TSTP Solution File: SEU265+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 : Wed May 31 12:36:31 EDT 2023
% Result : Theorem 2.06s 0.67s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n023.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 09:34:08 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 2.06/0.67 % Refutation found
% 2.06/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.06/0.67 % SZS output start CNFRefutation for theBenchmark
% 2.06/0.67 fof(f1,axiom,(
% 2.06/0.67 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f2,axiom,(
% 2.06/0.67 (! [A,B,C] :( element(C,powerset(cartesian_product2(A,B)))=> relation(C) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f4,axiom,(
% 2.06/0.67 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f13,axiom,(
% 2.06/0.67 (! [A,B,C] :( relation_of2(C,A,B)=> element(relation_dom_as_subset(A,B,C),powerset(A)) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f17,axiom,(
% 2.06/0.67 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> element(C,powerset(cartesian_product2(A,B))) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f18,axiom,(
% 2.06/0.67 (! [A,B] :(? [C] : relation_of2(C,A,B) ))),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f19,axiom,(
% 2.06/0.67 (! [A] :(? [B] : element(B,A) ))),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f21,axiom,(
% 2.06/0.67 empty(empty_set) ),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f25,axiom,(
% 2.06/0.67 (! [A,B,C] :( relation_of2(C,A,B)=> relation_dom_as_subset(A,B,C) = relation_dom(C) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f26,axiom,(
% 2.06/0.67 (! [A,B,C] :( relation_of2_as_subset(C,A,B)<=> relation_of2(C,A,B) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f28,axiom,(
% 2.06/0.67 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f29,axiom,(
% 2.06/0.67 (! [A,B,C] :( relation(C)=> ( in(ordered_pair(A,B),C)=> ( in(A,relation_dom(C))& in(B,relation_rng(C)) ) ) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f30,conjecture,(
% 2.06/0.67 (! [A,B,C] :( relation_of2_as_subset(C,B,A)=> ( (! [D] :~ ( in(D,B)& (! [E] : ~ in(ordered_pair(D,E),C) )))<=> relation_dom_as_subset(B,A,C) = B ) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f31,negated_conjecture,(
% 2.06/0.67 ~((! [A,B,C] :( relation_of2_as_subset(C,B,A)=> ( (! [D] :~ ( in(D,B)& (! [E] : ~ in(ordered_pair(D,E),C) )))<=> relation_dom_as_subset(B,A,C) = B ) ) ))),
% 2.06/0.67 inference(negated_conjecture,[status(cth)],[f30])).
% 2.06/0.67 fof(f32,axiom,(
% 2.06/0.67 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f33,axiom,(
% 2.06/0.67 (! [A,B] :( (! [C] :( in(C,A)<=> in(C,B) ))=> A = B ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f35,axiom,(
% 2.06/0.67 (! [A,B,C] :( ( in(A,B)& element(B,powerset(C)) )=> element(A,C) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f36,axiom,(
% 2.06/0.67 (! [A,B,C] :~ ( in(A,B)& element(B,powerset(C))& empty(C) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f37,axiom,(
% 2.06/0.67 (! [A] :( empty(A)=> A = empty_set ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f38,axiom,(
% 2.06/0.67 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 2.06/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.06/0.67 fof(f40,plain,(
% 2.06/0.67 ![A,B]: (~in(A,B)|~in(B,A))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 2.06/0.67 fof(f41,plain,(
% 2.06/0.67 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f40])).
% 2.06/0.67 fof(f42,plain,(
% 2.06/0.67 ![A,B,C]: (~element(C,powerset(cartesian_product2(A,B)))|relation(C))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 2.06/0.67 fof(f43,plain,(
% 2.06/0.67 ![C]: ((![A,B]: ~element(C,powerset(cartesian_product2(A,B))))|relation(C))),
% 2.06/0.67 inference(miniscoping,[status(esa)],[f42])).
% 2.06/0.67 fof(f44,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~element(X0,powerset(cartesian_product2(X1,X2)))|relation(X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f43])).
% 2.06/0.67 fof(f46,plain,(
% 2.06/0.67 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 2.06/0.67 fof(f47,plain,(
% 2.06/0.67 ![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)))))))))),
% 2.06/0.67 inference(NNF_transformation,[status(esa)],[f46])).
% 2.06/0.67 fof(f48,plain,(
% 2.06/0.67 ![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)))))))))),
% 2.06/0.67 inference(miniscoping,[status(esa)],[f47])).
% 2.06/0.67 fof(f49,plain,(
% 2.06/0.67 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sk0_0(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sk0_1(B,A),B)|(![D]: ~in(ordered_pair(sk0_1(B,A),D),A)))&(in(sk0_1(B,A),B)|in(ordered_pair(sk0_1(B,A),sk0_2(B,A)),A)))))))),
% 2.06/0.67 inference(skolemization,[status(esa)],[f48])).
% 2.06/0.67 fof(f50,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation(X0)|~X1=relation_dom(X0)|~in(X2,X1)|in(ordered_pair(X2,sk0_0(X2,X1,X0)),X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f49])).
% 2.06/0.67 fof(f51,plain,(
% 2.06/0.67 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f49])).
% 2.06/0.67 fof(f52,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation(X0)|X1=relation_dom(X0)|~in(sk0_1(X1,X0),X1)|~in(ordered_pair(sk0_1(X1,X0),X2),X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f49])).
% 2.06/0.67 fof(f53,plain,(
% 2.06/0.67 ![X0,X1]: (~relation(X0)|X1=relation_dom(X0)|in(sk0_1(X1,X0),X1)|in(ordered_pair(sk0_1(X1,X0),sk0_2(X1,X0)),X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f49])).
% 2.06/0.67 fof(f55,plain,(
% 2.06/0.67 ![A,B,C]: (~relation_of2(C,A,B)|element(relation_dom_as_subset(A,B,C),powerset(A)))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 2.06/0.67 fof(f56,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|element(relation_dom_as_subset(X1,X2,X0),powerset(X1)))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f55])).
