TSTP Solution File: SEU210+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU210+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:41:30 EDT 2024
% Result : Theorem 105.78s 13.69s
% Output : CNFRefutation 105.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU210+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:02:49 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 105.78/13.69 % Refutation found
% 105.78/13.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 105.78/13.69 % SZS output start CNFRefutation for theBenchmark
% 105.78/13.69 fof(f4,axiom,(
% 105.78/13.69 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f5,axiom,(
% 105.78/13.69 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f6,axiom,(
% 105.78/13.69 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f11,axiom,(
% 105.78/13.69 (! [A] :( relation(A)=> (! [B,C] :( C = relation_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(E,D),A)& in(E,B) ) )) )) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f12,axiom,(
% 105.78/13.69 (! [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) ) )) )) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f13,axiom,(
% 105.78/13.69 (! [A] :( relation(A)<=> (! [B] :~ ( in(B,A)& (! [C,D] : B != ordered_pair(C,D) )) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f14,axiom,(
% 105.78/13.69 (! [A,B] :( ( A != empty_set=> ( B = set_meet(A)<=> (! [C] :( in(C,B)<=> (! [D] :( in(D,A)=> in(C,D) ) )) )) )& ( A = empty_set=> ( B = set_meet(A)<=> B = empty_set ) ) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f15,axiom,(
% 105.78/13.69 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f16,axiom,(
% 105.78/13.69 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f19,axiom,(
% 105.78/13.69 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f24,axiom,(
% 105.78/13.69 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f27,axiom,(
% 105.78/13.69 (! [A] : cast_to_subset(A) = A )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f28,axiom,(
% 105.78/13.69 (! [A,B] :( B = union(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(C,D)& in(D,A) ) )) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f30,axiom,(
% 105.78/13.69 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f32,axiom,(
% 105.78/13.69 (! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f46,axiom,(
% 105.78/13.69 (! [A] : element(cast_to_subset(A),powerset(A)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f59,axiom,(
% 105.78/13.69 (! [A] : relation(identity_relation(A)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f67,axiom,(
% 105.78/13.69 (! [A] :(? [B] : element(B,A) ))),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f70,axiom,(
% 105.78/13.69 (! [A] : ~ empty(powerset(A)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f71,axiom,(
% 105.78/13.69 empty(empty_set) ),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f74,axiom,(
% 105.78/13.69 (! [A] : ~ empty(singleton(A)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f78,axiom,(
% 105.78/13.69 ( empty(empty_set)& relation(empty_set) ) ),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f83,axiom,(
% 105.78/13.69 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f85,axiom,(
% 105.78/13.69 (! [A,B] : set_union2(A,A) = A )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f91,lemma,(
% 105.78/13.69 (! [A] : singleton(A) != empty_set )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f107,axiom,(
% 105.78/13.69 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f113,axiom,(
% 105.78/13.69 (! [A,B] :( disjoint(A,B)=> disjoint(B,A) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f133,conjecture,(
% 105.78/13.69 (! [A,B] :( relation(B)=> ~ ( A != empty_set& subset(A,relation_rng(B))& relation_inverse_image(B,A) = empty_set ) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f134,negated_conjecture,(
% 105.78/13.69 ~((! [A,B] :( relation(B)=> ~ ( A != empty_set& subset(A,relation_rng(B))& relation_inverse_image(B,A) = empty_set ) ) ))),
% 105.78/13.69 inference(negated_conjecture,[status(cth)],[f133])).
% 105.78/13.69 fof(f137,axiom,(
% 105.78/13.69 (! [A] : set_union2(A,empty_set) = A )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f140,lemma,(
% 105.78/13.69 powerset(empty_set) = singleton(empty_set) ),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f149,lemma,(
% 105.78/13.69 (! [A] : subset(empty_set,A) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f158,lemma,(
% 105.78/13.69 (! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f161,axiom,(
% 105.78/13.69 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f163,lemma,(
% 105.78/13.69 (! [A] :( subset(A,empty_set)=> A = empty_set ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f164,lemma,(
% 105.78/13.69 (! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f175,lemma,(
% 105.78/13.69 (! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f176,axiom,(
% 105.78/13.69 (! [A] : set_difference(empty_set,A) = empty_set )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f183,lemma,(
% 105.78/13.69 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f184,lemma,(
% 105.78/13.69 (! [A,B] :~ ( subset(A,B)& proper_subset(B,A) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f186,lemma,(
% 105.78/13.69 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f189,lemma,(
% 105.78/13.69 (! [A] : unordered_pair(A,A) = singleton(A) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f190,axiom,(
% 105.78/13.69 (! [A] :( empty(A)=> A = empty_set ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f192,lemma,(
% 105.78/13.69 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f195,lemma,(
% 105.78/13.69 (! [A,B] : subset(A,set_union2(A,B)) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f196,lemma,(
% 105.78/13.69 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f206,lemma,(
% 105.78/13.69 (! [A] : union(powerset(A)) = A )),
% 105.78/13.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 105.78/13.69 fof(f215,plain,(
% 105.78/13.69 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f4])).
% 105.78/13.69 fof(f216,plain,(
% 105.78/13.69 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f5])).
% 105.78/13.69 fof(f217,plain,(
% 105.78/13.69 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f6])).
% 105.78/13.69 fof(f253,plain,(
% 105.78/13.69 ![A]: (~relation(A)|(![B,C]: (C=relation_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 105.78/13.69 fof(f254,plain,(
% 105.78/13.69 ![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))))))))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f253])).
% 105.78/13.69 fof(f255,plain,(
% 105.78/13.69 ![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))))))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f254])).
% 105.78/13.69 fof(f256,plain,(
% 105.78/13.69 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(sk0_6(D,C,B,A),D),A)&in(sk0_6(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(sk0_7(C,B,A),C)|(![E]: (~in(ordered_pair(E,sk0_7(C,B,A)),A)|~in(E,B))))&(in(sk0_7(C,B,A),C)|(in(ordered_pair(sk0_8(C,B,A),sk0_7(C,B,A)),A)&in(sk0_8(C,B,A),B))))))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f255])).
% 105.78/13.69 fof(f257,plain,(
% 105.78/13.69 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_image(X0,X2)|~in(X3,X1)|in(ordered_pair(sk0_6(X3,X1,X2,X0),X3),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f256])).
% 105.78/13.69 fof(f258,plain,(
% 105.78/13.69 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_image(X0,X2)|~in(X3,X1)|in(sk0_6(X3,X1,X2,X0),X2))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f256])).
% 105.78/13.69 fof(f261,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|X1=relation_image(X0,X2)|in(sk0_7(X1,X2,X0),X1)|in(ordered_pair(sk0_8(X1,X2,X0),sk0_7(X1,X2,X0)),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f256])).
% 105.78/13.69 fof(f262,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|X1=relation_image(X0,X2)|in(sk0_7(X1,X2,X0),X1)|in(sk0_8(X1,X2,X0),X2))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f256])).
% 105.78/13.69 fof(f263,plain,(
% 105.78/13.69 ![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))))))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 105.78/13.69 fof(f264,plain,(
% 105.78/13.69 ![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))))))))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f263])).
% 105.78/13.69 fof(f265,plain,(
% 105.78/13.69 ![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))))))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f264])).
% 105.78/13.69 fof(f266,plain,(
% 105.78/13.69 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sk0_9(D,C,B,A)),A)&in(sk0_9(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(sk0_10(C,B,A),C)|(![E]: (~in(ordered_pair(sk0_10(C,B,A),E),A)|~in(E,B))))&(in(sk0_10(C,B,A),C)|(in(ordered_pair(sk0_10(C,B,A),sk0_11(C,B,A)),A)&in(sk0_11(C,B,A),B))))))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f265])).
% 105.78/13.69 fof(f269,plain,(
% 105.78/13.69 ![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))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f266])).
% 105.78/13.69 fof(f273,plain,(
% 105.78/13.69 ![A]: (relation(A)<=>(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D)))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 105.78/13.69 fof(f274,plain,(
% 105.78/13.69 ![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))))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f273])).
% 105.78/13.69 fof(f275,plain,(
% 105.78/13.69 (![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))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f274])).
% 105.78/13.69 fof(f276,plain,(
% 105.78/13.69 (![A]: (~relation(A)|(![B]: (~in(B,A)|B=ordered_pair(sk0_12(B,A),sk0_13(B,A))))))&(![A]: (relation(A)|(in(sk0_14(A),A)&(![C,D]: ~sk0_14(A)=ordered_pair(C,D)))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f275])).
% 105.78/13.69 fof(f278,plain,(
% 105.78/13.69 ![X0]: (relation(X0)|in(sk0_14(X0),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f276])).
% 105.78/13.69 fof(f279,plain,(
% 105.78/13.69 ![X0,X1,X2]: (relation(X0)|~sk0_14(X0)=ordered_pair(X1,X2))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f276])).
