TSTP Solution File: SET996+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET996+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 : Wed May 31 12:35:40 EDT 2023
% Result : Theorem 183.66s 23.51s
% Output : CNFRefutation 184.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET996+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 10:15:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 183.66/23.51 % Refutation found
% 183.66/23.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 183.66/23.51 % SZS output start CNFRefutation for theBenchmark
% 183.66/23.51 fof(f2,axiom,(
% 183.66/23.51 (! [A] :( empty(A)=> function(A) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f3,axiom,(
% 183.66/23.51 (! [A] :( empty(A)=> relation(A) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f4,axiom,(
% 183.66/23.51 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f5,axiom,(
% 183.66/23.51 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f6,axiom,(
% 183.66/23.51 (! [A] :(? [B] : element(B,A) ))),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f7,axiom,(
% 183.66/23.51 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f11,axiom,(
% 183.66/23.51 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f12,axiom,(
% 183.66/23.51 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_rng(A)) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f13,axiom,(
% 183.66/23.51 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f14,axiom,(
% 183.66/23.51 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f17,axiom,(
% 183.66/23.51 (! [A] :( ~ empty(A)=> (? [B] :( element(B,powerset(A))& ~ empty(B) ) )) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f19,axiom,(
% 183.66/23.51 (? [A] :( ~ empty(A)& relation(A) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f23,axiom,(
% 183.66/23.51 (! [A,B] : subset(A,A) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f24,axiom,(
% 183.66/23.51 (! [A,B,C] :( element(C,A)=> (? [D] :( relation(D)& function(D)& relation_dom(D) = B& (! [E] :( in(E,B)=> apply(D,E) = C ) )) )) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f25,conjecture,(
% 183.66/23.51 (! [A,B] :~ ( ~ ( A = empty_set& B != empty_set )& (! [C] :( ( relation(C)& function(C) )=> ~ ( B = relation_dom(C)& subset(relation_rng(C),A) ) ) )) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f26,negated_conjecture,(
% 183.66/23.51 ~((! [A,B] :~ ( ~ ( A = empty_set& B != empty_set )& (! [C] :( ( relation(C)& function(C) )=> ~ ( B = relation_dom(C)& subset(relation_rng(C),A) ) ) )) ))),
% 183.66/23.51 inference(negated_conjecture,[status(cth)],[f25])).
% 183.66/23.51 fof(f28,axiom,(
% 183.66/23.51 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f30,axiom,(
% 183.66/23.51 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f32,axiom,(
% 183.66/23.51 (! [A,B,C] :~ ( in(A,B)& element(B,powerset(C))& empty(C) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f33,axiom,(
% 183.66/23.51 (! [A] :( empty(A)=> A = empty_set ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f34,axiom,(
% 183.66/23.51 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f35,axiom,(
% 183.66/23.51 (! [A,B] :~ ( empty(A)& A != B& empty(B) ) )),
% 183.66/23.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 183.66/23.51 fof(f38,plain,(
% 183.66/23.51 ![A]: (~empty(A)|function(A))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 183.66/23.51 fof(f39,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|function(X0))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f38])).
% 183.66/23.51 fof(f40,plain,(
% 183.66/23.51 ![A]: (~empty(A)|relation(A))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 183.66/23.51 fof(f41,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|relation(X0))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f40])).
% 183.66/23.51 fof(f42,plain,(
% 183.66/23.51 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 183.66/23.51 fof(f43,plain,(
% 183.66/23.51 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 183.66/23.51 inference(NNF_transformation,[status(esa)],[f42])).
% 183.66/23.51 fof(f44,plain,(
% 183.66/23.51 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f43])).
% 183.66/23.51 fof(f45,plain,(
% 183.66/23.51 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_0(B,A),A)&~in(sk0_0(B,A),B))))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f44])).
% 183.66/23.51 fof(f46,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f45])).
% 183.66/23.51 fof(f47,plain,(
% 183.66/23.51 ![X0,X1]: (subset(X0,X1)|in(sk0_0(X1,X0),X0))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f45])).
% 183.66/23.51 fof(f48,plain,(
% 183.66/23.51 ![X0,X1]: (subset(X0,X1)|~in(sk0_0(X1,X0),X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f45])).
% 183.66/23.51 fof(f49,plain,(
% 183.66/23.51 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 183.66/23.51 fof(f50,plain,(
% 183.66/23.51 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 183.66/23.51 inference(NNF_transformation,[status(esa)],[f49])).
% 183.66/23.51 fof(f51,plain,(
% 183.66/23.51 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f50])).
% 183.66/23.51 fof(f52,plain,(
% 183.66/23.51 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sk0_1(C,B,A),relation_dom(A))&C=apply(A,sk0_1(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sk0_2(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sk0_2(B,A)=apply(A,D))))&(in(sk0_2(B,A),B)|(in(sk0_3(B,A),relation_dom(A))&sk0_2(B,A)=apply(A,sk0_3(B,A)))))))))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f51])).
% 183.66/23.51 fof(f53,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(sk0_1(X2,X1,X0),relation_dom(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f52])).
% 183.66/23.51 fof(f54,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|X2=apply(X0,sk0_1(X2,X1,X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f52])).
