TSTP Solution File: SEU044+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 20:40:56 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 19:38:47 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.38 fof(f2,axiom,(
% 0.14/0.38 ( empty(empty_set)& relation(empty_set) ) ),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f5,axiom,(
% 0.14/0.38 (! [A] :(? [B] : element(B,A) ))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f6,axiom,(
% 0.14/0.38 (! [A] :( empty(A)=> function(A) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f7,axiom,(
% 0.14/0.38 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f11,axiom,(
% 0.14/0.38 (! [A] :( empty(A)=> relation(A) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f12,axiom,(
% 0.14/0.38 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f13,axiom,(
% 0.14/0.38 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f15,axiom,(
% 0.14/0.38 (! [A,B,C] :~ ( in(A,B)& element(B,powerset(C))& empty(C) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f16,axiom,(
% 0.14/0.38 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f19,axiom,(
% 0.14/0.38 (! [A,B] :( relation(B)=> relation(relation_rng_restriction(A,B)) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f20,axiom,(
% 0.14/0.38 (! [A,B] :( ( relation(B)& function(B) )=> ( relation(relation_rng_restriction(A,B))& function(relation_rng_restriction(A,B)) ) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f25,axiom,(
% 0.14/0.38 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f31,axiom,(
% 0.14/0.38 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f32,axiom,(
% 0.14/0.38 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f33,conjecture,(
% 0.14/0.38 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_rng_restriction(A,C)))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f34,negated_conjecture,(
% 0.14/0.38 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_rng_restriction(A,C)))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) ))),
% 0.14/0.38 inference(negated_conjecture,[status(cth)],[f33])).
% 0.14/0.38 fof(f35,axiom,(
% 0.14/0.38 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( B = relation_rng_restriction(A,C)<=> ( (! [D] :( in(D,relation_dom(B))<=> ( in(D,relation_dom(C))& in(apply(C,D),A) ) ))& (! [D] :( in(D,relation_dom(B))=> apply(B,D) = apply(C,D) ) )) ) ) )) )),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.38 fof(f38,plain,(
% 0.14/0.38 empty(empty_set)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f2])).
% 0.14/0.38 fof(f44,plain,(
% 0.14/0.38 ![A]: element(sk0_0(A),A)),
% 0.14/0.38 inference(skolemization,[status(esa)],[f5])).
% 0.14/0.38 fof(f45,plain,(
% 0.14/0.38 ![X0]: (element(sk0_0(X0),X0))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f44])).
% 0.14/0.38 fof(f46,plain,(
% 0.14/0.38 ![A]: (~empty(A)|function(A))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.14/0.38 fof(f47,plain,(
% 0.14/0.38 ![X0]: (~empty(X0)|function(X0))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f46])).
% 0.14/0.38 fof(f48,plain,(
% 0.14/0.38 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.14/0.38 fof(f51,plain,(
% 0.14/0.38 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f48])).
% 0.14/0.38 fof(f58,plain,(
% 0.14/0.38 ![A]: (~empty(A)|relation(A))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.14/0.38 fof(f59,plain,(
% 0.14/0.38 ![X0]: (~empty(X0)|relation(X0))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f58])).
% 0.14/0.38 fof(f60,plain,(
% 0.14/0.38 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.14/0.38 fof(f61,plain,(
% 0.14/0.38 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f60])).
% 0.14/0.38 fof(f62,plain,(
% 0.14/0.38 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 0.14/0.38 inference(NNF_transformation,[status(esa)],[f13])).
% 0.14/0.38 fof(f63,plain,(
% 0.14/0.38 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f62])).
% 0.14/0.38 fof(f64,plain,(
% 0.14/0.38 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f63])).
% 0.14/0.38 fof(f65,plain,(
% 0.14/0.38 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f63])).
% 0.14/0.38 fof(f69,plain,(
% 0.14/0.38 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|~empty(C))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.14/0.38 fof(f70,plain,(
% 0.14/0.38 ![C]: ((![B]: ((![A]: ~in(A,B))|~element(B,powerset(C))))|~empty(C))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f69])).
