,X538,X540,X541,X542,X543,X545] :
( ( in(ordered_pair(X538,esk10_4(X535,X536,X537,X538)),X535)
| ~ in(X538,X537)
| X537 != relation_inverse_image(X535,X536)
| ~ relation(X535) )
& ( in(esk10_4(X535,X536,X537,X538),X536)
| ~ in(X538,X537)
| X537 != relation_inverse_image(X535,X536)
| ~ relation(X535) )
& ( ~ in(ordered_pair(X540,X541),X535)
| ~ in(X541,X536)
| in(X540,X537)
| X537 != relation_inverse_image(X535,X536)
| ~ relation(X535) )
& ( ~ in(esk11_3(X535,X542,X543),X543)
| ~ in(ordered_pair(esk11_3(X535,X542,X543),X545),X535)
| ~ in(X545,X542)
| X543 = relation_inverse_image(X535,X542)
| ~ relation(X535) )
& ( in(ordered_pair(esk11_3(X535,X542,X543),esk12_3(X535,X542,X543)),X535)
| in(esk11_3(X535,X542,X543),X543)
| X543 = relation_inverse_image(X535,X542)
| ~ relation(X535) )
& ( in(esk12_3(X535,X542,X543),X542)
| in(esk11_3(X535,X542,X543),X543)
| X543 = relation_inverse_image(X535,X542)
| ~ relation(X535) ) ),
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_221,plain,
! [X701,X702,X703,X704,X705,X706] :
( ( ~ in(ordered_pair(X703,X704),X702)
| in(ordered_pair(X704,X703),X701)
| X702 != relation_inverse(X701)
| ~ relation(X702)
| ~ relation(X701) )
& ( ~ in(ordered_pair(X706,X705),X701)
| in(ordered_pair(X705,X706),X702)
| X702 != relation_inverse(X701)
| ~ relation(X702)
| ~ relation(X701) )
& ( ~ in(ordered_pair(esk45_2(X701,X702),esk46_2(X701,X702)),X702)
| ~ in(ordered_pair(esk46_2(X701,X702),esk45_2(X701,X702)),X701)
| X702 = relation_inverse(X701)
| ~ relation(X702)
| ~ relation(X701) )
& ( in(ordered_pair(esk45_2(X701,X702),esk46_2(X701,X702)),X702)
| in(ordered_pair(esk46_2(X701,X702),esk45_2(X701,X702)),X701)
| X702 = relation_inverse(X701)
| ~ relation(X702)
| ~ relation(X701) ) ),
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_222,plain,
! [X586,X587,X588,X589,X590,X591] :
( ( ~ in(ordered_pair(X588,X589),X586)
| in(ordered_pair(X588,X589),X587)
| X586 != X587
| ~ relation(X587)
| ~ relation(X586) )
& ( ~ in(ordered_pair(X590,X591),X587)
| in(ordered_pair(X590,X591),X586)
| X586 != X587
| ~ relation(X587)
| ~ relation(X586) )
& ( ~ in(ordered_pair(esk22_2(X586,X587),esk23_2(X586,X587)),X586)
| ~ in(ordered_pair(esk22_2(X586,X587),esk23_2(X586,X587)),X587)
| X586 = X587
| ~ relation(X587)
| ~ relation(X586) )
& ( in(ordered_pair(esk22_2(X586,X587),esk23_2(X586,X587)),X586)
| in(ordered_pair(esk22_2(X586,X587),esk23_2(X586,X587)),X587)
| X586 = X587
| ~ relation(X587)
| ~ relation(X586) ) ),
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_223,lemma,
! [X873,X874,X875,X877] :
( ( in(esk63_3(X873,X874,X875),relation_dom(X875))
| ~ in(X873,relation_image(X875,X874))
| ~ relation(X875) )
& ( in(ordered_pair(esk63_3(X873,X874,X875),X873),X875)
| ~ in(X873,relation_image(X875,X874))
| ~ relation(X875) )
& ( in(esk63_3(X873,X874,X875),X874)
| ~ in(X873,relation_image(X875,X874))
| ~ relation(X875) )
& ( ~ in(X877,relation_dom(X875))
| ~ in(ordered_pair(X877,X873),X875)
| ~ in(X877,X874)
| in(X873,relation_image(X875,X874))
| ~ relation(X875) ) ),
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_224,plain,
! [X686,X687,X688,X690,X691,X692,X694] :
( ( ~ in(X688,X687)
| in(ordered_pair(esk42_3(X686,X687,X688),X688),X686)
| X687 != relation_rng(X686)
| ~ relation(X686) )
& ( ~ in(ordered_pair(X691,X690),X686)
| in(X690,X687)
| X687 != relation_rng(X686)
| ~ relation(X686) )
& ( ~ in(esk43_2(X686,X692),X692)
| ~ in(ordered_pair(X694,esk43_2(X686,X692)),X686)
| X692 = relation_rng(X686)
| ~ relation(X686) )
& ( in(esk43_2(X686,X692),X692)
| in(ordered_pair(esk44_2(X686,X692),esk43_2(X686,X692)),X686)
| X692 = relation_rng(X686)
| ~ relation(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)],[d5_relat_1])])])])])]) ).
fof(i_0_225,plain,
! [X495,X496,X497,X498,X499,X500] :
( ( in(X497,X495)
| ~ in(ordered_pair(X497,X498),X496)
| X496 != identity_relation(X495)
| ~ relation(X496) )
& ( X497 = X498
| ~ in(ordered_pair(X497,X498),X496)
| X496 != identity_relation(X495)
| ~ relation(X496) )
& ( ~ in(X499,X495)
| X499 != X500
| in(ordered_pair(X499,X500),X496)
| X496 != identity_relation(X495)
| ~ relation(X496) )
& ( ~ in(ordered_pair(esk1_2(X495,X496),esk2_2(X495,X496)),X496)
| ~ in(esk1_2(X495,X496),X495)
| esk1_2(X495,X496) != esk2_2(X495,X496)
| X496 = identity_relation(X495)
| ~ relation(X496) )
& ( in(esk1_2(X495,X496),X495)
| in(ordered_pair(esk1_2(X495,X496),esk2_2(X495,X496)),X496)
| X496 = identity_relation(X495)
| ~ relation(X496) )
& ( esk1_2(X495,X496) = esk2_2(X495,X496)
| in(ordered_pair(esk1_2(X495,X496),esk2_2(X495,X496)),X496)
| X496 = identity_relation(X495)
| ~ relation(X496) ) ),
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_226,plain,
! [X631,X632,X633,X634] :
( ( ~ subset(X631,X632)
| ~ in(ordered_pair(X633,X634),X631)
| in(ordered_pair(X633,X634),X632)
| ~ relation(X632)
| ~ relation(X631) )
& ( in(ordered_pair(esk31_2(X631,X632),esk32_2(X631,X632)),X631)
| subset(X631,X632)
| ~ relation(X632)
| ~ relation(X631) )
& ( ~ in(ordered_pair(esk31_2(X631,X632),esk32_2(X631,X632)),X632)
| subset(X631,X632)
| ~ relation(X632)
| ~ relation(X631) ) ),
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_227,plain,
! [X655,X656,X657,X659,X660,X661,X663] :
( ( ~ in(X657,X656)
| in(ordered_pair(X657,esk35_3(X655,X656,X657)),X655)
| X656 != relation_dom(X655)
| ~ relation(X655) )
& ( ~ in(ordered_pair(X659,X660),X655)
| in(X659,X656)
| X656 != relation_dom(X655)
| ~ relation(X655) )
& ( ~ in(esk36_2(X655,X661),X661)
| ~ in(ordered_pair(esk36_2(X655,X661),X663),X655)
| X661 = relation_dom(X655)
| ~ relation(X655) )
& ( in(esk36_2(X655,X661),X661)
| in(ordered_pair(esk36_2(X655,X661),esk37_2(X655,X661)),X655)
| X661 = relation_dom(X655)
| ~ relation(X655) ) ),
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_228,lemma,
! [X885,X886,X887,X889] :
( ( in(esk64_3(X885,X886,X887),relation_rng(X887))
| ~ in(X885,relation_inverse_image(X887,X886))
| ~ relation(X887) )
& ( in(ordered_pair(X885,esk64_3(X885,X886,X887)),X887)
| ~ in(X885,relation_inverse_image(X887,X886))
| ~ relation(X887) )
& ( in(esk64_3(X885,X886,X887),X886)
| ~ in(X885,relation_inverse_image(X887,X886))
| ~ relation(X887) )
& ( ~ in(X889,relation_rng(X887))
| ~ in(ordered_pair(X885,X889),X887)
| ~ in(X889,X886)
| in(X885,relation_inverse_image(X887,X886))
| ~ relation(X887) ) ),
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_229,plain,
! [X643,X644,X645,X646,X647,X648,X649,X650] :
( ( in(X646,X643)
| ~ in(X646,X645)
| X645 != set_intersection2(X643,X644) )
& ( in(X646,X644)
| ~ in(X646,X645)
| X645 != set_intersection2(X643,X644) )
& ( ~ in(X647,X643)
| ~ in(X647,X644)
| in(X647,X645)
| X645 != set_intersection2(X643,X644) )
& ( ~ in(esk34_3(X648,X649,X650),X650)
| ~ in(esk34_3(X648,X649,X650),X648)
| ~ in(esk34_3(X648,X649,X650),X649)
| X650 = set_intersection2(X648,X649) )
& ( in(esk34_3(X648,X649,X650),X648)
| in(esk34_3(X648,X649,X650),X650)
| X650 = set_intersection2(X648,X649) )
& ( in(esk34_3(X648,X649,X650),X649)
| in(esk34_3(X648,X649,X650),X650)
| X650 = set_intersection2(X648,X649) ) ),
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_230,lemma,
! [X998,X999] : set_difference(X998,set_difference(X998,X999)) = set_intersection2(X998,X999),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(i_0_231,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_232,lemma,
! [X1036,X1037,X1038,X1039] :
( ( in(X1036,X1038)
| ~ in(ordered_pair(X1036,X1037),relation_composition(identity_relation(X1038),X1039))
| ~ relation(X1039) )
& ( in(ordered_pair(X1036,X1037),X1039)
| ~ in(ordered_pair(X1036,X1037),relation_composition(identity_relation(X1038),X1039))
| ~ relation(X1039) )
& ( ~ in(X1036,X1038)
| ~ in(ordered_pair(X1036,X1037),X1039)
| in(ordered_pair(X1036,X1037),relation_composition(identity_relation(X1038),X1039))
| ~ relation(X1039) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t74_relat_1])])]) ).
fof(i_0_233,plain,
! [X547,X548,X551,X553,X554] :
( ( ~ relation(X547)
| ~ in(X548,X547)
| X548 = ordered_pair(esk13_2(X547,X548),esk14_2(X547,X548)) )
& ( in(esk15_1(X551),X551)
| relation(X551) )
& ( esk15_1(X551) != ordered_pair(X553,X554)
| relation(X551) ) ),
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_234,plain,
! [X652,X653,X654] :
( ( X654 != apply(X652,X653)
| in(ordered_pair(X653,X654),X652)
| ~ in(X653,relation_dom(X652))
| ~ relation(X652)
| ~ function(X652) )
& ( ~ in(ordered_pair(X653,X654),X652)
| X654 = apply(X652,X653)
| ~ in(X653,relation_dom(X652))
| ~ relation(X652)
| ~ function(X652) )
& ( X654 != apply(X652,X653)
| X654 = empty_set
| in(X653,relation_dom(X652))
| ~ relation(X652)
| ~ function(X652) )
& ( X654 != empty_set
| X654 = apply(X652,X653)
| in(X653,relation_dom(X652))
| ~ relation(X652)
| ~ function(X652) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_206])])])]) ).
fof(i_0_235,lemma,
! [X836,X837,X838,X839] :
( ( in(X836,X838)
| ~ in(ordered_pair(X836,X837),cartesian_product2(X838,X839)) )
& ( in(X837,X839)
| ~ in(ordered_pair(X836,X837),cartesian_product2(X838,X839)) )
& ( ~ in(X836,X838)
| ~ in(X837,X839)
| in(ordered_pair(X836,X837),cartesian_product2(X838,X839)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(i_0_236,lemma,
! [X809,X810,X811,X812] :
( ( in(X809,X811)
| ~ in(ordered_pair(X809,X810),cartesian_product2(X811,X812)) )
& ( in(X810,X812)
| ~ in(ordered_pair(X809,X810),cartesian_product2(X811,X812)) )
& ( ~ in(X809,X811)
| ~ in(X810,X812)
| in(ordered_pair(X809,X810),cartesian_product2(X811,X812)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_237,lemma,
! [X1053,X1054,X1055] :
( ( in(X1053,relation_dom(X1055))
| ~ in(ordered_pair(X1053,X1054),X1055)
| ~ relation(X1055)
| ~ function(X1055) )
& ( X1054 = apply(X1055,X1053)
| ~ in(ordered_pair(X1053,X1054),X1055)
| ~ relation(X1055)
| ~ function(X1055) )
& ( ~ in(X1053,relation_dom(X1055))
| X1054 != apply(X1055,X1053)
| in(ordered_pair(X1053,X1054),X1055)
| ~ relation(X1055)
| ~ function(X1055) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])]) ).
fof(i_0_238,lemma,
! [X935,X936,X937] :
( ( in(X935,relation_field(X937))
| ~ in(ordered_pair(X935,X936),X937)
| ~ relation(X937) )
& ( in(X936,relation_field(X937))
| ~ in(ordered_pair(X935,X936),X937)
| ~ relation(X937) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_relat_1])])]) ).
fof(i_0_239,lemma,
! [X908,X909,X910] :
( ( in(X908,relation_dom(X910))
| ~ in(ordered_pair(X908,X909),X910)
| ~ relation(X910) )
& ( in(X909,relation_rng(X910))
| ~ in(ordered_pair(X908,X909),X910)
| ~ relation(X910) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
fof(i_0_240,lemma,
! [X1016] :
( ~ relation(X1016)
| in(ordered_pair(esk71_1(X1016),esk72_1(X1016)),X1016)
| X1016 = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_207])])]) ).
fof(i_0_241,plain,
! [X760,X761] : ~ empty(ordered_pair(X760,X761)),
inference(variable_rename,[status(thm)],[i_0_208]) ).
fof(i_0_242,lemma,
! [X941,X942,X943,X944] :
( ( X941 = X943
| ordered_pair(X941,X942) != ordered_pair(X943,X944) )
& ( X942 = X944
| ordered_pair(X941,X942) != ordered_pair(X943,X944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
fof(i_0_243,lemma,
! [X923,X924,X925] :
( ~ subset(X923,X924)
| subset(set_intersection2(X923,X925),set_intersection2(X924,X925)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_xboole_1])]) ).
