Drodi-SAT---4.1.1.THM-Ass.s

%------------------------------------------------------------------------------
% File     : Drodi-SAT---4.1.1
% Problem  : SEU293+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:22:14 PM UTC 2026

% Result   : Theorem 199.65s 25.72s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SEU293+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06  % Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43  % Computer : n004.cluster.edu
% 0.16/0.43  % Model    : x86_64 x86_64
% 0.16/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43  % Memory   : 8046.5625MB
% 0.16/0.43  % OS       : Linux 6.8.0-71-generic
% 0.16/0.43  % CPULimit : 300
% 0.16/0.43  % WCLimit  : 300
% 0.16/0.43  % DateTime : Mon Sep 21 06:08:20 UTC 2026
% 0.16/0.43  % CPUTime  : 
% 0.16/0.47  % Drodi V4.1.1
% 199.65/25.72  % Refutation found
% 199.65/25.72  % SZS status Theorem for theBenchmark: Theorem is valid
% 199.65/25.72  % SZS output start CNFRefutation for theBenchmark
% 199.65/25.72  fof(f1,axiom,(
% 199.65/25.72    (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f2,axiom,(
% 199.65/25.72    (! [A,B] :( proper_subset(A,B)=> ~ proper_subset(B,A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f5,axiom,(
% 199.65/25.72    (! [A] :( empty(A)=> relation(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f6,axiom,(
% 199.65/25.72    (! [A,B,C] :( element(C,powerset(cartesian_product2(A,B)))=> relation(C) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f7,axiom,(
% 199.65/25.72    (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f11,axiom,(
% 199.65/25.72    (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f14,axiom,(
% 199.65/25.72    (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f15,axiom,(
% 199.65/25.72    (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f16,axiom,(
% 199.65/25.72    (! [A] :( relation(A)=> (! [B,C] :( relation(C)=> ( C = relation_dom_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(D,B)& in(ordered_pair(D,E),A) ) ) )) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f18,axiom,(
% 199.65/25.72    (! [A,B] :( relation(B)=> (! [C] :( relation(C)=> ( C = relation_rng_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(E,A)& in(ordered_pair(D,E),B) ) ) )) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f20,axiom,(
% 199.65/25.72    (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,relation_dom(A))& in(apply(A,D),B) ) ) )) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f21,axiom,(
% 199.65/25.72    (! [A] :( relation(A)=> (! [B,C] :( C = relation_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(E,D),A)& in(E,B) ) )) )) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f22,axiom,(
% 199.65/25.72    (! [A] :( relation(A)=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(D,E),A)& in(E,B) ) )) )) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f26,axiom,(
% 199.65/25.72    (! [A] :( function(A)<=> (! [B,C,D] :( ( in(ordered_pair(B,C),A)& in(ordered_pair(B,D),A) )=> C = D ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f27,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( ( ( B = empty_set=> A = empty_set )=> ( quasi_total(C,A,B)<=> A = relation_dom_as_subset(A,B,C) ) )& ( B = empty_set=> ( A = empty_set| ( quasi_total(C,A,B)<=> C = empty_set ) ) ) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f29,axiom,(
% 199.65/25.72    (! [A] : succ(A) = set_union2(A,singleton(A)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f30,axiom,(
% 199.65/25.72    (! [A] :( relation(A)<=> (! [B] :~ ( in(B,A)& (! [C,D] : B != ordered_pair(C,D) )) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f32,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2(C,A,B)<=> subset(C,cartesian_product2(A,B)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f34,axiom,(
% 199.65/25.72    (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f37,axiom,(
% 199.65/25.72    (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f38,axiom,(
% 199.65/25.72    (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f43,axiom,(
% 199.65/25.72    (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f45,axiom,(
% 199.65/25.72    (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f52,axiom,(
% 199.65/25.72    (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f64,axiom,(
% 199.65/25.72    (! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f77,axiom,(
% 199.65/25.72    (! [A,B] :( proper_subset(A,B)<=> ( subset(A,B)& A != B ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f104,axiom,(
% 199.65/25.72    (! [A] :( relation(A)=> relation(relation_inverse(A)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f105,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2(C,A,B)=> element(relation_dom_as_subset(A,B,C),powerset(A)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f111,axiom,(
% 199.65/25.72    (! [A] : relation(identity_relation(A)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f120,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> element(C,powerset(cartesian_product2(A,B))) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f123,axiom,(
% 199.65/25.72    (! [A,B] :(? [C] : relation_of2_as_subset(C,A,B) ))),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f125,axiom,(
% 199.65/25.72    (! [A] :( empty(A)=> ( empty(relation_inverse(A))& relation(relation_inverse(A)) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f126,axiom,(
% 199.65/25.72    ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f129,axiom,(
% 199.65/25.72    (! [A] : ~ empty(succ(A)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f134,axiom,(
% 199.65/25.72    (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f135,axiom,(
% 199.65/25.72    ( relation(empty_set)& relation_empty_yielding(empty_set)& function(empty_set)& one_to_one(empty_set)& empty(empty_set)& epsilon_transitive(empty_set)& epsilon_connected(empty_set)& ordinal(empty_set) ) ),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f138,axiom,(
% 199.65/25.72    (! [A,B] :( ~ empty(A)=> ~ empty(set_union2(A,B)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f140,axiom,(
% 199.65/25.72    (! [A] :( ordinal(A)=> ( ~ empty(succ(A))& epsilon_transitive(succ(A))& epsilon_connected(succ(A))& ordinal(succ(A)) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f145,axiom,(
% 199.65/25.72    (! [A] :( ordinal(A)=> ( epsilon_transitive(union(A))& epsilon_connected(union(A))& ordinal(union(A)) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f157,axiom,(
% 199.65/25.72    (! [A] :( relation(A)=> relation_inverse(relation_inverse(A)) = A ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f161,lemma,(
% 199.65/25.72    (! [A] : singleton(A) != empty_set )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f176,lemma,(
% 199.65/25.72    (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f179,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& function(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f182,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f186,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f187,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f189,axiom,(
% 199.65/25.72    (? [A] :( ~ empty(A)& relation(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f190,axiom,(
% 199.65/25.72    (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f192,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f194,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f195,axiom,(
% 199.65/25.72    (? [A] :( relation(A)& relation_empty_yielding(A)& function(A) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f196,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2(C,A,B)=> relation_dom_as_subset(A,B,C) = relation_dom(C) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f201,axiom,(
% 199.65/25.72    (! [A,B,C] :( relation_of2_as_subset(C,A,B)<=> relation_of2(C,A,B) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f216,axiom,(
% 199.65/25.72    (! [A] :( (! [B,C,D] :( ( B = C& ordinal(C)& B = D& ordinal(D) )=> C = D ))=> (? [B] :(! [C] :( in(C,B)<=> (? [D] :( in(D,A)& D = C& ordinal(C) ) )) ))) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f225,lemma,(
% 199.65/25.72    (! [A] :(? [B] :( relation(B)& function(B)& relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = singleton(C) ) )) ))),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f229,lemma,(
% 199.65/25.72    (! [A] : in(A,succ(A)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f238,lemma,(
% 199.65/25.72    (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( subset(relation_dom(C),A)& subset(relation_rng(C),B) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f239,lemma,(
% 199.65/25.72    (! [A,B] :( subset(A,B)=> set_union2(A,B) = B ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f249,lemma,(
% 199.65/25.72    (! [A,B,C,D] :( relation_of2_as_subset(D,C,A)=> ( subset(relation_rng(D),B)=> relation_of2_as_subset(D,C,B) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f252,lemma,(
% 199.65/25.72    (! [A,B] :( relation(B)=> subset(relation_inverse_image(B,A),relation_dom(B)) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f253,lemma,(
% 199.65/25.72    (! [A,B,C,D] :( relation_of2_as_subset(D,C,A)=> ( subset(A,B)=> relation_of2_as_subset(D,C,B) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f255,lemma,(
% 199.65/25.72    (! [A,B] :( relation(B)=> ~ ( A != empty_set& subset(A,relation_rng(B))& relation_inverse_image(B,A) = empty_set ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f256,lemma,(
% 199.65/25.72    (! [A,B,C] :( relation(C)=> ( subset(A,B)=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f262,axiom,(
% 199.65/25.72    (! [A] : set_union2(A,empty_set) = A )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f263,axiom,(
% 199.65/25.72    (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f265,lemma,(
% 199.65/25.72    powerset(empty_set) = singleton(empty_set) ),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f269,lemma,(
% 199.65/25.72    (! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> (! [E] :( ( relation(E)& function(E) )=> ( in(C,A)=> ( B = empty_set| apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) )) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f293,lemma,(
% 199.65/25.72    (! [A] : subset(empty_set,A) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f317,lemma,(
% 199.65/25.72    (! [A] :( subset(A,empty_set)=> A = empty_set ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f325,conjecture,(
% 199.65/25.72    (! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( B != empty_set=> (! [E] :( in(E,relation_inverse_image(D,C))<=> ( in(E,A)& in(apply(D,E),C) ) ) )) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f326,negated_conjecture,(
% 199.65/25.72    ~((! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( B != empty_set=> (! [E] :( in(E,relation_inverse_image(D,C))<=> ( in(E,A)& in(apply(D,E),C) ) ) )) ) ))),
% 199.65/25.72    inference(negated_conjecture,[status(cth)],[f325])).
% 199.65/25.72  fof(f350,lemma,(
% 199.65/25.72    ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f354,lemma,(
% 199.65/25.72    (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f359,axiom,(
% 199.65/25.72    (! [A] :( empty(A)=> A = empty_set ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f360,lemma,(
% 199.65/25.72    (! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( in(C,A)=> ( B = empty_set| in(apply(D,C),relation_rng(D)) ) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f364,lemma,(
% 199.65/25.72    (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f371,lemma,(
% 199.65/25.72    (! [A,B] : subset(A,set_union2(A,B)) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f376,lemma,(
% 199.65/25.72    (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f384,lemma,(
% 199.65/25.72    (! [A] : union(powerset(A)) = A )),
% 199.65/25.72    file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.65/25.72  fof(f388,plain,(
% 199.65/25.72    ![A,B]: (~in(A,B)|~in(B,A))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f1])).
% 199.65/25.72  fof(f389,plain,(
% 199.65/25.72    ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f388])).
% 199.65/25.72  fof(f390,plain,(
% 199.65/25.72    ![A,B]: (~proper_subset(A,B)|~proper_subset(B,A))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f2])).
% 199.65/25.72  fof(f391,plain,(
% 199.65/25.72    ![X0,X1]: (~proper_subset(X0,X1)|~proper_subset(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f390])).
% 199.65/25.72  fof(f397,plain,(
% 199.65/25.72    ![A]: (~empty(A)|relation(A))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f5])).
% 199.65/25.72  fof(f398,plain,(
% 199.65/25.72    ![X0]: (~empty(X0)|relation(X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f397])).
% 199.65/25.72  fof(f399,plain,(
% 199.65/25.72    ![A,B,C]: (~element(C,powerset(cartesian_product2(A,B)))|relation(C))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f6])).
% 199.65/25.72  fof(f400,plain,(
% 199.65/25.72    ![C]: ((![A,B]: ~element(C,powerset(cartesian_product2(A,B))))|relation(C))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f399])).
% 199.65/25.72  fof(f401,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~element(X0,powerset(cartesian_product2(X1,X2)))|relation(X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f400])).
% 199.65/25.72  fof(f402,plain,(
% 199.65/25.72    ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f7])).
% 199.65/25.72  fof(f405,plain,(
% 199.65/25.72    ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f402])).
% 199.65/25.72  fof(f413,plain,(
% 199.65/25.72    ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f11])).
% 199.65/25.72  fof(f417,plain,(
% 199.65/25.72    ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f14])).
% 199.65/25.72  fof(f418,plain,(
% 199.65/25.72    ![A,B]: (~relation(B)|((~B=identity_relation(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|(in(C,A)&C=D))&(in(ordered_pair(C,D),B)|(~in(C,A)|~C=D)))))&(B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D)))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f417])).
% 199.65/25.72  fof(f419,plain,(
% 199.65/25.72    ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f418])).
% 199.65/25.72  fof(f420,plain,(
% 199.65/25.72    ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(~in(sK0_skl(A,B),A)|~sK0_skl(A,B)=sK1_skl(A,B)))&(in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(in(sK0_skl(A,B),A)&sK0_skl(A,B)=sK1_skl(A,B))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f419])).
% 199.65/25.72  fof(f425,plain,(
% 199.65/25.72    ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|in(sK0_skl(X1,X0),X1))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f420])).
% 199.65/25.72  fof(f426,plain,(
% 199.65/25.72    ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f420])).
% 199.65/25.72  fof(f427,plain,(
% 199.65/25.72    ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f15])).
% 199.65/25.72  fof(f428,plain,(
% 199.65/25.72    (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f427])).
% 199.65/25.72  fof(f429,plain,(
% 199.65/25.72    ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f428])).
% 199.65/25.72  fof(f431,plain,(
% 199.65/25.72    ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f428])).
% 199.65/25.72  fof(f432,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: (~relation(C)|(C=relation_dom_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(D,B)&in(ordered_pair(D,E),A))))))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f16])).
% 199.65/25.72  fof(f433,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: (~relation(C)|((~C=relation_dom_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A))))))&(C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f432])).
% 199.65/25.72  fof(f434,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f433])).
% 199.65/25.72  fof(f435,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|((~in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C)|(~in(sK2_skl(B,C,A),B)|~in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)))&(in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C)|(in(sK2_skl(B,C,A),B)&in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A))))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f434])).
% 199.65/25.72  fof(f440,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)|in(sK2_skl(X2,X1,X0),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f435])).
% 199.65/25.72  fof(f452,plain,(
% 199.65/25.72    ![A,B]: (~relation(B)|(![C]: (~relation(C)|(C=relation_rng_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(E,A)&in(ordered_pair(D,E),B))))))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f18])).
% 199.65/25.72  fof(f453,plain,(
% 199.65/25.72    ![A,B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_rng_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B))))))&(C=relation_rng_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f452])).
% 199.65/25.72  fof(f454,plain,(
% 199.65/25.72    ![B]: (~relation(B)|(![C]: (~relation(C)|((![A]: (~C=relation_rng_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))))))&(![A]: (C=relation_rng_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B)))))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f453])).
% 199.65/25.72  fof(f455,plain,(
% 199.65/25.72    ![B]: (~relation(B)|(![C]: (~relation(C)|((![A]: (~C=relation_rng_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))))))&(![A]: (C=relation_rng_restriction(A,B)|((~in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C)|(~in(sK8_skl(A,C,B),A)|~in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B)))&(in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C)|(in(sK8_skl(A,C,B),A)&in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B))))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(D,sK7_skl(A,C,B)),skolemize(E,sK8_skl(A,C,B))],[f454])).
% 199.65/25.72  fof(f460,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)|in(sK8_skl(X2,X1,X0),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f455])).
% 199.65/25.72  fof(f466,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(in(D,relation_dom(A))&in(apply(A,D),B)))))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f20])).
% 199.65/25.72  fof(f467,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))&(in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f466])).
% 199.65/25.72  fof(f468,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f467])).
% 199.65/25.72  fof(f469,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sK9_skl(C,B,A),C)|(~in(sK9_skl(C,B,A),relation_dom(A))|~in(apply(A,sK9_skl(C,B,A)),B)))&(in(sK9_skl(C,B,A),C)|(in(sK9_skl(C,B,A),relation_dom(A))&in(apply(A,sK9_skl(C,B,A)),B))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f468])).
% 199.65/25.72  fof(f470,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(X3,relation_dom(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f471,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(apply(X0,X3),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f472,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|in(X3,X1)|~in(X3,relation_dom(X0))|~in(apply(X0,X3),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f473,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|~in(sK9_skl(X1,X2,X0),X1)|~in(sK9_skl(X1,X2,X0),relation_dom(X0))|~in(apply(X0,sK9_skl(X1,X2,X0)),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f474,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sK9_skl(X1,X2,X0),X1)|in(sK9_skl(X1,X2,X0),relation_dom(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f475,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sK9_skl(X1,X2,X0),X1)|in(apply(X0,sK9_skl(X1,X2,X0)),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f469])).
% 199.65/25.72  fof(f476,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: (C=relation_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f21])).
% 199.65/25.72  fof(f477,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: ((~C=relation_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B)))))))&(C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f476])).
% 199.65/25.72  fof(f478,plain,(
% 199.65/25.72    ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f477])).
% 199.65/25.72  fof(f479,plain,(
% 199.65/25.72    ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(sK10_skl(D,C,B,A),D),A)&in(sK10_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|((~in(sK11_skl(C,B,A),C)|(![E]: (~in(ordered_pair(E,sK11_skl(C,B,A)),A)|~in(E,B))))&(in(sK11_skl(C,B,A),C)|(in(ordered_pair(sK12_skl(C,B,A),sK11_skl(C,B,A)),A)&in(sK12_skl(C,B,A),B))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(E,sK10_skl(D,C,B,A)),skolemize(D,sK11_skl(C,B,A)),skolemize(E,sK12_skl(C,B,A))],[f478])).
% 199.65/25.72  fof(f484,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|X1=relation_image(X0,X2)|in(sK11_skl(X1,X2,X0),X1)|in(ordered_pair(sK12_skl(X1,X2,X0),sK11_skl(X1,X2,X0)),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f479])).
% 199.65/25.72  fof(f486,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f22])).
% 199.65/25.72  fof(f487,plain,(
% 199.65/25.72    ![A]: (~relation(A)|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B)))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f486])).
% 199.65/25.72  fof(f488,plain,(
% 199.65/25.72    ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f487])).
% 199.65/25.72  fof(f489,plain,(
% 199.65/25.72    ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sK13_skl(D,C,B,A)),A)&in(sK13_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sK14_skl(C,B,A),C)|(![E]: (~in(ordered_pair(sK14_skl(C,B,A),E),A)|~in(E,B))))&(in(sK14_skl(C,B,A),C)|(in(ordered_pair(sK14_skl(C,B,A),sK15_skl(C,B,A)),A)&in(sK15_skl(C,B,A),B))))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(E,sK13_skl(D,C,B,A)),skolemize(D,sK14_skl(C,B,A)),skolemize(E,sK15_skl(C,B,A))],[f488])).
% 199.65/25.72  fof(f490,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(ordered_pair(X3,sK13_skl(X3,X1,X2,X0)),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f489])).
% 199.65/25.72  fof(f491,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(sK13_skl(X3,X1,X2,X0),X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f489])).
% 199.65/25.72  fof(f492,plain,(
% 199.65/25.72    ![X0,X1,X2,X3,X4]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|in(X3,X1)|~in(ordered_pair(X3,X4),X0)|~in(X4,X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f489])).
% 199.65/25.72  fof(f494,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|in(sK14_skl(X1,X2,X0),X1)|in(ordered_pair(sK14_skl(X1,X2,X0),sK15_skl(X1,X2,X0)),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f489])).
% 199.65/25.72  fof(f514,plain,(
% 199.65/25.72    ![A]: (function(A)<=>(![B,C,D]: ((~in(ordered_pair(B,C),A)|~in(ordered_pair(B,D),A))|C=D)))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f26])).
% 199.65/25.72  fof(f515,plain,(
% 199.65/25.72    ![A]: ((~function(A)|(![B,C,D]: ((~in(ordered_pair(B,C),A)|~in(ordered_pair(B,D),A))|C=D)))&(function(A)|(?[B,C,D]: ((in(ordered_pair(B,C),A)&in(ordered_pair(B,D),A))&~C=D))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f514])).
% 199.65/25.72  fof(f516,plain,(
% 199.65/25.72    (![A]: (~function(A)|(![C,D]: ((![B]: (~in(ordered_pair(B,C),A)|~in(ordered_pair(B,D),A)))|C=D))))&(![A]: (function(A)|(?[C,D]: ((?[B]: (in(ordered_pair(B,C),A)&in(ordered_pair(B,D),A)))&~C=D))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f515])).
% 199.65/25.72  fof(f517,plain,(
% 199.65/25.72    (![A]: (~function(A)|(![C,D]: ((![B]: (~in(ordered_pair(B,C),A)|~in(ordered_pair(B,D),A)))|C=D))))&(![A]: (function(A)|((in(ordered_pair(sK19_skl(A),sK17_skl(A)),A)&in(ordered_pair(sK19_skl(A),sK18_skl(A)),A))&~sK17_skl(A)=sK18_skl(A))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(C,sK17_skl(A)),skolemize(D,sK18_skl(A)),skolemize(B,sK19_skl(A))],[f516])).
% 199.65/25.72  fof(f518,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~function(X0)|~in(ordered_pair(X1,X2),X0)|~in(ordered_pair(X1,X3),X0)|X2=X3)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f517])).
% 199.65/25.72  fof(f519,plain,(
% 199.65/25.72    ![X0]: (function(X0)|in(ordered_pair(sK19_skl(X0),sK17_skl(X0)),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f517])).
% 199.65/25.72  fof(f520,plain,(
% 199.65/25.72    ![X0]: (function(X0)|in(ordered_pair(sK19_skl(X0),sK18_skl(X0)),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f517])).
% 199.65/25.72  fof(f522,plain,(
% 199.65/25.72    ![A,B,C]: (~relation_of2_as_subset(C,A,B)|(((B=empty_set&~A=empty_set)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f27])).
% 199.65/25.72  fof(f523,definition,(
% 199.65/25.72    ![A,B]: (sP2_prd(B,A)<=>(B=empty_set&~A=empty_set))),
% 199.65/25.72    introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 199.65/25.72  fof(f524,plain,(
% 199.65/25.72    ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((sP2_prd(B,A)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 199.65/25.72    inference(formula_renaming,[status(thm)],[f522,f523])).
% 199.65/25.72  fof(f525,plain,(
% 199.65/25.72    ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((sP2_prd(B,A)|((~quasi_total(C,A,B)|A=relation_dom_as_subset(A,B,C))&(quasi_total(C,A,B)|~A=relation_dom_as_subset(A,B,C))))&(~B=empty_set|(A=empty_set|((~quasi_total(C,A,B)|C=empty_set)&(quasi_total(C,A,B)|~C=empty_set))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f524])).
% 199.65/25.72  fof(f526,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|sP2_prd(X2,X1)|~quasi_total(X0,X1,X2)|X1=relation_dom_as_subset(X1,X2,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f525])).
% 199.65/25.72  fof(f527,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|sP2_prd(X2,X1)|quasi_total(X0,X1,X2)|~X1=relation_dom_as_subset(X1,X2,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f525])).
% 199.65/25.72  fof(f529,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|~X2=empty_set|X1=empty_set|quasi_total(X0,X1,X2)|~X0=empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f525])).
% 199.65/25.72  fof(f537,plain,(
% 199.65/25.72    ![X0]: (succ(X0)=set_union2(X0,singleton(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f29])).
% 199.65/25.72  fof(f538,plain,(
% 199.65/25.72    ![A]: (relation(A)<=>(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D)))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f30])).
% 199.65/25.72  fof(f539,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D)))))&(relation(A)|(?[B]: (in(B,A)&(![C,D]: ~B=ordered_pair(C,D))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f538])).
% 199.65/25.72  fof(f540,plain,(
% 199.65/25.72    (![A]: (~relation(A)|(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D))))))&(![A]: (relation(A)|(?[B]: (in(B,A)&(![C,D]: ~B=ordered_pair(C,D))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f539])).
% 199.65/25.72  fof(f541,plain,(
% 199.65/25.72    (![A]: (~relation(A)|(![B]: (~in(B,A)|B=ordered_pair(sK22_skl(B,A),sK23_skl(B,A))))))&(![A]: (relation(A)|(in(sK24_skl(A),A)&(![C,D]: ~sK24_skl(A)=ordered_pair(C,D)))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl]),skolemize(C,sK22_skl(B,A)),skolemize(D,sK23_skl(B,A)),skolemize(B,sK24_skl(A))],[f540])).
% 199.65/25.72  fof(f543,plain,(
% 199.65/25.72    ![X0]: (relation(X0)|in(sK24_skl(X0),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f541])).
% 199.65/25.72  fof(f552,plain,(
% 199.65/25.72    ![A,B,C]: ((~relation_of2(C,A,B)|subset(C,cartesian_product2(A,B)))&(relation_of2(C,A,B)|~subset(C,cartesian_product2(A,B))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f32])).
% 199.65/25.72  fof(f553,plain,(
% 199.65/25.72    (![A,B,C]: (~relation_of2(C,A,B)|subset(C,cartesian_product2(A,B))))&(![A,B,C]: (relation_of2(C,A,B)|~subset(C,cartesian_product2(A,B))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f552])).
% 199.65/25.72  fof(f555,plain,(
% 199.65/25.72    ![X0,X1,X2]: (relation_of2(X0,X1,X2)|~subset(X0,cartesian_product2(X1,X2)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f553])).
% 199.65/25.72  fof(f568,plain,(
% 199.65/25.72    ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f34])).
% 199.65/25.72  fof(f569,plain,(
% 199.65/25.72    (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f568])).
% 199.65/25.72  fof(f570,plain,(
% 199.65/25.72    (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK29_skl(B,A),B)|~sK29_skl(B,A)=A)&(in(sK29_skl(B,A),B)|sK29_skl(B,A)=A))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl]),skolemize(C,sK29_skl(B,A))],[f569])).
% 199.65/25.72  fof(f571,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f570])).
% 199.65/25.72  fof(f572,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f570])).
% 199.65/25.72  fof(f596,plain,(
% 199.65/25.72    ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f37])).
% 199.65/25.72  fof(f597,plain,(
% 199.65/25.72    (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f596])).
% 199.65/25.72  fof(f598,plain,(
% 199.65/25.72    (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK33_skl(A),A)))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl]),skolemize(B,sK33_skl(A))],[f597])).
% 199.65/25.72  fof(f599,plain,(
% 199.65/25.72    ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f598])).
% 199.65/25.72  fof(f600,plain,(
% 199.65/25.72    ![X0]: (X0=empty_set|in(sK33_skl(X0),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f598])).
% 199.65/25.72  fof(f601,plain,(
% 199.65/25.72    ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f38])).
% 199.65/25.72  fof(f602,plain,(
% 199.65/25.72    (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f601])).
% 199.65/25.72  fof(f603,plain,(
% 199.65/25.72    (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sK34_skl(B,A),B)|~subset(sK34_skl(B,A),A))&(in(sK34_skl(B,A),B)|subset(sK34_skl(B,A),A)))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl]),skolemize(C,sK34_skl(B,A))],[f602])).
% 199.65/25.72  fof(f605,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f603])).
% 199.65/25.72  fof(f637,plain,(
% 199.65/25.72    ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f43])).
% 199.65/25.72  fof(f638,plain,(
% 199.65/25.72    (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f637])).
% 199.65/25.72  fof(f639,plain,(
% 199.65/25.72    (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sK40_skl(C,B,A),C)|(~sK40_skl(C,B,A)=A&~sK40_skl(C,B,A)=B))&(in(sK40_skl(C,B,A),C)|(sK40_skl(C,B,A)=A|sK40_skl(C,B,A)=B)))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK40_skl]),skolemize(D,sK40_skl(C,B,A))],[f638])).
% 199.65/25.72  fof(f642,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f639])).
% 199.65/25.72  fof(f654,plain,(
% 199.65/25.72    ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f45])).
% 199.65/25.72  fof(f655,plain,(
% 199.65/25.72    (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f654])).
% 199.65/25.72  fof(f656,plain,(
% 199.65/25.72    (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sK43_skl(C,B,A),C)|(~in(sK43_skl(C,B,A),A)&~in(sK43_skl(C,B,A),B)))&(in(sK43_skl(C,B,A),C)|(in(sK43_skl(C,B,A),A)|in(sK43_skl(C,B,A),B))))))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(D,sK43_skl(C,B,A))],[f655])).
% 199.65/25.72  fof(f657,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|~in(X3,X0)|in(X3,X1)|in(X3,X2))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f656])).
% 199.65/25.72  fof(f658,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f656])).
% 199.65/25.72  fof(f713,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f52])).
% 199.65/25.72  fof(f714,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f713])).
% 199.65/25.72  fof(f715,plain,(
% 199.65/25.72    ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f714])).
% 199.65/25.72  fof(f716,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f715])).
% 199.65/25.72  fof(f718,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|~X2=apply(X0,X1)|X2=empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f715])).
% 199.65/25.72  fof(f799,plain,(
% 199.65/25.72    ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X0,X1),singleton(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f64])).
% 199.65/25.72  fof(f889,plain,(
% 199.65/25.72    ![A,B]: ((~proper_subset(A,B)|(subset(A,B)&~A=B))&(proper_subset(A,B)|(~subset(A,B)|A=B)))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f77])).
% 199.65/25.72  fof(f890,plain,(
% 199.65/25.72    (![A,B]: (~proper_subset(A,B)|(subset(A,B)&~A=B)))&(![A,B]: (proper_subset(A,B)|(~subset(A,B)|A=B)))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f889])).
