TSTP Solution File: SEU008+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:52 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 19:47:36 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.20/0.53 % Refutation found
% 0.20/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.53 fof(f4,axiom,(
% 0.20/0.53 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f5,axiom,(
% 0.20/0.53 (! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f7,axiom,(
% 0.20/0.53 (! [A] : relation(identity_relation(A)) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f10,axiom,(
% 0.20/0.53 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f15,axiom,(
% 0.20/0.53 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f17,axiom,(
% 0.20/0.53 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f21,axiom,(
% 0.20/0.53 (? [A] :( relation(A)& function(A) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f25,axiom,(
% 0.20/0.53 (? [A] :( ~ empty(A)& relation(A) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f28,axiom,(
% 0.20/0.53 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f31,axiom,(
% 0.20/0.53 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(B))=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) )) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f34,axiom,(
% 0.20/0.53 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f35,conjecture,(
% 0.20/0.53 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,set_intersection2(relation_dom(C),A))=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f36,negated_conjecture,(
% 0.20/0.53 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,set_intersection2(relation_dom(C),A))=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ) ))),
% 0.20/0.53 inference(negated_conjecture,[status(cth)],[f35])).
% 0.20/0.53 fof(f40,axiom,(
% 0.20/0.53 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.20/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.53 fof(f49,plain,(
% 0.20/0.53 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f4])).
% 0.20/0.53 fof(f50,plain,(
% 0.20/0.53 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.20/0.53 inference(NNF_transformation,[status(esa)],[f5])).
% 0.20/0.53 fof(f51,plain,(
% 0.20/0.53 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.20/0.53 inference(miniscoping,[status(esa)],[f50])).
% 0.20/0.53 fof(f52,plain,(
% 0.20/0.53 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|((~in(sk0_0(C,B,A),C)|(~in(sk0_0(C,B,A),A)|~in(sk0_0(C,B,A),B)))&(in(sk0_0(C,B,A),C)|(in(sk0_0(C,B,A),A)&in(sk0_0(C,B,A),B))))))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f51])).
% 0.20/0.53 fof(f53,plain,(
% 0.20/0.53 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f52])).
% 0.20/0.53 fof(f54,plain,(
% 0.20/0.53 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f52])).
% 0.20/0.53 fof(f55,plain,(
% 0.20/0.53 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|in(X3,X0)|~in(X3,X1)|~in(X3,X2))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f52])).
% 0.20/0.53 fof(f61,plain,(
% 0.20/0.53 ![X0]: (relation(identity_relation(X0)))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f7])).
% 0.20/0.53 fof(f67,plain,(
% 0.20/0.53 empty(empty_set)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f10])).
% 0.20/0.53 fof(f77,plain,(
% 0.20/0.53 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 0.20/0.53 inference(miniscoping,[status(esa)],[f15])).
% 0.20/0.53 fof(f79,plain,(
% 0.20/0.53 ![X0]: (function(identity_relation(X0)))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f77])).
% 0.20/0.53 fof(f82,plain,(
% 0.20/0.53 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.20/0.53 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.20/0.53 fof(f83,plain,(
% 0.20/0.53 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f82])).
% 0.20/0.53 fof(f92,plain,(
% 0.20/0.53 (relation(sk0_2)&function(sk0_2))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f21])).
% 0.20/0.53 fof(f93,plain,(
% 0.20/0.53 relation(sk0_2)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f92])).
% 0.20/0.53 fof(f94,plain,(
% 0.20/0.53 function(sk0_2)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f92])).
% 0.20/0.53 fof(f104,plain,(
% 0.20/0.53 (~empty(sk0_6)&relation(sk0_6))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f25])).
% 0.20/0.53 fof(f106,plain,(
% 0.20/0.53 relation(sk0_6)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f104])).
% 0.20/0.53 fof(f112,plain,(
% 0.20/0.53 (relation(sk0_9)&relation_empty_yielding(sk0_9))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f28])).
% 0.20/0.53 fof(f113,plain,(
% 0.20/0.53 relation(sk0_9)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f112])).
% 0.20/0.53 fof(f119,plain,(
% 0.20/0.53 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A))))))),
% 0.20/0.53 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 0.20/0.53 fof(f120,plain,(
% 0.20/0.53 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(![A]: (~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))))),
% 0.20/0.53 inference(miniscoping,[status(esa)],[f119])).
% 0.20/0.53 fof(f121,plain,(
% 0.20/0.53 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(X0))|apply(relation_composition(X0,X1),X2)=apply(X1,apply(X0,X2)))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f120])).
