TSTP Solution File: SEU213+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU213+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:36:17 EDT 2023
% Result : Theorem 0.15s 0.36s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU213+3 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n022.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue May 30 09:14:57 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 0.15/0.36 % Refutation found
% 0.15/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.36 fof(f5,axiom,(
% 0.15/0.36 (! [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 ) ) ) )) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f6,axiom,(
% 0.15/0.36 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f8,axiom,(
% 0.15/0.36 (! [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) ) )) )) ) )) )) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f9,axiom,(
% 0.15/0.36 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f13,axiom,(
% 0.15/0.36 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f33,conjecture,(
% 0.15/0.36 (! [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)) ) ) ) )) )),
% 0.15/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.36 fof(f34,negated_conjecture,(
% 0.15/0.36 ~((! [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)) ) ) ) )) ))),
% 0.15/0.36 inference(negated_conjecture,[status(cth)],[f33])).
% 0.15/0.36 fof(f49,plain,(
% 0.15/0.36 ![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)))))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.15/0.36 fof(f50,plain,(
% 0.15/0.36 ![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))))))),
% 0.15/0.36 inference(NNF_transformation,[status(esa)],[f49])).
% 0.15/0.36 fof(f51,plain,(
% 0.15/0.36 ![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)))))))),
% 0.15/0.36 inference(miniscoping,[status(esa)],[f50])).
% 0.15/0.36 fof(f52,plain,(
% 0.15/0.36 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f51])).
% 0.15/0.36 fof(f53,plain,(
% 0.15/0.36 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f51])).
% 0.15/0.36 fof(f56,plain,(
% 0.15/0.36 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.15/0.36 fof(f57,plain,(
% 0.15/0.36 ![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)))))))))),
% 0.15/0.36 inference(NNF_transformation,[status(esa)],[f56])).
% 0.15/0.36 fof(f58,plain,(
% 0.15/0.36 ![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)))))))))),
% 0.15/0.36 inference(miniscoping,[status(esa)],[f57])).
% 0.15/0.36 fof(f59,plain,(
% 0.15/0.36 ![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)))))))),
% 0.15/0.36 inference(skolemization,[status(esa)],[f58])).
% 0.15/0.36 fof(f61,plain,(
% 0.15/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f59])).
% 0.15/0.36 fof(f65,plain,(
% 0.15/0.36 ![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)))))))))))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.15/0.36 fof(f66,plain,(
% 0.15/0.36 ![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)))))))))))))),
% 0.15/0.36 inference(NNF_transformation,[status(esa)],[f65])).
% 0.15/0.36 fof(f67,plain,(
% 0.15/0.36 ![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)))))))))))))),
% 0.15/0.36 inference(miniscoping,[status(esa)],[f66])).
% 0.15/0.36 fof(f68,plain,(
% 0.15/0.36 ![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)))))))))))),
% 0.15/0.36 inference(skolemization,[status(esa)],[f67])).
% 0.15/0.36 fof(f69,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.15/0.36 fof(f70,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.15/0.36 fof(f71,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f68])).
% 0.15/0.36 fof(f75,plain,(
% 0.15/0.36 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.15/0.36 fof(f76,plain,(
% 0.15/0.36 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f75])).
% 0.15/0.36 fof(f85,plain,(
% 0.15/0.36 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.15/0.36 fof(f87,plain,(
% 0.15/0.36 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f85])).
% 0.15/0.36 fof(f130,plain,(
% 0.15/0.36 (?[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))))))))),
% 0.15/0.36 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 0.15/0.36 fof(f131,plain,(
% 0.15/0.36 ?[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))))))))),
% 0.15/0.36 inference(NNF_transformation,[status(esa)],[f130])).
% 0.15/0.36 fof(f132,plain,(
% 0.15/0.36 ?[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)))))))))),
% 0.15/0.36 inference(miniscoping,[status(esa)],[f131])).