fof(i_0_244,lemma,
! [X994,X995] :
( ~ element(X995,powerset(powerset(X994)))
| X995 = empty_set
| subset_difference(X994,cast_to_subset(X994),union_of_subsets(X994,X995)) = meet_of_subsets(X994,complements_of_subsets(X994,X995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).
fof(i_0_245,plain,
! [X665] : cast_to_subset(X665) = X665,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(i_0_246,lemma,
! [X996,X997] :
( ~ element(X997,powerset(powerset(X996)))
| X997 = empty_set
| union_of_subsets(X996,complements_of_subsets(X996,X997)) = subset_difference(X996,cast_to_subset(X996),meet_of_subsets(X996,X997)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(i_0_247,lemma,
! [X1004,X1005,X1007,X1008,X1009] :
( ( disjoint(X1004,X1005)
| in(esk70_2(X1004,X1005),set_intersection2(X1004,X1005)) )
& ( ~ in(X1009,set_intersection2(X1007,X1008))
| ~ disjoint(X1007,X1008) ) ),
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_209])])])])]) ).
fof(i_0_248,lemma,
! [X880,X881] :
( ~ relation(X881)
| relation_image(X881,X880) = relation_image(X881,set_intersection2(relation_dom(X881),X880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_relat_1])]) ).
fof(i_0_249,lemma,
! [X899,X900,X901] :
( ~ subset(X899,X900)
| ~ subset(X899,X901)
| subset(X899,set_intersection2(X900,X901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_250,lemma,
! [X802,X803,X804] :
( ~ subset(X802,X803)
| in(X804,X802)
| subset(X802,set_difference(X803,singleton(X804))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(i_0_251,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_252,lemma,
! [X1033,X1034] :
( ~ subset(singleton(X1033),singleton(X1034))
| X1033 = X1034 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
fof(i_0_253,plain,
! [X568,X569,X570,X571,X572,X573] :
( ( ~ in(X570,X569)
| X570 = X568
| X569 != singleton(X568) )
& ( X571 != X568
| in(X571,X569)
| X569 != singleton(X568) )
& ( ~ in(esk19_2(X572,X573),X573)
| esk19_2(X572,X573) != X572
| X573 = singleton(X572) )
& ( in(esk19_2(X572,X573),X573)
| esk19_2(X572,X573) = X572
| X573 = singleton(X572) ) ),
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_254,plain,
! [X757,X758] :
( ~ relation(X757)
| ~ relation(X758)
| relation(set_intersection2(X757,X758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_relat_1])]) ).
fof(i_0_255,lemma,
! [X856,X857] :
( ~ relation(X857)
| relation_rng(relation_rng_restriction(X856,X857)) = set_intersection2(relation_rng(X857),X856) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_relat_1])]) ).
fof(i_0_256,lemma,
! [X1062,X1063] :
( ~ relation(X1063)
| relation_dom(relation_dom_restriction(X1063,X1062)) = set_intersection2(relation_dom(X1063),X1062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_relat_1])]) ).
fof(i_0_257,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_258,lemma,
! [X897,X898] : subset(set_intersection2(X897,X898),X897),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_259,lemma,
! [X1029,X1030] :
( ( set_difference(X1029,singleton(X1030)) != X1029
| ~ in(X1030,X1029) )
& ( in(X1030,X1029)
| set_difference(X1029,singleton(X1030)) = X1029 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_210])]) ).
fof(i_0_260,lemma,
! [X791,X792] :
( ~ disjoint(singleton(X791),X792)
| ~ in(X791,X792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
fof(i_0_261,lemma,
! [X963,X964] :
( ( ~ subset(X963,singleton(X964))
| X963 = empty_set
| X963 = singleton(X964) )
& ( X963 != empty_set
| subset(X963,singleton(X964)) )
& ( X963 != singleton(X964)
| subset(X963,singleton(X964)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(i_0_262,lemma,
! [X805,X806] :
( ( ~ subset(X805,singleton(X806))
| X805 = empty_set
| X805 = singleton(X806) )
& ( X805 != empty_set
| subset(X805,singleton(X806)) )
& ( X805 != singleton(X806)
| subset(X805,singleton(X806)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_263,plain,
! [X493,X494] : set_intersection2(X493,X494) = set_intersection2(X494,X493),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_264,lemma,
! [X956,X957] :
( ( ~ subset(singleton(X956),X957)
| in(X956,X957) )
& ( ~ in(X956,X957)
| subset(singleton(X956),X957) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(i_0_265,lemma,
! [X795,X796] :
( ( ~ subset(singleton(X795),X796)
| in(X795,X796) )
& ( ~ in(X795,X796)
| subset(singleton(X795),X796) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(i_0_266,plain,
! [X709,X710] :
( ( ~ disjoint(X709,X710)
| set_intersection2(X709,X710) = empty_set )
& ( set_intersection2(X709,X710) != empty_set
| disjoint(X709,X710) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_267,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_268,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_269,lemma,
! [X990,X991] :
( ~ in(X990,X991)
| set_union2(singleton(X990),X991) = X991 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])]) ).
fof(i_0_270,lemma,
! [X789,X790] :
( ~ in(X789,X790)
| set_union2(singleton(X789),X790) = X790 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).
fof(i_0_271,lemma,
! [X926,X927] :
( ~ subset(X926,X927)
| set_intersection2(X926,X927) = X926 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(i_0_272,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_273,lemma,
! [X793,X794] :
( in(X793,X794)
| disjoint(singleton(X793),X794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_211])]) ).
fof(i_0_274,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_275,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_276,plain,
! [X765] : ~ empty(singleton(X765)),
inference(variable_rename,[status(thm)],[i_0_212]) ).
fof(i_0_277,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_278,lemma,
! [X1059,X1060,X1061] :
( singleton(X1059) != unordered_pair(X1060,X1061)
| X1059 = X1060 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
fof(i_0_279,lemma,
! [X1079,X1080,X1081] :
( singleton(X1079) != unordered_pair(X1080,X1081)
| X1080 = X1081 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
fof(i_0_280,plain,
! [X1,X2] :
( proper_subset(X1,X2)
=> ~ proper_subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(i_0_281,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_282,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_283,plain,
! [X781] : set_intersection2(X781,X781) = X781,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_284,plain,
! [X928] : set_intersection2(X928,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_285,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_286,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
fof(i_0_287,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_288,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_289,negated_conjecture,
~ ! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t35_funct_1]) ).
fof(i_0_290,plain,
! [X1,X2] : ~ proper_subset(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(i_0_291,lemma,
! [X788] : singleton(X788) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_292,plain,
! [X731] : element(cast_to_subset(X731),powerset(X731)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(i_0_293,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_294,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_295,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
cnf(i_0_296,plain,
( in(ordered_pair(esk47_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_213]) ).
cnf(i_0_297,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_214,c_0_215]) ).
cnf(i_0_298,plain,
( in(ordered_pair(X1,esk47_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_213]) ).
cnf(i_0_299,plain,
( in(ordered_pair(esk7_4(X1,X2,X3,X4),X4),X1)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]) ).
cnf(i_0_300,plain,
( X3 = relation_composition(X1,X2)
| ~ in(ordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),X3)
| ~ in(ordered_pair(esk48_3(X1,X2,X3),X4),X1)
| ~ in(ordered_pair(X4,esk49_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_213]) ).
cnf(i_0_301,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ in(ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),X3)
| ~ in(esk6_3(X1,X2,X3),X1)
| ~ in(ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_217]) ).
cnf(i_0_302,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_218]) ).
cnf(i_0_303,plain,
( X1 = ordered_pair(esk26_4(X2,X3,X4,X1),esk27_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_219]) ).
cnf(i_0_304,plain,
( in(ordered_pair(esk50_3(X1,X2,X3),esk49_3(X1,X2,X3)),X2)
| in(ordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_213]) ).
cnf(i_0_305,plain,
( in(ordered_pair(esk48_3(X1,X2,X3),esk50_3(X1,X2,X3)),X1)
| in(ordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),X3)
| X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_213]) ).
cnf(i_0_306,plain,
( in(ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),X2)
| in(ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_217]) ).
cnf(i_0_307,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_218]) ).
cnf(i_0_308,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk11_3(X1,X2,X3),X3)
| ~ in(ordered_pair(esk11_3(X1,X2,X3),X4),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_220]) ).
cnf(i_0_309,plain,
( in(ordered_pair(X1,esk10_4(X2,X3,X4,X1)),X2)
| ~ in(X1,X4)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_220]) ).
cnf(i_0_310,plain,
( in(esk6_3(X1,X2,X3),X1)
| in(ordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),X3)
| X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_217]) ).
cnf(i_0_311,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_218]) ).
cnf(i_0_312,plain,
( in(ordered_pair(esk11_3(X1,X2,X3),esk12_3(X1,X2,X3)),X1)
| in(esk11_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_220]) ).
cnf(i_0_313,plain,
( in(ordered_pair(esk9_3(X1,X2,X3),esk8_3(X1,X2,X3)),X1)
| in(esk8_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]) ).
cnf(i_0_314,plain,
( X2 = relation_inverse(X1)
| ~ in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2)
| ~ in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_221]) ).
cnf(i_0_315,plain,
( X1 = X2
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1)
| ~ in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_222]) ).
cnf(i_0_316,lemma,
( in(ordered_pair(esk63_3(X1,X2,X3),X1),X3)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_223]) ).
cnf(i_0_317,plain,
( in(ordered_pair(esk42_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_224]) ).
cnf(i_0_318,plain,
( in(ordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),X2)
| in(ordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),X1)
| X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_221]) ).
cnf(i_0_319,plain,
( in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X1)
| in(ordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| X1 = X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_222]) ).
cnf(i_0_320,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(ordered_pair(X4,esk8_3(X1,X2,X3)),X1)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]) ).
cnf(i_0_321,plain,
( esk28_3(X1,X2,X3) = ordered_pair(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3))
| in(esk28_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]) ).
cnf(i_0_322,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_225]) ).
cnf(i_0_323,plain,
( subset(X1,X2)
| ~ in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_226]) ).
cnf(i_0_324,plain,
( X2 = relation_dom(X1)
| ~ in(esk36_2(X1,X2),X2)
| ~ in(ordered_pair(esk36_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_227]) ).
fof(i_0_325,plain,
! [X724,X725,X726,X727] :
( ( ~ in(X727,X726)
| in(subset_complement(X724,X727),X725)
| ~ element(X727,powerset(X724))
| X726 != complements_of_subsets(X724,X725)
| ~ element(X726,powerset(powerset(X724)))
| ~ element(X725,powerset(powerset(X724))) )
& ( ~ in(subset_complement(X724,X727),X725)
| in(X727,X726)
| ~ element(X727,powerset(X724))
| X726 != complements_of_subsets(X724,X725)
| ~ element(X726,powerset(powerset(X724)))
| ~ element(X725,powerset(powerset(X724))) )
& ( element(esk51_3(X724,X725,X726),powerset(X724))
| X726 = complements_of_subsets(X724,X725)
| ~ element(X726,powerset(powerset(X724)))
| ~ element(X725,powerset(powerset(X724))) )
& ( ~ in(esk51_3(X724,X725,X726),X726)
| ~ in(subset_complement(X724,esk51_3(X724,X725,X726)),X725)
| X726 = complements_of_subsets(X724,X725)
| ~ element(X726,powerset(powerset(X724)))
| ~ element(X725,powerset(powerset(X724))) )
& ( in(esk51_3(X724,X725,X726),X726)
| in(subset_complement(X724,esk51_3(X724,X725,X726)),X725)
| X726 = complements_of_subsets(X724,X725)
| ~ element(X726,powerset(powerset(X724)))
| ~ element(X725,powerset(powerset(X724))) ) ),
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_326,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_213]) ).
cnf(i_0_327,lemma,
( in(ordered_pair(X1,esk64_3(X1,X2,X3)),X3)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_228]) ).
cnf(i_0_328,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk34_3(X1,X2,X3),X3)
| ~ in(esk34_3(X1,X2,X3),X1)
| ~ in(esk34_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
cnf(i_0_329,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_230]) ).
cnf(i_0_330,plain,
( in(esk43_2(X1,X2),X2)
| in(ordered_pair(esk44_2(X1,X2),esk43_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_224]) ).
cnf(i_0_331,plain,
( in(esk36_2(X1,X2),X2)
| in(ordered_pair(esk36_2(X1,X2),esk37_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_227]) ).
cnf(i_0_332,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_225]) ).
cnf(i_0_333,plain,
( in(ordered_pair(X1,esk35_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_227]) ).
cnf(i_0_334,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_225]) ).
cnf(i_0_335,plain,
( in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_226]) ).
fof(i_0_336,plain,
! [X677,X678,X679,X680,X681,X682,X683,X684] :
( ( in(X680,X677)
| ~ in(X680,X679)
| X679 != set_difference(X677,X678) )
& ( ~ in(X680,X678)
| ~ in(X680,X679)
| X679 != set_difference(X677,X678) )
& ( ~ in(X681,X677)
| in(X681,X678)
| in(X681,X679)
| X679 != set_difference(X677,X678) )
& ( ~ in(esk41_3(X682,X683,X684),X684)
| ~ in(esk41_3(X682,X683,X684),X682)
| in(esk41_3(X682,X683,X684),X683)
| X684 = set_difference(X682,X683) )
& ( in(esk41_3(X682,X683,X684),X682)
| in(esk41_3(X682,X683,X684),X684)
| X684 = set_difference(X682,X683) )
& ( ~ in(esk41_3(X682,X683,X684),X683)
| in(esk41_3(X682,X683,X684),X684)
| X684 = set_difference(X682,X683) ) ),
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_231])])])])])]) ).
cnf(i_0_337,plain,
( X2 = relation_rng(X1)
| ~ in(esk43_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk43_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_224]) ).
cnf(i_0_338,plain,
( X3 = cartesian_product2(X1,X2)
| ~ in(esk28_3(X1,X2,X3),X3)
| ~ in(X4,X1)
| ~ in(X5,X2)
| esk28_3(X1,X2,X3) != ordered_pair(X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_219]) ).
cnf(i_0_339,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_232]) ).
cnf(i_0_340,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_232]) ).
cnf(i_0_341,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_218]) ).
cnf(i_0_342,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_217]) ).
cnf(i_0_343,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_217]) ).
cnf(i_0_344,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_218]) ).
cnf(i_0_345,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_226]) ).