% 0.20/0.53 fof(f125,plain,(
% 0.20/0.53 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 0.20/0.53 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 0.20/0.53 fof(f126,plain,(
% 0.20/0.53 ![A,B]: ((~relation(B)|~function(B))|((~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C))))&(B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C))))))),
% 0.20/0.53 inference(NNF_transformation,[status(esa)],[f125])).
% 0.20/0.53 fof(f127,plain,(
% 0.20/0.53 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C)))))))),
% 0.20/0.53 inference(miniscoping,[status(esa)],[f126])).
% 0.20/0.53 fof(f128,plain,(
% 0.20/0.53 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(in(sk0_10(A,B),A)&~apply(B,sk0_10(A,B))=sk0_10(A,B)))))))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f127])).
% 0.20/0.53 fof(f129,plain,(
% 0.20/0.53 ![X0,X1]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|relation_dom(X0)=X1)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f128])).
% 0.20/0.53 fof(f130,plain,(
% 0.20/0.53 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|~in(X2,X1)|apply(X0,X2)=X2)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f128])).
% 0.20/0.53 fof(f133,plain,(
% 0.20/0.53 (?[A,B,C]: ((relation(C)&function(C))&(in(B,set_intersection2(relation_dom(C),A))&~apply(C,B)=apply(relation_composition(identity_relation(A),C),B))))),
% 0.20/0.53 inference(pre_NNF_transformation,[status(esa)],[f36])).
% 0.20/0.53 fof(f134,plain,(
% 0.20/0.53 ?[C]: ((relation(C)&function(C))&(?[A,B]: (in(B,set_intersection2(relation_dom(C),A))&~apply(C,B)=apply(relation_composition(identity_relation(A),C),B))))),
% 0.20/0.53 inference(miniscoping,[status(esa)],[f133])).
% 0.20/0.53 fof(f135,plain,(
% 0.20/0.53 ((relation(sk0_11)&function(sk0_11))&(in(sk0_13,set_intersection2(relation_dom(sk0_11),sk0_12))&~apply(sk0_11,sk0_13)=apply(relation_composition(identity_relation(sk0_12),sk0_11),sk0_13)))),
% 0.20/0.53 inference(skolemization,[status(esa)],[f134])).
% 0.20/0.53 fof(f136,plain,(
% 0.20/0.53 relation(sk0_11)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f135])).
% 0.20/0.53 fof(f137,plain,(
% 0.20/0.53 function(sk0_11)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f135])).
% 0.20/0.53 fof(f138,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(relation_dom(sk0_11),sk0_12))),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f135])).
% 0.20/0.53 fof(f139,plain,(
% 0.20/0.53 ~apply(sk0_11,sk0_13)=apply(relation_composition(identity_relation(sk0_12),sk0_11),sk0_13)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f135])).
% 0.20/0.53 fof(f150,plain,(
% 0.20/0.53 ![A]: (~empty(A)|A=empty_set)),
% 0.20/0.53 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 0.20/0.53 fof(f151,plain,(
% 0.20/0.53 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.20/0.53 inference(cnf_transformation,[status(esa)],[f150])).
% 0.20/0.53 fof(f158,plain,(
% 0.20/0.53 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X1))),
% 0.20/0.53 inference(destructive_equality_resolution,[status(esa)],[f53])).
% 0.20/0.53 fof(f159,plain,(
% 0.20/0.53 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
% 0.20/0.53 inference(destructive_equality_resolution,[status(esa)],[f54])).
% 0.20/0.53 fof(f160,plain,(
% 0.20/0.53 ![X0,X1,X2]: (in(X0,set_intersection2(X1,X2))|~in(X0,X1)|~in(X0,X2))),
% 0.20/0.53 inference(destructive_equality_resolution,[status(esa)],[f55])).
% 0.20/0.53 fof(f161,plain,(
% 0.20/0.53 ![X0]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 0.20/0.53 inference(destructive_equality_resolution,[status(esa)],[f129])).
% 0.20/0.53 fof(f162,plain,(
% 0.20/0.53 ![X0,X1]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 0.20/0.53 inference(destructive_equality_resolution,[status(esa)],[f130])).
% 0.20/0.53 fof(f166,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(sk0_12,relation_dom(sk0_11)))),
% 0.20/0.53 inference(paramodulation,[status(thm)],[f49,f138])).
% 0.20/0.53 fof(f168,plain,(
% 0.20/0.53 in(sk0_13,relation_dom(sk0_11))),
% 0.20/0.53 inference(resolution,[status(thm)],[f158,f138])).
