%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU223+2 : 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 : n026.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 02:22:03 PM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:02:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.42 fof(f11,axiom,(
% 0.12/0.42 (! [A] :( relation(A)=> (! [B,C] :( relation(C)=> ( C = relation_dom_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(D,B)& in(ordered_pair(D,E),A) ) ) )) ) )) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f28,axiom,(
% 0.12/0.42 (! [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 ) ) ) )) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f29,axiom,(
% 0.12/0.42 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f69,axiom,(
% 0.12/0.42 (! [A,B] :( relation(A)=> relation(relation_dom_restriction(A,B)) ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f91,axiom,(
% 0.12/0.42 (! [A,B] :( ( relation(A)& function(A) )=> ( relation(relation_dom_restriction(A,B))& function(relation_dom_restriction(A,B)) ) ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f220,conjecture,(
% 0.12/0.42 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f221,negated_conjecture,(
% 0.12/0.42 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) ))),
% 0.12/0.42 inference(negated_conjecture,[status(cth)],[f220])).
% 0.12/0.42 fof(f233,lemma,(
% 0.12/0.42 (! [A,B] :( relation(B)=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f270,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![B,C]: (~relation(C)|(C=relation_dom_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(D,B)&in(ordered_pair(D,E),A))))))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.12/0.42 fof(f271,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![B,C]: (~relation(C)|((~C=relation_dom_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A))))))&(C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))))))))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f270])).
% 0.12/0.42 fof(f272,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))))))))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f271])).
% 0.12/0.42 fof(f273,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|((~in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C)|(~in(sK2_skl(B,C,A),B)|~in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)))&(in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C)|(in(sK2_skl(B,C,A),B)&in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A))))))))))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f272])).
% 0.12/0.42 fof(f275,plain,(
% 0.12/0.42 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_dom_restriction(X0,X2)|~in(ordered_pair(X3,X4),X1)|in(ordered_pair(X3,X4),X0))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f273])).
% 0.12/0.42 fof(f412,plain,(
% 0.12/0.42 ![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)))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.12/0.42 fof(f413,plain,(
% 0.12/0.42 ![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))))))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f412])).
% 0.12/0.42 fof(f414,plain,(
% 0.12/0.42 ![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)))))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f413])).
% 0.12/0.42 fof(f415,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f414])).
% 0.12/0.42 fof(f416,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f414])).
% 0.12/0.42 fof(f419,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.12/0.42 fof(f420,plain,(
% 0.12/0.42 ![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)))))))))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f419])).
% 0.12/0.42 fof(f421,plain,(
% 0.12/0.42 ![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)))))))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f420])).
% 0.12/0.42 fof(f422,plain,(
% 0.12/0.42 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK34_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK35_skl(B,A),B)|(![D]: ~in(ordered_pair(sK35_skl(B,A),D),A)))&(in(sK35_skl(B,A),B)|in(ordered_pair(sK35_skl(B,A),sK36_skl(B,A)),A)))))))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl]),skolemize(D,sK34_skl(C,B,A)),skolemize(C,sK35_skl(B,A)),skolemize(D,sK36_skl(B,A))],[f421])).
% 0.12/0.42 fof(f424,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f422])).
% 0.12/0.42 fof(f521,plain,(
% 0.12/0.42 ![A,B]: (~relation(A)|relation(relation_dom_restriction(A,B)))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f69])).
% 0.12/0.42 fof(f522,plain,(
% 0.12/0.42 ![A]: (~relation(A)|(![B]: relation(relation_dom_restriction(A,B))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f521])).
% 0.12/0.42 fof(f523,plain,(
% 0.12/0.42 ![X0,X1]: (~relation(X0)|relation(relation_dom_restriction(X0,X1)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f522])).
% 0.12/0.42 fof(f568,plain,(
% 0.12/0.42 ![A,B]: ((~relation(A)|~function(A))|(relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f91])).
% 0.12/0.42 fof(f569,plain,(
% 0.12/0.42 ![A]: ((~relation(A)|~function(A))|((![B]: relation(relation_dom_restriction(A,B)))&(![B]: function(relation_dom_restriction(A,B)))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f568])).
% 0.12/0.42 fof(f571,plain,(
% 0.12/0.42 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_dom_restriction(X0,X1)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f569])).
% 0.12/0.42 fof(f955,plain,(
% 0.12/0.42 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_dom_restriction(C,A)))&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f221])).
% 0.12/0.42 fof(f956,plain,(
% 0.12/0.42 ?[C]: ((relation(C)&function(C))&(?[A,B]: (in(B,relation_dom(relation_dom_restriction(C,A)))&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f955])).