fof(i_0_346,plain,
! [X605,X606,X607,X608,X609,X610,X611,X612] :
( ( ~ in(X608,X607)
| in(X608,X605)
| in(X608,X606)
| X607 != set_union2(X605,X606) )
& ( ~ in(X609,X605)
| in(X609,X607)
| X607 != set_union2(X605,X606) )
& ( ~ in(X609,X606)
| in(X609,X607)
| X607 != set_union2(X605,X606) )
& ( ~ in(esk25_3(X610,X611,X612),X610)
| ~ in(esk25_3(X610,X611,X612),X612)
| X612 = set_union2(X610,X611) )
& ( ~ in(esk25_3(X610,X611,X612),X611)
| ~ in(esk25_3(X610,X611,X612),X612)
| X612 = set_union2(X610,X611) )
& ( in(esk25_3(X610,X611,X612),X612)
| in(esk25_3(X610,X611,X612),X610)
| in(esk25_3(X610,X611,X612),X611)
| X612 = set_union2(X610,X611) ) ),
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_347,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_221]) ).
cnf(i_0_348,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_221]) ).
cnf(i_0_349,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_228]) ).
cnf(i_0_350,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_223]) ).
cnf(i_0_351,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),relation_composition(identity_relation(X2),X4))
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_232]) ).
cnf(i_0_352,plain,
( X2 = ordered_pair(esk13_2(X1,X2),esk14_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_233]) ).
cnf(i_0_353,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_220]) ).
cnf(i_0_354,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_216]) ).
fof(i_0_355,plain,
! [X596,X597,X598,X599,X600,X601,X602,X603] :
( ( ~ in(X599,X598)
| X599 = X596
| X599 = X597
| X598 != unordered_pair(X596,X597) )
& ( X600 != X596
| in(X600,X598)
| X598 != unordered_pair(X596,X597) )
& ( X600 != X597
| in(X600,X598)
| X598 != unordered_pair(X596,X597) )
& ( esk24_3(X601,X602,X603) != X601
| ~ in(esk24_3(X601,X602,X603),X603)
| X603 = unordered_pair(X601,X602) )
& ( esk24_3(X601,X602,X603) != X602
| ~ in(esk24_3(X601,X602,X603),X603)
| X603 = unordered_pair(X601,X602) )
& ( in(esk24_3(X601,X602,X603),X603)
| esk24_3(X601,X602,X603) = X601
| esk24_3(X601,X602,X603) = X602
| X603 = unordered_pair(X601,X602) ) ),
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_356,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_234]) ).
cnf(i_0_357,plain,
( in(esk34_3(X1,X2,X3),X1)
| in(esk34_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
cnf(i_0_358,plain,
( in(esk34_3(X1,X2,X3),X2)
| in(esk34_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
cnf(i_0_359,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_235]) ).
cnf(i_0_360,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_236]) ).
cnf(i_0_361,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_235]) ).
cnf(i_0_362,lemma,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_236]) ).
cnf(i_0_363,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_217]) ).
cnf(i_0_364,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_218]) ).
cnf(i_0_365,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_237]) ).
cnf(i_0_366,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != identity_relation(X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[i_0_225]) ).
cnf(i_0_367,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_227]) ).
cnf(i_0_368,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_224]) ).
cnf(i_0_369,lemma,
( X1 = apply(X2,X3)
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_237]) ).
cnf(i_0_370,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_238]) ).
cnf(i_0_371,lemma,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_238]) ).
cnf(i_0_372,lemma,
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_239]) ).
cnf(i_0_373,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_239]) ).
cnf(i_0_374,lemma,
( in(ordered_pair(esk71_1(X1),esk72_1(X1)),X1)
| X1 = empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_240]) ).
cnf(i_0_375,plain,
( X1 = X2
| ~ in(ordered_pair(X1,X2),X3)
| X3 != identity_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_225]) ).
fof(i_0_376,lemma,
! [X915,X916,X917] :
( ~ relation(X916)
| ~ function(X916)
| ~ relation(X917)
| ~ function(X917)
| ~ in(X915,relation_dom(relation_composition(X917,X916)))
| apply(relation_composition(X917,X916),X915) = apply(X916,apply(X917,X915)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(i_0_377,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_235]) ).
cnf(i_0_378,lemma,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_236]) ).
fof(i_0_379,plain,
! [X555,X556,X557,X558,X559,X561,X564,X565,X566,X567] :
( ( ~ in(X557,X556)
| ~ in(X558,X555)
| in(X557,X558)
| X556 != set_meet(X555)
| X555 = empty_set )
& ( in(esk16_3(X555,X556,X559),X555)
| in(X559,X556)
| X556 != set_meet(X555)
| X555 = empty_set )
& ( ~ in(X559,esk16_3(X555,X556,X559))
| in(X559,X556)
| X556 != set_meet(X555)
| X555 = empty_set )
& ( in(esk18_2(X555,X561),X555)
| ~ in(esk17_2(X555,X561),X561)
| X561 = set_meet(X555)
| X555 = empty_set )
& ( ~ in(esk17_2(X555,X561),esk18_2(X555,X561))
| ~ in(esk17_2(X555,X561),X561)
| X561 = set_meet(X555)
| X555 = empty_set )
& ( in(esk17_2(X555,X561),X561)
| ~ in(X564,X555)
| in(esk17_2(X555,X561),X564)
| X561 = set_meet(X555)
| X555 = empty_set )
& ( X566 != set_meet(X565)
| X566 = empty_set
| X565 != empty_set )
& ( X567 != empty_set
| X567 = set_meet(X565)
| X565 != 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_380,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_237]) ).
cnf(i_0_381,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_234]) ).
cnf(i_0_382,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_241]) ).
cnf(i_0_383,lemma,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_242]) ).
cnf(i_0_384,lemma,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_242]) ).
fof(i_0_385,lemma,
! [X911,X912,X913] :
( ( in(X911,relation_dom(X913))
| ~ in(X911,relation_dom(relation_composition(X913,X912)))
| ~ relation(X913)
| ~ function(X913)
| ~ relation(X912)
| ~ function(X912) )
& ( in(apply(X913,X911),relation_dom(X912))
| ~ in(X911,relation_dom(relation_composition(X913,X912)))
| ~ relation(X913)
| ~ function(X913)
| ~ relation(X912)
| ~ function(X912) )
& ( ~ in(X911,relation_dom(X913))
| ~ in(apply(X913,X911),relation_dom(X912))
| in(X911,relation_dom(relation_composition(X913,X912)))
| ~ relation(X913)
| ~ function(X913)
| ~ relation(X912)
| ~ function(X912) ) ),
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_386,lemma,
( subset(set_intersection2(X1,X3),set_intersection2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_243]) ).
fof(i_0_387,plain,
! [X742,X743,X744] :
( ~ element(X743,powerset(X742))
| ~ element(X744,powerset(X742))
| element(subset_difference(X742,X743,X744),powerset(X742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
cnf(i_0_388,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_219]) ).
cnf(i_0_389,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_225]) ).
cnf(i_0_390,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_244]) ).
cnf(i_0_391,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_245]) ).
cnf(i_0_392,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_246]) ).
cnf(i_0_393,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
fof(i_0_394,plain,
! [X666,X667,X668,X670,X671,X672,X673,X675] :
( ( in(X668,esk38_3(X666,X667,X668))
| ~ in(X668,X667)
| X667 != union(X666) )
& ( in(esk38_3(X666,X667,X668),X666)
| ~ in(X668,X667)
| X667 != union(X666) )
& ( ~ in(X670,X671)
| ~ in(X671,X666)
| in(X670,X667)
| X667 != union(X666) )
& ( ~ in(esk39_2(X672,X673),X673)
| ~ in(esk39_2(X672,X673),X675)
| ~ in(X675,X672)
| X673 = union(X672) )
& ( in(esk39_2(X672,X673),esk40_2(X672,X673))
| in(esk39_2(X672,X673),X673)
| X673 = union(X672) )
& ( in(esk40_2(X672,X673),X672)
| in(esk39_2(X672,X673),X673)
| X673 = union(X672) ) ),
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_395,lemma,
( relation_image(X1,X2) = relation_image(X1,set_intersection2(relation_dom(X1),X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_248]) ).
fof(i_0_396,lemma,
! [X977,X978,X979] :
( ( ~ disjoint(X978,X979)
| subset(X978,subset_complement(X977,X979))
| ~ element(X979,powerset(X977))
| ~ element(X978,powerset(X977)) )
& ( ~ subset(X978,subset_complement(X977,X979))
| disjoint(X978,X979)
| ~ element(X979,powerset(X977))
| ~ element(X978,powerset(X977)) ) ),
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_397,lemma,
! [X844,X845,X846] :
( ( in(X844,X845)
| ~ in(X844,relation_rng(relation_rng_restriction(X845,X846)))
| ~ relation(X846) )
& ( in(X844,relation_rng(X846))
| ~ in(X844,relation_rng(relation_rng_restriction(X845,X846)))
| ~ relation(X846) )
& ( ~ in(X844,X845)
| ~ in(X844,relation_rng(X846))
| in(X844,relation_rng(relation_rng_restriction(X845,X846)))
| ~ relation(X846) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t115_relat_1])])]) ).
fof(i_0_398,lemma,
! [X1046,X1047,X1048] :
( ( in(X1046,X1047)
| ~ in(X1046,relation_dom(relation_dom_restriction(X1048,X1047)))
| ~ relation(X1048) )
& ( in(X1046,relation_dom(X1048))
| ~ in(X1046,relation_dom(relation_dom_restriction(X1048,X1047)))
| ~ relation(X1048) )
& ( ~ in(X1046,X1047)
| ~ in(X1046,relation_dom(X1048))
| in(X1046,relation_dom(relation_dom_restriction(X1048,X1047)))
| ~ relation(X1048) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])]) ).
fof(i_0_399,lemma,
! [X918,X919,X920] :
( ~ relation(X919)
| ~ function(X919)
| ~ relation(X920)
| ~ function(X920)
| ~ in(X918,relation_dom(X919))
| apply(relation_composition(X919,X920),X918) = apply(X920,apply(X919,X918)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(i_0_400,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_249]) ).
fof(i_0_401,plain,
! [X830,X831,X832] :
( ~ element(X831,powerset(X830))
| ~ element(X832,powerset(X830))
| subset_difference(X830,X831,X832) = set_difference(X831,X832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(i_0_402,lemma,
( disjoint(X1,X2)
| in(esk70_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_247]) ).
fof(i_0_403,plain,
! [X579,X580,X581,X582,X583,X584] :
( ( ~ in(X581,X580)
| subset(X581,X579)
| X580 != powerset(X579) )
& ( ~ subset(X582,X579)
| in(X582,X580)
| X580 != powerset(X579) )
& ( ~ in(esk21_2(X583,X584),X584)
| ~ subset(esk21_2(X583,X584),X583)
| X584 = powerset(X583) )
& ( in(esk21_2(X583,X584),X584)
| subset(esk21_2(X583,X584),X583)
| X584 = powerset(X583) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_zfmisc_1])])])])])]) ).
cnf(i_0_404,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_250]) ).
fof(i_0_405,plain,
! [X931,X932] :
( ( ~ in(esk65_2(X931,X932),X931)
| ~ in(esk65_2(X931,X932),X932)
| X931 = X932 )
& ( in(esk65_2(X931,X932),X931)
| in(esk65_2(X931,X932),X932)
| X931 = X932 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(i_0_406,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
fof(i_0_407,lemma,
! [X1013,X1014,X1015] :
( ~ element(X1015,powerset(X1013))
| ~ in(X1014,subset_complement(X1013,X1015))
| ~ in(X1014,X1015) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])]) ).
cnf(i_0_408,plain,
( relation(X1)
| esk15_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_233]) ).
fof(i_0_409,lemma,
! [X945,X946,X947] :
( ( relation_dom(X946) = X945
| X946 != identity_relation(X945)
| ~ relation(X946)
| ~ function(X946) )
& ( ~ in(X947,X945)
| apply(X946,X947) = X947
| X946 != identity_relation(X945)
| ~ relation(X946)
| ~ function(X946) )
& ( in(esk66_2(X945,X946),X945)
| relation_dom(X946) != X945
| X946 = identity_relation(X945)
| ~ relation(X946)
| ~ function(X946) )
& ( apply(X946,esk66_2(X945,X946)) != esk66_2(X945,X946)
| relation_dom(X946) != X945
| X946 = identity_relation(X945)
| ~ relation(X946)
| ~ function(X946) ) ),
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_410,lemma,
! [X858,X859,X860,X861] :
( ~ subset(X858,X859)
| ~ subset(X860,X861)
| subset(cartesian_product2(X858,X860),cartesian_product2(X859,X861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(i_0_411,lemma,
! [X1010,X1011,X1012] :
( X1010 = empty_set
| ~ element(X1011,powerset(X1010))
| ~ element(X1012,X1010)
| in(X1012,X1011)
| in(X1012,subset_complement(X1010,X1011)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_251])])]) ).
fof(i_0_412,plain,
! [X747,X748] :
( ~ element(X748,powerset(powerset(X747)))
| element(complements_of_subsets(X747,X748),powerset(powerset(X747))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
cnf(i_0_413,lemma,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_252]) ).
cnf(i_0_414,plain,
( X2 = singleton(X1)
| ~ in(esk19_2(X1,X2),X2)
| esk19_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
cnf(i_0_415,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
cnf(i_0_416,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_229]) ).
fof(i_0_417,plain,
! [X740,X741] :
( ~ element(X741,powerset(powerset(X740)))
| element(meet_of_subsets(X740,X741),powerset(X740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(i_0_418,plain,
! [X737,X738] :
( ~ element(X738,powerset(powerset(X737)))
| element(union_of_subsets(X737,X738),powerset(X737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(i_0_419,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_254]) ).
fof(i_0_420,lemma,
! [X894,X895,X896] :
( ~ relation(X896)
| ~ subset(X894,X895)
| subset(relation_inverse_image(X896,X894),relation_inverse_image(X896,X895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t178_relat_1])]) ).
cnf(i_0_421,lemma,
( relation_rng(relation_rng_restriction(X2,X1)) = set_intersection2(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_255]) ).
cnf(i_0_422,lemma,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_256]) ).
fof(i_0_423,plain,
! [X1071,X1073,X1074,X1075,X1077,X1078] :
( in(X1071,esk73_1(X1071))
& ( ~ in(X1073,esk73_1(X1071))
| ~ subset(X1074,X1073)
| in(X1074,esk73_1(X1071)) )
& ( in(esk74_2(X1071,X1075),esk73_1(X1071))
| ~ in(X1075,esk73_1(X1071)) )
& ( ~ subset(X1077,X1075)
| in(X1077,esk74_2(X1071,X1075))
| ~ in(X1075,esk73_1(X1071)) )
& ( ~ subset(X1078,esk73_1(X1071))
| are_equipotent(X1078,esk73_1(X1071))
| in(X1078,esk73_1(X1071)) ) ),
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_257])])])])]) ).