% 183.66/23.51 fof(f57,plain,(
% 183.66/23.51 ![X0,X1]: (~relation(X0)|~function(X0)|X1=relation_rng(X0)|in(sk0_2(X1,X0),X1)|in(sk0_3(X1,X0),relation_dom(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f52])).
% 183.66/23.51 fof(f59,plain,(
% 183.66/23.51 ![A]: element(sk0_4(A),A)),
% 183.66/23.51 inference(skolemization,[status(esa)],[f6])).
% 183.66/23.51 fof(f60,plain,(
% 183.66/23.51 ![X0]: (element(sk0_4(X0),X0))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f59])).
% 183.66/23.51 fof(f61,plain,(
% 183.66/23.51 empty(empty_set)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f7])).
% 183.66/23.51 fof(f62,plain,(
% 183.66/23.51 relation(empty_set)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f7])).
% 183.66/23.51 fof(f68,plain,(
% 183.66/23.51 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 183.66/23.51 fof(f69,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f68])).
% 183.66/23.51 fof(f70,plain,(
% 183.66/23.51 ![A]: ((empty(A)|~relation(A))|~empty(relation_rng(A)))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 183.66/23.51 fof(f71,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_rng(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f70])).
% 183.66/23.51 fof(f72,plain,(
% 183.66/23.51 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 183.66/23.51 fof(f73,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f72])).
% 183.66/23.51 fof(f75,plain,(
% 183.66/23.51 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 183.66/23.51 fof(f76,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f75])).
% 183.66/23.51 fof(f84,plain,(
% 183.66/23.51 ![A]: (empty(A)|(?[B]: (element(B,powerset(A))&~empty(B))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 183.66/23.51 fof(f85,plain,(
% 183.66/23.51 ![A]: (empty(A)|(element(sk0_7(A),powerset(A))&~empty(sk0_7(A))))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f84])).
% 183.66/23.51 fof(f86,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|element(sk0_7(X0),powerset(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f85])).
% 183.66/23.51 fof(f87,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|~empty(sk0_7(X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f85])).
% 183.66/23.51 fof(f90,plain,(
% 183.66/23.51 (~empty(sk0_9)&relation(sk0_9))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f19])).
% 183.66/23.51 fof(f91,plain,(
% 183.66/23.51 ~empty(sk0_9)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f90])).
% 183.66/23.51 fof(f92,plain,(
% 183.66/23.51 relation(sk0_9)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f90])).
% 183.66/23.51 fof(f101,plain,(
% 183.66/23.51 ![A]: subset(A,A)),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f23])).
% 183.66/23.51 fof(f102,plain,(
% 183.66/23.51 ![X0]: (subset(X0,X0))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f101])).
% 183.66/23.51 fof(f103,plain,(
% 183.66/23.51 ![A,B,C]: (~element(C,A)|(?[D]: (((relation(D)&function(D))&relation_dom(D)=B)&(![E]: (~in(E,B)|apply(D,E)=C)))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 183.66/23.51 fof(f104,plain,(
% 183.66/23.51 ![C]: ((![A]: ~element(C,A))|(![B]: ?[D]: (((relation(D)&function(D))&relation_dom(D)=B)&(![E]: (~in(E,B)|apply(D,E)=C)))))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f103])).
% 183.66/23.51 fof(f105,plain,(
% 183.66/23.51 ![C]: ((![A]: ~element(C,A))|(![B]: (((relation(sk0_13(B,C))&function(sk0_13(B,C)))&relation_dom(sk0_13(B,C))=B)&(![E]: (~in(E,B)|apply(sk0_13(B,C),E)=C)))))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f104])).
% 183.66/23.51 fof(f106,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~element(X0,X1)|relation(sk0_13(X2,X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f105])).
% 183.66/23.51 fof(f107,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~element(X0,X1)|function(sk0_13(X2,X0)))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f105])).
% 183.66/23.51 fof(f108,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~element(X0,X1)|relation_dom(sk0_13(X2,X0))=X2)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f105])).
% 183.66/23.51 fof(f109,plain,(
% 183.66/23.51 ![X0,X1,X2,X3]: (~element(X0,X1)|~in(X2,X3)|apply(sk0_13(X3,X0),X2)=X0)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f105])).
% 183.66/23.51 fof(f110,plain,(
% 183.66/23.51 (?[A,B]: ((~A=empty_set|B=empty_set)&(![C]: ((~relation(C)|~function(C))|(~B=relation_dom(C)|~subset(relation_rng(C),A))))))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 183.66/23.51 fof(f111,plain,(
% 183.66/23.51 ((~sk0_14=empty_set|sk0_15=empty_set)&(![C]: ((~relation(C)|~function(C))|(~sk0_15=relation_dom(C)|~subset(relation_rng(C),sk0_14)))))),
% 183.66/23.51 inference(skolemization,[status(esa)],[f110])).
% 183.66/23.51 fof(f112,plain,(
% 183.66/23.51 ~sk0_14=empty_set|sk0_15=empty_set),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f111])).
% 183.66/23.51 fof(f113,plain,(
% 183.66/23.51 ![X0]: (~relation(X0)|~function(X0)|~sk0_15=relation_dom(X0)|~subset(relation_rng(X0),sk0_14))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f111])).