% 2.06/0.67 fof(f57,plain,(
% 2.06/0.67 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 2.06/0.67 fof(f58,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|element(X0,powerset(cartesian_product2(X1,X2))))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f57])).
% 2.06/0.67 fof(f59,plain,(
% 2.06/0.67 ![A,B]: relation_of2(sk0_3(B,A),A,B)),
% 2.06/0.67 inference(skolemization,[status(esa)],[f18])).
% 2.06/0.67 fof(f60,plain,(
% 2.06/0.67 ![X0,X1]: (relation_of2(sk0_3(X0,X1),X1,X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f59])).
% 2.06/0.67 fof(f61,plain,(
% 2.06/0.67 ![A]: element(sk0_4(A),A)),
% 2.06/0.67 inference(skolemization,[status(esa)],[f19])).
% 2.06/0.67 fof(f62,plain,(
% 2.06/0.67 ![X0]: (element(sk0_4(X0),X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f61])).
% 2.06/0.67 fof(f65,plain,(
% 2.06/0.67 empty(empty_set)),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f21])).
% 2.06/0.67 fof(f71,plain,(
% 2.06/0.67 ![A,B,C]: (~relation_of2(C,A,B)|relation_dom_as_subset(A,B,C)=relation_dom(C))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 2.06/0.67 fof(f72,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|relation_dom_as_subset(X1,X2,X0)=relation_dom(X0))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f71])).
% 2.06/0.67 fof(f73,plain,(
% 2.06/0.67 ![A,B,C]: ((~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B))&(relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 2.06/0.67 inference(NNF_transformation,[status(esa)],[f26])).
% 2.06/0.67 fof(f74,plain,(
% 2.06/0.67 (![A,B,C]: (~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B)))&(![A,B,C]: (relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 2.06/0.67 inference(miniscoping,[status(esa)],[f73])).
% 2.06/0.67 fof(f75,plain,(
% 2.06/0.67 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation_of2(X0,X1,X2))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f74])).
% 2.06/0.67 fof(f79,plain,(
% 2.06/0.67 ![A,B]: (~in(A,B)|element(A,B))),
% 2.06/0.67 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 2.06/0.67 fof(f80,plain,(
% 2.06/0.67 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 2.06/0.67 inference(cnf_transformation,[status(esa)],[f79])).
% 2.06/0.67 fof(f81,plain,(
% 2.06/0.67 ![A,B,C]: (~relation(C)|(~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&in(B,relation_rng(C)))))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 2.06/0.69 fof(f82,plain,(
% 2.06/0.69 ![C]: (~relation(C)|(![A,B]: (~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&in(B,relation_rng(C))))))),
% 2.06/0.69 inference(miniscoping,[status(esa)],[f81])).
% 2.06/0.69 fof(f84,plain,(
% 2.06/0.69 ![X0,X1,X2]: (~relation(X0)|~in(ordered_pair(X1,X2),X0)|in(X2,relation_rng(X0)))),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f82])).
% 2.06/0.69 fof(f85,plain,(
% 2.06/0.69 (?[A,B,C]: (relation_of2_as_subset(C,B,A)&((![D]: (~in(D,B)|(?[E]: in(ordered_pair(D,E),C))))<~>relation_dom_as_subset(B,A,C)=B)))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 2.06/0.69 fof(f86,plain,(
% 2.06/0.69 ?[A,B,C]: (relation_of2_as_subset(C,B,A)&(((![D]: (~in(D,B)|(?[E]: in(ordered_pair(D,E),C))))|relation_dom_as_subset(B,A,C)=B)&((?[D]: (in(D,B)&(![E]: ~in(ordered_pair(D,E),C))))|~relation_dom_as_subset(B,A,C)=B)))),
% 2.06/0.69 inference(NNF_transformation,[status(esa)],[f85])).
% 2.06/0.69 fof(f87,plain,(
% 2.06/0.69 (relation_of2_as_subset(sk0_10,sk0_9,sk0_8)&(((![D]: (~in(D,sk0_9)|in(ordered_pair(D,sk0_11(D)),sk0_10)))|relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9)&((in(sk0_12,sk0_9)&(![E]: ~in(ordered_pair(sk0_12,E),sk0_10)))|~relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9)))),
% 2.06/0.69 inference(skolemization,[status(esa)],[f86])).
% 2.06/0.69 fof(f88,plain,(
% 2.06/0.69 relation_of2_as_subset(sk0_10,sk0_9,sk0_8)),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f87])).
% 2.06/0.69 fof(f89,plain,(
% 2.06/0.69 ![X0]: (~in(X0,sk0_9)|in(ordered_pair(X0,sk0_11(X0)),sk0_10)|relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9)),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f87])).
% 2.06/0.69 fof(f90,plain,(
% 2.06/0.69 in(sk0_12,sk0_9)|~relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f87])).
% 2.06/0.69 fof(f91,plain,(
% 2.06/0.69 ![X0]: (~in(ordered_pair(sk0_12,X0),sk0_10)|~relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9)),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f87])).
% 2.06/0.69 fof(f92,plain,(
% 2.06/0.69 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 2.06/0.69 fof(f93,plain,(
% 2.06/0.69 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f92])).
% 2.06/0.69 fof(f94,plain,(
% 2.06/0.69 ![A,B]: ((?[C]: (in(C,A)<~>in(C,B)))|A=B)),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 2.06/0.69 fof(f95,plain,(
% 2.06/0.69 ![A,B]: ((?[C]: ((in(C,A)|in(C,B))&(~in(C,A)|~in(C,B))))|A=B)),
% 2.06/0.69 inference(NNF_transformation,[status(esa)],[f94])).
% 2.06/0.69 fof(f96,plain,(
% 2.06/0.69 ![A,B]: (((in(sk0_13(B,A),A)|in(sk0_13(B,A),B))&(~in(sk0_13(B,A),A)|~in(sk0_13(B,A),B)))|A=B)),
% 2.06/0.69 inference(skolemization,[status(esa)],[f95])).