% 199.65/25.72  fof(f893,plain,(
% 199.65/25.72    ![X0,X1]: (proper_subset(X0,X1)|~subset(X0,X1)|X0=X1)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f890])).
% 199.65/25.72  fof(f910,plain,(
% 199.65/25.72    ![A]: (~relation(A)|relation(relation_inverse(A)))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f104])).
% 199.65/25.72  fof(f911,plain,(
% 199.65/25.72    ![X0]: (~relation(X0)|relation(relation_inverse(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f910])).
% 199.65/25.72  fof(f912,plain,(
% 199.65/25.72    ![A,B,C]: (~relation_of2(C,A,B)|element(relation_dom_as_subset(A,B,C),powerset(A)))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f105])).
% 199.65/25.72  fof(f913,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|element(relation_dom_as_subset(X1,X2,X0),powerset(X1)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f912])).
% 199.65/25.72  fof(f920,plain,(
% 199.65/25.72    ![X0]: (relation(identity_relation(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f111])).
% 199.65/25.72  fof(f933,plain,(
% 199.65/25.72    ![A,B,C]: (~relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f120])).
% 199.65/25.72  fof(f934,plain,(
% 199.65/25.72    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|element(X0,powerset(cartesian_product2(X1,X2))))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f933])).
% 199.65/25.72  fof(f939,plain,(
% 199.65/25.72    ![A,B]: relation_of2_as_subset(sK91_skl(B,A),A,B)),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK91_skl]),skolemize(C,sK91_skl(B,A))],[f123])).
% 199.65/25.72  fof(f940,plain,(
% 199.65/25.72    ![X0,X1]: (relation_of2_as_subset(sK91_skl(X0,X1),X1,X0))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f939])).
% 199.65/25.72  fof(f944,plain,(
% 199.65/25.72    ![A]: (~empty(A)|(empty(relation_inverse(A))&relation(relation_inverse(A))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f125])).
% 199.65/25.72  fof(f945,plain,(
% 199.65/25.72    ![X0]: (~empty(X0)|empty(relation_inverse(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f944])).
% 199.65/25.72  fof(f947,plain,(
% 199.65/25.72    empty(empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f126])).
% 199.65/25.72  fof(f948,plain,(
% 199.65/25.72    relation(empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f126])).
% 199.65/25.72  fof(f957,plain,(
% 199.65/25.72    ![X0]: (~empty(succ(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f129])).
% 199.65/25.72  fof(f963,plain,(
% 199.65/25.72    (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f134])).
% 199.65/25.72  fof(f965,plain,(
% 199.65/25.72    ![X0]: (function(identity_relation(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f963])).
% 199.65/25.72  fof(f968,plain,(
% 199.65/25.72    function(empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f135])).
% 199.65/25.72  fof(f973,plain,(
% 199.65/25.72    ordinal(empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f135])).
% 199.65/25.72  fof(f977,plain,(
% 199.65/25.72    ![A,B]: (empty(A)|~empty(set_union2(A,B)))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f138])).
% 199.65/25.72  fof(f978,plain,(
% 199.65/25.72    ![A]: (empty(A)|(![B]: ~empty(set_union2(A,B))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f977])).
% 199.65/25.72  fof(f979,plain,(
% 199.65/25.72    ![X0,X1]: (empty(X0)|~empty(set_union2(X0,X1)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f978])).
% 199.65/25.72  fof(f983,plain,(
% 199.65/25.72    ![A]: (~ordinal(A)|(((~empty(succ(A))&epsilon_transitive(succ(A)))&epsilon_connected(succ(A)))&ordinal(succ(A))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f140])).
% 199.65/25.72  fof(f985,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|epsilon_transitive(succ(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f983])).
% 199.65/25.72  fof(f986,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|epsilon_connected(succ(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f983])).
% 199.65/25.72  fof(f987,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|ordinal(succ(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f983])).
% 199.65/25.72  fof(f998,plain,(
% 199.65/25.72    ![A]: (~ordinal(A)|((epsilon_transitive(union(A))&epsilon_connected(union(A)))&ordinal(union(A))))),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f145])).
% 199.65/25.72  fof(f999,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|epsilon_transitive(union(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f998])).
% 199.65/25.72  fof(f1000,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|epsilon_connected(union(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f998])).
% 199.65/25.72  fof(f1001,plain,(
% 199.65/25.72    ![X0]: (~ordinal(X0)|ordinal(union(X0)))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f998])).
% 199.65/25.72  fof(f1029,plain,(
% 199.65/25.72    ![A]: (~relation(A)|relation_inverse(relation_inverse(A))=A)),
% 199.65/25.72    inference(pre_NNF_transformation,[status(thm)],[f157])).
% 199.65/25.72  fof(f1030,plain,(
% 199.65/25.72    ![X0]: (~relation(X0)|relation_inverse(relation_inverse(X0))=X0)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1029])).
% 199.65/25.72  fof(f1041,plain,(
% 199.65/25.72    ![X0]: (~singleton(X0)=empty_set)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f161])).
% 199.65/25.72  fof(f1100,plain,(
% 199.65/25.72    ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 199.65/25.72    inference(NNF_transformation,[status(thm)],[f176])).
% 199.65/25.72  fof(f1101,plain,(
% 199.65/25.72    (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 199.65/25.72    inference(miniscoping,[status(thm)],[f1100])).
% 199.65/25.72  fof(f1103,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1101])).
% 199.65/25.72  fof(f1104,plain,(
% 199.65/25.72    ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1101])).
% 199.65/25.72  fof(f1115,plain,(
% 199.65/25.72    (relation(sK102_skl)&function(sK102_skl))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK102_skl]),skolemize(A,sK102_skl)],[f179])).
% 199.65/25.72  fof(f1116,plain,(
% 199.65/25.72    relation(sK102_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1115])).
% 199.65/25.72  fof(f1117,plain,(
% 199.65/25.72    function(sK102_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1115])).
% 199.65/25.72  fof(f1127,plain,(
% 199.65/25.72    (((relation(sK105_skl)&function(sK105_skl))&one_to_one(sK105_skl))&empty(sK105_skl))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK105_skl]),skolemize(A,sK105_skl)],[f182])).
% 199.65/25.72  fof(f1128,plain,(
% 199.65/25.72    relation(sK105_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1127])).
% 199.65/25.72  fof(f1131,plain,(
% 199.65/25.72    empty(sK105_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1127])).
% 199.65/25.72  fof(f1141,plain,(
% 199.65/25.72    ((relation(sK109_skl)&empty(sK109_skl))&function(sK109_skl))),
% 199.65/25.72    inference(skolemize,[status(esa),new_symbols(skolem,[sK109_skl]),skolemize(A,sK109_skl)],[f186])).
% 199.65/25.72  fof(f1142,plain,(
% 199.65/25.72    relation(sK109_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1141])).
% 199.65/25.72  fof(f1143,plain,(
% 199.65/25.72    empty(sK109_skl)),
% 199.65/25.72    inference(cnf_transformation,[status(thm)],[f1141])).
% 199.65/25.72  fof(f1145,plain,(
% 199.65/25.72    ((((((relation(sK110_skl)&function(sK110_skl))&one_to_one(sK110_skl))&empty(sK110_skl))&epsilon_transitive(sK110_skl))&epsilon_connected(sK110_skl))&ordinal(sK110_skl))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK110_skl]),skolemize(A,sK110_skl)],[f187])).
% 199.65/25.74  fof(f1146,plain,(
% 199.65/25.74    relation(sK110_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1145])).
% 199.65/25.74  fof(f1149,plain,(
% 199.65/25.74    empty(sK110_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1145])).
% 199.65/25.74  fof(f1157,plain,(
% 199.65/25.74    (~empty(sK112_skl)&relation(sK112_skl))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK112_skl]),skolemize(A,sK112_skl)],[f189])).
% 199.65/25.74  fof(f1158,plain,(
% 199.65/25.74    ~empty(sK112_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1157])).
% 199.65/25.74  fof(f1159,plain,(
% 199.65/25.74    relation(sK112_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1157])).
% 199.65/25.74  fof(f1160,plain,(
% 199.65/25.74    ![A]: (element(sK113_skl(A),powerset(A))&empty(sK113_skl(A)))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK113_skl]),skolemize(B,sK113_skl(A))],[f190])).
% 199.65/25.74  fof(f1162,plain,(
% 199.65/25.74    ![X0]: (empty(sK113_skl(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1160])).
% 199.65/25.74  fof(f1165,plain,(
% 199.65/25.74    ((relation(sK115_skl)&function(sK115_skl))&one_to_one(sK115_skl))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK115_skl]),skolemize(A,sK115_skl)],[f192])).
% 199.65/25.74  fof(f1166,plain,(
% 199.65/25.74    relation(sK115_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1165])).
% 199.65/25.74  fof(f1167,plain,(
% 199.65/25.74    function(sK115_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1165])).
% 199.65/25.74  fof(f1174,plain,(
% 199.65/25.74    (relation(sK117_skl)&relation_empty_yielding(sK117_skl))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK117_skl]),skolemize(A,sK117_skl)],[f194])).
% 199.65/25.74  fof(f1175,plain,(
% 199.65/25.74    relation(sK117_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1174])).
% 199.65/25.74  fof(f1177,plain,(
% 199.65/25.74    ((relation(sK118_skl)&relation_empty_yielding(sK118_skl))&function(sK118_skl))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK118_skl]),skolemize(A,sK118_skl)],[f195])).
% 199.65/25.74  fof(f1178,plain,(
% 199.65/25.74    relation(sK118_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1177])).
% 199.65/25.74  fof(f1180,plain,(
% 199.65/25.74    function(sK118_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1177])).
% 199.65/25.74  fof(f1181,plain,(
% 199.65/25.74    ![A,B,C]: (~relation_of2(C,A,B)|relation_dom_as_subset(A,B,C)=relation_dom(C))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f196])).
% 199.65/25.74  fof(f1182,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|relation_dom_as_subset(X1,X2,X0)=relation_dom(X0))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1181])).
% 199.65/25.74  fof(f1191,plain,(
% 199.65/25.74    ![A,B,C]: ((~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B))&(relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f201])).
% 199.65/25.74  fof(f1192,plain,(
% 199.65/25.74    (![A,B,C]: (~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B)))&(![A,B,C]: (relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1191])).
% 199.65/25.74  fof(f1193,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation_of2(X0,X1,X2))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1192])).
% 199.65/25.74  fof(f1194,plain,(
% 199.65/25.74    ![X0,X1,X2]: (relation_of2_as_subset(X0,X1,X2)|~relation_of2(X0,X1,X2))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1192])).
% 199.65/25.74  fof(f1312,plain,(
% 199.65/25.74    ![A]: ((?[B,C,D]: ((((B=C&ordinal(C))&B=D)&ordinal(D))&~C=D))|(?[B]: ![C]: (in(C,B)<=>(?[D]: ((in(D,A)&D=C)&ordinal(C))))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f216])).
% 199.65/25.74  fof(f1313,definition,(
% 199.65/25.74    ![B,C,D]: (sP12_prd(D,C,B)<=>((((B=C&ordinal(C))&B=D)&ordinal(D))&~C=D))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sP12_prd])],[])).
% 199.65/25.74  fof(f1314,plain,(
% 199.65/25.74    ![A]: ((?[B,C,D]: sP12_prd(D,C,B))|(?[B]: ![C]: (in(C,B)<=>(?[D]: ((in(D,A)&D=C)&ordinal(C))))))),
% 199.65/25.74    inference(formula_renaming,[status(thm)],[f1312,f1313])).
% 199.65/25.74  fof(f1315,plain,(
% 199.65/25.74    ![A]: ((?[B,C,D]: sP12_prd(D,C,B))|(?[B]: ![C]: ((~in(C,B)|(?[D]: ((in(D,A)&D=C)&ordinal(C))))&(in(C,B)|(![D]: ((~in(D,A)|~D=C)|~ordinal(C)))))))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f1314])).
% 199.65/25.74  fof(f1316,plain,(
% 199.65/25.74    (?[B,C,D]: sP12_prd(D,C,B))|(![A]: ?[B]: ((![C]: (~in(C,B)|((?[D]: (in(D,A)&D=C))&ordinal(C))))&(![C]: (in(C,B)|((![D]: (~in(D,A)|~D=C))|~ordinal(C))))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1315])).
% 199.65/25.74  fof(f1317,plain,(
% 199.65/25.74    sP12_prd(sK168_skl,sK167_skl,sK166_skl)|(![A]: ((![C]: (~in(C,sK169_skl(A))|((in(sK170_skl(C,A),A)&sK170_skl(C,A)=C)&ordinal(C))))&(![C]: (in(C,sK169_skl(A))|((![D]: (~in(D,A)|~D=C))|~ordinal(C))))))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK166_skl,sK167_skl,sK168_skl,sK169_skl,sK170_skl]),skolemize(B,sK166_skl),skolemize(C,sK167_skl),skolemize(D,sK168_skl),skolemize(B,sK169_skl(A)),skolemize(D,sK170_skl(C,A))],[f1316])).
% 199.65/25.74  fof(f1318,plain,(
% 199.65/25.74    ![X0,X1]: (sP12_prd(sK168_skl,sK167_skl,sK166_skl)|~in(X0,sK169_skl(X1))|in(sK170_skl(X0,X1),X1))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1317])).
% 199.65/25.74  fof(f1319,plain,(
% 199.65/25.74    ![X0,X1]: (sP12_prd(sK168_skl,sK167_skl,sK166_skl)|~in(X0,sK169_skl(X1))|sK170_skl(X0,X1)=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1317])).
% 199.65/25.74  fof(f1320,plain,(
% 199.65/25.74    ![X0,X1]: (sP12_prd(sK168_skl,sK167_skl,sK166_skl)|~in(X0,sK169_skl(X1))|ordinal(X0))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1317])).
% 199.65/25.74  fof(f1321,plain,(
% 199.65/25.74    ![X0,X1,X2]: (sP12_prd(sK168_skl,sK167_skl,sK166_skl)|in(X0,sK169_skl(X1))|~in(X2,X1)|~X2=X0|~ordinal(X0))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1317])).
% 199.65/25.74  fof(f1395,plain,(
% 199.65/25.74    ![A]: (?[B]: (((relation(B)&function(B))&relation_dom(B)=A)&(![C]: (~in(C,A)|apply(B,C)=singleton(C)))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f225])).
% 199.65/25.74  fof(f1396,plain,(
% 199.65/25.74    ![A]: (((relation(sK194_skl(A))&function(sK194_skl(A)))&relation_dom(sK194_skl(A))=A)&(![C]: (~in(C,A)|apply(sK194_skl(A),C)=singleton(C))))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK194_skl]),skolemize(B,sK194_skl(A))],[f1395])).
% 199.65/25.74  fof(f1397,plain,(
% 199.65/25.74    ![X0]: (relation(sK194_skl(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1396])).
% 199.65/25.74  fof(f1398,plain,(
% 199.65/25.74    ![X0]: (function(sK194_skl(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1396])).
% 199.65/25.74  fof(f1399,plain,(
% 199.65/25.74    ![X0]: (relation_dom(sK194_skl(X0))=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1396])).
% 199.65/25.74  fof(f1410,plain,(
% 199.65/25.74    ![X0]: (in(X0,succ(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f229])).
% 199.65/25.74  fof(f1438,plain,(
% 199.65/25.74    ![A,B,C]: (~relation_of2_as_subset(C,A,B)|(subset(relation_dom(C),A)&subset(relation_rng(C),B)))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f238])).
% 199.65/25.74  fof(f1439,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|subset(relation_dom(X0),X1))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1438])).
% 199.65/25.74  fof(f1440,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|subset(relation_rng(X0),X2))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1438])).
% 199.65/25.74  fof(f1441,plain,(
% 199.65/25.74    ![A,B]: (~subset(A,B)|set_union2(A,B)=B)),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f239])).
% 199.65/25.74  fof(f1442,plain,(
% 199.65/25.74    ![X0,X1]: (~subset(X0,X1)|set_union2(X0,X1)=X1)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1441])).
% 199.65/25.74  fof(f1478,plain,(
% 199.65/25.74    ![A,B,C,D]: (~relation_of2_as_subset(D,C,A)|(~subset(relation_rng(D),B)|relation_of2_as_subset(D,C,B)))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f249])).
% 199.65/25.74  fof(f1479,plain,(
% 199.65/25.74    ![C,D]: ((![A]: ~relation_of2_as_subset(D,C,A))|(![B]: (~subset(relation_rng(D),B)|relation_of2_as_subset(D,C,B))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1478])).
% 199.65/25.74  fof(f1480,plain,(
% 199.65/25.74    ![X0,X1,X2,X3]: (~relation_of2_as_subset(X0,X1,X2)|~subset(relation_rng(X0),X3)|relation_of2_as_subset(X0,X1,X3))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1479])).
% 199.65/25.74  fof(f1491,plain,(
% 199.65/25.74    ![A,B]: (~relation(B)|subset(relation_inverse_image(B,A),relation_dom(B)))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f252])).
% 199.65/25.74  fof(f1492,plain,(
% 199.65/25.74    ![B]: (~relation(B)|(![A]: subset(relation_inverse_image(B,A),relation_dom(B))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1491])).
% 199.65/25.74  fof(f1493,plain,(
% 199.65/25.74    ![X0,X1]: (~relation(X0)|subset(relation_inverse_image(X0,X1),relation_dom(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1492])).
% 199.65/25.74  fof(f1494,plain,(
% 199.65/25.74    ![A,B,C,D]: (~relation_of2_as_subset(D,C,A)|(~subset(A,B)|relation_of2_as_subset(D,C,B)))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f253])).
% 199.65/25.74  fof(f1495,plain,(
% 199.65/25.74    ![A,C,D]: (~relation_of2_as_subset(D,C,A)|(![B]: (~subset(A,B)|relation_of2_as_subset(D,C,B))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1494])).
% 199.65/25.74  fof(f1496,plain,(
% 199.65/25.74    ![X0,X1,X2,X3]: (~relation_of2_as_subset(X0,X1,X2)|~subset(X2,X3)|relation_of2_as_subset(X0,X1,X3))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1495])).
% 199.65/25.74  fof(f1503,plain,(
% 199.65/25.74    ![A,B]: (~relation(B)|((A=empty_set|~subset(A,relation_rng(B)))|~relation_inverse_image(B,A)=empty_set))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f255])).
% 199.65/25.74  fof(f1504,plain,(
% 199.65/25.74    ![B]: (~relation(B)|(![A]: ((A=empty_set|~subset(A,relation_rng(B)))|~relation_inverse_image(B,A)=empty_set)))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1503])).
% 199.65/25.74  fof(f1505,plain,(
% 199.65/25.74    ![X0,X1]: (~relation(X0)|X1=empty_set|~subset(X1,relation_rng(X0))|~relation_inverse_image(X0,X1)=empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1504])).
% 199.65/25.74  fof(f1506,plain,(
% 199.65/25.74    ![A,B,C]: (~relation(C)|(~subset(A,B)|subset(relation_inverse_image(C,A),relation_inverse_image(C,B))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f256])).
% 199.65/25.74  fof(f1507,plain,(
% 199.65/25.74    ![C]: (~relation(C)|(![A,B]: (~subset(A,B)|subset(relation_inverse_image(C,A),relation_inverse_image(C,B)))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1506])).
% 199.65/25.74  fof(f1508,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~subset(X1,X2)|subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1507])).
% 199.65/25.74  fof(f1522,plain,(
% 199.65/25.74    ![X0]: (set_union2(X0,empty_set)=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f262])).
% 199.65/25.74  fof(f1523,plain,(
% 199.65/25.74    ![A,B]: (~in(A,B)|element(A,B))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f263])).
% 199.65/25.74  fof(f1524,plain,(
% 199.65/25.74    ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1523])).
% 199.65/25.74  fof(f1528,plain,(
% 199.65/25.74    powerset(empty_set)=singleton(empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f265])).
% 199.65/25.74  fof(f1543,plain,(
% 199.65/25.74    ![A,B,C,D]: (((~function(D)|~quasi_total(D,A,B))|~relation_of2_as_subset(D,A,B))|(![E]: ((~relation(E)|~function(E))|(~in(C,A)|(B=empty_set|apply(relation_composition(D,E),C)=apply(E,apply(D,C)))))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f269])).
% 199.65/25.74  fof(f1544,plain,(
% 199.65/25.74    ![A,B,D]: (((~function(D)|~quasi_total(D,A,B))|~relation_of2_as_subset(D,A,B))|(![E]: ((~relation(E)|~function(E))|(![C]: (~in(C,A)|(B=empty_set|apply(relation_composition(D,E),C)=apply(E,apply(D,C))))))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1543])).
% 199.65/25.74  fof(f1545,plain,(
% 199.65/25.74    ![X0,X1,X2,X3,X4]: (~function(X0)|~quasi_total(X0,X1,X2)|~relation_of2_as_subset(X0,X1,X2)|~relation(X3)|~function(X3)|~in(X4,X1)|X2=empty_set|apply(relation_composition(X0,X3),X4)=apply(X3,apply(X0,X4)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1544])).
% 199.65/25.74  fof(f1620,plain,(
% 199.65/25.74    ![X0]: (subset(empty_set,X0))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f293])).
% 199.65/25.74  fof(f1702,plain,(
% 199.65/25.74    ![A]: (~subset(A,empty_set)|A=empty_set)),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f317])).
% 199.65/25.74  fof(f1703,plain,(
% 199.65/25.74    ![X0]: (~subset(X0,empty_set)|X0=empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1702])).
% 199.65/25.74  fof(f1727,plain,(
% 199.65/25.74    (?[A,B,C,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[E]: (in(E,relation_inverse_image(D,C))<~>(in(E,A)&in(apply(D,E),C)))))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f326])).
% 199.65/25.74  fof(f1728,plain,(
% 199.65/25.74    ?[A,B,C,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[E]: ((in(E,relation_inverse_image(D,C))|(in(E,A)&in(apply(D,E),C)))&(~in(E,relation_inverse_image(D,C))|(~in(E,A)|~in(apply(D,E),C)))))))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f1727])).
% 199.65/25.74  fof(f1729,plain,(
% 199.65/25.74    ?[A,B,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[C,E]: ((in(E,relation_inverse_image(D,C))|(in(E,A)&in(apply(D,E),C)))&(~in(E,relation_inverse_image(D,C))|(~in(E,A)|~in(apply(D,E),C)))))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1728])).
% 199.65/25.74  fof(f1730,plain,(
% 199.65/25.74    (((function(sK214_skl)&quasi_total(sK214_skl,sK212_skl,sK213_skl))&relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl))&(~sK213_skl=empty_set&((in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|(in(sK216_skl,sK212_skl)&in(apply(sK214_skl,sK216_skl),sK215_skl)))&(~in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|(~in(sK216_skl,sK212_skl)|~in(apply(sK214_skl,sK216_skl),sK215_skl))))))),
% 199.65/25.74    inference(skolemize,[status(esa),new_symbols(skolem,[sK212_skl,sK213_skl,sK214_skl,sK215_skl,sK216_skl]),skolemize(A,sK212_skl),skolemize(B,sK213_skl),skolemize(D,sK214_skl),skolemize(C,sK215_skl),skolemize(E,sK216_skl)],[f1729])).
% 199.65/25.74  fof(f1731,plain,(
% 199.65/25.74    function(sK214_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1732,plain,(
% 199.65/25.74    quasi_total(sK214_skl,sK212_skl,sK213_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1733,plain,(
% 199.65/25.74    relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1734,plain,(
% 199.65/25.74    ~sK213_skl=empty_set),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1735,plain,(
% 199.65/25.74    in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|in(sK216_skl,sK212_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1736,plain,(
% 199.65/25.74    in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|in(apply(sK214_skl,sK216_skl),sK215_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1737,plain,(
% 199.65/25.74    ~in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|~in(sK216_skl,sK212_skl)|~in(apply(sK214_skl,sK216_skl),sK215_skl)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1730])).
% 199.65/25.74  fof(f1808,plain,(
% 199.65/25.74    relation_dom(empty_set)=empty_set),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f350])).
% 199.65/25.74  fof(f1809,plain,(
% 199.65/25.74    relation_rng(empty_set)=empty_set),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f350])).
% 199.65/25.74  fof(f1817,plain,(
% 199.65/25.74    ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f354])).
% 199.65/25.74  fof(f1818,plain,(
% 199.65/25.74    ![X0]: (~relation(X0)|~relation_dom(X0)=empty_set|X0=empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1817])).
% 199.65/25.74  fof(f1837,plain,(
% 199.65/25.74    ![A]: (~empty(A)|A=empty_set)),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f359])).
% 199.65/25.74  fof(f1838,plain,(
% 199.65/25.74    ![X0]: (~empty(X0)|X0=empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1837])).
% 199.65/25.74  fof(f1839,plain,(
% 199.65/25.74    ![A,B,C,D]: (((~function(D)|~quasi_total(D,A,B))|~relation_of2_as_subset(D,A,B))|(~in(C,A)|(B=empty_set|in(apply(D,C),relation_rng(D)))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f360])).
% 199.65/25.74  fof(f1840,plain,(
% 199.65/25.74    ![A,B,D]: (((~function(D)|~quasi_total(D,A,B))|~relation_of2_as_subset(D,A,B))|(![C]: (~in(C,A)|(B=empty_set|in(apply(D,C),relation_rng(D))))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1839])).
% 199.65/25.74  fof(f1841,plain,(
% 199.65/25.74    ![X0,X1,X2,X3]: (~function(X0)|~quasi_total(X0,X1,X2)|~relation_of2_as_subset(X0,X1,X2)|~in(X3,X1)|X2=empty_set|in(apply(X0,X3),relation_rng(X0)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1840])).
% 199.65/25.74  fof(f1849,plain,(
% 199.65/25.74    (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f364])).
% 199.65/25.74  fof(f1850,plain,(
% 199.65/25.74    ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1849])).
% 199.65/25.74  fof(f1874,plain,(
% 199.65/25.74    ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f371])).
% 199.65/25.74  fof(f1891,plain,(
% 199.65/25.74    ![A,B,C]: ((~relation(C)|~function(C))|(in(ordered_pair(A,B),C)<=>(in(A,relation_dom(C))&B=apply(C,A))))),
% 199.65/25.74    inference(pre_NNF_transformation,[status(thm)],[f376])).
% 199.65/25.74  fof(f1892,plain,(
% 199.65/25.74    ![A,B,C]: ((~relation(C)|~function(C))|((~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A)))))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f1891])).
% 199.65/25.74  fof(f1893,plain,(
% 199.65/25.74    ![C]: ((~relation(C)|~function(C))|((![A,B]: (~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A))))&(![A,B]: (in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A))))))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1892])).
% 199.65/25.74  fof(f1895,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(ordered_pair(X1,X2),X0)|X2=apply(X0,X1))),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1893])).
% 199.65/25.74  fof(f1917,plain,(
% 199.65/25.74    ![X0]: (union(powerset(X0))=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f384])).
% 199.65/25.74  fof(f1948,plain,(
% 199.65/25.74    ![A,B]: ((~sP2_prd(B,A)|(B=empty_set&~A=empty_set))&(sP2_prd(B,A)|(~B=empty_set|A=empty_set)))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f523])).
% 199.65/25.74  fof(f1949,plain,(
% 199.65/25.74    (![A,B]: (~sP2_prd(B,A)|(B=empty_set&~A=empty_set)))&(![A,B]: (sP2_prd(B,A)|(~B=empty_set|A=empty_set)))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f1948])).
% 199.65/25.74  fof(f1950,plain,(
% 199.65/25.74    ![X0,X1]: (~sP2_prd(X0,X1)|X0=empty_set)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f1949])).
% 199.65/25.74  fof(f2057,plain,(
% 199.65/25.74    ![B,C,D]: ((~sP12_prd(D,C,B)|((((B=C&ordinal(C))&B=D)&ordinal(D))&~C=D))&(sP12_prd(D,C,B)|((((~B=C|~ordinal(C))|~B=D)|~ordinal(D))|C=D)))),
% 199.65/25.74    inference(NNF_transformation,[status(thm)],[f1313])).
% 199.65/25.74  fof(f2058,plain,(
% 199.65/25.74    (![B,C,D]: (~sP12_prd(D,C,B)|((((B=C&ordinal(C))&B=D)&ordinal(D))&~C=D)))&(![B,C,D]: (sP12_prd(D,C,B)|((((~B=C|~ordinal(C))|~B=D)|~ordinal(D))|C=D)))),
% 199.65/25.74    inference(miniscoping,[status(thm)],[f2057])).
% 199.65/25.74  fof(f2059,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~sP12_prd(X0,X1,X2)|X2=X1)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f2058])).
