%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU241+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 : n001.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 02:22:06 PM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU241+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 06:08:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.40 fof(f2,axiom,(
% 0.15/0.40 (! [A] :( empty(A)=> function(A) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f3,axiom,(
% 0.15/0.40 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f6,axiom,(
% 0.15/0.40 (! [A] :( relation(A)=> ( antisymmetric(A)<=> is_antisymmetric_in(A,relation_field(A)) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f7,axiom,(
% 0.15/0.40 (! [A] :( relation(A)=> (! [B] :( is_antisymmetric_in(A,B)<=> (! [C,D] :( ( in(C,B)& in(D,B)& in(ordered_pair(C,D),A)& in(ordered_pair(D,C),A) )=> C = D ) )) )) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f20,axiom,(
% 0.15/0.40 empty(empty_set) ),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f25,conjecture,(
% 0.15/0.40 (! [A] :( relation(A)=> ( antisymmetric(A)<=> (! [B,C] :( ( in(ordered_pair(B,C),A)& in(ordered_pair(C,B),A) )=> B = C ) )) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f26,negated_conjecture,(
% 0.15/0.40 ~((! [A] :( relation(A)=> ( antisymmetric(A)<=> (! [B,C] :( ( in(ordered_pair(B,C),A)& in(ordered_pair(C,B),A) )=> B = C ) )) ) ))),
% 0.15/0.40 inference(negated_conjecture,[status(cth)],[f25])).
% 0.15/0.40 fof(f27,axiom,(
% 0.15/0.40 (? [A] :( relation(A)& function(A) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f28,axiom,(
% 0.15/0.40 (? [A] : empty(A) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f29,axiom,(
% 0.15/0.40 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f31,axiom,(
% 0.15/0.40 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f35,axiom,(
% 0.15/0.40 (! [A,B,C] :( relation(C)=> ( in(ordered_pair(A,B),C)=> ( in(A,relation_field(C))& in(B,relation_field(C)) ) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f36,axiom,(
% 0.15/0.40 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f37,axiom,(
% 0.15/0.40 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f41,plain,(
% 0.15/0.40 ![A]: (~empty(A)|function(A))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.40 fof(f42,plain,(
% 0.15/0.40 ![X0]: (~empty(X0)|function(X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f41])).
% 0.15/0.40 fof(f43,plain,(
% 0.15/0.40 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.15/0.40 fof(f46,plain,(
% 0.15/0.40 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f43])).
% 0.15/0.40 fof(f49,plain,(
% 0.15/0.40 ![A]: (~relation(A)|(antisymmetric(A)<=>is_antisymmetric_in(A,relation_field(A))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/0.40 fof(f50,plain,(
% 0.15/0.40 ![A]: (~relation(A)|((~antisymmetric(A)|is_antisymmetric_in(A,relation_field(A)))&(antisymmetric(A)|~is_antisymmetric_in(A,relation_field(A)))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f49])).
% 0.15/0.40 fof(f51,plain,(
% 0.15/0.40 ![X0]: (~relation(X0)|~antisymmetric(X0)|is_antisymmetric_in(X0,relation_field(X0)))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.40 fof(f52,plain,(
% 0.15/0.40 ![X0]: (~relation(X0)|antisymmetric(X0)|~is_antisymmetric_in(X0,relation_field(X0)))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.40 fof(f53,plain,(
% 0.15/0.40 ![A]: (~relation(A)|(![B]: (is_antisymmetric_in(A,B)<=>(![C,D]: ((((~in(C,B)|~in(D,B))|~in(ordered_pair(C,D),A))|~in(ordered_pair(D,C),A))|C=D)))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.15/0.40 fof(f54,plain,(
% 0.15/0.40 ![A]: (~relation(A)|(![B]: ((~is_antisymmetric_in(A,B)|(![C,D]: ((((~in(C,B)|~in(D,B))|~in(ordered_pair(C,D),A))|~in(ordered_pair(D,C),A))|C=D)))&(is_antisymmetric_in(A,B)|(?[C,D]: ((((in(C,B)&in(D,B))&in(ordered_pair(C,D),A))&in(ordered_pair(D,C),A))&~C=D))))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f53])).
% 0.15/0.40 fof(f55,plain,(
% 0.15/0.40 ![A]: (~relation(A)|((![B]: (~is_antisymmetric_in(A,B)|(![C,D]: ((((~in(C,B)|~in(D,B))|~in(ordered_pair(C,D),A))|~in(ordered_pair(D,C),A))|C=D))))&(![B]: (is_antisymmetric_in(A,B)|(?[C,D]: ((((in(C,B)&in(D,B))&in(ordered_pair(C,D),A))&in(ordered_pair(D,C),A))&~C=D))))))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f54])).