% 2.06/0.69 fof(f97,plain,(
% 2.06/0.69 ![X0,X1]: (in(sk0_13(X0,X1),X1)|in(sk0_13(X0,X1),X0)|X1=X0)),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f96])).
% 2.06/0.69 fof(f103,plain,(
% 2.06/0.69 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|element(A,C))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 2.06/0.69 fof(f104,plain,(
% 2.06/0.69 ![A,C]: ((![B]: (~in(A,B)|~element(B,powerset(C))))|element(A,C))),
% 2.06/0.69 inference(miniscoping,[status(esa)],[f103])).
% 2.06/0.69 fof(f105,plain,(
% 2.06/0.69 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|element(X0,X2))),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f104])).
% 2.06/0.69 fof(f106,plain,(
% 2.06/0.69 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|~empty(C))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f36])).
% 2.06/0.69 fof(f107,plain,(
% 2.06/0.69 ![C]: ((![B]: ((![A]: ~in(A,B))|~element(B,powerset(C))))|~empty(C))),
% 2.06/0.69 inference(miniscoping,[status(esa)],[f106])).
% 2.06/0.69 fof(f108,plain,(
% 2.06/0.69 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|~empty(X2))),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f107])).
% 2.06/0.69 fof(f109,plain,(
% 2.06/0.69 ![A]: (~empty(A)|A=empty_set)),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 2.06/0.69 fof(f110,plain,(
% 2.06/0.69 ![X0]: (~empty(X0)|X0=empty_set)),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f109])).
% 2.06/0.69 fof(f111,plain,(
% 2.06/0.69 ![A,B]: (~in(A,B)|~empty(B))),
% 2.06/0.69 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 2.06/0.69 fof(f112,plain,(
% 2.06/0.69 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 2.06/0.69 inference(miniscoping,[status(esa)],[f111])).
% 2.06/0.69 fof(f113,plain,(
% 2.06/0.69 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 2.06/0.69 inference(cnf_transformation,[status(esa)],[f112])).
% 2.06/0.69 fof(f117,plain,(
% 2.06/0.69 spl0_0 <=> ~in(X0,sk0_9)|in(ordered_pair(X0,sk0_11(X0)),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f118,plain,(
% 2.06/0.69 ![X0]: (~in(X0,sk0_9)|in(ordered_pair(X0,sk0_11(X0)),sk0_10)|~spl0_0)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f117])).
% 2.06/0.69 fof(f120,plain,(
% 2.06/0.69 spl0_1 <=> relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f121,plain,(
% 2.06/0.69 relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9|~spl0_1),
% 2.06/0.69 inference(component_clause,[status(thm)],[f120])).
% 2.06/0.69 fof(f122,plain,(
% 2.06/0.69 ~relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9|spl0_1),
% 2.06/0.69 inference(component_clause,[status(thm)],[f120])).
% 2.06/0.69 fof(f123,plain,(
% 2.06/0.69 spl0_0|spl0_1),
% 2.06/0.69 inference(split_clause,[status(thm)],[f89,f117,f120])).
% 2.06/0.69 fof(f124,plain,(
% 2.06/0.69 spl0_2 <=> in(sk0_12,sk0_9)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f125,plain,(
% 2.06/0.69 in(sk0_12,sk0_9)|~spl0_2),
% 2.06/0.69 inference(component_clause,[status(thm)],[f124])).
% 2.06/0.69 fof(f127,plain,(
% 2.06/0.69 spl0_2|~spl0_1),
% 2.06/0.69 inference(split_clause,[status(thm)],[f90,f124,f120])).
% 2.06/0.69 fof(f128,plain,(
% 2.06/0.69 spl0_3 <=> ~in(ordered_pair(sk0_12,X0),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f129,plain,(
% 2.06/0.69 ![X0]: (~in(ordered_pair(sk0_12,X0),sk0_10)|~spl0_3)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f128])).
% 2.06/0.69 fof(f131,plain,(
% 2.06/0.69 spl0_3|~spl0_1),
% 2.06/0.69 inference(split_clause,[status(thm)],[f91,f128,f120])).
% 2.06/0.69 fof(f132,plain,(
% 2.06/0.69 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,sk0_0(X1,relation_dom(X0),X0)),X0))),
% 2.06/0.69 inference(destructive_equality_resolution,[status(esa)],[f50])).
% 2.06/0.69 fof(f133,plain,(
% 2.06/0.69 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 2.06/0.69 inference(destructive_equality_resolution,[status(esa)],[f51])).
% 2.06/0.69 fof(f134,plain,(
% 2.06/0.69 relation_of2(sk0_10,sk0_9,sk0_8)),
% 2.06/0.69 inference(resolution,[status(thm)],[f75,f88])).
% 2.06/0.69 fof(f135,plain,(
% 2.06/0.69 element(relation_dom_as_subset(sk0_9,sk0_8,sk0_10),powerset(sk0_9))),
% 2.06/0.69 inference(resolution,[status(thm)],[f134,f56])).
% 2.06/0.69 fof(f137,plain,(
% 2.06/0.69 relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=relation_dom(sk0_10)),
% 2.06/0.69 inference(resolution,[status(thm)],[f72,f134])).
% 2.06/0.69 fof(f138,plain,(
% 2.06/0.69 element(relation_dom(sk0_10),powerset(sk0_9))),
% 2.06/0.69 inference(backward_demodulation,[status(thm)],[f137,f135])).
% 2.06/0.69 fof(f139,plain,(
% 2.06/0.69 ~relation_dom(sk0_10)=sk0_9|spl0_1),
% 2.06/0.69 inference(backward_demodulation,[status(thm)],[f137,f122])).
% 2.06/0.69 fof(f145,plain,(
% 2.06/0.69 element(sk0_10,powerset(cartesian_product2(sk0_9,sk0_8)))),
% 2.06/0.69 inference(resolution,[status(thm)],[f58,f88])).