% 0.15/0.36 fof(f133,plain,(
% 0.15/0.36 ((relation(sk0_16)&function(sk0_16))&((relation(sk0_17)&function(sk0_17))&((in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|(in(sk0_18,relation_dom(sk0_17))&in(apply(sk0_17,sk0_18),relation_dom(sk0_16))))&(~in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|(~in(sk0_18,relation_dom(sk0_17))|~in(apply(sk0_17,sk0_18),relation_dom(sk0_16)))))))),
% 0.15/0.36 inference(skolemization,[status(esa)],[f132])).
% 0.15/0.36 fof(f134,plain,(
% 0.15/0.36 relation(sk0_16)),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f135,plain,(
% 0.15/0.36 function(sk0_16)),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f136,plain,(
% 0.15/0.36 relation(sk0_17)),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f137,plain,(
% 0.15/0.36 function(sk0_17)),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f138,plain,(
% 0.15/0.36 in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|in(sk0_18,relation_dom(sk0_17))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f139,plain,(
% 0.15/0.36 in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|in(apply(sk0_17,sk0_18),relation_dom(sk0_16))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f140,plain,(
% 0.15/0.36 ~in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|~in(sk0_18,relation_dom(sk0_17))|~in(apply(sk0_17,sk0_18),relation_dom(sk0_16))),
% 0.15/0.36 inference(cnf_transformation,[status(esa)],[f133])).
% 0.15/0.36 fof(f161,plain,(
% 0.15/0.36 spl0_0 <=> in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))),
% 0.15/0.36 introduced(split_symbol_definition)).
% 0.15/0.36 fof(f162,plain,(
% 0.15/0.36 in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|~spl0_0),
% 0.15/0.36 inference(component_clause,[status(thm)],[f161])).
% 0.15/0.36 fof(f164,plain,(
% 0.15/0.36 spl0_1 <=> in(sk0_18,relation_dom(sk0_17))),
% 0.15/0.36 introduced(split_symbol_definition)).
% 0.15/0.36 fof(f165,plain,(
% 0.15/0.36 in(sk0_18,relation_dom(sk0_17))|~spl0_1),
% 0.15/0.36 inference(component_clause,[status(thm)],[f164])).
% 0.15/0.36 fof(f167,plain,(
% 0.15/0.36 spl0_0|spl0_1),
% 0.15/0.36 inference(split_clause,[status(thm)],[f138,f161,f164])).
% 0.15/0.36 fof(f168,plain,(
% 0.15/0.36 spl0_2 <=> in(apply(sk0_17,sk0_18),relation_dom(sk0_16))),
% 0.15/0.36 introduced(split_symbol_definition)).
% 0.15/0.36 fof(f169,plain,(
% 0.15/0.36 in(apply(sk0_17,sk0_18),relation_dom(sk0_16))|~spl0_2),
% 0.15/0.36 inference(component_clause,[status(thm)],[f168])).
% 0.15/0.36 fof(f171,plain,(
% 0.15/0.36 spl0_0|spl0_2),
% 0.15/0.36 inference(split_clause,[status(thm)],[f139,f161,f168])).
% 0.15/0.36 fof(f172,plain,(
% 0.15/0.36 ~spl0_0|~spl0_1|~spl0_2),
% 0.15/0.36 inference(split_clause,[status(thm)],[f140,f161,f164,f168])).
% 0.15/0.36 fof(f173,plain,(
% 0.15/0.36 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.15/0.36 inference(destructive_equality_resolution,[status(esa)],[f52])).
% 0.15/0.36 fof(f177,plain,(
% 0.15/0.36 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.15/0.36 inference(destructive_equality_resolution,[status(esa)],[f61])).
% 0.15/0.36 fof(f179,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(destructive_equality_resolution,[status(esa)],[f69])).
% 0.15/0.36 fof(f180,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(destructive_equality_resolution,[status(esa)],[f70])).
% 0.15/0.36 fof(f181,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(destructive_equality_resolution,[status(esa)],[f71])).