% 105.78/13.69 fof(f280,plain,(
% 105.78/13.69 ![A,B]: ((A=empty_set|(B=set_meet(A)<=>(![C]: (in(C,B)<=>(![D]: (~in(D,A)|in(C,D)))))))&(~A=empty_set|(B=set_meet(A)<=>B=empty_set)))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 105.78/13.69 fof(f281,plain,(
% 105.78/13.69 ![A,B]: ((A=empty_set|((~B=set_meet(A)|(![C]: ((~in(C,B)|(![D]: (~in(D,A)|in(C,D))))&(in(C,B)|(?[D]: (in(D,A)&~in(C,D)))))))&(B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))&(~A=empty_set|((~B=set_meet(A)|B=empty_set)&(B=set_meet(A)|~B=empty_set))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f280])).
% 105.78/13.69 fof(f282,plain,(
% 105.78/13.69 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(?[D]: (in(D,A)&~in(C,D))))))))&(![B]: (B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f281])).
% 105.78/13.69 fof(f283,plain,(
% 105.78/13.69 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(in(sk0_15(C,B,A),A)&~in(C,sk0_15(C,B,A))))))))&(![B]: (B=set_meet(A)|((~in(sk0_16(B,A),B)|(in(sk0_17(B,A),A)&~in(sk0_16(B,A),sk0_17(B,A))))&(in(sk0_16(B,A),B)|(![D]: (~in(D,A)|in(sk0_16(B,A),D))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f282])).
% 105.78/13.69 fof(f290,plain,(
% 105.78/13.69 ![X0,X1]: (~X0=empty_set|~X1=set_meet(X0)|X1=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f283])).
% 105.78/13.69 fof(f292,plain,(
% 105.78/13.69 ![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)))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f15])).
% 105.78/13.69 fof(f293,plain,(
% 105.78/13.69 (![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)))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f292])).
% 105.78/13.69 fof(f294,plain,(
% 105.78/13.69 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_18(B,A),B)|~sk0_18(B,A)=A)&(in(sk0_18(B,A),B)|sk0_18(B,A)=A))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f293])).
% 105.78/13.69 fof(f295,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f294])).
% 105.78/13.69 fof(f296,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f294])).
% 105.78/13.69 fof(f299,plain,(
% 105.78/13.69 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f16])).
% 105.78/13.69 fof(f300,plain,(
% 105.78/13.69 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f299])).
% 105.78/13.69 fof(f301,plain,(
% 105.78/13.69 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_19(A),A)))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f300])).
% 105.78/13.69 fof(f302,plain,(
% 105.78/13.69 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f301])).
% 105.78/13.69 fof(f303,plain,(
% 105.78/13.69 ![X0]: (X0=empty_set|in(sk0_19(X0),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f301])).
% 105.78/13.69 fof(f319,plain,(
% 105.78/13.69 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 105.78/13.69 fof(f320,plain,(
% 105.78/13.69 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f319])).
% 105.78/13.69 fof(f321,plain,(
% 105.78/13.69 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f320])).
% 105.78/13.69 fof(f322,plain,(
% 105.78/13.69 ![X0,X1]: (empty(X0)|~element(X1,X0)|in(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f321])).
% 105.78/13.69 fof(f359,plain,(
% 105.78/13.69 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 105.78/13.69 fof(f360,plain,(
% 105.78/13.69 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f359])).
% 105.78/13.69 fof(f361,plain,(
% 105.78/13.69 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f360])).
% 105.78/13.69 fof(f362,plain,(
% 105.78/13.69 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_32(B,A),A)&~in(sk0_32(B,A),B))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f361])).
% 105.78/13.69 fof(f363,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f362])).
% 105.78/13.69 fof(f364,plain,(
% 105.78/13.69 ![X0,X1]: (subset(X0,X1)|in(sk0_32(X1,X0),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f362])).
% 105.78/13.69 fof(f365,plain,(
% 105.78/13.69 ![X0,X1]: (subset(X0,X1)|~in(sk0_32(X1,X0),X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f362])).
% 105.78/13.69 fof(f383,plain,(
% 105.78/13.69 ![X0]: (cast_to_subset(X0)=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f27])).
% 105.78/13.69 fof(f384,plain,(
% 105.78/13.69 ![A,B]: ((~B=union(A)|(![C]: ((~in(C,B)|(?[D]: (in(C,D)&in(D,A))))&(in(C,B)|(![D]: (~in(C,D)|~in(D,A)))))))&(B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f28])).
% 105.78/13.69 fof(f385,plain,(
% 105.78/13.69 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(?[D]: (in(C,D)&in(D,A)))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f384])).
% 105.78/13.69 fof(f386,plain,(
% 105.78/13.69 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(in(C,sk0_37(C,B,A))&in(sk0_37(C,B,A),A))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|((~in(sk0_38(B,A),B)|(![D]: (~in(sk0_38(B,A),D)|~in(D,A))))&(in(sk0_38(B,A),B)|(in(sk0_38(B,A),sk0_39(B,A))&in(sk0_39(B,A),A))))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f385])).
% 105.78/13.69 fof(f388,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~X0=union(X1)|~in(X2,X0)|in(sk0_37(X2,X0,X1),X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f386])).
% 105.78/13.69 fof(f402,plain,(
% 105.78/13.69 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 105.78/13.69 fof(f403,plain,(
% 105.78/13.69 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f402])).
% 105.78/13.69 fof(f404,plain,(
% 105.78/13.69 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f403])).
% 105.78/13.69 fof(f405,plain,(
% 105.78/13.69 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sk0_41(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sk0_42(B,A),B)|(![D]: ~in(ordered_pair(D,sk0_42(B,A)),A)))&(in(sk0_42(B,A),B)|in(ordered_pair(sk0_43(B,A),sk0_42(B,A)),A)))))))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f404])).
% 105.78/13.69 fof(f406,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sk0_41(X2,X1,X0),X2),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f405])).
% 105.78/13.69 fof(f412,plain,(
% 105.78/13.69 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X0,X1),singleton(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f32])).
% 105.78/13.69 fof(f450,plain,(
% 105.78/13.69 ![X0]: (element(cast_to_subset(X0),powerset(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f46])).
% 105.78/13.69 fof(f459,plain,(
% 105.78/13.69 ![X0]: (relation(identity_relation(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f59])).
% 105.78/13.69 fof(f472,plain,(
% 105.78/13.69 ![A]: element(sk0_51(A),A)),
% 105.78/13.69 inference(skolemization,[status(esa)],[f67])).
% 105.78/13.69 fof(f473,plain,(
% 105.78/13.69 ![X0]: (element(sk0_51(X0),X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f472])).
% 105.78/13.69 fof(f479,plain,(
% 105.78/13.69 ![X0]: (~empty(powerset(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f70])).
% 105.78/13.69 fof(f480,plain,(
% 105.78/13.69 empty(empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f71])).
% 105.78/13.69 fof(f484,plain,(
% 105.78/13.69 ![X0]: (~empty(singleton(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f74])).
% 105.78/13.69 fof(f493,plain,(
% 105.78/13.69 relation(empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f78])).
% 105.78/13.69 fof(f503,plain,(
% 105.78/13.69 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f83])).
% 105.78/13.69 fof(f505,plain,(
% 105.78/13.69 ![X0]: (~empty(X0)|relation(relation_rng(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f503])).
% 105.78/13.69 fof(f509,plain,(
% 105.78/13.69 ![A]: set_union2(A,A)=A),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f85])).
% 105.78/13.69 fof(f510,plain,(
% 105.78/13.69 ![X0]: (set_union2(X0,X0)=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f509])).
% 105.78/13.69 fof(f521,plain,(
% 105.78/13.69 ![X0]: (~singleton(X0)=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f91])).
% 105.78/13.69 fof(f569,plain,(
% 105.78/13.69 ![A]: (element(sk0_57(A),powerset(A))&empty(sk0_57(A)))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f107])).
% 105.78/13.69 fof(f570,plain,(
% 105.78/13.69 ![X0]: (element(sk0_57(X0),powerset(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f569])).
% 105.78/13.69 fof(f571,plain,(
% 105.78/13.69 ![X0]: (empty(sk0_57(X0)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f569])).
% 105.78/13.69 fof(f582,plain,(
% 105.78/13.69 ![A,B]: (~disjoint(A,B)|disjoint(B,A))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f113])).
% 105.78/13.69 fof(f583,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(X0,X1)|disjoint(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f582])).
% 105.78/13.69 fof(f657,plain,(
% 105.78/13.69 (?[A,B]: (relation(B)&((~A=empty_set&subset(A,relation_rng(B)))&relation_inverse_image(B,A)=empty_set)))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f134])).
% 105.78/13.69 fof(f658,plain,(
% 105.78/13.69 ?[B]: (relation(B)&(?[A]: ((~A=empty_set&subset(A,relation_rng(B)))&relation_inverse_image(B,A)=empty_set)))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f657])).