% 0.14/0.38 fof(f71,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|~empty(X2))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f70])).
% 0.14/0.38 fof(f72,plain,(
% 0.14/0.38 ![A]: (~empty(A)|A=empty_set)),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.14/0.38 fof(f73,plain,(
% 0.14/0.38 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f72])).
% 0.14/0.38 fof(f79,plain,(
% 0.14/0.38 ![A,B]: (~relation(B)|relation(relation_rng_restriction(A,B)))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.14/0.38 fof(f80,plain,(
% 0.14/0.38 ![B]: (~relation(B)|(![A]: relation(relation_rng_restriction(A,B))))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f79])).
% 0.14/0.38 fof(f81,plain,(
% 0.14/0.38 ![X0,X1]: (~relation(X0)|relation(relation_rng_restriction(X1,X0)))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f80])).
% 0.14/0.38 fof(f82,plain,(
% 0.14/0.38 ![A,B]: ((~relation(B)|~function(B))|(relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.14/0.38 fof(f83,plain,(
% 0.14/0.38 ![B]: ((~relation(B)|~function(B))|((![A]: relation(relation_rng_restriction(A,B)))&(![A]: function(relation_rng_restriction(A,B)))))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f82])).
% 0.14/0.38 fof(f85,plain,(
% 0.14/0.38 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_rng_restriction(X1,X0)))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f83])).
% 0.14/0.38 fof(f101,plain,(
% 0.14/0.38 ![A]: (element(sk0_5(A),powerset(A))&empty(sk0_5(A)))),
% 0.14/0.38 inference(skolemization,[status(esa)],[f25])).
% 0.14/0.38 fof(f102,plain,(
% 0.14/0.38 ![X0]: (element(sk0_5(X0),powerset(X0)))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f101])).
% 0.14/0.38 fof(f103,plain,(
% 0.14/0.38 ![X0]: (empty(sk0_5(X0)))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f101])).
% 0.14/0.38 fof(f117,plain,(
% 0.14/0.38 ![A,B]: (~in(A,B)|element(A,B))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.14/0.38 fof(f118,plain,(
% 0.14/0.38 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f117])).
% 0.14/0.38 fof(f119,plain,(
% 0.14/0.38 ![A,B]: (~in(A,B)|~empty(B))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 0.14/0.38 fof(f120,plain,(
% 0.14/0.38 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f119])).
% 0.14/0.38 fof(f121,plain,(
% 0.14/0.38 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f120])).
% 0.14/0.38 fof(f122,plain,(
% 0.14/0.38 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_rng_restriction(A,C)))<~>(in(B,relation_dom(C))&in(apply(C,B),A)))))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 0.14/0.38 fof(f123,plain,(
% 0.14/0.38 ?[A,B,C]: ((relation(C)&function(C))&((in(B,relation_dom(relation_rng_restriction(A,C)))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_rng_restriction(A,C)))|(~in(B,relation_dom(C))|~in(apply(C,B),A)))))),
% 0.14/0.38 inference(NNF_transformation,[status(esa)],[f122])).
% 0.14/0.38 fof(f124,plain,(
% 0.14/0.38 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(B,relation_dom(relation_rng_restriction(A,C)))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_rng_restriction(A,C)))|(~in(B,relation_dom(C))|~in(apply(C,B),A))))))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f123])).
% 0.14/0.38 fof(f125,plain,(
% 0.14/0.38 ((relation(sk0_11)&function(sk0_11))&((in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|(in(sk0_13,relation_dom(sk0_11))&in(apply(sk0_11,sk0_13),sk0_12)))&(~in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|(~in(sk0_13,relation_dom(sk0_11))|~in(apply(sk0_11,sk0_13),sk0_12)))))),
% 0.14/0.38 inference(skolemization,[status(esa)],[f124])).
% 0.14/0.38 fof(f126,plain,(
% 0.14/0.38 relation(sk0_11)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f125])).
% 0.14/0.38 fof(f127,plain,(
% 0.14/0.38 function(sk0_11)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f125])).