% 0.15/0.36 fof(f182,plain,(
% 0.15/0.36 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 0.15/0.36 inference(backward_subsumption_resolution,[status(thm)],[f53,f177])).
% 0.15/0.36 fof(f183,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(backward_subsumption_resolution,[status(thm)],[f181,f76])).
% 0.15/0.36 fof(f184,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.37 inference(backward_subsumption_resolution,[status(thm)],[f180,f76])).
% 0.15/0.37 fof(f185,plain,(
% 0.15/0.37 ![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))),
% 0.15/0.37 inference(backward_subsumption_resolution,[status(thm)],[f179,f76])).
% 0.15/0.37 fof(f187,plain,(
% 0.15/0.37 spl0_3 <=> relation(relation_composition(sk0_17,sk0_16))),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f189,plain,(
% 0.15/0.37 ~relation(relation_composition(sk0_17,sk0_16))|spl0_3),
% 0.15/0.37 inference(component_clause,[status(thm)],[f187])).
% 0.15/0.37 fof(f190,plain,(
% 0.15/0.37 spl0_4 <=> function(relation_composition(sk0_17,sk0_16))),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f192,plain,(
% 0.15/0.37 ~function(relation_composition(sk0_17,sk0_16))|spl0_4),
% 0.15/0.37 inference(component_clause,[status(thm)],[f190])).
% 0.15/0.37 fof(f193,plain,(
% 0.15/0.37 spl0_5 <=> in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16))),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f194,plain,(
% 0.15/0.37 in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16))|~spl0_5),
% 0.15/0.37 inference(component_clause,[status(thm)],[f193])).
% 0.15/0.37 fof(f196,plain,(
% 0.15/0.37 ~relation(relation_composition(sk0_17,sk0_16))|~function(relation_composition(sk0_17,sk0_16))|in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16))|~spl0_0),
% 0.15/0.37 inference(resolution,[status(thm)],[f173,f162])).
% 0.15/0.37 fof(f197,plain,(
% 0.15/0.37 ~spl0_3|~spl0_4|spl0_5|~spl0_0),
% 0.15/0.37 inference(split_clause,[status(thm)],[f196,f187,f190,f193,f161])).
% 0.15/0.37 fof(f198,plain,(
% 0.15/0.37 spl0_6 <=> relation(sk0_17)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f200,plain,(
% 0.15/0.37 ~relation(sk0_17)|spl0_6),
% 0.15/0.37 inference(component_clause,[status(thm)],[f198])).
% 0.15/0.37 fof(f201,plain,(
% 0.15/0.37 spl0_7 <=> function(sk0_17)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f203,plain,(
% 0.15/0.37 ~function(sk0_17)|spl0_7),
% 0.15/0.37 inference(component_clause,[status(thm)],[f201])).
% 0.15/0.37 fof(f204,plain,(
% 0.15/0.37 spl0_8 <=> relation(sk0_16)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f206,plain,(
% 0.15/0.37 ~relation(sk0_16)|spl0_8),
% 0.15/0.37 inference(component_clause,[status(thm)],[f204])).
% 0.15/0.37 fof(f207,plain,(
% 0.15/0.37 spl0_9 <=> function(sk0_16)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f209,plain,(
% 0.15/0.37 ~function(sk0_16)|spl0_9),
% 0.15/0.37 inference(component_clause,[status(thm)],[f207])).
% 0.15/0.37 fof(f210,plain,(
% 0.15/0.37 ~relation(sk0_17)|~function(sk0_17)|~relation(sk0_16)|~function(sk0_16)|spl0_4),
% 0.15/0.37 inference(resolution,[status(thm)],[f192,f87])).
% 0.15/0.37 fof(f211,plain,(
% 0.15/0.37 ~spl0_6|~spl0_7|~spl0_8|~spl0_9|spl0_4),
% 0.15/0.37 inference(split_clause,[status(thm)],[f210,f198,f201,f204,f207,f190])).
