TSTP Solution File: SET980+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:50 EDT 2024
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 21:40:11 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.52 fof(f1,axiom,(
% 0.19/0.52 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f3,axiom,(
% 0.19/0.52 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f7,axiom,(
% 0.19/0.52 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f10,axiom,(
% 0.19/0.52 (! [A,B] :( cartesian_product2(A,B) = empty_set<=> ( A = empty_set| B = empty_set ) ) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f11,conjecture,(
% 0.19/0.52 (! [A,B,C,D] :( cartesian_product2(A,B) = cartesian_product2(C,D)=> ( A = empty_set| B = empty_set| ( A = C& B = D ) ) ) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f12,negated_conjecture,(
% 0.19/0.52 ~((! [A,B,C,D] :( cartesian_product2(A,B) = cartesian_product2(C,D)=> ( A = empty_set| B = empty_set| ( A = C& B = D ) ) ) ))),
% 0.19/0.52 inference(negated_conjecture,[status(cth)],[f11])).
% 0.19/0.52 fof(f13,axiom,(
% 0.19/0.52 (! [A,B] :( (! [C] :( in(C,A)<=> in(C,B) ))=> A = B ) )),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f14,plain,(
% 0.19/0.52 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.19/0.52 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.19/0.52 fof(f15,plain,(
% 0.19/0.52 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f14])).
% 0.19/0.52 fof(f17,plain,(
% 0.19/0.52 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.52 inference(NNF_transformation,[status(esa)],[f3])).
% 0.19/0.52 fof(f18,plain,(
% 0.19/0.52 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.52 inference(miniscoping,[status(esa)],[f17])).
% 0.19/0.52 fof(f19,plain,(
% 0.19/0.52 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_0(A),A)))),
% 0.19/0.52 inference(skolemization,[status(esa)],[f18])).
% 0.19/0.52 fof(f20,plain,(
% 0.19/0.52 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f19])).
% 0.19/0.52 fof(f21,plain,(
% 0.19/0.52 ![X0]: (X0=empty_set|in(sk0_0(X0),X0))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f19])).
% 0.19/0.52 fof(f25,plain,(
% 0.19/0.52 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.19/0.52 inference(NNF_transformation,[status(esa)],[f7])).
% 0.19/0.52 fof(f26,plain,(
% 0.19/0.52 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.19/0.52 inference(miniscoping,[status(esa)],[f25])).
% 0.19/0.52 fof(f27,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f26])).
% 0.19/0.52 fof(f28,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f26])).
% 0.19/0.52 fof(f29,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f26])).
% 0.19/0.52 fof(f34,plain,(
% 0.19/0.52 ![A,B]: ((~cartesian_product2(A,B)=empty_set|(A=empty_set|B=empty_set))&(cartesian_product2(A,B)=empty_set|(~A=empty_set&~B=empty_set)))),
% 0.19/0.52 inference(NNF_transformation,[status(esa)],[f10])).
% 0.19/0.52 fof(f35,plain,(
% 0.19/0.52 (![A,B]: (~cartesian_product2(A,B)=empty_set|(A=empty_set|B=empty_set)))&(![A,B]: (cartesian_product2(A,B)=empty_set|(~A=empty_set&~B=empty_set)))),
% 0.19/0.52 inference(miniscoping,[status(esa)],[f34])).
% 0.19/0.52 fof(f36,plain,(
% 0.19/0.52 ![X0,X1]: (~cartesian_product2(X0,X1)=empty_set|X0=empty_set|X1=empty_set)),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f35])).
% 0.19/0.52 fof(f38,plain,(
% 0.19/0.52 ![X0,X1]: (cartesian_product2(X0,X1)=empty_set|~X1=empty_set)),
% 0.19/0.52 inference(cnf_transformation,[status(esa)],[f35])).
% 0.19/0.52 fof(f39,plain,(
% 0.19/0.52 (?[A,B,C,D]: (cartesian_product2(A,B)=cartesian_product2(C,D)&((~A=empty_set&~B=empty_set)&(~A=C|~B=D))))),
% 0.19/0.52 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.19/0.52 fof(f40,plain,(
% 0.19/0.52 (cartesian_product2(sk0_3,sk0_4)=cartesian_product2(sk0_5,sk0_6)&((~sk0_3=empty_set&~sk0_4=empty_set)&(~sk0_3=sk0_5|~sk0_4=sk0_6)))),
% 0.19/0.54 inference(skolemization,[status(esa)],[f39])).
% 0.19/0.54 fof(f41,plain,(
% 0.19/0.54 cartesian_product2(sk0_3,sk0_4)=cartesian_product2(sk0_5,sk0_6)),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f40])).