% 0.15/0.40 fof(f56,plain,(
% 0.15/0.40 ![A]: (~relation(A)|((![B]: (~is_antisymmetric_in(A,B)|(![C,D]: ((((~in(C,B)|~in(D,B))|~in(ordered_pair(C,D),A))|~in(ordered_pair(D,C),A))|C=D))))&(![B]: (is_antisymmetric_in(A,B)|((((in(sK0_skl(B,A),B)&in(sK1_skl(B,A),B))&in(ordered_pair(sK0_skl(B,A),sK1_skl(B,A)),A))&in(ordered_pair(sK1_skl(B,A),sK0_skl(B,A)),A))&~sK0_skl(B,A)=sK1_skl(B,A))))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(B,A)),skolemize(D,sK1_skl(B,A))],[f55])).
% 0.15/0.40 fof(f57,plain,(
% 0.15/0.40 ![X0,X1,X2,X3]: (~relation(X0)|~is_antisymmetric_in(X0,X1)|~in(X2,X1)|~in(X3,X1)|~in(ordered_pair(X2,X3),X0)|~in(ordered_pair(X3,X2),X0)|X2=X3)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/0.40 fof(f60,plain,(
% 0.15/0.40 ![X0,X1]: (~relation(X0)|is_antisymmetric_in(X0,X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/0.40 fof(f61,plain,(
% 0.15/0.40 ![X0,X1]: (~relation(X0)|is_antisymmetric_in(X0,X1)|in(ordered_pair(sK1_skl(X1,X0),sK0_skl(X1,X0)),X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/0.40 fof(f62,plain,(
% 0.15/0.40 ![X0,X1]: (~relation(X0)|is_antisymmetric_in(X0,X1)|~sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/0.40 fof(f68,plain,(
% 0.15/0.40 empty(empty_set)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f20])).
% 0.15/0.40 fof(f78,plain,(
% 0.15/0.40 (?[A]: (relation(A)&(antisymmetric(A)<~>(![B,C]: ((~in(ordered_pair(B,C),A)|~in(ordered_pair(C,B),A))|B=C)))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.15/0.40 fof(f79,plain,(
% 0.15/0.40 ?[A]: (relation(A)&((antisymmetric(A)|(![B,C]: ((~in(ordered_pair(B,C),A)|~in(ordered_pair(C,B),A))|B=C)))&(~antisymmetric(A)|(?[B,C]: ((in(ordered_pair(B,C),A)&in(ordered_pair(C,B),A))&~B=C)))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f78])).
% 0.15/0.40 fof(f80,plain,(
% 0.15/0.40 (relation(sK3_skl)&((antisymmetric(sK3_skl)|(![B,C]: ((~in(ordered_pair(B,C),sK3_skl)|~in(ordered_pair(C,B),sK3_skl))|B=C)))&(~antisymmetric(sK3_skl)|((in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)&in(ordered_pair(sK5_skl,sK4_skl),sK3_skl))&~sK4_skl=sK5_skl))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f79])).
% 0.15/0.40 fof(f81,plain,(
% 0.15/0.40 relation(sK3_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f80])).
% 0.15/0.40 fof(f82,plain,(
% 0.15/0.40 ![X0,X1]: (antisymmetric(sK3_skl)|~in(ordered_pair(X0,X1),sK3_skl)|~in(ordered_pair(X1,X0),sK3_skl)|X0=X1)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f80])).
% 0.15/0.40 fof(f83,plain,(
% 0.15/0.40 ~antisymmetric(sK3_skl)|in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f80])).
% 0.15/0.40 fof(f84,plain,(
% 0.15/0.40 ~antisymmetric(sK3_skl)|in(ordered_pair(sK5_skl,sK4_skl),sK3_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f80])).
% 0.15/0.40 fof(f85,plain,(
% 0.15/0.40 ~antisymmetric(sK3_skl)|~sK4_skl=sK5_skl),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f80])).
% 0.15/0.40 fof(f86,plain,(
% 0.15/0.40 (relation(sK6_skl)&function(sK6_skl))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f27])).
% 0.15/0.40 fof(f87,plain,(
% 0.15/0.40 relation(sK6_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f86])).
% 0.15/0.40 fof(f89,plain,(
% 0.15/0.40 empty(sK7_skl)),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f28])).
% 0.15/0.40 fof(f90,plain,(
% 0.15/0.40 empty(sK7_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f89])).
% 0.15/0.40 fof(f91,plain,(
% 0.15/0.40 ((relation(sK8_skl)&empty(sK8_skl))&function(sK8_skl))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f29])).
% 0.15/0.40 fof(f92,plain,(
% 0.15/0.40 relation(sK8_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/0.40 fof(f93,plain,(
% 0.15/0.40 empty(sK8_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f91])).