% 199.65/25.74  fof(f2061,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~sP12_prd(X0,X1,X2)|X2=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f2058])).
% 199.65/25.74  fof(f2063,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~sP12_prd(X0,X1,X2)|~X1=X0)),
% 199.65/25.74    inference(cnf_transformation,[status(thm)],[f2058])).
% 199.65/25.74  fof(f2145,definition,(
% 199.65/25.74    sQ2_spl <=> (sP12_prd(sK168_skl,sK167_skl,sK166_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2146,plain,(
% 199.65/25.74    sP12_prd(sK168_skl,sK167_skl,sK166_skl)|~sQ2_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2145])).
% 199.65/25.74  fof(f2148,definition,(
% 199.65/25.74    ![X0,X1]: (sQ3_spl <=> (~in(X0,sK169_skl(X1))|in(sK170_skl(X0,X1),X1)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2151,plain,(
% 199.65/25.74    sQ2_spl|sQ3_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1318,f2145,f2148])).
% 199.65/25.74  fof(f2152,definition,(
% 199.65/25.74    ![X0,X1]: (sQ4_spl <=> (~in(X0,sK169_skl(X1))|sK170_skl(X0,X1)=X0))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2155,plain,(
% 199.65/25.74    sQ2_spl|sQ4_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1319,f2145,f2152])).
% 199.65/25.74  fof(f2156,definition,(
% 199.65/25.74    ![X0,X1]: (sQ5_spl <=> (~in(X0,sK169_skl(X1))|ordinal(X0)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2159,plain,(
% 199.65/25.74    sQ2_spl|sQ5_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1320,f2145,f2156])).
% 199.65/25.74  fof(f2160,definition,(
% 199.65/25.74    ![X0,X1,X2]: (sQ6_spl <=> (in(X0,sK169_skl(X1))|~in(X2,X1)|~X2=X0|~ordinal(X0)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2163,plain,(
% 199.65/25.74    sQ2_spl|sQ6_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1321,f2145,f2160])).
% 199.65/25.74  fof(f2164,definition,(
% 199.65/25.74    sQ7_spl <=> (in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2165,plain,(
% 199.65/25.74    in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|~sQ7_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2164])).
% 199.65/25.74  fof(f2167,definition,(
% 199.65/25.74    sQ8_spl <=> (in(sK216_skl,sK212_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2168,plain,(
% 199.65/25.74    in(sK216_skl,sK212_skl)|~sQ8_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2167])).
% 199.65/25.74  fof(f2170,plain,(
% 199.65/25.74    sQ7_spl|sQ8_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1735,f2164,f2167])).
% 199.65/25.74  fof(f2171,definition,(
% 199.65/25.74    sQ9_spl <=> (in(apply(sK214_skl,sK216_skl),sK215_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2172,plain,(
% 199.65/25.74    in(apply(sK214_skl,sK216_skl),sK215_skl)|~sQ9_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2171])).
% 199.65/25.74  fof(f2174,plain,(
% 199.65/25.74    sQ7_spl|sQ9_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1736,f2164,f2171])).
% 199.65/25.74  fof(f2175,plain,(
% 199.65/25.74    ~sQ7_spl|~sQ8_spl|~sQ9_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f1737,f2164,f2167,f2171])).
% 199.65/25.74  fof(f2176,plain,(
% 199.65/25.74    ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 199.65/25.74    inference(forward_subsumption_resolution,[status(thm)],[f405,f398])).
% 199.65/25.74  fof(f2180,plain,(
% 199.65/25.74    ![X0]: (subset(X0,X0))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f429])).
% 199.65/25.74  fof(f2190,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_inverse_image(X0,X2))|in(X1,relation_dom(X0)))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f470])).
% 199.65/25.74  fof(f2191,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_inverse_image(X0,X2))|in(apply(X0,X1),X2))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f471])).
% 199.65/25.74  fof(f2192,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_inverse_image(X0,X2))|~in(X1,relation_dom(X0))|~in(apply(X0,X1),X2))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f472])).
% 199.65/25.74  fof(f2196,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(ordered_pair(X1,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f490])).
% 199.65/25.74  fof(f2197,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f491])).
% 199.65/25.74  fof(f2198,plain,(
% 199.65/25.74    ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_inverse_image(X0,X2))|~in(ordered_pair(X1,X3),X0)|~in(X3,X2))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f492])).
% 199.65/25.74  fof(f2202,plain,(
% 199.65/25.74    ![X0]: (~relation_of2_as_subset(empty_set,X0,empty_set)|X0=empty_set|quasi_total(empty_set,X0,empty_set))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f529])).
% 199.65/25.74  fof(f2211,plain,(
% 199.65/25.74    ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f571])).
% 199.65/25.74  fof(f2212,plain,(
% 199.65/25.74    ![X0]: (in(X0,singleton(X0)))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f572])).
% 199.65/25.74  fof(f2223,plain,(
% 199.65/25.74    ![X0]: (~in(X0,empty_set))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f599])).
% 199.65/25.74  fof(f2225,plain,(
% 199.65/25.74    ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f605])).
% 199.65/25.74  fof(f2231,plain,(
% 199.65/25.74    ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f642])).
% 199.65/25.74  fof(f2232,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~in(X0,set_union2(X1,X2))|in(X0,X1)|in(X0,X2))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f657])).
% 199.65/25.74  fof(f2233,plain,(
% 199.65/25.74    ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f658])).
% 199.65/25.74  fof(f2240,plain,(
% 199.65/25.74    ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f716])).
% 199.65/25.74  fof(f2241,plain,(
% 199.65/25.74    ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|apply(X0,X1)=empty_set)),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f718])).
% 199.65/25.74  fof(f2388,plain,(
% 199.65/25.74    ![X0,X1]: (~sP12_prd(X0,X0,X1))),
% 199.65/25.74    inference(destructive_equality_resolution,[status(thm)],[f2063])).
% 199.65/25.74  fof(f2407,plain,(
% 199.65/25.74    ~relation(sK214_skl)|~function(sK214_skl)|in(apply(sK214_skl,sK216_skl),sK215_skl)|~sQ7_spl),
% 199.65/25.74    inference(resolution,[status(thm)],[f2165,f2191])).
% 199.65/25.74  fof(f2408,plain,(
% 199.65/25.74    ~relation(sK214_skl)|~function(sK214_skl)|in(sK216_skl,relation_dom(sK214_skl))|~sQ7_spl),
% 199.65/25.74    inference(resolution,[status(thm)],[f2165,f2190])).
% 199.65/25.74  fof(f2410,definition,(
% 199.65/25.74    sQ10_spl <=> (relation(sK214_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2412,plain,(
% 199.65/25.74    ~relation(sK214_skl)|sQ10_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2410])).
% 199.65/25.74  fof(f2413,definition,(
% 199.65/25.74    sQ11_spl <=> (function(sK214_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2415,plain,(
% 199.65/25.74    ~function(sK214_skl)|sQ11_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2413])).
% 199.65/25.74  fof(f2416,plain,(
% 199.65/25.74    ~sQ10_spl|~sQ11_spl|sQ9_spl|~sQ7_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2407,f2410,f2413,f2171,f2164])).
% 199.65/25.74  fof(f2417,definition,(
% 199.65/25.74    sQ12_spl <=> (in(sK216_skl,relation_dom(sK214_skl)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2418,plain,(
% 199.65/25.74    in(sK216_skl,relation_dom(sK214_skl))|~sQ12_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2417])).
% 199.65/25.74  fof(f2419,plain,(
% 199.65/25.74    ~in(sK216_skl,relation_dom(sK214_skl))|sQ12_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2417])).
% 199.65/25.74  fof(f2420,plain,(
% 199.65/25.74    ~sQ10_spl|~sQ11_spl|sQ12_spl|~sQ7_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2408,f2410,f2413,f2417,f2164])).
% 199.65/25.74  fof(f2423,plain,(
% 199.65/25.74    subset(relation_dom(sK214_skl),sK212_skl)),
% 199.65/25.74    inference(resolution,[status(thm)],[f1439,f1733])).
% 199.65/25.74  fof(f2434,definition,(
% 199.65/25.74    sQ15_spl <=> (relation_dom(empty_set)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2436,plain,(
% 199.65/25.74    ~relation_dom(empty_set)=empty_set|sQ15_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2434])).
% 199.65/25.74  fof(f2437,definition,(
% 199.65/25.74    sQ16_spl <=> (empty_set=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2441,plain,(
% 199.65/25.74    ~empty_set=empty_set|sQ15_spl),
% 199.65/25.74    inference(forward_demodulation,[status(thm)],[f1808,f2436])).
% 199.65/25.74  fof(f2442,plain,(
% 199.65/25.74    $false|sQ15_spl),
% 199.65/25.74    inference(trivial_equality_resolution,[status(thm)],[f2441])).
% 199.65/25.74  fof(f2443,plain,(
% 199.65/25.74    sQ15_spl),
% 199.65/25.74    inference(contradiction_clause,[status(thm)],[f2442])).
% 199.65/25.74  fof(f2444,plain,(
% 199.65/25.74    ![X0]: (~relation(empty_set)|subset(relation_inverse_image(empty_set,X0),empty_set))),
% 199.65/25.74    inference(paramodulation,[status(thm)],[f1808,f1493])).
% 199.65/25.74  fof(f2445,definition,(
% 199.65/25.74    sQ17_spl <=> (relation(empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2447,plain,(
% 199.65/25.74    ~relation(empty_set)|sQ17_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2445])).
% 199.65/25.74  fof(f2448,definition,(
% 199.65/25.74    ![X0]: (sQ18_spl <=> (subset(relation_inverse_image(empty_set,X0),empty_set)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2449,plain,(
% 199.65/25.74    ![X0]: (subset(relation_inverse_image(empty_set,X0),empty_set)|~sQ18_spl)),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2448])).
% 199.65/25.74  fof(f2451,plain,(
% 199.65/25.74    ~sQ17_spl|sQ18_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2444,f2445,f2448])).
% 199.65/25.74  fof(f2452,plain,(
% 199.65/25.74    $false|sQ17_spl),
% 199.65/25.74    inference(forward_subsumption_resolution,[status(thm)],[f2447,f948])).
% 199.65/25.74  fof(f2453,plain,(
% 199.65/25.74    sQ17_spl),
% 199.65/25.74    inference(contradiction_clause,[status(thm)],[f2452])).
% 199.65/25.74  fof(f2455,plain,(
% 199.65/25.74    ~relation_dom(sK105_skl)=empty_set|sK105_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1128,f1818])).
% 199.65/25.74  fof(f2456,definition,(
% 199.65/25.74    sQ19_spl <=> (relation_dom(sK105_skl)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2458,plain,(
% 199.65/25.74    ~relation_dom(sK105_skl)=empty_set|sQ19_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2456])).
% 199.65/25.74  fof(f2459,definition,(
% 199.65/25.74    sQ20_spl <=> (sK105_skl=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2462,plain,(
% 199.65/25.74    ~sQ19_spl|sQ20_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2455,f2456,f2459])).
% 199.65/25.74  fof(f2463,plain,(
% 199.65/25.74    sK105_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1131,f1838])).
% 199.65/25.74  fof(f2468,plain,(
% 199.65/25.74    ~relation_dom(empty_set)=empty_set|sQ19_spl),
% 199.65/25.74    inference(backward_demodulation,[status(thm)],[f2463,f2458])).
% 199.65/25.74  fof(f2469,plain,(
% 199.65/25.74    ~sQ15_spl|sQ19_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2468,f2434,f2456])).
% 199.65/25.74  fof(f2476,plain,(
% 199.65/25.74    ~relation_dom(sK109_skl)=empty_set|sK109_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1142,f1818])).
% 199.65/25.74  fof(f2477,definition,(
% 199.65/25.74    sQ21_spl <=> (relation_dom(sK109_skl)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2479,plain,(
% 199.65/25.74    ~relation_dom(sK109_skl)=empty_set|sQ21_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2477])).
% 199.65/25.74  fof(f2480,definition,(
% 199.65/25.74    sQ22_spl <=> (sK109_skl=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2483,plain,(
% 199.65/25.74    ~sQ21_spl|sQ22_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2476,f2477,f2480])).
% 199.65/25.74  fof(f2484,plain,(
% 199.65/25.74    sK109_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1143,f1838])).
% 199.65/25.74  fof(f2487,plain,(
% 199.65/25.74    ~relation_dom(empty_set)=empty_set|sQ21_spl),
% 199.65/25.74    inference(backward_demodulation,[status(thm)],[f2484,f2479])).
% 199.65/25.74  fof(f2489,plain,(
% 199.65/25.74    ~sQ15_spl|sQ21_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2487,f2434,f2477])).
% 199.65/25.74  fof(f2491,plain,(
% 199.65/25.74    ~relation_dom(sK110_skl)=empty_set|sK110_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1146,f1818])).
% 199.65/25.74  fof(f2492,definition,(
% 199.65/25.74    sQ23_spl <=> (relation_dom(sK110_skl)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2494,plain,(
% 199.65/25.74    ~relation_dom(sK110_skl)=empty_set|sQ23_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2492])).
% 199.65/25.74  fof(f2495,definition,(
% 199.65/25.74    sQ24_spl <=> (sK110_skl=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2498,plain,(
% 199.65/25.74    ~sQ23_spl|sQ24_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2491,f2492,f2495])).
% 199.65/25.74  fof(f2502,plain,(
% 199.65/25.74    ![X0]: (relation_inverse_image(empty_set,X0)=empty_set|~sQ18_spl)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2449,f1703])).
% 199.65/25.74  fof(f2504,plain,(
% 199.65/25.74    ~relation(empty_set)|subset(empty_set,relation_dom(empty_set))|~sQ18_spl),
% 199.65/25.74    inference(paramodulation,[status(thm)],[f2502,f1493])).
% 199.65/25.74  fof(f2505,plain,(
% 199.65/25.74    ![X0,X1]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(apply(empty_set,X0),X1)|~sQ18_spl)),
% 199.65/25.74    inference(paramodulation,[status(thm)],[f2502,f2191])).
% 199.65/25.74  fof(f2506,plain,(
% 199.65/25.74    ![X0]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(X0,relation_dom(empty_set))|~sQ18_spl)),
% 199.65/25.74    inference(paramodulation,[status(thm)],[f2502,f2190])).
% 199.65/25.74  fof(f2507,definition,(
% 199.65/25.74    sQ25_spl <=> (subset(empty_set,relation_dom(empty_set)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2510,plain,(
% 199.65/25.74    ~sQ17_spl|sQ25_spl|~sQ18_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2504,f2445,f2507,f2448])).
% 199.65/25.74  fof(f2511,definition,(
% 199.65/25.74    sQ26_spl <=> (function(empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2513,plain,(
% 199.65/25.74    ~function(empty_set)|sQ26_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2511])).
% 199.65/25.74  fof(f2514,definition,(
% 199.65/25.74    ![X0,X1]: (sQ27_spl <=> (~in(X0,empty_set)|in(apply(empty_set,X0),X1)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2517,plain,(
% 199.65/25.74    ~sQ17_spl|~sQ26_spl|sQ27_spl|~sQ18_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2505,f2445,f2511,f2514,f2448])).
% 199.65/25.74  fof(f2518,definition,(
% 199.65/25.74    ![X0]: (sQ28_spl <=> (~in(X0,empty_set)|in(X0,relation_dom(empty_set))))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2521,plain,(
% 199.65/25.74    ~sQ17_spl|~sQ26_spl|sQ28_spl|~sQ18_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2506,f2445,f2511,f2518,f2448])).
% 199.65/25.74  fof(f2522,plain,(
% 199.65/25.74    $false|sQ26_spl),
% 199.65/25.74    inference(forward_subsumption_resolution,[status(thm)],[f2513,f968])).
% 199.65/25.74  fof(f2523,plain,(
% 199.65/25.74    sQ26_spl),
% 199.65/25.74    inference(contradiction_clause,[status(thm)],[f2522])).
% 199.65/25.74  fof(f2529,plain,(
% 199.65/25.74    ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation(X0))),
% 199.65/25.74    inference(resolution,[status(thm)],[f934,f401])).
% 199.65/25.74  fof(f2530,plain,(
% 199.65/25.74    relation(sK214_skl)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2529,f1733])).
% 199.65/25.74  fof(f2531,plain,(
% 199.65/25.74    $false|sQ10_spl),
% 199.65/25.74    inference(forward_subsumption_resolution,[status(thm)],[f2530,f2412])).
% 199.65/25.74  fof(f2532,plain,(
% 199.65/25.74    sQ10_spl),
% 199.65/25.74    inference(contradiction_clause,[status(thm)],[f2531])).
% 199.65/25.74  fof(f2533,plain,(
% 199.65/25.74    $false|sQ11_spl),
% 199.65/25.74    inference(forward_subsumption_resolution,[status(thm)],[f2415,f1731])).
% 199.65/25.74  fof(f2534,plain,(
% 199.65/25.74    sQ11_spl),
% 199.65/25.74    inference(contradiction_clause,[status(thm)],[f2533])).
% 199.65/25.74  fof(f2535,plain,(
% 199.65/25.74    ~relation_dom(sK214_skl)=empty_set|sK214_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f2530,f1818])).
% 199.65/25.74  fof(f2536,definition,(
% 199.65/25.74    sQ29_spl <=> (relation_dom(sK214_skl)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2539,definition,(
% 199.65/25.74    sQ30_spl <=> (sK214_skl=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2540,plain,(
% 199.65/25.74    sK214_skl=empty_set|~sQ30_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2539])).
% 199.65/25.74  fof(f2542,plain,(
% 199.65/25.74    ~sQ29_spl|sQ30_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2535,f2536,f2539])).
% 199.65/25.74  fof(f2543,plain,(
% 199.65/25.74    ![X0]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(ordered_pair(X0,apply(empty_set,X0)),empty_set))),
% 199.65/25.74    inference(paramodulation,[status(thm)],[f1808,f2240])).
% 199.65/25.74  fof(f2544,definition,(
% 199.65/25.74    ![X0]: (sQ31_spl <=> (~in(X0,empty_set)|in(ordered_pair(X0,apply(empty_set,X0)),empty_set)))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2547,plain,(
% 199.65/25.74    ~sQ17_spl|~sQ26_spl|sQ31_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2543,f2445,f2511,f2544])).
% 199.65/25.74  fof(f2549,plain,(
% 199.65/25.74    sK110_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1149,f1838])).
% 199.65/25.74  fof(f2551,plain,(
% 199.65/25.74    ~relation_dom(empty_set)=empty_set|sQ23_spl),
% 199.65/25.74    inference(backward_demodulation,[status(thm)],[f2549,f2494])).
% 199.65/25.74  fof(f2558,plain,(
% 199.65/25.74    ~sQ15_spl|sQ23_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2551,f2434,f2492])).
% 199.65/25.74  fof(f2578,plain,(
% 199.65/25.74    ~relation_dom(sK117_skl)=empty_set|sK117_skl=empty_set),
% 199.65/25.74    inference(resolution,[status(thm)],[f1175,f1818])).
% 199.65/25.74  fof(f2579,definition,(
% 199.65/25.74    sQ36_spl <=> (relation_dom(sK117_skl)=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2581,plain,(
% 199.65/25.74    ~relation_dom(sK117_skl)=empty_set|sQ36_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2579])).
% 199.65/25.74  fof(f2582,definition,(
% 199.65/25.74    sQ37_spl <=> (sK117_skl=empty_set)),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2585,plain,(
% 199.65/25.74    ~sQ36_spl|sQ37_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2578,f2579,f2582])).
% 199.65/25.74  fof(f2586,plain,(
% 199.65/25.74    ~function(empty_set)|one_to_one(empty_set)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2176,f947])).
% 199.65/25.74  fof(f2587,definition,(
% 199.65/25.74    sQ38_spl <=> (one_to_one(empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2590,plain,(
% 199.65/25.74    ~sQ26_spl|sQ38_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2586,f2511,f2587])).
% 199.65/25.74  fof(f2597,plain,(
% 199.65/25.74    ~relation(sK214_skl)|~function(sK214_skl)|in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))|~in(sK216_skl,relation_dom(sK214_skl))|~sQ9_spl),
% 199.65/25.74    inference(resolution,[status(thm)],[f2172,f2192])).
% 199.65/25.74  fof(f2601,plain,(
% 199.65/25.74    ~sQ10_spl|~sQ11_spl|sQ7_spl|~sQ12_spl|~sQ9_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2597,f2410,f2413,f2164,f2417,f2171])).
% 199.65/25.74  fof(f2602,plain,(
% 199.65/25.74    ![X0]: (~subset(sK213_skl,X0)|relation_of2_as_subset(sK214_skl,sK212_skl,X0))),
% 199.65/25.74    inference(resolution,[status(thm)],[f1496,f1733])).
% 199.65/25.74  fof(f2603,plain,(
% 199.65/25.74    ![X0]: (~relation(sK115_skl)|in(X0,relation_dom(sK115_skl))|apply(sK115_skl,X0)=empty_set)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2241,f1167])).
% 199.65/25.74  fof(f2604,plain,(
% 199.65/25.74    ![X0]: (~relation(sK102_skl)|in(X0,relation_dom(sK102_skl))|apply(sK102_skl,X0)=empty_set)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2241,f1117])).
% 199.65/25.74  fof(f2605,plain,(
% 199.65/25.74    ![X0]: (~relation(empty_set)|in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2241,f968])).
% 199.65/25.74  fof(f2606,plain,(
% 199.65/25.74    ![X0]: (~relation(sK214_skl)|in(X0,relation_dom(sK214_skl))|apply(sK214_skl,X0)=empty_set)),
% 199.65/25.74    inference(resolution,[status(thm)],[f2241,f1731])).
% 199.65/25.74  fof(f2608,definition,(
% 199.65/25.74    sQ39_spl <=> (relation(sK115_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2610,plain,(
% 199.65/25.74    ~relation(sK115_skl)|sQ39_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2608])).
% 199.65/25.74  fof(f2611,definition,(
% 199.65/25.74    ![X0]: (sQ40_spl <=> (in(X0,relation_dom(sK115_skl))|apply(sK115_skl,X0)=empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2612,plain,(
% 199.65/25.74    ![X0]: (in(X0,relation_dom(sK115_skl))|apply(sK115_skl,X0)=empty_set|~sQ40_spl)),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2611])).
% 199.65/25.74  fof(f2614,plain,(
% 199.65/25.74    ~sQ39_spl|sQ40_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2603,f2608,f2611])).
% 199.65/25.74  fof(f2615,definition,(
% 199.65/25.74    sQ41_spl <=> (relation(sK102_skl))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2617,plain,(
% 199.65/25.74    ~relation(sK102_skl)|sQ41_spl),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2615])).
% 199.65/25.74  fof(f2618,definition,(
% 199.65/25.74    ![X0]: (sQ42_spl <=> (in(X0,relation_dom(sK102_skl))|apply(sK102_skl,X0)=empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2619,plain,(
% 199.65/25.74    ![X0]: (in(X0,relation_dom(sK102_skl))|apply(sK102_skl,X0)=empty_set|~sQ42_spl)),
% 199.65/25.74    inference(component_clause,[status(thm)],[f2618])).
% 199.65/25.74  fof(f2621,plain,(
% 199.65/25.74    ~sQ41_spl|sQ42_spl),
% 199.65/25.74    inference(split_clause,[status(thm)],[f2604,f2615,f2618])).
% 199.65/25.74  fof(f2622,definition,(
% 199.65/25.74    ![X0]: (sQ43_spl <=> (in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set))),
% 199.65/25.74    introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 199.65/25.74  fof(f2623,plain,(
% 199.65/25.76    ![X0]: (in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set|~sQ43_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2622])).
% 199.65/25.76  fof(f2625,plain,(
% 199.65/25.76    ~sQ17_spl|sQ43_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2605,f2445,f2622])).
% 199.65/25.76  fof(f2626,definition,(
% 199.65/25.76    ![X0]: (sQ44_spl <=> (in(X0,relation_dom(sK214_skl))|apply(sK214_skl,X0)=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2627,plain,(
% 199.65/25.76    ![X0]: (in(X0,relation_dom(sK214_skl))|apply(sK214_skl,X0)=empty_set|~sQ44_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2626])).
% 199.65/25.76  fof(f2629,plain,(
% 199.65/25.76    ~sQ10_spl|sQ44_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2606,f2410,f2626])).
% 199.65/25.76  fof(f2631,plain,(
% 199.65/25.76    ![X0]: (in(X0,empty_set)|apply(empty_set,X0)=empty_set|~sQ43_spl)),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f1808,f2623])).
% 199.65/25.76  fof(f2632,plain,(
% 199.65/25.76    ![X0]: (apply(empty_set,X0)=empty_set|~sQ43_spl)),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2631,f2223])).
% 199.65/25.76  fof(f2633,plain,(
% 199.65/25.76    $false|sQ41_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2617,f1116])).
% 199.65/25.76  fof(f2634,plain,(
% 199.65/25.76    sQ41_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2633])).
% 199.65/25.76  fof(f2635,plain,(
% 199.65/25.76    $false|sQ39_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2610,f1166])).
% 199.65/25.76  fof(f2636,plain,(
% 199.65/25.76    sQ39_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2635])).
% 199.65/25.76  fof(f2637,plain,(
% 199.65/25.76    ![X0]: (~subset(relation_rng(sK214_skl),X0)|relation_of2_as_subset(sK214_skl,sK212_skl,X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1480,f1733])).
% 199.65/25.76  fof(f2646,plain,(
% 199.65/25.76    ![X0]: (~relation(sK118_skl)|in(X0,relation_dom(sK118_skl))|apply(sK118_skl,X0)=empty_set)),
% 199.65/25.76    inference(resolution,[status(thm)],[f1180,f2241])).
% 199.65/25.76  fof(f2647,definition,(
% 199.65/25.76    sQ47_spl <=> (relation(sK118_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2649,plain,(
% 199.65/25.76    ~relation(sK118_skl)|sQ47_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2647])).
% 199.65/25.76  fof(f2650,definition,(
% 199.65/25.76    ![X0]: (sQ48_spl <=> (in(X0,relation_dom(sK118_skl))|apply(sK118_skl,X0)=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2651,plain,(
% 199.65/25.76    ![X0]: (in(X0,relation_dom(sK118_skl))|apply(sK118_skl,X0)=empty_set|~sQ48_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2650])).
% 199.65/25.76  fof(f2653,plain,(
% 199.65/25.76    ~sQ47_spl|sQ48_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2646,f2647,f2650])).
% 199.65/25.76  fof(f2654,plain,(
% 199.65/25.76    $false|sQ47_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2649,f1178])).
% 199.65/25.76  fof(f2655,plain,(
% 199.65/25.76    sQ47_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2654])).
% 199.65/25.76  fof(f2657,plain,(
% 199.65/25.76    ![X0]: (~relation_dom(identity_relation(X0))=empty_set|identity_relation(X0)=empty_set)),
% 199.65/25.76    inference(resolution,[status(thm)],[f920,f1818])).
% 199.65/25.76  fof(f2658,plain,(
% 199.65/25.76    ![X0]: (~X0=empty_set|identity_relation(X0)=empty_set)),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f1850,f2657])).
% 199.65/25.76  fof(f2659,plain,(
% 199.65/25.76    identity_relation(empty_set)=empty_set),
% 199.65/25.76    inference(destructive_equality_resolution,[status(thm)],[f2658])).
% 199.65/25.76  fof(f2673,plain,(
% 199.65/25.76    ![X0,X1,X2]: (apply(sK214_skl,ordered_pair(X0,X1))=empty_set|~function(relation_dom(sK214_skl))|~in(ordered_pair(X0,X2),relation_dom(sK214_skl))|X2=X1|~sQ44_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2627,f518])).
% 199.65/25.76  fof(f2674,plain,(
% 199.65/25.76    ![X0,X1,X2]: (apply(sK214_skl,ordered_pair(X0,X1))=empty_set|~relation(relation_dom(sK214_skl))|in(X0,relation_inverse_image(relation_dom(sK214_skl),X2))|~in(X1,X2)|~sQ44_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2627,f2198])).
% 199.65/25.76  fof(f2676,plain,(
% 199.65/25.76    ![X0]: (apply(sK214_skl,X0)=empty_set|~relation(sK214_skl)|~function(sK214_skl)|in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)|~sQ44_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2627,f2240])).
% 199.65/25.76  fof(f2700,definition,(
% 199.65/25.76    ![X0,X1,X2]: (sQ53_spl <=> (apply(sK214_skl,ordered_pair(X0,X1))=empty_set|~in(ordered_pair(X0,X2),relation_dom(sK214_skl))|X2=X1))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2703,definition,(
% 199.65/25.76    sQ54_spl <=> (function(relation_dom(sK214_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2704,plain,(
% 199.65/25.76    function(relation_dom(sK214_skl))|~sQ54_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2703])).
