%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:21:56 PM UTC 2026
% Result : Theorem 0.87s 0.79s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 05:56:21 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.87/0.79 % Refutation found
% 0.87/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.87/0.79 % SZS output start CNFRefutation for theBenchmark
% 0.87/0.79 fof(f2,axiom,(
% 0.87/0.79 (! [A] :( empty(A)=> relation(A) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f4,axiom,(
% 0.87/0.79 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f6,axiom,(
% 0.87/0.79 (! [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) ) )) )) ) )) )) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f11,axiom,(
% 0.87/0.79 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f12,axiom,(
% 0.87/0.79 (! [A] : relation(identity_relation(A)) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f22,axiom,(
% 0.87/0.79 (? [A] :( empty(A)& relation(A) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f23,axiom,(
% 0.87/0.79 (? [A] : empty(A) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f29,conjecture,(
% 0.87/0.79 (! [A,B,C,D] :( relation(D)=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))<=> ( in(A,C)& in(ordered_pair(A,B),D) ) ) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f30,negated_conjecture,(
% 0.87/0.79 ~((! [A,B,C,D] :( relation(D)=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))<=> ( in(A,C)& in(ordered_pair(A,B),D) ) ) ) ))),
% 0.87/0.79 inference(negated_conjecture,[status(cth)],[f29])).
% 0.87/0.79 fof(f31,axiom,(
% 0.87/0.79 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.87/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.87/0.79 fof(f35,plain,(
% 0.87/0.79 ![A]: (~empty(A)|relation(A))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.87/0.79 fof(f36,plain,(
% 0.87/0.79 ![X0]: (~empty(X0)|relation(X0))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f35])).
% 0.87/0.79 fof(f38,plain,(
% 0.87/0.79 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.87/0.79 fof(f39,plain,(
% 0.87/0.79 ![A,B]: (~relation(B)|((~B=identity_relation(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|(in(C,A)&C=D))&(in(ordered_pair(C,D),B)|(~in(C,A)|~C=D)))))&(B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D)))))))),
% 0.87/0.79 inference(NNF_transformation,[status(thm)],[f38])).
% 0.87/0.79 fof(f40,plain,(
% 0.87/0.79 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D))))))))),
% 0.87/0.79 inference(miniscoping,[status(thm)],[f39])).
% 0.87/0.79 fof(f41,plain,(
% 0.87/0.79 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(~in(sK0_skl(A,B),A)|~sK0_skl(A,B)=sK1_skl(A,B)))&(in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(in(sK0_skl(A,B),A)&sK0_skl(A,B)=sK1_skl(A,B))))))))),
% 0.87/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f40])).
% 0.87/0.79 fof(f42,plain,(
% 0.87/0.79 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|~in(ordered_pair(X2,X3),X0)|in(X2,X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f41])).
% 0.87/0.79 fof(f43,plain,(
% 0.87/0.79 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|~in(ordered_pair(X2,X3),X0)|X2=X3)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f41])).
% 0.87/0.79 fof(f44,plain,(
% 0.87/0.79 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|in(ordered_pair(X2,X3),X0)|~in(X2,X1)|~X2=X3)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f41])).
% 0.87/0.79 fof(f46,plain,(
% 0.87/0.79 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|in(sK0_skl(X1,X0),X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f41])).
% 0.87/0.79 fof(f47,plain,(
% 0.87/0.79 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f41])).
% 0.87/0.79 fof(f49,plain,(
% 0.87/0.79 ![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)))))))))))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.87/0.79 fof(f50,plain,(
% 0.87/0.79 ![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)))))))))))))),
% 0.87/0.79 inference(NNF_transformation,[status(thm)],[f49])).
% 0.87/0.79 fof(f51,plain,(
% 0.87/0.79 ![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)))))))))))))),
% 0.87/0.79 inference(miniscoping,[status(thm)],[f50])).
% 0.87/0.79 fof(f52,plain,(
% 0.87/0.79 ![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,sK2_skl(E,D,C,B,A)),A)&in(ordered_pair(sK2_skl(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(sK3_skl(C,B,A),sK4_skl(C,B,A)),C)|(![F]: (~in(ordered_pair(sK3_skl(C,B,A),F),A)|~in(ordered_pair(F,sK4_skl(C,B,A)),B))))&(in(ordered_pair(sK3_skl(C,B,A),sK4_skl(C,B,A)),C)|(in(ordered_pair(sK3_skl(C,B,A),sK5_skl(C,B,A)),A)&in(ordered_pair(sK5_skl(C,B,A),sK4_skl(C,B,A)),B)))))))))))),
% 0.87/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(F,sK2_skl(E,D,C,B,A)),skolemize(D,sK3_skl(C,B,A)),skolemize(E,sK4_skl(C,B,A)),skolemize(F,sK5_skl(C,B,A))],[f51])).