% 0.20/0.53 fof(f172,plain,(
% 0.20/0.53 in(sk0_13,sk0_12)),
% 0.20/0.53 inference(resolution,[status(thm)],[f159,f138])).
% 0.20/0.53 fof(f175,plain,(
% 0.20/0.53 ![X0]: (in(sk0_13,set_intersection2(X0,relation_dom(sk0_11)))|~in(sk0_13,X0))),
% 0.20/0.53 inference(resolution,[status(thm)],[f160,f168])).
% 0.20/0.53 fof(f198,plain,(
% 0.20/0.53 ![X0]: (in(sk0_13,set_intersection2(X0,sk0_12))|~in(sk0_13,X0))),
% 0.20/0.53 inference(resolution,[status(thm)],[f172,f160])).
% 0.20/0.53 fof(f209,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(set_intersection2(sk0_12,relation_dom(sk0_11)),sk0_12))),
% 0.20/0.53 inference(resolution,[status(thm)],[f198,f166])).
% 0.20/0.53 fof(f210,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11))))),
% 0.20/0.53 inference(forward_demodulation,[status(thm)],[f49,f209])).
% 0.20/0.53 fof(f222,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11))),relation_dom(sk0_11)))),
% 0.20/0.53 inference(resolution,[status(thm)],[f210,f175])).
% 0.20/0.53 fof(f223,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(relation_dom(sk0_11),set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11)))))),
% 0.20/0.53 inference(forward_demodulation,[status(thm)],[f49,f222])).
% 0.20/0.53 fof(f258,plain,(
% 0.20/0.53 ![X0]: (in(sk0_13,set_intersection2(X0,set_intersection2(relation_dom(sk0_11),set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11))))))|~in(sk0_13,X0))),
% 0.20/0.53 inference(resolution,[status(thm)],[f223,f160])).
% 0.20/0.53 fof(f445,plain,(
% 0.20/0.53 spl0_0 <=> ~in(sk0_13,X0)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f446,plain,(
% 0.20/0.53 ![X0]: (~in(sk0_13,X0)|~spl0_0)),
% 0.20/0.53 inference(component_clause,[status(thm)],[f445])).
% 0.20/0.53 fof(f448,plain,(
% 0.20/0.53 spl0_1 <=> in(sk0_13,set_intersection2(relation_dom(sk0_11),set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11)))))),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f449,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(relation_dom(sk0_11),set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11)))))|~spl0_1),
% 0.20/0.53 inference(component_clause,[status(thm)],[f448])).
% 0.20/0.53 fof(f451,plain,(
% 0.20/0.53 ![X0]: (~in(sk0_13,X0)|in(sk0_13,set_intersection2(relation_dom(sk0_11),set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11))))))),
% 0.20/0.53 inference(resolution,[status(thm)],[f258,f159])).
% 0.20/0.53 fof(f452,plain,(
% 0.20/0.53 spl0_0|spl0_1),
% 0.20/0.53 inference(split_clause,[status(thm)],[f451,f445,f448])).
% 0.20/0.53 fof(f557,plain,(
% 0.20/0.53 $false|~spl0_0),
% 0.20/0.53 inference(backward_subsumption_resolution,[status(thm)],[f172,f446])).
% 0.20/0.53 fof(f558,plain,(
% 0.20/0.53 ~spl0_0),
% 0.20/0.53 inference(contradiction_clause,[status(thm)],[f557])).
% 0.20/0.53 fof(f560,plain,(
% 0.20/0.53 in(sk0_13,set_intersection2(sk0_12,set_intersection2(sk0_12,relation_dom(sk0_11))))|~spl0_1),
% 0.20/0.53 inference(resolution,[status(thm)],[f449,f159])).
% 0.20/0.53 fof(f567,plain,(
% 0.20/0.53 in(sk0_13,sk0_12)|~spl0_1),
% 0.20/0.53 inference(resolution,[status(thm)],[f560,f158])).
% 0.20/0.53 fof(f1374,plain,(
% 0.20/0.53 spl0_12 <=> relation(sk0_9)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1376,plain,(
% 0.20/0.53 ~relation(sk0_9)|spl0_12),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1374])).
% 0.20/0.53 fof(f1381,plain,(
% 0.20/0.53 spl0_13 <=> function(empty_set)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1383,plain,(
% 0.20/0.53 ~function(empty_set)|spl0_13),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1381])).
% 0.20/0.53 fof(f1398,plain,(
% 0.20/0.53 spl0_16 <=> relation(sk0_6)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1400,plain,(
% 0.20/0.53 ~relation(sk0_6)|spl0_16),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1398])).