% 0.19/0.54 fof(f42,plain,(
% 0.19/0.54 ~sk0_3=empty_set),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f40])).
% 0.19/0.54 fof(f43,plain,(
% 0.19/0.54 ~sk0_4=empty_set),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f40])).
% 0.19/0.54 fof(f44,plain,(
% 0.19/0.54 ~sk0_3=sk0_5|~sk0_4=sk0_6),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f40])).
% 0.19/0.54 fof(f45,plain,(
% 0.19/0.54 ![A,B]: ((?[C]: (in(C,A)<~>in(C,B)))|A=B)),
% 0.19/0.54 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.19/0.54 fof(f46,plain,(
% 0.19/0.54 ![A,B]: ((?[C]: ((in(C,A)|in(C,B))&(~in(C,A)|~in(C,B))))|A=B)),
% 0.19/0.54 inference(NNF_transformation,[status(esa)],[f45])).
% 0.19/0.54 fof(f47,plain,(
% 0.19/0.54 ![A,B]: (((in(sk0_7(B,A),A)|in(sk0_7(B,A),B))&(~in(sk0_7(B,A),A)|~in(sk0_7(B,A),B)))|A=B)),
% 0.19/0.54 inference(skolemization,[status(esa)],[f46])).
% 0.19/0.54 fof(f48,plain,(
% 0.19/0.54 ![X0,X1]: (in(sk0_7(X0,X1),X1)|in(sk0_7(X0,X1),X0)|X1=X0)),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f47])).
% 0.19/0.54 fof(f49,plain,(
% 0.19/0.54 ![X0,X1]: (~in(sk0_7(X0,X1),X1)|~in(sk0_7(X0,X1),X0)|X1=X0)),
% 0.19/0.54 inference(cnf_transformation,[status(esa)],[f47])).
% 0.19/0.54 fof(f50,plain,(
% 0.19/0.54 spl0_0 <=> sk0_3=sk0_5),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f53,plain,(
% 0.19/0.54 spl0_1 <=> sk0_4=sk0_6),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f56,plain,(
% 0.19/0.54 ~spl0_0|~spl0_1),
% 0.19/0.54 inference(split_clause,[status(thm)],[f44,f50,f53])).
% 0.19/0.54 fof(f57,plain,(
% 0.19/0.54 ![X0]: (~in(X0,empty_set))),
% 0.19/0.54 inference(destructive_equality_resolution,[status(esa)],[f20])).
% 0.19/0.54 fof(f59,plain,(
% 0.19/0.54 ![X0]: (cartesian_product2(X0,empty_set)=empty_set)),
% 0.19/0.54 inference(destructive_equality_resolution,[status(esa)],[f38])).
% 0.19/0.54 fof(f70,plain,(
% 0.19/0.54 spl0_4 <=> cartesian_product2(sk0_3,sk0_4)=empty_set),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f73,plain,(
% 0.19/0.54 spl0_5 <=> sk0_5=empty_set),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f74,plain,(
% 0.19/0.54 sk0_5=empty_set|~spl0_5),
% 0.19/0.54 inference(component_clause,[status(thm)],[f73])).
% 0.19/0.54 fof(f76,plain,(
% 0.19/0.54 spl0_6 <=> sk0_6=empty_set),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f77,plain,(
% 0.19/0.54 sk0_6=empty_set|~spl0_6),
% 0.19/0.54 inference(component_clause,[status(thm)],[f76])).
% 0.19/0.54 fof(f79,plain,(
% 0.19/0.54 ~cartesian_product2(sk0_3,sk0_4)=empty_set|sk0_5=empty_set|sk0_6=empty_set),
% 0.19/0.54 inference(paramodulation,[status(thm)],[f41,f36])).
% 0.19/0.54 fof(f80,plain,(
% 0.19/0.54 ~spl0_4|spl0_5|spl0_6),
% 0.19/0.54 inference(split_clause,[status(thm)],[f79,f70,f73,f76])).
% 0.19/0.54 fof(f98,plain,(
% 0.19/0.54 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_3,sk0_4))|in(X0,sk0_5))),
% 0.19/0.54 inference(paramodulation,[status(thm)],[f41,f27])).
% 0.19/0.54 fof(f114,plain,(
% 0.19/0.54 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_3,sk0_4))|in(X1,sk0_6))),
% 0.19/0.54 inference(paramodulation,[status(thm)],[f41,f28])).
% 0.19/0.54 fof(f116,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,empty_set),X0)|empty_set=X0)),
% 0.19/0.54 inference(resolution,[status(thm)],[f48,f57])).