% 0.87/0.79 fof(f53,plain,(
% 0.87/0.79 ![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,sK2_skl(X4,X3,X2,X1,X0)),X0))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f54,plain,(
% 0.87/0.79 ![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(sK2_skl(X4,X3,X2,X1,X0),X4),X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f55,plain,(
% 0.87/0.79 ![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))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f56,plain,(
% 0.87/0.79 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~relation(X2)|X2=relation_composition(X0,X1)|~in(ordered_pair(sK3_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X2)|~in(ordered_pair(sK3_skl(X2,X1,X0),X3),X0)|~in(ordered_pair(X3,sK4_skl(X2,X1,X0)),X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f57,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|~relation(X2)|X2=relation_composition(X0,X1)|in(ordered_pair(sK3_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X2)|in(ordered_pair(sK3_skl(X2,X1,X0),sK5_skl(X2,X1,X0)),X0))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f58,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|~relation(X2)|X2=relation_composition(X0,X1)|in(ordered_pair(sK3_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X2)|in(ordered_pair(sK5_skl(X2,X1,X0),sK4_skl(X2,X1,X0)),X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f52])).
% 0.87/0.79 fof(f59,plain,(
% 0.87/0.79 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.87/0.79 fof(f60,plain,(
% 0.87/0.79 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f59])).
% 0.87/0.79 fof(f61,plain,(
% 0.87/0.79 ![X0]: (relation(identity_relation(X0)))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f12])).
% 0.87/0.79 fof(f76,plain,(
% 0.87/0.79 (empty(sK7_skl)&relation(sK7_skl))),
% 0.87/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f22])).
% 0.87/0.79 fof(f77,plain,(
% 0.87/0.79 empty(sK7_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f76])).
% 0.87/0.79 fof(f78,plain,(
% 0.87/0.79 relation(sK7_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f76])).
% 0.87/0.79 fof(f79,plain,(
% 0.87/0.79 empty(sK8_skl)),
% 0.87/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f23])).
% 0.87/0.79 fof(f80,plain,(
% 0.87/0.79 empty(sK8_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f79])).
% 0.87/0.79 fof(f92,plain,(
% 0.87/0.79 (?[A,B,C,D]: (relation(D)&(in(ordered_pair(A,B),relation_composition(identity_relation(C),D))<~>(in(A,C)&in(ordered_pair(A,B),D)))))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.87/0.79 fof(f93,plain,(
% 0.87/0.79 ?[A,B,C,D]: (relation(D)&((in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|(in(A,C)&in(ordered_pair(A,B),D)))&(~in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|(~in(A,C)|~in(ordered_pair(A,B),D)))))),
% 0.87/0.79 inference(NNF_transformation,[status(thm)],[f92])).
% 0.87/0.79 fof(f94,plain,(
% 0.87/0.79 ?[D]: (relation(D)&(?[A,B,C]: ((in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|(in(A,C)&in(ordered_pair(A,B),D)))&(~in(ordered_pair(A,B),relation_composition(identity_relation(C),D))|(~in(A,C)|~in(ordered_pair(A,B),D))))))),
% 0.87/0.79 inference(miniscoping,[status(thm)],[f93])).
% 0.87/0.79 fof(f95,plain,(
% 0.87/0.79 (relation(sK11_skl)&((in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|(in(sK12_skl,sK14_skl)&in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)))&(~in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|(~in(sK12_skl,sK14_skl)|~in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)))))),
% 0.87/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(D,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl),skolemize(C,sK14_skl)],[f94])).
% 0.87/0.79 fof(f96,plain,(
% 0.87/0.79 relation(sK11_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f95])).
% 0.87/0.79 fof(f97,plain,(
% 0.87/0.79 in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|in(sK12_skl,sK14_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f95])).
% 0.87/0.79 fof(f98,plain,(
% 0.87/0.79 in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f95])).
% 0.87/0.79 fof(f99,plain,(
% 0.87/0.79 ~in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|~in(sK12_skl,sK14_skl)|~in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f95])).