% 0.20/0.53 fof(f1419,plain,(
% 0.20/0.53 spl0_19 <=> relation(sk0_2)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1421,plain,(
% 0.20/0.53 ~relation(sk0_2)|spl0_19),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1419])).
% 0.20/0.53 fof(f1426,plain,(
% 0.20/0.53 spl0_20 <=> function(sk0_2)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1428,plain,(
% 0.20/0.53 ~function(sk0_2)|spl0_20),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1426])).
% 0.20/0.53 fof(f1452,plain,(
% 0.20/0.53 spl0_22 <=> relation(sk0_11)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1454,plain,(
% 0.20/0.53 ~relation(sk0_11)|spl0_22),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1452])).
% 0.20/0.53 fof(f1459,plain,(
% 0.20/0.53 spl0_23 <=> function(sk0_11)),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1461,plain,(
% 0.20/0.53 ~function(sk0_11)|spl0_23),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1459])).
% 0.20/0.53 fof(f1473,plain,(
% 0.20/0.53 spl0_25 <=> ~relation(identity_relation(X0))),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1474,plain,(
% 0.20/0.53 ![X0]: (~relation(identity_relation(X0))|~spl0_25)),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1473])).
% 0.20/0.53 fof(f1506,plain,(
% 0.20/0.53 spl0_29 <=> ~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_11),X1)=apply(sk0_11,apply(X0,X1))),
% 0.20/0.53 introduced(split_symbol_definition)).
% 0.20/0.53 fof(f1507,plain,(
% 0.20/0.53 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_11),X1)=apply(sk0_11,apply(X0,X1))|~spl0_29)),
% 0.20/0.53 inference(component_clause,[status(thm)],[f1506])).
% 0.20/0.53 fof(f1509,plain,(
% 0.20/0.53 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(sk0_11)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_11),X1)=apply(sk0_11,apply(X0,X1)))),
% 0.20/0.53 inference(resolution,[status(thm)],[f121,f137])).
% 0.20/0.53 fof(f1510,plain,(
% 0.20/0.53 spl0_29|~spl0_22),
% 0.20/0.53 inference(split_clause,[status(thm)],[f1509,f1506,f1452])).
% 0.20/0.53 fof(f1513,plain,(
% 0.20/0.53 $false|spl0_22),
% 0.20/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1454,f136])).
% 0.20/0.53 fof(f1514,plain,(
% 0.20/0.53 spl0_22),
% 0.20/0.53 inference(contradiction_clause,[status(thm)],[f1513])).
% 0.20/0.53 fof(f1515,plain,(
% 0.20/0.53 $false|spl0_19),
% 0.20/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1421,f93])).
% 0.20/0.53 fof(f1516,plain,(
% 0.20/0.53 spl0_19),
% 0.20/0.53 inference(contradiction_clause,[status(thm)],[f1515])).
% 0.20/0.53 fof(f1517,plain,(
% 0.20/0.53 ![X0]: (~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 0.20/0.53 inference(forward_subsumption_resolution,[status(thm)],[f161,f61])).
% 0.20/0.53 fof(f1518,plain,(
% 0.20/0.53 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 0.20/0.53 inference(resolution,[status(thm)],[f1517,f79])).
% 0.20/0.53 fof(f1520,plain,(
% 0.20/0.53 ![X0]: (empty(identity_relation(X0))|~relation(identity_relation(X0))|~empty(X0))),
% 0.20/0.53 inference(paramodulation,[status(thm)],[f1518,f83])).
% 0.20/0.53 fof(f1521,plain,(
% 0.20/0.53 ![X0]: (empty(identity_relation(X0))|~empty(X0))),
% 0.20/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1520,f61])).
% 0.20/0.53 fof(f1525,plain,(
% 0.20/0.53 empty(identity_relation(empty_set))),
% 0.20/0.53 inference(resolution,[status(thm)],[f1521,f67])).
% 0.20/0.53 fof(f1530,plain,(
% 0.20/0.53 identity_relation(empty_set)=empty_set),
% 0.20/0.53 inference(resolution,[status(thm)],[f1525,f151])).
% 0.20/0.53 fof(f1537,plain,(
% 0.20/0.53 function(empty_set)),
% 0.20/0.53 inference(paramodulation,[status(thm)],[f1530,f79])).
% 0.20/0.54 fof(f1567,plain,(
% 0.20/0.54 ![X0,X1]: (~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f162,f61])).
% 0.20/0.54 fof(f1568,plain,(
% 0.20/0.54 ![X0,X1]: (~in(X0,X1)|apply(identity_relation(X1),X0)=X0)),
% 0.20/0.54 inference(resolution,[status(thm)],[f1567,f79])).