% 105.78/13.69 fof(f659,plain,(
% 105.78/13.69 (relation(sk0_62)&((~sk0_63=empty_set&subset(sk0_63,relation_rng(sk0_62)))&relation_inverse_image(sk0_62,sk0_63)=empty_set))),
% 105.78/13.69 inference(skolemization,[status(esa)],[f658])).
% 105.78/13.69 fof(f660,plain,(
% 105.78/13.69 relation(sk0_62)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f659])).
% 105.78/13.69 fof(f661,plain,(
% 105.78/13.69 ~sk0_63=empty_set),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f659])).
% 105.78/13.69 fof(f662,plain,(
% 105.78/13.69 subset(sk0_63,relation_rng(sk0_62))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f659])).
% 105.78/13.69 fof(f663,plain,(
% 105.78/13.69 relation_inverse_image(sk0_62,sk0_63)=empty_set),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f659])).
% 105.78/13.69 fof(f667,plain,(
% 105.78/13.69 ![X0]: (set_union2(X0,empty_set)=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f137])).
% 105.78/13.69 fof(f673,plain,(
% 105.78/13.69 powerset(empty_set)=singleton(empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f140])).
% 105.78/13.69 fof(f696,plain,(
% 105.78/13.69 ![X0]: (subset(empty_set,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f149])).
% 105.78/13.69 fof(f724,plain,(
% 105.78/13.69 ![X0,X1]: (set_union2(X0,set_difference(X1,X0))=set_union2(X0,X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f158])).
% 105.78/13.69 fof(f731,plain,(
% 105.78/13.69 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f161])).
% 105.78/13.69 fof(f732,plain,(
% 105.78/13.69 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f731])).
% 105.78/13.69 fof(f733,plain,(
% 105.78/13.69 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f732])).
% 105.78/13.69 fof(f741,plain,(
% 105.78/13.69 ![A]: (~subset(A,empty_set)|A=empty_set)),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f163])).
% 105.78/13.69 fof(f742,plain,(
% 105.78/13.69 ![X0]: (~subset(X0,empty_set)|X0=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f741])).
% 105.78/13.69 fof(f743,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(set_union2(X0,X1),X1)=set_difference(X0,X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f164])).
% 105.78/13.69 fof(f766,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(X0,set_difference(X0,X1))=set_intersection2(X0,X1))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f175])).
% 105.78/13.69 fof(f767,plain,(
% 105.78/13.69 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f176])).
% 105.78/13.69 fof(f787,plain,(
% 105.78/13.69 relation_dom(empty_set)=empty_set),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f183])).
% 105.78/13.69 fof(f788,plain,(
% 105.78/13.69 relation_rng(empty_set)=empty_set),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f183])).
% 105.78/13.69 fof(f789,plain,(
% 105.78/13.69 ![A,B]: (~subset(A,B)|~proper_subset(B,A))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f184])).
% 105.78/13.69 fof(f790,plain,(
% 105.78/13.69 ![X0,X1]: (~subset(X0,X1)|~proper_subset(X1,X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f789])).
% 105.78/13.69 fof(f794,plain,(
% 105.78/13.69 ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f186])).
% 105.78/13.69 fof(f796,plain,(
% 105.78/13.69 ![X0]: (~relation(X0)|~relation_rng(X0)=empty_set|X0=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f794])).
% 105.78/13.69 fof(f805,plain,(
% 105.78/13.69 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f189])).
% 105.78/13.69 fof(f806,plain,(
% 105.78/13.69 ![A]: (~empty(A)|A=empty_set)),
% 105.78/13.69 inference(pre_NNF_transformation,[status(esa)],[f190])).
% 105.78/13.69 fof(f807,plain,(
% 105.78/13.69 ![X0]: (~empty(X0)|X0=empty_set)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f806])).
% 105.78/13.69 fof(f810,plain,(
% 105.78/13.69 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f192])).
% 105.78/13.69 fof(f812,plain,(
% 105.78/13.69 ![X0]: (relation_rng(identity_relation(X0))=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f810])).
% 105.78/13.69 fof(f822,plain,(
% 105.78/13.69 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f195])).
% 105.78/13.69 fof(f823,plain,(
% 105.78/13.69 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 105.78/13.69 inference(NNF_transformation,[status(esa)],[f196])).
% 105.78/13.69 fof(f824,plain,(
% 105.78/13.69 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 105.78/13.69 inference(miniscoping,[status(esa)],[f823])).
% 105.78/13.69 fof(f826,plain,(
% 105.78/13.69 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f824])).
% 105.78/13.69 fof(f855,plain,(
% 105.78/13.69 ![X0]: (union(powerset(X0))=X0)),
% 105.78/13.69 inference(cnf_transformation,[status(esa)],[f206])).
% 105.78/13.69 fof(f884,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_image(X0,X2))|in(ordered_pair(sk0_6(X1,relation_image(X0,X2),X2,X0),X1),X0))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f257])).
% 105.78/13.69 fof(f885,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_image(X0,X2))|in(sk0_6(X1,relation_image(X0,X2),X2,X0),X2))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f258])).
% 105.78/13.69 fof(f889,plain,(
% 105.78/13.69 ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_inverse_image(X0,X2))|~in(ordered_pair(X1,X3),X0)|~in(X3,X2))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f269])).
% 105.78/13.69 fof(f893,plain,(
% 105.78/13.69 set_meet(empty_set)=empty_set),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f290])).
% 105.78/13.69 fof(f895,plain,(
% 105.78/13.69 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f295])).
% 105.78/13.69 fof(f896,plain,(
% 105.78/13.69 ![X0]: (in(X0,singleton(X0)))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f296])).
% 105.78/13.69 fof(f897,plain,(
% 105.78/13.69 ![X0]: (~in(X0,empty_set))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f302])).
% 105.78/13.69 fof(f914,plain,(
% 105.78/13.69 ![X0,X1]: (~in(X0,union(X1))|in(sk0_37(X0,union(X1),X1),X1))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f388])).
% 105.78/13.69 fof(f919,plain,(
% 105.78/13.69 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sk0_41(X1,relation_rng(X0),X0),X1),X0))),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f406])).
% 105.78/13.69 fof(f934,plain,(
% 105.78/13.69 spl0_0 <=> empty(empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f936,plain,(
% 105.78/13.69 ~empty(empty_set)|spl0_0),
% 105.78/13.69 inference(component_clause,[status(thm)],[f934])).
% 105.78/13.69 fof(f939,plain,(
% 105.78/13.69 spl0_1 <=> relation(empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f942,plain,(
% 105.78/13.69 ~empty(empty_set)|relation(empty_set)),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f788,f505])).
% 105.78/13.69 fof(f943,plain,(
% 105.78/13.69 ~spl0_0|spl0_1),
% 105.78/13.69 inference(split_clause,[status(thm)],[f942,f934,f939])).
% 105.78/13.69 fof(f959,plain,(
% 105.78/13.69 $false|spl0_0),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f936,f480])).
% 105.78/13.69 fof(f960,plain,(
% 105.78/13.69 spl0_0),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f959])).
% 105.78/13.69 fof(f987,plain,(
% 105.78/13.69 spl0_8 <=> relation(sk0_62)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f989,plain,(
% 105.78/13.69 ~relation(sk0_62)|spl0_8),
% 105.78/13.69 inference(component_clause,[status(thm)],[f987])).
% 105.78/13.69 fof(f995,plain,(
% 105.78/13.69 $false|spl0_8),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f989,f660])).
% 105.78/13.69 fof(f996,plain,(
% 105.78/13.69 spl0_8),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f995])).
% 105.78/13.69 fof(f1595,plain,(
% 105.78/13.69 ![X0]: (X0=set_union2(empty_set,X0))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f667,f216])).
% 105.78/13.69 fof(f1955,plain,(
% 105.78/13.69 spl0_122 <=> subset(sk0_63,X0)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f1956,plain,(
% 105.78/13.69 ![X0]: (subset(sk0_63,X0)|~spl0_122)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f1955])).
% 105.78/13.69 fof(f2470,plain,(
% 105.78/13.69 ![X0]: (sk0_57(X0)=empty_set)),
% 105.78/13.69 inference(resolution,[status(thm)],[f807,f571])).
% 105.78/13.69 fof(f2529,plain,(
% 105.78/13.69 ![X0]: (~relation(identity_relation(X0))|~X0=empty_set|identity_relation(X0)=empty_set)),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f812,f796])).
% 105.78/13.69 fof(f2530,plain,(
% 105.78/13.69 ~relation(identity_relation(empty_set))|identity_relation(empty_set)=empty_set),
% 105.78/13.69 inference(destructive_equality_resolution,[status(esa)],[f2529])).
% 105.78/13.69 fof(f2531,plain,(
% 105.78/13.69 identity_relation(empty_set)=empty_set),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f2530,f459])).