% 183.66/23.51 fof(f116,plain,(
% 183.66/23.51 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 183.66/23.51 fof(f117,plain,(
% 183.66/23.51 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f116])).
% 183.66/23.51 fof(f119,plain,(
% 183.66/23.51 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 183.66/23.51 inference(NNF_transformation,[status(esa)],[f30])).
% 183.66/23.51 fof(f120,plain,(
% 183.66/23.51 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f119])).
% 183.66/23.51 fof(f121,plain,(
% 183.66/23.51 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f120])).
% 183.66/23.51 fof(f122,plain,(
% 183.66/23.51 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f120])).
% 183.66/23.51 fof(f126,plain,(
% 183.66/23.51 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|~empty(C))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 183.66/23.51 fof(f127,plain,(
% 183.66/23.51 ![C]: ((![B]: ((![A]: ~in(A,B))|~element(B,powerset(C))))|~empty(C))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f126])).
% 183.66/23.51 fof(f128,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|~empty(X2))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f127])).
% 183.66/23.51 fof(f129,plain,(
% 183.66/23.51 ![A]: (~empty(A)|A=empty_set)),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 183.66/23.51 fof(f130,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|X0=empty_set)),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f129])).
% 183.66/23.51 fof(f131,plain,(
% 183.66/23.51 ![A,B]: (~in(A,B)|~empty(B))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 183.66/23.51 fof(f132,plain,(
% 183.66/23.51 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f131])).
% 183.66/23.51 fof(f133,plain,(
% 183.66/23.51 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f132])).
% 183.66/23.51 fof(f134,plain,(
% 183.66/23.51 ![A,B]: ((~empty(A)|A=B)|~empty(B))),
% 183.66/23.51 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 183.66/23.51 fof(f135,plain,(
% 183.66/23.51 ![B]: ((![A]: (~empty(A)|A=B))|~empty(B))),
% 183.66/23.51 inference(miniscoping,[status(esa)],[f134])).
% 183.66/23.51 fof(f136,plain,(
% 183.66/23.51 ![X0,X1]: (~empty(X0)|X0=X1|~empty(X1))),
% 183.66/23.51 inference(cnf_transformation,[status(esa)],[f135])).
% 183.66/23.51 fof(f137,plain,(
% 183.66/23.51 spl0_0 <=> sk0_14=empty_set),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f139,plain,(
% 183.66/23.51 ~sk0_14=empty_set|spl0_0),
% 183.66/23.51 inference(component_clause,[status(thm)],[f137])).
% 183.66/23.51 fof(f140,plain,(
% 183.66/23.51 spl0_1 <=> sk0_15=empty_set),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f143,plain,(
% 183.66/23.51 ~spl0_0|spl0_1),
% 183.66/23.51 inference(split_clause,[status(thm)],[f112,f137,f140])).
% 183.66/23.51 fof(f144,plain,(
% 183.66/23.51 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|in(sk0_1(X1,relation_rng(X0),X0),relation_dom(X0)))),
% 183.66/23.51 inference(destructive_equality_resolution,[status(esa)],[f53])).
% 183.66/23.51 fof(f145,plain,(
% 183.66/23.51 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,sk0_1(X1,relation_rng(X0),X0)))),
% 183.66/23.51 inference(destructive_equality_resolution,[status(esa)],[f54])).
% 183.66/23.51 fof(f147,plain,(
% 183.66/23.51 function(empty_set)),
% 183.66/23.51 inference(resolution,[status(thm)],[f39,f61])).
% 183.66/23.51 fof(f149,plain,(
% 183.66/23.51 empty(relation_dom(empty_set))),
% 183.66/23.51 inference(resolution,[status(thm)],[f73,f61])).
% 183.66/23.51 fof(f151,plain,(
% 183.66/23.51 relation_dom(empty_set)=empty_set),
% 183.66/23.51 inference(resolution,[status(thm)],[f149,f130])).
% 183.66/23.51 fof(f157,plain,(
% 183.66/23.51 spl0_2 <=> empty(empty_set)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f160,plain,(
% 183.66/23.51 spl0_3 <=> relation(empty_set)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f162,plain,(
% 183.66/23.51 ~relation(empty_set)|spl0_3),
% 183.66/23.51 inference(component_clause,[status(thm)],[f160])).
% 183.66/23.51 fof(f190,plain,(
% 183.66/23.51 empty(relation_rng(empty_set))),
% 183.66/23.51 inference(resolution,[status(thm)],[f76,f61])).
% 183.66/23.51 fof(f191,plain,(
% 183.66/23.51 empty(empty_set)|~relation(empty_set)),
% 183.66/23.51 inference(resolution,[status(thm)],[f190,f71])).
% 183.66/23.51 fof(f192,plain,(
% 183.66/23.51 spl0_2|~spl0_3),
% 183.66/23.51 inference(split_clause,[status(thm)],[f191,f157,f160])).
% 183.66/23.51 fof(f196,plain,(
% 183.66/23.51 relation_rng(empty_set)=empty_set),
% 183.66/23.51 inference(resolution,[status(thm)],[f190,f130])).
