%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:22:00 PM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 05:58:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.32 % Refutation found
% 0.03/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% 0.03/0.32 fof(f2,axiom,(
% 0.03/0.32 (! [A] :( empty(A)=> function(A) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f3,axiom,(
% 0.03/0.32 (! [A] :( empty(A)=> relation(A) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f5,axiom,(
% 0.03/0.32 (! [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 ) ) ) )) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f6,axiom,(
% 0.03/0.32 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f9,axiom,(
% 0.03/0.32 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f16,axiom,(
% 0.03/0.32 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f17,axiom,(
% 0.03/0.32 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f18,axiom,(
% 0.03/0.32 (? [A] :( relation(A)& function(A) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f19,axiom,(
% 0.03/0.32 (? [A] :( empty(A)& relation(A) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f21,axiom,(
% 0.03/0.32 (? [A] : empty(A) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f35,conjecture,(
% 0.03/0.32 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) )),
% 0.03/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.32 fof(f36,negated_conjecture,(
% 0.03/0.32 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) ))),
% 0.03/0.32 inference(negated_conjecture,[status(cth)],[f35])).
% 0.03/0.32 fof(f39,plain,(
% 0.03/0.32 ![A]: (~empty(A)|function(A))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.03/0.32 fof(f40,plain,(
% 0.03/0.32 ![X0]: (~empty(X0)|function(X0))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f39])).
% 0.03/0.32 fof(f41,plain,(
% 0.03/0.32 ![A]: (~empty(A)|relation(A))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.03/0.32 fof(f42,plain,(
% 0.03/0.32 ![X0]: (~empty(X0)|relation(X0))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f41])).
% 0.03/0.32 fof(f44,plain,(
% 0.03/0.32 ![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)))))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.03/0.32 fof(f45,plain,(
% 0.03/0.32 ![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))))))),
% 0.03/0.32 inference(NNF_transformation,[status(thm)],[f44])).
% 0.03/0.32 fof(f46,plain,(
% 0.03/0.32 ![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)))))))),
% 0.03/0.32 inference(miniscoping,[status(thm)],[f45])).
% 0.03/0.32 fof(f47,plain,(
% 0.03/0.32 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f46])).
% 0.03/0.32 fof(f48,plain,(
% 0.03/0.32 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f46])).
% 0.03/0.32 fof(f49,plain,(
% 0.03/0.32 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|~X2=apply(X0,X1)|X2=empty_set)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f46])).
% 0.03/0.32 fof(f51,plain,(
% 0.03/0.32 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.03/0.32 fof(f52,plain,(
% 0.03/0.32 ![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)))))))))),
% 0.03/0.32 inference(NNF_transformation,[status(thm)],[f51])).
% 0.03/0.32 fof(f53,plain,(
% 0.03/0.32 ![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)))))))))),
% 0.03/0.32 inference(miniscoping,[status(thm)],[f52])).
% 0.03/0.32 fof(f54,plain,(
% 0.03/0.32 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK0_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK1_skl(B,A),B)|(![D]: ~in(ordered_pair(sK1_skl(B,A),D),A)))&(in(sK1_skl(B,A),B)|in(ordered_pair(sK1_skl(B,A),sK2_skl(B,A)),A)))))))),
% 0.03/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f53])).
% 0.03/0.32 fof(f56,plain,(
% 0.03/0.32 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f54])).
% 0.03/0.32 fof(f62,plain,(
% 0.03/0.32 empty(empty_set)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f9])).
% 0.03/0.32 fof(f63,plain,(
% 0.03/0.32 relation(empty_set)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f9])).
% 0.03/0.32 fof(f72,plain,(
% 0.03/0.32 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.03/0.32 fof(f73,plain,(
% 0.03/0.32 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f72])).
% 0.03/0.32 fof(f74,plain,(
% 0.03/0.32 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.03/0.32 fof(f75,plain,(
% 0.03/0.32 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f74])).
