TSTP Solution File: SEU213+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU213+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU213+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31 % Computer : n018.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 29 20:03:12 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Drodi V3.6.0
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.36 fof(f5,axiom,(
% 0.11/0.36 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f6,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f8,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B] :( relation(B)=> (! [C] :( relation(C)=> ( C = relation_composition(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> (? [F] :( in(ordered_pair(D,F),A)& in(ordered_pair(F,E),B) ) )) )) ) )) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f15,axiom,(
% 0.11/0.36 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f20,axiom,(
% 0.11/0.36 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f36,conjecture,(
% 0.11/0.36 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(relation_composition(C,B)))<=> ( in(A,relation_dom(C))& in(apply(C,A),relation_dom(B)) ) ) ) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f37,negated_conjecture,(
% 0.11/0.36 ~((! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(relation_composition(C,B)))<=> ( in(A,relation_dom(C))& in(apply(C,A),relation_dom(B)) ) ) ) )) ))),
% 0.11/0.36 inference(negated_conjecture,[status(cth)],[f36])).
% 0.11/0.36 fof(f49,plain,(
% 0.11/0.36 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.11/0.36 fof(f50,plain,(
% 0.11/0.36 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f49])).
% 0.11/0.36 fof(f51,plain,(
% 0.11/0.36 ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f50])).
% 0.11/0.36 fof(f52,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f51])).
% 0.11/0.36 fof(f53,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f51])).
% 0.11/0.36 fof(f56,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.11/0.36 fof(f57,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: ((~B=relation_dom(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(C,D),A)))&(in(C,B)|(![D]: ~in(ordered_pair(C,D),A))))))&(B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f56])).
% 0.11/0.36 fof(f58,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(C,D),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f57])).
% 0.11/0.36 fof(f59,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sk0_0(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sk0_1(B,A),B)|(![D]: ~in(ordered_pair(sk0_1(B,A),D),A)))&(in(sk0_1(B,A),B)|in(ordered_pair(sk0_1(B,A),sk0_2(B,A)),A)))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f58])).
% 0.11/0.36 fof(f61,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f59])).
% 0.11/0.36 fof(f65,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|(C=relation_composition(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.11/0.36 fof(f66,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f65])).
% 0.11/0.36 fof(f67,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))&(![D,E]: (in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f66])).
% 0.11/0.36 fof(f68,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(ordered_pair(D,sk0_3(E,D,C,B,A)),A)&in(ordered_pair(sk0_3(E,D,C,B,A),E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|((~in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)|(![F]: (~in(ordered_pair(sk0_4(C,B,A),F),A)|~in(ordered_pair(F,sk0_5(C,B,A)),B))))&(in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)|(in(ordered_pair(sk0_4(C,B,A),sk0_6(C,B,A)),A)&in(ordered_pair(sk0_6(C,B,A),sk0_5(C,B,A)),B)))))))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f67])).
% 0.11/0.36 fof(f69,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~relation(X2)|~X2=relation_composition(X0,X1)|~in(ordered_pair(X3,X4),X2)|in(ordered_pair(X3,sk0_3(X4,X3,X2,X1,X0)),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.11/0.36 fof(f70,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~relation(X2)|~X2=relation_composition(X0,X1)|~in(ordered_pair(X3,X4),X2)|in(ordered_pair(sk0_3(X4,X3,X2,X1,X0),X4),X1))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.11/0.36 fof(f71,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4,X5]: (~relation(X0)|~relation(X1)|~relation(X2)|~X2=relation_composition(X0,X1)|in(ordered_pair(X3,X4),X2)|~in(ordered_pair(X3,X5),X0)|~in(ordered_pair(X5,X4),X1))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.11/0.36 fof(f75,plain,(
% 0.11/0.36 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.11/0.36 fof(f76,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f75])).
% 0.11/0.36 fof(f85,plain,(
% 0.11/0.36 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.11/0.36 fof(f87,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f85])).
% 0.11/0.36 fof(f120,plain,(
% 0.11/0.36 (?[A,B]: ((relation(B)&function(B))&(?[C]: ((relation(C)&function(C))&(in(A,relation_dom(relation_composition(C,B)))<~>(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B))))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 0.11/0.36 fof(f121,plain,(
% 0.11/0.36 ?[A,B]: ((relation(B)&function(B))&(?[C]: ((relation(C)&function(C))&((in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B))))&(~in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f120])).