% 2.06/0.69 fof(f146,plain,(
% 2.06/0.69 relation(sk0_10)),
% 2.06/0.69 inference(resolution,[status(thm)],[f145,f44])).
% 2.06/0.69 fof(f148,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|in(ordered_pair(sk0_1(X0,sk0_10),sk0_2(X0,sk0_10)),sk0_10))),
% 2.06/0.69 inference(resolution,[status(thm)],[f53,f146])).
% 2.06/0.69 fof(f149,plain,(
% 2.06/0.69 spl0_4 <=> X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|X0=relation_dom(sk0_10)|~in(sk0_1(X0,sk0_10),X0)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f152,plain,(
% 2.06/0.69 spl0_5 <=> relation(sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f154,plain,(
% 2.06/0.69 ~relation(sk0_10)|spl0_5),
% 2.06/0.69 inference(component_clause,[status(thm)],[f152])).
% 2.06/0.69 fof(f155,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|~relation(sk0_10)|X0=relation_dom(sk0_10)|~in(sk0_1(X0,sk0_10),X0))),
% 2.06/0.69 inference(resolution,[status(thm)],[f148,f52])).
% 2.06/0.69 fof(f156,plain,(
% 2.06/0.69 spl0_4|~spl0_5),
% 2.06/0.69 inference(split_clause,[status(thm)],[f155,f149,f152])).
% 2.06/0.69 fof(f157,plain,(
% 2.06/0.69 spl0_6 <=> X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|in(sk0_1(X0,sk0_10),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f158,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|in(sk0_1(X0,sk0_10),relation_dom(sk0_10))|~spl0_6)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f157])).
% 2.06/0.69 fof(f160,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|~relation(sk0_10)|in(sk0_1(X0,sk0_10),relation_dom(sk0_10)))),
% 2.06/0.69 inference(resolution,[status(thm)],[f148,f133])).
% 2.06/0.69 fof(f161,plain,(
% 2.06/0.69 spl0_6|~spl0_5),
% 2.06/0.69 inference(split_clause,[status(thm)],[f160,f157,f152])).
% 2.06/0.69 fof(f172,plain,(
% 2.06/0.69 $false|spl0_5),
% 2.06/0.69 inference(forward_subsumption_resolution,[status(thm)],[f154,f146])).
% 2.06/0.69 fof(f173,plain,(
% 2.06/0.69 spl0_5),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f172])).
% 2.06/0.69 fof(f174,plain,(
% 2.06/0.69 relation_dom(sk0_10)=sk0_9|~spl0_1),
% 2.06/0.69 inference(forward_demodulation,[status(thm)],[f137,f121])).
% 2.06/0.69 fof(f177,plain,(
% 2.06/0.69 relation_dom_as_subset(sk0_9,sk0_8,sk0_10)=sk0_9|~spl0_1),
% 2.06/0.69 inference(backward_demodulation,[status(thm)],[f174,f137])).
% 2.06/0.69 fof(f178,plain,(
% 2.06/0.69 spl0_9 <=> ~in(X0,sk0_9)|in(ordered_pair(X0,sk0_0(X0,relation_dom(sk0_10),sk0_10)),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f179,plain,(
% 2.06/0.69 ![X0]: (~in(X0,sk0_9)|in(ordered_pair(X0,sk0_0(X0,relation_dom(sk0_10),sk0_10)),sk0_10)|~spl0_9)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f178])).
% 2.06/0.69 fof(f181,plain,(
% 2.06/0.69 ![X0]: (~relation(sk0_10)|~in(X0,sk0_9)|in(ordered_pair(X0,sk0_0(X0,relation_dom(sk0_10),sk0_10)),sk0_10)|~spl0_1)),
% 2.06/0.69 inference(paramodulation,[status(thm)],[f174,f132])).
% 2.06/0.69 fof(f182,plain,(
% 2.06/0.69 ~spl0_5|spl0_9|~spl0_1),
% 2.06/0.69 inference(split_clause,[status(thm)],[f181,f152,f178,f120])).
% 2.06/0.69 fof(f197,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),relation_dom(sk0_10))|element(sk0_1(X0,sk0_10),X0)|~spl0_6)),
% 2.06/0.69 inference(resolution,[status(thm)],[f158,f80])).
% 2.06/0.69 fof(f203,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),relation_dom(sk0_10))|~empty(X0)|~spl0_6)),
% 2.06/0.69 inference(resolution,[status(thm)],[f158,f113])).
% 2.06/0.69 fof(f210,plain,(
% 2.06/0.69 spl0_15 <=> X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|in(ordered_pair(sk0_1(X0,sk0_10),sk0_0(sk0_1(X0,sk0_10),relation_dom(sk0_10),sk0_10)),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f213,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|in(sk0_1(X0,sk0_10),X0)|~relation(sk0_10)|in(ordered_pair(sk0_1(X0,sk0_10),sk0_0(sk0_1(X0,sk0_10),relation_dom(sk0_10),sk0_10)),sk0_10)|~spl0_6)),
% 2.06/0.69 inference(resolution,[status(thm)],[f158,f132])).
% 2.06/0.69 fof(f214,plain,(
% 2.06/0.69 spl0_15|~spl0_5|~spl0_6),
% 2.06/0.69 inference(split_clause,[status(thm)],[f213,f210,f152,f157])).
% 2.06/0.69 fof(f240,plain,(
% 2.06/0.69 spl0_19 <=> X0=relation_dom(sk0_10)|element(sk0_1(X0,sk0_10),X0)|in(ordered_pair(sk0_1(X0,sk0_10),sk0_0(sk0_1(X0,sk0_10),relation_dom(sk0_10),sk0_10)),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f243,plain,(
% 2.06/0.69 ![X0]: (X0=relation_dom(sk0_10)|element(sk0_1(X0,sk0_10),X0)|~relation(sk0_10)|in(ordered_pair(sk0_1(X0,sk0_10),sk0_0(sk0_1(X0,sk0_10),relation_dom(sk0_10),sk0_10)),sk0_10)|~spl0_6)),
% 2.06/0.69 inference(resolution,[status(thm)],[f197,f132])).