% 0.03/0.32 fof(f77,plain,(
% 0.03/0.32 (relation(sK4_skl)&function(sK4_skl))),
% 0.03/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f18])).
% 0.03/0.32 fof(f78,plain,(
% 0.03/0.32 relation(sK4_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f77])).
% 0.03/0.32 fof(f79,plain,(
% 0.03/0.32 function(sK4_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f77])).
% 0.03/0.32 fof(f80,plain,(
% 0.03/0.32 (empty(sK5_skl)&relation(sK5_skl))),
% 0.03/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f19])).
% 0.03/0.32 fof(f81,plain,(
% 0.03/0.32 empty(sK5_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f80])).
% 0.03/0.32 fof(f82,plain,(
% 0.03/0.32 relation(sK5_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f80])).
% 0.03/0.32 fof(f87,plain,(
% 0.03/0.32 empty(sK7_skl)),
% 0.03/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f21])).
% 0.03/0.32 fof(f88,plain,(
% 0.03/0.32 empty(sK7_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f87])).
% 0.03/0.32 fof(f124,plain,(
% 0.03/0.32 (?[A,B,C]: ((relation(C)&function(C))&(in(ordered_pair(A,B),C)<~>(in(A,relation_dom(C))&B=apply(C,A)))))),
% 0.03/0.32 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.03/0.32 fof(f125,plain,(
% 0.03/0.32 ?[A,B,C]: ((relation(C)&function(C))&((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A)))))),
% 0.03/0.32 inference(NNF_transformation,[status(thm)],[f124])).
% 0.03/0.32 fof(f126,plain,(
% 0.03/0.32 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A))))))),
% 0.03/0.32 inference(miniscoping,[status(thm)],[f125])).
% 0.03/0.32 fof(f127,plain,(
% 0.03/0.32 ((relation(sK12_skl)&function(sK12_skl))&((in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|(in(sK13_skl,relation_dom(sK12_skl))&sK14_skl=apply(sK12_skl,sK13_skl)))&(~in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|(~in(sK13_skl,relation_dom(sK12_skl))|~sK14_skl=apply(sK12_skl,sK13_skl)))))),
% 0.03/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK12_skl),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f126])).
% 0.03/0.32 fof(f128,plain,(
% 0.03/0.32 relation(sK12_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f127])).
% 0.03/0.32 fof(f129,plain,(
% 0.03/0.32 function(sK12_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f127])).
% 0.03/0.32 fof(f130,plain,(
% 0.03/0.32 in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|in(sK13_skl,relation_dom(sK12_skl))),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f127])).
% 0.03/0.32 fof(f131,plain,(
% 0.03/0.32 in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|sK14_skl=apply(sK12_skl,sK13_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f127])).
% 0.03/0.32 fof(f132,plain,(
% 0.03/0.32 ~in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|~in(sK13_skl,relation_dom(sK12_skl))|~sK14_skl=apply(sK12_skl,sK13_skl)),
% 0.03/0.32 inference(cnf_transformation,[status(thm)],[f127])).
% 0.03/0.32 fof(f133,definition,(
% 0.03/0.32 sQ0_spl <=> (in(ordered_pair(sK13_skl,sK14_skl),sK12_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f134,plain,(
% 0.03/0.32 in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|~sQ0_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f133])).
% 0.03/0.32 fof(f135,plain,(
% 0.03/0.32 ~in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|sQ0_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f133])).
% 0.03/0.32 fof(f136,definition,(
% 0.03/0.32 sQ1_spl <=> (in(sK13_skl,relation_dom(sK12_skl)))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f137,plain,(
% 0.03/0.32 in(sK13_skl,relation_dom(sK12_skl))|~sQ1_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f136])).
% 0.03/0.32 fof(f139,plain,(
% 0.03/0.32 sQ0_spl|sQ1_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f130,f133,f136])).
% 0.03/0.32 fof(f140,definition,(
% 0.03/0.32 sQ2_spl <=> (sK14_skl=apply(sK12_skl,sK13_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f141,plain,(
% 0.03/0.32 sK14_skl=apply(sK12_skl,sK13_skl)|~sQ2_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f140])).