% 183.66/23.51 fof(f199,plain,(
% 183.66/23.51 $false|spl0_3),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f162,f62])).
% 183.66/23.51 fof(f200,plain,(
% 183.66/23.51 spl0_3),
% 183.66/23.51 inference(contradiction_clause,[status(thm)],[f199])).
% 183.66/23.51 fof(f204,plain,(
% 183.66/23.51 spl0_4 <=> function(empty_set)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f206,plain,(
% 183.66/23.51 ~function(empty_set)|spl0_4),
% 183.66/23.51 inference(component_clause,[status(thm)],[f204])).
% 183.66/23.51 fof(f217,plain,(
% 183.66/23.51 $false|spl0_4),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f206,f147])).
% 183.66/23.51 fof(f218,plain,(
% 183.66/23.51 spl0_4),
% 183.66/23.51 inference(contradiction_clause,[status(thm)],[f217])).
% 183.66/23.51 fof(f251,plain,(
% 183.66/23.51 ![X0]: (~in(X0,empty_set))),
% 183.66/23.51 inference(resolution,[status(thm)],[f133,f61])).
% 183.66/23.51 fof(f253,plain,(
% 183.66/23.51 ![X0,X1]: (~relation(X0)|~function(X0)|in(sk0_1(sk0_0(X1,relation_rng(X0)),relation_rng(X0),X0),relation_dom(X0))|subset(relation_rng(X0),X1))),
% 183.66/23.51 inference(resolution,[status(thm)],[f144,f47])).
% 183.66/23.51 fof(f343,plain,(
% 183.66/23.51 ![X0]: (element(X0,powerset(X0)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f122,f102])).
% 183.66/23.51 fof(f345,plain,(
% 183.66/23.51 ![X0,X1]: (function(sk0_13(X0,X1)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f343,f107])).
% 183.66/23.51 fof(f346,plain,(
% 183.66/23.51 ![X0,X1]: (relation(sk0_13(X0,X1)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f343,f106])).
% 183.66/23.51 fof(f347,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~function(sk0_13(X0,X1))|~in(X2,relation_rng(sk0_13(X0,X1)))|X2=apply(sk0_13(X0,X1),sk0_1(X2,relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1))))),
% 183.66/23.51 inference(resolution,[status(thm)],[f346,f145])).
% 183.66/23.51 fof(f348,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~in(X0,relation_rng(sk0_13(X1,X2)))|X0=apply(sk0_13(X1,X2),sk0_1(X0,relation_rng(sk0_13(X1,X2)),sk0_13(X1,X2))))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f347,f345])).
% 183.66/23.51 fof(f349,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|subset(sk0_7(X0),X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f86,f121])).
% 183.66/23.51 fof(f351,plain,(
% 183.66/23.51 ![X0,X1]: (empty(X0)|~in(X1,sk0_7(X0))|in(X1,X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f349,f46])).
% 183.66/23.51 fof(f355,plain,(
% 183.66/23.51 ![X0,X1]: (relation_dom(sk0_13(X0,X1))=X0)),
% 183.66/23.51 inference(resolution,[status(thm)],[f108,f343])).
% 183.66/23.51 fof(f366,plain,(
% 183.66/23.51 ![X0,X1]: (empty(sk0_13(X0,X1))|~relation(sk0_13(X0,X1))|~empty(X0))),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f355,f69])).
% 183.66/23.51 fof(f367,plain,(
% 183.66/23.51 ![X0,X1]: (empty(sk0_13(X0,X1))|~empty(X0))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f366,f346])).
% 183.66/23.51 fof(f368,plain,(
% 183.66/23.51 ![X0]: (empty(sk0_13(empty_set,X0)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f367,f61])).
% 183.66/23.51 fof(f378,plain,(
% 183.66/23.51 ![X0]: (sk0_13(empty_set,X0)=empty_set)),
% 183.66/23.51 inference(resolution,[status(thm)],[f368,f130])).
% 183.66/23.51 fof(f410,plain,(
% 183.66/23.51 spl0_21 <=> X0=relation_rng(empty_set)|in(sk0_2(X0,empty_set),X0)|in(sk0_3(X0,empty_set),relation_dom(empty_set))),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f411,plain,(
% 183.66/23.51 ![X0]: (X0=relation_rng(empty_set)|in(sk0_2(X0,empty_set),X0)|in(sk0_3(X0,empty_set),relation_dom(empty_set))|~spl0_21)),
% 183.66/23.51 inference(component_clause,[status(thm)],[f410])).
% 183.66/23.51 fof(f413,plain,(
% 183.66/23.51 ![X0]: (~function(empty_set)|X0=relation_rng(empty_set)|in(sk0_2(X0,empty_set),X0)|in(sk0_3(X0,empty_set),relation_dom(empty_set)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f57,f62])).
% 183.66/23.51 fof(f414,plain,(
% 183.66/23.51 ~spl0_4|spl0_21),
% 183.66/23.51 inference(split_clause,[status(thm)],[f413,f204,f410])).
% 183.66/23.51 fof(f415,plain,(
% 183.66/23.51 ![X0]: (X0=empty_set|in(sk0_2(X0,empty_set),X0)|in(sk0_3(X0,empty_set),relation_dom(empty_set))|~spl0_21)),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f196,f411])).