% 0.14/0.38 fof(f128,plain,(
% 0.14/0.38 in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|in(sk0_13,relation_dom(sk0_11))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f125])).
% 0.14/0.38 fof(f129,plain,(
% 0.14/0.38 in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|in(apply(sk0_11,sk0_13),sk0_12)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f125])).
% 0.14/0.38 fof(f130,plain,(
% 0.14/0.38 ~in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|~in(sk0_13,relation_dom(sk0_11))|~in(apply(sk0_11,sk0_13),sk0_12)),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f125])).
% 0.14/0.38 fof(f131,plain,(
% 0.14/0.38 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_rng_restriction(A,C)<=>((![D]: (in(D,relation_dom(B))<=>(in(D,relation_dom(C))&in(apply(C,D),A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.14/0.38 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 0.14/0.38 fof(f132,plain,(
% 0.14/0.38 ![A,C,D]: (pd0_0(D,C,A)<=>(in(D,relation_dom(C))&in(apply(C,D),A)))),
% 0.14/0.38 introduced(predicate_definition,[f131])).
% 0.14/0.38 fof(f133,plain,(
% 0.14/0.38 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_rng_restriction(A,C)<=>((![D]: (in(D,relation_dom(B))<=>pd0_0(D,C,A)))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.14/0.38 inference(formula_renaming,[status(thm)],[f131,f132])).
% 0.14/0.38 fof(f134,plain,(
% 0.14/0.38 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~B=relation_rng_restriction(A,C)|((![D]: ((~in(D,relation_dom(B))|pd0_0(D,C,A))&(in(D,relation_dom(B))|~pd0_0(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D)))))&(B=relation_rng_restriction(A,C)|((?[D]: ((~in(D,relation_dom(B))|~pd0_0(D,C,A))&(in(D,relation_dom(B))|pd0_0(D,C,A))))|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D)))))))))),
% 0.14/0.38 inference(NNF_transformation,[status(esa)],[f133])).
% 0.14/0.38 fof(f135,plain,(
% 0.14/0.38 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_rng_restriction(A,C)|(((![D]: (~in(D,relation_dom(B))|pd0_0(D,C,A)))&(![D]: (in(D,relation_dom(B))|~pd0_0(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_rng_restriction(A,C)|((?[D]: ((~in(D,relation_dom(B))|~pd0_0(D,C,A))&(in(D,relation_dom(B))|pd0_0(D,C,A))))|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D))))))))))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f134])).
% 0.14/0.38 fof(f136,plain,(
% 0.14/0.38 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_rng_restriction(A,C)|(((![D]: (~in(D,relation_dom(B))|pd0_0(D,C,A)))&(![D]: (in(D,relation_dom(B))|~pd0_0(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_rng_restriction(A,C)|(((~in(sk0_14(A,C,B),relation_dom(B))|~pd0_0(sk0_14(A,C,B),C,A))&(in(sk0_14(A,C,B),relation_dom(B))|pd0_0(sk0_14(A,C,B),C,A)))|(in(sk0_15(A,C,B),relation_dom(B))&~apply(B,sk0_15(A,C,B))=apply(C,sk0_15(A,C,B))))))))))),
% 0.14/0.38 inference(skolemization,[status(esa)],[f135])).
% 0.14/0.38 fof(f137,plain,(
% 0.14/0.38 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_rng_restriction(X2,X1)|~in(X3,relation_dom(X0))|pd0_0(X3,X1,X2))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f136])).
% 0.14/0.38 fof(f138,plain,(
% 0.14/0.38 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_rng_restriction(X2,X1)|in(X3,relation_dom(X0))|~pd0_0(X3,X1,X2))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f136])).
% 0.14/0.38 fof(f144,plain,(
% 0.14/0.38 ![A,C,D]: ((~pd0_0(D,C,A)|(in(D,relation_dom(C))&in(apply(C,D),A)))&(pd0_0(D,C,A)|(~in(D,relation_dom(C))|~in(apply(C,D),A))))),
% 0.14/0.38 inference(NNF_transformation,[status(esa)],[f132])).