% 0.19/0.54 fof(f126,plain,(
% 0.19/0.54 spl0_8 <=> ~in(X0,sk0_3)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f127,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_3)|~spl0_8)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f126])).
% 0.19/0.54 fof(f129,plain,(
% 0.19/0.54 spl0_9 <=> ~in(X1,sk0_4)|in(X1,sk0_6)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f130,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_4)|in(X0,sk0_6)|~spl0_9)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f129])).
% 0.19/0.54 fof(f132,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_3)|~in(X1,sk0_4)|in(X1,sk0_6))),
% 0.19/0.54 inference(resolution,[status(thm)],[f29,f114])).
% 0.19/0.54 fof(f133,plain,(
% 0.19/0.54 spl0_8|spl0_9),
% 0.19/0.54 inference(split_clause,[status(thm)],[f132,f126,f129])).
% 0.19/0.54 fof(f134,plain,(
% 0.19/0.54 spl0_10 <=> ~in(X0,sk0_3)|in(X0,sk0_5)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f135,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_3)|in(X0,sk0_5)|~spl0_10)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f134])).
% 0.19/0.54 fof(f137,plain,(
% 0.19/0.54 spl0_11 <=> ~in(X1,sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f138,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_4)|~spl0_11)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f137])).
% 0.19/0.54 fof(f140,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_3)|~in(X1,sk0_4)|in(X0,sk0_5))),
% 0.19/0.54 inference(resolution,[status(thm)],[f29,f98])).
% 0.19/0.54 fof(f141,plain,(
% 0.19/0.54 spl0_10|spl0_11),
% 0.19/0.54 inference(split_clause,[status(thm)],[f140,f134,f137])).
% 0.19/0.54 fof(f142,plain,(
% 0.19/0.54 spl0_12 <=> ~in(X0,X1)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f143,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,X1)|~spl0_12)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f142])).
% 0.19/0.54 fof(f145,plain,(
% 0.19/0.54 spl0_13 <=> ~in(X2,X3)|in(X2,X3)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f148,plain,(
% 0.19/0.54 ![X0,X1,X2,X3]: (~in(X0,X1)|~in(X2,X3)|in(X2,X3))),
% 0.19/0.54 inference(resolution,[status(thm)],[f29,f28])).
% 0.19/0.54 fof(f149,plain,(
% 0.19/0.54 spl0_12|spl0_13),
% 0.19/0.54 inference(split_clause,[status(thm)],[f148,f142,f145])).
% 0.19/0.54 fof(f154,plain,(
% 0.19/0.54 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(sk0_3,sk0_4))|~in(X0,sk0_5)|~in(X1,sk0_6))),
% 0.19/0.54 inference(paramodulation,[status(thm)],[f41,f29])).
% 0.19/0.54 fof(f227,plain,(
% 0.19/0.54 spl0_14 <=> ~in(X0,sk0_5)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f228,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_5)|~spl0_14)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f227])).
% 0.19/0.54 fof(f230,plain,(
% 0.19/0.54 spl0_15 <=> ~in(X1,sk0_6)|in(X1,sk0_6)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f233,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_5)|~in(X1,sk0_6)|in(X1,sk0_6))),
% 0.19/0.54 inference(resolution,[status(thm)],[f154,f114])).
% 0.19/0.54 fof(f234,plain,(
% 0.19/0.54 spl0_14|spl0_15),
% 0.19/0.54 inference(split_clause,[status(thm)],[f233,f227,f230])).
% 0.19/0.54 fof(f235,plain,(
% 0.19/0.54 spl0_16 <=> ~in(X0,sk0_5)|in(X0,sk0_5)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f238,plain,(
% 0.19/0.54 spl0_17 <=> ~in(X1,sk0_6)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f239,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_6)|~spl0_17)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f238])).
% 0.19/0.54 fof(f241,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_5)|~in(X1,sk0_6)|in(X0,sk0_5))),
% 0.19/0.54 inference(resolution,[status(thm)],[f154,f98])).
% 0.19/0.54 fof(f242,plain,(
% 0.19/0.54 spl0_16|spl0_17),
% 0.19/0.54 inference(split_clause,[status(thm)],[f241,f235,f238])).
% 0.19/0.54 fof(f243,plain,(
% 0.19/0.54 spl0_18 <=> ~in(X1,sk0_6)|in(X1,sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f244,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_6)|in(X0,sk0_4)|~spl0_18)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f243])).
% 0.19/0.54 fof(f246,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_5)|~in(X1,sk0_6)|in(X1,sk0_4))),
% 0.19/0.54 inference(resolution,[status(thm)],[f154,f28])).