% 183.66/23.51 fof(f416,plain,(
% 183.66/23.51 ![X0]: (X0=empty_set|in(sk0_2(X0,empty_set),X0)|in(sk0_3(X0,empty_set),empty_set)|~spl0_21)),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f151,f415])).
% 183.66/23.51 fof(f417,plain,(
% 183.66/23.51 ![X0]: (X0=empty_set|in(sk0_2(X0,empty_set),X0)|~spl0_21)),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f416,f251])).
% 183.66/23.51 fof(f443,plain,(
% 183.66/23.51 spl0_24 <=> relation_dom(sk0_9)=empty_set),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f444,plain,(
% 183.66/23.51 relation_dom(sk0_9)=empty_set|~spl0_24),
% 183.66/23.51 inference(component_clause,[status(thm)],[f443])).
% 183.66/23.51 fof(f445,plain,(
% 183.66/23.51 ~relation_dom(sk0_9)=empty_set|spl0_24),
% 183.66/23.51 inference(component_clause,[status(thm)],[f443])).
% 183.66/23.51 fof(f1273,plain,(
% 183.66/23.51 ![X0,X1,X2]: (sk0_0(X0,relation_rng(sk0_13(X1,X2)))=apply(sk0_13(X1,X2),sk0_1(sk0_0(X0,relation_rng(sk0_13(X1,X2))),relation_rng(sk0_13(X1,X2)),sk0_13(X1,X2)))|subset(relation_rng(sk0_13(X1,X2)),X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f348,f47])).
% 183.66/23.51 fof(f1311,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|in(sk0_4(X0),X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f117,f60])).
% 183.66/23.51 fof(f1322,plain,(
% 183.66/23.51 ![X0]: (empty(sk0_7(X0))|empty(X0)|in(sk0_4(sk0_7(X0)),X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1311,f351])).
% 183.66/23.51 fof(f1323,plain,(
% 183.66/23.51 ![X0]: (empty(X0)|in(sk0_4(sk0_7(X0)),X0))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f1322,f87])).
% 183.66/23.51 fof(f1364,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~in(X0,X1)|apply(sk0_13(X1,X2),X0)=X2)),
% 183.66/23.51 inference(resolution,[status(thm)],[f109,f343])).
% 183.66/23.51 fof(f1913,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|empty(X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1364,f1311])).
% 183.66/23.51 fof(f1964,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|empty(relation_rng(X0)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1913,f76])).
% 183.66/23.51 fof(f1968,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|relation(X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1913,f41])).
% 183.66/23.51 fof(f1969,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|function(X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1913,f39])).
% 183.66/23.51 fof(f2070,plain,(
% 183.66/23.51 ![X0,X1]: (~in(X0,X1)|~element(X1,powerset(empty_set)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f128,f61])).
% 183.66/23.51 fof(f2207,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~function(sk0_13(X0,X1))|in(sk0_1(sk0_0(X2,relation_rng(sk0_13(X0,X1))),relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1)),relation_dom(sk0_13(X0,X1)))|subset(relation_rng(sk0_13(X0,X1)),X2))),
% 183.66/23.51 inference(resolution,[status(thm)],[f253,f346])).
% 183.66/23.51 fof(f2208,plain,(
% 183.66/23.51 ![X0,X1,X2]: (~function(sk0_13(X0,X1))|in(sk0_1(sk0_0(X2,relation_rng(sk0_13(X0,X1))),relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1)),X0)|subset(relation_rng(sk0_13(X0,X1)),X2))),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f355,f2207])).
% 183.66/23.51 fof(f2209,plain,(
% 183.66/23.51 ![X0,X1,X2]: (in(sk0_1(sk0_0(X0,relation_rng(sk0_13(X1,X2))),relation_rng(sk0_13(X1,X2)),sk0_13(X1,X2)),X1)|subset(relation_rng(sk0_13(X1,X2)),X0))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f2208,f345])).
% 183.66/23.51 fof(f3626,plain,(
% 183.66/23.51 spl0_288 <=> relation(sk0_9)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f3628,plain,(
% 183.66/23.51 ~relation(sk0_9)|spl0_288),
% 183.66/23.51 inference(component_clause,[status(thm)],[f3626])).
% 183.66/23.51 fof(f3634,plain,(
% 183.66/23.51 spl0_290 <=> empty(sk0_9)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f3635,plain,(
% 183.66/23.51 empty(sk0_9)|~spl0_290),
% 183.66/23.51 inference(component_clause,[status(thm)],[f3634])).
% 183.66/23.51 fof(f3637,plain,(
% 183.66/23.51 empty(sk0_9)|~relation(sk0_9)|~empty(empty_set)|~spl0_24),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f444,f69])).
% 183.66/23.51 fof(f3638,plain,(
% 183.66/23.51 spl0_290|~spl0_288|~spl0_2|~spl0_24),
% 183.66/23.51 inference(split_clause,[status(thm)],[f3637,f3634,f3626,f157,f443])).
% 183.66/23.51 fof(f3639,plain,(
% 183.66/23.51 $false|spl0_288),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f3628,f92])).