% 0.14/0.38 fof(f145,plain,(
% 0.14/0.38 (![A,C,D]: (~pd0_0(D,C,A)|(in(D,relation_dom(C))&in(apply(C,D),A))))&(![A,C,D]: (pd0_0(D,C,A)|(~in(D,relation_dom(C))|~in(apply(C,D),A))))),
% 0.14/0.38 inference(miniscoping,[status(esa)],[f144])).
% 0.14/0.38 fof(f146,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|in(X0,relation_dom(X1)))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f145])).
% 0.14/0.38 fof(f147,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|in(apply(X1,X0),X2))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f145])).
% 0.14/0.38 fof(f148,plain,(
% 0.14/0.38 ![X0,X1,X2]: (pd0_0(X0,X1,X2)|~in(X0,relation_dom(X1))|~in(apply(X1,X0),X2))),
% 0.14/0.38 inference(cnf_transformation,[status(esa)],[f145])).
% 0.14/0.38 fof(f149,plain,(
% 0.14/0.38 spl0_0 <=> in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f150,plain,(
% 0.14/0.38 in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|~spl0_0),
% 0.14/0.38 inference(component_clause,[status(thm)],[f149])).
% 0.14/0.38 fof(f151,plain,(
% 0.14/0.38 ~in(sk0_13,relation_dom(relation_rng_restriction(sk0_12,sk0_11)))|spl0_0),
% 0.14/0.38 inference(component_clause,[status(thm)],[f149])).
% 0.14/0.38 fof(f152,plain,(
% 0.14/0.38 spl0_1 <=> in(sk0_13,relation_dom(sk0_11))),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f154,plain,(
% 0.14/0.38 ~in(sk0_13,relation_dom(sk0_11))|spl0_1),
% 0.14/0.38 inference(component_clause,[status(thm)],[f152])).
% 0.14/0.38 fof(f155,plain,(
% 0.14/0.38 spl0_0|spl0_1),
% 0.14/0.38 inference(split_clause,[status(thm)],[f128,f149,f152])).
% 0.14/0.38 fof(f156,plain,(
% 0.14/0.38 spl0_2 <=> in(apply(sk0_11,sk0_13),sk0_12)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f157,plain,(
% 0.14/0.38 in(apply(sk0_11,sk0_13),sk0_12)|~spl0_2),
% 0.14/0.38 inference(component_clause,[status(thm)],[f156])).
% 0.14/0.38 fof(f158,plain,(
% 0.14/0.38 ~in(apply(sk0_11,sk0_13),sk0_12)|spl0_2),
% 0.14/0.38 inference(component_clause,[status(thm)],[f156])).
% 0.14/0.38 fof(f159,plain,(
% 0.14/0.38 spl0_0|spl0_2),
% 0.14/0.38 inference(split_clause,[status(thm)],[f129,f149,f156])).
% 0.14/0.38 fof(f160,plain,(
% 0.14/0.38 ~spl0_0|~spl0_1|~spl0_2),
% 0.14/0.38 inference(split_clause,[status(thm)],[f130,f149,f152,f156])).
% 0.14/0.38 fof(f161,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_rng_restriction(X0,X1)))|pd0_0(X2,X1,X0))),
% 0.14/0.38 inference(destructive_equality_resolution,[status(esa)],[f137])).
% 0.14/0.38 fof(f162,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~pd0_0(X2,X1,X0))),
% 0.14/0.38 inference(destructive_equality_resolution,[status(esa)],[f138])).
% 0.14/0.38 fof(f174,plain,(
% 0.14/0.38 function(empty_set)),
% 0.14/0.38 inference(resolution,[status(thm)],[f38,f47])).
% 0.14/0.38 fof(f180,plain,(
% 0.14/0.38 ![X0,X1]: (~in(X0,sk0_5(X1))|~empty(X1))),
% 0.14/0.38 inference(resolution,[status(thm)],[f71,f102])).
% 0.14/0.38 fof(f182,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~empty(X0)|~pd0_0(X1,X2,sk0_5(X0)))),
% 0.14/0.38 inference(resolution,[status(thm)],[f180,f147])).