% 0.20/0.54 fof(f1575,plain,(
% 0.20/0.54 $false|spl0_13),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1383,f1537])).
% 0.20/0.54 fof(f1576,plain,(
% 0.20/0.54 spl0_13),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1575])).
% 0.20/0.54 fof(f1614,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(identity_relation(X0))|~in(X1,relation_dom(identity_relation(X0)))|apply(relation_composition(identity_relation(X0),sk0_11),X1)=apply(sk0_11,apply(identity_relation(X0),X1))|~spl0_29)),
% 0.20/0.54 inference(resolution,[status(thm)],[f1507,f79])).
% 0.20/0.54 fof(f1615,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(identity_relation(X0))|~in(X1,X0)|apply(relation_composition(identity_relation(X0),sk0_11),X1)=apply(sk0_11,apply(identity_relation(X0),X1))|~spl0_29)),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f1518,f1614])).
% 0.20/0.54 fof(f1616,plain,(
% 0.20/0.54 ![X0,X1]: (~in(X0,X1)|apply(relation_composition(identity_relation(X1),sk0_11),X0)=apply(sk0_11,apply(identity_relation(X1),X0))|~spl0_29)),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1615,f61])).
% 0.20/0.54 fof(f1629,plain,(
% 0.20/0.54 apply(relation_composition(identity_relation(sk0_12),sk0_11),sk0_13)=apply(sk0_11,apply(identity_relation(sk0_12),sk0_13))|~spl0_29|~spl0_1),
% 0.20/0.54 inference(resolution,[status(thm)],[f1616,f567])).
% 0.20/0.54 fof(f1677,plain,(
% 0.20/0.54 ~apply(sk0_11,sk0_13)=apply(sk0_11,apply(identity_relation(sk0_12),sk0_13))|~spl0_29|~spl0_1),
% 0.20/0.54 inference(backward_demodulation,[status(thm)],[f1629,f139])).
% 0.20/0.54 fof(f1728,plain,(
% 0.20/0.54 $false|spl0_20),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1428,f94])).
% 0.20/0.54 fof(f1729,plain,(
% 0.20/0.54 spl0_20),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1728])).
% 0.20/0.54 fof(f1755,plain,(
% 0.20/0.54 $false|spl0_23),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1461,f137])).
% 0.20/0.54 fof(f1756,plain,(
% 0.20/0.54 spl0_23),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1755])).
% 0.20/0.54 fof(f2075,plain,(
% 0.20/0.54 apply(identity_relation(sk0_12),sk0_13)=sk0_13|~spl0_1),
% 0.20/0.54 inference(resolution,[status(thm)],[f1568,f567])).
% 0.20/0.54 fof(f2518,plain,(
% 0.20/0.54 $false|spl0_12),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1376,f113])).
% 0.20/0.54 fof(f2519,plain,(
% 0.20/0.54 spl0_12),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f2518])).
% 0.20/0.54 fof(f2520,plain,(
% 0.20/0.54 $false|spl0_16),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1400,f106])).
% 0.20/0.54 fof(f2521,plain,(
% 0.20/0.54 spl0_16),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f2520])).
% 0.20/0.54 fof(f2522,plain,(
% 0.20/0.54 $false|~spl0_25),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1474,f61])).
% 0.20/0.54 fof(f2523,plain,(
% 0.20/0.54 ~spl0_25),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f2522])).
% 0.20/0.54 fof(f2609,plain,(
% 0.20/0.54 ~apply(sk0_11,sk0_13)=apply(sk0_11,sk0_13)|~spl0_29|~spl0_1),
% 0.20/0.54 inference(backward_demodulation,[status(thm)],[f2075,f1677])).
% 0.20/0.54 fof(f2610,plain,(
% 0.20/0.54 $false|~spl0_29|~spl0_1),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f2609])).
% 0.20/0.54 fof(f2611,plain,(
% 0.20/0.54 ~spl0_29|~spl0_1),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f2610])).
% 0.20/0.54 fof(f2612,plain,(
% 0.20/0.54 $false),
% 0.20/0.54 inference(sat_refutation,[status(thm)],[f452,f558,f1510,f1514,f1516,f1576,f1729,f1756,f2519,f2521,f2523,f2611])).
% 0.20/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.55 % Elapsed time: 0.189493 seconds
% 0.20/0.55 % CPU time: 1.397069 seconds
% 0.20/0.55 % Total memory used: 82.269 MB
% 0.20/0.55 % Net memory used: 81.234 MB
%------------------------------------------------------------------------------