% 199.65/25.76  fof(f2706,plain,(
% 199.65/25.76    sQ53_spl|~sQ54_spl|~sQ44_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2673,f2700,f2703,f2626])).
% 199.65/25.76  fof(f2707,definition,(
% 199.65/25.76    ![X0,X1,X2]: (sQ55_spl <=> (apply(sK214_skl,ordered_pair(X0,X1))=empty_set|in(X0,relation_inverse_image(relation_dom(sK214_skl),X2))|~in(X1,X2)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2710,definition,(
% 199.65/25.76    sQ56_spl <=> (relation(relation_dom(sK214_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2711,plain,(
% 199.65/25.76    relation(relation_dom(sK214_skl))|~sQ56_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2710])).
% 199.65/25.76  fof(f2712,plain,(
% 199.65/25.76    ~relation(relation_dom(sK214_skl))|sQ56_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2710])).
% 199.65/25.76  fof(f2713,plain,(
% 199.65/25.76    sQ55_spl|~sQ56_spl|~sQ44_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2674,f2707,f2710,f2626])).
% 199.65/25.76  fof(f2714,definition,(
% 199.65/25.76    ![X0]: (sQ57_spl <=> (apply(sK214_skl,X0)=empty_set|in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2717,plain,(
% 199.65/25.76    sQ57_spl|~sQ10_spl|~sQ11_spl|~sQ44_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2676,f2714,f2410,f2413,f2626])).
% 199.65/25.76  fof(f2735,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(empty_set)|~function(empty_set)|in(X0,relation_inverse_image(empty_set,X1))|~in(X0,relation_dom(empty_set))|~in(empty_set,X1)|~sQ43_spl)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f2632,f2192])).
% 199.65/25.76  fof(f2736,definition,(
% 199.65/25.76    ![X0,X1]: (sQ60_spl <=> (in(X0,relation_inverse_image(empty_set,X1))|~in(X0,relation_dom(empty_set))|~in(empty_set,X1)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2739,plain,(
% 199.65/25.76    ~sQ17_spl|~sQ26_spl|sQ60_spl|~sQ43_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2735,f2445,f2511,f2736,f2622])).
% 199.65/25.76  fof(f2749,plain,(
% 199.65/25.76    ~relation(sK214_skl)|~function(sK214_skl)|in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl)|~sQ12_spl),
% 199.65/25.76    inference(resolution,[status(thm)],[f2418,f2240])).
% 199.65/25.76  fof(f2753,definition,(
% 199.65/25.76    sQ63_spl <=> (in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2754,plain,(
% 199.65/25.76    in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl)|~sQ63_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2753])).
% 199.65/25.76  fof(f2756,plain,(
% 199.65/25.76    ~sQ10_spl|~sQ11_spl|sQ63_spl|~sQ12_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2749,f2410,f2413,f2753,f2417])).
% 199.65/25.76  fof(f2760,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(X0)|relation_rng(X1)=empty_set|~relation_inverse_image(X0,relation_rng(X1))=empty_set|~relation_of2_as_subset(X1,X2,relation_rng(X0)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1505,f1440])).
% 199.65/25.76  fof(f2762,plain,(
% 199.65/25.76    ![X0]: (~relation(X0)|relation_rng(X0)=empty_set|~relation_inverse_image(X0,relation_rng(X0))=empty_set)),
% 199.65/25.76    inference(resolution,[status(thm)],[f1505,f2180])).
% 199.65/25.76  fof(f2763,definition,(
% 199.65/25.76    ![X0]: (sQ64_spl <=> (~relation(X0)|~relation_inverse_image(X0,empty_set)=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2764,plain,(
% 199.65/25.76    ![X0]: (~relation(X0)|~relation_inverse_image(X0,empty_set)=empty_set|~sQ64_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2763])).
% 199.65/25.76  fof(f2767,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(empty_set)|~subset(X0,X1)|subset(empty_set,relation_inverse_image(empty_set,X1))|~sQ18_spl)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f2502,f1508])).
% 199.65/25.76  fof(f2768,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(empty_set)|~subset(X0,X1)|subset(relation_inverse_image(empty_set,X0),empty_set)|~sQ18_spl)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f2502,f1508])).
% 199.65/25.76  fof(f2769,definition,(
% 199.65/25.76    ![X0,X1]: (sQ65_spl <=> (~subset(X0,X1)|subset(empty_set,relation_inverse_image(empty_set,X1))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2772,plain,(
% 199.65/25.76    ~sQ17_spl|sQ65_spl|~sQ18_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2767,f2445,f2769,f2448])).
% 199.65/25.76  fof(f2773,definition,(
% 199.65/25.76    ![X0,X1]: (sQ66_spl <=> (~subset(X0,X1)|subset(relation_inverse_image(empty_set,X0),empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2776,plain,(
% 199.65/25.76    ~sQ17_spl|sQ66_spl|~sQ18_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2768,f2445,f2773,f2448])).
% 199.65/25.76  fof(f2784,plain,(
% 199.65/25.76    ![X0]: (sK113_skl(X0)=empty_set)),
% 199.65/25.76    inference(resolution,[status(thm)],[f1162,f1838])).
% 199.65/25.76  fof(f2792,definition,(
% 199.65/25.76    ![X0]: (sQ67_spl <=> (~function(sK113_skl(X0))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2793,plain,(
% 199.65/25.76    ![X0]: (~function(sK113_skl(X0))|~sQ67_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2792])).
% 199.65/25.76  fof(f2796,plain,(
% 199.65/25.76    ~function(empty_set)|~sQ67_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f2784,f2793])).
% 199.65/25.76  fof(f2797,plain,(
% 199.65/25.76    $false|~sQ67_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2796,f968])).
% 199.65/25.76  fof(f2798,plain,(
% 199.65/25.76    ~sQ67_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2797])).
% 199.65/25.76  fof(f2799,plain,(
% 199.65/25.76    ![X0]: (~relation_dom(sK194_skl(X0))=empty_set|sK194_skl(X0)=empty_set)),
% 199.65/25.76    inference(resolution,[status(thm)],[f1397,f1818])).
% 199.65/25.76  fof(f2800,plain,(
% 199.65/25.76    ![X0]: (~X0=empty_set|sK194_skl(X0)=empty_set)),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f1399,f2799])).
% 199.65/25.76  fof(f2801,plain,(
% 199.65/25.76    sK194_skl(empty_set)=empty_set),
% 199.65/25.76    inference(destructive_equality_resolution,[status(thm)],[f2800])).
% 199.65/25.76  fof(f2829,plain,(
% 199.65/25.76    relation_of2_as_subset(sK214_skl,sK212_skl,relation_rng(sK214_skl))),
% 199.65/25.76    inference(resolution,[status(thm)],[f2637,f2180])).
% 199.65/25.76  fof(f2843,plain,(
% 199.65/25.76    ~relation_inverse_image(empty_set,empty_set)=empty_set|~sQ64_spl),
% 199.65/25.76    inference(resolution,[status(thm)],[f2764,f948])).
% 199.65/25.76  fof(f2844,plain,(
% 199.65/25.76    ~empty_set=empty_set|~sQ18_spl|~sQ64_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f2502,f2843])).
% 199.65/25.76  fof(f2845,plain,(
% 199.65/25.76    $false|~sQ18_spl|~sQ64_spl),
% 199.65/25.76    inference(trivial_equality_resolution,[status(thm)],[f2844])).
% 199.65/25.76  fof(f2846,plain,(
% 199.65/25.76    ~sQ18_spl|~sQ64_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2845])).
% 199.65/25.76  fof(f2873,plain,(
% 199.65/25.76    ![X0,X1]: (~function(sK214_skl)|~relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)|~relation(X0)|~function(X0)|~in(X1,sK212_skl)|sK213_skl=empty_set|apply(relation_composition(sK214_skl,X0),X1)=apply(X0,apply(sK214_skl,X1)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1545,f1732])).
% 199.65/25.76  fof(f2874,definition,(
% 199.65/25.76    sQ69_spl <=> (relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2876,plain,(
% 199.65/25.76    ~relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)|sQ69_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2874])).
% 199.65/25.76  fof(f2877,definition,(
% 199.65/25.76    ![X0,X1]: (sQ70_spl <=> (~relation(X0)|~function(X0)|~in(X1,sK212_skl)|apply(relation_composition(sK214_skl,X0),X1)=apply(X0,apply(sK214_skl,X1))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2880,definition,(
% 199.65/25.76    sQ71_spl <=> (sK213_skl=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2881,plain,(
% 199.65/25.76    sK213_skl=empty_set|~sQ71_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2880])).
% 199.65/25.76  fof(f2883,plain,(
% 199.65/25.76    ~sQ11_spl|~sQ69_spl|sQ70_spl|sQ71_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2873,f2413,f2874,f2877,f2880])).
% 199.65/25.76  fof(f2884,plain,(
% 199.65/25.76    $false|~sQ71_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2881,f1734])).
% 199.65/25.76  fof(f2885,plain,(
% 199.65/25.76    ~sQ71_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2884])).
% 199.65/25.76  fof(f2886,plain,(
% 199.65/25.76    $false|sQ69_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2876,f1733])).
% 199.65/25.76  fof(f2887,plain,(
% 199.65/25.76    sQ69_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2886])).
% 199.65/25.76  fof(f2888,plain,(
% 199.65/25.76    ![X0]: (~function(sK214_skl)|~relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)|~in(X0,sK212_skl)|sK213_skl=empty_set|in(apply(sK214_skl,X0),relation_rng(sK214_skl)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1841,f1732])).
% 199.65/25.76  fof(f2889,definition,(
% 199.65/25.76    ![X0]: (sQ72_spl <=> (~in(X0,sK212_skl)|in(apply(sK214_skl,X0),relation_rng(sK214_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2890,plain,(
% 199.65/25.76    ![X0]: (~in(X0,sK212_skl)|in(apply(sK214_skl,X0),relation_rng(sK214_skl))|~sQ72_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2889])).
% 199.65/25.76  fof(f2892,plain,(
% 199.65/25.76    ~sQ11_spl|~sQ69_spl|sQ72_spl|sQ71_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2888,f2413,f2874,f2889,f2880])).
% 199.65/25.76  fof(f2895,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_inverse_image(X0,singleton(apply(X0,X1))))|~in(X1,relation_dom(X0)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f2212,f2192])).
% 199.65/25.76  fof(f2910,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK194_skl(X0))|~function(sK194_skl(X0))|~in(X1,X0)|in(ordered_pair(X1,apply(sK194_skl(X0),X1)),sK194_skl(X0)))),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f1399,f2240])).
% 199.65/25.76  fof(f2912,plain,(
% 199.65/25.76    ![X0,X1]: (~function(sK194_skl(X0))|~in(X1,X0)|in(ordered_pair(X1,apply(sK194_skl(X0),X1)),sK194_skl(X0)))),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2910,f1397])).
% 199.65/25.76  fof(f2916,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_inverse_image(X0,succ(apply(X0,X1))))|~in(X1,relation_dom(X0)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1410,f2192])).
% 199.65/25.76  fof(f2922,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(relation_dom(X0))|relation_dom(X0)=identity_relation(X1)|in(sK0_skl(X1,relation_dom(X0)),X1)|~relation(X0)|~function(X0)|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(X0)),sK1_skl(X1,relation_dom(X0))),apply(X0,ordered_pair(sK0_skl(X1,relation_dom(X0)),sK1_skl(X1,relation_dom(X0))))),X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f425,f2240])).
% 199.65/25.76  fof(f2923,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(relation_inverse_image(X0,X1))|relation_inverse_image(X0,X1)=identity_relation(X2)|in(sK0_skl(X2,relation_inverse_image(X0,X1)),X2)|~relation(X0)|~function(X0)|in(apply(X0,ordered_pair(sK0_skl(X2,relation_inverse_image(X0,X1)),sK1_skl(X2,relation_inverse_image(X0,X1)))),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f425,f2191])).
% 199.65/25.76  fof(f2924,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(relation_inverse_image(X0,X1))|relation_inverse_image(X0,X1)=identity_relation(X2)|in(sK0_skl(X2,relation_inverse_image(X0,X1)),X2)|~relation(X0)|~function(X0)|in(ordered_pair(sK0_skl(X2,relation_inverse_image(X0,X1)),sK1_skl(X2,relation_inverse_image(X0,X1))),relation_dom(X0)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f425,f2190])).
% 199.65/25.76  fof(f2925,plain,(
% 199.65/25.76    ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|in(sK0_skl(X0,empty_set),X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f425,f2223])).
% 199.65/25.76  fof(f2930,definition,(
% 199.65/25.76    ![X0]: (sQ73_spl <=> (empty_set=identity_relation(X0)|in(sK0_skl(X0,empty_set),X0)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2933,plain,(
% 199.65/25.76    ~sQ17_spl|sQ73_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2925,f2445,f2930])).
% 199.65/25.76  fof(f2935,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(X0)|X0=identity_relation(X1)|sK0_skl(X1,X0)=sK1_skl(X1,X0)|~relation(X0)|in(sK0_skl(X1,X0),relation_inverse_image(X0,X2))|~in(sK1_skl(X1,X0),X2))),
% 199.65/25.76    inference(resolution,[status(thm)],[f426,f2198])).
% 199.65/25.76  fof(f2936,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(relation_dom(X0))|relation_dom(X0)=identity_relation(X1)|sK0_skl(X1,relation_dom(X0))=sK1_skl(X1,relation_dom(X0))|~relation(X0)|~function(X0)|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(X0)),sK1_skl(X1,relation_dom(X0))),apply(X0,ordered_pair(sK0_skl(X1,relation_dom(X0)),sK1_skl(X1,relation_dom(X0))))),X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f426,f2240])).
% 199.65/25.76  fof(f2937,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(relation_inverse_image(X0,X1))|relation_inverse_image(X0,X1)=identity_relation(X2)|sK0_skl(X2,relation_inverse_image(X0,X1))=sK1_skl(X2,relation_inverse_image(X0,X1))|~relation(X0)|~function(X0)|in(apply(X0,ordered_pair(sK0_skl(X2,relation_inverse_image(X0,X1)),sK1_skl(X2,relation_inverse_image(X0,X1)))),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f426,f2191])).
% 199.65/25.76  fof(f2938,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(relation_inverse_image(X0,X1))|relation_inverse_image(X0,X1)=identity_relation(X2)|sK0_skl(X2,relation_inverse_image(X0,X1))=sK1_skl(X2,relation_inverse_image(X0,X1))|~relation(X0)|~function(X0)|in(ordered_pair(sK0_skl(X2,relation_inverse_image(X0,X1)),sK1_skl(X2,relation_inverse_image(X0,X1))),relation_dom(X0)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f426,f2190])).
% 199.65/25.76  fof(f2939,plain,(
% 199.65/25.76    ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set))),
% 199.65/25.76    inference(resolution,[status(thm)],[f426,f2223])).
% 199.65/25.76  fof(f2943,plain,(
% 199.65/25.76    ![X0,X1,X2]: (~relation(X0)|X0=identity_relation(X1)|sK0_skl(X1,X0)=sK1_skl(X1,X0)|in(sK0_skl(X1,X0),relation_inverse_image(X0,X2))|~in(sK1_skl(X1,X0),X2))),
% 199.65/25.76    inference(duplicate_literals_removal,[status(thm)],[f2935])).
% 199.65/25.76  fof(f2944,definition,(
% 199.65/25.76    ![X0]: (sQ74_spl <=> (empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2947,plain,(
% 199.65/25.76    ~sQ17_spl|sQ74_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f2939,f2445,f2944])).
% 199.65/25.76  fof(f2949,definition,(
% 199.65/25.76    sQ75_spl <=> (relation(identity_relation(sK212_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2951,plain,(
% 199.65/25.76    ~relation(identity_relation(sK212_skl))|sQ75_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2949])).
% 199.65/25.76  fof(f2952,definition,(
% 199.65/25.76    sQ76_spl <=> (function(identity_relation(sK212_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2954,plain,(
% 199.65/25.76    ~function(identity_relation(sK212_skl))|sQ76_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2952])).
% 199.65/25.76  fof(f2958,definition,(
% 199.65/25.76    sQ78_spl <=> (in(sK216_skl,relation_dom(identity_relation(sK212_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f2960,plain,(
% 199.65/25.76    ~in(sK216_skl,relation_dom(identity_relation(sK212_skl)))|sQ78_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f2958])).
% 199.65/25.76  fof(f2962,plain,(
% 199.65/25.76    ~in(sK216_skl,sK212_skl)|sQ78_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f1850,f2960])).
% 199.65/25.76  fof(f2963,plain,(
% 199.65/25.76    $false|sQ76_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2954,f965])).
% 199.65/25.76  fof(f2964,plain,(
% 199.65/25.76    sQ76_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2963])).
% 199.65/25.76  fof(f2965,plain,(
% 199.65/25.76    $false|sQ75_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2951,f920])).
% 199.65/25.76  fof(f2966,plain,(
% 199.65/25.76    sQ75_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2965])).
% 199.65/25.76  fof(f2973,plain,(
% 199.65/25.76    $false|sQ78_spl|~sQ8_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2168,f2962])).
% 199.65/25.76  fof(f2974,plain,(
% 199.65/25.76    sQ78_spl|~sQ8_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f2973])).
% 199.65/25.76  fof(f3014,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|sK1_skl(X1,X0)=apply(X0,sK0_skl(X1,X0))|~relation(X0)|X0=identity_relation(X1)|sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1895,f426])).
% 199.65/25.76  fof(f3015,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|sK1_skl(X1,X0)=apply(X0,sK0_skl(X1,X0))|~relation(X0)|X0=identity_relation(X1)|in(sK0_skl(X1,X0),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f1895,f425])).
% 199.65/25.76  fof(f3018,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(relation_dom(sK214_skl))|~function(relation_dom(sK214_skl))|X0=apply(relation_dom(sK214_skl),X1)|apply(sK214_skl,ordered_pair(X1,X0))=empty_set|~sQ44_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f1895,f2627])).
% 199.65/25.76  fof(f3020,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|sK1_skl(X1,X0)=apply(X0,sK0_skl(X1,X0))|X0=identity_relation(X1)|sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 199.65/25.76    inference(duplicate_literals_removal,[status(thm)],[f3014])).
% 199.65/25.76  fof(f3021,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~function(X0)|sK1_skl(X1,X0)=apply(X0,sK0_skl(X1,X0))|X0=identity_relation(X1)|in(sK0_skl(X1,X0),X1))),
% 199.65/25.76    inference(duplicate_literals_removal,[status(thm)],[f3015])).
% 199.65/25.76  fof(f3022,definition,(
% 199.65/25.76    ![X0,X1]: (sQ81_spl <=> (X0=apply(relation_dom(sK214_skl),X1)|apply(sK214_skl,ordered_pair(X1,X0))=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3025,plain,(
% 199.65/25.76    ~sQ56_spl|~sQ54_spl|sQ81_spl|~sQ44_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3018,f2710,f2703,f3022,f2626])).
% 199.65/25.76  fof(f3041,plain,(
% 199.65/25.76    ![X0]: (set_union2(empty_set,X0)=X0)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f413,f1522])).
% 199.65/25.76  fof(f3047,plain,(
% 199.65/25.76    ![X0]: (~relation(empty_set)|X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(empty_set,X0)=empty_set)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f1809,f1505])).
% 199.65/25.76  fof(f3049,definition,(
% 199.65/25.76    ![X0]: (sQ82_spl <=> (X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(empty_set,X0)=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3052,plain,(
% 199.65/25.76    ~sQ17_spl|sQ82_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3047,f2445,f3049])).
% 199.65/25.76  fof(f3075,plain,(
% 199.65/25.76    ![X0,X1,X2]: (X0=relation_rng(X1)|~subset(X0,relation_rng(X1))|~relation_of2_as_subset(X1,X2,X0))),
% 199.65/25.76    inference(resolution,[status(thm)],[f431,f1440])).
% 199.65/25.76  fof(f3079,definition,(
% 199.65/25.76    sQ83_spl <=> (sK212_skl=relation_dom(sK214_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3080,plain,(
% 199.65/25.76    sK212_skl=relation_dom(sK214_skl)|~sQ83_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3079])).
% 199.65/25.76  fof(f3081,plain,(
% 199.65/25.76    ~sK212_skl=relation_dom(sK214_skl)|sQ83_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3079])).
% 199.65/25.76  fof(f3082,definition,(
% 199.65/25.76    sQ84_spl <=> (subset(sK212_skl,relation_dom(sK214_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3084,plain,(
% 199.65/25.76    ~subset(sK212_skl,relation_dom(sK214_skl))|sQ84_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3082])).
% 199.65/25.76  fof(f3088,plain,(
% 199.65/25.76    in(sK216_skl,sK212_skl)|~sQ83_spl|~sQ12_spl),
% 199.65/25.76    inference(backward_demodulation,[status(thm)],[f3080,f2418])).
% 199.65/25.76  fof(f3112,plain,(
% 199.65/25.76    ~subset(sK212_skl,sK212_skl)|~sQ83_spl|sQ84_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f3080,f3084])).
% 199.65/25.76  fof(f3113,plain,(
% 199.65/25.76    $false|~sQ83_spl|sQ84_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3112,f2180])).
% 199.65/25.76  fof(f3114,plain,(
% 199.65/25.76    ~sQ83_spl|sQ84_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3113])).
% 199.65/25.76  fof(f3122,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_dom_restriction(X0,X1)|in(sK2_skl(X1,empty_set,X0),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f440,f2223])).
% 199.65/25.76  fof(f3128,definition,(
% 199.65/25.76    ![X0,X1]: (sQ85_spl <=> (~relation(X0)|empty_set=relation_dom_restriction(X0,X1)|in(sK2_skl(X1,empty_set,X0),X1)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3131,plain,(
% 199.65/25.76    sQ85_spl|~sQ17_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3122,f3128,f2445])).
% 199.65/25.76  fof(f3132,plain,(
% 199.65/25.76    sQ8_spl|~sQ83_spl|~sQ12_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3088,f2167,f3079,f2417])).
% 199.65/25.76  fof(f3162,plain,(
% 199.65/25.76    ~in(sK216_skl,sK212_skl)|~sQ83_spl|sQ12_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f3080,f2419])).
% 199.65/25.76  fof(f3171,plain,(
% 199.65/25.76    $false|~sQ83_spl|sQ12_spl|~sQ8_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f2168,f3162])).
% 199.65/25.76  fof(f3172,plain,(
% 199.65/25.76    ~sQ83_spl|sQ12_spl|~sQ8_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3171])).
% 199.65/25.76  fof(f3315,plain,(
% 199.65/25.76    ![X0]: (apply(sK102_skl,X0)=empty_set|~relation(sK102_skl)|~function(sK102_skl)|in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)|~sQ42_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2619,f2240])).
% 199.65/25.76  fof(f3340,definition,(
% 199.65/25.76    ![X0]: (sQ95_spl <=> (apply(sK102_skl,X0)=empty_set|in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3343,definition,(
% 199.65/25.76    sQ96_spl <=> (function(sK102_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3345,plain,(
% 199.65/25.76    ~function(sK102_skl)|sQ96_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3343])).
% 199.65/25.76  fof(f3346,plain,(
% 199.65/25.76    sQ95_spl|~sQ41_spl|~sQ96_spl|~sQ42_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3315,f3340,f2615,f3343,f2618])).
% 199.65/25.76  fof(f3355,plain,(
% 199.65/25.76    $false|sQ96_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3345,f1117])).
% 199.65/25.76  fof(f3356,plain,(
% 199.65/25.76    sQ96_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3355])).
% 199.65/25.76  fof(f3480,plain,(
% 199.65/25.76    ![X0]: (apply(sK115_skl,X0)=empty_set|~relation(sK115_skl)|~function(sK115_skl)|in(ordered_pair(X0,apply(sK115_skl,X0)),sK115_skl)|~sQ40_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2612,f2240])).
% 199.65/25.76  fof(f3505,definition,(
% 199.65/25.76    ![X0]: (sQ107_spl <=> (apply(sK115_skl,X0)=empty_set|in(ordered_pair(X0,apply(sK115_skl,X0)),sK115_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3508,definition,(
% 199.65/25.76    sQ108_spl <=> (function(sK115_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3510,plain,(
% 199.65/25.76    ~function(sK115_skl)|sQ108_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3508])).
% 199.65/25.76  fof(f3511,plain,(
% 199.65/25.76    sQ107_spl|~sQ39_spl|~sQ108_spl|~sQ40_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3480,f3505,f2608,f3508,f2611])).
% 199.65/25.76  fof(f3520,plain,(
% 199.65/25.76    $false|sQ108_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3510,f1167])).
% 199.65/25.76  fof(f3521,plain,(
% 199.65/25.76    sQ108_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3520])).
% 199.65/25.76  fof(f3548,plain,(
% 199.65/25.76    ![X0]: (apply(sK118_skl,X0)=empty_set|~relation(sK118_skl)|~function(sK118_skl)|in(ordered_pair(X0,apply(sK118_skl,X0)),sK118_skl)|~sQ48_spl)),
% 199.65/25.76    inference(resolution,[status(thm)],[f2651,f2240])).
% 199.65/25.76  fof(f3573,definition,(
% 199.65/25.76    ![X0]: (sQ116_spl <=> (apply(sK118_skl,X0)=empty_set|in(ordered_pair(X0,apply(sK118_skl,X0)),sK118_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3576,definition,(
% 199.65/25.76    sQ117_spl <=> (function(sK118_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3578,plain,(
% 199.65/25.76    ~function(sK118_skl)|sQ117_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3576])).
% 199.65/25.76  fof(f3579,plain,(
% 199.65/25.76    sQ116_spl|~sQ47_spl|~sQ117_spl|~sQ48_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3548,f3573,f2647,f3576,f2650])).
% 199.65/25.76  fof(f3588,plain,(
% 199.65/25.76    $false|sQ117_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3578,f1180])).
% 199.65/25.76  fof(f3589,plain,(
% 199.65/25.76    sQ117_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3588])).
% 199.65/25.76  fof(f3600,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_rng_restriction(X1,X0)|in(sK8_skl(X1,empty_set,X0),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f460,f2223])).
% 199.65/25.76  fof(f3614,definition,(
% 199.65/25.76    ![X0,X1]: (sQ122_spl <=> (~relation(X0)|empty_set=relation_rng_restriction(X1,X0)|in(sK8_skl(X1,empty_set,X0),X1)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3617,plain,(
% 199.65/25.76    sQ122_spl|~sQ17_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3600,f3614,f2445])).
% 199.65/25.76  fof(f3653,definition,(
% 199.65/25.76    sQ123_spl <=> (relation(identity_relation(relation_dom(sK214_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3655,plain,(
% 199.65/25.76    ~relation(identity_relation(relation_dom(sK214_skl)))|sQ123_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3653])).
% 199.65/25.76  fof(f3656,definition,(
% 199.65/25.76    sQ124_spl <=> (function(identity_relation(relation_dom(sK214_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3658,plain,(
% 199.65/25.76    ~function(identity_relation(relation_dom(sK214_skl)))|sQ124_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3656])).
% 199.65/25.76  fof(f3667,plain,(
% 199.65/25.76    $false|sQ124_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3658,f965])).
% 199.65/25.76  fof(f3668,plain,(
% 199.65/25.76    sQ124_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3667])).
% 199.65/25.76  fof(f3669,plain,(
% 199.65/25.76    $false|sQ123_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f3655,f920])).
% 199.65/25.76  fof(f3670,plain,(
% 199.65/25.76    sQ123_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f3669])).
% 199.65/25.76  fof(f3764,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(empty_set)|relation_rng(X0)=empty_set|~relation_inverse_image(empty_set,relation_rng(X0))=empty_set|~relation_of2_as_subset(X0,X1,empty_set))),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f1809,f2760])).
% 199.65/25.76  fof(f3765,definition,(
% 199.65/25.76    sQ127_spl <=> (relation_rng(sK214_skl)=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3766,plain,(
% 199.65/25.76    relation_rng(sK214_skl)=empty_set|~sQ127_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3765])).
% 199.65/25.76  fof(f3767,plain,(
% 199.65/25.76    ~relation_rng(sK214_skl)=empty_set|sQ127_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3765])).
% 199.65/25.76  fof(f3768,definition,(
% 199.65/25.76    sQ128_spl <=> (relation_inverse_image(sK214_skl,relation_rng(sK214_skl))=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3773,definition,(
% 199.65/25.76    ![X0,X1]: (sQ129_spl <=> (relation_rng(X0)=empty_set|~relation_inverse_image(empty_set,relation_rng(X0))=empty_set|~relation_of2_as_subset(X0,X1,empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3776,plain,(
% 199.65/25.76    ~sQ17_spl|sQ129_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3764,f2445,f3773])).