% 0.15/0.37 fof(f213,plain,(
% 0.15/0.37 $false|spl0_9),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f209,f135])).
% 0.15/0.37 fof(f214,plain,(
% 0.15/0.37 spl0_9),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f213])).
% 0.15/0.37 fof(f215,plain,(
% 0.15/0.37 $false|spl0_8),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f206,f134])).
% 0.15/0.37 fof(f216,plain,(
% 0.15/0.37 spl0_8),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f215])).
% 0.15/0.37 fof(f217,plain,(
% 0.15/0.37 $false|spl0_7),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f203,f137])).
% 0.15/0.37 fof(f218,plain,(
% 0.15/0.37 spl0_7),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f217])).
% 0.15/0.37 fof(f219,plain,(
% 0.15/0.37 $false|spl0_6),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f200,f136])).
% 0.15/0.37 fof(f220,plain,(
% 0.15/0.37 spl0_6),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f219])).
% 0.15/0.37 fof(f231,plain,(
% 0.15/0.37 ~relation(sk0_17)|~relation(sk0_16)|spl0_3),
% 0.15/0.37 inference(resolution,[status(thm)],[f189,f76])).
% 0.15/0.37 fof(f232,plain,(
% 0.15/0.37 ~spl0_6|~spl0_8|spl0_3),
% 0.15/0.37 inference(split_clause,[status(thm)],[f231,f198,f204,f187])).
% 0.15/0.37 fof(f234,plain,(
% 0.15/0.37 ~relation(relation_composition(sk0_17,sk0_16))|in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|~spl0_5),
% 0.15/0.37 inference(resolution,[status(thm)],[f177,f194])).
% 0.15/0.37 fof(f235,plain,(
% 0.15/0.37 ~spl0_3|spl0_0|~spl0_5),
% 0.15/0.37 inference(split_clause,[status(thm)],[f234,f187,f161,f193])).
% 0.15/0.37 fof(f236,plain,(
% 0.15/0.37 spl0_12 <=> in(ordered_pair(sk0_18,apply(sk0_17,sk0_18)),sk0_17)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f237,plain,(
% 0.15/0.37 in(ordered_pair(sk0_18,apply(sk0_17,sk0_18)),sk0_17)|~spl0_12),
% 0.15/0.37 inference(component_clause,[status(thm)],[f236])).
% 0.15/0.37 fof(f239,plain,(
% 0.15/0.37 ~relation(sk0_17)|~function(sk0_17)|in(ordered_pair(sk0_18,apply(sk0_17,sk0_18)),sk0_17)|~spl0_1),
% 0.15/0.37 inference(resolution,[status(thm)],[f165,f173])).
% 0.15/0.37 fof(f240,plain,(
% 0.15/0.37 ~spl0_6|~spl0_7|spl0_12|~spl0_1),
% 0.15/0.37 inference(split_clause,[status(thm)],[f239,f198,f201,f236,f164])).
% 0.15/0.37 fof(f242,plain,(
% 0.15/0.37 spl0_13 <=> in(ordered_pair(apply(sk0_17,sk0_18),apply(sk0_16,apply(sk0_17,sk0_18))),sk0_16)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f243,plain,(
% 0.15/0.37 in(ordered_pair(apply(sk0_17,sk0_18),apply(sk0_16,apply(sk0_17,sk0_18))),sk0_16)|~spl0_13),
% 0.15/0.37 inference(component_clause,[status(thm)],[f242])).
% 0.15/0.37 fof(f245,plain,(
% 0.15/0.37 ~relation(sk0_16)|~function(sk0_16)|in(ordered_pair(apply(sk0_17,sk0_18),apply(sk0_16,apply(sk0_17,sk0_18))),sk0_16)|~spl0_2),
% 0.15/0.37 inference(resolution,[status(thm)],[f169,f173])).