% 0.15/0.40 fof(f97,plain,(
% 0.15/0.40 ((relation(sK10_skl)&function(sK10_skl))&one_to_one(sK10_skl))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f31])).
% 0.15/0.40 fof(f98,plain,(
% 0.15/0.40 relation(sK10_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f97])).
% 0.15/0.40 fof(f106,plain,(
% 0.15/0.40 ![A,B,C]: (~relation(C)|(~in(ordered_pair(A,B),C)|(in(A,relation_field(C))&in(B,relation_field(C)))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f35])).
% 0.15/0.40 fof(f107,plain,(
% 0.15/0.40 ![C]: (~relation(C)|(![A,B]: (~in(ordered_pair(A,B),C)|(in(A,relation_field(C))&in(B,relation_field(C))))))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f106])).
% 0.15/0.40 fof(f108,plain,(
% 0.15/0.40 ![X0,X1,X2]: (~relation(X0)|~in(ordered_pair(X1,X2),X0)|in(X1,relation_field(X0)))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f107])).
% 0.15/0.40 fof(f109,plain,(
% 0.15/0.40 ![X0,X1,X2]: (~relation(X0)|~in(ordered_pair(X1,X2),X0)|in(X2,relation_field(X0)))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f107])).
% 0.15/0.40 fof(f110,plain,(
% 0.15/0.40 ![A]: (~empty(A)|A=empty_set)),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.15/0.40 fof(f111,plain,(
% 0.15/0.40 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f110])).
% 0.15/0.40 fof(f112,plain,(
% 0.15/0.40 ![A,B]: (~in(A,B)|~empty(B))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.15/0.40 fof(f113,plain,(
% 0.15/0.40 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f112])).
% 0.15/0.40 fof(f114,plain,(
% 0.15/0.40 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f113])).
% 0.15/0.40 fof(f118,definition,(
% 0.15/0.40 sQ0_spl <=> (antisymmetric(sK3_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f121,definition,(
% 0.15/0.40 ![X0,X1]: (sQ1_spl <=> (~in(ordered_pair(X0,X1),sK3_skl)|~in(ordered_pair(X1,X0),sK3_skl)|X0=X1))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f122,plain,(
% 0.15/0.40 ![X0,X1]: (~in(ordered_pair(X0,X1),sK3_skl)|~in(ordered_pair(X1,X0),sK3_skl)|X0=X1|~sQ1_spl)),
% 0.15/0.40 inference(component_clause,[status(thm)],[f121])).
% 0.15/0.40 fof(f124,plain,(
% 0.15/0.40 sQ0_spl|sQ1_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f82,f118,f121])).
% 0.15/0.40 fof(f125,definition,(
% 0.15/0.40 sQ2_spl <=> (in(ordered_pair(sK4_skl,sK5_skl),sK3_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f126,plain,(
% 0.15/0.40 in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)|~sQ2_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f125])).
% 0.15/0.40 fof(f128,plain,(
% 0.15/0.40 ~sQ0_spl|sQ2_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f83,f118,f125])).
% 0.15/0.40 fof(f129,definition,(
% 0.15/0.40 sQ3_spl <=> (in(ordered_pair(sK5_skl,sK4_skl),sK3_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f130,plain,(
% 0.15/0.40 in(ordered_pair(sK5_skl,sK4_skl),sK3_skl)|~sQ3_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f129])).
% 0.15/0.40 fof(f132,plain,(
% 0.15/0.40 ~sQ0_spl|sQ3_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f84,f118,f129])).
% 0.15/0.40 fof(f133,definition,(
% 0.15/0.40 sQ4_spl <=> (sK4_skl=sK5_skl)),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f136,plain,(
% 0.15/0.40 ~sQ0_spl|~sQ4_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f85,f118,f133])).
% 0.15/0.40 fof(f140,plain,(
% 0.15/0.40 ![X0]: (~relation(X0)|~empty(X0)|one_to_one(X0))),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f46,f42])).
% 0.15/0.40 fof(f141,plain,(
% 0.15/0.40 ~relation(sK8_skl)|one_to_one(sK8_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f140,f93])).
% 0.15/0.40 fof(f142,plain,(
% 0.15/0.40 ~relation(sK7_skl)|one_to_one(sK7_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f140,f90])).
% 0.15/0.40 fof(f143,plain,(
% 0.15/0.40 ~relation(empty_set)|one_to_one(empty_set)),
% 0.15/0.40 inference(resolution,[status(thm)],[f140,f68])).
% 0.15/0.40 fof(f144,definition,(
% 0.15/0.40 sQ5_spl <=> (relation(sK8_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f146,plain,(
% 0.15/0.40 ~relation(sK8_skl)|sQ5_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f144])).