% 105.78/13.69 fof(f3024,plain,(
% 105.78/13.69 ![X0]: (~in(X0,sk0_63)|in(X0,relation_rng(sk0_62)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f662,f363])).
% 105.78/13.69 fof(f3176,plain,(
% 105.78/13.69 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f216,f822])).
% 105.78/13.69 fof(f3238,plain,(
% 105.78/13.69 sk0_63=empty_set|~spl0_122),
% 105.78/13.69 inference(resolution,[status(thm)],[f1956,f742])).
% 105.78/13.69 fof(f3239,plain,(
% 105.78/13.69 $false|~spl0_122),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f3238,f661])).
% 105.78/13.69 fof(f3240,plain,(
% 105.78/13.69 ~spl0_122),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f3239])).
% 105.78/13.69 fof(f3695,plain,(
% 105.78/13.69 spl0_230 <=> relation(set_union2(sk0_62,empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f3697,plain,(
% 105.78/13.69 ~relation(set_union2(sk0_62,empty_set))|spl0_230),
% 105.78/13.69 inference(component_clause,[status(thm)],[f3695])).
% 105.78/13.69 fof(f3702,plain,(
% 105.78/13.69 spl0_231 <=> relation(set_union2(sk0_62,sk0_62))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f3704,plain,(
% 105.78/13.69 ~relation(set_union2(sk0_62,sk0_62))|spl0_231),
% 105.78/13.69 inference(component_clause,[status(thm)],[f3702])).
% 105.78/13.69 fof(f3707,plain,(
% 105.78/13.69 ~relation(sk0_62)|spl0_231),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f510,f3704])).
% 105.78/13.69 fof(f3708,plain,(
% 105.78/13.69 $false|spl0_231),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f3707,f660])).
% 105.78/13.69 fof(f3709,plain,(
% 105.78/13.69 spl0_231),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f3708])).
% 105.78/13.69 fof(f3710,plain,(
% 105.78/13.69 ~relation(sk0_62)|spl0_230),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f667,f3697])).
% 105.78/13.69 fof(f3711,plain,(
% 105.78/13.69 $false|spl0_230),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f3710,f660])).
% 105.78/13.69 fof(f3712,plain,(
% 105.78/13.69 spl0_230),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f3711])).
% 105.78/13.69 fof(f3741,plain,(
% 105.78/13.69 spl0_233 <=> empty(relation_dom(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f3743,plain,(
% 105.78/13.69 ~empty(relation_dom(empty_set))|spl0_233),
% 105.78/13.69 inference(component_clause,[status(thm)],[f3741])).
% 105.78/13.69 fof(f3751,plain,(
% 105.78/13.69 ~empty(empty_set)|spl0_233),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f787,f3743])).
% 105.78/13.69 fof(f3752,plain,(
% 105.78/13.69 $false|spl0_233),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f3751,f480])).
% 105.78/13.69 fof(f3753,plain,(
% 105.78/13.69 spl0_233),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f3752])).
% 105.78/13.69 fof(f3756,plain,(
% 105.78/13.69 spl0_235 <=> relation(set_union2(empty_set,sk0_62))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f3758,plain,(
% 105.78/13.69 ~relation(set_union2(empty_set,sk0_62))|spl0_235),
% 105.78/13.69 inference(component_clause,[status(thm)],[f3756])).
% 105.78/13.69 fof(f3765,plain,(
% 105.78/13.69 ~relation(sk0_62)|spl0_235),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f1595,f3758])).
% 105.78/13.69 fof(f3766,plain,(
% 105.78/13.69 $false|spl0_235),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f3765,f660])).
% 105.78/13.69 fof(f3767,plain,(
% 105.78/13.69 spl0_235),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f3766])).
% 105.78/13.69 fof(f3943,plain,(
% 105.78/13.69 ![X0]: (element(X0,powerset(X0)))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f383,f450])).
% 105.78/13.69 fof(f3952,plain,(
% 105.78/13.69 ![X0]: (element(empty_set,powerset(X0)))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f2470,f570])).
% 105.78/13.69 fof(f4097,plain,(
% 105.78/13.69 spl0_244 <=> ~subset(X0,sk0_63)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f4098,plain,(
% 105.78/13.69 ![X0]: (~subset(X0,sk0_63)|~spl0_244)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f4097])).
% 105.78/13.69 fof(f4218,plain,(
% 105.78/13.69 spl0_254 <=> ~empty(X0)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f4219,plain,(
% 105.78/13.69 ![X0]: (~empty(X0)|~spl0_254)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f4218])).
% 105.78/13.69 fof(f4269,plain,(
% 105.78/13.69 spl0_258 <=> subset(identity_relation(empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f4271,plain,(
% 105.78/13.69 ~subset(identity_relation(empty_set),empty_set)|spl0_258),
% 105.78/13.69 inference(component_clause,[status(thm)],[f4269])).
% 105.78/13.69 fof(f4281,plain,(
% 105.78/13.69 ~subset(empty_set,empty_set)|spl0_258),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f2531,f4271])).
% 105.78/13.69 fof(f4282,plain,(
% 105.78/13.69 $false|spl0_258),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f4281,f696])).
% 105.78/13.69 fof(f4283,plain,(
% 105.78/13.69 spl0_258),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f4282])).
% 105.78/13.69 fof(f4341,plain,(
% 105.78/13.69 spl0_263 <=> in(sk0_0(empty_set,empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f4342,plain,(
% 105.78/13.69 in(sk0_0(empty_set,empty_set),empty_set)|~spl0_263),
% 105.78/13.69 inference(component_clause,[status(thm)],[f4341])).
% 105.78/13.69 fof(f4355,plain,(
% 105.78/13.69 $false|~spl0_263),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f4342,f897])).
% 105.78/13.69 fof(f4356,plain,(
% 105.78/13.69 ~spl0_263),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f4355])).
% 105.78/13.69 fof(f4583,plain,(
% 105.78/13.69 union(singleton(empty_set))=empty_set),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f673,f855])).
% 105.78/13.69 fof(f4608,plain,(
% 105.78/13.69 ![X0]: (~proper_subset(X0,empty_set))),
% 105.78/13.69 inference(resolution,[status(thm)],[f790,f696])).
% 105.78/13.69 fof(f5090,plain,(
% 105.78/13.69 ![X0]: (relation(singleton(X0))|sk0_14(singleton(X0))=X0)),
% 105.78/13.69 inference(resolution,[status(thm)],[f278,f895])).
% 105.78/13.69 fof(f5664,plain,(
% 105.78/13.69 spl0_304 <=> ~in(X0,relation_image(empty_set,X1))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f5665,plain,(
% 105.78/13.69 ![X0,X1]: (~in(X0,relation_image(empty_set,X1))|~spl0_304)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f5664])).
% 105.78/13.69 fof(f5667,plain,(
% 105.78/13.69 ![X0,X1]: (~relation(empty_set)|~in(X0,relation_image(empty_set,X1)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f884,f897])).
% 105.78/13.69 fof(f5668,plain,(
% 105.78/13.69 ~spl0_1|spl0_304),
% 105.78/13.69 inference(split_clause,[status(thm)],[f5667,f939,f5664])).
% 105.78/13.69 fof(f5783,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_image(X0,relation_image(empty_set,X2)))|~spl0_304)),
% 105.78/13.69 inference(resolution,[status(thm)],[f5665,f885])).
% 105.78/13.69 fof(f5785,plain,(
% 105.78/13.69 ![X0]: (relation_image(empty_set,X0)=empty_set|~spl0_304)),
% 105.78/13.69 inference(resolution,[status(thm)],[f5665,f303])).
% 105.78/13.69 fof(f5860,plain,(
% 105.78/13.69 ![X0,X1]: (~relation(X0)|~in(X1,relation_image(X0,empty_set))|~spl0_304)),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f5785,f5783])).
% 105.78/13.69 fof(f5903,plain,(
% 105.78/13.69 spl0_316 <=> ~relation(X0)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f5904,plain,(
% 105.78/13.69 ![X0]: (~relation(X0)|~spl0_316)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f5903])).
% 105.78/13.69 fof(f6275,plain,(
% 105.78/13.69 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_image(X0,X2)|in(sk0_7(X1,X2,X0),X1)|~relation(X0)|in(sk0_8(X1,X2,X0),relation_inverse_image(X0,X3))|~in(sk0_7(X1,X2,X0),X3))),
% 105.78/13.69 inference(resolution,[status(thm)],[f261,f889])).
% 105.78/13.69 fof(f6276,plain,(
% 105.78/13.69 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_image(X0,X2)|in(sk0_7(X1,X2,X0),X1)|in(sk0_8(X1,X2,X0),relation_inverse_image(X0,X3))|~in(sk0_7(X1,X2,X0),X3))),
% 105.78/13.69 inference(duplicate_literals_removal,[status(esa)],[f6275])).