% 0.19/0.54 fof(f247,plain,(
% 0.19/0.54 spl0_14|spl0_18),
% 0.19/0.54 inference(split_clause,[status(thm)],[f246,f227,f243])).
% 0.19/0.54 fof(f248,plain,(
% 0.19/0.54 spl0_19 <=> ~in(X0,sk0_5)|in(X0,sk0_3)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f249,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_5)|in(X0,sk0_3)|~spl0_19)),
% 0.19/0.54 inference(component_clause,[status(thm)],[f248])).
% 0.19/0.54 fof(f251,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,sk0_5)|~in(X1,sk0_6)|in(X0,sk0_3))),
% 0.19/0.54 inference(resolution,[status(thm)],[f154,f27])).
% 0.19/0.54 fof(f252,plain,(
% 0.19/0.54 spl0_19|spl0_17),
% 0.19/0.54 inference(split_clause,[status(thm)],[f251,f248,f238])).
% 0.19/0.54 fof(f282,plain,(
% 0.19/0.54 empty_set=sk0_3|~spl0_8),
% 0.19/0.54 inference(resolution,[status(thm)],[f127,f116])).
% 0.19/0.54 fof(f283,plain,(
% 0.19/0.54 $false|~spl0_8),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f282,f42])).
% 0.19/0.54 fof(f284,plain,(
% 0.19/0.54 ~spl0_8),
% 0.19/0.54 inference(contradiction_clause,[status(thm)],[f283])).
% 0.19/0.54 fof(f286,plain,(
% 0.19/0.54 empty_set=sk0_6|~spl0_17),
% 0.19/0.54 inference(resolution,[status(thm)],[f239,f116])).
% 0.19/0.54 fof(f291,plain,(
% 0.19/0.54 cartesian_product2(sk0_3,sk0_4)=cartesian_product2(sk0_5,empty_set)|~spl0_17),
% 0.19/0.54 inference(backward_demodulation,[status(thm)],[f286,f41])).
% 0.19/0.54 fof(f292,plain,(
% 0.19/0.54 cartesian_product2(sk0_3,sk0_4)=empty_set|~spl0_17),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f59,f291])).
% 0.19/0.54 fof(f294,plain,(
% 0.19/0.54 spl0_20 <=> sk0_3=empty_set),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f295,plain,(
% 0.19/0.54 sk0_3=empty_set|~spl0_20),
% 0.19/0.54 inference(component_clause,[status(thm)],[f294])).
% 0.19/0.54 fof(f297,plain,(
% 0.19/0.54 spl0_21 <=> sk0_4=empty_set),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f298,plain,(
% 0.19/0.54 sk0_4=empty_set|~spl0_21),
% 0.19/0.54 inference(component_clause,[status(thm)],[f297])).
% 0.19/0.54 fof(f300,plain,(
% 0.19/0.54 sk0_3=empty_set|sk0_4=empty_set|~spl0_17),
% 0.19/0.54 inference(resolution,[status(thm)],[f292,f36])).
% 0.19/0.54 fof(f301,plain,(
% 0.19/0.54 spl0_20|spl0_21|~spl0_17),
% 0.19/0.54 inference(split_clause,[status(thm)],[f300,f294,f297,f238])).
% 0.19/0.54 fof(f309,plain,(
% 0.19/0.54 $false|~spl0_21),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f298,f43])).
% 0.19/0.54 fof(f310,plain,(
% 0.19/0.54 ~spl0_21),
% 0.19/0.54 inference(contradiction_clause,[status(thm)],[f309])).
% 0.19/0.54 fof(f311,plain,(
% 0.19/0.54 $false|~spl0_20),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f295,f42])).
% 0.19/0.54 fof(f312,plain,(
% 0.19/0.54 ~spl0_20),
% 0.19/0.54 inference(contradiction_clause,[status(thm)],[f311])).
% 0.19/0.54 fof(f313,plain,(
% 0.19/0.54 empty_set=sk0_5|~spl0_14),
% 0.19/0.54 inference(resolution,[status(thm)],[f228,f116])).
% 0.19/0.54 fof(f319,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_3)|in(X0,empty_set)|~spl0_14|~spl0_10)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f313,f135])).
% 0.19/0.54 fof(f320,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_3)|~spl0_14|~spl0_10)),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f319,f57])).
% 0.19/0.54 fof(f321,plain,(
% 0.19/0.54 empty_set=sk0_3|~spl0_14|~spl0_10),
% 0.19/0.54 inference(resolution,[status(thm)],[f320,f116])).