% 0.15/0.40 fof(f147,definition,(
% 0.15/0.40 sQ6_spl <=> (one_to_one(sK8_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f150,plain,(
% 0.15/0.40 ~sQ5_spl|sQ6_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f141,f144,f147])).
% 0.15/0.40 fof(f151,definition,(
% 0.15/0.40 sQ7_spl <=> (relation(sK7_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f153,plain,(
% 0.15/0.40 ~relation(sK7_skl)|sQ7_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f151])).
% 0.15/0.40 fof(f154,definition,(
% 0.15/0.40 sQ8_spl <=> (one_to_one(sK7_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f157,plain,(
% 0.15/0.40 ~sQ7_spl|sQ8_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f142,f151,f154])).
% 0.15/0.40 fof(f158,definition,(
% 0.15/0.40 sQ9_spl <=> (relation(empty_set))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f160,plain,(
% 0.15/0.40 ~relation(empty_set)|sQ9_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f158])).
% 0.15/0.40 fof(f161,definition,(
% 0.15/0.40 sQ10_spl <=> (one_to_one(empty_set))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f164,plain,(
% 0.15/0.40 ~sQ9_spl|sQ10_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f143,f158,f161])).
% 0.15/0.40 fof(f165,plain,(
% 0.15/0.40 $false|sQ5_spl),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f146,f92])).
% 0.15/0.40 fof(f166,plain,(
% 0.15/0.40 sQ5_spl),
% 0.15/0.40 inference(contradiction_clause,[status(thm)],[f165])).
% 0.15/0.40 fof(f170,plain,(
% 0.15/0.40 sK8_skl=empty_set),
% 0.15/0.40 inference(resolution,[status(thm)],[f111,f93])).
% 0.15/0.40 fof(f171,plain,(
% 0.15/0.40 sK7_skl=empty_set),
% 0.15/0.40 inference(resolution,[status(thm)],[f111,f90])).
% 0.15/0.40 fof(f175,plain,(
% 0.15/0.40 ~relation(sK8_skl)|sQ9_spl),
% 0.15/0.40 inference(backward_demodulation,[status(thm)],[f170,f160])).
% 0.15/0.40 fof(f178,plain,(
% 0.15/0.40 ~sQ5_spl|sQ9_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f175,f144,f158])).
% 0.15/0.40 fof(f181,plain,(
% 0.15/0.40 ~relation(sK8_skl)|sQ7_spl),
% 0.15/0.40 inference(backward_demodulation,[status(thm)],[f184,f153])).
% 0.15/0.40 fof(f184,plain,(
% 0.15/0.40 sK7_skl=sK8_skl),
% 0.15/0.40 inference(forward_demodulation,[status(thm)],[f170,f171])).
% 0.15/0.40 fof(f185,plain,(
% 0.15/0.40 ~sQ5_spl|sQ7_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f181,f144,f151])).
% 0.15/0.40 fof(f199,plain,(
% 0.15/0.40 ~antisymmetric(sK3_skl)|is_antisymmetric_in(sK3_skl,relation_field(sK3_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f51,f81])).
% 0.15/0.40 fof(f221,definition,(
% 0.15/0.40 sQ17_spl <=> (is_antisymmetric_in(sK3_skl,relation_field(sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f222,plain,(
% 0.15/0.40 is_antisymmetric_in(sK3_skl,relation_field(sK3_skl))|~sQ17_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f221])).
% 0.15/0.40 fof(f223,plain,(
% 0.15/0.40 ~is_antisymmetric_in(sK3_skl,relation_field(sK3_skl))|sQ17_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f221])).
% 0.15/0.40 fof(f224,plain,(
% 0.15/0.40 ~sQ0_spl|sQ17_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f199,f118,f221])).
% 0.15/0.40 fof(f259,plain,(
% 0.15/0.40 ~relation(sK3_skl)|antisymmetric(sK3_skl)|~sQ17_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f222,f52])).
% 0.15/0.40 fof(f260,definition,(
% 0.15/0.40 sQ20_spl <=> (relation(sK3_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f262,plain,(
% 0.15/0.40 ~relation(sK3_skl)|sQ20_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f260])).
% 0.15/0.40 fof(f263,plain,(
% 0.15/0.40 ~sQ20_spl|sQ0_spl|~sQ17_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f259,f260,f118,f221])).
% 0.15/0.40 fof(f281,plain,(
% 0.15/0.40 ![X0]: (~relation(sK3_skl)|~is_antisymmetric_in(sK3_skl,X0)|~in(sK4_skl,X0)|~in(sK5_skl,X0)|~in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)|sK4_skl=sK5_skl|~sQ3_spl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f57,f130])).