% 0.87/0.79 fof(f100,plain,(
% 0.87/0.79 ![A,B]: (~in(A,B)|~empty(B))),
% 0.87/0.79 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.87/0.79 fof(f101,plain,(
% 0.87/0.79 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.87/0.79 inference(miniscoping,[status(thm)],[f100])).
% 0.87/0.79 fof(f102,plain,(
% 0.87/0.79 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.87/0.79 inference(cnf_transformation,[status(thm)],[f101])).
% 0.87/0.79 fof(f106,definition,(
% 0.87/0.79 sQ0_spl <=> (in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl)))),
% 0.87/0.79 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.87/0.79 fof(f107,plain,(
% 0.87/0.79 in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|~sQ0_spl),
% 0.87/0.79 inference(component_clause,[status(thm)],[f106])).
% 0.87/0.79 fof(f108,plain,(
% 0.87/0.79 ~in(ordered_pair(sK12_skl,sK13_skl),relation_composition(identity_relation(sK14_skl),sK11_skl))|sQ0_spl),
% 0.87/0.79 inference(component_clause,[status(thm)],[f106])).
% 0.87/0.79 fof(f109,definition,(
% 0.87/0.79 sQ1_spl <=> (in(sK12_skl,sK14_skl))),
% 0.87/0.79 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.87/0.79 fof(f111,plain,(
% 0.87/0.79 ~in(sK12_skl,sK14_skl)|sQ1_spl),
% 0.87/0.79 inference(component_clause,[status(thm)],[f109])).
% 0.87/0.79 fof(f112,plain,(
% 0.87/0.79 sQ0_spl|sQ1_spl),
% 0.87/0.79 inference(split_clause,[status(thm)],[f97,f106,f109])).
% 0.87/0.79 fof(f113,definition,(
% 0.87/0.79 sQ2_spl <=> (in(ordered_pair(sK12_skl,sK13_skl),sK11_skl))),
% 0.87/0.79 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.87/0.79 fof(f114,plain,(
% 0.87/0.79 in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)|~sQ2_spl),
% 0.87/0.79 inference(component_clause,[status(thm)],[f113])).
% 0.87/0.79 fof(f115,plain,(
% 0.87/0.79 ~in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)|sQ2_spl),
% 0.87/0.79 inference(component_clause,[status(thm)],[f113])).
% 0.87/0.79 fof(f116,plain,(
% 0.87/0.79 sQ0_spl|sQ2_spl),
% 0.87/0.79 inference(split_clause,[status(thm)],[f98,f106,f113])).
% 0.87/0.79 fof(f117,plain,(
% 0.87/0.79 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.87/0.79 inference(split_clause,[status(thm)],[f99,f106,f109,f113])).
% 0.87/0.79 fof(f118,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~relation(identity_relation(X0))|~in(ordered_pair(X1,X2),identity_relation(X0))|in(X1,X0))),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f42])).
% 0.87/0.79 fof(f119,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~relation(identity_relation(X0))|~in(ordered_pair(X1,X2),identity_relation(X0))|X1=X2)),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f43])).
% 0.87/0.79 fof(f120,plain,(
% 0.87/0.79 ![X0,X1]: (~relation(identity_relation(X0))|in(ordered_pair(X1,X1),identity_relation(X0))|~in(X1,X0))),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f44])).
% 0.87/0.79 fof(f121,plain,(
% 0.87/0.79 ![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,sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f53])).
% 0.87/0.79 fof(f122,plain,(
% 0.87/0.79 ![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(sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f54])).
% 0.87/0.79 fof(f123,plain,(
% 0.87/0.79 ![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))),
% 0.87/0.79 inference(destructive_equality_resolution,[status(thm)],[f55])).
% 0.87/0.79 fof(f130,plain,(
% 0.87/0.79 ![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))),
% 0.87/0.79 inference(forward_subsumption_resolution,[status(thm)],[f123,f60])).
% 0.87/0.79 fof(f132,plain,(
% 0.87/0.79 ![X0,X1]: (in(ordered_pair(X0,X0),identity_relation(X1))|~in(X0,X1))),
% 0.87/0.79 inference(backward_subsumption_resolution,[status(thm)],[f120,f61])).
% 0.87/0.79 fof(f133,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~in(ordered_pair(X0,X1),identity_relation(X2))|X0=X1)),
% 0.87/0.79 inference(backward_subsumption_resolution,[status(thm)],[f119,f61])).