% 0.11/0.36 fof(f122,plain,(
% 0.11/0.36 ?[B]: ((relation(B)&function(B))&(?[C]: ((relation(C)&function(C))&(?[A]: ((in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B))))&(~in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B)))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f121])).
% 0.11/0.36 fof(f123,plain,(
% 0.11/0.36 ((relation(sk0_14)&function(sk0_14))&((relation(sk0_15)&function(sk0_15))&((in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|(in(sk0_16,relation_dom(sk0_15))&in(apply(sk0_15,sk0_16),relation_dom(sk0_14))))&(~in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|(~in(sk0_16,relation_dom(sk0_15))|~in(apply(sk0_15,sk0_16),relation_dom(sk0_14)))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f122])).
% 0.11/0.36 fof(f124,plain,(
% 0.11/0.36 relation(sk0_14)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f125,plain,(
% 0.11/0.36 function(sk0_14)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f126,plain,(
% 0.11/0.36 relation(sk0_15)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f127,plain,(
% 0.11/0.36 function(sk0_15)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f128,plain,(
% 0.11/0.36 in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|in(sk0_16,relation_dom(sk0_15))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f129,plain,(
% 0.11/0.36 in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|in(apply(sk0_15,sk0_16),relation_dom(sk0_14))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f130,plain,(
% 0.11/0.36 ~in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|~in(sk0_16,relation_dom(sk0_15))|~in(apply(sk0_15,sk0_16),relation_dom(sk0_14))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f123])).
% 0.11/0.36 fof(f141,plain,(
% 0.11/0.36 spl0_0 <=> in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f142,plain,(
% 0.11/0.36 in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|~spl0_0),
% 0.11/0.36 inference(component_clause,[status(thm)],[f141])).
% 0.11/0.36 fof(f144,plain,(
% 0.11/0.36 spl0_1 <=> in(sk0_16,relation_dom(sk0_15))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f147,plain,(
% 0.11/0.36 spl0_0|spl0_1),
% 0.11/0.36 inference(split_clause,[status(thm)],[f128,f141,f144])).
% 0.11/0.36 fof(f148,plain,(
% 0.11/0.36 spl0_2 <=> in(apply(sk0_15,sk0_16),relation_dom(sk0_14))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f149,plain,(
% 0.11/0.36 in(apply(sk0_15,sk0_16),relation_dom(sk0_14))|~spl0_2),
% 0.11/0.36 inference(component_clause,[status(thm)],[f148])).
% 0.11/0.36 fof(f151,plain,(
% 0.11/0.36 spl0_0|spl0_2),
% 0.11/0.36 inference(split_clause,[status(thm)],[f129,f141,f148])).
% 0.11/0.37 fof(f152,plain,(
% 0.11/0.37 ~spl0_0|~spl0_1|~spl0_2),
% 0.11/0.37 inference(split_clause,[status(thm)],[f130,f141,f144,f148])).
% 0.11/0.37 fof(f153,plain,(
% 0.11/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.11/0.37 inference(destructive_equality_resolution,[status(esa)],[f52])).
% 0.11/0.37 fof(f157,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.11/0.37 inference(destructive_equality_resolution,[status(esa)],[f61])).
% 0.11/0.37 fof(f158,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~relation(relation_composition(X0,X1))|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 0.11/0.37 inference(destructive_equality_resolution,[status(esa)],[f69])).
% 0.11/0.37 fof(f159,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~relation(relation_composition(X0,X1))|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 0.11/0.37 inference(destructive_equality_resolution,[status(esa)],[f70])).
% 0.11/0.37 fof(f160,plain,(
% 0.11/0.37 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~relation(relation_composition(X0,X1))|in(ordered_pair(X2,X3),relation_composition(X0,X1))|~in(ordered_pair(X2,X4),X0)|~in(ordered_pair(X4,X3),X1))),
% 0.11/0.37 inference(destructive_equality_resolution,[status(esa)],[f71])).