% 0.15/0.40 fof(f283,definition,(
% 0.15/0.40 ![X0]: (sQ22_spl <=> (~is_antisymmetric_in(sK3_skl,X0)|~in(sK4_skl,X0)|~in(sK5_skl,X0)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f284,plain,(
% 0.15/0.40 ![X0]: (~is_antisymmetric_in(sK3_skl,X0)|~in(sK4_skl,X0)|~in(sK5_skl,X0)|~sQ22_spl)),
% 0.15/0.40 inference(component_clause,[status(thm)],[f283])).
% 0.15/0.40 fof(f286,plain,(
% 0.15/0.40 ~sQ20_spl|sQ22_spl|~sQ2_spl|sQ4_spl|~sQ3_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f281,f260,f283,f125,f133,f129])).
% 0.15/0.40 fof(f288,plain,(
% 0.15/0.40 $false|sQ20_spl),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f262,f81])).
% 0.15/0.40 fof(f289,plain,(
% 0.15/0.40 sQ20_spl),
% 0.15/0.40 inference(contradiction_clause,[status(thm)],[f288])).
% 0.15/0.40 fof(f321,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK10_skl,X0)|in(ordered_pair(sK0_skl(X0,sK10_skl),sK1_skl(X0,sK10_skl)),sK10_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f60,f98])).
% 0.15/0.40 fof(f322,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK8_skl,X0)|in(ordered_pair(sK0_skl(X0,sK8_skl),sK1_skl(X0,sK8_skl)),sK8_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f60,f92])).
% 0.15/0.40 fof(f323,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK6_skl,X0)|in(ordered_pair(sK0_skl(X0,sK6_skl),sK1_skl(X0,sK6_skl)),sK6_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f60,f87])).
% 0.15/0.40 fof(f324,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK3_skl,X0)|in(ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl)),sK3_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f60,f81])).
% 0.15/0.40 fof(f361,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK3_skl,X0)|in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f61,f81])).
% 0.15/0.40 fof(f375,definition,(
% 0.15/0.40 sQ24_spl <=> (empty(relation_field(sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f387,plain,(
% 0.15/0.40 ![X0,X1]: (is_antisymmetric_in(sK3_skl,X0)|~relation(sK3_skl)|~is_antisymmetric_in(sK3_skl,X1)|~in(sK1_skl(X0,sK3_skl),X1)|~in(sK0_skl(X0,sK3_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)|sK1_skl(X0,sK3_skl)=sK0_skl(X0,sK3_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f324,f57])).
% 0.15/0.40 fof(f391,definition,(
% 0.15/0.40 ![X0,X1]: (sQ26_spl <=> (is_antisymmetric_in(sK3_skl,X0)|~is_antisymmetric_in(sK3_skl,X1)|~in(sK1_skl(X0,sK3_skl),X1)|~in(sK0_skl(X0,sK3_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)|sK1_skl(X0,sK3_skl)=sK0_skl(X0,sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f394,plain,(
% 0.15/0.40 sQ26_spl|~sQ20_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f387,f391,f260])).
% 0.15/0.40 fof(f395,definition,(
% 0.15/0.40 ![X0]: (sQ27_spl <=> (is_antisymmetric_in(sK3_skl,X0)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f396,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK3_skl,X0)|~sQ27_spl)),
% 0.15/0.40 inference(component_clause,[status(thm)],[f395])).
% 0.15/0.40 fof(f400,plain,(
% 0.15/0.40 ~relation(sK3_skl)|antisymmetric(sK3_skl)|~sQ27_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f396,f52])).
% 0.15/0.40 fof(f401,plain,(
% 0.15/0.40 ~sQ20_spl|sQ0_spl|~sQ27_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f400,f260,f118,f395])).
% 0.15/0.40 fof(f407,plain,(
% 0.15/0.40 ![X0,X1]: (is_antisymmetric_in(sK3_skl,X0)|~relation(sK3_skl)|~is_antisymmetric_in(sK3_skl,X1)|~in(sK0_skl(X0,sK3_skl),X1)|~in(sK1_skl(X0,sK3_skl),X1)|~in(ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl)),sK3_skl)|sK0_skl(X0,sK3_skl)=sK1_skl(X0,sK3_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f361,f57])).
% 0.15/0.40 fof(f411,definition,(
% 0.15/0.40 ![X0,X1]: (sQ28_spl <=> (is_antisymmetric_in(sK3_skl,X0)|~is_antisymmetric_in(sK3_skl,X1)|~in(sK0_skl(X0,sK3_skl),X1)|~in(sK1_skl(X0,sK3_skl),X1)|~in(ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl)),sK3_skl)|sK0_skl(X0,sK3_skl)=sK1_skl(X0,sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f414,plain,(
% 0.15/0.40 sQ28_spl|~sQ20_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f407,f411,f260])).