% 199.65/25.76  fof(f3837,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK118_skl)|X0=relation_inverse_image(sK118_skl,X1)|in(sK9_skl(X0,X1,sK118_skl),X0)|in(sK9_skl(X0,X1,sK118_skl),relation_dom(sK118_skl)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f474,f1180])).
% 199.65/25.76  fof(f3838,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK115_skl)|X0=relation_inverse_image(sK115_skl,X1)|in(sK9_skl(X0,X1,sK115_skl),X0)|in(sK9_skl(X0,X1,sK115_skl),relation_dom(sK115_skl)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f474,f1167])).
% 199.65/25.76  fof(f3839,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK102_skl)|X0=relation_inverse_image(sK102_skl,X1)|in(sK9_skl(X0,X1,sK102_skl),X0)|in(sK9_skl(X0,X1,sK102_skl),relation_dom(sK102_skl)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f474,f1117])).
% 199.65/25.76  fof(f3840,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f474,f968])).
% 199.65/25.76  fof(f3841,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK214_skl)|X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl)))),
% 199.65/25.76    inference(resolution,[status(thm)],[f474,f1731])).
% 199.65/25.76  fof(f3849,definition,(
% 199.65/25.76    ![X0,X1]: (sQ131_spl <=> (X0=relation_inverse_image(sK118_skl,X1)|in(sK9_skl(X0,X1,sK118_skl),X0)|in(sK9_skl(X0,X1,sK118_skl),relation_dom(sK118_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3852,plain,(
% 199.65/25.76    ~sQ47_spl|sQ131_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3837,f2647,f3849])).
% 199.65/25.76  fof(f3853,definition,(
% 199.65/25.76    ![X0,X1]: (sQ132_spl <=> (X0=relation_inverse_image(sK115_skl,X1)|in(sK9_skl(X0,X1,sK115_skl),X0)|in(sK9_skl(X0,X1,sK115_skl),relation_dom(sK115_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3856,plain,(
% 199.65/25.76    ~sQ39_spl|sQ132_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3838,f2608,f3853])).
% 199.65/25.76  fof(f3857,definition,(
% 199.65/25.76    ![X0,X1]: (sQ133_spl <=> (X0=relation_inverse_image(sK102_skl,X1)|in(sK9_skl(X0,X1,sK102_skl),X0)|in(sK9_skl(X0,X1,sK102_skl),relation_dom(sK102_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3860,plain,(
% 199.65/25.76    ~sQ41_spl|sQ133_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3839,f2615,f3857])).
% 199.65/25.76  fof(f3861,definition,(
% 199.65/25.76    ![X0,X1]: (sQ134_spl <=> (X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3864,plain,(
% 199.65/25.76    ~sQ17_spl|sQ134_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3840,f2445,f3861])).
% 199.65/25.76  fof(f3865,definition,(
% 199.65/25.76    ![X0,X1]: (sQ135_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3866,plain,(
% 199.65/25.76    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~sQ135_spl)),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3865])).
% 199.65/25.76  fof(f3868,plain,(
% 199.65/25.76    ~sQ10_spl|sQ135_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3841,f2410,f3865])).
% 199.65/25.76  fof(f3893,definition,(
% 199.65/25.76    sQ137_spl <=> (relation(apply(sK214_skl,sK216_skl)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3894,plain,(
% 199.65/25.76    relation(apply(sK214_skl,sK216_skl))|~sQ137_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3893])).
% 199.65/25.76  fof(f3895,plain,(
% 199.65/25.76    ~relation(apply(sK214_skl,sK216_skl))|sQ137_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3893])).
% 199.65/25.76  fof(f3965,plain,(
% 199.65/25.76    relation_rng(sK117_skl)=empty_set|~relation_inverse_image(sK117_skl,relation_rng(sK117_skl))=empty_set),
% 199.65/25.76    inference(resolution,[status(thm)],[f2762,f1175])).
% 199.65/25.76  fof(f3968,plain,(
% 199.65/25.76    relation_rng(sK214_skl)=empty_set|~relation_inverse_image(sK214_skl,relation_rng(sK214_skl))=empty_set),
% 199.65/25.76    inference(resolution,[status(thm)],[f2762,f2530])).
% 199.65/25.76  fof(f3970,plain,(
% 199.65/25.76    relation_rng(empty_set)=empty_set|~relation_inverse_image(empty_set,relation_rng(empty_set))=empty_set),
% 199.65/25.76    inference(resolution,[status(thm)],[f2762,f948])).
% 199.65/25.76  fof(f3980,definition,(
% 199.65/25.76    sQ143_spl <=> (relation_rng(sK117_skl)=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3981,plain,(
% 199.65/25.76    relation_rng(sK117_skl)=empty_set|~sQ143_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3980])).
% 199.65/25.76  fof(f3983,definition,(
% 199.65/25.76    sQ144_spl <=> (relation_inverse_image(sK117_skl,relation_rng(sK117_skl))=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f3985,plain,(
% 199.65/25.76    ~relation_inverse_image(sK117_skl,relation_rng(sK117_skl))=empty_set|sQ144_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f3983])).
% 199.65/25.76  fof(f3986,plain,(
% 199.65/25.76    sQ143_spl|~sQ144_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3965,f3980,f3983])).
% 199.65/25.76  fof(f4001,plain,(
% 199.65/25.76    sQ127_spl|~sQ128_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3968,f3765,f3768])).
% 199.65/25.76  fof(f4009,definition,(
% 199.65/25.76    sQ151_spl <=> (relation_rng(empty_set)=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4012,definition,(
% 199.65/25.76    sQ152_spl <=> (relation_inverse_image(empty_set,relation_rng(empty_set))=empty_set)),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4014,plain,(
% 199.65/25.76    ~relation_inverse_image(empty_set,relation_rng(empty_set))=empty_set|sQ152_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f4012])).
% 199.65/25.76  fof(f4015,plain,(
% 199.65/25.76    sQ151_spl|~sQ152_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f3970,f4009,f4012])).
% 199.65/25.76  fof(f4016,plain,(
% 199.65/25.76    ~empty_set=empty_set|~sQ18_spl|sQ152_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f2502,f4014])).
% 199.65/25.76  fof(f4017,plain,(
% 199.65/25.76    $false|~sQ18_spl|sQ152_spl),
% 199.65/25.76    inference(trivial_equality_resolution,[status(thm)],[f4016])).
% 199.65/25.76  fof(f4018,plain,(
% 199.65/25.76    ~sQ18_spl|sQ152_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f4017])).
% 199.65/25.76  fof(f4097,definition,(
% 199.65/25.76    sQ155_spl <=> (relation(sK112_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4099,plain,(
% 199.65/25.76    ~relation(sK112_skl)|sQ155_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f4097])).
% 199.65/25.76  fof(f4108,plain,(
% 199.65/25.76    $false|sQ155_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f4099,f1159])).
% 199.65/25.76  fof(f4109,plain,(
% 199.65/25.76    sQ155_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f4108])).
% 199.65/25.76  fof(f4121,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK117_skl)|relation_rng(X0)=empty_set|~relation_inverse_image(sK117_skl,relation_rng(X0))=empty_set|~relation_of2_as_subset(X0,X1,empty_set)|~sQ143_spl)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f3981,f2760])).
% 199.65/25.76  fof(f4122,plain,(
% 199.65/25.76    ![X0]: (~relation(sK117_skl)|X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(sK117_skl,X0)=empty_set|~sQ143_spl)),
% 199.65/25.76    inference(paramodulation,[status(thm)],[f3981,f1505])).
% 199.65/25.76  fof(f4124,definition,(
% 199.65/25.76    sQ160_spl <=> (relation(sK117_skl))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4126,plain,(
% 199.65/25.76    ~relation(sK117_skl)|sQ160_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f4124])).
% 199.65/25.76  fof(f4127,definition,(
% 199.65/25.76    ![X0,X1]: (sQ161_spl <=> (relation_rng(X0)=empty_set|~relation_inverse_image(sK117_skl,relation_rng(X0))=empty_set|~relation_of2_as_subset(X0,X1,empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4130,plain,(
% 199.65/25.76    ~sQ160_spl|sQ161_spl|~sQ143_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f4121,f4124,f4127,f3980])).
% 199.65/25.76  fof(f4131,definition,(
% 199.65/25.76    ![X0]: (sQ162_spl <=> (X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(sK117_skl,X0)=empty_set))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4134,plain,(
% 199.65/25.76    ~sQ160_spl|sQ162_spl|~sQ143_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f4122,f4124,f4131,f3980])).
% 199.65/25.76  fof(f4135,plain,(
% 199.65/25.76    $false|sQ160_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f4126,f1175])).
% 199.65/25.76  fof(f4136,plain,(
% 199.65/25.76    sQ160_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f4135])).
% 199.65/25.76  fof(f4154,plain,(
% 199.65/25.76    ![X0,X1]: (subset(relation_dom(sK91_skl(X0,X1)),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f940,f1439])).
% 199.65/25.76  fof(f4159,plain,(
% 199.65/25.76    empty(relation_inverse(empty_set))),
% 199.65/25.76    inference(resolution,[status(thm)],[f945,f947])).
% 199.65/25.76  fof(f4166,plain,(
% 199.65/25.76    ~function(relation_inverse(empty_set))|one_to_one(relation_inverse(empty_set))),
% 199.65/25.76    inference(resolution,[status(thm)],[f4159,f2176])).
% 199.65/25.76  fof(f4168,plain,(
% 199.65/25.76    relation_inverse(empty_set)=empty_set),
% 199.65/25.76    inference(resolution,[status(thm)],[f4159,f1838])).
% 199.65/25.76  fof(f4169,definition,(
% 199.65/25.76    sQ165_spl <=> (function(relation_inverse(empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4171,plain,(
% 199.65/25.76    ~function(relation_inverse(empty_set))|sQ165_spl),
% 199.65/25.76    inference(component_clause,[status(thm)],[f4169])).
% 199.65/25.76  fof(f4172,definition,(
% 199.65/25.76    sQ166_spl <=> (one_to_one(relation_inverse(empty_set)))),
% 199.65/25.76    introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition])).
% 199.65/25.76  fof(f4175,plain,(
% 199.65/25.76    ~sQ165_spl|sQ166_spl),
% 199.65/25.76    inference(split_clause,[status(thm)],[f4166,f4169,f4172])).
% 199.65/25.76  fof(f4187,plain,(
% 199.65/25.76    ~function(empty_set)|sQ165_spl),
% 199.65/25.76    inference(forward_demodulation,[status(thm)],[f4168,f4171])).
% 199.65/25.76  fof(f4188,plain,(
% 199.65/25.76    $false|sQ165_spl),
% 199.65/25.76    inference(forward_subsumption_resolution,[status(thm)],[f4187,f968])).
% 199.65/25.76  fof(f4189,plain,(
% 199.65/25.76    sQ165_spl),
% 199.65/25.76    inference(contradiction_clause,[status(thm)],[f4188])).
% 199.65/25.76  fof(f4200,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK118_skl)|X0=relation_inverse_image(sK118_skl,X1)|in(sK9_skl(X0,X1,sK118_skl),X0)|in(apply(sK118_skl,sK9_skl(X0,X1,sK118_skl)),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f475,f1180])).
% 199.65/25.76  fof(f4201,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK115_skl)|X0=relation_inverse_image(sK115_skl,X1)|in(sK9_skl(X0,X1,sK115_skl),X0)|in(apply(sK115_skl,sK9_skl(X0,X1,sK115_skl)),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f475,f1167])).
% 199.65/25.76  fof(f4202,plain,(
% 199.65/25.76    ![X0,X1]: (~relation(sK102_skl)|X0=relation_inverse_image(sK102_skl,X1)|in(sK9_skl(X0,X1,sK102_skl),X0)|in(apply(sK102_skl,sK9_skl(X0,X1,sK102_skl)),X1))),
% 199.65/25.76    inference(resolution,[status(thm)],[f475,f1117])).
% 199.65/25.76  fof(f4203,plain,(
% 199.65/25.77    ![X0,X1]: (~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1))),
% 199.65/25.77    inference(resolution,[status(thm)],[f475,f968])).
% 199.65/25.77  fof(f4204,plain,(
% 199.65/25.77    ![X0,X1]: (~relation(sK214_skl)|X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1))),
% 199.65/25.77    inference(resolution,[status(thm)],[f475,f1731])).
% 199.65/25.77  fof(f4210,definition,(
% 199.65/25.77    ![X0,X1]: (sQ167_spl <=> (X0=relation_inverse_image(sK118_skl,X1)|in(sK9_skl(X0,X1,sK118_skl),X0)|in(apply(sK118_skl,sK9_skl(X0,X1,sK118_skl)),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4213,plain,(
% 199.65/25.77    ~sQ47_spl|sQ167_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4200,f2647,f4210])).
% 199.65/25.77  fof(f4214,definition,(
% 199.65/25.77    ![X0,X1]: (sQ168_spl <=> (X0=relation_inverse_image(sK115_skl,X1)|in(sK9_skl(X0,X1,sK115_skl),X0)|in(apply(sK115_skl,sK9_skl(X0,X1,sK115_skl)),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4217,plain,(
% 199.65/25.77    ~sQ39_spl|sQ168_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4201,f2608,f4214])).
% 199.65/25.77  fof(f4218,definition,(
% 199.65/25.77    ![X0,X1]: (sQ169_spl <=> (X0=relation_inverse_image(sK102_skl,X1)|in(sK9_skl(X0,X1,sK102_skl),X0)|in(apply(sK102_skl,sK9_skl(X0,X1,sK102_skl)),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4221,plain,(
% 199.65/25.77    ~sQ41_spl|sQ169_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4202,f2615,f4218])).
% 199.65/25.77  fof(f4222,definition,(
% 199.65/25.77    ![X0,X1]: (sQ170_spl <=> (X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4225,plain,(
% 199.65/25.77    ~sQ17_spl|sQ170_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4203,f2445,f4222])).
% 199.65/25.77  fof(f4226,definition,(
% 199.65/25.77    ![X0,X1]: (sQ171_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4227,plain,(
% 199.65/25.77    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)|~sQ171_spl)),
% 199.65/25.77    inference(component_clause,[status(thm)],[f4226])).
% 199.65/25.77  fof(f4229,plain,(
% 199.65/25.77    ~sQ10_spl|sQ171_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4204,f2410,f4226])).
% 199.65/25.77  fof(f4246,definition,(
% 199.65/25.77    sQ172_spl <=> (relation(sK194_skl(sK212_skl)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4248,plain,(
% 199.65/25.77    ~relation(sK194_skl(sK212_skl))|sQ172_spl),
% 199.65/25.77    inference(component_clause,[status(thm)],[f4246])).
% 199.65/25.77  fof(f4249,definition,(
% 199.65/25.77    sQ173_spl <=> (function(sK194_skl(sK212_skl)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4251,plain,(
% 199.65/25.77    ~function(sK194_skl(sK212_skl))|sQ173_spl),
% 199.65/25.77    inference(component_clause,[status(thm)],[f4249])).
% 199.65/25.77  fof(f4255,definition,(
% 199.65/25.77    sQ175_spl <=> (in(sK216_skl,relation_dom(sK194_skl(sK212_skl))))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4257,plain,(
% 199.65/25.77    ~in(sK216_skl,relation_dom(sK194_skl(sK212_skl)))|sQ175_spl),
% 199.65/25.77    inference(component_clause,[status(thm)],[f4255])).
% 199.65/25.77  fof(f4259,plain,(
% 199.65/25.77    ~in(sK216_skl,sK212_skl)|sQ175_spl),
% 199.65/25.77    inference(forward_demodulation,[status(thm)],[f1399,f4257])).
% 199.65/25.77  fof(f4260,plain,(
% 199.65/25.77    $false|sQ173_spl),
% 199.65/25.77    inference(forward_subsumption_resolution,[status(thm)],[f4251,f1398])).
% 199.65/25.77  fof(f4261,plain,(
% 199.65/25.77    sQ173_spl),
% 199.65/25.77    inference(contradiction_clause,[status(thm)],[f4260])).
% 199.65/25.77  fof(f4262,plain,(
% 199.65/25.77    $false|sQ172_spl),
% 199.65/25.77    inference(forward_subsumption_resolution,[status(thm)],[f4248,f1397])).
% 199.65/25.77  fof(f4263,plain,(
% 199.65/25.77    sQ172_spl),
% 199.65/25.77    inference(contradiction_clause,[status(thm)],[f4262])).
% 199.65/25.77  fof(f4279,plain,(
% 199.65/25.77    $false|sQ175_spl|~sQ8_spl),
% 199.65/25.77    inference(forward_subsumption_resolution,[status(thm)],[f2168,f4259])).
% 199.65/25.77  fof(f4280,plain,(
% 199.65/25.77    sQ175_spl|~sQ8_spl),
% 199.65/25.77    inference(contradiction_clause,[status(thm)],[f4279])).
% 199.65/25.77  fof(f4300,plain,(
% 199.65/25.77    ![X0]: (relation_dom(sK91_skl(X0,empty_set))=empty_set)),
% 199.65/25.77    inference(resolution,[status(thm)],[f4154,f1703])).
% 199.65/25.77  fof(f4312,plain,(
% 199.65/25.77    ![X0]: (~ordinal(powerset(X0))|epsilon_transitive(X0))),
% 199.65/25.77    inference(paramodulation,[status(thm)],[f1917,f999])).
% 199.65/25.77  fof(f4313,plain,(
% 199.65/25.77    ![X0]: (~ordinal(powerset(X0))|epsilon_connected(X0))),
% 199.65/25.77    inference(paramodulation,[status(thm)],[f1917,f1000])).
% 199.65/25.77  fof(f4317,plain,(
% 199.65/25.77    ![X0]: (~ordinal(powerset(X0))|ordinal(X0))),
% 199.65/25.77    inference(paramodulation,[status(thm)],[f1917,f1001])).
% 199.65/25.77  fof(f4361,plain,(
% 199.65/25.77    ![X0,X1]: (~relation(empty_set)|X0=relation_image(empty_set,X1)|in(sK11_skl(X0,X1,empty_set),X0))),
% 199.65/25.77    inference(resolution,[status(thm)],[f484,f2223])).
% 199.65/25.77  fof(f4367,definition,(
% 199.65/25.77    ![X0,X1]: (sQ176_spl <=> (X0=relation_image(empty_set,X1)|in(sK11_skl(X0,X1,empty_set),X0)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4370,plain,(
% 199.65/25.77    ~sQ17_spl|sQ176_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4361,f2445,f4367])).
% 199.65/25.77  fof(f4379,plain,(
% 199.65/25.77    ![X0]: (~in(X0,sK212_skl)|~relation(sK214_skl)|~function(sK214_skl)|in(X0,relation_inverse_image(sK214_skl,relation_rng(sK214_skl)))|~in(X0,relation_dom(sK214_skl))|~sQ72_spl)),
% 199.65/25.77    inference(resolution,[status(thm)],[f2890,f2192])).
% 199.65/25.77  fof(f4385,definition,(
% 199.65/25.77    ![X0]: (sQ177_spl <=> (~in(X0,sK212_skl)|in(X0,relation_inverse_image(sK214_skl,relation_rng(sK214_skl)))|~in(X0,relation_dom(sK214_skl))))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4388,plain,(
% 199.65/25.77    sQ177_spl|~sQ10_spl|~sQ11_spl|~sQ72_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4379,f4385,f2410,f2413,f2889])).
% 199.65/25.77  fof(f4392,definition,(
% 199.65/25.77    sQ179_spl <=> (in(empty_set,relation_rng(sK214_skl)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4393,plain,(
% 199.65/25.77    in(empty_set,relation_rng(sK214_skl))|~sQ179_spl),
% 199.65/25.77    inference(component_clause,[status(thm)],[f4392])).
% 199.65/25.77  fof(f4492,plain,(
% 199.65/25.77    ![X0,X1]: (~relation(empty_set)|~in(X0,empty_set)|in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)|~sQ18_spl)),
% 199.65/25.77    inference(paramodulation,[status(thm)],[f2502,f2196])).
% 199.65/25.77  fof(f4497,definition,(
% 199.65/25.77    ![X0,X1]: (sQ185_spl <=> (~in(X0,empty_set)|in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition])).
% 199.65/25.77  fof(f4500,plain,(
% 199.65/25.77    ~sQ17_spl|sQ185_spl|~sQ18_spl),
% 199.65/25.77    inference(split_clause,[status(thm)],[f4492,f2445,f4497,f2448])).
% 199.65/25.77  fof(f4563,plain,(
% 199.65/25.77    ![X0,X1]: (~relation(empty_set)|~in(X0,empty_set)|in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)|~sQ18_spl)),
% 199.65/25.77    inference(paramodulation,[status(thm)],[f2502,f2197])).
% 199.65/25.77  fof(f4564,definition,(
% 199.65/25.77    ![X0,X1]: (sQ186_spl <=> (~in(X0,empty_set)|in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)))),
% 199.65/25.77    introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4567,plain,(
% 199.65/25.78    ~sQ17_spl|sQ186_spl|~sQ18_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4563,f2445,f4564,f2448])).
% 199.65/25.78  fof(f4584,definition,(
% 199.65/25.78    ![X0]: (sQ187_spl <=> (in(sK216_skl,relation_inverse_image(sK214_skl,X0))|~in(empty_set,X0)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4592,plain,(
% 199.65/25.78    relation_rng(apply(sK214_skl,sK216_skl))=empty_set|~relation_inverse_image(apply(sK214_skl,sK216_skl),relation_rng(apply(sK214_skl,sK216_skl)))=empty_set|~sQ137_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f3894,f2762])).
% 199.65/25.78  fof(f4595,plain,(
% 199.65/25.78    ~relation_dom(apply(sK214_skl,sK216_skl))=empty_set|apply(sK214_skl,sK216_skl)=empty_set|~sQ137_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f3894,f1818])).
% 199.65/25.78  fof(f4596,definition,(
% 199.65/25.78    sQ188_spl <=> (relation_rng(apply(sK214_skl,sK216_skl))=empty_set)),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4597,plain,(
% 199.65/25.78    relation_rng(apply(sK214_skl,sK216_skl))=empty_set|~sQ188_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4596])).
% 199.65/25.78  fof(f4599,definition,(
% 199.65/25.78    sQ189_spl <=> (relation_inverse_image(apply(sK214_skl,sK216_skl),relation_rng(apply(sK214_skl,sK216_skl)))=empty_set)),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4601,plain,(
% 199.65/25.78    ~relation_inverse_image(apply(sK214_skl,sK216_skl),relation_rng(apply(sK214_skl,sK216_skl)))=empty_set|sQ189_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4599])).
% 199.65/25.78  fof(f4602,plain,(
% 199.65/25.78    sQ188_spl|~sQ189_spl|~sQ137_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4592,f4596,f4599,f3893])).
% 199.65/25.78  fof(f4603,definition,(
% 199.65/25.78    sQ190_spl <=> (relation_dom(apply(sK214_skl,sK216_skl))=empty_set)),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4605,plain,(
% 199.65/25.78    ~relation_dom(apply(sK214_skl,sK216_skl))=empty_set|sQ190_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4603])).
% 199.65/25.78  fof(f4606,definition,(
% 199.65/25.78    sQ191_spl <=> (apply(sK214_skl,sK216_skl)=empty_set)),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4607,plain,(
% 199.65/25.78    apply(sK214_skl,sK216_skl)=empty_set|~sQ191_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4606])).
% 199.65/25.78  fof(f4608,plain,(
% 199.65/25.78    ~apply(sK214_skl,sK216_skl)=empty_set|sQ191_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4606])).
% 199.65/25.78  fof(f4609,plain,(
% 199.65/25.78    ~sQ190_spl|sQ191_spl|~sQ137_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4595,f4603,f4606,f3893])).
% 199.65/25.78  fof(f4611,plain,(
% 199.65/25.78    ~relation_dom(empty_set)=empty_set|~sQ191_spl|sQ190_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f4607,f4605])).
% 199.65/25.78  fof(f4631,plain,(
% 199.65/25.78    ~relation_inverse_image(empty_set,relation_rng(apply(sK214_skl,sK216_skl)))=empty_set|~sQ191_spl|sQ189_spl),
% 199.65/25.78    inference(forward_demodulation,[status(thm)],[f4607,f4601])).
% 199.65/25.78  fof(f4632,plain,(
% 199.65/25.78    ~empty_set=empty_set|~sQ18_spl|~sQ191_spl|sQ189_spl),
% 199.65/25.78    inference(forward_demodulation,[status(thm)],[f2502,f4631])).
% 199.65/25.78  fof(f4633,plain,(
% 199.65/25.78    $false|~sQ18_spl|~sQ191_spl|sQ189_spl),
% 199.65/25.78    inference(trivial_equality_resolution,[status(thm)],[f4632])).
% 199.65/25.78  fof(f4634,plain,(
% 199.65/25.78    ~sQ18_spl|~sQ191_spl|sQ189_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f4633])).
% 199.65/25.78  fof(f4665,plain,(
% 199.65/25.78    ~sQ15_spl|~sQ191_spl|sQ190_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4611,f2434,f4606,f4603])).
% 199.65/25.78  fof(f4682,plain,(
% 199.65/25.78    in(ordered_pair(sK216_skl,empty_set),sK214_skl)|~sQ191_spl|~sQ63_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f4607,f2754])).
% 199.65/25.78  fof(f4789,plain,(
% 199.65/25.78    ![X0,X1]: (~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sK14_skl(X0,X1,empty_set),X0))),
% 199.65/25.78    inference(resolution,[status(thm)],[f494,f2223])).
% 199.65/25.78  fof(f4796,definition,(
% 199.65/25.78    ![X0,X1]: (sQ193_spl <=> (X0=relation_inverse_image(empty_set,X1)|in(sK14_skl(X0,X1,empty_set),X0)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4799,plain,(
% 199.65/25.78    ~sQ17_spl|sQ193_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4789,f2445,f4796])).
% 199.65/25.78  fof(f4822,plain,(
% 199.65/25.78    ~in(sK216_skl,sK212_skl)|in(empty_set,relation_rng(sK214_skl))|~sQ72_spl|~sQ191_spl),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f4607,f2890])).
% 199.65/25.78  fof(f4823,plain,(
% 199.65/25.78    ![X0]: (~relation(sK214_skl)|~function(sK214_skl)|in(sK216_skl,relation_inverse_image(sK214_skl,X0))|~in(sK216_skl,relation_dom(sK214_skl))|~in(empty_set,X0)|~sQ191_spl)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f4607,f2192])).
% 199.65/25.78  fof(f4824,plain,(
% 199.65/25.78    ~sQ8_spl|sQ179_spl|~sQ72_spl|~sQ191_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4822,f2167,f4392,f2889,f4606])).
% 199.65/25.78  fof(f4825,plain,(
% 199.65/25.78    ~sQ10_spl|~sQ11_spl|sQ187_spl|~sQ12_spl|~sQ191_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4823,f2410,f2413,f4584,f2417,f4606])).
% 199.65/25.78  fof(f4880,plain,(
% 199.65/25.78    ![X0]: (~relation(sK118_skl)|in(X0,relation_inverse_image(sK118_skl,singleton(apply(sK118_skl,X0))))|~in(X0,relation_dom(sK118_skl)))),
% 199.65/25.78    inference(resolution,[status(thm)],[f2895,f1180])).
% 199.65/25.78  fof(f4881,plain,(
% 199.65/25.78    ![X0]: (~relation(sK115_skl)|in(X0,relation_inverse_image(sK115_skl,singleton(apply(sK115_skl,X0))))|~in(X0,relation_dom(sK115_skl)))),
% 199.65/25.78    inference(resolution,[status(thm)],[f2895,f1167])).
% 199.65/25.78  fof(f4882,plain,(
% 199.65/25.78    ![X0]: (~relation(sK102_skl)|in(X0,relation_inverse_image(sK102_skl,singleton(apply(sK102_skl,X0))))|~in(X0,relation_dom(sK102_skl)))),
% 199.65/25.78    inference(resolution,[status(thm)],[f2895,f1117])).
% 199.65/25.78  fof(f4883,plain,(
% 199.65/25.78    ![X0]: (~relation(empty_set)|in(X0,relation_inverse_image(empty_set,singleton(apply(empty_set,X0))))|~in(X0,relation_dom(empty_set)))),
% 199.65/25.78    inference(resolution,[status(thm)],[f2895,f968])).
% 199.65/25.78  fof(f4884,plain,(
% 199.65/25.78    ![X0]: (~relation(sK214_skl)|in(X0,relation_inverse_image(sK214_skl,singleton(apply(sK214_skl,X0))))|~in(X0,relation_dom(sK214_skl)))),
% 199.65/25.78    inference(resolution,[status(thm)],[f2895,f1731])).