fof(i_0_424,lemma,
! [X982,X983] :
( ~ relation(X982)
| ~ relation(X983)
| subset(relation_rng(relation_composition(X982,X983)),relation_rng(X983)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_relat_1])])]) ).
fof(i_0_425,lemma,
! [X980,X981] :
( ~ relation(X980)
| ~ relation(X981)
| subset(relation_dom(relation_composition(X980,X981)),relation_dom(X980)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_relat_1])])]) ).
fof(i_0_426,plain,
! [X785,X786] :
( ~ element(X786,powerset(powerset(X785)))
| complements_of_subsets(X785,complements_of_subsets(X785,X786)) = X786 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(i_0_427,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_258]) ).
fof(i_0_428,lemma,
! [X992,X993] :
( ~ relation(X992)
| ~ relation(X993)
| ~ subset(relation_dom(X992),relation_rng(X993))
| relation_rng(relation_composition(X993,X992)) = relation_rng(X992) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).
fof(i_0_429,lemma,
! [X986,X987] :
( ~ relation(X986)
| ~ relation(X987)
| ~ subset(relation_rng(X986),relation_dom(X987))
| relation_dom(relation_composition(X986,X987)) = relation_dom(X986) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
fof(i_0_430,lemma,
! [X938,X939,X940] :
( ~ subset(X938,X939)
| subset(set_difference(X938,X940),set_difference(X939,X940)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
fof(i_0_431,lemma,
! [X853,X854,X855] :
( ( subset(cartesian_product2(X853,X855),cartesian_product2(X854,X855))
| ~ subset(X853,X854) )
& ( subset(cartesian_product2(X855,X853),cartesian_product2(X855,X854))
| ~ subset(X853,X854) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
cnf(i_0_432,lemma,
( set_difference(X1,singleton(X2)) != X1
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
fof(i_0_433,lemma,
! [X870,X871,X872] :
( ~ relation(X872)
| relation_dom_restriction(relation_rng_restriction(X870,X872),X871) = relation_rng_restriction(X870,relation_dom_restriction(X872,X871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t140_relat_1])]) ).
cnf(i_0_434,lemma,
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_260]) ).
fof(i_0_435,lemma,
! [X1056,X1057,X1058] :
( ~ subset(X1056,X1057)
| ~ subset(X1058,X1057)
| subset(set_union2(X1056,X1058),X1057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_436,lemma,
! [X958,X959,X960] :
( ( in(X958,X960)
| ~ subset(unordered_pair(X958,X959),X960) )
& ( in(X959,X960)
| ~ subset(unordered_pair(X958,X959),X960) )
& ( ~ in(X958,X960)
| ~ in(X959,X960)
| subset(unordered_pair(X958,X959),X960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(i_0_437,lemma,
! [X851,X852] :
( ~ relation(X852)
| subset(relation_rng(relation_rng_restriction(X851,X852)),relation_rng(X852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_relat_1])]) ).
fof(i_0_438,lemma,
! [X1068,X1069] :
( ~ relation(X1069)
| subset(relation_rng(relation_dom_restriction(X1069,X1068)),relation_rng(X1069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t99_relat_1])]) ).
fof(i_0_439,lemma,
! [X813,X814] :
( ( in(esk53_2(X813,X814),X813)
| element(X813,powerset(X814)) )
& ( ~ in(esk53_2(X813,X814),X814)
| element(X813,powerset(X814)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l71_subset_1])])])]) ).
cnf(i_0_440,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_441,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_262]) ).
cnf(i_0_442,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_263]) ).
fof(i_0_443,lemma,
! [X847,X848] :
( ~ relation(X848)
| subset(relation_rng(relation_rng_restriction(X847,X848)),X847) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t116_relat_1])]) ).
fof(i_0_444,plain,
! [X732,X733] :
( ~ element(X733,powerset(X732))
| element(subset_complement(X732,X733),powerset(X732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(i_0_445,plain,
! [X637,X638,X639,X640,X641] :
( ( ~ subset(X637,X638)
| ~ in(X639,X637)
| in(X639,X638) )
& ( in(esk33_2(X640,X641),X640)
| subset(X640,X641) )
& ( ~ in(esk33_2(X640,X641),X641)
| subset(X640,X641) ) ),
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_446,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_264]) ).
cnf(i_0_447,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_265]) ).
cnf(i_0_448,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_266]) ).
fof(i_0_449,lemma,
! [X988,X989] :
( ~ element(X989,powerset(powerset(X988)))
| X989 = empty_set
| complements_of_subsets(X988,X989) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(i_0_450,lemma,
! [X864,X866,X867,X868,X869] :
( in(X864,esk62_1(X864))
& ( ~ in(X866,esk62_1(X864))
| ~ subset(X867,X866)
| in(X867,esk62_1(X864)) )
& ( ~ in(X868,esk62_1(X864))
| in(powerset(X868),esk62_1(X864)) )
& ( ~ subset(X869,esk62_1(X864))
| are_equipotent(X869,esk62_1(X864))
| in(X869,esk62_1(X864)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_267])])])]) ).
fof(i_0_451,plain,
! [X782,X783] :
( ~ element(X783,powerset(X782))
| subset_complement(X782,subset_complement(X782,X783)) = X783 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(i_0_452,lemma,
! [X914] :
( ~ relation(X914)
| subset(X914,cartesian_product2(relation_dom(X914),relation_rng(X914))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
cnf(i_0_453,plain,
( in(esk19_2(X1,X2),X2)
| esk19_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
fof(i_0_454,plain,
! [X828,X829] :
( ~ element(X829,powerset(powerset(X828)))
| meet_of_subsets(X828,X829) = set_meet(X829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])]) ).
fof(i_0_455,plain,
! [X826,X827] :
( ~ element(X827,powerset(powerset(X826)))
| union_of_subsets(X826,X827) = union(X827) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(i_0_456,plain,
! [X1001,X1002,X1003] :
( ~ in(X1001,X1002)
| ~ element(X1002,powerset(X1003))
| element(X1001,X1003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_457,lemma,
! [X799,X800,X801] :
( ~ element(X800,powerset(X799))
| ~ in(X801,X800)
| in(X801,X799) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
fof(i_0_458,lemma,
! [X968,X969,X971,X972,X973] :
( ( in(esk69_2(X968,X969),X968)
| disjoint(X968,X969) )
& ( in(esk69_2(X968,X969),X969)
| disjoint(X968,X969) )
& ( ~ in(X973,X971)
| ~ in(X973,X972)
| ~ disjoint(X971,X972) ) ),
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_268])])])])])]) ).
fof(i_0_459,lemma,
! [X883,X884] :
( ~ relation(X883)
| ~ relation(X884)
| relation_rng(relation_composition(X883,X884)) = relation_image(X884,relation_rng(X883)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t160_relat_1])])]) ).
cnf(i_0_460,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_461,lemma,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_262]) ).
cnf(i_0_462,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_269]) ).
cnf(i_0_463,lemma,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_270]) ).
cnf(i_0_464,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_271]) ).
fof(i_0_465,lemma,
! [X984,X985] :
( ~ subset(X984,X985)
| X985 = set_union2(X984,set_difference(X985,X984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t45_xboole_1])]) ).
fof(i_0_466,lemma,
! [X921,X922] :
( ( subset(relation_dom(X921),relation_dom(X922))
| ~ subset(X921,X922)
| ~ relation(X922)
| ~ relation(X921) )
& ( subset(relation_rng(X921),relation_rng(X922))
| ~ subset(X921,X922)
| ~ relation(X922)
| ~ relation(X921) ) ),
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_467,lemma,
! [X892,X893] :
( ~ relation(X893)
| X892 = empty_set
| ~ subset(X892,relation_rng(X893))
| relation_inverse_image(X893,X892) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t174_relat_1])]) ).
cnf(i_0_468,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_264]) ).
cnf(i_0_469,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_265]) ).
cnf(i_0_470,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_266]) ).
fof(i_0_471,plain,
! [X1019,X1020,X1021] :
( ~ in(X1019,X1020)
| ~ element(X1020,powerset(X1021))
| ~ empty(X1021) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_472,plain,
! [X696,X697] :
( ~ element(X697,powerset(X696))
| subset_complement(X696,X697) = set_difference(X696,X697) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(i_0_473,lemma,
! [X1024,X1025,X1026] :
( ~ subset(X1024,X1025)
| ~ disjoint(X1025,X1026)
| disjoint(X1024,X1026) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(i_0_474,lemma,
! [X905,X906,X907] :
( ~ subset(X905,X906)
| ~ subset(X906,X907)
| subset(X905,X907) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_475,plain,
! [X755,X756] :
( ( relation(relation_composition(X755,X756))
| ~ relation(X755)
| ~ function(X755)
| ~ relation(X756)
| ~ function(X756) )
& ( function(relation_composition(X755,X756))
| ~ relation(X755)
| ~ function(X755)
| ~ relation(X756)
| ~ function(X756) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(i_0_476,plain,
! [X772,X773] :
( empty(X772)
| empty(X773)
| ~ empty(cartesian_product2(X772,X773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_272])]) ).
cnf(i_0_477,lemma,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_259]) ).
cnf(i_0_478,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_273]) ).
fof(i_0_479,lemma,
! [X975,X976] : set_difference(set_union2(X975,X976),X976) = set_difference(X975,X976),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(i_0_480,lemma,
! [X961,X962] : set_union2(X961,set_difference(X962,X961)) = set_union2(X961,X962),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(i_0_481,lemma,
! [X890,X891] :
( ~ relation(X891)
| subset(relation_inverse_image(X891,X890),relation_dom(X891)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t167_relat_1])]) ).
fof(i_0_482,lemma,
! [X878,X879] :
( ~ relation(X879)
| subset(relation_image(X879,X878),relation_rng(X879)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_relat_1])]) ).
fof(i_0_483,plain,
! [X766,X767] :
( empty(X766)
| ~ empty(set_union2(X766,X767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_274])]) ).
fof(i_0_484,plain,
! [X770,X771] :
( empty(X770)
| ~ empty(set_union2(X771,X770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_275])]) ).
cnf(i_0_485,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
fof(i_0_486,lemma,
! [X840,X841,X842,X843] :
( unordered_pair(X840,X841) != unordered_pair(X842,X843)
| X840 = X842
| X840 = X843 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(i_0_487,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_276]) ).
fof(i_0_488,plain,
! [X768,X769] : ~ empty(unordered_pair(X768,X769)),
inference(variable_rename,[status(thm)],[i_0_277]) ).
fof(i_0_489,plain,
! [X503,X504] :
( ( subset(X503,X504)
| X503 != X504 )
& ( subset(X504,X503)
| X503 != X504 )
& ( ~ subset(X503,X504)
| ~ subset(X504,X503)
| X503 = X504 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_490,lemma,
! [X849,X850] :
( ~ relation(X850)
| subset(relation_rng_restriction(X849,X850),X850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_relat_1])]) ).
fof(i_0_491,lemma,
! [X1049,X1050] :
( ~ relation(X1050)
| subset(relation_dom_restriction(X1050,X1049),X1050) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t88_relat_1])]) ).
fof(i_0_492,plain,
! [X966,X967] :
( ( ~ element(X966,powerset(X967))
| subset(X966,X967) )
& ( ~ subset(X966,X967)
| element(X966,powerset(X967)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(i_0_493,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_278]) ).
cnf(i_0_494,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_279]) ).
fof(i_0_495,lemma,
! [X1022,X1023] :
( ~ subset(X1022,X1023)
| ~ proper_subset(X1023,X1022) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t60_xboole_1])]) ).
fof(i_0_496,plain,
! [X485,X486] :
( ~ proper_subset(X485,X486)
| ~ proper_subset(X486,X485) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_280])]) ).
fof(i_0_497,plain,
! [X483,X484] :
( ~ in(X483,X484)
| ~ in(X484,X483) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_281])]) ).
fof(i_0_498,plain,
! [X735,X736] :
( ~ relation(X735)
| ~ relation(X736)
| relation(relation_composition(X735,X736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(i_0_499,plain,
! [X778,X779] :
( ( empty(relation_composition(X778,X779))
| ~ empty(X778)
| ~ relation(X779) )
& ( relation(relation_composition(X778,X779))
| ~ empty(X778)
| ~ relation(X779) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_relat_1])])]) ).
fof(i_0_500,plain,
! [X753,X754] :
( ( empty(relation_composition(X754,X753))
| ~ empty(X753)
| ~ relation(X754) )
& ( relation(relation_composition(X754,X753))
| ~ empty(X753)
| ~ relation(X754) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_relat_1])])]) ).
fof(i_0_501,plain,
! [X763,X764] :
( ~ relation(X763)
| ~ relation(X764)
| relation(set_union2(X763,X764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_502,lemma,
! [X1064,X1065] :
( ~ in(X1064,X1065)
| subset(X1064,union(X1065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
fof(i_0_503,lemma,
! [X807,X808] :
( ~ in(X807,X808)
| subset(X807,union(X808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(i_0_504,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_261]) ).
cnf(i_0_505,lemma,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_262]) ).
cnf(i_0_506,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_253]) ).
fof(i_0_507,plain,
! [X594,X595] :
( ( ~ element(X595,X594)
| in(X595,X594)
| empty(X594) )
& ( ~ in(X595,X594)
| element(X595,X594)
| empty(X594) )
& ( ~ element(X595,X594)
| empty(X595)
| ~ empty(X594) )
& ( ~ empty(X595)
| element(X595,X594)
| ~ empty(X594) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_282])])]) ).
fof(i_0_508,plain,
! [X929,X930] :
( ~ element(X929,X930)
| empty(X930)
| in(X929,X930) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_509,lemma,
! [X1066,X1067] :
( ~ relation(X1067)
| relation_dom_restriction(X1067,X1066) = relation_composition(identity_relation(X1066),X1067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t94_relat_1])]) ).
cnf(i_0_510,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_283]) ).
fof(i_0_511,lemma,
! [X951,X952] : subset(set_difference(X951,X952),X951),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(i_0_512,lemma,
! [X1042,X1043] : subset(X1042,set_union2(X1042,X1043)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_513,plain,
! [X729,X730] :
( ( subset(X729,X730)
| ~ proper_subset(X729,X730) )
& ( X729 != X730
| ~ proper_subset(X729,X730) )
& ( ~ subset(X729,X730)
| X729 = X730
| proper_subset(X729,X730) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
fof(i_0_514,lemma,
! [X1044,X1045] :
( ( ~ disjoint(X1044,X1045)
| set_difference(X1044,X1045) = X1044 )
& ( set_difference(X1044,X1045) != X1044
| disjoint(X1044,X1045) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
fof(i_0_515,lemma,
! [X862,X863] :
( ~ subset(X862,X863)
| set_union2(X862,X863) = X863 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(i_0_516,plain,
! [X700] :
( ~ relation(X700)
| relation_field(X700) = set_union2(relation_dom(X700),relation_rng(X700)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(i_0_517,plain,
! [X749,X750] :
( ~ relation(X750)
| relation(relation_rng_restriction(X749,X750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(i_0_518,plain,
! [X745,X746] :
( ~ relation(X745)
| relation(relation_dom_restriction(X745,X746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
cnf(i_0_519,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_284]) ).