% 0.15/0.40 fof(f446,plain,(
% 0.15/0.40 ![X0]: (~relation(sK3_skl)|in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))|is_antisymmetric_in(sK3_skl,X0))),
% 0.15/0.40 inference(resolution,[status(thm)],[f108,f324])).
% 0.15/0.40 fof(f447,plain,(
% 0.15/0.40 ![X0]: (~relation(sK3_skl)|in(sK1_skl(X0,sK3_skl),relation_field(sK3_skl))|is_antisymmetric_in(sK3_skl,X0))),
% 0.15/0.40 inference(resolution,[status(thm)],[f108,f361])).
% 0.15/0.40 fof(f449,plain,(
% 0.15/0.40 ~relation(sK3_skl)|in(sK4_skl,relation_field(sK3_skl))|~sQ2_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f108,f126])).
% 0.15/0.40 fof(f450,definition,(
% 0.15/0.40 ![X0]: (sQ29_spl <=> (in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))|is_antisymmetric_in(sK3_skl,X0)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f451,plain,(
% 0.15/0.40 ![X0]: (in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))|is_antisymmetric_in(sK3_skl,X0)|~sQ29_spl)),
% 0.15/0.40 inference(component_clause,[status(thm)],[f450])).
% 0.15/0.40 fof(f453,plain,(
% 0.15/0.40 ~sQ20_spl|sQ29_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f446,f260,f450])).
% 0.15/0.40 fof(f454,definition,(
% 0.15/0.40 ![X0]: (sQ30_spl <=> (in(sK1_skl(X0,sK3_skl),relation_field(sK3_skl))|is_antisymmetric_in(sK3_skl,X0)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f457,plain,(
% 0.15/0.40 ~sQ20_spl|sQ30_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f447,f260,f454])).
% 0.15/0.40 fof(f458,definition,(
% 0.15/0.40 sQ31_spl <=> (in(sK5_skl,relation_field(sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f462,definition,(
% 0.15/0.40 sQ32_spl <=> (in(sK4_skl,relation_field(sK3_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f463,plain,(
% 0.15/0.40 in(sK4_skl,relation_field(sK3_skl))|~sQ32_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f462])).
% 0.15/0.40 fof(f465,plain,(
% 0.15/0.40 ~sQ20_spl|sQ32_spl|~sQ2_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f449,f260,f462,f125])).
% 0.15/0.40 fof(f469,plain,(
% 0.15/0.40 ~relation(sK3_skl)|in(sK5_skl,relation_field(sK3_skl))|~sQ2_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f109,f126])).
% 0.15/0.40 fof(f473,plain,(
% 0.15/0.40 ~sQ20_spl|sQ31_spl|~sQ2_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f469,f260,f458,f125])).
% 0.15/0.40 fof(f500,plain,(
% 0.15/0.40 ~is_antisymmetric_in(sK3_skl,relation_field(sK3_skl))|~in(sK5_skl,relation_field(sK3_skl))|~sQ22_spl|~sQ32_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f284,f463])).
% 0.15/0.40 fof(f502,plain,(
% 0.15/0.40 ~sQ17_spl|~sQ31_spl|~sQ22_spl|~sQ32_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f500,f221,f458,f283,f462])).
% 0.15/0.40 fof(f505,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK3_skl,X0)|~empty(relation_field(sK3_skl))|~sQ29_spl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f451,f114])).
% 0.15/0.40 fof(f507,plain,(
% 0.15/0.40 sQ27_spl|~sQ24_spl|~sQ29_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f505,f395,f375,f450])).
% 0.15/0.40 fof(f512,plain,(
% 0.15/0.40 ![X0]: (~in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)|sK1_skl(X0,sK3_skl)=sK0_skl(X0,sK3_skl)|is_antisymmetric_in(sK3_skl,X0)|~sQ1_spl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f122,f324])).
% 0.15/0.40 fof(f514,plain,(
% 0.15/0.40 ![X0]: (sK1_skl(X0,sK3_skl)=sK0_skl(X0,sK3_skl)|is_antisymmetric_in(sK3_skl,X0)|~sQ1_spl)),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f512,f361])).
% 0.15/0.40 fof(f584,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK10_skl,X0)|~relation(sK10_skl)|in(sK1_skl(X0,sK10_skl),relation_field(sK10_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f321,f109])).
% 0.15/0.40 fof(f585,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK10_skl,X0)|~relation(sK10_skl)|in(sK0_skl(X0,sK10_skl),relation_field(sK10_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f321,f108])).