% 0.87/0.79 fof(f134,plain,(
% 0.87/0.79 ![X0,X1,X2]: (~in(ordered_pair(X0,X1),identity_relation(X2))|in(X0,X2))),
% 0.87/0.80 inference(backward_subsumption_resolution,[status(thm)],[f118,f61])).
% 0.87/0.80 fof(f136,plain,(
% 0.87/0.80 relation(sK8_skl)),
% 0.87/0.80 inference(resolution,[status(thm)],[f80,f36])).
% 0.87/0.80 fof(f164,plain,(
% 0.87/0.80 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(X2,sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f121,f60])).
% 0.87/0.80 fof(f167,plain,(
% 0.87/0.80 ~relation(identity_relation(sK14_skl))|~relation(sK11_skl)|in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl))|~sQ0_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f164,f107])).
% 0.87/0.80 fof(f171,definition,(
% 0.87/0.80 sQ3_spl <=> (relation(identity_relation(sK14_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f173,plain,(
% 0.87/0.80 ~relation(identity_relation(sK14_skl))|sQ3_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f171])).
% 0.87/0.80 fof(f174,definition,(
% 0.87/0.80 sQ4_spl <=> (relation(sK11_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f176,plain,(
% 0.87/0.80 ~relation(sK11_skl)|sQ4_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f174])).
% 0.87/0.80 fof(f177,definition,(
% 0.87/0.80 sQ5_spl <=> (in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f178,plain,(
% 0.87/0.80 in(ordered_pair(sK12_skl,sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))),identity_relation(sK14_skl))|~sQ5_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f177])).
% 0.87/0.80 fof(f180,plain,(
% 0.87/0.80 ~sQ3_spl|~sQ4_spl|sQ5_spl|~sQ0_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f167,f171,f174,f177,f106])).
% 0.87/0.80 fof(f182,plain,(
% 0.87/0.80 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(sK2_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f122,f60])).
% 0.87/0.80 fof(f185,plain,(
% 0.87/0.80 ~relation(identity_relation(sK14_skl))|~relation(sK11_skl)|in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl)|~sQ0_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f182,f107])).
% 0.87/0.80 fof(f189,definition,(
% 0.87/0.80 sQ6_spl <=> (in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f190,plain,(
% 0.87/0.80 in(ordered_pair(sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl)),sK13_skl),sK11_skl)|~sQ6_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f189])).
% 0.87/0.80 fof(f192,plain,(
% 0.87/0.80 ~sQ3_spl|~sQ4_spl|sQ6_spl|~sQ0_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f185,f171,f174,f189,f106])).
% 0.87/0.80 fof(f194,plain,(
% 0.87/0.80 $false|sQ4_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f176,f96])).
% 0.87/0.80 fof(f195,plain,(
% 0.87/0.80 sQ4_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f194])).
% 0.87/0.80 fof(f196,plain,(
% 0.87/0.80 $false|sQ3_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f173,f61])).
% 0.87/0.80 fof(f197,plain,(
% 0.87/0.80 sQ3_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f196])).
% 0.87/0.80 fof(f200,plain,(
% 0.87/0.80 sK12_skl=sK2_skl(sK13_skl,sK12_skl,relation_composition(identity_relation(sK14_skl),sK11_skl),sK11_skl,identity_relation(sK14_skl))|~sQ5_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f178,f133])).
% 0.87/0.80 fof(f201,plain,(
% 0.87/0.80 in(sK12_skl,sK14_skl)|~sQ5_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f178,f134])).
% 0.87/0.80 fof(f204,plain,(
% 0.87/0.80 $false|sQ1_spl|~sQ5_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f201,f111])).
% 0.87/0.80 fof(f205,plain,(
% 0.87/0.80 sQ1_spl|~sQ5_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f204])).
% 0.87/0.80 fof(f206,plain,(
% 0.87/0.80 ![X0]: (~relation(identity_relation(sK14_skl))|~relation(sK11_skl)|~in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl))|~in(ordered_pair(X0,sK13_skl),sK11_skl)|sQ0_spl)),
% 0.87/0.80 inference(resolution,[status(thm)],[f108,f130])).
% 0.87/0.80 fof(f207,definition,(
% 0.87/0.80 ![X0]: (sQ7_spl <=> (~in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl))|~in(ordered_pair(X0,sK13_skl),sK11_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f208,plain,(
% 0.87/0.80 ![X0]: (~in(ordered_pair(sK12_skl,X0),identity_relation(sK14_skl))|~in(ordered_pair(X0,sK13_skl),sK11_skl)|~sQ7_spl)),
% 0.87/0.80 inference(component_clause,[status(thm)],[f207])).