fof(i_0_520,plain,
! [X834,X835] :
( ~ disjoint(X834,X835)
| disjoint(X835,X834) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_521,plain,
! [X903,X904] :
( ~ in(X903,X904)
| element(X903,X904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_522,lemma,
! [X954,X955] :
( ( set_difference(X954,X955) != empty_set
| subset(X954,X955) )
& ( ~ subset(X954,X955)
| set_difference(X954,X955) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_523,lemma,
! [X797,X798] :
( ( set_difference(X797,X798) != empty_set
| subset(X797,X798) )
& ( ~ subset(X797,X798)
| set_difference(X797,X798) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(i_0_524,lemma,
! [X882] :
( ~ relation(X882)
| relation_image(X882,relation_dom(X882)) = relation_rng(X882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_relat_1])]) ).
fof(i_0_525,plain,
! [X818] :
( ( element(esk56_1(X818),powerset(X818))
| empty(X818) )
& ( ~ empty(esk56_1(X818))
| empty(X818) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_285])])])]) ).
fof(i_0_526,plain,
! [X1040,X1041] :
( ~ in(X1040,X1041)
| ~ empty(X1041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_527,plain,
! [X775] :
( empty(X775)
| ~ relation(X775)
| ~ empty(relation_rng(X775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_286])]) ).
fof(i_0_528,plain,
! [X774] :
( empty(X774)
| ~ relation(X774)
| ~ empty(relation_dom(X774)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_287])]) ).
fof(i_0_529,plain,
! [X491,X492] : set_union2(X491,X492) = set_union2(X492,X491),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_530,plain,
! [X489,X490] : unordered_pair(X489,X490) = unordered_pair(X490,X489),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_531,plain,
! [X822] :
( element(esk59_1(X822),powerset(X822))
& empty(esk59_1(X822)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_532,plain,
! [X575,X576,X577] :
( ( X575 != empty_set
| ~ in(X576,X575) )
& ( in(esk20_1(X577),X577)
| X577 = 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_288])])])])]) ).
fof(i_0_533,negated_conjecture,
( in(esk68_0,esk67_0)
& apply(identity_relation(esk67_0),esk68_0) != esk68_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_289])])]) ).
fof(i_0_534,plain,
! [X787] : ~ proper_subset(X787,X787),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_290])]) ).
cnf(i_0_535,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_291]) ).
fof(i_0_536,lemma,
! [X974] :
( ~ subset(X974,empty_set)
| X974 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_537,lemma,
! [X953] :
( ( relation_rng(X953) = relation_dom(relation_inverse(X953))
| ~ relation(X953) )
& ( relation_dom(X953) = relation_rng(relation_inverse(X953))
| ~ relation(X953) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
fof(i_0_538,plain,
! [X751] : element(esk52_1(X751),X751),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(i_0_539,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_292]) ).
fof(i_0_540,lemma,
! [X1028] :
( ( relation_dom(X1028) != empty_set
| relation_rng(X1028) = empty_set
| ~ relation(X1028) )
& ( relation_rng(X1028) != empty_set
| relation_dom(X1028) = empty_set
| ~ relation(X1028) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])]) ).
fof(i_0_541,plain,
! [X784] :
( ~ relation(X784)
| relation_inverse(relation_inverse(X784)) = X784 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
fof(i_0_542,plain,
! [X734] :
( ~ relation(X734)
| relation(relation_inverse(X734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relat_1])]) ).
fof(i_0_543,plain,
! [X777] :
( ( empty(relation_rng(X777))
| ~ empty(X777) )
& ( relation(relation_rng(X777))
| ~ empty(X777) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(i_0_544,plain,
! [X776] :
( ( empty(relation_dom(X776))
| ~ empty(X776) )
& ( relation(relation_dom(X776))
| ~ empty(X776) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_545,plain,
! [X759] : ~ empty(powerset(X759)),
inference(variable_rename,[status(thm)],[i_0_293]) ).
fof(i_0_546,plain,
! [X1051,X1052] :
( ~ empty(X1051)
| X1051 = X1052
| ~ empty(X1052) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_547,lemma,
! [X1027] :
( ( relation_dom(X1027) != empty_set
| X1027 = empty_set
| ~ relation(X1027) )
& ( relation_rng(X1027) != empty_set
| X1027 = empty_set
| ~ relation(X1027) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).
fof(i_0_548,plain,
! [X780] : set_union2(X780,X780) = X780,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_549,plain,
! [X833] : subset(X833,X833),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(i_0_550,lemma,
powerset(empty_set) = singleton(empty_set),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
fof(i_0_551,plain,
! [X965] : set_difference(X965,empty_set) = X965,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_552,plain,
! [X902] : set_union2(X902,empty_set) = X902,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_553,lemma,
! [X934] : subset(empty_set,X934),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_554,plain,
! [X1000] : set_difference(empty_set,X1000) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_555,plain,
! [X488] :
( ~ empty(X488)
| relation(X488) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_556,plain,
! [X487] :
( ~ empty(X487)
| function(X487) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_557,lemma,
! [X1035] :
( relation_dom(identity_relation(X1035)) = X1035
& relation_rng(identity_relation(X1035)) = X1035 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(i_0_558,lemma,
! [X1070] : union(powerset(X1070)) = X1070,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(i_0_559,plain,
! [X762] :
( relation(identity_relation(X762))
& function(identity_relation(X762)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(i_0_560,plain,
! [X739] : relation(identity_relation(X739)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(i_0_561,plain,
! [X1032] :
( ~ empty(X1032)
| X1032 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_562,plain,
~ empty(esk60_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_294])]) ).
fof(i_0_563,plain,
( ~ empty(esk58_0)
& relation(esk58_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_295])]) ).
fof(i_0_564,plain,
( relation(esk61_0)
& relation_empty_yielding(esk61_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_565,plain,
( empty(esk55_0)
& relation(esk55_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_566,plain,
( relation(esk54_0)
& function(esk54_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_567,plain,
empty(esk57_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_568,plain,
( in(unordered_pair(unordered_pair(esk47_5(X1,X2,X3,X4,X5),X5),unordered_pair(esk47_5(X1,X2,X3,X4,X5),esk47_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_296,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_569,plain,
( in(unordered_pair(unordered_pair(X1,esk47_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_298,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_570,plain,
( in(unordered_pair(unordered_pair(esk7_4(X1,X2,X3,X4),X4),unordered_pair(esk7_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[i_0_299,c_0_297]),
[final] ).
cnf(i_0_571,plain,
( X3 = relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,esk49_3(X1,X2,X3)),unordered_pair(X4,X4)),X2)
| ~ in(unordered_pair(unordered_pair(esk48_3(X1,X2,X3),X4),unordered_pair(esk48_3(X1,X2,X3),esk48_3(X1,X2,X3))),X1)
| ~ in(unordered_pair(unordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),unordered_pair(esk48_3(X1,X2,X3),esk48_3(X1,X2,X3))),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_300,c_0_297]),c_0_297]),c_0_297]),
[final] ).
cnf(i_0_572,plain,
( X3 = relation_rng_restriction(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(esk6_3(X1,X2,X3),X1)
| ~ in(unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk5_3(X1,X2,X3))),X3)
| ~ in(unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk5_3(X1,X2,X3))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_301,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_573,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_302,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_574,plain,
( X1 = unordered_pair(unordered_pair(esk26_4(X2,X3,X4,X1),esk27_4(X2,X3,X4,X1)),unordered_pair(esk26_4(X2,X3,X4,X1),esk26_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[i_0_303,c_0_297]),
[final] ).
cnf(i_0_575,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),unordered_pair(esk48_3(X1,X2,X3),esk48_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk50_3(X1,X2,X3),esk49_3(X1,X2,X3)),unordered_pair(esk50_3(X1,X2,X3),esk50_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_304,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_576,plain,
( X3 = relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk48_3(X1,X2,X3),esk49_3(X1,X2,X3)),unordered_pair(esk48_3(X1,X2,X3),esk48_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk48_3(X1,X2,X3),esk50_3(X1,X2,X3)),unordered_pair(esk48_3(X1,X2,X3),esk48_3(X1,X2,X3))),X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_305,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_577,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk5_3(X1,X2,X3))),X3)
| in(unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk5_3(X1,X2,X3))),X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_306,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_578,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_307,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_579,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk11_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(esk11_3(X1,X2,X3),X4),unordered_pair(esk11_3(X1,X2,X3),esk11_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[i_0_308,c_0_297]),
[final] ).
cnf(i_0_580,plain,
( in(unordered_pair(unordered_pair(X1,esk10_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_309,c_0_297]),
[final] ).
cnf(i_0_581,plain,
( X3 = relation_rng_restriction(X1,X2)
| in(esk6_3(X1,X2,X3),X1)
| in(unordered_pair(unordered_pair(esk5_3(X1,X2,X3),esk6_3(X1,X2,X3)),unordered_pair(esk5_3(X1,X2,X3),esk5_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[i_0_310,c_0_297]),
[final] ).
cnf(i_0_582,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_311,c_0_297]),
[final] ).
cnf(i_0_583,plain,
( X3 = relation_inverse_image(X1,X2)
| in(esk11_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk11_3(X1,X2,X3),esk12_3(X1,X2,X3)),unordered_pair(esk11_3(X1,X2,X3),esk11_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_312,c_0_297]),
[final] ).
cnf(i_0_584,plain,
( X3 = relation_image(X1,X2)
| in(esk8_3(X1,X2,X3),X3)
| in(unordered_pair(unordered_pair(esk9_3(X1,X2,X3),esk8_3(X1,X2,X3)),unordered_pair(esk9_3(X1,X2,X3),esk9_3(X1,X2,X3))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_313,c_0_297]),
[final] ).
cnf(i_0_585,plain,
( X2 = relation_inverse(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),unordered_pair(esk45_2(X1,X2),esk45_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),unordered_pair(esk46_2(X1,X2),esk46_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_314,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_586,plain,
( X1 = X2
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_315,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_587,lemma,
( in(unordered_pair(unordered_pair(esk63_3(X1,X2,X3),X1),unordered_pair(esk63_3(X1,X2,X3),esk63_3(X1,X2,X3))),X3)
| ~ relation(X3)
| ~ in(X1,relation_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_316,c_0_297]),
[final] ).
cnf(i_0_588,plain,
( in(unordered_pair(unordered_pair(esk42_3(X3,X2,X1),X1),unordered_pair(esk42_3(X3,X2,X1),esk42_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_317,c_0_297]),
[final] ).
cnf(i_0_589,plain,
( X2 = relation_inverse(X1)
| in(unordered_pair(unordered_pair(esk45_2(X1,X2),esk46_2(X1,X2)),unordered_pair(esk45_2(X1,X2),esk45_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk46_2(X1,X2),esk45_2(X1,X2)),unordered_pair(esk46_2(X1,X2),esk46_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_318,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_590,plain,
( X1 = X2
| in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2))),X2)
| in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_319,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_591,plain,
( X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(esk8_3(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X4,esk8_3(X1,X2,X3)),unordered_pair(X4,X4)),X1) ),
inference(rw,[status(thm)],[i_0_320,c_0_297]),
[final] ).
cnf(i_0_592,plain,
( X3 = cartesian_product2(X1,X2)
| esk28_3(X1,X2,X3) = unordered_pair(unordered_pair(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)),unordered_pair(esk29_3(X1,X2,X3),esk29_3(X1,X2,X3)))
| in(esk28_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_321,c_0_297]),
[final] ).
cnf(i_0_593,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_322,c_0_297]),
[final] ).
cnf(i_0_594,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[i_0_323,c_0_297]),
[final] ).
cnf(i_0_595,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk36_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk36_2(X1,X2),X3),unordered_pair(esk36_2(X1,X2),esk36_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[i_0_324,c_0_297]),
[final] ).
cnf(i_0_596,plain,
( X3 = complements_of_subsets(X1,X2)
| ~ in(esk51_3(X1,X2,X3),X3)
| ~ in(subset_complement(X1,esk51_3(X1,X2,X3)),X2)
| ~ element(X3,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_325]),
[final] ).
cnf(i_0_597,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_326,c_0_297]),c_0_297]),c_0_297]),
[final] ).
cnf(i_0_598,lemma,
( in(unordered_pair(unordered_pair(X1,esk64_3(X1,X2,X3)),unordered_pair(X1,X1)),X3)
| ~ relation(X3)
| ~ in(X1,relation_inverse_image(X3,X2)) ),
inference(rw,[status(thm)],[i_0_327,c_0_297]),
[final] ).
cnf(i_0_599,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| ~ in(esk34_3(X1,X2,X3),X3)
| ~ in(esk34_3(X1,X2,X3),X2)
| ~ in(esk34_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_328,c_0_329]),
[final] ).
cnf(i_0_600,plain,
( X2 = relation_rng(X1)
| in(esk43_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk44_2(X1,X2),esk43_2(X1,X2)),unordered_pair(esk44_2(X1,X2),esk44_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_330,c_0_297]),
[final] ).
cnf(i_0_601,plain,
( X2 = relation_dom(X1)
| in(esk36_2(X1,X2),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(X1) ),
inference(rw,[status(thm)],[i_0_331,c_0_297]),
[final] ).
cnf(i_0_602,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_332,c_0_297]),
[final] ).
cnf(i_0_603,plain,
( in(unordered_pair(unordered_pair(X1,esk35_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_333,c_0_297]),
[final] ).
cnf(i_0_604,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_334,c_0_297]),
[final] ).
cnf(i_0_605,plain,
( subset(X1,X2)
| in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_335,c_0_297]),
[final] ).
cnf(i_0_606,plain,
( in(esk10_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_607,plain,
( in(esk7_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_608,plain,
( in(esk27_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_609,plain,
( in(esk26_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_610,plain,
( in(esk41_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| ~ in(esk41_3(X1,X2,X3),X3)
| ~ in(esk41_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_611,plain,
( in(esk51_3(X1,X2,X3),X3)
| in(subset_complement(X1,esk51_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_325]),
[final] ).
cnf(i_0_612,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk43_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk43_2(X1,X2)),unordered_pair(X3,X3)),X1) ),
inference(rw,[status(thm)],[i_0_337,c_0_297]),
[final] ).