% 0.11/0.37 fof(f161,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f53,f157])).
% 0.11/0.37 fof(f162,plain,(
% 0.11/0.37 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,X3),relation_composition(X0,X1))|~in(ordered_pair(X2,X4),X0)|~in(ordered_pair(X4,X3),X1))),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f160,f76])).
% 0.11/0.37 fof(f163,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f159,f76])).
% 0.11/0.37 fof(f164,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 0.11/0.37 inference(backward_subsumption_resolution,[status(thm)],[f158,f76])).
% 0.11/0.37 fof(f167,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,apply(X1,X3)),relation_composition(X0,X1))|~in(ordered_pair(X2,X3),X0)|~relation(X1)|~function(X1)|~in(X3,relation_dom(X1)))),
% 0.11/0.37 inference(resolution,[status(thm)],[f162,f153])).
% 0.11/0.37 fof(f168,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,apply(X1,X3)),relation_composition(X0,X1))|~in(ordered_pair(X2,X3),X0)|~function(X1)|~in(X3,relation_dom(X1)))),
% 0.11/0.37 inference(duplicate_literals_removal,[status(esa)],[f167])).
% 0.11/0.37 fof(f169,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0),apply(relation_composition(X0,X1),X2)),X1)|~relation(relation_composition(X0,X1))|~function(relation_composition(X0,X1))|~in(X2,relation_dom(relation_composition(X0,X1))))),
% 0.11/0.37 inference(resolution,[status(thm)],[f163,f153])).
% 0.11/0.37 fof(f170,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0),apply(relation_composition(X0,X1),X2)),X1)|~function(relation_composition(X0,X1))|~in(X2,relation_dom(relation_composition(X0,X1))))),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f169,f76])).
% 0.11/0.37 fof(f171,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0),apply(relation_composition(X0,X1),X2)),X1)|~in(X2,relation_dom(relation_composition(X0,X1)))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1))),
% 0.11/0.37 inference(resolution,[status(thm)],[f170,f87])).
% 0.11/0.37 fof(f172,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0),apply(relation_composition(X0,X1),X2)),X1)|~in(X2,relation_dom(relation_composition(X0,X1)))|~function(X0)|~function(X1))),
% 0.11/0.37 inference(duplicate_literals_removal,[status(esa)],[f171])).
% 0.11/0.37 fof(f175,plain,(
% 0.11/0.37 spl0_3 <=> relation(sk0_15)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f177,plain,(
% 0.11/0.37 ~relation(sk0_15)|spl0_3),
% 0.11/0.37 inference(component_clause,[status(thm)],[f175])).
% 0.11/0.37 fof(f178,plain,(
% 0.11/0.37 spl0_4 <=> relation(sk0_14)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f180,plain,(
% 0.11/0.37 ~relation(sk0_14)|spl0_4),
% 0.11/0.37 inference(component_clause,[status(thm)],[f178])).
% 0.11/0.37 fof(f181,plain,(
% 0.11/0.37 spl0_5 <=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f182,plain,(
% 0.11/0.37 in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)|~spl0_5),
% 0.11/0.37 inference(component_clause,[status(thm)],[f181])).
% 0.11/0.37 fof(f184,plain,(
% 0.11/0.37 spl0_6 <=> function(sk0_15)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f186,plain,(
% 0.11/0.37 ~function(sk0_15)|spl0_6),
% 0.11/0.37 inference(component_clause,[status(thm)],[f184])).
% 0.11/0.37 fof(f187,plain,(
% 0.11/0.37 spl0_7 <=> function(sk0_14)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f189,plain,(
% 0.11/0.37 ~function(sk0_14)|spl0_7),
% 0.11/0.37 inference(component_clause,[status(thm)],[f187])).
% 0.11/0.37 fof(f190,plain,(
% 0.11/0.37 ~relation(sk0_15)|~relation(sk0_14)|in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)|~function(sk0_15)|~function(sk0_14)|~spl0_0),
% 0.11/0.37 inference(resolution,[status(thm)],[f172,f142])).
% 0.11/0.37 fof(f191,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_5|~spl0_6|~spl0_7|~spl0_0),
% 0.11/0.37 inference(split_clause,[status(thm)],[f190,f175,f178,f181,f184,f187,f141])).