% 0.03/0.32 fof(f143,plain,(
% 0.03/0.32 sQ0_spl|sQ2_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f131,f133,f140])).
% 0.03/0.32 fof(f144,plain,(
% 0.03/0.32 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f132,f133,f136,f140])).
% 0.03/0.32 fof(f145,plain,(
% 0.03/0.32 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.03/0.32 inference(destructive_equality_resolution,[status(thm)],[f47])).
% 0.03/0.32 fof(f146,plain,(
% 0.03/0.32 ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|apply(X0,X1)=empty_set)),
% 0.03/0.32 inference(destructive_equality_resolution,[status(thm)],[f49])).
% 0.03/0.32 fof(f149,plain,(
% 0.03/0.32 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.03/0.32 inference(destructive_equality_resolution,[status(thm)],[f56])).
% 0.03/0.32 fof(f152,plain,(
% 0.03/0.32 ~relation(sK12_skl)|in(sK13_skl,relation_dom(sK12_skl))|~sQ0_spl),
% 0.03/0.32 inference(resolution,[status(thm)],[f149,f134])).
% 0.03/0.32 fof(f153,definition,(
% 0.03/0.32 sQ3_spl <=> (relation(sK12_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f155,plain,(
% 0.03/0.32 ~relation(sK12_skl)|sQ3_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f153])).
% 0.03/0.32 fof(f156,plain,(
% 0.03/0.32 ~sQ3_spl|sQ1_spl|~sQ0_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f152,f153,f136,f133])).
% 0.03/0.32 fof(f159,plain,(
% 0.03/0.32 ~relation(sK12_skl)|~function(sK12_skl)|in(ordered_pair(sK13_skl,apply(sK12_skl,sK13_skl)),sK12_skl)|~sQ1_spl),
% 0.03/0.32 inference(resolution,[status(thm)],[f145,f137])).
% 0.03/0.32 fof(f160,definition,(
% 0.03/0.32 sQ4_spl <=> (function(sK12_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f162,plain,(
% 0.03/0.32 ~function(sK12_skl)|sQ4_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f160])).
% 0.03/0.32 fof(f163,definition,(
% 0.03/0.32 sQ5_spl <=> (in(ordered_pair(sK13_skl,apply(sK12_skl,sK13_skl)),sK12_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f164,plain,(
% 0.03/0.32 in(ordered_pair(sK13_skl,apply(sK12_skl,sK13_skl)),sK12_skl)|~sQ5_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f163])).
% 0.03/0.32 fof(f166,plain,(
% 0.03/0.32 ~sQ3_spl|~sQ4_spl|sQ5_spl|~sQ1_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f159,f153,f160,f163,f136])).
% 0.03/0.32 fof(f167,plain,(
% 0.03/0.32 $false|sQ3_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f155,f128])).
% 0.03/0.32 fof(f168,plain,(
% 0.03/0.32 sQ3_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f167])).
% 0.03/0.32 fof(f169,plain,(
% 0.03/0.32 $false|sQ4_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f162,f129])).
% 0.03/0.32 fof(f170,plain,(
% 0.03/0.32 sQ4_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f169])).
% 0.03/0.32 fof(f171,plain,(
% 0.03/0.32 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f48,f149])).
% 0.03/0.32 fof(f173,plain,(
% 0.03/0.32 empty(relation_dom(empty_set))),
% 0.03/0.32 inference(resolution,[status(thm)],[f62,f75])).
% 0.03/0.32 fof(f175,plain,(
% 0.03/0.32 function(empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f62,f40])).
% 0.03/0.32 fof(f177,plain,(
% 0.03/0.32 empty(relation_dom(sK5_skl))),
% 0.03/0.32 inference(resolution,[status(thm)],[f81,f75])).
% 0.03/0.32 fof(f179,plain,(
% 0.03/0.32 function(sK5_skl)),
% 0.03/0.32 inference(resolution,[status(thm)],[f81,f40])).