% 2.06/0.69 fof(f244,plain,(
% 2.06/0.69 spl0_19|~spl0_5|~spl0_6),
% 2.06/0.69 inference(split_clause,[status(thm)],[f243,f240,f152,f157])).
% 2.06/0.69 fof(f293,plain,(
% 2.06/0.69 spl0_22 <=> sk0_9=relation_dom(sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f294,plain,(
% 2.06/0.69 sk0_9=relation_dom(sk0_10)|~spl0_22),
% 2.06/0.69 inference(component_clause,[status(thm)],[f293])).
% 2.06/0.69 fof(f296,plain,(
% 2.06/0.69 spl0_23 <=> in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f297,plain,(
% 2.06/0.69 in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))|~spl0_23),
% 2.06/0.69 inference(component_clause,[status(thm)],[f296])).
% 2.06/0.69 fof(f299,plain,(
% 2.06/0.69 spl0_24 <=> in(ordered_pair(sk0_1(sk0_9,sk0_10),sk0_11(sk0_1(sk0_9,sk0_10))),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f300,plain,(
% 2.06/0.69 in(ordered_pair(sk0_1(sk0_9,sk0_10),sk0_11(sk0_1(sk0_9,sk0_10))),sk0_10)|~spl0_24),
% 2.06/0.69 inference(component_clause,[status(thm)],[f299])).
% 2.06/0.69 fof(f302,plain,(
% 2.06/0.69 sk0_9=relation_dom(sk0_10)|in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))|in(ordered_pair(sk0_1(sk0_9,sk0_10),sk0_11(sk0_1(sk0_9,sk0_10))),sk0_10)|~spl0_6|~spl0_0),
% 2.06/0.69 inference(resolution,[status(thm)],[f158,f118])).
% 2.06/0.69 fof(f303,plain,(
% 2.06/0.69 spl0_22|spl0_23|spl0_24|~spl0_6|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f302,f293,f296,f299,f157,f117])).
% 2.06/0.69 fof(f359,plain,(
% 2.06/0.69 spl0_25 <=> in(sk0_1(sk0_9,sk0_10),sk0_9)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f360,plain,(
% 2.06/0.69 in(sk0_1(sk0_9,sk0_10),sk0_9)|~spl0_25),
% 2.06/0.69 inference(component_clause,[status(thm)],[f359])).
% 2.06/0.69 fof(f361,plain,(
% 2.06/0.69 ~in(sk0_1(sk0_9,sk0_10),sk0_9)|spl0_25),
% 2.06/0.69 inference(component_clause,[status(thm)],[f359])).
% 2.06/0.69 fof(f362,plain,(
% 2.06/0.69 ~relation(sk0_10)|sk0_9=relation_dom(sk0_10)|~in(sk0_1(sk0_9,sk0_10),sk0_9)|~spl0_24),
% 2.06/0.69 inference(resolution,[status(thm)],[f300,f52])).
% 2.06/0.69 fof(f363,plain,(
% 2.06/0.69 ~spl0_5|spl0_22|~spl0_25|~spl0_24),
% 2.06/0.69 inference(split_clause,[status(thm)],[f362,f152,f293,f359,f299])).
% 2.06/0.69 fof(f368,plain,(
% 2.06/0.69 $false|spl0_1|~spl0_22),
% 2.06/0.69 inference(forward_subsumption_resolution,[status(thm)],[f294,f139])).
% 2.06/0.69 fof(f369,plain,(
% 2.06/0.69 spl0_1|~spl0_22),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f368])).
% 2.06/0.69 fof(f377,plain,(
% 2.06/0.69 sk0_9=relation_dom(sk0_10)|in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))|spl0_25|~spl0_6),
% 2.06/0.69 inference(resolution,[status(thm)],[f361,f158])).
% 2.06/0.69 fof(f378,plain,(
% 2.06/0.69 spl0_22|spl0_23|spl0_25|~spl0_6),
% 2.06/0.69 inference(split_clause,[status(thm)],[f377,f293,f296,f359,f157])).
% 2.06/0.69 fof(f425,plain,(
% 2.06/0.69 ![X0,X1]: (relation_dom_as_subset(X0,X1,sk0_3(X1,X0))=relation_dom(sk0_3(X1,X0)))),
% 2.06/0.69 inference(resolution,[status(thm)],[f60,f72])).
% 2.06/0.69 fof(f427,plain,(
% 2.06/0.69 ![X0,X1]: (element(relation_dom_as_subset(X0,X1,sk0_3(X1,X0)),powerset(X0)))),
% 2.06/0.69 inference(resolution,[status(thm)],[f60,f56])).
% 2.06/0.69 fof(f486,plain,(
% 2.06/0.69 ![X0]: (empty(X0)|in(sk0_4(X0),X0))),
% 2.06/0.69 inference(resolution,[status(thm)],[f93,f62])).
% 2.06/0.69 fof(f538,plain,(
% 2.06/0.69 spl0_39 <=> empty(sk0_9)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f539,plain,(
% 2.06/0.69 empty(sk0_9)|~spl0_39),
% 2.06/0.69 inference(component_clause,[status(thm)],[f538])).
% 2.06/0.69 fof(f541,plain,(
% 2.06/0.69 spl0_40 <=> in(ordered_pair(sk0_4(sk0_9),sk0_11(sk0_4(sk0_9))),sk0_10)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f542,plain,(
% 2.06/0.69 in(ordered_pair(sk0_4(sk0_9),sk0_11(sk0_4(sk0_9))),sk0_10)|~spl0_40),
% 2.06/0.69 inference(component_clause,[status(thm)],[f541])).
% 2.06/0.69 fof(f544,plain,(
% 2.06/0.69 empty(sk0_9)|in(ordered_pair(sk0_4(sk0_9),sk0_11(sk0_4(sk0_9))),sk0_10)|~spl0_0),
% 2.06/0.69 inference(resolution,[status(thm)],[f486,f118])).