% 0.11/0.37 fof(f192,plain,(
% 0.11/0.37 $false|spl0_7),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f189,f125])).
% 0.11/0.37 fof(f193,plain,(
% 0.11/0.37 spl0_7),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f192])).
% 0.11/0.37 fof(f194,plain,(
% 0.11/0.37 $false|spl0_6),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f186,f127])).
% 0.11/0.37 fof(f195,plain,(
% 0.11/0.37 spl0_6),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f194])).
% 0.11/0.37 fof(f196,plain,(
% 0.11/0.37 $false|spl0_4),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f180,f124])).
% 0.11/0.37 fof(f197,plain,(
% 0.11/0.37 spl0_4),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f196])).
% 0.11/0.37 fof(f198,plain,(
% 0.11/0.37 $false|spl0_3),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f177,f126])).
% 0.11/0.37 fof(f199,plain,(
% 0.11/0.37 spl0_3),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f198])).
% 0.11/0.37 fof(f205,plain,(
% 0.11/0.37 spl0_9 <=> in(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),relation_dom(sk0_14))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f206,plain,(
% 0.11/0.37 in(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),relation_dom(sk0_14))|~spl0_9),
% 0.11/0.37 inference(component_clause,[status(thm)],[f205])).
% 0.11/0.37 fof(f208,plain,(
% 0.11/0.37 ~relation(sk0_14)|in(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),relation_dom(sk0_14))|~spl0_5),
% 0.11/0.37 inference(resolution,[status(thm)],[f182,f157])).
% 0.11/0.37 fof(f209,plain,(
% 0.11/0.37 ~spl0_4|spl0_9|~spl0_5),
% 0.11/0.37 inference(split_clause,[status(thm)],[f208,f178,f205,f181])).
% 0.11/0.37 fof(f229,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0)),X0)|~relation(relation_composition(X0,X1))|~function(relation_composition(X0,X1))|~in(X2,relation_dom(relation_composition(X0,X1))))),
% 0.11/0.37 inference(resolution,[status(thm)],[f164,f153])).
% 0.11/0.37 fof(f230,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0)),X0)|~function(relation_composition(X0,X1))|~in(X2,relation_dom(relation_composition(X0,X1))))),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f229,f76])).
% 0.11/0.37 fof(f236,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,apply(X1,apply(X0,X2))),relation_composition(X0,X1))|~function(X1)|~in(apply(X0,X2),relation_dom(X1))|~relation(X0)|~function(X0)|~in(X2,relation_dom(X0)))),
% 0.11/0.37 inference(resolution,[status(thm)],[f168,f153])).
% 0.11/0.37 fof(f237,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,apply(X1,apply(X0,X2))),relation_composition(X0,X1))|~function(X1)|~in(apply(X0,X2),relation_dom(X1))|~function(X0)|~in(X2,relation_dom(X0)))),
% 0.11/0.37 inference(duplicate_literals_removal,[status(esa)],[f236])).
% 0.11/0.37 fof(f238,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0)),X0)|~in(X2,relation_dom(relation_composition(X0,X1)))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1))),
% 0.11/0.37 inference(resolution,[status(thm)],[f230,f87])).
% 0.11/0.37 fof(f239,plain,(
% 0.11/0.37 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|in(ordered_pair(X2,sk0_3(apply(relation_composition(X0,X1),X2),X2,relation_composition(X0,X1),X1,X0)),X0)|~in(X2,relation_dom(relation_composition(X0,X1)))|~function(X0)|~function(X1))),
% 0.11/0.37 inference(duplicate_literals_removal,[status(esa)],[f238])).
% 0.11/0.37 fof(f242,plain,(
% 0.11/0.37 spl0_14 <=> in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f243,plain,(
% 0.11/0.37 in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)|~spl0_14),
% 0.11/0.37 inference(component_clause,[status(thm)],[f242])).
% 0.11/0.37 fof(f245,plain,(
% 0.11/0.37 ~relation(sk0_15)|~relation(sk0_14)|in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)|~function(sk0_15)|~function(sk0_14)|~spl0_0),
% 0.11/0.37 inference(resolution,[status(thm)],[f239,f142])).