% 199.65/25.78  fof(f4893,definition,(
% 199.65/25.78    ![X0]: (sQ194_spl <=> (in(X0,relation_inverse_image(sK118_skl,singleton(apply(sK118_skl,X0))))|~in(X0,relation_dom(sK118_skl))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4896,plain,(
% 199.65/25.78    ~sQ47_spl|sQ194_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4880,f2647,f4893])).
% 199.65/25.78  fof(f4897,definition,(
% 199.65/25.78    ![X0]: (sQ195_spl <=> (in(X0,relation_inverse_image(sK115_skl,singleton(apply(sK115_skl,X0))))|~in(X0,relation_dom(sK115_skl))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4900,plain,(
% 199.65/25.78    ~sQ39_spl|sQ195_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4881,f2608,f4897])).
% 199.65/25.78  fof(f4901,definition,(
% 199.65/25.78    ![X0]: (sQ196_spl <=> (in(X0,relation_inverse_image(sK102_skl,singleton(apply(sK102_skl,X0))))|~in(X0,relation_dom(sK102_skl))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4904,plain,(
% 199.65/25.78    ~sQ41_spl|sQ196_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4882,f2615,f4901])).
% 199.65/25.78  fof(f4905,definition,(
% 199.65/25.78    ![X0]: (sQ197_spl <=> (in(X0,relation_inverse_image(empty_set,singleton(apply(empty_set,X0))))|~in(X0,relation_dom(empty_set))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4908,plain,(
% 199.65/25.78    ~sQ17_spl|sQ197_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4883,f2445,f4905])).
% 199.65/25.78  fof(f4909,definition,(
% 199.65/25.78    ![X0]: (sQ198_spl <=> (in(X0,relation_inverse_image(sK214_skl,singleton(apply(sK214_skl,X0))))|~in(X0,relation_dom(sK214_skl))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4912,plain,(
% 199.65/25.78    ~sQ10_spl|sQ198_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f4884,f2410,f4909])).
% 199.65/25.78  fof(f4918,definition,(
% 199.65/25.78    ![X0]: (sQ199_spl <=> (X0=empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f4919,plain,(
% 199.65/25.78    ![X0]: (X0=empty_set|~sQ199_spl)),
% 199.65/25.78    inference(component_clause,[status(thm)],[f4918])).
% 199.65/25.78  fof(f4922,plain,(
% 199.65/25.78    $false|~sQ199_spl|sQ191_spl),
% 199.65/25.78    inference(backward_subsumption_resolution,[status(thm)],[f4608,f4919])).
% 199.65/25.78  fof(f4942,plain,(
% 199.65/25.78    ~sQ199_spl|sQ191_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f4922])).
% 199.65/25.78  fof(f5058,plain,(
% 199.65/25.78    relation_dom(empty_set)=empty_set),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f2659,f1850])).
% 199.65/25.78  fof(f5077,plain,(
% 199.65/25.78    ![X0]: (~function(sK214_skl)|~in(ordered_pair(sK216_skl,X0),sK214_skl)|X0=empty_set|~sQ191_spl|~sQ63_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f4682,f518])).
% 199.65/25.78  fof(f5084,definition,(
% 199.65/25.78    ![X0]: (sQ200_spl <=> (~in(ordered_pair(sK216_skl,X0),sK214_skl)|X0=empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5087,plain,(
% 199.65/25.78    ~sQ11_spl|sQ200_spl|~sQ191_spl|~sQ63_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5077,f2413,f5084,f4606,f2753])).
% 199.65/25.78  fof(f5181,plain,(
% 199.65/25.78    sK166_skl=sK168_skl|~sQ2_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f2146,f2061])).
% 199.65/25.78  fof(f5182,plain,(
% 199.65/25.78    sK166_skl=sK167_skl|~sQ2_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f2146,f2059])).
% 199.65/25.78  fof(f5183,plain,(
% 199.65/25.78    sP12_prd(sK166_skl,sK167_skl,sK166_skl)|~sQ2_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f5181,f2146])).
% 199.65/25.78  fof(f5186,plain,(
% 199.65/25.78    sP12_prd(sK166_skl,sK166_skl,sK166_skl)|~sQ2_spl),
% 199.65/25.78    inference(forward_demodulation,[status(thm)],[f5182,f5183])).
% 199.65/25.78  fof(f5187,plain,(
% 199.65/25.78    $false|~sQ2_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5186,f2388])).
% 199.65/25.78  fof(f5188,plain,(
% 199.65/25.78    ~sQ2_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5187])).
% 199.65/25.78  fof(f5191,plain,(
% 199.65/25.78    ~ordinal(singleton(empty_set))|epsilon_transitive(empty_set)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f1528,f4312])).
% 199.65/25.78  fof(f5192,definition,(
% 199.65/25.78    sQ201_spl <=> (ordinal(singleton(empty_set)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5193,plain,(
% 199.65/25.78    ordinal(singleton(empty_set))|~sQ201_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5192])).
% 199.65/25.78  fof(f5194,plain,(
% 199.65/25.78    ~ordinal(singleton(empty_set))|sQ201_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5192])).
% 199.65/25.78  fof(f5195,definition,(
% 199.65/25.78    sQ202_spl <=> (epsilon_transitive(empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5198,plain,(
% 199.65/25.78    ~sQ201_spl|sQ202_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5191,f5192,f5195])).
% 199.65/25.78  fof(f5200,definition,(
% 199.65/25.78    sQ203_spl <=> (epsilon_transitive(singleton(empty_set)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5202,plain,(
% 199.65/25.78    ~epsilon_transitive(singleton(empty_set))|sQ203_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5200])).
% 199.65/25.78  fof(f5203,definition,(
% 199.65/25.78    sQ204_spl <=> (epsilon_connected(singleton(empty_set)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5205,plain,(
% 199.65/25.78    ~epsilon_connected(singleton(empty_set))|sQ204_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5203])).
% 199.65/25.78  fof(f5265,plain,(
% 199.65/25.78    ~ordinal(singleton(empty_set))|epsilon_connected(empty_set)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f1528,f4313])).
% 199.65/25.78  fof(f5266,definition,(
% 199.65/25.78    sQ205_spl <=> (epsilon_connected(empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5269,plain,(
% 199.65/25.78    ~sQ201_spl|sQ205_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5265,f5192,f5266])).
% 199.65/25.78  fof(f5273,plain,(
% 199.65/25.78    ~ordinal(singleton(empty_set))|ordinal(empty_set)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f1528,f4317])).
% 199.65/25.78  fof(f5274,definition,(
% 199.65/25.78    sQ206_spl <=> (ordinal(empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5277,plain,(
% 199.65/25.78    ~sQ201_spl|sQ206_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5273,f5192,f5274])).
% 199.65/25.78  fof(f5350,plain,(
% 199.65/25.78    ~relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)|sP2_prd(sK213_skl,sK212_skl)|sK212_skl=relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f526,f1732])).
% 199.65/25.78  fof(f5351,definition,(
% 199.65/25.78    sQ207_spl <=> (sP2_prd(sK213_skl,sK212_skl))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5352,plain,(
% 199.65/25.78    sP2_prd(sK213_skl,sK212_skl)|~sQ207_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5351])).
% 199.65/25.78  fof(f5354,definition,(
% 199.65/25.78    sQ208_spl <=> (sK212_skl=relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5355,plain,(
% 199.65/25.78    sK212_skl=relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)|~sQ208_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5354])).
% 199.65/25.78  fof(f5357,plain,(
% 199.65/25.78    ~sQ69_spl|sQ207_spl|sQ208_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5350,f2874,f5351,f5354])).
% 199.65/25.78  fof(f5358,plain,(
% 199.65/25.78    sK213_skl=empty_set|~sQ207_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f5352,f1950])).
% 199.65/25.78  fof(f5359,plain,(
% 199.65/25.78    sQ71_spl|~sQ207_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5358,f2880,f5351])).
% 199.65/25.78  fof(f5362,plain,(
% 199.65/25.78    ![X0]: (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~relation(sK214_skl)|~function(sK214_skl)|relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)|~sQ135_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f3866,f473])).
% 199.65/25.78  fof(f5363,plain,(
% 199.65/25.78    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~relation(sK214_skl)|~function(sK214_skl)|X0=relation_inverse_image(sK214_skl,X1)|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)|~sQ135_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f3866,f473])).
% 199.65/25.78  fof(f5368,plain,(
% 199.65/25.78    ![X0]: (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~relation(sK214_skl)|~function(sK214_skl)|in(ordered_pair(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl))),sK214_skl)|~sQ135_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f3866,f2240])).
% 199.65/25.78  fof(f5383,plain,(
% 199.65/25.78    ![X0]: (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|~relation(sK214_skl)|~function(sK214_skl)|relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)|~sQ135_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f3866,f473])).
% 199.65/25.78  fof(f5384,plain,(
% 199.65/25.78    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|~relation(sK214_skl)|~function(sK214_skl)|in(ordered_pair(sK9_skl(X0,X1,sK214_skl),apply(sK214_skl,sK9_skl(X0,X1,sK214_skl))),sK214_skl)|~sQ135_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f3866,f2240])).
% 199.65/25.78  fof(f5390,definition,(
% 199.65/25.78    ![X0]: (sQ209_spl <=> (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5393,plain,(
% 199.65/25.78    sQ209_spl|~sQ10_spl|~sQ11_spl|~sQ135_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5362,f5390,f2410,f2413,f3865])).
% 199.65/25.78  fof(f5394,definition,(
% 199.65/25.78    ![X0,X1]: (sQ210_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|X0=relation_inverse_image(sK214_skl,X1)|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5397,plain,(
% 199.65/25.78    sQ210_spl|~sQ10_spl|~sQ11_spl|~sQ135_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5363,f5394,f2410,f2413,f3865])).
% 199.65/25.78  fof(f5398,definition,(
% 199.65/25.78    ![X0]: (sQ211_spl <=> (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|in(ordered_pair(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl))),sK214_skl)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5401,plain,(
% 199.65/25.78    sQ211_spl|~sQ10_spl|~sQ11_spl|~sQ135_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5368,f5398,f2410,f2413,f3865])).
% 199.65/25.78  fof(f5402,definition,(
% 199.65/25.78    ![X0]: (sQ212_spl <=> (relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|relation_dom(sK214_skl)=relation_inverse_image(sK214_skl,X0)|~in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5405,plain,(
% 199.65/25.78    sQ212_spl|~sQ10_spl|~sQ11_spl|~sQ135_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5383,f5402,f2410,f2413,f3865])).
% 199.65/25.78  fof(f5406,definition,(
% 199.65/25.78    ![X0,X1]: (sQ213_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(ordered_pair(sK9_skl(X0,X1,sK214_skl),apply(sK214_skl,sK9_skl(X0,X1,sK214_skl))),sK214_skl)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5409,plain,(
% 199.65/25.78    sQ213_spl|~sQ10_spl|~sQ11_spl|~sQ135_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5384,f5406,f2410,f2413,f3865])).
% 199.65/25.78  fof(f5458,plain,(
% 199.65/25.78    ![X0]: (~function(empty_set)|~in(X0,empty_set)|in(ordered_pair(X0,apply(sK194_skl(empty_set),X0)),sK194_skl(empty_set)))),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f2801,f2912])).
% 199.65/25.78  fof(f5459,definition,(
% 199.65/25.78    ![X0]: (sQ214_spl <=> (~in(X0,empty_set)|in(ordered_pair(X0,apply(sK194_skl(empty_set),X0)),sK194_skl(empty_set))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5462,plain,(
% 199.65/25.78    ~sQ26_spl|sQ214_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5458,f2511,f5459])).
% 199.65/25.78  fof(f5466,plain,(
% 199.65/25.78    succ(empty_set)=singleton(empty_set)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f3041,f537])).
% 199.65/25.78  fof(f5469,plain,(
% 199.65/25.78    ![X0]: (subset(X0,succ(X0)))),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f537,f1874])).
% 199.65/25.78  fof(f5471,plain,(
% 199.65/25.78    ~ordinal(succ(empty_set))|sQ201_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f5466,f5194])).
% 199.65/25.78  fof(f5472,plain,(
% 199.65/25.78    ~epsilon_transitive(succ(empty_set))|sQ203_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f5466,f5202])).
% 199.65/25.78  fof(f5473,plain,(
% 199.65/25.78    ~epsilon_connected(succ(empty_set))|sQ204_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f5466,f5205])).
% 199.65/25.78  fof(f5475,plain,(
% 199.65/25.78    relation_of2_as_subset(sK214_skl,sK212_skl,succ(sK213_skl))),
% 199.65/25.78    inference(resolution,[status(thm)],[f5469,f2602])).
% 199.65/25.78  fof(f5478,plain,(
% 199.65/25.78    ~ordinal(empty_set)|sQ201_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f5471,f987])).
% 199.65/25.78  fof(f5480,plain,(
% 199.65/25.78    $false|sQ201_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5478,f973])).
% 199.65/25.78  fof(f5481,plain,(
% 199.65/25.78    sQ201_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5480])).
% 199.65/25.78  fof(f5482,plain,(
% 199.65/25.78    ordinal(succ(empty_set))|~sQ201_spl),
% 199.65/25.78    inference(forward_demodulation,[status(thm)],[f5466,f5193])).
% 199.65/25.78  fof(f5483,plain,(
% 199.65/25.78    ~ordinal(empty_set)|sQ203_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f5472,f985])).
% 199.65/25.78  fof(f5484,plain,(
% 199.65/25.78    $false|sQ203_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5483,f973])).
% 199.65/25.78  fof(f5485,plain,(
% 199.65/25.78    sQ203_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5484])).
% 199.65/25.78  fof(f5487,plain,(
% 199.65/25.78    ~ordinal(empty_set)|sQ204_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f5473,f986])).
% 199.65/25.78  fof(f5488,plain,(
% 199.65/25.78    $false|sQ204_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5487,f973])).
% 199.65/25.78  fof(f5489,plain,(
% 199.65/25.78    sQ204_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5488])).
% 199.65/25.78  fof(f5495,plain,(
% 199.65/25.78    sP2_prd(relation_rng(sK214_skl),sK212_skl)|quasi_total(sK214_skl,sK212_skl,relation_rng(sK214_skl))|~sK212_skl=relation_dom_as_subset(sK212_skl,relation_rng(sK214_skl),sK214_skl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f527,f2829])).
% 199.65/25.78  fof(f5496,plain,(
% 199.65/25.78    sP2_prd(sK213_skl,sK212_skl)|quasi_total(sK214_skl,sK212_skl,sK213_skl)|~sK212_skl=relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f527,f1733])).
% 199.65/25.78  fof(f5497,definition,(
% 199.65/25.78    sQ215_spl <=> (sP2_prd(relation_rng(sK214_skl),sK212_skl))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5498,plain,(
% 199.65/25.78    sP2_prd(relation_rng(sK214_skl),sK212_skl)|~sQ215_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5497])).
% 199.65/25.78  fof(f5500,definition,(
% 199.65/25.78    sQ216_spl <=> (quasi_total(sK214_skl,sK212_skl,relation_rng(sK214_skl)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5501,plain,(
% 199.65/25.78    quasi_total(sK214_skl,sK212_skl,relation_rng(sK214_skl))|~sQ216_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5500])).
% 199.65/25.78  fof(f5503,definition,(
% 199.65/25.78    sQ217_spl <=> (sK212_skl=relation_dom_as_subset(sK212_skl,relation_rng(sK214_skl),sK214_skl))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5506,plain,(
% 199.65/25.78    sQ215_spl|sQ216_spl|~sQ217_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5495,f5497,f5500,f5503])).
% 199.65/25.78  fof(f5507,definition,(
% 199.65/25.78    sQ218_spl <=> (quasi_total(sK214_skl,sK212_skl,sK213_skl))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5510,plain,(
% 199.65/25.78    sQ207_spl|sQ218_spl|~sQ208_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5496,f5351,f5507,f5354])).
% 199.65/25.78  fof(f5543,plain,(
% 199.65/25.78    relation_rng(sK214_skl)=empty_set|~sQ215_spl),
% 199.65/25.78    inference(resolution,[status(thm)],[f5498,f1950])).
% 199.65/25.78  fof(f5548,plain,(
% 199.65/25.78    in(empty_set,empty_set)|~sQ215_spl|~sQ179_spl),
% 199.65/25.78    inference(backward_demodulation,[status(thm)],[f5543,f4393])).
% 199.65/25.78  fof(f5566,plain,(
% 199.65/25.78    $false|~sQ215_spl|~sQ179_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5548,f2223])).
% 199.65/25.78  fof(f5567,plain,(
% 199.65/25.78    ~sQ215_spl|~sQ179_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5566])).
% 199.65/25.78  fof(f5578,plain,(
% 199.65/25.78    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)|~relation(sK214_skl)|~function(sK214_skl)|X0=relation_inverse_image(sK214_skl,X1)|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)|~sQ171_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f4227,f473])).
% 199.65/25.78  fof(f5593,plain,(
% 199.65/25.78    ![X0,X1]: (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|~relation(sK214_skl)|~function(sK214_skl)|in(sK9_skl(X0,X1,sK214_skl),relation_inverse_image(sK214_skl,X1))|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~sQ171_spl)),
% 199.65/25.78    inference(resolution,[status(thm)],[f4227,f2192])).
% 199.65/25.78  fof(f5608,definition,(
% 199.65/25.78    ![X0,X1]: (sQ219_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)|X0=relation_inverse_image(sK214_skl,X1)|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))|~in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5611,plain,(
% 199.65/25.78    sQ219_spl|~sQ10_spl|~sQ11_spl|~sQ171_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5578,f5608,f2410,f2413,f4226])).
% 199.65/25.78  fof(f5612,definition,(
% 199.65/25.78    ![X0,X1]: (sQ220_spl <=> (X0=relation_inverse_image(sK214_skl,X1)|in(sK9_skl(X0,X1,sK214_skl),X0)|in(sK9_skl(X0,X1,sK214_skl),relation_inverse_image(sK214_skl,X1))|~in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5615,plain,(
% 199.65/25.78    sQ220_spl|~sQ10_spl|~sQ11_spl|~sQ171_spl),
% 199.65/25.78    inference(split_clause,[status(thm)],[f5593,f5612,f2410,f2413,f4226])).
% 199.65/25.78  fof(f5633,plain,(
% 199.65/25.78    ~succ(empty_set)=empty_set),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f5466,f1041])).
% 199.65/25.78  fof(f5651,definition,(
% 199.65/25.78    sQ221_spl <=> (ordinal(succ(empty_set)))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5653,plain,(
% 199.65/25.78    ~ordinal(succ(empty_set))|sQ221_spl),
% 199.65/25.78    inference(component_clause,[status(thm)],[f5651])).
% 199.65/25.78  fof(f5657,plain,(
% 199.65/25.78    $false|~sQ201_spl|sQ221_spl),
% 199.65/25.78    inference(forward_subsumption_resolution,[status(thm)],[f5653,f5482])).
% 199.65/25.78  fof(f5658,plain,(
% 199.65/25.78    ~sQ201_spl|sQ221_spl),
% 199.65/25.78    inference(contradiction_clause,[status(thm)],[f5657])).
% 199.65/25.78  fof(f5740,plain,(
% 199.65/25.78    ![X0]: (~relation(apply(sK214_skl,sK216_skl))|X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(apply(sK214_skl,sK216_skl),X0)=empty_set|~sQ188_spl)),
% 199.65/25.78    inference(paramodulation,[status(thm)],[f4597,f1505])).
% 199.65/25.78  fof(f5742,definition,(
% 199.65/25.78    ![X0]: (sQ222_spl <=> (X0=empty_set|~subset(X0,empty_set)|~relation_inverse_image(apply(sK214_skl,sK216_skl),X0)=empty_set))),
% 199.65/25.78    introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition])).
% 199.65/25.78  fof(f5745,plain,(
% 199.65/25.78    ~sQ137_spl|sQ222_spl|~sQ188_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5740,f3893,f5742,f4596])).
% 199.65/25.79  fof(f5780,plain,(
% 199.65/25.79    ![X0]: (~relation(sK118_skl)|in(X0,relation_inverse_image(sK118_skl,succ(apply(sK118_skl,X0))))|~in(X0,relation_dom(sK118_skl)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2916,f1180])).
% 199.65/25.79  fof(f5781,plain,(
% 199.65/25.79    ![X0]: (~relation(sK115_skl)|in(X0,relation_inverse_image(sK115_skl,succ(apply(sK115_skl,X0))))|~in(X0,relation_dom(sK115_skl)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2916,f1167])).
% 199.65/25.79  fof(f5782,plain,(
% 199.65/25.79    ![X0]: (~relation(sK102_skl)|in(X0,relation_inverse_image(sK102_skl,succ(apply(sK102_skl,X0))))|~in(X0,relation_dom(sK102_skl)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2916,f1117])).
% 199.65/25.79  fof(f5783,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|in(X0,relation_inverse_image(empty_set,succ(apply(empty_set,X0))))|~in(X0,relation_dom(empty_set)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2916,f968])).
% 199.65/25.79  fof(f5784,plain,(
% 199.65/25.79    ![X0]: (~relation(sK214_skl)|in(X0,relation_inverse_image(sK214_skl,succ(apply(sK214_skl,X0))))|~in(X0,relation_dom(sK214_skl)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2916,f1731])).
% 199.65/25.79  fof(f5793,definition,(
% 199.65/25.79    ![X0]: (sQ226_spl <=> (in(X0,relation_inverse_image(sK118_skl,succ(apply(sK118_skl,X0))))|~in(X0,relation_dom(sK118_skl))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5796,plain,(
% 199.65/25.79    ~sQ47_spl|sQ226_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5780,f2647,f5793])).
% 199.65/25.79  fof(f5797,definition,(
% 199.65/25.79    ![X0]: (sQ227_spl <=> (in(X0,relation_inverse_image(sK115_skl,succ(apply(sK115_skl,X0))))|~in(X0,relation_dom(sK115_skl))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5800,plain,(
% 199.65/25.79    ~sQ39_spl|sQ227_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5781,f2608,f5797])).
% 199.65/25.79  fof(f5801,definition,(
% 199.65/25.79    ![X0]: (sQ228_spl <=> (in(X0,relation_inverse_image(sK102_skl,succ(apply(sK102_skl,X0))))|~in(X0,relation_dom(sK102_skl))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5804,plain,(
% 199.65/25.79    ~sQ41_spl|sQ228_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5782,f2615,f5801])).
% 199.65/25.79  fof(f5805,definition,(
% 199.65/25.79    ![X0]: (sQ229_spl <=> (in(X0,relation_inverse_image(empty_set,succ(apply(empty_set,X0))))|~in(X0,relation_dom(empty_set))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5808,plain,(
% 199.65/25.79    ~sQ17_spl|sQ229_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5783,f2445,f5805])).
% 199.65/25.79  fof(f5809,definition,(
% 199.65/25.79    ![X0]: (sQ230_spl <=> (in(X0,relation_inverse_image(sK214_skl,succ(apply(sK214_skl,X0))))|~in(X0,relation_dom(sK214_skl))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5812,plain,(
% 199.65/25.79    ~sQ10_spl|sQ230_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5784,f2410,f5809])).
% 199.65/25.79  fof(f5842,plain,(
% 199.65/25.79    ![X0]: (empty(empty_set)|~empty(X0))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f3041,f979])).
% 199.65/25.79  fof(f5848,definition,(
% 199.65/25.79    sQ231_spl <=> (empty(empty_set))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5851,definition,(
% 199.65/25.79    ![X0]: (sQ232_spl <=> (~empty(X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5852,plain,(
% 199.65/25.79    ![X0]: (~empty(X0)|~sQ232_spl)),
% 199.65/25.79    inference(component_clause,[status(thm)],[f5851])).
% 199.65/25.79  fof(f5854,plain,(
% 199.65/25.79    sQ231_spl|sQ232_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5842,f5848,f5851])).
% 199.65/25.79  fof(f5855,plain,(
% 199.65/25.79    $false|~sQ232_spl),
% 199.65/25.79    inference(backward_subsumption_resolution,[status(thm)],[f947,f5852])).
% 199.65/25.79  fof(f5891,plain,(
% 199.65/25.79    ~sQ232_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f5855])).
% 199.65/25.79  fof(f5902,plain,(
% 199.65/25.79    ![X0,X1]: (relation_of2(empty_set,X0,X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f555,f1620])).
% 199.65/25.79  fof(f5911,plain,(
% 199.65/25.79    ~relation_of2_as_subset(sK214_skl,sK212_skl,relation_rng(sK214_skl))|sP2_prd(relation_rng(sK214_skl),sK212_skl)|sK212_skl=relation_dom_as_subset(sK212_skl,relation_rng(sK214_skl),sK214_skl)|~sQ216_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f5501,f526])).
% 199.65/25.79  fof(f5914,definition,(
% 199.65/25.79    sQ233_spl <=> (relation_of2_as_subset(sK214_skl,sK212_skl,relation_rng(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f5916,plain,(
% 199.65/25.79    ~relation_of2_as_subset(sK214_skl,sK212_skl,relation_rng(sK214_skl))|sQ233_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f5914])).
% 199.65/25.79  fof(f5917,plain,(
% 199.65/25.79    ~sQ233_spl|sQ215_spl|sQ217_spl|~sQ216_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f5911,f5914,f5497,f5503,f5500])).
% 199.65/25.79  fof(f5920,plain,(
% 199.65/25.79    $false|sQ233_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f5916,f2829])).
% 199.65/25.79  fof(f5921,plain,(
% 199.65/25.79    sQ233_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f5920])).
% 199.65/25.79  fof(f5926,plain,(
% 199.65/25.79    in(empty_set,empty_set)|~sQ127_spl|~sQ179_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f3766,f4393])).
% 199.65/25.79  fof(f5946,plain,(
% 199.65/25.79    $false|~sQ127_spl|~sQ179_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f5926,f2223])).
% 199.65/25.79  fof(f5947,plain,(
% 199.65/25.79    ~sQ127_spl|~sQ179_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f5946])).
% 199.65/25.79  fof(f6017,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_dom(sK91_skl(X0,empty_set))=identity_relation(X1)|in(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),X1)|~relation(sK91_skl(X0,empty_set))|~function(sK91_skl(X0,empty_set))|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))),apply(sK91_skl(X0,empty_set),ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))))),sK91_skl(X0,empty_set)))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f4300,f2922])).
% 199.65/25.79  fof(f6018,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|relation_dom(empty_set)=identity_relation(X0)|in(sK0_skl(X0,relation_dom(empty_set)),X0)|~relation(empty_set)|~function(empty_set)|in(ordered_pair(ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))),apply(empty_set,ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))))),empty_set))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f5058,f2922])).
% 199.65/25.79  fof(f6021,definition,(
% 199.65/25.79    ![X0,X1]: (sQ234_spl <=> (relation_dom(sK91_skl(X0,empty_set))=identity_relation(X1)|in(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),X1)|~relation(sK91_skl(X0,empty_set))|~function(sK91_skl(X0,empty_set))|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))),apply(sK91_skl(X0,empty_set),ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))))),sK91_skl(X0,empty_set))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6024,plain,(
% 199.65/25.79    ~sQ17_spl|sQ234_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6017,f2445,f6021])).
% 199.65/25.79  fof(f6025,definition,(
% 199.65/25.79    ![X0]: (sQ235_spl <=> (relation_dom(empty_set)=identity_relation(X0)|in(sK0_skl(X0,relation_dom(empty_set)),X0)|in(ordered_pair(ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))),apply(empty_set,ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))))),empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6028,plain,(
% 199.65/25.79    ~sQ17_spl|sQ235_spl|~sQ26_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6018,f2445,f6025,f2511])).
% 199.65/25.79  fof(f6055,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_inverse_image(empty_set,X0)=identity_relation(X1)|in(sK0_skl(X1,relation_inverse_image(empty_set,X0)),X1)|~relation(empty_set)|~function(empty_set)|in(apply(empty_set,ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0)))),X0)|~sQ18_spl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f2502,f2923])).
% 199.65/25.79  fof(f6056,definition,(
% 199.65/25.79    ![X0,X1]: (sQ236_spl <=> (relation_inverse_image(empty_set,X0)=identity_relation(X1)|in(sK0_skl(X1,relation_inverse_image(empty_set,X0)),X1)|in(apply(empty_set,ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0)))),X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6059,plain,(
% 199.65/25.79    ~sQ17_spl|sQ236_spl|~sQ26_spl|~sQ18_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6055,f2445,f6056,f2511,f2448])).
% 199.65/25.79  fof(f6091,plain,(
% 199.65/25.79    relation_inverse(relation_inverse(sK117_skl))=sK117_skl),
% 199.65/25.79    inference(resolution,[status(thm)],[f1030,f1175])).
% 199.65/25.79  fof(f6093,plain,(
% 199.65/25.79    relation_inverse(relation_inverse(sK112_skl))=sK112_skl),
% 199.65/25.79    inference(resolution,[status(thm)],[f1030,f1159])).