cnf(i_0_613,plain,
( X3 = cartesian_product2(X1,X2)
| esk28_3(X1,X2,X3) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X2)
| ~ in(X4,X1)
| ~ in(esk28_3(X1,X2,X3),X3) ),
inference(rw,[status(thm)],[i_0_338,c_0_297]),
[final] ).
cnf(i_0_614,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_339,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_615,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_340,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_616,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_341,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_617,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_342,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_618,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_343,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_619,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_344,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_620,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_345,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_621,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk25_3(X1,X2,X3),X1)
| ~ in(esk25_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_622,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk25_3(X1,X2,X3),X2)
| ~ in(esk25_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_623,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_347,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_624,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_348,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_625,plain,
( in(esk25_3(X1,X2,X3),X3)
| in(esk25_3(X1,X2,X3),X1)
| in(esk25_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_626,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_349,c_0_297]),
[final] ).
cnf(i_0_627,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_350,c_0_297]),
[final] ).
cnf(i_0_628,plain,
( in(esk41_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk41_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_629,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_351,c_0_297]),
[final] ).
cnf(i_0_630,plain,
( X2 = unordered_pair(unordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)),unordered_pair(esk13_2(X1,X2),esk13_2(X1,X2)))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_352,c_0_297]),
[final] ).
cnf(i_0_631,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_353,c_0_297]),
[final] ).
cnf(i_0_632,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_354,c_0_297]),
[final] ).
cnf(i_0_633,plain,
( X3 = unordered_pair(X1,X2)
| esk24_3(X1,X2,X3) != X1
| ~ in(esk24_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_634,plain,
( X3 = unordered_pair(X1,X2)
| esk24_3(X1,X2,X3) != X2
| ~ in(esk24_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_635,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_356,c_0_297]),
[final] ).
cnf(i_0_636,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk34_3(X1,X2,X3),X3)
| in(esk34_3(X1,X2,X3),X1) ),
inference(rw,[status(thm)],[i_0_357,c_0_329]),
[final] ).
cnf(i_0_637,plain,
( X3 = set_difference(X1,set_difference(X1,X2))
| in(esk34_3(X1,X2,X3),X3)
| in(esk34_3(X1,X2,X3),X2) ),
inference(rw,[status(thm)],[i_0_358,c_0_329]),
[final] ).
cnf(i_0_638,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_359,c_0_297]),
[final] ).
cnf(i_0_639,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_360,c_0_297]),
[final] ).
cnf(i_0_640,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_361,c_0_297]),
[final] ).
cnf(i_0_641,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_362,c_0_297]),
[final] ).
cnf(i_0_642,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_363,c_0_297]),
[final] ).
cnf(i_0_643,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_364,c_0_297]),
[final] ).
cnf(i_0_644,plain,
( in(esk12_3(X1,X2,X3),X2)
| in(esk11_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_220]),
[final] ).
cnf(i_0_645,plain,
( in(esk9_3(X1,X2,X3),X2)
| in(esk8_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_216]),
[final] ).
cnf(i_0_646,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_365,c_0_297]),
[final] ).
cnf(i_0_647,plain,
( in(esk41_3(X1,X2,X3),X1)
| in(esk41_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_648,plain,
( in(esk30_3(X1,X2,X3),X2)
| in(esk28_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_649,plain,
( in(esk29_3(X1,X2,X3),X1)
| in(esk28_3(X1,X2,X3),X3)
| X3 = cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_219]),
[final] ).
cnf(i_0_650,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_366,c_0_297]),
[final] ).
cnf(i_0_651,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_367,c_0_297]),
[final] ).
cnf(i_0_652,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_368,c_0_297]),
[final] ).
cnf(i_0_653,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_369,c_0_297]),
[final] ).
cnf(i_0_654,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_370,c_0_297]),
[final] ).
cnf(i_0_655,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_371,c_0_297]),
[final] ).
cnf(i_0_656,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_372,c_0_297]),
[final] ).
cnf(i_0_657,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_373,c_0_297]),
[final] ).
cnf(i_0_658,lemma,
( X1 = empty_set
| in(unordered_pair(unordered_pair(esk71_1(X1),esk72_1(X1)),unordered_pair(esk71_1(X1),esk71_1(X1))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_374,c_0_297]),
[final] ).
cnf(i_0_659,plain,
( in(esk24_3(X1,X2,X3),X3)
| esk24_3(X1,X2,X3) = X1
| esk24_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_660,plain,
( element(esk51_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_325]),
[final] ).
cnf(i_0_661,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_375,c_0_297]),
[final] ).
cnf(i_0_662,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_325]),
[final] ).
cnf(i_0_663,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_376]),
[final] ).
cnf(i_0_664,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_325]),
[final] ).
cnf(i_0_665,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_377,c_0_297]),
[final] ).
cnf(i_0_666,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_378,c_0_297]),
[final] ).
cnf(i_0_667,plain,
( in(X1,X3)
| X2 = empty_set
| ~ in(X1,esk16_3(X2,X3,X1))
| X3 != set_meet(X2) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_668,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_380,c_0_297]),
[final] ).
cnf(i_0_669,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_381,c_0_297]),
[final] ).
cnf(i_0_670,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))),
inference(rw,[status(thm)],[i_0_382,c_0_297]),
[final] ).
cnf(i_0_671,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_383,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_672,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_384,c_0_297]),c_0_297]),
[final] ).
cnf(i_0_673,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_385]),
[final] ).
cnf(i_0_674,lemma,
( in(esk64_3(X1,X2,X3),relation_rng(X3))
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_675,lemma,
( in(esk63_3(X1,X2,X3),relation_dom(X3))
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_676,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_386,c_0_329]),c_0_329]),
[final] ).
cnf(i_0_677,plain,
( element(subset_difference(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_387]),
[final] ).
cnf(i_0_678,lemma,
( in(esk64_3(X1,X2,X3),X2)
| ~ in(X1,relation_inverse_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_228]),
[final] ).
cnf(i_0_679,lemma,
( in(esk63_3(X1,X2,X3),X2)
| ~ in(X1,relation_image(X3,X2))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_223]),
[final] ).
cnf(i_0_680,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_388,c_0_297]),
[final] ).
cnf(i_0_681,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_385]),
[final] ).
cnf(i_0_682,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_389,c_0_297]),
[final] ).
cnf(i_0_683,plain,
( X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk17_2(X1,X2),esk18_2(X1,X2))
| ~ in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_684,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_390,c_0_391]),
[final] ).
cnf(i_0_685,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_392,c_0_391]),
[final] ).
cnf(i_0_686,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[i_0_393,c_0_329]),
[final] ).
cnf(i_0_687,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_385]),
[final] ).
cnf(i_0_688,plain,
( X2 = union(X1)
| ~ in(esk39_2(X1,X2),X2)
| ~ in(esk39_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_689,plain,
( in(esk38_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_690,plain,
( in(X1,esk38_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_691,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_395,c_0_329]),
[final] ).
cnf(i_0_692,plain,
( in(esk16_3(X1,X2,X3),X1)
| in(X3,X2)
| X1 = empty_set
| X2 != set_meet(X1) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_693,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_396]),
[final] ).
cnf(i_0_694,lemma,
( in(X1,relation_rng(X2))
| ~ in(X1,relation_rng(relation_rng_restriction(X3,X2)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_695,lemma,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_398]),
[final] ).
cnf(i_0_696,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_399]),
[final] ).
cnf(i_0_697,lemma,
( subset(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_400,c_0_329]),
[final] ).
cnf(i_0_698,lemma,
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X3)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_397]),
[final] ).
cnf(i_0_699,lemma,
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[i_0_398]),
[final] ).
cnf(i_0_700,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_397]),
[final] ).
cnf(i_0_701,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_398]),
[final] ).
cnf(i_0_702,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_401]),
[final] ).
cnf(i_0_703,lemma,
( disjoint(X1,X2)
| in(esk70_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[i_0_402,c_0_329]),
[final] ).
cnf(i_0_704,plain,
( X2 = powerset(X1)
| ~ in(esk21_2(X1,X2),X2)
| ~ subset(esk21_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_403]),
[final] ).
cnf(i_0_705,lemma,
( in(X3,X1)
| subset(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_404,c_0_215]),
[final] ).
cnf(i_0_706,plain,
( X1 = X2
| ~ in(esk65_2(X1,X2),X1)
| ~ in(esk65_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_405]),
[final] ).
cnf(i_0_707,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_396]),
[final] ).
cnf(i_0_708,plain,
( in(X1,X4)
| X4 != set_difference(X2,set_difference(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_406,c_0_329]),
[final] ).
cnf(i_0_709,lemma,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_407]),
[final] ).
cnf(i_0_710,plain,
( relation(X1)
| esk15_1(X1) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[i_0_408,c_0_297]),
[final] ).
cnf(i_0_711,lemma,
( X1 = identity_relation(X2)
| apply(X1,esk66_2(X2,X1)) != esk66_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_409]),
[final] ).
cnf(i_0_712,plain,
( in(esk39_2(X1,X2),esk40_2(X1,X2))
| in(esk39_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_713,lemma,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_410]),
[final] ).
cnf(i_0_714,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_411]),
[final] ).
cnf(i_0_715,plain,
( in(esk18_2(X1,X2),X1)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(esk17_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_716,plain,
( in(esk17_2(X1,X2),X2)
| in(esk17_2(X1,X2),X3)
| X2 = set_meet(X1)
| X1 = empty_set
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_717,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_412]),
[final] ).
cnf(i_0_718,lemma,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_413,c_0_215]),c_0_215]),
[final] ).
cnf(i_0_719,plain,
( X2 = unordered_pair(X1,X1)
| esk19_2(X1,X2) != X1
| ~ in(esk19_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_414,c_0_215]),
[final] ).
cnf(i_0_720,plain,
( in(X1,X2)
| X3 != set_difference(X2,set_difference(X2,X4))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_415,c_0_329]),
[final] ).
cnf(i_0_721,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[i_0_416,c_0_329]),
[final] ).
cnf(i_0_722,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_417]),
[final] ).
cnf(i_0_723,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_418]),
[final] ).
cnf(i_0_724,plain,
( relation(set_difference(X1,set_difference(X1,X2)))
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[i_0_419,c_0_329]),
[final] ).
cnf(i_0_725,lemma,
( subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_420]),
[final] ).
cnf(i_0_726,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_421,c_0_329]),
[final] ).
cnf(i_0_727,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_422,c_0_329]),
[final] ).
cnf(i_0_728,plain,
( in(X1,esk74_2(X3,X2))
| ~ subset(X1,X2)
| ~ in(X2,esk73_1(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_423]),
[final] ).
cnf(i_0_729,lemma,
( subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_424]),
[final] ).
cnf(i_0_730,lemma,
( subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_425]),
[final] ).
cnf(i_0_731,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_426]),
[final] ).
cnf(i_0_732,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X1),
inference(rw,[status(thm)],[i_0_427,c_0_329]),
[final] ).
cnf(i_0_733,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_428]),
[final] ).
cnf(i_0_734,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_429]),
[final] ).
cnf(i_0_735,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_430]),
[final] ).
cnf(i_0_736,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_431]),
[final] ).
cnf(i_0_737,lemma,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_431]),
[final] ).
cnf(i_0_738,lemma,
( set_difference(X1,unordered_pair(X2,X2)) != X1
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[i_0_432,c_0_215]),
[final] ).
cnf(i_0_739,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_433]),
[final] ).
cnf(i_0_740,lemma,
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_434,c_0_215]),
[final] ).
cnf(i_0_741,plain,
( in(esk40_2(X1,X2),X1)
| in(esk39_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_742,plain,
( in(esk21_2(X1,X2),X2)
| subset(esk21_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[i_0_403]),
[final] ).
cnf(i_0_743,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_435]),
[final] ).
cnf(i_0_744,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_436]),
[final] ).
cnf(i_0_745,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_437]),
[final] ).
cnf(i_0_746,lemma,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_438]),
[final] ).
cnf(i_0_747,lemma,
( element(X1,powerset(X2))
| ~ in(esk53_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_748,plain,
( in(esk65_2(X1,X2),X1)
| in(esk65_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_405]),
[final] ).
cnf(i_0_749,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_440,c_0_215]),c_0_215]),
[final] ).
cnf(i_0_750,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_441,c_0_215]),c_0_215]),
[final] ).
cnf(i_0_751,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_442,c_0_329]),c_0_329]),
[final] ).
cnf(i_0_752,lemma,
( subset(relation_rng(relation_rng_restriction(X2,X1)),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_443]),
[final] ).
cnf(i_0_753,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_444]),
[final] ).
cnf(i_0_754,plain,
( in(esk74_2(X1,X2),esk73_1(X1))
| ~ in(X2,esk73_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_423]),
[final] ).
cnf(i_0_755,plain,
( subset(X1,X2)
| ~ in(esk33_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_445]),
[final] ).
cnf(i_0_756,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_446,c_0_215]),
[final] ).
cnf(i_0_757,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_447,c_0_215]),
[final] ).
cnf(i_0_758,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_436]),
[final] ).
cnf(i_0_759,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_436]),
[final] ).
cnf(i_0_760,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[i_0_448,c_0_329]),
[final] ).
cnf(i_0_761,lemma,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_449]),
[final] ).
cnf(i_0_762,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_763,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_764,plain,
( in(X3,esk73_1(X2))
| ~ in(X1,esk73_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_423]),
[final] ).
cnf(i_0_765,lemma,
( in(X3,esk62_1(X2))
| ~ in(X1,esk62_1(X2))
| ~ subset(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_766,plain,
( are_equipotent(X1,esk73_1(X2))
| in(X1,esk73_1(X2))
| ~ subset(X1,esk73_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_423]),
[final] ).
cnf(i_0_767,lemma,
( are_equipotent(X1,esk62_1(X2))
| in(X1,esk62_1(X2))
| ~ subset(X1,esk62_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_768,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_451]),
[final] ).
cnf(i_0_769,lemma,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_452]),
[final] ).
cnf(i_0_770,plain,
( X2 = unordered_pair(X1,X1)
| esk19_2(X1,X2) = X1
| in(esk19_2(X1,X2),X2) ),
inference(rw,[status(thm)],[i_0_453,c_0_215]),
[final] ).
cnf(i_0_771,plain,
( in(X1,X3)
| X4 = empty_set
| ~ in(X1,X2)
| ~ in(X3,X4)
| X2 != set_meet(X4) ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_772,plain,
( meet_of_subsets(X2,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_454]),
[final] ).
cnf(i_0_773,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_455]),
[final] ).
cnf(i_0_774,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_456]),
[final] ).
cnf(i_0_775,lemma,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_457]),
[final] ).
cnf(i_0_776,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_777,lemma,
( in(esk66_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_409]),
[final] ).