% 105.78/13.69 fof(f6305,plain,(
% 105.78/13.69 ![X0,X1]: (~relation(X0)|X1=relation_image(X0,empty_set)|in(sk0_7(X1,empty_set,X0),X1))),
% 105.78/13.69 inference(resolution,[status(thm)],[f262,f897])).
% 105.78/13.69 fof(f6458,plain,(
% 105.78/13.69 spl0_350 <=> relation(relation_inverse_image(sk0_62,sk0_63))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f6460,plain,(
% 105.78/13.69 ~relation(relation_inverse_image(sk0_62,sk0_63))|spl0_350),
% 105.78/13.69 inference(component_clause,[status(thm)],[f6458])).
% 105.78/13.69 fof(f6483,plain,(
% 105.78/13.69 ~relation(empty_set)|spl0_350),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f663,f6460])).
% 105.78/13.69 fof(f6484,plain,(
% 105.78/13.69 $false|spl0_350),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f6483,f493])).
% 105.78/13.69 fof(f6485,plain,(
% 105.78/13.69 spl0_350),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f6484])).
% 105.78/13.69 fof(f6506,plain,(
% 105.78/13.69 spl0_355 <=> powerset(empty_set)=empty_set),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f6507,plain,(
% 105.78/13.69 powerset(empty_set)=empty_set|~spl0_355),
% 105.78/13.69 inference(component_clause,[status(thm)],[f6506])).
% 105.78/13.69 fof(f6538,plain,(
% 105.78/13.69 singleton(empty_set)=empty_set|~spl0_355),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f673,f6507])).
% 105.78/13.69 fof(f6539,plain,(
% 105.78/13.69 $false|~spl0_355),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f6538,f521])).
% 105.78/13.69 fof(f6540,plain,(
% 105.78/13.69 ~spl0_355),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f6539])).
% 105.78/13.69 fof(f6737,plain,(
% 105.78/13.69 spl0_371 <=> ~empty(X0)|~empty(X0)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f6738,plain,(
% 105.78/13.69 ![X0]: (~empty(X0)|~empty(X0)|~spl0_371)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f6737])).
% 105.78/13.69 fof(f6745,plain,(
% 105.78/13.69 ![X0]: (~empty(X0)|~spl0_371)),
% 105.78/13.69 inference(duplicate_literals_removal,[status(esa)],[f6738])).
% 105.78/13.69 fof(f7133,plain,(
% 105.78/13.69 $false|~spl0_371),
% 105.78/13.69 inference(backward_subsumption_resolution,[status(thm)],[f480,f6745])).
% 105.78/13.69 fof(f7134,plain,(
% 105.78/13.69 ~spl0_371),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f7133])).
% 105.78/13.69 fof(f9361,plain,(
% 105.78/13.69 ![X0]: (subset(sk0_51(powerset(X0)),X0))),
% 105.78/13.69 inference(resolution,[status(thm)],[f733,f473])).
% 105.78/13.69 fof(f9375,plain,(
% 105.78/13.69 spl0_457 <=> relation(sk0_51(powerset(empty_set)))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f9377,plain,(
% 105.78/13.69 ~relation(sk0_51(powerset(empty_set)))|spl0_457),
% 105.78/13.69 inference(component_clause,[status(thm)],[f9375])).
% 105.78/13.69 fof(f9387,plain,(
% 105.78/13.69 sk0_51(powerset(empty_set))=empty_set),
% 105.78/13.69 inference(resolution,[status(thm)],[f9361,f742])).
% 105.78/13.69 fof(f9388,plain,(
% 105.78/13.69 sk0_51(singleton(empty_set))=empty_set),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f673,f9387])).
% 105.78/13.69 fof(f9395,plain,(
% 105.78/13.69 ~relation(sk0_51(singleton(empty_set)))|spl0_457),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f673,f9377])).
% 105.78/13.69 fof(f9396,plain,(
% 105.78/13.69 spl0_459 <=> empty(singleton(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f9397,plain,(
% 105.78/13.69 empty(singleton(empty_set))|~spl0_459),
% 105.78/13.69 inference(component_clause,[status(thm)],[f9396])).
% 105.78/13.69 fof(f9616,plain,(
% 105.78/13.69 spl0_468 <=> sk0_63=empty_set),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f9617,plain,(
% 105.78/13.69 sk0_63=empty_set|~spl0_468),
% 105.78/13.69 inference(component_clause,[status(thm)],[f9616])).
% 105.78/13.69 fof(f9627,plain,(
% 105.78/13.69 ~relation(empty_set)|spl0_457),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f9388,f9395])).
% 105.78/13.69 fof(f9628,plain,(
% 105.78/13.69 $false|spl0_457),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f9627,f493])).
% 105.78/13.69 fof(f9629,plain,(
% 105.78/13.69 spl0_457),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f9628])).
% 105.78/13.69 fof(f10096,plain,(
% 105.78/13.69 ![X0]: (empty(powerset(X0))|in(empty_set,powerset(X0)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f322,f3952])).
% 105.78/13.69 fof(f10097,plain,(
% 105.78/13.69 ![X0]: (in(empty_set,powerset(X0)))),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f10096,f479])).
% 105.78/13.69 fof(f10108,plain,(
% 105.78/13.69 ![X0]: (empty(powerset(X0))|in(X0,powerset(X0)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f322,f3943])).
% 105.78/13.69 fof(f10109,plain,(
% 105.78/13.69 ![X0]: (in(X0,powerset(X0)))),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f10108,f479])).
% 105.78/13.69 fof(f10655,plain,(
% 105.78/13.69 $false|~spl0_459),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f9397,f484])).
% 105.78/13.69 fof(f10656,plain,(
% 105.78/13.69 ~spl0_459),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f10655])).
% 105.78/13.69 fof(f11138,plain,(
% 105.78/13.69 spl0_494 <=> empty_set=identity_relation(powerset(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f11139,plain,(
% 105.78/13.69 empty_set=identity_relation(powerset(empty_set))|~spl0_494),
% 105.78/13.69 inference(component_clause,[status(thm)],[f11138])).
% 105.78/13.69 fof(f11184,plain,(
% 105.78/13.69 empty_set=identity_relation(singleton(empty_set))|~spl0_494),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f673,f11139])).
% 105.78/13.69 fof(f11594,plain,(
% 105.78/13.69 ![X0,X1]: (subset(relation_image(X0,empty_set),X1)|~relation(X0)|~spl0_304)),
% 105.78/13.69 inference(resolution,[status(thm)],[f364,f5860])).
% 105.78/13.69 fof(f12032,plain,(
% 105.78/13.69 $false|~spl0_244),
% 105.78/13.69 inference(resolution,[status(thm)],[f4098,f9361])).
% 105.78/13.69 fof(f12033,plain,(
% 105.78/13.69 ~spl0_244),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f12032])).
% 105.78/13.69 fof(f12085,plain,(
% 105.78/13.69 spl0_549 <=> ~in(X0,singleton(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f12086,plain,(
% 105.78/13.69 ![X0]: (~in(X0,singleton(empty_set))|~spl0_549)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f12085])).
% 105.78/13.69 fof(f12110,plain,(
% 105.78/13.69 spl0_552 <=> singleton(empty_set)=empty_set),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f12111,plain,(
% 105.78/13.69 singleton(empty_set)=empty_set|~spl0_552),
% 105.78/13.69 inference(component_clause,[status(thm)],[f12110])).
% 105.78/13.69 fof(f12223,plain,(
% 105.78/13.69 relation_rng(empty_set)=singleton(empty_set)|~spl0_494),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f11184,f812])).
% 105.78/13.69 fof(f12224,plain,(
% 105.78/13.69 empty_set=singleton(empty_set)|~spl0_494),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f788,f12223])).
% 105.78/13.69 fof(f12225,plain,(
% 105.78/13.69 $false|~spl0_494),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f12224,f521])).
% 105.78/13.69 fof(f12226,plain,(
% 105.78/13.69 ~spl0_494),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f12225])).
% 105.78/13.69 fof(f12272,plain,(
% 105.78/13.69 spl0_570 <=> in(sk0_7(empty_set,X1,empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f12273,plain,(
% 105.78/13.69 ![X0]: (in(sk0_7(empty_set,X0,empty_set),empty_set)|~spl0_570)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f12272])).
% 105.78/13.69 fof(f12334,plain,(
% 105.78/13.69 spl0_571 <=> empty(identity_relation(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f12336,plain,(
% 105.78/13.69 ~empty(identity_relation(empty_set))|spl0_571),
% 105.78/13.69 inference(component_clause,[status(thm)],[f12334])).
% 105.78/13.69 fof(f12767,plain,(
% 105.78/13.69 ![X0]: (subset(X0,relation_rng(sk0_62))|~in(sk0_32(relation_rng(sk0_62),X0),sk0_63))),
% 105.78/13.69 inference(resolution,[status(thm)],[f365,f3024])).