% 0.15/0.40 fof(f586,plain,(
% 0.15/0.40 ![X0,X1]: (is_antisymmetric_in(sK10_skl,X0)|~relation(sK10_skl)|~is_antisymmetric_in(sK10_skl,X1)|~in(sK1_skl(X0,sK10_skl),X1)|~in(sK0_skl(X0,sK10_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK10_skl),sK0_skl(X0,sK10_skl)),sK10_skl)|sK1_skl(X0,sK10_skl)=sK0_skl(X0,sK10_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f321,f57])).
% 0.15/0.40 fof(f590,definition,(
% 0.15/0.40 ![X0]: (sQ43_spl <=> (is_antisymmetric_in(sK10_skl,X0)|in(sK1_skl(X0,sK10_skl),relation_field(sK10_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f593,definition,(
% 0.15/0.40 sQ44_spl <=> (relation(sK10_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f595,plain,(
% 0.15/0.40 ~relation(sK10_skl)|sQ44_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f593])).
% 0.15/0.40 fof(f596,plain,(
% 0.15/0.40 sQ43_spl|~sQ44_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f584,f590,f593])).
% 0.15/0.40 fof(f597,definition,(
% 0.15/0.40 ![X0]: (sQ45_spl <=> (is_antisymmetric_in(sK10_skl,X0)|in(sK0_skl(X0,sK10_skl),relation_field(sK10_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f600,plain,(
% 0.15/0.40 sQ45_spl|~sQ44_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f585,f597,f593])).
% 0.15/0.40 fof(f601,definition,(
% 0.15/0.40 ![X0,X1]: (sQ46_spl <=> (is_antisymmetric_in(sK10_skl,X0)|~is_antisymmetric_in(sK10_skl,X1)|~in(sK1_skl(X0,sK10_skl),X1)|~in(sK0_skl(X0,sK10_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK10_skl),sK0_skl(X0,sK10_skl)),sK10_skl)|sK1_skl(X0,sK10_skl)=sK0_skl(X0,sK10_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f604,plain,(
% 0.15/0.40 sQ46_spl|~sQ44_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f586,f601,f593])).
% 0.15/0.40 fof(f612,plain,(
% 0.15/0.40 $false|sQ44_spl),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f595,f98])).
% 0.15/0.40 fof(f613,plain,(
% 0.15/0.40 sQ44_spl),
% 0.15/0.40 inference(contradiction_clause,[status(thm)],[f612])).
% 0.15/0.40 fof(f614,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK8_skl,X0)|~relation(sK8_skl)|in(sK1_skl(X0,sK8_skl),relation_field(sK8_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f322,f109])).
% 0.15/0.40 fof(f615,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK8_skl,X0)|~relation(sK8_skl)|in(sK0_skl(X0,sK8_skl),relation_field(sK8_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f322,f108])).
% 0.15/0.40 fof(f616,plain,(
% 0.15/0.40 ![X0,X1]: (is_antisymmetric_in(sK8_skl,X0)|~relation(sK8_skl)|~is_antisymmetric_in(sK8_skl,X1)|~in(sK1_skl(X0,sK8_skl),X1)|~in(sK0_skl(X0,sK8_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK8_skl),sK0_skl(X0,sK8_skl)),sK8_skl)|sK1_skl(X0,sK8_skl)=sK0_skl(X0,sK8_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f322,f57])).
% 0.15/0.40 fof(f620,definition,(
% 0.15/0.40 ![X0]: (sQ49_spl <=> (is_antisymmetric_in(sK8_skl,X0)|in(sK1_skl(X0,sK8_skl),relation_field(sK8_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f623,plain,(
% 0.15/0.40 sQ49_spl|~sQ5_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f614,f620,f144])).
% 0.15/0.40 fof(f624,definition,(
% 0.15/0.40 ![X0]: (sQ50_spl <=> (is_antisymmetric_in(sK8_skl,X0)|in(sK0_skl(X0,sK8_skl),relation_field(sK8_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f627,plain,(
% 0.15/0.40 sQ50_spl|~sQ5_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f615,f624,f144])).
% 0.15/0.40 fof(f628,definition,(
% 0.15/0.40 ![X0,X1]: (sQ51_spl <=> (is_antisymmetric_in(sK8_skl,X0)|~is_antisymmetric_in(sK8_skl,X1)|~in(sK1_skl(X0,sK8_skl),X1)|~in(sK0_skl(X0,sK8_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK8_skl),sK0_skl(X0,sK8_skl)),sK8_skl)|sK1_skl(X0,sK8_skl)=sK0_skl(X0,sK8_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f631,plain,(
% 0.15/0.40 sQ51_spl|~sQ5_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f616,f628,f144])).