% 183.66/23.51 fof(f3640,plain,(
% 183.66/23.51 spl0_288),
% 183.66/23.51 inference(contradiction_clause,[status(thm)],[f3639])).
% 183.66/23.51 fof(f3641,plain,(
% 183.66/23.51 $false|~spl0_290),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f3635,f91])).
% 183.66/23.51 fof(f3642,plain,(
% 183.66/23.51 ~spl0_290),
% 183.66/23.51 inference(contradiction_clause,[status(thm)],[f3641])).
% 183.66/23.51 fof(f4026,plain,(
% 183.66/23.51 spl0_308 <=> apply(sk0_13(empty_set,X0),sk0_4(empty_set))=X0),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f4027,plain,(
% 183.66/23.51 ![X0]: (apply(sk0_13(empty_set,X0),sk0_4(empty_set))=X0|~spl0_308)),
% 183.66/23.51 inference(component_clause,[status(thm)],[f4026])).
% 183.66/23.51 fof(f4031,plain,(
% 183.66/23.51 ![X0]: (apply(empty_set,sk0_4(empty_set))=X0|~spl0_308)),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f378,f4027])).
% 183.66/23.51 fof(f4038,plain,(
% 183.66/23.51 ![X0,X1,X2]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|~in(X2,relation_rng(X0)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1964,f133])).
% 183.66/23.51 fof(f4471,plain,(
% 183.66/23.51 ![X0,X1]: (X0=X1|~spl0_308)),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f4031,f4031])).
% 183.66/23.51 fof(f5047,plain,(
% 183.66/23.51 ![X0,X1,X2,X3]: (subset(relation_rng(sk0_13(X0,X1)),X2)|apply(sk0_13(X0,X3),sk0_1(sk0_0(X2,relation_rng(sk0_13(X0,X1))),relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1)))=X3)),
% 183.66/23.51 inference(resolution,[status(thm)],[f2209,f1364])).
% 183.66/23.51 fof(f9023,plain,(
% 183.66/23.51 relation_dom(empty_set)=empty_set),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f378,f355])).
% 183.66/23.51 fof(f10075,plain,(
% 183.66/23.51 ![X0,X1,X2]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|subset(relation_rng(X0),X2))),
% 183.66/23.51 inference(resolution,[status(thm)],[f4038,f47])).
% 183.66/23.51 fof(f10692,plain,(
% 183.66/23.51 $false|~spl0_308|spl0_24),
% 183.66/23.51 inference(backward_subsumption_resolution,[status(thm)],[f445,f4471])).
% 183.66/23.51 fof(f10693,plain,(
% 183.66/23.51 ~spl0_308|spl0_24),
% 183.66/23.51 inference(contradiction_clause,[status(thm)],[f10692])).
% 183.66/23.51 fof(f12537,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|~relation(X0)|~function(X0)|~sk0_15=relation_dom(X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f10075,f113])).
% 183.66/23.51 fof(f12538,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|~function(X0)|~sk0_15=relation_dom(X0))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f12537,f1968])).
% 183.66/23.51 fof(f12642,plain,(
% 183.66/23.51 ![X0]: (sk0_7(X0)=empty_set|empty(X0)|in(sk0_2(sk0_7(X0),empty_set),X0)|~spl0_21)),
% 183.66/23.51 inference(resolution,[status(thm)],[f417,f351])).
% 183.66/23.51 fof(f12827,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(X0,X1),sk0_4(X0))=X1|~sk0_15=relation_dom(X0))),
% 183.66/23.51 inference(backward_subsumption_resolution,[status(thm)],[f12538,f1969])).
% 183.66/23.51 fof(f13218,plain,(
% 183.66/23.51 ![X0]: (apply(sk0_13(empty_set,X0),sk0_4(empty_set))=X0|~sk0_15=empty_set)),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f9023,f12827])).
% 183.66/23.51 fof(f13219,plain,(
% 183.66/23.51 spl0_308|~spl0_1),
% 183.66/23.51 inference(split_clause,[status(thm)],[f13218,f4026,f140])).
% 183.66/23.51 fof(f22154,plain,(
% 183.66/23.51 ![X0,X1]: (sk0_0(sk0_14,relation_rng(sk0_13(X0,X1)))=apply(sk0_13(X0,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(X0,X1))),relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1)))|~relation(sk0_13(X0,X1))|~function(sk0_13(X0,X1))|~sk0_15=relation_dom(sk0_13(X0,X1)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f1273,f113])).
% 183.66/23.51 fof(f22155,plain,(
% 183.66/23.51 ![X0,X1]: (sk0_0(sk0_14,relation_rng(sk0_13(X0,X1)))=apply(sk0_13(X0,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(X0,X1))),relation_rng(sk0_13(X0,X1)),sk0_13(X0,X1)))|~relation(sk0_13(X0,X1))|~function(sk0_13(X0,X1))|~sk0_15=X0)),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f355,f22154])).