% 0.12/0.42 fof(f957,plain,(
% 0.12/0.42 ((relation(sK79_skl)&function(sK79_skl))&(in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl)))&~apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)=apply(sK79_skl,sK81_skl)))),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK79_skl,sK80_skl,sK81_skl]),skolemize(C,sK79_skl),skolemize(A,sK80_skl),skolemize(B,sK81_skl)],[f956])).
% 0.12/0.42 fof(f958,plain,(
% 0.12/0.42 relation(sK79_skl)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f957])).
% 0.12/0.42 fof(f959,plain,(
% 0.12/0.42 function(sK79_skl)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f957])).
% 0.12/0.42 fof(f960,plain,(
% 0.12/0.42 in(sK81_skl,relation_dom(relation_dom_restriction(sK79_skl,sK80_skl)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f957])).
% 0.12/0.42 fof(f961,plain,(
% 0.12/0.42 ~apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)=apply(sK79_skl,sK81_skl)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f957])).
% 0.12/0.42 fof(f1002,plain,(
% 0.12/0.42 ![A,B]: (~relation(B)|relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f233])).
% 0.12/0.42 fof(f1003,plain,(
% 0.12/0.42 ![B]: (~relation(B)|(![A]: relation_dom(relation_dom_restriction(B,A))=set_intersection2(relation_dom(B),A)))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f1002])).
% 0.12/0.42 fof(f1004,plain,(
% 0.12/0.42 ![X0,X1]: (~relation(X0)|relation_dom(relation_dom_restriction(X0,X1))=set_intersection2(relation_dom(X0),X1))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f1003])).
% 0.12/0.42 fof(f1044,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))|in(ordered_pair(X2,X3),X0))),
% 0.12/0.42 inference(destructive_equality_resolution,[status(thm)],[f275])).
% 0.12/0.42 fof(f1076,plain,(
% 0.12/0.42 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.12/0.42 inference(destructive_equality_resolution,[status(thm)],[f415])).
% 0.12/0.42 fof(f1080,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.12/0.43 inference(destructive_equality_resolution,[status(thm)],[f424])).
% 0.12/0.43 fof(f1118,plain,(
% 0.12/0.43 ![X0,X1,X2,X3]: (~relation(X0)|~in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))|in(ordered_pair(X1,X2),X0))),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1044,f523])).
% 0.12/0.43 fof(f1121,plain,(
% 0.12/0.43 ![X0]: (relation_dom(relation_dom_restriction(sK79_skl,X0))=set_intersection2(relation_dom(sK79_skl),X0))),
% 0.12/0.43 inference(resolution,[status(thm)],[f1004,f958])).
% 0.12/0.43 fof(f1124,plain,(
% 0.12/0.43 in(sK81_skl,set_intersection2(relation_dom(sK79_skl),sK80_skl))),
% 0.12/0.43 inference(backward_demodulation,[status(thm)],[f1121,f960])).
% 0.12/0.43 fof(f1129,plain,(
% 0.12/0.43 ![X0,X1]: (~relation(relation_dom_restriction(sK79_skl,X0))|~function(relation_dom_restriction(sK79_skl,X0))|~in(X1,set_intersection2(relation_dom(sK79_skl),X0))|in(ordered_pair(X1,apply(relation_dom_restriction(sK79_skl,X0),X1)),relation_dom_restriction(sK79_skl,X0)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f1121,f1076])).
% 0.12/0.43 fof(f1164,plain,(
% 0.12/0.43 ~relation(relation_dom_restriction(sK79_skl,sK80_skl))|~function(relation_dom_restriction(sK79_skl,sK80_skl))|in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),relation_dom_restriction(sK79_skl,sK80_skl))),
% 0.12/0.43 inference(resolution,[status(thm)],[f1129,f1124])).
% 0.12/0.43 fof(f1165,definition,(
% 0.12/0.43 sQ4_spl <=> (relation(relation_dom_restriction(sK79_skl,sK80_skl)))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1167,plain,(
% 0.12/0.43 ~relation(relation_dom_restriction(sK79_skl,sK80_skl))|sQ4_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1165])).
% 0.12/0.43 fof(f1168,definition,(
% 0.12/0.43 sQ5_spl <=> (function(relation_dom_restriction(sK79_skl,sK80_skl)))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1170,plain,(
% 0.12/0.43 ~function(relation_dom_restriction(sK79_skl,sK80_skl))|sQ5_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1168])).
% 0.12/0.43 fof(f1171,definition,(
% 0.12/0.43 sQ6_spl <=> (in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),relation_dom_restriction(sK79_skl,sK80_skl)))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1172,plain,(
% 0.12/0.43 in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),relation_dom_restriction(sK79_skl,sK80_skl))|~sQ6_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1171])).