% 2.06/0.69 fof(f545,plain,(
% 2.06/0.69 spl0_39|spl0_40|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f544,f538,f541,f117])).
% 2.06/0.69 fof(f549,plain,(
% 2.06/0.69 sk0_9=relation_dom(sk0_10)|in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))|~spl0_39|~spl0_6),
% 2.06/0.69 inference(resolution,[status(thm)],[f539,f203])).
% 2.06/0.69 fof(f550,plain,(
% 2.06/0.69 spl0_22|spl0_23|~spl0_39|~spl0_6),
% 2.06/0.69 inference(split_clause,[status(thm)],[f549,f293,f296,f538,f157])).
% 2.06/0.69 fof(f552,plain,(
% 2.06/0.69 sk0_9=empty_set|~spl0_39),
% 2.06/0.69 inference(resolution,[status(thm)],[f539,f110])).
% 2.06/0.69 fof(f584,plain,(
% 2.06/0.69 relation_dom(sk0_10)=sk0_9|~spl0_1),
% 2.06/0.69 inference(forward_demodulation,[status(thm)],[f137,f177])).
% 2.06/0.69 fof(f616,plain,(
% 2.06/0.69 ![X0]: (~relation(sk0_10)|~in(X0,sk0_9)|in(ordered_pair(X0,sk0_0(X0,relation_dom(sk0_10),sk0_10)),sk0_10)|~spl0_22)),
% 2.06/0.69 inference(paramodulation,[status(thm)],[f294,f132])).
% 2.06/0.69 fof(f617,plain,(
% 2.06/0.69 ~spl0_5|spl0_9|~spl0_22),
% 2.06/0.69 inference(split_clause,[status(thm)],[f616,f152,f178,f293])).
% 2.06/0.69 fof(f686,plain,(
% 2.06/0.69 spl0_46 <=> empty(empty_set)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f688,plain,(
% 2.06/0.69 ~empty(empty_set)|spl0_46),
% 2.06/0.69 inference(component_clause,[status(thm)],[f686])).
% 2.06/0.69 fof(f691,plain,(
% 2.06/0.69 $false|spl0_46),
% 2.06/0.69 inference(forward_subsumption_resolution,[status(thm)],[f688,f65])).
% 2.06/0.69 fof(f692,plain,(
% 2.06/0.69 spl0_46),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f691])).
% 2.06/0.69 fof(f706,plain,(
% 2.06/0.69 ~empty(sk0_9)|~spl0_2),
% 2.06/0.69 inference(resolution,[status(thm)],[f125,f113])).
% 2.06/0.69 fof(f721,plain,(
% 2.06/0.69 ![X0]: (in(ordered_pair(sk0_13(sk0_9,X0),sk0_11(sk0_13(sk0_9,X0))),sk0_10)|in(sk0_13(sk0_9,X0),X0)|X0=sk0_9|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f118,f97])).
% 2.06/0.69 fof(f724,plain,(
% 2.06/0.69 ![X0]: (in(ordered_pair(sk0_13(X0,sk0_9),sk0_11(sk0_13(X0,sk0_9))),sk0_10)|in(sk0_13(X0,sk0_9),X0)|sk0_9=X0|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f118,f97])).
% 2.06/0.69 fof(f787,plain,(
% 2.06/0.69 spl0_52 <=> empty_set=sk0_9),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f788,plain,(
% 2.06/0.69 empty_set=sk0_9|~spl0_52),
% 2.06/0.69 inference(component_clause,[status(thm)],[f787])).
% 2.06/0.69 fof(f806,plain,(
% 2.06/0.69 ~empty(empty_set)|~spl0_52|~spl0_2),
% 2.06/0.69 inference(backward_demodulation,[status(thm)],[f788,f706])).
% 2.06/0.69 fof(f807,plain,(
% 2.06/0.69 ~spl0_46|~spl0_52|~spl0_2),
% 2.06/0.69 inference(split_clause,[status(thm)],[f806,f686,f787,f124])).
% 2.06/0.69 fof(f808,plain,(
% 2.06/0.69 spl0_52|~spl0_39),
% 2.06/0.69 inference(split_clause,[status(thm)],[f552,f787,f538])).
% 2.06/0.69 fof(f848,plain,(
% 2.06/0.69 spl0_54 <=> element(sk0_1(sk0_9,sk0_10),sk0_9)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f849,plain,(
% 2.06/0.69 element(sk0_1(sk0_9,sk0_10),sk0_9)|~spl0_54),
% 2.06/0.69 inference(component_clause,[status(thm)],[f848])).
% 2.06/0.69 fof(f850,plain,(
% 2.06/0.69 ~element(sk0_1(sk0_9,sk0_10),sk0_9)|spl0_54),
% 2.06/0.69 inference(component_clause,[status(thm)],[f848])).
% 2.06/0.69 fof(f864,plain,(
% 2.06/0.69 spl0_56 <=> X0=sk0_9|in(sk0_1(X0,sk0_10),X0)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f865,plain,(
% 2.06/0.69 ![X0]: (X0=sk0_9|in(sk0_1(X0,sk0_10),X0)|~spl0_56)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f864])).
% 2.06/0.69 fof(f881,plain,(
% 2.06/0.69 ![X0]: (~in(X0,sk0_9)|in(ordered_pair(X0,sk0_0(X0,sk0_9,sk0_10)),sk0_10)|~spl0_1|~spl0_9)),
% 2.06/0.69 inference(forward_demodulation,[status(thm)],[f584,f179])).
% 2.06/0.69 fof(f882,plain,(
% 2.06/0.69 in(ordered_pair(sk0_12,sk0_0(sk0_12,sk0_9,sk0_10)),sk0_10)|~spl0_1|~spl0_9|~spl0_2),
% 2.06/0.69 inference(resolution,[status(thm)],[f881,f125])).