cnf(i_0_778,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_394]),
[final] ).
cnf(i_0_779,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_458]),
[final] ).
cnf(i_0_780,lemma,
( relation_rng(relation_composition(X1,X2)) = relation_image(X2,relation_rng(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_459]),
[final] ).
cnf(i_0_781,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_460,c_0_215]),c_0_215]),
[final] ).
cnf(i_0_782,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_461,c_0_215]),c_0_215]),
[final] ).
cnf(i_0_783,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_462,c_0_215]),
[final] ).
cnf(i_0_784,lemma,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_463,c_0_215]),
[final] ).
cnf(i_0_785,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_464,c_0_329]),
[final] ).
cnf(i_0_786,lemma,
( X2 = set_union2(X1,set_difference(X2,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_465]),
[final] ).
cnf(i_0_787,lemma,
( subset(relation_rng(X1),relation_rng(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_466]),
[final] ).
cnf(i_0_788,lemma,
( subset(relation_dom(X1),relation_dom(X2))
| ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_466]),
[final] ).
cnf(i_0_789,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_467]),
[final] ).
cnf(i_0_790,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_468,c_0_215]),
[final] ).
cnf(i_0_791,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_469,c_0_215]),
[final] ).
cnf(i_0_792,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[i_0_470,c_0_329]),
[final] ).
cnf(i_0_793,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_471]),
[final] ).
cnf(i_0_794,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_336]),
[final] ).
cnf(i_0_795,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_796,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_346]),
[final] ).
cnf(i_0_797,lemma,
( in(esk53_2(X1,X2),X1)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_439]),
[final] ).
cnf(i_0_798,lemma,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[i_0_409]),
[final] ).
cnf(i_0_799,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_472]),
[final] ).
cnf(i_0_800,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_801,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_473]),
[final] ).
cnf(i_0_802,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_474]),
[final] ).
cnf(i_0_803,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_445]),
[final] ).
cnf(i_0_804,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_475]),
[final] ).
cnf(i_0_805,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_475]),
[final] ).
cnf(i_0_806,lemma,
( in(powerset(X1),esk62_1(X2))
| ~ in(X1,esk62_1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_807,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_476]),
[final] ).
cnf(i_0_808,lemma,
( set_difference(X2,unordered_pair(X1,X1)) = X2
| in(X1,X2) ),
inference(rw,[status(thm)],[i_0_477,c_0_215]),
[final] ).
cnf(i_0_809,lemma,
( in(esk69_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_458]),
[final] ).
cnf(i_0_810,lemma,
( in(esk69_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_458]),
[final] ).
cnf(i_0_811,plain,
( in(esk33_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_445]),
[final] ).
cnf(i_0_812,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[i_0_478,c_0_215]),
[final] ).
cnf(i_0_813,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_479]),
[final] ).
cnf(i_0_814,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_480]),
[final] ).
cnf(i_0_815,lemma,
( subset(relation_inverse_image(X1,X2),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_481]),
[final] ).
cnf(i_0_816,lemma,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_482]),
[final] ).
cnf(i_0_817,plain,
( X1 = apply(X2,X3)
| in(X3,relation_dom(X2))
| X1 != empty_set
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_234]),
[final] ).
cnf(i_0_818,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_483]),
[final] ).
cnf(i_0_819,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_484]),
[final] ).
cnf(i_0_820,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_821,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_485,c_0_215]),
[final] ).
cnf(i_0_822,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_486]),
[final] ).
cnf(i_0_823,plain,
~ empty(unordered_pair(X1,X1)),
inference(rw,[status(thm)],[i_0_487,c_0_215]),
[final] ).
cnf(i_0_824,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_488]),
[final] ).
cnf(i_0_825,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_489]),
[final] ).
cnf(i_0_826,lemma,
( subset(relation_rng_restriction(X2,X1),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_490]),
[final] ).
cnf(i_0_827,lemma,
( subset(relation_dom_restriction(X1,X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_491]),
[final] ).
cnf(i_0_828,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_492]),
[final] ).
cnf(i_0_829,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_493,c_0_215]),
[final] ).
cnf(i_0_830,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[i_0_494,c_0_215]),
[final] ).
cnf(i_0_831,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[i_0_403]),
[final] ).
cnf(i_0_832,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[i_0_403]),
[final] ).
cnf(i_0_833,lemma,
( ~ subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_495]),
[final] ).
cnf(i_0_834,plain,
( ~ proper_subset(X1,X2)
| ~ proper_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_496]),
[final] ).
cnf(i_0_835,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_497]),
[final] ).
cnf(i_0_836,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_498]),
[final] ).
cnf(i_0_837,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_499]),
[final] ).
cnf(i_0_838,plain,
( relation(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_500]),
[final] ).
cnf(i_0_839,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_501]),
[final] ).
cnf(i_0_840,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_499]),
[final] ).
cnf(i_0_841,plain,
( empty(relation_composition(X1,X2))
| ~ empty(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_500]),
[final] ).
cnf(i_0_842,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_492]),
[final] ).
cnf(i_0_843,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_502]),
[final] ).
cnf(i_0_844,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_503]),
[final] ).
cnf(i_0_845,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_504,c_0_215]),
[final] ).
cnf(i_0_846,lemma,
( subset(X1,unordered_pair(X2,X2))
| X1 != empty_set ),
inference(rw,[status(thm)],[i_0_505,c_0_215]),
[final] ).
cnf(i_0_847,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X2) ),
inference(rw,[status(thm)],[i_0_506,c_0_215]),
[final] ).
cnf(i_0_848,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_849,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_355]),
[final] ).
cnf(i_0_850,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_851,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_508]),
[final] ).
cnf(i_0_852,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_853,lemma,
( relation_dom_restriction(X1,X2) = relation_composition(identity_relation(X2),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_509]),
[final] ).
cnf(i_0_854,plain,
set_difference(X1,set_difference(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_510,c_0_329]),
[final] ).
cnf(i_0_855,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_511]),
[final] ).
cnf(i_0_856,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_512]),
[final] ).
cnf(i_0_857,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_513]),
[final] ).
cnf(i_0_858,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_514]),
[final] ).
cnf(i_0_859,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_514]),
[final] ).
cnf(i_0_860,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_515]),
[final] ).
cnf(i_0_861,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_516]),
[final] ).
cnf(i_0_862,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_517]),
[final] ).
cnf(i_0_863,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_518]),
[final] ).
cnf(i_0_864,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[i_0_519,c_0_329]),
[final] ).
cnf(i_0_865,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_520]),
[final] ).
cnf(i_0_866,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_521]),
[final] ).
cnf(i_0_867,plain,
( subset(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_513]),
[final] ).
cnf(i_0_868,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_522]),
[final] ).
cnf(i_0_869,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_523]),
[final] ).
cnf(i_0_870,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_522]),
[final] ).
cnf(i_0_871,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_523]),
[final] ).
cnf(i_0_872,plain,
( empty(X1)
| ~ element(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_873,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_524]),
[final] ).
cnf(i_0_874,plain,
( element(esk56_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_525]),
[final] ).
cnf(i_0_875,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_876,plain,
( element(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_507]),
[final] ).
cnf(i_0_877,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_527]),
[final] ).
cnf(i_0_878,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_528]),
[final] ).
cnf(i_0_879,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_529]),
[final] ).
cnf(i_0_880,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_530]),
[final] ).
cnf(i_0_881,lemma,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_409]),
[final] ).
cnf(i_0_882,plain,
element(esk59_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_531]),
[final] ).
cnf(i_0_883,plain,
( X1 != X2
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_513]),
[final] ).
cnf(i_0_884,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_532]),
[final] ).
cnf(i_0_885,negated_conjecture,
apply(identity_relation(esk67_0),esk68_0) != esk68_0,
inference(split_conjunct,[status(thm)],[i_0_533]),
[final] ).
cnf(i_0_886,plain,
( in(esk15_1(X1),X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_233]),
[final] ).
cnf(i_0_887,plain,
~ proper_subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_534]),
[final] ).
cnf(i_0_888,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[i_0_535,c_0_215]),
[final] ).
cnf(i_0_889,plain,
( in(esk20_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_532]),
[final] ).
cnf(i_0_890,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_536]),
[final] ).
cnf(i_0_891,lemma,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_537]),
[final] ).
cnf(i_0_892,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_537]),
[final] ).
cnf(i_0_893,plain,
( empty(X1)
| ~ empty(esk56_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_525]),
[final] ).
cnf(i_0_894,plain,
element(esk52_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_538]),
[final] ).
cnf(i_0_895,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[i_0_539,c_0_391]),
[final] ).
cnf(i_0_896,plain,
in(X1,esk73_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_423]),
[final] ).
cnf(i_0_897,lemma,
in(X1,esk62_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_450]),
[final] ).
cnf(i_0_898,lemma,
( relation_rng(X1) = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_540]),
[final] ).
cnf(i_0_899,lemma,
( relation_dom(X1) = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_540]),
[final] ).
cnf(i_0_900,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_541]),
[final] ).
cnf(i_0_901,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_489]),
[final] ).
cnf(i_0_902,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_489]),
[final] ).
cnf(i_0_903,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_542]),
[final] ).
cnf(i_0_904,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_543]),
[final] ).
cnf(i_0_905,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_544]),
[final] ).
cnf(i_0_906,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_543]),
[final] ).
cnf(i_0_907,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_544]),
[final] ).
cnf(i_0_908,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_545]),
[final] ).
cnf(i_0_909,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_546]),
[final] ).
cnf(i_0_910,lemma,
( X1 = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_547]),
[final] ).
cnf(i_0_911,lemma,
( X1 = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[i_0_547]),
[final] ).
cnf(i_0_912,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_548]),
[final] ).
cnf(i_0_913,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_549]),
[final] ).
cnf(i_0_914,lemma,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[i_0_550,c_0_215]),
[final] ).
cnf(i_0_915,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_551]),
[final] ).
cnf(i_0_916,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_552]),
[final] ).
cnf(i_0_917,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_553]),
[final] ).
cnf(i_0_918,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_554]),
[final] ).
cnf(i_0_919,plain,
( X1 = empty_set
| X1 != set_meet(X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_920,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_555]),
[final] ).
cnf(i_0_921,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_556]),
[final] ).
cnf(i_0_922,negated_conjecture,
in(esk68_0,esk67_0),
inference(split_conjunct,[status(thm)],[i_0_533]),
[final] ).
cnf(i_0_923,lemma,
relation_rng(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_557]),
[final] ).
cnf(i_0_924,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_558]),
[final] ).
cnf(i_0_925,lemma,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_557]),
[final] ).
cnf(i_0_926,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_559]),
[final] ).
cnf(i_0_927,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_560]),
[final] ).
cnf(i_0_928,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[i_0_559]),
[final] ).
cnf(i_0_929,plain,
empty(esk59_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_531]),
[final] ).
cnf(i_0_930,plain,
( X1 = set_meet(X2)
| X1 != empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_379]),
[final] ).
cnf(i_0_931,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_561]),
[final] ).
cnf(i_0_932,plain,
~ empty(esk60_0),
inference(split_conjunct,[status(thm)],[i_0_562]),
[final] ).
cnf(i_0_933,plain,
~ empty(esk58_0),
inference(split_conjunct,[status(thm)],[i_0_563]),
[final] ).
cnf(i_0_934,plain,
relation_empty_yielding(esk61_0),
inference(split_conjunct,[status(thm)],[i_0_564]),
[final] ).
cnf(i_0_935,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_936,plain,
relation(esk61_0),
inference(split_conjunct,[status(thm)],[i_0_564]),
[final] ).
cnf(i_0_937,plain,
relation(esk58_0),
inference(split_conjunct,[status(thm)],[i_0_563]),
[final] ).
cnf(i_0_938,plain,
relation(esk55_0),
inference(split_conjunct,[status(thm)],[i_0_565]),
[final] ).
cnf(i_0_939,plain,
relation(esk54_0),
inference(split_conjunct,[status(thm)],[i_0_566]),
[final] ).
cnf(i_0_940,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_941,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_942,plain,
function(esk54_0),
inference(split_conjunct,[status(thm)],[i_0_566]),
[final] ).
cnf(i_0_943,plain,
empty(esk57_0),
inference(split_conjunct,[status(thm)],[i_0_567]),
[final] ).
cnf(i_0_944,plain,
empty(esk55_0),
inference(split_conjunct,[status(thm)],[i_0_565]),
[final] ).
cnf(i_0_945,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_946,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_947,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_948,lemma,
relation_rng(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_949,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]),
[final] ).
cnf(i_0_950,axiom,
X1 = X1 ).
cnf(i_0_951,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_952,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_953,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_954,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_955,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_956,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_957,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_958,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_959,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_960,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_961,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_962,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_963,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_964,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_965,axiom,
( X1 != X2
| esk28_3(X1,X3,X4) = esk28_3(X2,X3,X4) ) ).
cnf(i_0_966,axiom,
( X1 != X2
| esk28_3(X3,X1,X4) = esk28_3(X3,X2,X4) ) ).
cnf(i_0_967,axiom,
( X1 != X2
| esk28_3(X3,X4,X1) = esk28_3(X3,X4,X2) ) ).
cnf(i_0_968,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_969,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_970,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_971,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_972,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_973,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_974,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_975,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_976,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_977,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_978,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_979,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_980,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_981,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_982,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_983,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_984,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_985,axiom,
( X1 != X2
| esk24_3(X1,X3,X4) = esk24_3(X2,X3,X4) ) ).
cnf(i_0_986,axiom,
( X1 != X2
| esk24_3(X3,X1,X4) = esk24_3(X3,X2,X4) ) ).
cnf(i_0_987,axiom,
( X1 != X2
| esk24_3(X3,X4,X1) = esk24_3(X3,X4,X2) ) ).
cnf(i_0_988,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_989,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_990,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_991,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_992,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_993,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_994,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_995,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_996,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_997,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_998,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_999,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_1000,axiom,
( X1 != X2
| esk15_1(X1) = esk15_1(X2) ) ).
cnf(i_0_1001,axiom,
( X1 != X2
| esk66_2(X1,X3) = esk66_2(X2,X3) ) ).
cnf(i_0_1002,axiom,
( X1 != X2
| esk66_2(X3,X1) = esk66_2(X3,X2) ) ).
cnf(i_0_1003,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1004,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1005,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_1006,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_1007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_1008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_1009,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_1010,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_1011,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_1012,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_1013,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_1014,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_1015,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_1016,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_1017,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_1018,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_1019,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_1020,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_1021,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_1022,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_950_001,axiom,
X1 = X1 ).
cnf(i_0_951_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_952_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_953_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_954_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_955_006,axiom,
( X1 != X2
| relation_dom_restriction(X1,X3) = relation_dom_restriction(X2,X3) ) ).