% 0.87/0.80 fof(f210,plain,(
% 0.87/0.80 ~sQ3_spl|~sQ4_spl|sQ7_spl|sQ0_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f206,f171,f174,f207,f106])).
% 0.87/0.80 fof(f213,plain,(
% 0.87/0.80 ~in(ordered_pair(sK12_skl,sK12_skl),identity_relation(sK14_skl))|~sQ2_spl|~sQ7_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f114,f208])).
% 0.87/0.80 fof(f216,plain,(
% 0.87/0.80 ![X0]: (~in(X0,sK8_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f102,f80])).
% 0.87/0.80 fof(f219,plain,(
% 0.87/0.80 ![X0]: (~in(X0,sK7_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f102,f77])).
% 0.87/0.80 fof(f220,plain,(
% 0.87/0.80 ![X0]: (~relation(X0)|sK8_skl=relation_composition(X0,sK8_skl)|in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,X0),sK4_skl(sK8_skl,sK8_skl,X0)),sK8_skl)|in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,X0),sK5_skl(sK8_skl,sK8_skl,X0)),X0))),
% 0.87/0.80 inference(resolution,[status(thm)],[f57,f136])).
% 0.87/0.80 fof(f224,plain,(
% 0.87/0.80 ![X0]: (~relation(X0)|sK7_skl=relation_composition(X0,sK7_skl)|in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,X0),sK4_skl(sK7_skl,sK7_skl,X0)),sK7_skl)|in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,X0),sK5_skl(sK7_skl,sK7_skl,X0)),X0))),
% 0.87/0.80 inference(resolution,[status(thm)],[f57,f78])).
% 0.87/0.80 fof(f259,plain,(
% 0.87/0.80 ![X0]: (~relation(X0)|sK11_skl=relation_composition(X0,sK11_skl)|in(ordered_pair(sK3_skl(sK11_skl,sK11_skl,X0),sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl)|in(ordered_pair(sK5_skl(sK11_skl,sK11_skl,X0),sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f58,f96])).
% 0.87/0.80 fof(f276,plain,(
% 0.87/0.80 ~in(sK12_skl,sK14_skl)|~sQ2_spl|~sQ7_spl),
% 0.87/0.80 inference(resolution,[status(thm)],[f213,f132])).
% 0.87/0.80 fof(f277,plain,(
% 0.87/0.80 ~sQ1_spl|~sQ2_spl|~sQ7_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f276,f109,f113,f207])).
% 0.87/0.80 fof(f278,plain,(
% 0.87/0.80 in(ordered_pair(sK12_skl,sK13_skl),sK11_skl)|~sQ5_spl|~sQ6_spl),
% 0.87/0.80 inference(forward_demodulation,[status(thm)],[f200,f190])).
% 0.87/0.80 fof(f360,plain,(
% 0.87/0.80 ![X0]: (~relation(sK8_skl)|sK8_skl=identity_relation(X0)|sK0_skl(X0,sK8_skl)=sK1_skl(X0,sK8_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f216,f47])).
% 0.87/0.80 fof(f361,plain,(
% 0.87/0.80 ![X0]: (~relation(sK8_skl)|sK8_skl=identity_relation(X0)|in(sK0_skl(X0,sK8_skl),X0))),
% 0.87/0.80 inference(resolution,[status(thm)],[f216,f46])).
% 0.87/0.80 fof(f362,definition,(
% 0.87/0.80 sQ22_spl <=> (relation(sK8_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f364,plain,(
% 0.87/0.80 ~relation(sK8_skl)|sQ22_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f362])).
% 0.87/0.80 fof(f365,definition,(
% 0.87/0.80 ![X0]: (sQ23_spl <=> (sK8_skl=identity_relation(X0)|sK0_skl(X0,sK8_skl)=sK1_skl(X0,sK8_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f368,plain,(
% 0.87/0.80 ~sQ22_spl|sQ23_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f360,f362,f365])).
% 0.87/0.80 fof(f369,definition,(
% 0.87/0.80 ![X0]: (sQ24_spl <=> (sK8_skl=identity_relation(X0)|in(sK0_skl(X0,sK8_skl),X0)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f372,plain,(
% 0.87/0.80 ~sQ22_spl|sQ24_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f361,f362,f369])).