% 0.15/0.37 fof(f246,plain,(
% 0.15/0.37 ~spl0_8|~spl0_9|spl0_13|~spl0_2),
% 0.15/0.37 inference(split_clause,[status(thm)],[f245,f204,f207,f242,f168])).
% 0.15/0.37 fof(f264,plain,(
% 0.15/0.37 spl0_16 <=> ~relation(X0)|in(ordered_pair(X1,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(X0,sk0_16))|~in(ordered_pair(X1,apply(sk0_17,sk0_18)),X0)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f265,plain,(
% 0.15/0.37 ![X0,X1]: (~relation(X0)|in(ordered_pair(X1,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(X0,sk0_16))|~in(ordered_pair(X1,apply(sk0_17,sk0_18)),X0)|~spl0_16)),
% 0.15/0.37 inference(component_clause,[status(thm)],[f264])).
% 0.15/0.37 fof(f267,plain,(
% 0.15/0.37 ![X0,X1]: (~relation(X0)|~relation(sk0_16)|in(ordered_pair(X1,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(X0,sk0_16))|~in(ordered_pair(X1,apply(sk0_17,sk0_18)),X0)|~spl0_13)),
% 0.15/0.37 inference(resolution,[status(thm)],[f183,f243])).
% 0.15/0.37 fof(f268,plain,(
% 0.15/0.37 spl0_16|~spl0_8|~spl0_13),
% 0.15/0.37 inference(split_clause,[status(thm)],[f267,f264,f204,f242])).
% 0.15/0.37 fof(f274,plain,(
% 0.15/0.37 spl0_18 <=> in(ordered_pair(sk0_18,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(sk0_17,sk0_16))),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f275,plain,(
% 0.15/0.37 in(ordered_pair(sk0_18,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(sk0_17,sk0_16))|~spl0_18),
% 0.15/0.37 inference(component_clause,[status(thm)],[f274])).
% 0.15/0.37 fof(f277,plain,(
% 0.15/0.37 ~relation(sk0_17)|in(ordered_pair(sk0_18,apply(sk0_16,apply(sk0_17,sk0_18))),relation_composition(sk0_17,sk0_16))|~spl0_16|~spl0_12),
% 0.15/0.37 inference(resolution,[status(thm)],[f265,f237])).
% 0.15/0.37 fof(f278,plain,(
% 0.15/0.37 ~spl0_6|spl0_18|~spl0_16|~spl0_12),
% 0.15/0.37 inference(split_clause,[status(thm)],[f277,f198,f274,f264,f236])).
% 0.15/0.37 fof(f289,plain,(
% 0.15/0.37 ~relation(relation_composition(sk0_17,sk0_16))|in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))|~spl0_18),
% 0.15/0.37 inference(resolution,[status(thm)],[f275,f177])).
% 0.15/0.37 fof(f290,plain,(
% 0.15/0.37 ~spl0_3|spl0_0|~spl0_18),
% 0.15/0.37 inference(split_clause,[status(thm)],[f289,f187,f161,f274])).
% 0.15/0.37 fof(f308,plain,(
% 0.15/0.37 spl0_23 <=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f309,plain,(
% 0.15/0.37 in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)|~spl0_23),
% 0.15/0.37 inference(component_clause,[status(thm)],[f308])).
% 0.15/0.37 fof(f311,plain,(
% 0.15/0.37 ~relation(sk0_17)|~relation(sk0_16)|in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)|~spl0_5),
% 0.15/0.37 inference(resolution,[status(thm)],[f184,f194])).
% 0.15/0.37 fof(f312,plain,(
% 0.15/0.37 ~spl0_6|~spl0_8|spl0_23|~spl0_5),
% 0.15/0.37 inference(split_clause,[status(thm)],[f311,f198,f204,f308,f193])).
% 0.15/0.37 fof(f323,plain,(
% 0.15/0.37 spl0_26 <=> in(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),relation_dom(sk0_16))),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f324,plain,(
% 0.15/0.37 in(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),relation_dom(sk0_16))|~spl0_26),
% 0.15/0.37 inference(component_clause,[status(thm)],[f323])).