cnf(i_0_956_007,axiom,
( X1 != X2
| relation_dom_restriction(X3,X1) = relation_dom_restriction(X3,X2) ) ).
cnf(i_0_957_008,axiom,
( X1 != X2
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_958_009,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_959_010,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_960_011,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_961_012,axiom,
( X1 != X2
| relation_inverse(X1) = relation_inverse(X2) ) ).
cnf(i_0_962_013,axiom,
( X1 != X2
| relation_composition(X1,X3) = relation_composition(X2,X3) ) ).
cnf(i_0_963_014,axiom,
( X1 != X2
| relation_composition(X3,X1) = relation_composition(X3,X2) ) ).
cnf(i_0_964_015,axiom,
( X1 != X2
| relation_rng(X1) = relation_rng(X2) ) ).
cnf(i_0_965_016,axiom,
( X1 != X2
| esk28_3(X1,X3,X4) = esk28_3(X2,X3,X4) ) ).
cnf(i_0_966_017,axiom,
( X1 != X2
| esk28_3(X3,X1,X4) = esk28_3(X3,X2,X4) ) ).
cnf(i_0_967_018,axiom,
( X1 != X2
| esk28_3(X3,X4,X1) = esk28_3(X3,X4,X2) ) ).
cnf(i_0_968_019,axiom,
( X1 != X2
| identity_relation(X1) = identity_relation(X2) ) ).
cnf(i_0_969_020,axiom,
( X1 != X2
| esk2_2(X1,X3) = esk2_2(X2,X3) ) ).
cnf(i_0_970_021,axiom,
( X1 != X2
| esk2_2(X3,X1) = esk2_2(X3,X2) ) ).
cnf(i_0_971_022,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_972_023,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_973_024,axiom,
( X1 != X2
| relation_dom(X1) = relation_dom(X2) ) ).
cnf(i_0_974_025,axiom,
( X1 != X2
| complements_of_subsets(X1,X3) = complements_of_subsets(X2,X3) ) ).
cnf(i_0_975_026,axiom,
( X1 != X2
| complements_of_subsets(X3,X1) = complements_of_subsets(X3,X2) ) ).
cnf(i_0_976_027,axiom,
( X1 != X2
| subset_complement(X1,X3) = subset_complement(X2,X3) ) ).
cnf(i_0_977_028,axiom,
( X1 != X2
| subset_complement(X3,X1) = subset_complement(X3,X2) ) ).
cnf(i_0_978_029,axiom,
( X1 != X2
| powerset(X1) = powerset(X2) ) ).
cnf(i_0_979_030,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_980_031,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_981_032,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_982_033,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_983_034,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_984_035,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_985_036,axiom,
( X1 != X2
| esk24_3(X1,X3,X4) = esk24_3(X2,X3,X4) ) ).
cnf(i_0_986_037,axiom,
( X1 != X2
| esk24_3(X3,X1,X4) = esk24_3(X3,X2,X4) ) ).
cnf(i_0_987_038,axiom,
( X1 != X2
| esk24_3(X3,X4,X1) = esk24_3(X3,X4,X2) ) ).
cnf(i_0_988_039,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_989_040,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_990_041,axiom,
( X1 != X2
| relation_field(X1) = relation_field(X2) ) ).
cnf(i_0_991_042,axiom,
( X1 != X2
| set_meet(X1) = set_meet(X2) ) ).
cnf(i_0_992_043,axiom,
( X1 != X2
| subset_difference(X1,X3,X4) = subset_difference(X2,X3,X4) ) ).
cnf(i_0_993_044,axiom,
( X1 != X2
| subset_difference(X3,X1,X4) = subset_difference(X3,X2,X4) ) ).
cnf(i_0_994_045,axiom,
( X1 != X2
| subset_difference(X3,X4,X1) = subset_difference(X3,X4,X2) ) ).
cnf(i_0_995_046,axiom,
( X1 != X2
| union_of_subsets(X1,X3) = union_of_subsets(X2,X3) ) ).
cnf(i_0_996_047,axiom,
( X1 != X2
| union_of_subsets(X3,X1) = union_of_subsets(X3,X2) ) ).
cnf(i_0_997_048,axiom,
( X1 != X2
| meet_of_subsets(X1,X3) = meet_of_subsets(X2,X3) ) ).
cnf(i_0_998_049,axiom,
( X1 != X2
| meet_of_subsets(X3,X1) = meet_of_subsets(X3,X2) ) ).
cnf(i_0_999_050,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_1000_051,axiom,
( X1 != X2
| esk15_1(X1) = esk15_1(X2) ) ).
cnf(i_0_1001_052,axiom,
( X1 != X2
| esk66_2(X1,X3) = esk66_2(X2,X3) ) ).
cnf(i_0_1002_053,axiom,
( X1 != X2
| esk66_2(X3,X1) = esk66_2(X3,X2) ) ).
cnf(i_0_1003_054,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1004_055,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1005_056,axiom,
( X1 != X2
| relation_rng_restriction(X1,X3) = relation_rng_restriction(X2,X3) ) ).
cnf(i_0_1006_057,axiom,
( X1 != X2
| relation_rng_restriction(X3,X1) = relation_rng_restriction(X3,X2) ) ).
cnf(i_0_1007_058,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_1008_059,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_1009_060,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_1010_061,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_1011_062,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_1012_063,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_1013_064,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_1014_065,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_1015_066,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_1016_067,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_1017_068,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_1018_069,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_1019_070,axiom,
( X1 != X2
| ~ are_equipotent(X1,X3)
| are_equipotent(X2,X3) ) ).
cnf(i_0_1020_071,axiom,
( X1 != X2
| ~ are_equipotent(X3,X1)
| are_equipotent(X3,X2) ) ).
cnf(i_0_1021_072,axiom,
( X1 != X2
| ~ proper_subset(X1,X3)
| proper_subset(X2,X3) ) ).
cnf(i_0_1022_073,axiom,
( X1 != X2
| ~ proper_subset(X3,X1)
| proper_subset(X3,X2) ) ).
cnf(i_0_1023,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(esk47_5(X1,X2,relation_composition(X1,X2),X3,X4),X4),unordered_pair(esk47_5(X1,X2,relation_composition(X1,X2),X3,X4),esk47_5(X1,X2,relation_composition(X1,X2),X3,X4))),X2) ),
inference(equality_inference,[],[568]) ).
cnf(i_0_1024,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,esk47_5(X1,X2,relation_composition(X1,X2),X3,X4)),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[569]) ).
cnf(i_0_1025,plain,
( ~ relation(X1)
| ~ in(X2,relation_image(X1,X3))
| in(unordered_pair(unordered_pair(esk7_4(X1,X3,relation_image(X1,X3),X2),X2),unordered_pair(esk7_4(X1,X3,relation_image(X1,X3),X2),esk7_4(X1,X3,relation_image(X1,X3),X2))),X1) ),
inference(equality_inference,[],[570]) ).
cnf(i_0_1026,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| X1 = unordered_pair(unordered_pair(esk26_4(X2,X3,cartesian_product2(X2,X3),X1),esk27_4(X2,X3,cartesian_product2(X2,X3),X1)),unordered_pair(esk26_4(X2,X3,cartesian_product2(X2,X3),X1),esk26_4(X2,X3,cartesian_product2(X2,X3),X1))) ),
inference(equality_inference,[],[574]) ).
cnf(i_0_1027,plain,
( ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3))
| in(unordered_pair(unordered_pair(X2,esk10_4(X1,X3,relation_inverse_image(X1,X3),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[580]) ).
cnf(i_0_1028,plain,
( ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| in(unordered_pair(unordered_pair(esk42_3(X1,relation_rng(X1),X2),X2),unordered_pair(esk42_3(X1,relation_rng(X1),X2),esk42_3(X1,relation_rng(X1),X2))),X1) ),
inference(equality_inference,[],[588]) ).
cnf(i_0_1029,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,[],[597]) ).
cnf(i_0_1030,plain,
( ~ relation(X1)
| ~ in(X2,relation_dom(X1))
| in(unordered_pair(unordered_pair(X2,esk35_3(X1,relation_dom(X1),X2)),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[603]) ).
cnf(i_0_1031,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| in(esk10_4(X2,X3,relation_inverse_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[606]) ).
cnf(i_0_1032,plain,
( ~ in(X1,relation_image(X2,X3))
| ~ relation(X2)
| in(esk7_4(X2,X3,relation_image(X2,X3),X1),X3) ),
inference(equality_inference,[],[607]) ).
cnf(i_0_1033,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk27_4(X2,X3,cartesian_product2(X2,X3),X1),X3) ),
inference(equality_inference,[],[608]) ).
cnf(i_0_1034,plain,
( ~ in(X1,cartesian_product2(X2,X3))
| in(esk26_4(X2,X3,cartesian_product2(X2,X3),X1),X2) ),
inference(equality_inference,[],[609]) ).
cnf(i_0_1035,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,[],[616]) ).
cnf(i_0_1036,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,[],[617]) ).
cnf(i_0_1037,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,[],[618]) ).
cnf(i_0_1038,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,[],[619]) ).
cnf(i_0_1039,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,[],[623]) ).
cnf(i_0_1040,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,[],[624]) ).
cnf(i_0_1041,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,[],[631]) ).
cnf(i_0_1042,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,[],[632]) ).
cnf(i_0_1043,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,[],[642]) ).
cnf(i_0_1044,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,[],[643]) ).
cnf(i_0_1045,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,[],[650]) ).
cnf(i_0_1046,plain,
( ~ relation(X1)
| in(X2,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(equality_inference,[],[651]) ).
cnf(i_0_1047,plain,
( ~ relation(X1)
| in(X2,relation_rng(X1))
| ~ in(unordered_pair(unordered_pair(X3,X2),unordered_pair(X3,X3)),X1) ),
inference(equality_inference,[],[652]) ).
cnf(i_0_1048,plain,
( ~ relation(identity_relation(X1))
| X2 = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),identity_relation(X1)) ),
inference(equality_inference,[],[661]) ).
cnf(i_0_1049,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,[],[662]) ).
cnf(i_0_1050,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,[],[664]) ).
cnf(i_0_1051,plain,
( in(X1,set_meet(X2))
| ~ in(X1,esk16_3(X2,set_meet(X2),X1))
| X2 = empty_set ),
inference(equality_inference,[],[667]) ).
cnf(i_0_1052,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,[],[669]) ).
cnf(i_0_1053,plain,
X1 = X1,
inference(equality_inference,[],[671]) ).
cnf(i_0_1054,plain,
X1 = X1,
inference(equality_inference,[],[672]) ).
cnf(i_0_1055,plain,
( ~ in(X1,union(X2))
| in(esk38_3(X2,union(X2),X1),X2) ),
inference(equality_inference,[],[689]) ).
cnf(i_0_1056,plain,
( ~ in(X1,union(X2))
| in(X1,esk38_3(X2,union(X2),X1)) ),
inference(equality_inference,[],[690]) ).
cnf(i_0_1057,plain,
( in(X1,set_meet(X2))
| X2 = empty_set
| in(esk16_3(X2,set_meet(X2),X1),X2) ),
inference(equality_inference,[],[692]) ).
cnf(i_0_1058,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(equality_inference,[],[708]) ).
cnf(i_0_1059,plain,
( ~ in(X1,set_difference(X2,set_difference(X2,X3)))
| in(X1,X3) ),
inference(equality_inference,[],[721]) ).
cnf(i_0_1060,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[762]) ).
cnf(i_0_1061,plain,
( in(X1,X2)
| in(X1,set_difference(X3,X2))
| ~ in(X1,X3) ),
inference(equality_inference,[],[763]) ).
cnf(i_0_1062,plain,
( ~ in(X1,X2)
| in(X3,X1)
| ~ in(X3,set_meet(X2))
| X2 = empty_set ),
inference(equality_inference,[],[771]) ).
cnf(i_0_1063,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(equality_inference,[],[776]) ).
cnf(i_0_1064,plain,
( ~ relation(X1)
| ~ function(X1)
| X1 = identity_relation(relation_dom(X1))
| in(esk66_2(relation_dom(X1),X1),relation_dom(X1)) ),
inference(equality_inference,[],[777]) ).
cnf(i_0_1065,plain,
( in(X1,union(X2))
| ~ in(X1,X3)
| ~ in(X3,X2) ),
inference(equality_inference,[],[778]) ).
cnf(i_0_1066,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(equality_inference,[],[794]) ).
cnf(i_0_1067,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[795]) ).
cnf(i_0_1068,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[796]) ).
cnf(i_0_1069,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(equality_inference,[],[798]) ).
cnf(i_0_1070,plain,
( ~ relation(X1)
| ~ function(X1)
| apply(X1,X2) = empty_set
| in(X2,relation_dom(X1)) ),
inference(equality_inference,[],[800]) ).
cnf(i_0_1071,plain,
( ~ relation(X1)
| ~ function(X1)
| in(X2,relation_dom(X1))
| empty_set = apply(X1,X2) ),
inference(equality_inference,[],[817]) ).
cnf(i_0_1072,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[820]) ).
cnf(i_0_1073,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(equality_inference,[],[821]) ).
cnf(i_0_1074,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[822]) ).
cnf(i_0_1075,plain,
X1 = X1,
inference(equality_inference,[],[829]) ).
cnf(i_0_1076,plain,
X1 = X1,
inference(equality_inference,[],[830]) ).
cnf(i_0_1077,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(equality_inference,[],[831]) ).
cnf(i_0_1078,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(equality_inference,[],[832]) ).
cnf(i_0_1079,plain,
subset(empty_set,unordered_pair(X1,X1)),
inference(equality_inference,[],[846]) ).
cnf(i_0_1080,plain,
( ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| relation_dom(identity_relation(X1)) = X1 ),
inference(equality_inference,[],[881]) ).
cnf(i_0_1081,plain,
~ proper_subset(X1,X1),
inference(equality_inference,[],[883]) ).
cnf(i_0_1082,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[884]) ).
cnf(i_0_1083,plain,
subset(X1,X1),
inference(equality_inference,[],[901]) ).
cnf(i_0_1084,plain,
subset(X1,X1),
inference(equality_inference,[],[902]) ).
cnf(i_0_1085,plain,
$false,
inference(scs_inference,[],[i_0_927,i_0_928,i_0_922,i_0_885,i_0_1069]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU217+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:48:28 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 0.57/1.67 % Version : CSE_E---1.7
% 0.57/1.67 % Problem : theBenchmark.p
% 0.57/1.67 % SZS status Theorem for theBenchmark.p
% 0.57/1.67 % SZS output start CNFRefutation
% See solution above
% 0.62/1.73 % Total time : 1.324s
%------------------------------------------------------------------------------