% 199.65/25.79  fof(f6094,plain,(
% 199.65/25.79    relation_inverse(relation_inverse(sK214_skl))=sK214_skl),
% 199.65/25.79    inference(resolution,[status(thm)],[f1030,f2530])).
% 199.65/25.79  fof(f6100,definition,(
% 199.65/25.79    sQ237_spl <=> (relation(relation_inverse(sK118_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6102,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK118_skl))|sQ237_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6100])).
% 199.65/25.79  fof(f6104,plain,(
% 199.65/25.79    ~relation(sK118_skl)|sQ237_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6102,f911])).
% 199.65/25.79  fof(f6106,plain,(
% 199.65/25.79    ~sQ47_spl|sQ237_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6104,f2647,f6100])).
% 199.65/25.79  fof(f6149,definition,(
% 199.65/25.79    sQ238_spl <=> (relation(relation_inverse(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6150,plain,(
% 199.65/25.79    relation(relation_inverse(sK214_skl))|~sQ238_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6149])).
% 199.65/25.79  fof(f6151,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK214_skl))|sQ238_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6149])).
% 199.65/25.79  fof(f6153,plain,(
% 199.65/25.79    ~relation(sK214_skl)|sQ238_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6151,f911])).
% 199.65/25.79  fof(f6155,plain,(
% 199.65/25.79    ~sQ10_spl|sQ238_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6153,f2410,f6149])).
% 199.65/25.79  fof(f6158,plain,(
% 199.65/25.79    ~relation_dom(relation_inverse(sK214_skl))=empty_set|relation_inverse(sK214_skl)=empty_set|~sQ238_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6150,f1818])).
% 199.65/25.79  fof(f6164,definition,(
% 199.65/25.79    sQ239_spl <=> (relation_dom(relation_inverse(sK214_skl))=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6167,definition,(
% 199.65/25.79    sQ240_spl <=> (relation_inverse(sK214_skl)=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6168,plain,(
% 199.65/25.79    relation_inverse(sK214_skl)=empty_set|~sQ240_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6167])).
% 199.65/25.79  fof(f6170,plain,(
% 199.65/25.79    ~sQ239_spl|sQ240_spl|~sQ238_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6158,f6164,f6167,f6149])).
% 199.65/25.79  fof(f6172,plain,(
% 199.65/25.79    relation_inverse(empty_set)=sK214_skl|~sQ240_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f6168,f6094])).
% 199.65/25.79  fof(f6205,plain,(
% 199.65/25.79    in(sK216_skl,relation_dom(empty_set))|~sQ240_spl|~sQ12_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f6396,f2418])).
% 199.65/25.79  fof(f6396,plain,(
% 199.65/25.79    empty_set=sK214_skl|~sQ240_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f4168,f6172])).
% 199.65/25.79  fof(f6449,plain,(
% 199.65/25.79    in(sK216_skl,empty_set)|~sQ240_spl|~sQ12_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f5058,f6205])).
% 199.65/25.79  fof(f6450,plain,(
% 199.65/25.79    $false|~sQ240_spl|~sQ12_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f6449,f2223])).
% 199.65/25.79  fof(f6451,plain,(
% 199.65/25.79    ~sQ240_spl|~sQ12_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f6450])).
% 199.65/25.79  fof(f6452,plain,(
% 199.65/25.79    ~relation(apply(empty_set,sK216_skl))|~sQ30_spl|sQ137_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f2540,f3895])).
% 199.65/25.79  fof(f6453,plain,(
% 199.65/25.79    ~relation(empty_set)|~sQ43_spl|~sQ30_spl|sQ137_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f2632,f6452])).
% 199.65/25.79  fof(f6454,plain,(
% 199.65/25.79    $false|~sQ43_spl|~sQ30_spl|sQ137_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f6453,f948])).
% 199.65/25.79  fof(f6455,plain,(
% 199.65/25.79    ~sQ43_spl|~sQ30_spl|sQ137_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f6454])).
% 199.65/25.79  fof(f6760,definition,(
% 199.65/25.79    sQ243_spl <=> (relation(relation_inverse(sK117_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6761,plain,(
% 199.65/25.79    relation(relation_inverse(sK117_skl))|~sQ243_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6760])).
% 199.65/25.79  fof(f6762,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK117_skl))|sQ243_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6760])).
% 199.65/25.79  fof(f6764,plain,(
% 199.65/25.79    ~relation(sK117_skl)|sQ243_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6762,f911])).
% 199.65/25.79  fof(f6766,plain,(
% 199.65/25.79    ~sQ160_spl|sQ243_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6764,f4124,f6760])).
% 199.65/25.79  fof(f6769,plain,(
% 199.65/25.79    ~relation_dom(relation_inverse(sK117_skl))=empty_set|relation_inverse(sK117_skl)=empty_set|~sQ243_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6761,f1818])).
% 199.65/25.79  fof(f6775,definition,(
% 199.65/25.79    sQ244_spl <=> (relation_dom(relation_inverse(sK117_skl))=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6777,plain,(
% 199.65/25.79    ~relation_dom(relation_inverse(sK117_skl))=empty_set|sQ244_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6775])).
% 199.65/25.79  fof(f6778,definition,(
% 199.65/25.79    sQ245_spl <=> (relation_inverse(sK117_skl)=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6779,plain,(
% 199.65/25.79    relation_inverse(sK117_skl)=empty_set|~sQ245_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6778])).
% 199.65/25.79  fof(f6781,plain,(
% 199.65/25.79    ~sQ244_spl|sQ245_spl|~sQ243_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6769,f6775,f6778,f6760])).
% 199.65/25.79  fof(f6783,plain,(
% 199.65/25.79    relation_inverse(empty_set)=sK117_skl|~sQ245_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f6779,f6091])).
% 199.65/25.79  fof(f6784,plain,(
% 199.65/25.79    ~relation_dom(empty_set)=empty_set|~sQ245_spl|sQ244_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f6779,f6777])).
% 199.65/25.79  fof(f6792,plain,(
% 199.65/25.79    ~relation_dom(empty_set)=empty_set|~sQ245_spl|sQ36_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f6803,f2581])).
% 199.65/25.79  fof(f6803,plain,(
% 199.65/25.79    empty_set=sK117_skl|~sQ245_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f4168,f6783])).
% 199.65/25.79  fof(f6804,plain,(
% 199.65/25.79    ~sQ15_spl|~sQ245_spl|sQ244_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6784,f2434,f6778,f6775])).
% 199.65/25.79  fof(f6826,plain,(
% 199.65/25.79    ~sQ15_spl|~sQ245_spl|sQ36_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6792,f2434,f6778,f2579])).
% 199.65/25.79  fof(f6845,plain,(
% 199.65/25.79    ~relation_inverse_image(empty_set,relation_rng(sK117_skl))=empty_set|~sQ245_spl|sQ144_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f6803,f3985])).
% 199.65/25.79  fof(f6846,plain,(
% 199.65/25.79    ~empty_set=empty_set|~sQ18_spl|~sQ245_spl|sQ144_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f2502,f6845])).
% 199.65/25.79  fof(f6847,plain,(
% 199.65/25.79    $false|~sQ18_spl|~sQ245_spl|sQ144_spl),
% 199.65/25.79    inference(trivial_equality_resolution,[status(thm)],[f6846])).
% 199.65/25.79  fof(f6848,plain,(
% 199.65/25.79    ~sQ18_spl|~sQ245_spl|sQ144_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f6847])).
% 199.65/25.79  fof(f6854,definition,(
% 199.65/25.79    sQ246_spl <=> (relation(relation_inverse(sK115_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f6856,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK115_skl))|sQ246_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f6854])).
% 199.65/25.79  fof(f6858,plain,(
% 199.65/25.79    ~relation(sK115_skl)|sQ246_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f6856,f911])).
% 199.65/25.79  fof(f6860,plain,(
% 199.65/25.79    ~sQ39_spl|sQ246_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f6858,f2608,f6854])).
% 199.65/25.79  fof(f7172,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_inverse_image(empty_set,X0)=identity_relation(X1)|in(sK0_skl(X1,relation_inverse_image(empty_set,X0)),X1)|~relation(empty_set)|~function(empty_set)|in(ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0))),relation_dom(empty_set))|~sQ18_spl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f2502,f2924])).
% 199.65/25.79  fof(f7173,definition,(
% 199.65/25.79    ![X0,X1]: (sQ249_spl <=> (relation_inverse_image(empty_set,X0)=identity_relation(X1)|in(sK0_skl(X1,relation_inverse_image(empty_set,X0)),X1)|in(ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0))),relation_dom(empty_set))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7176,plain,(
% 199.65/25.79    ~sQ17_spl|sQ249_spl|~sQ26_spl|~sQ18_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7172,f2445,f7173,f2511,f2448])).
% 199.65/25.79  fof(f7199,definition,(
% 199.65/25.79    sQ250_spl <=> (relation(relation_inverse(sK112_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7200,plain,(
% 199.65/25.79    relation(relation_inverse(sK112_skl))|~sQ250_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f7199])).
% 199.65/25.79  fof(f7201,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK112_skl))|sQ250_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f7199])).
% 199.65/25.79  fof(f7203,plain,(
% 199.65/25.79    ~relation(sK112_skl)|sQ250_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f7201,f911])).
% 199.65/25.79  fof(f7205,plain,(
% 199.65/25.79    ~sQ155_spl|sQ250_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7203,f4097,f7199])).
% 199.65/25.79  fof(f7209,plain,(
% 199.65/25.79    ~relation_dom(relation_inverse(sK112_skl))=empty_set|relation_inverse(sK112_skl)=empty_set|~sQ250_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f7200,f1818])).
% 199.65/25.79  fof(f7215,definition,(
% 199.65/25.79    sQ251_spl <=> (relation_dom(relation_inverse(sK112_skl))=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7218,definition,(
% 199.65/25.79    sQ252_spl <=> (relation_inverse(sK112_skl)=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7219,plain,(
% 199.65/25.79    relation_inverse(sK112_skl)=empty_set|~sQ252_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f7218])).
% 199.65/25.79  fof(f7221,plain,(
% 199.65/25.79    ~sQ251_spl|sQ252_spl|~sQ250_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7209,f7215,f7218,f7199])).
% 199.65/25.79  fof(f7223,plain,(
% 199.65/25.79    relation_inverse(empty_set)=sK112_skl|~sQ252_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f7219,f6093])).
% 199.65/25.79  fof(f7232,plain,(
% 199.65/25.79    ~empty(empty_set)|~sQ252_spl),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f7245,f1158])).
% 199.65/25.79  fof(f7245,plain,(
% 199.65/25.79    empty_set=sK112_skl|~sQ252_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f4168,f7223])).
% 199.65/25.79  fof(f7268,plain,(
% 199.65/25.79    $false|~sQ252_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f7232,f947])).
% 199.65/25.79  fof(f7269,plain,(
% 199.65/25.79    ~sQ252_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f7268])).
% 199.65/25.79  fof(f7294,definition,(
% 199.65/25.79    sQ253_spl <=> (relation(relation_inverse(sK102_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7296,plain,(
% 199.65/25.79    ~relation(relation_inverse(sK102_skl))|sQ253_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f7294])).
% 199.65/25.79  fof(f7298,plain,(
% 199.65/25.79    ~relation(sK102_skl)|sQ253_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f7296,f911])).
% 199.65/25.79  fof(f7300,plain,(
% 199.65/25.79    ~sQ41_spl|sQ253_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7298,f2615,f7294])).
% 199.65/25.79  fof(f7629,definition,(
% 199.65/25.79    sQ269_spl <=> (in(ordered_pair(sK31_skl(relation_field(empty_set),empty_set),sK32_skl(relation_field(empty_set),empty_set)),empty_set))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7630,plain,(
% 199.65/25.79    in(ordered_pair(sK31_skl(relation_field(empty_set),empty_set),sK32_skl(relation_field(empty_set),empty_set)),empty_set)|~sQ269_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f7629])).
% 199.65/25.79  fof(f7636,plain,(
% 199.65/25.79    $false|~sQ269_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f7630,f2223])).
% 199.65/25.79  fof(f7637,plain,(
% 199.65/25.79    ~sQ269_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f7636])).
% 199.65/25.79  fof(f7818,plain,(
% 199.65/25.79    ![X0]: (in(empty_set,powerset(X0)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2225,f1620])).
% 199.65/25.79  fof(f7855,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set)|in(sK0_skl(X0,empty_set),empty_set)|~in(sK1_skl(X0,empty_set),X1)|~sQ18_spl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f2502,f2943])).
% 199.65/25.79  fof(f7860,definition,(
% 199.65/25.79    ![X0,X1]: (sQ295_spl <=> (empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set)|in(sK0_skl(X0,empty_set),empty_set)|~in(sK1_skl(X0,empty_set),X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7863,plain,(
% 199.65/25.79    ~sQ17_spl|sQ295_spl|~sQ18_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7855,f2445,f7860,f2448])).
% 199.65/25.79  fof(f7865,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_dom(sK91_skl(X0,empty_set))=identity_relation(X1)|sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set)))=sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))|~relation(sK91_skl(X0,empty_set))|~function(sK91_skl(X0,empty_set))|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))),apply(sK91_skl(X0,empty_set),ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))))),sK91_skl(X0,empty_set)))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f4300,f2936])).
% 199.65/25.79  fof(f7866,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|relation_dom(empty_set)=identity_relation(X0)|sK0_skl(X0,relation_dom(empty_set))=sK1_skl(X0,relation_dom(empty_set))|~relation(empty_set)|~function(empty_set)|in(ordered_pair(ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))),apply(empty_set,ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))))),empty_set))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f5058,f2936])).
% 199.65/25.79  fof(f7869,definition,(
% 199.65/25.79    ![X0,X1]: (sQ296_spl <=> (relation_dom(sK91_skl(X0,empty_set))=identity_relation(X1)|sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set)))=sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))|~relation(sK91_skl(X0,empty_set))|~function(sK91_skl(X0,empty_set))|in(ordered_pair(ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))),apply(sK91_skl(X0,empty_set),ordered_pair(sK0_skl(X1,relation_dom(sK91_skl(X0,empty_set))),sK1_skl(X1,relation_dom(sK91_skl(X0,empty_set)))))),sK91_skl(X0,empty_set))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7872,plain,(
% 199.65/25.79    ~sQ17_spl|sQ296_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7865,f2445,f7869])).
% 199.65/25.79  fof(f7873,definition,(
% 199.65/25.79    ![X0]: (sQ297_spl <=> (relation_dom(empty_set)=identity_relation(X0)|sK0_skl(X0,relation_dom(empty_set))=sK1_skl(X0,relation_dom(empty_set))|in(ordered_pair(ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))),apply(empty_set,ordered_pair(sK0_skl(X0,relation_dom(empty_set)),sK1_skl(X0,relation_dom(empty_set))))),empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f7876,plain,(
% 199.65/25.79    ~sQ17_spl|sQ297_spl|~sQ26_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f7866,f2445,f7873,f2511])).
% 199.65/25.79  fof(f8030,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_inverse_image(empty_set,X0)=identity_relation(X1)|sK0_skl(X1,relation_inverse_image(empty_set,X0))=sK1_skl(X1,relation_inverse_image(empty_set,X0))|~relation(empty_set)|~function(empty_set)|in(apply(empty_set,ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0)))),X0)|~sQ18_spl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f2502,f2937])).
% 199.65/25.79  fof(f8031,definition,(
% 199.65/25.79    ![X0,X1]: (sQ310_spl <=> (relation_inverse_image(empty_set,X0)=identity_relation(X1)|sK0_skl(X1,relation_inverse_image(empty_set,X0))=sK1_skl(X1,relation_inverse_image(empty_set,X0))|in(apply(empty_set,ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0)))),X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8034,plain,(
% 199.65/25.79    ~sQ17_spl|sQ310_spl|~sQ26_spl|~sQ18_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8030,f2445,f8031,f2511,f2448])).
% 199.65/25.79  fof(f8040,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|relation_inverse_image(empty_set,X0)=identity_relation(X1)|sK0_skl(X1,relation_inverse_image(empty_set,X0))=sK1_skl(X1,relation_inverse_image(empty_set,X0))|~relation(empty_set)|~function(empty_set)|in(ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0))),relation_dom(empty_set))|~sQ18_spl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f2502,f2938])).
% 199.65/25.79  fof(f8041,definition,(
% 199.65/25.79    ![X0,X1]: (sQ311_spl <=> (relation_inverse_image(empty_set,X0)=identity_relation(X1)|sK0_skl(X1,relation_inverse_image(empty_set,X0))=sK1_skl(X1,relation_inverse_image(empty_set,X0))|in(ordered_pair(sK0_skl(X1,relation_inverse_image(empty_set,X0)),sK1_skl(X1,relation_inverse_image(empty_set,X0))),relation_dom(empty_set))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8044,plain,(
% 199.65/25.79    ~sQ17_spl|sQ311_spl|~sQ26_spl|~sQ18_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8040,f2445,f8041,f2511,f2448])).
% 199.65/25.79  fof(f8171,definition,(
% 199.65/25.79    sQ312_spl <=> (sP2_prd(succ(sK213_skl),sK212_skl))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8172,plain,(
% 199.65/25.79    sP2_prd(succ(sK213_skl),sK212_skl)|~sQ312_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f8171])).
% 199.65/25.79  fof(f8181,plain,(
% 199.65/25.79    succ(sK213_skl)=empty_set|~sQ312_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f8172,f1950])).
% 199.65/25.79  fof(f8192,plain,(
% 199.65/25.79    ~empty(empty_set)|~sQ312_spl),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8181,f957])).
% 199.65/25.79  fof(f8214,plain,(
% 199.65/25.79    $false|~sQ312_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f8192,f947])).
% 199.65/25.79  fof(f8215,plain,(
% 199.65/25.79    ~sQ312_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f8214])).
% 199.65/25.79  fof(f8265,plain,(
% 199.65/25.79    set_union2(relation_dom(sK214_skl),sK212_skl)=sK212_skl),
% 199.65/25.79    inference(resolution,[status(thm)],[f1442,f2423])).
% 199.65/25.79  fof(f8371,definition,(
% 199.65/25.79    sQ315_spl <=> (relation_of2_as_subset(sK214_skl,sK212_skl,succ(sK213_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8373,plain,(
% 199.65/25.79    ~relation_of2_as_subset(sK214_skl,sK212_skl,succ(sK213_skl))|sQ315_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f8371])).
% 199.65/25.79  fof(f8375,definition,(
% 199.65/25.79    sQ316_spl <=> (succ(sK213_skl)=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8376,plain,(
% 199.65/25.79    succ(sK213_skl)=empty_set|~sQ316_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f8375])).
% 199.65/25.79  fof(f8380,plain,(
% 199.65/25.79    $false|sQ315_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f8373,f5475])).
% 199.65/25.79  fof(f8381,plain,(
% 199.65/25.79    sQ315_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f8380])).
% 199.65/25.79  fof(f8394,plain,(
% 199.65/25.79    ~empty(empty_set)|~sQ316_spl),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8376,f957])).
% 199.65/25.79  fof(f8417,plain,(
% 199.65/25.79    $false|~sQ316_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f8394,f947])).
% 199.65/25.79  fof(f8418,plain,(
% 199.65/25.79    ~sQ316_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f8417])).
% 199.65/25.79  fof(f8442,plain,(
% 199.65/25.79    ![X0]: (~relation(sK214_skl)|sK1_skl(X0,sK214_skl)=apply(sK214_skl,sK0_skl(X0,sK214_skl))|sK214_skl=identity_relation(X0)|sK0_skl(X0,sK214_skl)=sK1_skl(X0,sK214_skl))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3020,f1731])).
% 199.65/25.79  fof(f8448,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|sK1_skl(X0,empty_set)=apply(empty_set,sK0_skl(X0,empty_set))|empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3020,f968])).
% 199.65/25.79  fof(f8449,definition,(
% 199.65/25.79    ![X0]: (sQ317_spl <=> (sK1_skl(X0,sK214_skl)=apply(sK214_skl,sK0_skl(X0,sK214_skl))|sK214_skl=identity_relation(X0)|sK0_skl(X0,sK214_skl)=sK1_skl(X0,sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8452,plain,(
% 199.65/25.79    ~sQ10_spl|sQ317_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8442,f2410,f8449])).
% 199.65/25.79  fof(f8458,definition,(
% 199.65/25.79    ![X0]: (sQ318_spl <=> (sK1_skl(X0,empty_set)=apply(empty_set,sK0_skl(X0,empty_set))|empty_set=identity_relation(X0)|sK0_skl(X0,empty_set)=sK1_skl(X0,empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8461,plain,(
% 199.65/25.79    ~sQ17_spl|sQ318_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8448,f2445,f8458])).
% 199.65/25.79  fof(f8463,plain,(
% 199.65/25.79    ![X0]: (~relation(sK214_skl)|sK1_skl(X0,sK214_skl)=apply(sK214_skl,sK0_skl(X0,sK214_skl))|sK214_skl=identity_relation(X0)|in(sK0_skl(X0,sK214_skl),X0))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3021,f1731])).
% 199.65/25.79  fof(f8469,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|sK1_skl(X0,empty_set)=apply(empty_set,sK0_skl(X0,empty_set))|empty_set=identity_relation(X0)|in(sK0_skl(X0,empty_set),X0))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3021,f968])).
% 199.65/25.79  fof(f8470,definition,(
% 199.65/25.79    ![X0]: (sQ319_spl <=> (sK1_skl(X0,sK214_skl)=apply(sK214_skl,sK0_skl(X0,sK214_skl))|sK214_skl=identity_relation(X0)|in(sK0_skl(X0,sK214_skl),X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8473,plain,(
% 199.65/25.79    ~sQ10_spl|sQ319_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8463,f2410,f8470])).
% 199.65/25.79  fof(f8479,definition,(
% 199.65/25.79    ![X0]: (sQ320_spl <=> (sK1_skl(X0,empty_set)=apply(empty_set,sK0_skl(X0,empty_set))|empty_set=identity_relation(X0)|in(sK0_skl(X0,empty_set),X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8482,plain,(
% 199.65/25.79    ~sQ17_spl|sQ320_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8469,f2445,f8479])).
% 199.65/25.79  fof(f8637,plain,(
% 199.65/25.79    ![X0,X1]: (in(empty_set,set_union2(powerset(X0),X1)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2233,f7818])).
% 199.65/25.79  fof(f8758,plain,(
% 199.65/25.79    ![X0]: (singleton(X0)=empty_set|sK33_skl(singleton(X0))=X0)),
% 199.65/25.79    inference(resolution,[status(thm)],[f600,f2211])).
% 199.65/25.79  fof(f8766,plain,(
% 199.65/25.79    ![X0]: (X0=empty_set|element(sK33_skl(X0),X0))),
% 199.65/25.79    inference(resolution,[status(thm)],[f600,f1524])).
% 199.65/25.79  fof(f8769,plain,(
% 199.65/25.79    ![X0]: (X0=empty_set|~in(X0,sK33_skl(X0)))),
% 199.65/25.79    inference(resolution,[status(thm)],[f600,f389])).
% 199.65/25.79  fof(f8770,plain,(
% 199.65/25.79    ![X0]: (sK33_skl(singleton(X0))=X0)),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f8758,f1041])).
% 199.65/25.79  fof(f8771,plain,(
% 199.65/25.79    sK33_skl(succ(empty_set))=empty_set),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f5466,f8770])).
% 199.65/25.79  fof(f8773,plain,(
% 199.65/25.79    succ(empty_set)=empty_set|in(empty_set,succ(empty_set))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8771,f600])).
% 199.65/25.79  fof(f8774,definition,(
% 199.65/25.79    sQ321_spl <=> (succ(empty_set)=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8775,plain,(
% 199.65/25.79    succ(empty_set)=empty_set|~sQ321_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f8774])).
% 199.65/25.79  fof(f8777,definition,(
% 199.65/25.79    sQ322_spl <=> (in(empty_set,succ(empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8780,plain,(
% 199.65/25.79    sQ321_spl|sQ322_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8773,f8774,f8777])).
% 199.65/25.79  fof(f8781,plain,(
% 199.65/25.79    $false|~sQ321_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f8775,f5633])).
% 199.65/25.79  fof(f8782,plain,(
% 199.65/25.79    ~sQ321_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f8781])).
% 199.65/25.79  fof(f8894,plain,(
% 199.65/25.79    succ(empty_set)=empty_set|~in(succ(empty_set),empty_set)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8771,f8769])).
% 199.65/25.79  fof(f8896,definition,(
% 199.65/25.79    sQ323_spl <=> (in(succ(empty_set),empty_set))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8899,plain,(
% 199.65/25.79    sQ321_spl|~sQ323_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8894,f8774,f8896])).
% 199.65/25.79  fof(f8934,plain,(
% 199.65/25.79    ![X0,X1]: (in(empty_set,powerset(X0))|in(empty_set,X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f8637,f2232])).
% 199.65/25.79  fof(f8950,definition,(
% 199.65/25.79    ![X0]: (sQ324_spl <=> (in(empty_set,powerset(X0))))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8953,definition,(
% 199.65/25.79    ![X1]: (sQ325_spl <=> (in(empty_set,X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f8954,plain,(
% 199.65/25.79    ![X0]: (in(empty_set,X0)|~sQ325_spl)),
% 199.65/25.79    inference(component_clause,[status(thm)],[f8953])).
% 199.65/25.79  fof(f8956,plain,(
% 199.65/25.79    sQ324_spl|sQ325_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f8934,f8950,f8953])).
% 199.65/25.79  fof(f8991,plain,(
% 199.65/25.79    $false|~sQ325_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f8954,f2223])).
% 199.65/25.79  fof(f9047,plain,(
% 199.65/25.79    ~sQ325_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f8991])).
% 199.65/25.79  fof(f9272,plain,(
% 199.65/25.79    empty(relation_dom(sK214_skl))|~empty(sK212_skl)),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8265,f979])).
% 199.65/25.79  fof(f9287,definition,(
% 199.65/25.79    sQ326_spl <=> (empty(sK212_skl))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9291,definition,(
% 199.65/25.79    sQ327_spl <=> (empty(relation_dom(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9292,plain,(
% 199.65/25.79    empty(relation_dom(sK214_skl))|~sQ327_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f9291])).
% 199.65/25.79  fof(f9294,plain,(
% 199.65/25.79    sQ327_spl|~sQ326_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f9272,f9291,f9287])).
% 199.65/25.79  fof(f9307,plain,(
% 199.65/25.79    relation(relation_dom(sK214_skl))|~sQ327_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f9292,f398])).
% 199.65/25.79  fof(f9319,plain,(
% 199.65/25.79    $false|sQ56_spl|~sQ327_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f9307,f2712])).
% 199.65/25.79  fof(f9320,plain,(
% 199.65/25.79    sQ56_spl|~sQ327_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f9319])).
% 199.65/25.79  fof(f9586,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(sK214_skl)|~in(ordered_pair(X0,X1),sK214_skl)|X1=apply(sK214_skl,X0))),
% 199.65/25.79    inference(resolution,[status(thm)],[f1895,f1731])).
% 199.65/25.79  fof(f9592,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|~in(ordered_pair(X0,X1),empty_set)|X1=apply(empty_set,X0))),
% 199.65/25.79    inference(resolution,[status(thm)],[f1895,f968])).
% 199.65/25.79  fof(f9593,definition,(
% 199.65/25.79    ![X0,X1]: (sQ330_spl <=> (~in(ordered_pair(X0,X1),sK214_skl)|X1=apply(sK214_skl,X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9596,plain,(
% 199.65/25.79    ~sQ10_spl|sQ330_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f9586,f2410,f9593])).
% 199.65/25.79  fof(f9602,definition,(
% 199.65/25.79    ![X0,X1]: (sQ331_spl <=> (~in(ordered_pair(X0,X1),empty_set)|X1=apply(empty_set,X0)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9605,plain,(
% 199.65/25.79    ~sQ17_spl|sQ331_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f9592,f2445,f9602])).
% 199.65/25.79  fof(f9620,plain,(
% 199.65/25.79    ![X0]: (in(empty_set,set_union2(relation_rng(sK214_skl),X0))|~sQ179_spl)),
% 199.65/25.79    inference(resolution,[status(thm)],[f4393,f2233])).
% 199.65/25.79  fof(f9846,plain,(
% 199.65/25.79    ![X0]: (~relation(sK214_skl)|~in(X0,relation_dom(sK214_skl))|in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2240,f1731])).
% 199.65/25.79  fof(f9852,plain,(
% 199.65/25.79    ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set))|in(ordered_pair(X0,apply(empty_set,X0)),empty_set))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2240,f968])).
% 199.65/25.79  fof(f9853,definition,(
% 199.65/25.79    ![X0]: (sQ334_spl <=> (~in(X0,relation_dom(sK214_skl))|in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9854,plain,(
% 199.65/25.79    ![X0]: (~in(X0,relation_dom(sK214_skl))|in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)|~sQ334_spl)),
% 199.65/25.79    inference(component_clause,[status(thm)],[f9853])).