% 2.06/0.69 fof(f883,plain,(
% 2.06/0.69 $false|~spl0_3|~spl0_1|~spl0_9|~spl0_2),
% 2.06/0.69 inference(forward_subsumption_resolution,[status(thm)],[f882,f129])).
% 2.06/0.69 fof(f884,plain,(
% 2.06/0.69 ~spl0_3|~spl0_1|~spl0_9|~spl0_2),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f883])).
% 2.06/0.69 fof(f1016,plain,(
% 2.06/0.69 ![X0,X1]: (element(relation_dom(sk0_3(X0,X1)),powerset(X1)))),
% 2.06/0.69 inference(forward_demodulation,[status(thm)],[f425,f427])).
% 2.06/0.69 fof(f1018,plain,(
% 2.06/0.69 ![X0,X1,X2]: (~in(X0,relation_dom(sk0_3(X1,X2)))|~empty(X2))),
% 2.06/0.69 inference(resolution,[status(thm)],[f1016,f108])).
% 2.06/0.69 fof(f1065,plain,(
% 2.06/0.69 ![X0,X1]: (~empty(X0)|empty(relation_dom(sk0_3(X1,X0))))),
% 2.06/0.69 inference(resolution,[status(thm)],[f1018,f486])).
% 2.06/0.69 fof(f1066,plain,(
% 2.06/0.69 ![X0]: (empty(relation_dom(sk0_3(X0,empty_set))))),
% 2.06/0.69 inference(resolution,[status(thm)],[f1065,f65])).
% 2.06/0.69 fof(f1094,plain,(
% 2.06/0.69 ![X0]: (relation_dom(sk0_3(X0,empty_set))=empty_set)),
% 2.06/0.69 inference(resolution,[status(thm)],[f1066,f110])).
% 2.06/0.69 fof(f1136,plain,(
% 2.06/0.69 spl0_76 <=> in(relation_dom(sk0_10),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1137,plain,(
% 2.06/0.69 in(relation_dom(sk0_10),relation_dom(sk0_10))|~spl0_76),
% 2.06/0.69 inference(component_clause,[status(thm)],[f1136])).
% 2.06/0.69 fof(f1162,plain,(
% 2.06/0.69 ~in(relation_dom(sk0_10),relation_dom(sk0_10))|~spl0_76),
% 2.06/0.69 inference(resolution,[status(thm)],[f1137,f41])).
% 2.06/0.69 fof(f1163,plain,(
% 2.06/0.69 $false|~spl0_76),
% 2.06/0.69 inference(forward_subsumption_resolution,[status(thm)],[f1162,f1137])).
% 2.06/0.69 fof(f1164,plain,(
% 2.06/0.69 ~spl0_76),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f1163])).
% 2.06/0.69 fof(f1169,plain,(
% 2.06/0.69 spl0_81 <=> ~in(X0,empty_set)),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1170,plain,(
% 2.06/0.69 ![X0]: (~in(X0,empty_set)|~spl0_81)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f1169])).
% 2.06/0.69 fof(f1172,plain,(
% 2.06/0.69 ![X0]: (~in(X0,empty_set)|~empty(empty_set))),
% 2.06/0.69 inference(paramodulation,[status(thm)],[f1094,f1018])).
% 2.06/0.69 fof(f1173,plain,(
% 2.06/0.69 spl0_81|~spl0_46),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1172,f1169,f686])).
% 2.06/0.69 fof(f1184,plain,(
% 2.06/0.69 spl0_82 <=> ~in(X0,relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1185,plain,(
% 2.06/0.69 ![X0]: (~in(X0,relation_dom(sk0_10))|~spl0_82)),
% 2.06/0.69 inference(component_clause,[status(thm)],[f1184])).
% 2.06/0.69 fof(f1187,plain,(
% 2.06/0.69 ![X0]: (~in(X0,relation_dom(sk0_10))|~empty(sk0_9))),
% 2.06/0.69 inference(resolution,[status(thm)],[f138,f108])).
% 2.06/0.69 fof(f1188,plain,(
% 2.06/0.69 spl0_82|~spl0_39),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1187,f1184,f538])).
% 2.06/0.69 fof(f1189,plain,(
% 2.06/0.69 ![X0]: (~in(X0,relation_dom(sk0_10))|element(X0,sk0_9))),
% 2.06/0.69 inference(resolution,[status(thm)],[f138,f105])).
% 2.06/0.69 fof(f1195,plain,(
% 2.06/0.69 $false|~spl0_82|~spl0_23),
% 2.06/0.69 inference(backward_subsumption_resolution,[status(thm)],[f297,f1185])).
% 2.06/0.69 fof(f1196,plain,(
% 2.06/0.69 ~spl0_82|~spl0_23),
% 2.06/0.69 inference(contradiction_clause,[status(thm)],[f1195])).
% 2.06/0.69 fof(f1245,plain,(
% 2.06/0.69 empty(sk0_9)|in(sk0_1(sk0_9,sk0_10),sk0_9)|~spl0_54),
% 2.06/0.69 inference(resolution,[status(thm)],[f849,f93])).
% 2.06/0.69 fof(f1246,plain,(
% 2.06/0.69 spl0_39|spl0_25|~spl0_54),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1245,f538,f359,f848])).
% 2.06/0.69 fof(f1253,plain,(
% 2.06/0.69 sk0_9=relation_dom(sk0_10)|in(sk0_1(sk0_9,sk0_10),relation_dom(sk0_10))|spl0_54|~spl0_6),
% 2.06/0.69 inference(resolution,[status(thm)],[f850,f197])).
% 2.06/0.69 fof(f1254,plain,(
% 2.06/0.69 spl0_22|spl0_23|spl0_54|~spl0_6),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1253,f293,f296,f848,f157])).