% 0.14/0.38 fof(f183,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_rng_restriction(X0,X1)))|pd0_0(X2,X1,X0))),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f161,f81])).
% 0.14/0.38 fof(f186,plain,(
% 0.14/0.38 spl0_3 <=> function(relation_rng_restriction(sk0_12,sk0_11))),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f188,plain,(
% 0.14/0.38 ~function(relation_rng_restriction(sk0_12,sk0_11))|spl0_3),
% 0.14/0.38 inference(component_clause,[status(thm)],[f186])).
% 0.14/0.38 fof(f189,plain,(
% 0.14/0.38 spl0_4 <=> relation(sk0_11)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f191,plain,(
% 0.14/0.38 ~relation(sk0_11)|spl0_4),
% 0.14/0.38 inference(component_clause,[status(thm)],[f189])).
% 0.14/0.38 fof(f192,plain,(
% 0.14/0.38 spl0_5 <=> function(sk0_11)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f194,plain,(
% 0.14/0.38 ~function(sk0_11)|spl0_5),
% 0.14/0.38 inference(component_clause,[status(thm)],[f192])).
% 0.14/0.38 fof(f195,plain,(
% 0.14/0.38 spl0_6 <=> pd0_0(sk0_13,sk0_11,sk0_12)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f196,plain,(
% 0.14/0.38 pd0_0(sk0_13,sk0_11,sk0_12)|~spl0_6),
% 0.14/0.38 inference(component_clause,[status(thm)],[f195])).
% 0.14/0.38 fof(f198,plain,(
% 0.14/0.38 ~function(relation_rng_restriction(sk0_12,sk0_11))|~relation(sk0_11)|~function(sk0_11)|pd0_0(sk0_13,sk0_11,sk0_12)|~spl0_0),
% 0.14/0.38 inference(resolution,[status(thm)],[f183,f150])).
% 0.14/0.38 fof(f199,plain,(
% 0.14/0.38 ~spl0_3|~spl0_4|~spl0_5|spl0_6|~spl0_0),
% 0.14/0.38 inference(split_clause,[status(thm)],[f198,f186,f189,f192,f195,f149])).
% 0.14/0.38 fof(f200,plain,(
% 0.14/0.38 $false|spl0_5),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f194,f127])).
% 0.14/0.38 fof(f201,plain,(
% 0.14/0.38 spl0_5),
% 0.14/0.38 inference(contradiction_clause,[status(thm)],[f200])).
% 0.14/0.38 fof(f202,plain,(
% 0.14/0.38 $false|spl0_4),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f191,f126])).
% 0.14/0.38 fof(f203,plain,(
% 0.14/0.38 spl0_4),
% 0.14/0.38 inference(contradiction_clause,[status(thm)],[f202])).
% 0.14/0.38 fof(f204,plain,(
% 0.14/0.38 ~relation(sk0_11)|~function(sk0_11)|spl0_3),
% 0.14/0.38 inference(resolution,[status(thm)],[f188,f85])).
% 0.14/0.38 fof(f205,plain,(
% 0.14/0.38 ~spl0_4|~spl0_5|spl0_3),
% 0.14/0.38 inference(split_clause,[status(thm)],[f204,f189,f192,f186])).
% 0.14/0.38 fof(f207,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~pd0_0(X2,X1,X0))),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f162,f81])).
% 0.14/0.38 fof(f208,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~pd0_0(X2,X1,X0)|element(X2,relation_dom(relation_rng_restriction(X0,X1))))),
% 0.14/0.38 inference(resolution,[status(thm)],[f207,f118])).
% 0.14/0.38 fof(f209,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~pd0_0(X1,X0,X2)|element(X1,relation_dom(relation_rng_restriction(X2,X0))))),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f208,f85])).
% 0.14/0.38 fof(f212,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~pd0_0(X2,X1,X0)|~empty(relation_dom(relation_rng_restriction(X0,X1))))),
% 0.14/0.38 inference(resolution,[status(thm)],[f207,f121])).