% 0.11/0.37 fof(f246,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_14|~spl0_6|~spl0_7|~spl0_0),
% 0.11/0.37 inference(split_clause,[status(thm)],[f245,f175,f178,f242,f184,f187,f141])).
% 0.11/0.37 fof(f261,plain,(
% 0.11/0.37 spl0_15 <=> relation(relation_composition(sk0_15,sk0_14))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f263,plain,(
% 0.11/0.37 ~relation(relation_composition(sk0_15,sk0_14))|spl0_15),
% 0.11/0.37 inference(component_clause,[status(thm)],[f261])).
% 0.11/0.37 fof(f264,plain,(
% 0.11/0.37 spl0_16 <=> function(relation_composition(sk0_15,sk0_14))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f265,plain,(
% 0.11/0.37 function(relation_composition(sk0_15,sk0_14))|~spl0_16),
% 0.11/0.37 inference(component_clause,[status(thm)],[f264])).
% 0.11/0.37 fof(f266,plain,(
% 0.11/0.37 ~function(relation_composition(sk0_15,sk0_14))|spl0_16),
% 0.11/0.37 inference(component_clause,[status(thm)],[f264])).
% 0.11/0.37 fof(f282,plain,(
% 0.11/0.37 ~relation(sk0_15)|~function(sk0_15)|~relation(sk0_14)|~function(sk0_14)|spl0_16),
% 0.11/0.37 inference(resolution,[status(thm)],[f266,f87])).
% 0.11/0.37 fof(f283,plain,(
% 0.11/0.37 ~spl0_3|~spl0_6|~spl0_4|~spl0_7|spl0_16),
% 0.11/0.37 inference(split_clause,[status(thm)],[f282,f175,f184,f178,f187,f264])).
% 0.11/0.37 fof(f295,plain,(
% 0.11/0.37 ~relation(sk0_15)|~relation(sk0_14)|spl0_15),
% 0.11/0.37 inference(resolution,[status(thm)],[f263,f76])).
% 0.11/0.37 fof(f296,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_15),
% 0.11/0.37 inference(split_clause,[status(thm)],[f295,f175,f178,f261])).
% 0.11/0.37 fof(f297,plain,(
% 0.11/0.37 spl0_22 <=> in(ordered_pair(X0,sk0_3(apply(relation_composition(sk0_15,sk0_14),X0),X0,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)|~in(X0,relation_dom(relation_composition(sk0_15,sk0_14)))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f300,plain,(
% 0.11/0.37 ![X0]: (~relation(sk0_15)|~relation(sk0_14)|in(ordered_pair(X0,sk0_3(apply(relation_composition(sk0_15,sk0_14),X0),X0,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)|~in(X0,relation_dom(relation_composition(sk0_15,sk0_14)))|~spl0_16)),
% 0.11/0.37 inference(resolution,[status(thm)],[f265,f230])).
% 0.11/0.37 fof(f301,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_22|~spl0_16),
% 0.11/0.37 inference(split_clause,[status(thm)],[f300,f175,f178,f297,f264])).
% 0.11/0.37 fof(f302,plain,(
% 0.11/0.37 spl0_23 <=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),X0),X0,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),X0)),sk0_14)|~in(X0,relation_dom(relation_composition(sk0_15,sk0_14)))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f305,plain,(
% 0.11/0.37 ![X0]: (~relation(sk0_15)|~relation(sk0_14)|in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),X0),X0,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),X0)),sk0_14)|~in(X0,relation_dom(relation_composition(sk0_15,sk0_14)))|~spl0_16)),
% 0.11/0.37 inference(resolution,[status(thm)],[f265,f170])).
% 0.11/0.37 fof(f306,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_23|~spl0_16),
% 0.11/0.37 inference(split_clause,[status(thm)],[f305,f175,f178,f302,f264])).
% 0.11/0.37 fof(f335,plain,(
% 0.11/0.37 ~relation(sk0_15)|in(sk0_16,relation_dom(sk0_15))|~spl0_14),
% 0.11/0.37 inference(resolution,[status(thm)],[f243,f157])).