% 0.15/0.37 fof(f326,plain,(
% 0.15/0.37 ~relation(sk0_16)|in(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),relation_dom(sk0_16))|~spl0_23),
% 0.15/0.37 inference(resolution,[status(thm)],[f309,f177])).
% 0.15/0.37 fof(f327,plain,(
% 0.15/0.37 ~spl0_8|spl0_26|~spl0_23),
% 0.15/0.37 inference(split_clause,[status(thm)],[f326,f204,f323,f308])).
% 0.15/0.37 fof(f340,plain,(
% 0.15/0.37 spl0_29 <=> in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f341,plain,(
% 0.15/0.37 in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17)|~spl0_29),
% 0.15/0.37 inference(component_clause,[status(thm)],[f340])).
% 0.15/0.37 fof(f343,plain,(
% 0.15/0.37 ~relation(sk0_17)|~relation(sk0_16)|in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17)|~spl0_5),
% 0.15/0.37 inference(resolution,[status(thm)],[f185,f194])).
% 0.15/0.37 fof(f344,plain,(
% 0.15/0.37 ~spl0_6|~spl0_8|spl0_29|~spl0_5),
% 0.15/0.37 inference(split_clause,[status(thm)],[f343,f198,f204,f340,f193])).
% 0.15/0.37 fof(f352,plain,(
% 0.15/0.37 spl0_31 <=> sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)=apply(sk0_17,sk0_18)),
% 0.15/0.37 introduced(split_symbol_definition)).
% 0.15/0.37 fof(f353,plain,(
% 0.15/0.37 sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)=apply(sk0_17,sk0_18)|~spl0_31),
% 0.15/0.37 inference(component_clause,[status(thm)],[f352])).
% 0.15/0.37 fof(f355,plain,(
% 0.15/0.37 ~relation(sk0_17)|~function(sk0_17)|sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)=apply(sk0_17,sk0_18)|~spl0_29),
% 0.15/0.37 inference(resolution,[status(thm)],[f341,f182])).
% 0.15/0.37 fof(f356,plain,(
% 0.15/0.37 ~spl0_6|~spl0_7|spl0_31|~spl0_29),
% 0.15/0.37 inference(split_clause,[status(thm)],[f355,f198,f201,f352,f340])).
% 0.15/0.37 fof(f357,plain,(
% 0.15/0.37 ~relation(sk0_17)|in(sk0_18,relation_dom(sk0_17))|~spl0_29),
% 0.15/0.37 inference(resolution,[status(thm)],[f341,f177])).
% 0.15/0.37 fof(f358,plain,(
% 0.15/0.37 ~spl0_6|spl0_1|~spl0_29),
% 0.15/0.37 inference(split_clause,[status(thm)],[f357,f198,f164,f340])).
% 0.15/0.37 fof(f366,plain,(
% 0.15/0.37 in(apply(sk0_17,sk0_18),relation_dom(sk0_16))|~spl0_31|~spl0_26),
% 0.15/0.37 inference(backward_demodulation,[status(thm)],[f353,f324])).
% 0.15/0.37 fof(f367,plain,(
% 0.15/0.37 spl0_2|~spl0_31|~spl0_26),
% 0.15/0.37 inference(split_clause,[status(thm)],[f366,f168,f352,f323])).
% 0.15/0.37 fof(f372,plain,(
% 0.15/0.37 $false),
% 0.15/0.37 inference(sat_refutation,[status(thm)],[f167,f171,f172,f197,f211,f214,f216,f218,f220,f232,f235,f240,f246,f268,f278,f290,f312,f327,f344,f356,f358,f367])).
% 0.15/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.32/0.60 % Elapsed time: 0.055948 seconds
% 0.32/0.60 % CPU time: 0.114256 seconds
% 0.32/0.60 % Memory used: 16.039 MB
%------------------------------------------------------------------------------