% 2.06/0.69 fof(f1345,plain,(
% 2.06/0.69 spl0_83 <=> in(sk0_13(sk0_9,X0),X0)|X0=sk0_9|in(sk0_11(sk0_13(sk0_9,X0)),relation_rng(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1348,plain,(
% 2.06/0.69 ![X0]: (in(sk0_13(sk0_9,X0),X0)|X0=sk0_9|~relation(sk0_10)|in(sk0_11(sk0_13(sk0_9,X0)),relation_rng(sk0_10))|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f721,f84])).
% 2.06/0.69 fof(f1349,plain,(
% 2.06/0.69 spl0_83|~spl0_5|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1348,f1345,f152,f117])).
% 2.06/0.69 fof(f1350,plain,(
% 2.06/0.69 spl0_84 <=> in(sk0_13(sk0_9,X0),X0)|X0=sk0_9|in(sk0_13(sk0_9,X0),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1353,plain,(
% 2.06/0.69 ![X0]: (in(sk0_13(sk0_9,X0),X0)|X0=sk0_9|~relation(sk0_10)|in(sk0_13(sk0_9,X0),relation_dom(sk0_10))|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f721,f133])).
% 2.06/0.69 fof(f1354,plain,(
% 2.06/0.69 spl0_84|~spl0_5|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1353,f1350,f152,f117])).
% 2.06/0.69 fof(f1364,plain,(
% 2.06/0.69 empty_set=sk0_9|~spl0_56|~spl0_81),
% 2.06/0.69 inference(resolution,[status(thm)],[f865,f1170])).
% 2.06/0.69 fof(f1365,plain,(
% 2.06/0.69 spl0_52|~spl0_56|~spl0_81),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1364,f787,f864,f1169])).
% 2.06/0.69 fof(f1424,plain,(
% 2.06/0.69 spl0_86 <=> in(sk0_13(X0,sk0_9),X0)|sk0_9=X0|in(sk0_11(sk0_13(X0,sk0_9)),relation_rng(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1427,plain,(
% 2.06/0.69 ![X0]: (in(sk0_13(X0,sk0_9),X0)|sk0_9=X0|~relation(sk0_10)|in(sk0_11(sk0_13(X0,sk0_9)),relation_rng(sk0_10))|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f724,f84])).
% 2.06/0.69 fof(f1428,plain,(
% 2.06/0.69 spl0_86|~spl0_5|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1427,f1424,f152,f117])).
% 2.06/0.69 fof(f1429,plain,(
% 2.06/0.69 spl0_87 <=> in(sk0_13(X0,sk0_9),X0)|sk0_9=X0|in(sk0_13(X0,sk0_9),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1432,plain,(
% 2.06/0.69 ![X0]: (in(sk0_13(X0,sk0_9),X0)|sk0_9=X0|~relation(sk0_10)|in(sk0_13(X0,sk0_9),relation_dom(sk0_10))|~spl0_0)),
% 2.06/0.69 inference(resolution,[status(thm)],[f724,f133])).
% 2.06/0.69 fof(f1433,plain,(
% 2.06/0.69 spl0_87|~spl0_5|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1432,f1429,f152,f117])).
% 2.06/0.69 fof(f1839,plain,(
% 2.06/0.69 element(sk0_1(sk0_9,sk0_10),sk0_9)|~spl0_23),
% 2.06/0.69 inference(resolution,[status(thm)],[f1189,f297])).
% 2.06/0.69 fof(f1840,plain,(
% 2.06/0.69 spl0_54|~spl0_23),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1839,f848,f296])).
% 2.06/0.69 fof(f1926,plain,(
% 2.06/0.69 spl0_111 <=> in(sk0_11(sk0_4(sk0_9)),relation_rng(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1929,plain,(
% 2.06/0.69 ~relation(sk0_10)|in(sk0_11(sk0_4(sk0_9)),relation_rng(sk0_10))|~spl0_40),
% 2.06/0.69 inference(resolution,[status(thm)],[f542,f84])).
% 2.06/0.69 fof(f1930,plain,(
% 2.06/0.69 ~spl0_5|spl0_111|~spl0_40),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1929,f152,f1926,f541])).
% 2.06/0.69 fof(f1931,plain,(
% 2.06/0.69 spl0_112 <=> in(sk0_4(sk0_9),relation_dom(sk0_10))),
% 2.06/0.69 introduced(split_symbol_definition)).
% 2.06/0.69 fof(f1934,plain,(
% 2.06/0.69 ~relation(sk0_10)|in(sk0_4(sk0_9),relation_dom(sk0_10))|~spl0_40),
% 2.06/0.69 inference(resolution,[status(thm)],[f542,f133])).
% 2.06/0.69 fof(f1935,plain,(
% 2.06/0.69 ~spl0_5|spl0_112|~spl0_40),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1934,f152,f1931,f541])).
% 2.06/0.69 fof(f1940,plain,(
% 2.06/0.69 in(ordered_pair(sk0_1(sk0_9,sk0_10),sk0_11(sk0_1(sk0_9,sk0_10))),sk0_10)|~spl0_25|~spl0_0),
% 2.06/0.69 inference(resolution,[status(thm)],[f360,f118])).
% 2.06/0.69 fof(f1941,plain,(
% 2.06/0.69 spl0_24|~spl0_25|~spl0_0),
% 2.06/0.69 inference(split_clause,[status(thm)],[f1940,f299,f359,f117])).
% 2.06/0.69 fof(f1942,plain,(
% 2.06/0.69 $false),
% 2.06/0.69 inference(sat_refutation,[status(thm)],[f123,f127,f131,f156,f161,f173,f182,f214,f244,f303,f363,f369,f378,f545,f550,f617,f692,f807,f808,f884,f1164,f1173,f1188,f1196,f1246,f1254,f1349,f1354,f1365,f1428,f1433,f1840,f1930,f1935,f1941])).
% 2.06/0.69 % SZS output end CNFRefutation for theBenchmark.p
% 2.06/0.70 % Elapsed time: 0.387018 seconds
% 2.06/0.70 % CPU time: 2.293330 seconds
% 2.06/0.70 % Memory used: 82.898 MB
%------------------------------------------------------------------------------