% 183.66/23.51 fof(f22156,plain,(
% 183.66/23.51 ![X1]: (sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X1)))=apply(sk0_13(sk0_15,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X1))),relation_rng(sk0_13(sk0_15,X1)),sk0_13(sk0_15,X1)))|~relation(sk0_13(sk0_15,X1))|~function(sk0_13(sk0_15,X1)))),
% 183.66/23.51 inference(destructive_equality_resolution,[status(esa)],[f22155])).
% 183.66/23.51 fof(f22157,plain,(
% 183.66/23.51 ![X0]: (sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X0)))=apply(sk0_13(sk0_15,X0),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X0))),relation_rng(sk0_13(sk0_15,X0)),sk0_13(sk0_15,X0)))|~function(sk0_13(sk0_15,X0)))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f22156,f346])).
% 183.66/23.51 fof(f23341,plain,(
% 183.66/23.51 ![X0]: (sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X0)))=apply(sk0_13(sk0_15,X0),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X0))),relation_rng(sk0_13(sk0_15,X0)),sk0_13(sk0_15,X0))))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f22157,f345])).
% 183.66/23.51 fof(f45472,plain,(
% 183.66/23.51 ![X0]: (~empty(X0)|X0=empty_set)),
% 183.66/23.51 inference(resolution,[status(thm)],[f136,f61])).
% 183.66/23.51 fof(f60020,plain,(
% 183.66/23.51 ![X0,X1,X2]: (apply(sk0_13(X0,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(X0,X2))),relation_rng(sk0_13(X0,X2)),sk0_13(X0,X2)))=X1|~relation(sk0_13(X0,X2))|~function(sk0_13(X0,X2))|~sk0_15=relation_dom(sk0_13(X0,X2)))),
% 183.66/23.51 inference(resolution,[status(thm)],[f5047,f113])).
% 183.66/23.51 fof(f60021,plain,(
% 183.66/23.51 ![X0,X1,X2]: (apply(sk0_13(X0,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(X0,X2))),relation_rng(sk0_13(X0,X2)),sk0_13(X0,X2)))=X1|~relation(sk0_13(X0,X2))|~function(sk0_13(X0,X2))|~sk0_15=X0)),
% 183.66/23.51 inference(forward_demodulation,[status(thm)],[f355,f60020])).
% 183.66/23.51 fof(f60022,plain,(
% 183.66/23.51 ![X1,X2]: (apply(sk0_13(sk0_15,X1),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X2))),relation_rng(sk0_13(sk0_15,X2)),sk0_13(sk0_15,X2)))=X1|~relation(sk0_13(sk0_15,X2))|~function(sk0_13(sk0_15,X2)))),
% 183.66/23.51 inference(destructive_equality_resolution,[status(esa)],[f60021])).
% 183.66/23.51 fof(f60023,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(sk0_15,X0),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X1))),relation_rng(sk0_13(sk0_15,X1)),sk0_13(sk0_15,X1)))=X0|~function(sk0_13(sk0_15,X1)))),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f60022,f346])).
% 183.66/23.51 fof(f63850,plain,(
% 183.66/23.51 ![X0,X1]: (apply(sk0_13(sk0_15,X0),sk0_1(sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X1))),relation_rng(sk0_13(sk0_15,X1)),sk0_13(sk0_15,X1)))=X0)),
% 183.66/23.51 inference(forward_subsumption_resolution,[status(thm)],[f60023,f345])).
% 183.66/23.51 fof(f63851,plain,(
% 183.66/23.51 ![X0]: (sk0_0(sk0_14,relation_rng(sk0_13(sk0_15,X0)))=X0)),
% 183.66/23.51 inference(backward_demodulation,[status(thm)],[f63850,f23341])).
% 183.66/23.51 fof(f63892,plain,(
% 183.66/23.51 ![X0]: (subset(relation_rng(sk0_13(sk0_15,X0)),sk0_14)|~in(X0,sk0_14))),
% 183.66/23.51 inference(paramodulation,[status(thm)],[f63851,f48])).
% 183.66/23.51 fof(f63916,plain,(
% 183.66/23.51 spl0_3216 <=> sk0_7(sk0_14)=empty_set),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f63917,plain,(
% 183.66/23.51 sk0_7(sk0_14)=empty_set|~spl0_3216),
% 183.66/23.51 inference(component_clause,[status(thm)],[f63916])).
% 183.66/23.51 fof(f63919,plain,(
% 183.66/23.51 spl0_3217 <=> empty(sk0_14)),
% 183.66/23.51 introduced(split_symbol_definition)).
% 183.66/23.51 fof(f63920,plain,(
% 183.66/23.51 empty(sk0_14)|~spl0_3217),
% 183.66/23.51 inference(component_clause,[status(thm)],[f63919])).
% 183.66/23.51 fof(f64006,plain,(
% 183.66/23.51 ![X0]: (subset(relation_rng(sk0_13(sk0_15,sk0_0(X0,sk0_14))),sk0_14)|subset(sk0_14,X0))),
% 183.66/23.51 inference(resolution,[status(thm)],[f63892,f47])).
% 184.75/23.67 fof(f64692,plain,(
% 184.75/23.67 sk0_14=empty_set|~spl0_3217),
% 184.75/23.67 inference(resolution,[status(thm)],[f63920,f45472])).