% 105.78/13.69 fof(f13127,plain,(
% 105.78/13.69 spl0_613 <=> in(sk0_10(empty_set,X1,empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f13128,plain,(
% 105.78/13.69 ![X0]: (in(sk0_10(empty_set,X0,empty_set),empty_set)|~spl0_613)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f13127])).
% 105.78/13.69 fof(f14066,plain,(
% 105.78/13.69 spl0_638 <=> relation(set_meet(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f14068,plain,(
% 105.78/13.69 ~relation(set_meet(empty_set))|spl0_638),
% 105.78/13.69 inference(component_clause,[status(thm)],[f14066])).
% 105.78/13.69 fof(f14723,plain,(
% 105.78/13.69 spl0_653 <=> X0=relation_image(sk0_62,X1)|in(sk0_7(X0,X1,sk0_62),X0)|in(sk0_8(X0,X1,sk0_62),empty_set)|~in(sk0_7(X0,X1,sk0_62),sk0_63)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f14724,plain,(
% 105.78/13.69 ![X0,X1]: (X0=relation_image(sk0_62,X1)|in(sk0_7(X0,X1,sk0_62),X0)|in(sk0_8(X0,X1,sk0_62),empty_set)|~in(sk0_7(X0,X1,sk0_62),sk0_63)|~spl0_653)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f14723])).
% 105.78/13.69 fof(f14726,plain,(
% 105.78/13.69 ![X0,X1]: (~relation(sk0_62)|X0=relation_image(sk0_62,X1)|in(sk0_7(X0,X1,sk0_62),X0)|in(sk0_8(X0,X1,sk0_62),empty_set)|~in(sk0_7(X0,X1,sk0_62),sk0_63))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f663,f6276])).
% 105.78/13.69 fof(f14727,plain,(
% 105.78/13.69 ~spl0_8|spl0_653),
% 105.78/13.69 inference(split_clause,[status(thm)],[f14726,f987,f14723])).
% 105.78/13.69 fof(f14728,plain,(
% 105.78/13.69 ![X0,X1]: (X0=relation_image(sk0_62,X1)|in(sk0_7(X0,X1,sk0_62),X0)|~in(sk0_7(X0,X1,sk0_62),sk0_63)|~spl0_653)),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f14724,f897])).
% 105.78/13.69 fof(f15828,plain,(
% 105.78/13.69 ![X0]: (set_difference(X0,X0)=set_difference(empty_set,X0))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f1595,f743])).
% 105.78/13.69 fof(f15829,plain,(
% 105.78/13.69 ![X0]: (set_difference(X0,X0)=empty_set)),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f767,f15828])).
% 105.78/13.69 fof(f15831,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(set_union2(X0,X1),X0)=set_difference(X1,X0))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f216,f743])).
% 105.78/13.69 fof(f17052,plain,(
% 105.78/13.69 ![X0]: (~in(X0,union(empty_set)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f914,f897])).
% 105.78/13.69 fof(f17143,plain,(
% 105.78/13.69 spl0_720 <=> sk0_63=relation_image(sk0_62,empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f17144,plain,(
% 105.78/13.69 sk0_63=relation_image(sk0_62,empty_set)|~spl0_720),
% 105.78/13.69 inference(component_clause,[status(thm)],[f17143])).
% 105.78/13.69 fof(f17146,plain,(
% 105.78/13.69 spl0_721 <=> in(sk0_7(sk0_63,empty_set,sk0_62),sk0_63)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f17147,plain,(
% 105.78/13.69 in(sk0_7(sk0_63,empty_set,sk0_62),sk0_63)|~spl0_721),
% 105.78/13.69 inference(component_clause,[status(thm)],[f17146])).
% 105.78/13.69 fof(f17149,plain,(
% 105.78/13.69 sk0_63=relation_image(sk0_62,empty_set)|in(sk0_7(sk0_63,empty_set,sk0_62),sk0_63)|~relation(sk0_62)|sk0_63=relation_image(sk0_62,empty_set)|~spl0_653),
% 105.78/13.69 inference(resolution,[status(thm)],[f14728,f6305])).
% 105.78/13.69 fof(f17150,plain,(
% 105.78/13.69 spl0_720|spl0_721|~spl0_8|~spl0_653),
% 105.78/13.69 inference(split_clause,[status(thm)],[f17149,f17143,f17146,f987,f14723])).
% 105.78/13.69 fof(f17155,plain,(
% 105.78/13.69 ![X0]: (subset(sk0_63,X0)|~relation(sk0_62)|~spl0_304|~spl0_720)),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f17144,f11594])).
% 105.78/13.69 fof(f17156,plain,(
% 105.78/13.69 spl0_122|~spl0_8|~spl0_304|~spl0_720),
% 105.78/13.69 inference(split_clause,[status(thm)],[f17155,f1955,f987,f5664,f17143])).
% 105.78/13.69 fof(f17689,plain,(
% 105.78/13.69 union(empty_set)=empty_set),
% 105.78/13.69 inference(resolution,[status(thm)],[f17052,f303])).
% 105.78/13.69 fof(f17701,plain,(
% 105.78/13.69 spl0_766 <=> relation(union(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f17703,plain,(
% 105.78/13.69 ~relation(union(empty_set))|spl0_766),
% 105.78/13.69 inference(component_clause,[status(thm)],[f17701])).
% 105.78/13.69 fof(f18243,plain,(
% 105.78/13.69 ~relation(empty_set)|spl0_766),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f17689,f17703])).
% 105.78/13.69 fof(f18244,plain,(
% 105.78/13.69 $false|spl0_766),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f18243,f493])).
% 105.78/13.69 fof(f18245,plain,(
% 105.78/13.69 spl0_766),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f18244])).
% 105.78/13.69 fof(f19552,plain,(
% 105.78/13.69 ![X0,X1]: (relation(singleton(ordered_pair(X0,X1)))|relation(singleton(ordered_pair(X0,X1))))),
% 105.78/13.69 inference(resolution,[status(thm)],[f5090,f279])).
% 105.78/13.69 fof(f19553,plain,(
% 105.78/13.69 ![X0,X1]: (relation(singleton(ordered_pair(X0,X1))))),
% 105.78/13.69 inference(duplicate_literals_removal,[status(esa)],[f19552])).
% 105.78/13.69 fof(f19671,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_rng(X0))|~relation(X0)|in(sk0_41(X1,relation_rng(X0),X0),relation_inverse_image(X0,X2))|~in(X1,X2))),
% 105.78/13.69 inference(resolution,[status(thm)],[f919,f889])).
% 105.78/13.69 fof(f19672,plain,(
% 105.78/13.69 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_rng(X0))|in(sk0_41(X1,relation_rng(X0),X0),relation_inverse_image(X0,X2))|~in(X1,X2))),
% 105.78/13.69 inference(duplicate_literals_removal,[status(esa)],[f19671])).
% 105.78/13.69 fof(f20276,plain,(
% 105.78/13.69 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X0,X1)))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f215,f412])).
% 105.78/13.69 fof(f20278,plain,(
% 105.78/13.69 ![X0]: (ordered_pair(X0,X0)=unordered_pair(singleton(X0),singleton(X0)))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f805,f20276])).
% 105.78/13.69 fof(f20279,plain,(
% 105.78/13.69 ![X0]: (ordered_pair(X0,X0)=singleton(singleton(X0)))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f805,f20278])).
% 105.78/13.69 fof(f20947,plain,(
% 105.78/13.69 ![X0]: (relation(singleton(singleton(singleton(X0)))))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f20279,f19553])).
% 105.78/13.69 fof(f21050,plain,(
% 105.78/13.69 ![X0]: (relation(singleton(singleton(ordered_pair(X0,X0)))))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f20279,f20947])).
% 105.78/13.69 fof(f21611,plain,(
% 105.78/13.69 spl0_875 <=> powerset(sk0_63)=empty_set),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f21612,plain,(
% 105.78/13.69 powerset(sk0_63)=empty_set|~spl0_875),
% 105.78/13.69 inference(component_clause,[status(thm)],[f21611])).
% 105.78/13.69 fof(f23406,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(set_union2(X0,X1),X0)=set_difference(set_difference(X1,X0),X0))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f724,f15831])).
% 105.78/13.69 fof(f23407,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(X0,X1)=set_difference(set_difference(X0,X1),X1))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f15831,f23406])).
% 105.78/13.69 fof(f23975,plain,(
% 105.78/13.69 spl0_917 <=> in(sk0_10(empty_set,X0,empty_set),relation_rng(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f23976,plain,(
% 105.78/13.69 ![X0]: (in(sk0_10(empty_set,X0,empty_set),relation_rng(empty_set))|~spl0_917)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f23975])).
% 105.78/13.69 fof(f23991,plain,(
% 105.78/13.69 ![X0]: (in(sk0_10(empty_set,X0,empty_set),empty_set)|~spl0_917)),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f788,f23976])).
% 105.78/13.69 fof(f23992,plain,(
% 105.78/13.69 $false|~spl0_917),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f23991,f897])).