% 0.87/0.80 fof(f373,plain,(
% 0.87/0.80 $false|sQ22_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f364,f136])).
% 0.87/0.80 fof(f374,plain,(
% 0.87/0.80 sQ22_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f373])).
% 0.87/0.80 fof(f375,plain,(
% 0.87/0.80 ![X0]: (~relation(sK7_skl)|sK7_skl=identity_relation(X0)|sK0_skl(X0,sK7_skl)=sK1_skl(X0,sK7_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f219,f47])).
% 0.87/0.80 fof(f376,plain,(
% 0.87/0.80 ![X0]: (~relation(sK7_skl)|sK7_skl=identity_relation(X0)|in(sK0_skl(X0,sK7_skl),X0))),
% 0.87/0.80 inference(resolution,[status(thm)],[f219,f46])).
% 0.87/0.80 fof(f377,definition,(
% 0.87/0.80 sQ25_spl <=> (relation(sK7_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f379,plain,(
% 0.87/0.80 ~relation(sK7_skl)|sQ25_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f377])).
% 0.87/0.80 fof(f380,definition,(
% 0.87/0.80 ![X0]: (sQ26_spl <=> (sK7_skl=identity_relation(X0)|sK0_skl(X0,sK7_skl)=sK1_skl(X0,sK7_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f383,plain,(
% 0.87/0.80 ~sQ25_spl|sQ26_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f375,f377,f380])).
% 0.87/0.80 fof(f384,definition,(
% 0.87/0.80 ![X0]: (sQ27_spl <=> (sK7_skl=identity_relation(X0)|in(sK0_skl(X0,sK7_skl),X0)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f387,plain,(
% 0.87/0.80 ~sQ25_spl|sQ27_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f376,f377,f384])).
% 0.87/0.80 fof(f388,plain,(
% 0.87/0.80 $false|sQ25_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f379,f78])).
% 0.87/0.80 fof(f389,plain,(
% 0.87/0.80 sQ25_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f388])).
% 0.87/0.80 fof(f390,plain,(
% 0.87/0.80 ![X0]: (~relation(X0)|sK8_skl=relation_composition(X0,sK8_skl)|in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,X0),sK5_skl(sK8_skl,sK8_skl,X0)),X0))),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f220,f216])).
% 0.87/0.80 fof(f391,plain,(
% 0.87/0.80 sK8_skl=relation_composition(sK8_skl,sK8_skl)|in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK8_skl),sK5_skl(sK8_skl,sK8_skl,sK8_skl)),sK8_skl)),
% 0.87/0.80 inference(resolution,[status(thm)],[f390,f136])).
% 0.87/0.80 fof(f393,plain,(
% 0.87/0.80 sK8_skl=relation_composition(sK7_skl,sK8_skl)|in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK7_skl),sK5_skl(sK8_skl,sK8_skl,sK7_skl)),sK7_skl)),
% 0.87/0.80 inference(resolution,[status(thm)],[f390,f78])).
% 0.87/0.80 fof(f399,definition,(
% 0.87/0.80 sQ28_spl <=> (sK8_skl=relation_composition(sK8_skl,sK8_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f402,definition,(
% 0.87/0.80 sQ29_spl <=> (in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK8_skl),sK5_skl(sK8_skl,sK8_skl,sK8_skl)),sK8_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f403,plain,(
% 0.87/0.80 in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK8_skl),sK5_skl(sK8_skl,sK8_skl,sK8_skl)),sK8_skl)|~sQ29_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f402])).
% 0.87/0.80 fof(f405,plain,(
% 0.87/0.80 sQ28_spl|sQ29_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f391,f399,f402])).
% 0.87/0.80 fof(f413,definition,(
% 0.87/0.80 sQ32_spl <=> (sK8_skl=relation_composition(sK7_skl,sK8_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f416,definition,(
% 0.87/0.80 sQ33_spl <=> (in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK7_skl),sK5_skl(sK8_skl,sK8_skl,sK7_skl)),sK7_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f417,plain,(
% 0.87/0.80 in(ordered_pair(sK3_skl(sK8_skl,sK8_skl,sK7_skl),sK5_skl(sK8_skl,sK8_skl,sK7_skl)),sK7_skl)|~sQ33_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f416])).
% 0.87/0.80 fof(f419,plain,(
% 0.87/0.80 sQ32_spl|sQ33_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f393,f413,f416])).