% 184.75/23.67 fof(f64693,plain,(
% 184.75/23.67 $false|spl0_0|~spl0_3217),
% 184.75/23.67 inference(forward_subsumption_resolution,[status(thm)],[f64692,f139])).
% 184.75/23.67 fof(f64694,plain,(
% 184.75/23.67 spl0_0|~spl0_3217),
% 184.75/23.67 inference(contradiction_clause,[status(thm)],[f64693])).
% 184.75/23.67 fof(f64951,plain,(
% 184.75/23.67 spl0_3285 <=> in(sk0_4(empty_set),sk0_14)),
% 184.75/23.67 introduced(split_symbol_definition)).
% 184.75/23.67 fof(f64952,plain,(
% 184.75/23.67 in(sk0_4(empty_set),sk0_14)|~spl0_3285),
% 184.75/23.67 inference(component_clause,[status(thm)],[f64951])).
% 184.75/23.67 fof(f64954,plain,(
% 184.75/23.67 empty(sk0_14)|in(sk0_4(empty_set),sk0_14)|~spl0_3216),
% 184.75/23.67 inference(paramodulation,[status(thm)],[f63917,f1323])).
% 184.75/23.67 fof(f64955,plain,(
% 184.75/23.67 spl0_3217|spl0_3285|~spl0_3216),
% 184.75/23.67 inference(split_clause,[status(thm)],[f64954,f63919,f64951,f63916])).
% 184.75/23.67 fof(f68535,plain,(
% 184.75/23.67 ![X0]: (subset(sk0_14,X0)|~relation(sk0_13(sk0_15,sk0_0(X0,sk0_14)))|~function(sk0_13(sk0_15,sk0_0(X0,sk0_14)))|~sk0_15=relation_dom(sk0_13(sk0_15,sk0_0(X0,sk0_14))))),
% 184.75/23.67 inference(resolution,[status(thm)],[f64006,f113])).
% 184.75/23.67 fof(f68536,plain,(
% 184.75/23.67 ![X0]: (subset(sk0_14,X0)|~relation(sk0_13(sk0_15,sk0_0(X0,sk0_14)))|~function(sk0_13(sk0_15,sk0_0(X0,sk0_14)))|~sk0_15=sk0_15)),
% 184.75/23.67 inference(forward_demodulation,[status(thm)],[f355,f68535])).
% 184.75/23.67 fof(f68537,plain,(
% 184.75/23.67 ![X0]: (subset(sk0_14,X0)|~relation(sk0_13(sk0_15,sk0_0(X0,sk0_14)))|~function(sk0_13(sk0_15,sk0_0(X0,sk0_14))))),
% 184.75/23.67 inference(trivial_equality_resolution,[status(esa)],[f68536])).
% 184.75/23.67 fof(f68538,plain,(
% 184.75/23.67 ![X0]: (subset(sk0_14,X0)|~function(sk0_13(sk0_15,sk0_0(X0,sk0_14))))),
% 184.75/23.67 inference(forward_subsumption_resolution,[status(thm)],[f68537,f346])).
% 184.75/23.67 fof(f68546,plain,(
% 184.75/23.67 ![X0]: (subset(sk0_14,X0))),
% 184.75/23.67 inference(forward_subsumption_resolution,[status(thm)],[f68538,f345])).
% 184.75/23.67 fof(f68547,plain,(
% 184.75/23.67 ![X0]: (element(sk0_14,powerset(X0)))),
% 184.75/23.67 inference(resolution,[status(thm)],[f68546,f122])).
% 184.75/23.67 fof(f68549,plain,(
% 184.75/23.67 ![X0]: (~in(X0,sk0_14))),
% 184.75/23.67 inference(resolution,[status(thm)],[f68547,f2070])).
% 184.75/23.67 fof(f68556,plain,(
% 184.75/23.67 $false|~spl0_3285),
% 184.75/23.67 inference(backward_subsumption_resolution,[status(thm)],[f64952,f68549])).
% 184.75/23.67 fof(f68557,plain,(
% 184.75/23.67 ~spl0_3285),
% 184.75/23.67 inference(contradiction_clause,[status(thm)],[f68556])).
% 184.75/23.67 fof(f68560,plain,(
% 184.75/23.67 sk0_7(sk0_14)=empty_set|empty(sk0_14)|~spl0_21),
% 184.75/23.67 inference(resolution,[status(thm)],[f68549,f12642])).
% 184.75/23.67 fof(f68561,plain,(
% 184.75/23.67 spl0_3216|spl0_3217|~spl0_21),
% 184.75/23.67 inference(split_clause,[status(thm)],[f68560,f63916,f63919,f410])).
% 184.75/23.67 fof(f68567,plain,(
% 184.75/23.67 $false),
% 184.75/23.67 inference(sat_refutation,[status(thm)],[f143,f192,f200,f218,f414,f3638,f3640,f3642,f10693,f13219,f64694,f64955,f68557,f68561])).
% 184.75/23.67 % SZS output end CNFRefutation for theBenchmark.p
% 185.68/23.81 % Elapsed time: 23.457058 seconds
% 185.68/23.81 % CPU time: 185.376827 seconds
% 185.68/23.81 % Memory used: 669.597 MB
%------------------------------------------------------------------------------