% 0.11/0.37 fof(f336,plain,(
% 0.11/0.37 ~spl0_3|spl0_1|~spl0_14),
% 0.11/0.37 inference(split_clause,[status(thm)],[f335,f175,f144,f242])).
% 0.11/0.37 fof(f337,plain,(
% 0.11/0.37 spl0_26 <=> sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)=apply(sk0_15,sk0_16)),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f338,plain,(
% 0.11/0.37 sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)=apply(sk0_15,sk0_16)|~spl0_26),
% 0.11/0.37 inference(component_clause,[status(thm)],[f337])).
% 0.11/0.37 fof(f340,plain,(
% 0.11/0.37 ~relation(sk0_15)|~function(sk0_15)|sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)=apply(sk0_15,sk0_16)|~spl0_14),
% 0.11/0.37 inference(resolution,[status(thm)],[f243,f161])).
% 0.11/0.37 fof(f341,plain,(
% 0.11/0.37 ~spl0_3|~spl0_6|spl0_26|~spl0_14),
% 0.11/0.37 inference(split_clause,[status(thm)],[f340,f175,f184,f337,f242])).
% 0.11/0.37 fof(f345,plain,(
% 0.11/0.37 in(apply(sk0_15,sk0_16),relation_dom(sk0_14))|~spl0_26|~spl0_9),
% 0.11/0.37 inference(backward_demodulation,[status(thm)],[f338,f206])).
% 0.11/0.37 fof(f346,plain,(
% 0.11/0.37 spl0_2|~spl0_26|~spl0_9),
% 0.11/0.37 inference(split_clause,[status(thm)],[f345,f148,f337,f205])).
% 0.11/0.37 fof(f487,plain,(
% 0.11/0.37 spl0_42 <=> in(ordered_pair(sk0_16,apply(sk0_14,apply(sk0_15,sk0_16))),relation_composition(sk0_15,sk0_14))),
% 0.11/0.37 introduced(split_symbol_definition)).
% 0.11/0.37 fof(f488,plain,(
% 0.11/0.37 in(ordered_pair(sk0_16,apply(sk0_14,apply(sk0_15,sk0_16))),relation_composition(sk0_15,sk0_14))|~spl0_42),
% 0.11/0.37 inference(component_clause,[status(thm)],[f487])).
% 0.11/0.37 fof(f490,plain,(
% 0.11/0.37 ~relation(sk0_15)|~relation(sk0_14)|in(ordered_pair(sk0_16,apply(sk0_14,apply(sk0_15,sk0_16))),relation_composition(sk0_15,sk0_14))|~function(sk0_14)|~function(sk0_15)|~in(sk0_16,relation_dom(sk0_15))|~spl0_2),
% 0.11/0.37 inference(resolution,[status(thm)],[f237,f149])).
% 0.11/0.37 fof(f491,plain,(
% 0.11/0.37 ~spl0_3|~spl0_4|spl0_42|~spl0_7|~spl0_6|~spl0_1|~spl0_2),
% 0.11/0.37 inference(split_clause,[status(thm)],[f490,f175,f178,f487,f187,f184,f144,f148])).
% 0.11/0.37 fof(f524,plain,(
% 0.11/0.37 ~relation(relation_composition(sk0_15,sk0_14))|in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))|~spl0_42),
% 0.11/0.37 inference(resolution,[status(thm)],[f488,f157])).
% 0.11/0.37 fof(f525,plain,(
% 0.11/0.37 ~spl0_15|spl0_0|~spl0_42),
% 0.11/0.37 inference(split_clause,[status(thm)],[f524,f261,f141,f487])).
% 0.11/0.37 fof(f532,plain,(
% 0.11/0.37 $false),
% 0.11/0.37 inference(sat_refutation,[status(thm)],[f147,f151,f152,f191,f193,f195,f197,f199,f209,f246,f283,f296,f301,f306,f336,f341,f346,f491,f525])).
% 0.11/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.37 % Elapsed time: 0.054287 seconds
% 0.11/0.37 % CPU time: 0.309777 seconds
% 0.11/0.37 % Total memory used: 64.086 MB
% 0.11/0.37 % Net memory used: 63.807 MB
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