% 0.14/0.38 fof(f213,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~pd0_0(X1,X0,X2)|~empty(relation_dom(relation_rng_restriction(X2,X0))))),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f212,f85])).
% 0.14/0.38 fof(f254,plain,(
% 0.14/0.38 ![X0]: (sk0_5(X0)=empty_set)),
% 0.14/0.38 inference(resolution,[status(thm)],[f103,f73])).
% 0.14/0.38 fof(f261,plain,(
% 0.14/0.38 spl0_8 <=> ~empty(X0)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f262,plain,(
% 0.14/0.38 ![X0]: (~empty(X0)|~spl0_8)),
% 0.14/0.38 inference(component_clause,[status(thm)],[f261])).
% 0.14/0.38 fof(f264,plain,(
% 0.14/0.38 spl0_9 <=> ~pd0_0(X1,X2,empty_set)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f267,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~empty(X0)|~pd0_0(X1,X2,empty_set))),
% 0.14/0.38 inference(backward_demodulation,[status(thm)],[f254,f182])).
% 0.14/0.38 fof(f268,plain,(
% 0.14/0.38 spl0_8|spl0_9),
% 0.14/0.38 inference(split_clause,[status(thm)],[f267,f261,f264])).
% 0.14/0.38 fof(f269,plain,(
% 0.14/0.38 spl0_10 <=> ~in(X0,empty_set)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f272,plain,(
% 0.14/0.38 ![X0,X1]: (~in(X0,empty_set)|~empty(X1))),
% 0.14/0.38 inference(backward_demodulation,[status(thm)],[f254,f180])).
% 0.14/0.38 fof(f273,plain,(
% 0.14/0.38 spl0_10|spl0_8),
% 0.14/0.38 inference(split_clause,[status(thm)],[f272,f269,f261])).
% 0.14/0.38 fof(f274,plain,(
% 0.14/0.38 ![X0]: (element(empty_set,powerset(X0)))),
% 0.14/0.38 inference(backward_demodulation,[status(thm)],[f254,f102])).
% 0.14/0.38 fof(f275,plain,(
% 0.14/0.38 $false|~spl0_8),
% 0.14/0.38 inference(backward_subsumption_resolution,[status(thm)],[f38,f262])).
% 0.14/0.38 fof(f276,plain,(
% 0.14/0.38 ~spl0_8),
% 0.14/0.38 inference(contradiction_clause,[status(thm)],[f275])).
% 0.14/0.38 fof(f295,plain,(
% 0.14/0.38 ![X0]: (subset(empty_set,X0))),
% 0.14/0.38 inference(resolution,[status(thm)],[f64,f274])).
% 0.14/0.38 fof(f297,plain,(
% 0.14/0.38 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|~empty(X1))),
% 0.14/0.38 inference(resolution,[status(thm)],[f65,f71])).
% 0.14/0.38 fof(f310,plain,(
% 0.14/0.38 ![X0]: (empty(X0)|in(sk0_0(X0),X0))),
% 0.14/0.38 inference(resolution,[status(thm)],[f61,f45])).
% 0.14/0.38 fof(f313,plain,(
% 0.14/0.38 ![X0,X1,X2]: (empty(relation_dom(relation_rng_restriction(X0,X1)))|in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~relation(X1)|~function(X1)|~pd0_0(X2,X1,X0))),
% 0.14/0.38 inference(resolution,[status(thm)],[f61,f209])).
% 0.14/0.38 fof(f314,plain,(
% 0.14/0.38 ![X0,X1,X2]: (in(X0,relation_dom(relation_rng_restriction(X1,X2)))|~relation(X2)|~function(X2)|~pd0_0(X0,X2,X1))),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f313,f213])).
% 0.14/0.38 fof(f327,plain,(
% 0.14/0.38 ![X0,X1]: (empty(X0)|~subset(X0,X1)|~empty(X1))),
% 0.14/0.38 inference(resolution,[status(thm)],[f310,f297])).
% 0.14/0.38 fof(f338,plain,(
% 0.14/0.38 spl0_12 <=> empty(empty_set)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f341,plain,(
% 0.14/0.38 ![X0]: (empty(empty_set)|~empty(X0))),
% 0.14/0.38 inference(resolution,[status(thm)],[f327,f295])).