% 0.87/0.80 fof(f429,plain,(
% 0.87/0.80 $false|~sQ33_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f417,f219])).
% 0.87/0.80 fof(f430,plain,(
% 0.87/0.80 ~sQ33_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f429])).
% 0.87/0.80 fof(f431,plain,(
% 0.87/0.80 $false|~sQ29_spl),
% 0.87/0.80 inference(forward_subsumption_resolution,[status(thm)],[f403,f216])).
% 0.87/0.80 fof(f432,plain,(
% 0.87/0.80 ~sQ29_spl),
% 0.87/0.80 inference(contradiction_clause,[status(thm)],[f431])).
% 0.87/0.80 fof(f488,plain,(
% 0.87/0.80 ![X0,X1]: (~relation(X0)|sK11_skl=relation_composition(X0,sK11_skl)|in(ordered_pair(sK5_skl(sK11_skl,sK11_skl,X0),sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl)|~relation(X0)|~relation(sK11_skl)|~relation(sK11_skl)|sK11_skl=relation_composition(X0,sK11_skl)|~in(ordered_pair(sK3_skl(sK11_skl,sK11_skl,X0),X1),X0)|~in(ordered_pair(X1,sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl))),
% 0.87/0.80 inference(resolution,[status(thm)],[f259,f56])).
% 0.87/0.80 fof(f491,definition,(
% 0.87/0.80 ![X0,X1]: (sQ42_spl <=> (~relation(X0)|sK11_skl=relation_composition(X0,sK11_skl)|in(ordered_pair(sK5_skl(sK11_skl,sK11_skl,X0),sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl)|~relation(X0)|sK11_skl=relation_composition(X0,sK11_skl)|~in(ordered_pair(sK3_skl(sK11_skl,sK11_skl,X0),X1),X0)|~in(ordered_pair(X1,sK4_skl(sK11_skl,sK11_skl,X0)),sK11_skl)))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f494,plain,(
% 0.87/0.80 sQ42_spl|~sQ4_spl),
% 0.87/0.80 inference(split_clause,[status(thm)],[f488,f491,f174])).
% 0.87/0.80 fof(f552,definition,(
% 0.87/0.80 sQ48_spl <=> (in(ordered_pair(sK3_skl(sK9_skl,sK9_skl,sK8_skl),sK5_skl(sK9_skl,sK9_skl,sK8_skl)),sK8_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.87/0.80 fof(f553,plain,(
% 0.87/0.80 in(ordered_pair(sK3_skl(sK9_skl,sK9_skl,sK8_skl),sK5_skl(sK9_skl,sK9_skl,sK8_skl)),sK8_skl)|~sQ48_spl),
% 0.87/0.80 inference(component_clause,[status(thm)],[f552])).
% 0.87/0.80 fof(f572,definition,(
% 0.87/0.80 sQ54_spl <=> (in(ordered_pair(sK3_skl(sK9_skl,sK9_skl,sK7_skl),sK5_skl(sK9_skl,sK9_skl,sK7_skl)),sK7_skl))),
% 0.87/0.80 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.87/0.81 fof(f573,plain,(
% 0.87/0.81 in(ordered_pair(sK3_skl(sK9_skl,sK9_skl,sK7_skl),sK5_skl(sK9_skl,sK9_skl,sK7_skl)),sK7_skl)|~sQ54_spl),
% 0.87/0.81 inference(component_clause,[status(thm)],[f572])).
% 0.87/0.81 fof(f588,plain,(
% 0.87/0.81 $false|~sQ54_spl),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f573,f219])).
% 0.87/0.81 fof(f589,plain,(
% 0.87/0.81 ~sQ54_spl),
% 0.87/0.81 inference(contradiction_clause,[status(thm)],[f588])).
% 0.87/0.81 fof(f590,plain,(
% 0.87/0.81 $false|~sQ48_spl),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f553,f216])).
% 0.87/0.81 fof(f591,plain,(
% 0.87/0.81 ~sQ48_spl),
% 0.87/0.81 inference(contradiction_clause,[status(thm)],[f590])).
% 0.87/0.81 fof(f679,plain,(
% 0.87/0.81 ![X0]: (~relation(X0)|sK7_skl=relation_composition(X0,sK7_skl)|in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,X0),sK5_skl(sK7_skl,sK7_skl,X0)),X0))),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f224,f219])).