% 0.03/0.32 fof(f182,plain,(
% 0.03/0.32 relation(sK7_skl)),
% 0.03/0.32 inference(resolution,[status(thm)],[f88,f42])).
% 0.03/0.32 fof(f183,plain,(
% 0.03/0.32 function(sK7_skl)),
% 0.03/0.32 inference(resolution,[status(thm)],[f88,f40])).
% 0.03/0.32 fof(f188,plain,(
% 0.03/0.32 ![X0]: (~relation(sK4_skl)|in(X0,relation_dom(sK4_skl))|apply(sK4_skl,X0)=empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f146,f79])).
% 0.03/0.32 fof(f189,plain,(
% 0.03/0.32 ![X0]: (~relation(sK12_skl)|in(X0,relation_dom(sK12_skl))|apply(sK12_skl,X0)=empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f146,f129])).
% 0.03/0.32 fof(f190,definition,(
% 0.03/0.32 sQ6_spl <=> (relation(sK4_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f192,plain,(
% 0.03/0.32 ~relation(sK4_skl)|sQ6_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f190])).
% 0.03/0.32 fof(f193,definition,(
% 0.03/0.32 ![X0]: (sQ7_spl <=> (in(X0,relation_dom(sK4_skl))|apply(sK4_skl,X0)=empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f196,plain,(
% 0.03/0.32 ~sQ6_spl|sQ7_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f188,f190,f193])).
% 0.03/0.32 fof(f197,definition,(
% 0.03/0.32 ![X0]: (sQ8_spl <=> (in(X0,relation_dom(sK12_skl))|apply(sK12_skl,X0)=empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f200,plain,(
% 0.03/0.32 ~sQ3_spl|sQ8_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f189,f153,f197])).
% 0.03/0.32 fof(f201,plain,(
% 0.03/0.32 $false|sQ6_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f192,f78])).
% 0.03/0.32 fof(f202,plain,(
% 0.03/0.32 sQ6_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f201])).
% 0.03/0.32 fof(f207,plain,(
% 0.03/0.32 ![X0]: (~relation(empty_set)|in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f175,f146])).
% 0.03/0.32 fof(f208,definition,(
% 0.03/0.32 sQ9_spl <=> (relation(empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f210,plain,(
% 0.03/0.32 ~relation(empty_set)|sQ9_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f208])).
% 0.03/0.32 fof(f211,definition,(
% 0.03/0.32 ![X0]: (sQ10_spl <=> (in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f214,plain,(
% 0.03/0.32 ~sQ9_spl|sQ10_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f207,f208,f211])).
% 0.03/0.32 fof(f215,plain,(
% 0.03/0.32 $false|sQ9_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f210,f63])).
% 0.03/0.32 fof(f216,plain,(
% 0.03/0.32 sQ9_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f215])).
% 0.03/0.32 fof(f217,plain,(
% 0.03/0.32 ![X0]: (~relation(sK5_skl)|in(X0,relation_dom(sK5_skl))|apply(sK5_skl,X0)=empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f179,f146])).
% 0.03/0.32 fof(f218,definition,(
% 0.03/0.32 sQ11_spl <=> (relation(sK5_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f220,plain,(
% 0.03/0.32 ~relation(sK5_skl)|sQ11_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f218])).
% 0.03/0.32 fof(f221,definition,(
% 0.03/0.32 ![X0]: (sQ12_spl <=> (in(X0,relation_dom(sK5_skl))|apply(sK5_skl,X0)=empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f224,plain,(
% 0.03/0.32 ~sQ11_spl|sQ12_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f217,f218,f221])).
% 0.03/0.32 fof(f225,plain,(
% 0.03/0.32 $false|sQ11_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f220,f82])).
% 0.03/0.32 fof(f226,plain,(
% 0.03/0.32 sQ11_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f225])).
% 0.03/0.32 fof(f227,plain,(
% 0.03/0.32 ![X0]: (~relation(sK7_skl)|in(X0,relation_dom(sK7_skl))|apply(sK7_skl,X0)=empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f183,f146])).