% 0.12/0.43 fof(f1174,plain,(
% 0.12/0.43 ~sQ4_spl|~sQ5_spl|sQ6_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f1164,f1165,f1168,f1171])).
% 0.12/0.43 fof(f1175,plain,(
% 0.12/0.43 ~relation(sK79_skl)|in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),sK79_skl)|~sQ6_spl),
% 0.12/0.43 inference(resolution,[status(thm)],[f1172,f1118])).
% 0.12/0.43 fof(f1180,definition,(
% 0.12/0.43 sQ7_spl <=> (relation(sK79_skl))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1182,plain,(
% 0.12/0.43 ~relation(sK79_skl)|sQ7_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1180])).
% 0.12/0.43 fof(f1183,definition,(
% 0.12/0.43 sQ8_spl <=> (in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),sK79_skl))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1184,plain,(
% 0.12/0.43 in(ordered_pair(sK81_skl,apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)),sK79_skl)|~sQ8_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1183])).
% 0.12/0.43 fof(f1186,plain,(
% 0.12/0.43 ~sQ7_spl|sQ8_spl|~sQ6_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f1175,f1180,f1183,f1171])).
% 0.12/0.43 fof(f1199,plain,(
% 0.12/0.43 $false|sQ7_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1182,f958])).
% 0.12/0.43 fof(f1200,plain,(
% 0.12/0.43 sQ7_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f1199])).
% 0.12/0.43 fof(f1201,plain,(
% 0.12/0.43 ~relation(sK79_skl)|sQ4_spl),
% 0.12/0.43 inference(resolution,[status(thm)],[f1167,f523])).
% 0.12/0.43 fof(f1203,plain,(
% 0.12/0.43 ~sQ7_spl|sQ4_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f1201,f1180,f1165])).
% 0.12/0.43 fof(f1210,plain,(
% 0.12/0.43 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f416,f1080])).
% 0.12/0.43 fof(f1308,definition,(
% 0.12/0.43 sQ29_spl <=> (function(sK79_skl))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1310,plain,(
% 0.12/0.43 ~function(sK79_skl)|sQ29_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1308])).
% 0.12/0.43 fof(f1363,plain,(
% 0.12/0.43 ~relation(sK79_skl)|~function(sK79_skl)|apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)=apply(sK79_skl,sK81_skl)|~sQ8_spl),
% 0.12/0.43 inference(resolution,[status(thm)],[f1184,f1210])).
% 0.12/0.43 fof(f1367,definition,(
% 0.12/0.43 sQ33_spl <=> (apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)=apply(sK79_skl,sK81_skl))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f1368,plain,(
% 0.12/0.43 apply(relation_dom_restriction(sK79_skl,sK80_skl),sK81_skl)=apply(sK79_skl,sK81_skl)|~sQ33_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f1367])).
% 0.12/0.43 fof(f1370,plain,(
% 0.12/0.43 ~sQ7_spl|~sQ29_spl|sQ33_spl|~sQ8_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f1363,f1180,f1308,f1367,f1183])).
% 0.12/0.43 fof(f1379,plain,(
% 0.12/0.43 $false|sQ29_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1310,f959])).
% 0.12/0.43 fof(f1380,plain,(
% 0.12/0.43 sQ29_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f1379])).
% 0.12/0.43 fof(f1381,plain,(
% 0.12/0.43 $false|~sQ33_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1368,f961])).
% 0.12/0.43 fof(f1382,plain,(
% 0.12/0.43 ~sQ33_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f1381])).
% 0.12/0.43 fof(f1401,plain,(
% 0.12/0.43 ~relation(sK79_skl)|~function(sK79_skl)|sQ5_spl),
% 0.12/0.43 inference(resolution,[status(thm)],[f1170,f571])).
% 0.12/0.43 fof(f1403,plain,(
% 0.12/0.43 ~sQ7_spl|~sQ29_spl|sQ5_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f1401,f1180,f1308,f1168])).
% 0.12/0.43 fof(f1404,plain,(
% 0.12/0.43 $false),
% 0.12/0.43 inference(sat_refutation,[status(thm)],[f1174,f1186,f1200,f1203,f1370,f1380,f1382,f1403])).
% 0.12/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.46 % Elapsed time: 0.096576 seconds
% 0.12/0.46 % CPU time: 0.335396 seconds
% 0.12/0.46 % Total memory used: 124.233 MB
% 0.12/0.46 % Net memory used: 123.586 MB
%------------------------------------------------------------------------------