% 0.15/0.40 fof(f636,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK6_skl,X0)|~relation(sK6_skl)|in(sK1_skl(X0,sK6_skl),relation_field(sK6_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f323,f109])).
% 0.15/0.40 fof(f637,plain,(
% 0.15/0.40 ![X0]: (is_antisymmetric_in(sK6_skl,X0)|~relation(sK6_skl)|in(sK0_skl(X0,sK6_skl),relation_field(sK6_skl)))),
% 0.15/0.40 inference(resolution,[status(thm)],[f323,f108])).
% 0.15/0.40 fof(f638,plain,(
% 0.15/0.40 ![X0,X1]: (is_antisymmetric_in(sK6_skl,X0)|~relation(sK6_skl)|~is_antisymmetric_in(sK6_skl,X1)|~in(sK1_skl(X0,sK6_skl),X1)|~in(sK0_skl(X0,sK6_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK6_skl),sK0_skl(X0,sK6_skl)),sK6_skl)|sK1_skl(X0,sK6_skl)=sK0_skl(X0,sK6_skl))),
% 0.15/0.40 inference(resolution,[status(thm)],[f323,f57])).
% 0.15/0.40 fof(f642,definition,(
% 0.15/0.40 ![X0]: (sQ53_spl <=> (is_antisymmetric_in(sK6_skl,X0)|in(sK1_skl(X0,sK6_skl),relation_field(sK6_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f645,definition,(
% 0.15/0.40 sQ54_spl <=> (relation(sK6_skl))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f647,plain,(
% 0.15/0.40 ~relation(sK6_skl)|sQ54_spl),
% 0.15/0.40 inference(component_clause,[status(thm)],[f645])).
% 0.15/0.40 fof(f648,plain,(
% 0.15/0.40 sQ53_spl|~sQ54_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f636,f642,f645])).
% 0.15/0.40 fof(f649,definition,(
% 0.15/0.40 ![X0]: (sQ55_spl <=> (is_antisymmetric_in(sK6_skl,X0)|in(sK0_skl(X0,sK6_skl),relation_field(sK6_skl))))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f652,plain,(
% 0.15/0.40 sQ55_spl|~sQ54_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f637,f649,f645])).
% 0.15/0.40 fof(f653,definition,(
% 0.15/0.40 ![X0,X1]: (sQ56_spl <=> (is_antisymmetric_in(sK6_skl,X0)|~is_antisymmetric_in(sK6_skl,X1)|~in(sK1_skl(X0,sK6_skl),X1)|~in(sK0_skl(X0,sK6_skl),X1)|~in(ordered_pair(sK1_skl(X0,sK6_skl),sK0_skl(X0,sK6_skl)),sK6_skl)|sK1_skl(X0,sK6_skl)=sK0_skl(X0,sK6_skl)))),
% 0.15/0.40 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 0.15/0.40 fof(f656,plain,(
% 0.15/0.40 sQ56_spl|~sQ54_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f638,f653,f645])).
% 0.15/0.40 fof(f664,plain,(
% 0.15/0.40 $false|sQ54_spl),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f647,f87])).
% 0.15/0.40 fof(f665,plain,(
% 0.15/0.40 sQ54_spl),
% 0.15/0.40 inference(contradiction_clause,[status(thm)],[f664])).
% 0.15/0.40 fof(f666,plain,(
% 0.15/0.40 sK1_skl(relation_field(sK3_skl),sK3_skl)=sK0_skl(relation_field(sK3_skl),sK3_skl)|~sQ1_spl|sQ17_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f514,f223])).
% 0.15/0.40 fof(f676,plain,(
% 0.15/0.40 ~relation(sK3_skl)|is_antisymmetric_in(sK3_skl,relation_field(sK3_skl))|~sQ1_spl|sQ17_spl),
% 0.15/0.40 inference(resolution,[status(thm)],[f666,f62])).
% 0.15/0.40 fof(f688,plain,(
% 0.15/0.40 ~sQ20_spl|sQ17_spl|~sQ1_spl),
% 0.15/0.40 inference(split_clause,[status(thm)],[f676,f260,f221,f121])).
% 0.15/0.40 fof(f721,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(sat_refutation,[status(thm)],[f124,f128,f132,f136,f150,f157,f164,f166,f178,f185,f224,f263,f286,f289,f394,f401,f414,f453,f457,f465,f473,f502,f507,f596,f600,f604,f613,f623,f627,f631,f648,f652,f656,f665,f688])).
% 0.15/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.43 % Elapsed time: 0.055045 seconds
% 0.15/0.43 % CPU time: 0.173551 seconds
% 0.15/0.43 % Total memory used: 103.532 MB
% 0.15/0.43 % Net memory used: 103.474 MB
%------------------------------------------------------------------------------