% 0.03/0.32 fof(f228,definition,(
% 0.03/0.32 sQ13_spl <=> (relation(sK7_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f230,plain,(
% 0.03/0.32 ~relation(sK7_skl)|sQ13_spl),
% 0.03/0.32 inference(component_clause,[status(thm)],[f228])).
% 0.03/0.32 fof(f231,definition,(
% 0.03/0.32 ![X0]: (sQ14_spl <=> (in(X0,relation_dom(sK7_skl))|apply(sK7_skl,X0)=empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f234,plain,(
% 0.03/0.32 ~sQ13_spl|sQ14_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f227,f228,f231])).
% 0.03/0.32 fof(f235,plain,(
% 0.03/0.32 $false|sQ13_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f230,f182])).
% 0.03/0.32 fof(f236,plain,(
% 0.03/0.32 sQ13_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f235])).
% 0.03/0.32 fof(f237,plain,(
% 0.03/0.32 empty(empty_set)|~relation(empty_set)),
% 0.03/0.32 inference(resolution,[status(thm)],[f173,f73])).
% 0.03/0.32 fof(f242,definition,(
% 0.03/0.32 sQ15_spl <=> (empty(empty_set))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f245,plain,(
% 0.03/0.32 sQ15_spl|~sQ9_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f237,f242,f208])).
% 0.03/0.32 fof(f246,plain,(
% 0.03/0.32 empty(sK5_skl)|~relation(sK5_skl)),
% 0.03/0.32 inference(resolution,[status(thm)],[f177,f73])).
% 0.03/0.32 fof(f251,definition,(
% 0.03/0.32 sQ16_spl <=> (empty(sK5_skl))),
% 0.03/0.32 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.03/0.32 fof(f254,plain,(
% 0.03/0.32 sQ16_spl|~sQ11_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f246,f251,f218])).
% 0.03/0.32 fof(f255,plain,(
% 0.03/0.32 in(ordered_pair(sK13_skl,sK14_skl),sK12_skl)|~sQ2_spl|~sQ5_spl),
% 0.03/0.32 inference(forward_demodulation,[status(thm)],[f141,f164])).
% 0.03/0.32 fof(f256,plain,(
% 0.03/0.32 $false|sQ0_spl|~sQ2_spl|~sQ5_spl),
% 0.03/0.32 inference(forward_subsumption_resolution,[status(thm)],[f255,f135])).
% 0.03/0.32 fof(f257,plain,(
% 0.03/0.32 sQ0_spl|~sQ2_spl|~sQ5_spl),
% 0.03/0.32 inference(contradiction_clause,[status(thm)],[f256])).
% 0.03/0.32 fof(f258,plain,(
% 0.03/0.32 ~relation(sK12_skl)|~function(sK12_skl)|sK14_skl=apply(sK12_skl,sK13_skl)|~sQ0_spl),
% 0.03/0.32 inference(resolution,[status(thm)],[f134,f171])).
% 0.03/0.32 fof(f262,plain,(
% 0.03/0.32 ~sQ3_spl|~sQ4_spl|sQ2_spl|~sQ0_spl),
% 0.03/0.32 inference(split_clause,[status(thm)],[f258,f153,f160,f140,f133])).
% 0.03/0.32 fof(f264,plain,(
% 0.03/0.32 $false),
% 0.03/0.32 inference(sat_refutation,[status(thm)],[f139,f143,f144,f156,f166,f168,f170,f196,f200,f202,f214,f216,f224,f226,f234,f236,f245,f254,f257,f262])).
% 0.03/0.32 % SZS output end CNFRefutation for theBenchmark.p
% 0.03/0.33 % Elapsed time: 0.034365 seconds
% 0.03/0.33 % CPU time: 0.086376 seconds
% 0.03/0.33 % Total memory used: 45.232 MB
% 0.03/0.33 % Net memory used: 45.212 MB
%------------------------------------------------------------------------------