% 0.21/0.38 fof(f342,plain,(
% 0.21/0.38 spl0_12|spl0_8),
% 0.21/0.38 inference(split_clause,[status(thm)],[f341,f338,f261])).
% 0.21/0.38 fof(f352,plain,(
% 0.21/0.38 in(sk0_13,relation_dom(sk0_11))|~spl0_6),
% 0.21/0.38 inference(resolution,[status(thm)],[f146,f196])).
% 0.21/0.38 fof(f353,plain,(
% 0.21/0.38 $false|spl0_1|~spl0_6),
% 0.21/0.38 inference(forward_subsumption_resolution,[status(thm)],[f352,f154])).
% 0.21/0.38 fof(f354,plain,(
% 0.21/0.38 spl0_1|~spl0_6),
% 0.21/0.38 inference(contradiction_clause,[status(thm)],[f353])).
% 0.21/0.38 fof(f358,plain,(
% 0.21/0.38 ~relation(sk0_11)|~function(sk0_11)|~pd0_0(sk0_13,sk0_11,sk0_12)|spl0_0),
% 0.21/0.38 inference(resolution,[status(thm)],[f151,f314])).
% 0.21/0.38 fof(f359,plain,(
% 0.21/0.38 ~spl0_4|~spl0_5|~spl0_6|spl0_0),
% 0.21/0.38 inference(split_clause,[status(thm)],[f358,f189,f192,f195,f149])).
% 0.21/0.38 fof(f379,plain,(
% 0.21/0.38 ~pd0_0(sk0_13,sk0_11,sk0_12)|spl0_2),
% 0.21/0.38 inference(resolution,[status(thm)],[f158,f147])).
% 0.21/0.38 fof(f380,plain,(
% 0.21/0.38 $false|~spl0_6|spl0_2),
% 0.21/0.38 inference(forward_subsumption_resolution,[status(thm)],[f379,f196])).
% 0.21/0.38 fof(f381,plain,(
% 0.21/0.38 ~spl0_6|spl0_2),
% 0.21/0.38 inference(contradiction_clause,[status(thm)],[f380])).
% 0.21/0.38 fof(f391,plain,(
% 0.21/0.38 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.21/0.38 inference(forward_subsumption_resolution,[status(thm)],[f51,f59])).
% 0.21/0.38 fof(f396,plain,(
% 0.21/0.38 spl0_14 <=> one_to_one(empty_set)),
% 0.21/0.38 introduced(split_symbol_definition)).
% 0.21/0.38 fof(f399,plain,(
% 0.21/0.38 ~empty(empty_set)|one_to_one(empty_set)),
% 0.21/0.38 inference(resolution,[status(thm)],[f391,f174])).
% 0.21/0.38 fof(f400,plain,(
% 0.21/0.38 ~spl0_12|spl0_14),
% 0.21/0.38 inference(split_clause,[status(thm)],[f399,f338,f396])).
% 0.21/0.38 fof(f466,plain,(
% 0.21/0.38 pd0_0(sk0_13,sk0_11,sk0_12)|~in(sk0_13,relation_dom(sk0_11))|~spl0_2),
% 0.21/0.38 inference(resolution,[status(thm)],[f148,f157])).
% 0.21/0.38 fof(f467,plain,(
% 0.21/0.38 spl0_6|~spl0_1|~spl0_2),
% 0.21/0.38 inference(split_clause,[status(thm)],[f466,f195,f152,f156])).
% 0.21/0.38 fof(f470,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(sat_refutation,[status(thm)],[f155,f159,f160,f199,f201,f203,f205,f268,f273,f276,f342,f354,f359,f381,f400,f467])).
% 0.21/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.39 % Elapsed time: 0.033224 seconds
% 0.21/0.39 % CPU time: 0.130526 seconds
% 0.21/0.39 % Total memory used: 19.725 MB
% 0.21/0.39 % Net memory used: 19.672 MB
%------------------------------------------------------------------------------