% 105.78/13.69 fof(f23993,plain,(
% 105.78/13.69 ~spl0_917),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f23992])).
% 105.78/13.69 fof(f24152,plain,(
% 105.78/13.69 spl0_929 <=> subset(sk0_63,relation_rng(sk0_62))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f24155,plain,(
% 105.78/13.69 subset(sk0_63,relation_rng(sk0_62))|subset(sk0_63,relation_rng(sk0_62))),
% 105.78/13.69 inference(resolution,[status(thm)],[f12767,f364])).
% 105.78/13.69 fof(f24156,plain,(
% 105.78/13.69 spl0_929),
% 105.78/13.69 inference(split_clause,[status(thm)],[f24155,f24152])).
% 105.78/13.69 fof(f24690,plain,(
% 105.78/13.69 $false|~spl0_552),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f12111,f521])).
% 105.78/13.69 fof(f24691,plain,(
% 105.78/13.69 ~spl0_552),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f24690])).
% 105.78/13.69 fof(f25667,plain,(
% 105.78/13.69 spl0_1025 <=> in(sk0_0(empty_set,empty_set),relation_rng(empty_set))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f25668,plain,(
% 105.78/13.69 in(sk0_0(empty_set,empty_set),relation_rng(empty_set))|~spl0_1025),
% 105.78/13.69 inference(component_clause,[status(thm)],[f25667])).
% 105.78/13.69 fof(f25684,plain,(
% 105.78/13.69 in(sk0_0(empty_set,empty_set),empty_set)|~spl0_1025),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f788,f25668])).
% 105.78/13.69 fof(f25685,plain,(
% 105.78/13.69 $false|~spl0_1025),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f25684,f897])).
% 105.78/13.69 fof(f25686,plain,(
% 105.78/13.69 ~spl0_1025),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f25685])).
% 105.78/13.69 fof(f28939,plain,(
% 105.78/13.69 spl0_1083 <=> ~relation(identity_relation(X0))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f28940,plain,(
% 105.78/13.69 ![X0]: (~relation(identity_relation(X0))|~spl0_1083)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f28939])).
% 105.78/13.69 fof(f29691,plain,(
% 105.78/13.69 ![X0,X1]: (disjoint(set_difference(X0,X1),X1))),
% 105.78/13.69 inference(resolution,[status(thm)],[f23407,f826])).
% 105.78/13.69 fof(f29745,plain,(
% 105.78/13.69 ![X0,X1]: (set_difference(set_difference(X0,X1),set_difference(X0,X1))=set_intersection2(set_difference(X0,X1),X1))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f23407,f766])).
% 105.78/13.69 fof(f29746,plain,(
% 105.78/13.69 ![X0,X1]: (empty_set=set_intersection2(set_difference(X0,X1),X1))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f15829,f29745])).
% 105.78/13.69 fof(f29747,plain,(
% 105.78/13.69 ![X0,X1]: (empty_set=set_intersection2(X0,set_difference(X1,X0)))),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f217,f29746])).
% 105.78/13.69 fof(f29817,plain,(
% 105.78/13.69 ![X0,X1]: (disjoint(X0,set_difference(X1,X0)))),
% 105.78/13.69 inference(resolution,[status(thm)],[f29691,f583])).
% 105.78/13.69 fof(f29829,plain,(
% 105.78/13.69 ![X0,X1]: (disjoint(set_difference(X0,X1),set_intersection2(X0,X1)))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f766,f29817])).
% 105.78/13.69 fof(f29895,plain,(
% 105.78/13.69 spl0_1096 <=> ~disjoint(set_difference(X1,X2),X2)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f29896,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(set_difference(X0,X1),X1)|~spl0_1096)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f29895])).
% 105.78/13.69 fof(f29900,plain,(
% 105.78/13.69 spl0_1097 <=> ~disjoint(X0,set_difference(X1,X0))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f29901,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(X0,set_difference(X1,X0))|~spl0_1097)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f29900])).
% 105.78/13.69 fof(f30114,plain,(
% 105.78/13.69 ![X0,X1]: (disjoint(set_difference(X0,X1),set_intersection2(X1,X0)))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f217,f29829])).
% 105.78/13.69 fof(f30805,plain,(
% 105.78/13.69 ~relation(empty_set)|spl0_638),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f893,f14068])).
% 105.78/13.69 fof(f30806,plain,(
% 105.78/13.69 $false|spl0_638),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f30805,f493])).
% 105.78/13.69 fof(f30807,plain,(
% 105.78/13.69 spl0_638),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30806])).
% 105.78/13.69 fof(f30808,plain,(
% 105.78/13.69 ~empty(empty_set)|spl0_571),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f2531,f12336])).
% 105.78/13.69 fof(f30809,plain,(
% 105.78/13.69 $false|spl0_571),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f30808,f480])).
% 105.78/13.69 fof(f30810,plain,(
% 105.78/13.69 spl0_571),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30809])).
% 105.78/13.69 fof(f30813,plain,(
% 105.78/13.69 $false|~spl0_1097),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f29901,f29817])).
% 105.78/13.69 fof(f30814,plain,(
% 105.78/13.69 ~spl0_1097),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30813])).
% 105.78/13.69 fof(f30817,plain,(
% 105.78/13.69 $false|~spl0_1096),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f29896,f29691])).
% 105.78/13.69 fof(f30818,plain,(
% 105.78/13.69 ~spl0_1096),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30817])).
% 105.78/13.69 fof(f30819,plain,(
% 105.78/13.69 $false|~spl0_468),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f9617,f661])).
% 105.78/13.69 fof(f30820,plain,(
% 105.78/13.69 ~spl0_468),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30819])).
% 105.78/13.69 fof(f30822,plain,(
% 105.78/13.69 $false|~spl0_1083),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f28940,f459])).
% 105.78/13.69 fof(f30823,plain,(
% 105.78/13.69 ~spl0_1083),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30822])).
% 105.78/13.69 fof(f30826,plain,(
% 105.78/13.69 $false|~spl0_613),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f13128,f897])).
% 105.78/13.69 fof(f30827,plain,(
% 105.78/13.69 ~spl0_613),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30826])).
% 105.78/13.69 fof(f30834,plain,(
% 105.78/13.69 $false|~spl0_570),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f12273,f897])).
% 105.78/13.69 fof(f30835,plain,(
% 105.78/13.69 ~spl0_570),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f30834])).
% 105.78/13.69 fof(f31273,plain,(
% 105.78/13.69 spl0_1125 <=> ~subset(X0,set_union2(X0,X1))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f31274,plain,(
% 105.78/13.69 ![X0,X1]: (~subset(X0,set_union2(X0,X1))|~spl0_1125)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f31273])).
% 105.78/13.69 fof(f31329,plain,(
% 105.78/13.69 $false|~spl0_1125),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f31274,f822])).
% 105.78/13.69 fof(f31330,plain,(
% 105.78/13.69 ~spl0_1125),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f31329])).
% 105.78/13.69 fof(f31759,plain,(
% 105.78/13.69 spl0_1127 <=> ~subset(X0,set_union2(X1,X0))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f31760,plain,(
% 105.78/13.69 ![X0,X1]: (~subset(X0,set_union2(X1,X0))|~spl0_1127)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f31759])).
% 105.78/13.69 fof(f31815,plain,(
% 105.78/13.69 $false|~spl0_1127),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f31760,f3176])).
% 105.78/13.69 fof(f31816,plain,(
% 105.78/13.69 ~spl0_1127),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f31815])).
% 105.78/13.69 fof(f31941,plain,(
% 105.78/13.69 $false|~spl0_254),
% 105.78/13.69 inference(backward_subsumption_resolution,[status(thm)],[f480,f4219])).
% 105.78/13.69 fof(f31942,plain,(
% 105.78/13.69 ~spl0_254),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f31941])).
% 105.78/13.69 fof(f31952,plain,(
% 105.78/13.69 $false|~spl0_316),
% 105.78/13.69 inference(backward_subsumption_resolution,[status(thm)],[f21050,f5904])).
% 105.78/13.69 fof(f31953,plain,(
% 105.78/13.69 ~spl0_316),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f31952])).
% 105.78/13.69 fof(f31980,plain,(
% 105.78/13.69 spl0_1134 <=> proper_subset(sk0_63,empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f31981,plain,(
% 105.78/13.69 proper_subset(sk0_63,empty_set)|~spl0_1134),
% 105.78/13.69 inference(component_clause,[status(thm)],[f31980])).
% 105.78/13.69 fof(f31992,plain,(
% 105.78/13.69 $false|~spl0_1134),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f31981,f4608])).
% 105.78/13.69 fof(f31993,plain,(
% 105.78/13.69 ~spl0_1134),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f31992])).
% 105.78/13.69 fof(f32045,plain,(
% 105.78/13.69 in(sk0_63,empty_set)|~spl0_875),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f21612,f10109])).