% 0.87/0.81 fof(f681,plain,(
% 0.87/0.81 sK7_skl=relation_composition(sK8_skl,sK7_skl)|in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK8_skl),sK5_skl(sK7_skl,sK7_skl,sK8_skl)),sK8_skl)),
% 0.87/0.81 inference(resolution,[status(thm)],[f679,f136])).
% 0.87/0.81 fof(f683,plain,(
% 0.87/0.81 sK7_skl=relation_composition(sK7_skl,sK7_skl)|in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK7_skl),sK5_skl(sK7_skl,sK7_skl,sK7_skl)),sK7_skl)),
% 0.87/0.81 inference(resolution,[status(thm)],[f679,f78])).
% 0.87/0.81 fof(f696,definition,(
% 0.87/0.81 sQ60_spl <=> (sK7_skl=relation_composition(sK8_skl,sK7_skl))),
% 0.87/0.81 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 0.87/0.81 fof(f699,definition,(
% 0.87/0.81 sQ61_spl <=> (in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK8_skl),sK5_skl(sK7_skl,sK7_skl,sK8_skl)),sK8_skl))),
% 0.87/0.81 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 0.87/0.81 fof(f700,plain,(
% 0.87/0.81 in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK8_skl),sK5_skl(sK7_skl,sK7_skl,sK8_skl)),sK8_skl)|~sQ61_spl),
% 0.87/0.81 inference(component_clause,[status(thm)],[f699])).
% 0.87/0.81 fof(f702,plain,(
% 0.87/0.81 sQ60_spl|sQ61_spl),
% 0.87/0.81 inference(split_clause,[status(thm)],[f681,f696,f699])).
% 0.87/0.81 fof(f710,definition,(
% 0.87/0.81 sQ64_spl <=> (sK7_skl=relation_composition(sK7_skl,sK7_skl))),
% 0.87/0.81 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 0.87/0.81 fof(f713,definition,(
% 0.87/0.81 sQ65_spl <=> (in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK7_skl),sK5_skl(sK7_skl,sK7_skl,sK7_skl)),sK7_skl))),
% 0.87/0.81 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 0.87/0.81 fof(f714,plain,(
% 0.87/0.81 in(ordered_pair(sK3_skl(sK7_skl,sK7_skl,sK7_skl),sK5_skl(sK7_skl,sK7_skl,sK7_skl)),sK7_skl)|~sQ65_spl),
% 0.87/0.81 inference(component_clause,[status(thm)],[f713])).
% 0.87/0.81 fof(f716,plain,(
% 0.87/0.81 sQ64_spl|sQ65_spl),
% 0.87/0.81 inference(split_clause,[status(thm)],[f683,f710,f713])).
% 0.87/0.81 fof(f726,plain,(
% 0.87/0.81 $false|~sQ65_spl),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f714,f219])).
% 0.87/0.81 fof(f727,plain,(
% 0.87/0.81 ~sQ65_spl),
% 0.87/0.81 inference(contradiction_clause,[status(thm)],[f726])).
% 0.87/0.81 fof(f728,plain,(
% 0.87/0.81 $false|~sQ61_spl),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f700,f216])).
% 0.87/0.81 fof(f729,plain,(
% 0.87/0.81 ~sQ61_spl),
% 0.87/0.81 inference(contradiction_clause,[status(thm)],[f728])).
% 0.87/0.81 fof(f780,plain,(
% 0.87/0.81 $false|sQ2_spl|~sQ5_spl|~sQ6_spl),
% 0.87/0.81 inference(forward_subsumption_resolution,[status(thm)],[f278,f115])).
% 0.87/0.81 fof(f781,plain,(
% 0.87/0.81 sQ2_spl|~sQ5_spl|~sQ6_spl),
% 0.87/0.81 inference(contradiction_clause,[status(thm)],[f780])).
% 0.87/0.81 fof(f782,plain,(
% 0.87/0.81 $false),
% 0.87/0.81 inference(sat_refutation,[status(thm)],[f112,f116,f117,f180,f192,f195,f197,f205,f210,f277,f368,f372,f374,f383,f387,f389,f405,f419,f430,f432,f494,f589,f591,f702,f716,f727,f729,f781])).
% 0.87/0.81 % SZS output end CNFRefutation for theBenchmark.p
% 0.87/0.81 % Elapsed time: 0.380190 seconds
% 0.87/0.81 % CPU time: 2.670104 seconds
% 0.87/0.81 % Total memory used: 135.902 MB
% 0.87/0.81 % Net memory used: 133.533 MB
%------------------------------------------------------------------------------