% 199.65/25.79  fof(f9856,plain,(
% 199.65/25.79    ~sQ10_spl|sQ334_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f9846,f2410,f9853])).
% 199.65/25.79  fof(f9863,definition,(
% 199.65/25.79    ![X0]: (sQ335_spl <=> (~in(X0,relation_dom(empty_set))|in(ordered_pair(X0,apply(empty_set,X0)),empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f9866,plain,(
% 199.65/25.79    ~sQ17_spl|sQ335_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f9852,f2445,f9863])).
% 199.65/25.79  fof(f10419,plain,(
% 199.65/25.79    succ(empty_set)=empty_set|element(empty_set,succ(empty_set))),
% 199.65/25.79    inference(paramodulation,[status(thm)],[f8771,f8766])).
% 199.65/25.79  fof(f10421,definition,(
% 199.65/25.79    sQ336_spl <=> (element(empty_set,succ(empty_set)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f10424,plain,(
% 199.65/25.79    sQ321_spl|sQ336_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f10419,f8774,f10421])).
% 199.65/25.79  fof(f10789,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(sK214_skl)|in(X0,relation_inverse_image(sK214_skl,X1))|~in(X0,relation_dom(sK214_skl))|~in(apply(sK214_skl,X0),X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2192,f1731])).
% 199.65/25.79  fof(f10795,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|in(X0,relation_inverse_image(empty_set,X1))|~in(X0,relation_dom(empty_set))|~in(apply(empty_set,X0),X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2192,f968])).
% 199.65/25.79  fof(f10796,definition,(
% 199.65/25.79    ![X0,X1]: (sQ351_spl <=> (in(X0,relation_inverse_image(sK214_skl,X1))|~in(X0,relation_dom(sK214_skl))|~in(apply(sK214_skl,X0),X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f10797,plain,(
% 199.65/25.79    ![X0,X1]: (in(X0,relation_inverse_image(sK214_skl,X1))|~in(X0,relation_dom(sK214_skl))|~in(apply(sK214_skl,X0),X1)|~sQ351_spl)),
% 199.65/25.79    inference(component_clause,[status(thm)],[f10796])).
% 199.65/25.79  fof(f10799,plain,(
% 199.65/25.79    ~sQ10_spl|sQ351_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f10789,f2410,f10796])).
% 199.65/25.79  fof(f10807,definition,(
% 199.65/25.79    ![X0,X1]: (sQ352_spl <=> (in(X0,relation_inverse_image(empty_set,X1))|~in(X0,relation_dom(empty_set))|~in(apply(empty_set,X0),X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f10810,plain,(
% 199.65/25.79    ~sQ17_spl|sQ352_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f10795,f2445,f10807])).
% 199.65/25.79  fof(f10812,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(sK214_skl)|~in(X0,relation_inverse_image(sK214_skl,X1))|in(apply(sK214_skl,X0),X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2191,f1731])).
% 199.65/25.79  fof(f10818,plain,(
% 199.65/25.79    ![X0,X1]: (~relation(empty_set)|~in(X0,relation_inverse_image(empty_set,X1))|in(apply(empty_set,X0),X1))),
% 199.65/25.79    inference(resolution,[status(thm)],[f2191,f968])).
% 199.65/25.79  fof(f10819,definition,(
% 199.65/25.79    ![X0,X1]: (sQ353_spl <=> (~in(X0,relation_inverse_image(sK214_skl,X1))|in(apply(sK214_skl,X0),X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f10822,plain,(
% 199.65/25.79    ~sQ10_spl|sQ353_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f10812,f2410,f10819])).
% 199.65/25.79  fof(f10828,definition,(
% 199.65/25.79    ![X0,X1]: (sQ354_spl <=> (~in(X0,relation_inverse_image(empty_set,X1))|in(apply(empty_set,X0),X1)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f10831,plain,(
% 199.65/25.79    ~sQ17_spl|sQ354_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f10818,f2445,f10828])).
% 199.65/25.79  fof(f11247,plain,(
% 199.65/25.79    ~relation_dom(relation_dom(sK214_skl))=empty_set|relation_dom(sK214_skl)=empty_set|~sQ56_spl),
% 199.65/25.79    inference(resolution,[status(thm)],[f1818,f2711])).
% 199.65/25.79  fof(f11270,definition,(
% 199.65/25.79    sQ357_spl <=> (relation_dom(relation_dom(sK214_skl))=empty_set)),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11273,plain,(
% 199.65/25.79    ~sQ357_spl|sQ29_spl|~sQ56_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f11247,f11270,f2536,f2710])).
% 199.65/25.79  fof(f11728,plain,(
% 199.65/25.79    relation_rng(sK214_skl)=relation_rng(sK214_skl)|~subset(relation_rng(sK214_skl),relation_rng(sK214_skl))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3075,f2829])).
% 199.65/25.79  fof(f11729,plain,(
% 199.65/25.79    succ(sK213_skl)=relation_rng(sK214_skl)|~subset(succ(sK213_skl),relation_rng(sK214_skl))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3075,f5475])).
% 199.65/25.79  fof(f11730,plain,(
% 199.65/25.79    sK213_skl=relation_rng(sK214_skl)|~subset(sK213_skl,relation_rng(sK214_skl))),
% 199.65/25.79    inference(resolution,[status(thm)],[f3075,f1733])).
% 199.65/25.79  fof(f11732,definition,(
% 199.65/25.79    sQ364_spl <=> (relation_rng(sK214_skl)=relation_rng(sK214_skl))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11735,definition,(
% 199.65/25.79    sQ365_spl <=> (subset(relation_rng(sK214_skl),relation_rng(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11737,plain,(
% 199.65/25.79    ~subset(relation_rng(sK214_skl),relation_rng(sK214_skl))|sQ365_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f11735])).
% 199.65/25.79  fof(f11738,plain,(
% 199.65/25.79    sQ364_spl|~sQ365_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f11728,f11732,f11735])).
% 199.65/25.79  fof(f11739,definition,(
% 199.65/25.79    sQ366_spl <=> (succ(sK213_skl)=relation_rng(sK214_skl))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11740,plain,(
% 199.65/25.79    succ(sK213_skl)=relation_rng(sK214_skl)|~sQ366_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f11739])).
% 199.65/25.79  fof(f11742,definition,(
% 199.65/25.79    sQ367_spl <=> (subset(succ(sK213_skl),relation_rng(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11744,plain,(
% 199.65/25.79    ~subset(succ(sK213_skl),relation_rng(sK214_skl))|sQ367_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f11742])).
% 199.65/25.79  fof(f11745,plain,(
% 199.65/25.79    sQ366_spl|~sQ367_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f11729,f11739,f11742])).
% 199.65/25.79  fof(f11746,definition,(
% 199.65/25.79    sQ368_spl <=> (sK213_skl=relation_rng(sK214_skl))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11747,plain,(
% 199.65/25.79    sK213_skl=relation_rng(sK214_skl)|~sQ368_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f11746])).
% 199.65/25.79  fof(f11749,definition,(
% 199.65/25.79    sQ369_spl <=> (subset(sK213_skl,relation_rng(sK214_skl)))),
% 199.65/25.79    introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition])).
% 199.65/25.79  fof(f11751,plain,(
% 199.65/25.79    ~subset(sK213_skl,relation_rng(sK214_skl))|sQ369_spl),
% 199.65/25.79    inference(component_clause,[status(thm)],[f11749])).
% 199.65/25.79  fof(f11752,plain,(
% 199.65/25.79    sQ368_spl|~sQ369_spl),
% 199.65/25.79    inference(split_clause,[status(thm)],[f11730,f11746,f11749])).
% 199.65/25.79  fof(f11769,plain,(
% 199.65/25.79    ![X0]: (in(empty_set,set_union2(sK213_skl,X0))|~sQ368_spl|~sQ179_spl)),
% 199.65/25.79    inference(backward_demodulation,[status(thm)],[f11747,f9620])).
% 199.65/25.79  fof(f11792,plain,(
% 199.65/25.79    succ(sK213_skl)=sK213_skl|~sQ368_spl|~sQ366_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f11747,f11740])).
% 199.65/25.79  fof(f11793,plain,(
% 199.65/25.79    ~subset(sK213_skl,sK213_skl)|~sQ368_spl|sQ369_spl),
% 199.65/25.79    inference(forward_demodulation,[status(thm)],[f11747,f11751])).
% 199.65/25.79  fof(f11794,plain,(
% 199.65/25.79    $false|~sQ368_spl|sQ369_spl),
% 199.65/25.79    inference(forward_subsumption_resolution,[status(thm)],[f11793,f2180])).
% 199.65/25.79  fof(f11795,plain,(
% 199.65/25.79    ~sQ368_spl|sQ369_spl),
% 199.65/25.79    inference(contradiction_clause,[status(thm)],[f11794])).
% 199.65/25.80  fof(f11796,plain,(
% 199.65/25.80    $false|sQ365_spl),
% 199.65/25.80    inference(forward_subsumption_resolution,[status(thm)],[f11737,f2180])).
% 199.65/25.80  fof(f11797,plain,(
% 199.65/25.80    sQ365_spl),
% 199.65/25.80    inference(contradiction_clause,[status(thm)],[f11796])).
% 199.65/25.80  fof(f11831,plain,(
% 199.65/25.80    ~subset(succ(sK213_skl),succ(sK213_skl))|~sQ366_spl|sQ367_spl),
% 199.65/25.80    inference(backward_demodulation,[status(thm)],[f11740,f11744])).
% 199.65/25.80  fof(f11882,plain,(
% 199.65/25.80    ~subset(sK213_skl,succ(sK213_skl))|~sQ368_spl|~sQ366_spl|sQ367_spl),
% 199.65/25.80    inference(forward_demodulation,[status(thm)],[f11792,f11831])).
% 199.65/25.80  fof(f11883,plain,(
% 199.65/25.80    ~subset(sK213_skl,sK213_skl)|~sQ368_spl|~sQ366_spl|sQ367_spl),
% 199.65/25.80    inference(forward_demodulation,[status(thm)],[f11792,f11882])).
% 199.65/25.80  fof(f11884,plain,(
% 199.65/25.80    $false|~sQ368_spl|~sQ366_spl|sQ367_spl),
% 199.65/25.80    inference(forward_subsumption_resolution,[status(thm)],[f11883,f2180])).
% 199.65/25.80  fof(f11885,plain,(
% 199.65/25.80    ~sQ368_spl|~sQ366_spl|sQ367_spl),
% 199.65/25.80    inference(contradiction_clause,[status(thm)],[f11884])).
% 199.65/25.80  fof(f11997,plain,(
% 199.65/25.80    ![X0]: (in(empty_set,sK213_skl)|in(empty_set,X0)|~sQ368_spl|~sQ179_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f11769,f2232])).
% 199.65/25.80  fof(f12018,definition,(
% 199.65/25.80    sQ370_spl <=> (in(empty_set,sK213_skl))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12021,plain,(
% 199.65/25.80    sQ370_spl|sQ325_spl|~sQ368_spl|~sQ179_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f11997,f12018,f8953,f11746,f4392])).
% 199.65/25.80  fof(f12427,plain,(
% 199.65/25.80    ![X0,X1]: (~in(X0,relation_dom(sK214_skl))|~function(sK214_skl)|~in(ordered_pair(X0,X1),sK214_skl)|X1=apply(sK214_skl,X0)|~sQ334_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f9854,f518])).
% 199.65/25.80  fof(f12439,definition,(
% 199.65/25.80    ![X0,X1]: (sQ375_spl <=> (~in(X0,relation_dom(sK214_skl))|~in(ordered_pair(X0,X1),sK214_skl)|X1=apply(sK214_skl,X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12442,plain,(
% 199.65/25.80    sQ375_spl|~sQ11_spl|~sQ334_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12427,f12439,f2413,f9853])).
% 199.65/25.80  fof(f12535,plain,(
% 199.65/25.80    ![X0]: (proper_subset(empty_set,X0)|empty_set=X0)),
% 199.65/25.80    inference(resolution,[status(thm)],[f893,f1620])).
% 199.65/25.80  fof(f12547,plain,(
% 199.65/25.80    ![X0]: (empty_set=X0|~proper_subset(X0,empty_set))),
% 199.65/25.80    inference(resolution,[status(thm)],[f12535,f391])).
% 199.65/25.80  fof(f12552,plain,(
% 199.65/25.80    empty_set=empty_set|empty_set=empty_set),
% 199.65/25.80    inference(resolution,[status(thm)],[f12547,f12535])).
% 199.65/25.80  fof(f12553,plain,(
% 199.65/25.80    sQ16_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12552,f2437])).
% 199.65/25.80  fof(f12592,plain,(
% 199.65/25.80    relation_of2(sK214_skl,sK212_skl,sK213_skl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f1193,f1733])).
% 199.65/25.80  fof(f12779,plain,(
% 199.65/25.80    ![X0]: (in(sK24_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,sK24_skl(relation_dom(sK214_skl))),X0)|relation(relation_dom(sK214_skl))|~sQ351_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f10797,f543])).
% 199.65/25.80  fof(f12797,plain,(
% 199.65/25.80    ![X0]: (in(sK33_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,sK33_skl(relation_dom(sK214_skl))),X0)|relation_dom(sK214_skl)=empty_set|~sQ351_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f10797,f600])).
% 199.65/25.80  fof(f12812,plain,(
% 199.65/25.80    ![X0]: (in(ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK18_skl(relation_dom(sK214_skl))),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK18_skl(relation_dom(sK214_skl)))),X0)|function(relation_dom(sK214_skl))|~sQ351_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f10797,f520])).
% 199.65/25.80  fof(f12813,plain,(
% 199.65/25.80    ![X0]: (in(ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK17_skl(relation_dom(sK214_skl))),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK17_skl(relation_dom(sK214_skl)))),X0)|function(relation_dom(sK214_skl))|~sQ351_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f10797,f519])).
% 199.65/25.80  fof(f12815,definition,(
% 199.65/25.80    ![X0]: (sQ392_spl <=> (in(sK24_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,sK24_skl(relation_dom(sK214_skl))),X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12818,plain,(
% 199.65/25.80    sQ392_spl|sQ56_spl|~sQ351_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12779,f12815,f2710,f10796])).
% 199.65/25.80  fof(f12828,definition,(
% 199.65/25.80    ![X0]: (sQ395_spl <=> (in(sK33_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,sK33_skl(relation_dom(sK214_skl))),X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12831,plain,(
% 199.65/25.80    sQ395_spl|sQ29_spl|~sQ351_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12797,f12828,f2536,f10796])).
% 199.65/25.80  fof(f12857,definition,(
% 199.65/25.80    ![X0]: (sQ403_spl <=> (in(ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK18_skl(relation_dom(sK214_skl))),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK18_skl(relation_dom(sK214_skl)))),X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12860,plain,(
% 199.65/25.80    sQ403_spl|sQ54_spl|~sQ351_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12812,f12857,f2703,f10796])).
% 199.65/25.80  fof(f12861,definition,(
% 199.65/25.80    ![X0]: (sQ404_spl <=> (in(ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK17_skl(relation_dom(sK214_skl))),relation_inverse_image(sK214_skl,X0))|~in(apply(sK214_skl,ordered_pair(sK19_skl(relation_dom(sK214_skl)),sK17_skl(relation_dom(sK214_skl)))),X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f12864,plain,(
% 199.65/25.80    sQ404_spl|sQ54_spl|~sQ351_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f12813,f12861,f2703,f10796])).
% 199.65/25.80  fof(f13198,plain,(
% 199.65/25.80    ~subset(sK213_skl,succ(sK213_skl))|~sQ366_spl|sQ369_spl),
% 199.65/25.80    inference(forward_demodulation,[status(thm)],[f11740,f11751])).
% 199.65/25.80  fof(f13199,plain,(
% 199.65/25.80    $false|~sQ366_spl|sQ369_spl),
% 199.65/25.80    inference(forward_subsumption_resolution,[status(thm)],[f13198,f5469])).
% 199.65/25.80  fof(f13200,plain,(
% 199.65/25.80    ~sQ366_spl|sQ369_spl),
% 199.65/25.80    inference(contradiction_clause,[status(thm)],[f13199])).
% 199.65/25.80  fof(f13531,plain,(
% 199.65/25.80    ![X0,X1]: (~relation(relation_dom(sK214_skl))|~in(X0,relation_inverse_image(relation_dom(sK214_skl),X1))|in(apply(relation_dom(sK214_skl),X0),X1)|~sQ54_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f2704,f2191])).
% 199.65/25.80  fof(f13532,plain,(
% 199.65/25.80    ![X0,X1]: (~relation(relation_dom(sK214_skl))|in(X0,relation_inverse_image(relation_dom(sK214_skl),X1))|~in(X0,relation_dom(relation_dom(sK214_skl)))|~in(apply(relation_dom(sK214_skl),X0),X1)|~sQ54_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f2704,f2192])).
% 199.65/25.80  fof(f13533,plain,(
% 199.65/25.80    ![X0]: (~relation(relation_dom(sK214_skl))|~in(X0,relation_dom(relation_dom(sK214_skl)))|in(ordered_pair(X0,apply(relation_dom(sK214_skl),X0)),relation_dom(sK214_skl))|~sQ54_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f2704,f2240])).
% 199.65/25.80  fof(f13534,plain,(
% 199.65/25.80    ![X0,X1]: (~relation(relation_dom(sK214_skl))|~in(ordered_pair(X0,X1),relation_dom(sK214_skl))|X1=apply(relation_dom(sK214_skl),X0)|~sQ54_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f2704,f1895])).
% 199.65/25.80  fof(f13535,plain,(
% 199.65/25.80    ![X0]: (~relation(relation_dom(sK214_skl))|in(X0,relation_dom(relation_dom(sK214_skl)))|apply(relation_dom(sK214_skl),X0)=empty_set|~sQ54_spl)),
% 199.65/25.80    inference(resolution,[status(thm)],[f2704,f2241])).
% 199.65/25.80  fof(f13536,definition,(
% 199.65/25.80    ![X0,X1]: (sQ406_spl <=> (~in(X0,relation_inverse_image(relation_dom(sK214_skl),X1))|in(apply(relation_dom(sK214_skl),X0),X1)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f13539,plain,(
% 199.65/25.80    ~sQ56_spl|sQ406_spl|~sQ54_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f13531,f2710,f13536,f2703])).
% 199.65/25.80  fof(f13540,definition,(
% 199.65/25.80    ![X0,X1]: (sQ407_spl <=> (in(X0,relation_inverse_image(relation_dom(sK214_skl),X1))|~in(X0,relation_dom(relation_dom(sK214_skl)))|~in(apply(relation_dom(sK214_skl),X0),X1)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f13543,plain,(
% 199.65/25.80    ~sQ56_spl|sQ407_spl|~sQ54_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f13532,f2710,f13540,f2703])).
% 199.65/25.80  fof(f13544,definition,(
% 199.65/25.80    ![X0]: (sQ408_spl <=> (~in(X0,relation_dom(relation_dom(sK214_skl)))|in(ordered_pair(X0,apply(relation_dom(sK214_skl),X0)),relation_dom(sK214_skl))))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f13547,plain,(
% 199.65/25.80    ~sQ56_spl|sQ408_spl|~sQ54_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f13533,f2710,f13544,f2703])).
% 199.65/25.80  fof(f13548,definition,(
% 199.65/25.80    ![X0,X1]: (sQ409_spl <=> (~in(ordered_pair(X0,X1),relation_dom(sK214_skl))|X1=apply(relation_dom(sK214_skl),X0)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f13551,plain,(
% 199.65/25.80    ~sQ56_spl|sQ409_spl|~sQ54_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f13534,f2710,f13548,f2703])).
% 199.65/25.80  fof(f13552,definition,(
% 199.65/25.80    ![X0]: (sQ410_spl <=> (in(X0,relation_dom(relation_dom(sK214_skl)))|apply(relation_dom(sK214_skl),X0)=empty_set))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f13555,plain,(
% 199.65/25.80    ~sQ56_spl|sQ410_spl|~sQ54_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f13535,f2710,f13552,f2703])).
% 199.65/25.80  fof(f13635,plain,(
% 199.65/25.80    ![X0,X1]: (in(singleton(X0),ordered_pair(X0,X1)))),
% 199.65/25.80    inference(paramodulation,[status(thm)],[f799,f2231])).
% 199.65/25.80  fof(f14098,plain,(
% 199.65/25.80    ~relation_of2(sK214_skl,sK212_skl,sK213_skl)|element(sK212_skl,powerset(sK212_skl))|~sQ208_spl),
% 199.65/25.80    inference(paramodulation,[status(thm)],[f5355,f913])).
% 199.65/25.80  fof(f14100,definition,(
% 199.65/25.80    sQ427_spl <=> (relation_of2(sK214_skl,sK212_skl,sK213_skl))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f14102,plain,(
% 199.65/25.80    ~relation_of2(sK214_skl,sK212_skl,sK213_skl)|sQ427_spl),
% 199.65/25.80    inference(component_clause,[status(thm)],[f14100])).
% 199.65/25.80  fof(f14103,definition,(
% 199.65/25.80    sQ428_spl <=> (element(sK212_skl,powerset(sK212_skl)))),
% 199.65/25.80    introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition])).
% 199.65/25.80  fof(f14106,plain,(
% 199.65/25.80    ~sQ427_spl|sQ428_spl|~sQ208_spl),
% 199.65/25.80    inference(split_clause,[status(thm)],[f14098,f14100,f14103,f5354])).
% 199.65/25.80  fof(f14107,plain,(
% 199.65/25.80    $false|sQ427_spl),
% 199.65/25.80    inference(forward_subsumption_resolution,[status(thm)],[f14102,f12592])).
% 199.65/25.80  fof(f14108,plain,(
% 199.65/25.80    sQ427_spl),
% 199.65/25.80    inference(contradiction_clause,[status(thm)],[f14107])).
% 199.65/25.80  fof(f14695,plain,(
% 199.65/25.80    ![X0,X1]: (relation_of2_as_subset(empty_set,X0,X1))),
% 68.57/25.82    inference(resolution,[status(thm)],[f1194,f5902])).
% 68.57/25.82  fof(f14699,plain,(
% 68.57/25.82    ![X0]: (X0=empty_set|quasi_total(empty_set,X0,empty_set))),
% 68.57/25.82    inference(backward_subsumption_resolution,[status(thm)],[f2202,f14695])).
% 68.57/25.82  fof(f14712,definition,(
% 68.57/25.82    ![X0]: (sQ431_spl <=> (X0=empty_set|~quasi_total(empty_set,X0,empty_set)))),
% 68.57/25.82    introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition])).
% 68.57/25.82  fof(f14713,plain,(
% 68.57/25.82    ![X0]: (X0=empty_set|~quasi_total(empty_set,X0,empty_set)|~sQ431_spl)),
% 68.57/25.82    inference(component_clause,[status(thm)],[f14712])).
% 68.57/25.82  fof(f14720,plain,(
% 68.57/25.82    $false|~sQ431_spl|sQ127_spl),
% 68.57/25.82    inference(backward_subsumption_resolution,[status(thm)],[f3767,f14743])).
% 68.57/25.82  fof(f14743,plain,(
% 68.57/25.82    ![X0]: (X0=empty_set|~sQ431_spl)),
% 68.57/25.82    inference(forward_subsumption_resolution,[status(thm)],[f14713,f14699])).
% 68.57/25.82  fof(f14744,plain,(
% 68.57/25.82    ~sQ431_spl|sQ127_spl),
% 68.57/25.82    inference(contradiction_clause,[status(thm)],[f14720])).
% 68.57/25.82  fof(f15249,plain,(
% 68.57/25.82    ![X0,X1,X2,X3]: (~in(X0,X1)|~in(X2,X3)|in(X2,X3))),
% 68.57/25.82    inference(resolution,[status(thm)],[f1104,f1103])).
% 68.57/25.82  fof(f15264,definition,(
% 68.57/25.82    ![X0,X1]: (sQ432_spl <=> (~in(X0,X1)))),
% 68.57/25.82    introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition])).
% 68.57/25.82  fof(f15265,plain,(
% 68.57/25.82    ![X0,X1]: (~in(X0,X1)|~sQ432_spl)),
% 68.57/25.82    inference(component_clause,[status(thm)],[f15264])).
% 68.57/25.82  fof(f15267,definition,(
% 68.57/25.82    ![X2,X3]: (sQ433_spl <=> (~in(X2,X3)|in(X2,X3)))),
% 68.57/25.82    introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition])).
% 68.57/25.82  fof(f15270,plain,(
% 68.57/25.82    sQ432_spl|sQ433_spl),
% 68.57/25.82    inference(split_clause,[status(thm)],[f15249,f15264,f15267])).
% 68.57/25.82  fof(f15284,plain,(
% 68.57/25.82    $false|~sQ432_spl),
% 68.57/25.82    inference(backward_subsumption_resolution,[status(thm)],[f13635,f15265])).
% 68.57/25.82  fof(f16688,plain,(
% 68.57/25.82    ~sQ432_spl),
% 68.57/25.82    inference(contradiction_clause,[status(thm)],[f15284])).
% 68.57/25.82  fof(f16690,plain,(
% 68.57/25.82    relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)=relation_dom(sK214_skl)),
% 68.57/25.82    inference(resolution,[status(thm)],[f1182,f12592])).
% 68.57/25.82  fof(f16697,plain,(
% 68.57/25.82    sK212_skl=relation_dom(sK214_skl)|~sQ208_spl),
% 68.57/25.82    inference(forward_demodulation,[status(thm)],[f5355,f16690])).
% 68.57/25.82  fof(f16698,plain,(
% 68.57/25.82    $false|sQ83_spl|~sQ208_spl),
% 68.57/25.82    inference(forward_subsumption_resolution,[status(thm)],[f16697,f3081])).
% 68.57/25.82  fof(f16699,plain,(
% 68.57/25.82    sQ83_spl|~sQ208_spl),
% 68.57/25.82    inference(contradiction_clause,[status(thm)],[f16698])).
% 68.57/25.82  fof(f16700,plain,(
% 68.57/25.82    $false),
% 68.57/25.82    inference(sat_refutation,[status(thm)],[f2151,f2155,f2159,f2163,f2170,f2174,f2175,f2416,f2420,f2443,f2451,f2453,f2462,f2469,f2483,f2489,f2498,f2510,f2517,f2521,f2523,f2532,f2534,f2542,f2547,f2558,f2585,f2590,f2601,f2614,f2621,f2625,f2629,f2634,f2636,f2653,f2655,f2706,f2713,f2717,f2739,f2756,f2772,f2776,f2798,f2846,f2883,f2885,f2887,f2892,f2933,f2947,f2964,f2966,f2974,f3025,f3052,f3114,f3131,f3132,f3172,f3346,f3356,f3511,f3521,f3579,f3589,f3617,f3668,f3670,f3776,f3852,f3856,f3860,f3864,f3868,f3986,f4001,f4015,f4018,f4109,f4130,f4134,f4136,f4175,f4189,f4213,f4217,f4221,f4225,f4229,f4261,f4263,f4280,f4370,f4388,f4500,f4567,f4602,f4609,f4634,f4665,f4799,f4824,f4825,f4896,f4900,f4904,f4908,f4912,f4942,f5087,f5188,f5198,f5269,f5277,f5357,f5359,f5393,f5397,f5401,f5405,f5409,f5462,f5481,f5485,f5489,f5506,f5510,f5567,f5611,f5615,f5658,f5745,f5796,f5800,f5804,f5808,f5812,f5854,f5891,f5917,f5921,f5947,f6024,f6028,f6059,f6106,f6155,f6170,f6451,f6455,f6766,f6781,f6804,f6826,f6848,f6860,f7176,f7205,f7221,f7269,f7300,f7637,f7863,f7872,f7876,f8034,f8044,f8215,f8381,f8418,f8452,f8461,f8473,f8482,f8780,f8782,f8899,f8956,f9047,f9294,f9320,f9596,f9605,f9856,f9866,f10424,f10799,f10810,f10822,f10831,f11273,f11738,f11745,f11752,f11795,f11797,f11885,f12021,f12442,f12553,f12818,f12831,f12860,f12864,f13200,f13539,f13543,f13547,f13551,f13555,f14106,f14108,f14744,f15270,f16688,f16699])).
% 68.57/25.82  % SZS output end CNFRefutation for theBenchmark.p
% 68.57/25.84  % Elapsed time: 25.390394 seconds
% 68.57/25.84  % CPU time: 200.379411 seconds
% 68.57/25.84  % Total memory used: 753.070 MB
% 68.57/25.84  % Net memory used: 678.280 MB
%------------------------------------------------------------------------------