% 105.78/13.69 fof(f32046,plain,(
% 105.78/13.69 $false|~spl0_875),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f32045,f897])).
% 105.78/13.69 fof(f32047,plain,(
% 105.78/13.69 ~spl0_875),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f32046])).
% 105.78/13.69 fof(f32420,plain,(
% 105.78/13.69 $false|~spl0_549),
% 105.78/13.69 inference(resolution,[status(thm)],[f12086,f896])).
% 105.78/13.69 fof(f32421,plain,(
% 105.78/13.69 ~spl0_549),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f32420])).
% 105.78/13.69 fof(f33013,plain,(
% 105.78/13.69 spl0_1146 <=> in(sk0_35(empty_set,empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f33014,plain,(
% 105.78/13.69 in(sk0_35(empty_set,empty_set),empty_set)|~spl0_1146),
% 105.78/13.69 inference(component_clause,[status(thm)],[f33013])).
% 105.78/13.69 fof(f33056,plain,(
% 105.78/13.69 $false|~spl0_1146),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f33014,f897])).
% 105.78/13.69 fof(f33057,plain,(
% 105.78/13.69 ~spl0_1146),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f33056])).
% 105.78/13.69 fof(f33926,plain,(
% 105.78/13.69 spl0_1154 <=> ~in(X0,X1)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f33927,plain,(
% 105.78/13.69 ![X0,X1]: (~in(X0,X1)|~spl0_1154)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f33926])).
% 105.78/13.69 fof(f34122,plain,(
% 105.78/13.69 spl0_1164 <=> ~disjoint(X0,X1)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f34123,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(X0,X1)|~spl0_1164)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f34122])).
% 105.78/13.69 fof(f34177,plain,(
% 105.78/13.69 $false|~spl0_1154),
% 105.78/13.69 inference(backward_subsumption_resolution,[status(thm)],[f10097,f33927])).
% 105.78/13.69 fof(f34178,plain,(
% 105.78/13.69 ~spl0_1154),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f34177])).
% 105.78/13.69 fof(f35218,plain,(
% 105.78/13.69 spl0_1173 <=> ~disjoint(X0,set_difference(X1,X0))|~relation(set_intersection2(X0,set_difference(X1,X0)))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f35219,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(X0,set_difference(X1,X0))|~relation(set_intersection2(X0,set_difference(X1,X0)))|~spl0_1173)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f35218])).
% 105.78/13.69 fof(f35250,plain,(
% 105.78/13.69 ![X0,X1]: (~disjoint(X0,set_difference(X1,X0))|~relation(empty_set)|~spl0_1173)),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f29747,f35219])).
% 105.78/13.69 fof(f35251,plain,(
% 105.78/13.69 ~relation(empty_set)|~spl0_1173),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f35250,f29817])).
% 105.78/13.69 fof(f35458,plain,(
% 105.78/13.69 $false|~spl0_1164),
% 105.78/13.69 inference(backward_subsumption_resolution,[status(thm)],[f30114,f34123])).
% 105.78/13.69 fof(f35459,plain,(
% 105.78/13.69 ~spl0_1164),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f35458])).
% 105.78/13.69 fof(f35462,plain,(
% 105.78/13.69 $false|~spl0_1173),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f35251,f493])).
% 105.78/13.69 fof(f35463,plain,(
% 105.78/13.69 ~spl0_1173),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f35462])).
% 105.78/13.69 fof(f36041,plain,(
% 105.78/13.69 spl0_1189 <=> in(sk0_42(empty_set,empty_set),empty_set)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f36042,plain,(
% 105.78/13.69 in(sk0_42(empty_set,empty_set),empty_set)|~spl0_1189),
% 105.78/13.69 inference(component_clause,[status(thm)],[f36041])).
% 105.78/13.69 fof(f36077,plain,(
% 105.78/13.69 $false|~spl0_1189),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f36042,f897])).
% 105.78/13.69 fof(f36078,plain,(
% 105.78/13.69 ~spl0_1189),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f36077])).
% 105.78/13.69 fof(f41071,plain,(
% 105.78/13.69 spl0_1292 <=> relation(union(singleton(empty_set)))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f41073,plain,(
% 105.78/13.69 ~relation(union(singleton(empty_set)))|spl0_1292),
% 105.78/13.69 inference(component_clause,[status(thm)],[f41071])).
% 105.78/13.69 fof(f41078,plain,(
% 105.78/13.69 ~relation(empty_set)|spl0_1292),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f4583,f41073])).
% 105.78/13.69 fof(f41079,plain,(
% 105.78/13.69 $false|spl0_1292),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f41078,f493])).
% 105.78/13.69 fof(f41080,plain,(
% 105.78/13.69 spl0_1292),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f41079])).
% 105.78/13.69 fof(f41909,plain,(
% 105.78/13.69 spl0_1298 <=> element(singleton(empty_set),powerset(powerset(empty_set)))),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f41911,plain,(
% 105.78/13.69 ~element(singleton(empty_set),powerset(powerset(empty_set)))|spl0_1298),
% 105.78/13.69 inference(component_clause,[status(thm)],[f41909])).
% 105.78/13.69 fof(f41917,plain,(
% 105.78/13.69 ~element(singleton(empty_set),powerset(singleton(empty_set)))|spl0_1298),
% 105.78/13.69 inference(forward_demodulation,[status(thm)],[f673,f41911])).
% 105.78/13.69 fof(f41918,plain,(
% 105.78/13.69 $false|spl0_1298),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f41917,f3943])).
% 105.78/13.69 fof(f41919,plain,(
% 105.78/13.69 spl0_1298),
% 105.78/13.69 inference(contradiction_clause,[status(thm)],[f41918])).
% 105.78/13.69 fof(f42624,plain,(
% 105.78/13.69 spl0_1309 <=> ~in(X0,relation_rng(sk0_62))|in(sk0_41(X0,relation_rng(sk0_62),sk0_62),empty_set)|~in(X0,sk0_63)),
% 105.78/13.69 introduced(split_symbol_definition)).
% 105.78/13.69 fof(f42625,plain,(
% 105.78/13.69 ![X0]: (~in(X0,relation_rng(sk0_62))|in(sk0_41(X0,relation_rng(sk0_62),sk0_62),empty_set)|~in(X0,sk0_63)|~spl0_1309)),
% 105.78/13.69 inference(component_clause,[status(thm)],[f42624])).
% 105.78/13.69 fof(f42627,plain,(
% 105.78/13.69 ![X0]: (~relation(sk0_62)|~in(X0,relation_rng(sk0_62))|in(sk0_41(X0,relation_rng(sk0_62),sk0_62),empty_set)|~in(X0,sk0_63))),
% 105.78/13.69 inference(paramodulation,[status(thm)],[f663,f19672])).
% 105.78/13.69 fof(f42628,plain,(
% 105.78/13.69 ~spl0_8|spl0_1309),
% 105.78/13.69 inference(split_clause,[status(thm)],[f42627,f987,f42624])).
% 105.78/13.69 fof(f42638,plain,(
% 105.78/13.69 ![X0]: (in(sk0_41(X0,relation_rng(sk0_62),sk0_62),empty_set)|~in(X0,sk0_63)|~spl0_1309)),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f42625,f3024])).
% 105.78/13.69 fof(f42910,plain,(
% 105.78/13.69 ![X0]: (~in(X0,sk0_63)|~spl0_1309)),
% 105.78/13.69 inference(forward_subsumption_resolution,[status(thm)],[f42638,f897])).
% 105.78/13.72 fof(f42911,plain,(
% 105.78/13.72 $false|~spl0_1309|~spl0_721),
% 105.78/13.72 inference(backward_subsumption_resolution,[status(thm)],[f17147,f42910])).
% 105.78/13.72 fof(f42912,plain,(
% 105.78/13.72 ~spl0_1309|~spl0_721),
% 105.78/13.72 inference(contradiction_clause,[status(thm)],[f42911])).
% 105.78/13.72 fof(f42913,plain,(
% 105.78/13.72 $false),
% 105.78/13.72 inference(sat_refutation,[status(thm)],[f943,f960,f996,f3240,f3709,f3712,f3753,f3767,f4283,f4356,f5668,f6485,f6540,f7134,f9629,f10656,f12033,f12226,f14727,f17150,f17156,f18245,f23993,f24156,f24691,f25686,f30807,f30810,f30814,f30818,f30820,f30823,f30827,f30835,f31330,f31816,f31942,f31953,f31993,f32047,f32421,f33057,f34178,f35459,f35463,f36078,f41080,f41919,f42628,f42912])).
% 105.78/13.72 % SZS output end CNFRefutation for theBenchmark.p
% 106.45/13.77 % Elapsed time: 13.410701 seconds
% 106.45/13.77 % CPU time: 106.299891 seconds
% 106.45/13.77 % Total memory used: 528.913 MB
% 106.45/13.77 % Net memory used: 496.015 MB
%------------------------------------------------------------------------------