% 0.19/0.54 fof(f322,plain,(
% 0.19/0.54 spl0_20|~spl0_14|~spl0_10),
% 0.19/0.54 inference(split_clause,[status(thm)],[f321,f294,f227,f134])).
% 0.19/0.54 fof(f327,plain,(
% 0.19/0.54 empty_set=sk0_4|~spl0_11),
% 0.19/0.54 inference(resolution,[status(thm)],[f138,f116])).
% 0.19/0.54 fof(f328,plain,(
% 0.19/0.54 spl0_21|~spl0_11),
% 0.19/0.54 inference(split_clause,[status(thm)],[f327,f297,f137])).
% 0.19/0.54 fof(f334,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_4)|~in(sk0_6,X0)|~spl0_9)),
% 0.19/0.54 inference(resolution,[status(thm)],[f130,f15])).
% 0.19/0.54 fof(f341,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,sk0_5),sk0_3)|in(sk0_7(X0,sk0_5),X0)|sk0_5=X0|~spl0_19)),
% 0.19/0.54 inference(resolution,[status(thm)],[f249,f48])).
% 0.19/0.54 fof(f349,plain,(
% 0.19/0.54 spl0_24 <=> in(sk0_7(sk0_6,empty_set),sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f352,plain,(
% 0.19/0.54 in(sk0_7(sk0_6,empty_set),sk0_4)|empty_set=sk0_6|~spl0_18),
% 0.19/0.54 inference(resolution,[status(thm)],[f244,f116])).
% 0.19/0.54 fof(f353,plain,(
% 0.19/0.54 spl0_24|spl0_6|~spl0_18),
% 0.19/0.54 inference(split_clause,[status(thm)],[f352,f349,f76,f243])).
% 0.19/0.54 fof(f355,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,sk0_6),sk0_4)|in(sk0_7(X0,sk0_6),X0)|sk0_6=X0|~spl0_18)),
% 0.19/0.54 inference(resolution,[status(thm)],[f244,f48])).
% 0.19/0.54 fof(f356,plain,(
% 0.19/0.54 spl0_25 <=> in(sk0_0(sk0_6),sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f359,plain,(
% 0.19/0.54 in(sk0_0(sk0_6),sk0_4)|sk0_6=empty_set|~spl0_18),
% 0.19/0.54 inference(resolution,[status(thm)],[f244,f21])).
% 0.19/0.54 fof(f360,plain,(
% 0.19/0.54 spl0_25|spl0_6|~spl0_18),
% 0.19/0.54 inference(split_clause,[status(thm)],[f359,f356,f76,f243])).
% 0.19/0.54 fof(f362,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_4)|in(X0,empty_set)|~spl0_6|~spl0_9)),
% 0.19/0.54 inference(backward_demodulation,[status(thm)],[f77,f130])).
% 0.19/0.54 fof(f363,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_4)|~spl0_6|~spl0_9)),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f362,f57])).
% 0.19/0.54 fof(f364,plain,(
% 0.19/0.54 ![X0,X1]: (in(sk0_7(X0,X1),X0)|X1=X0|~spl0_12)),
% 0.19/0.54 inference(backward_subsumption_resolution,[status(thm)],[f48,f143])).
% 0.19/0.54 fof(f365,plain,(
% 0.19/0.54 ![X0,X1]: (X0=X1|~spl0_12)),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f364,f143])).
% 0.19/0.54 fof(f368,plain,(
% 0.19/0.54 $false|~spl0_12),
% 0.19/0.54 inference(backward_subsumption_resolution,[status(thm)],[f43,f365])).
% 0.19/0.54 fof(f369,plain,(
% 0.19/0.54 ~spl0_12),
% 0.19/0.54 inference(contradiction_clause,[status(thm)],[f368])).
% 0.19/0.54 fof(f387,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,empty_set),sk0_4)|in(sk0_7(X0,sk0_6),X0)|sk0_6=X0|~spl0_6|~spl0_18)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f77,f355])).
% 0.19/0.54 fof(f388,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,empty_set),sk0_4)|in(sk0_7(X0,empty_set),X0)|sk0_6=X0|~spl0_6|~spl0_18)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f77,f387])).
% 0.19/0.54 fof(f389,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,empty_set),sk0_4)|in(sk0_7(X0,empty_set),X0)|empty_set=X0|~spl0_6|~spl0_18)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f77,f388])).
% 0.19/0.54 fof(f390,plain,(
% 0.19/0.54 ![X0]: (in(sk0_7(X0,empty_set),X0)|empty_set=X0|~spl0_9|~spl0_6|~spl0_18)),
% 0.19/0.54 inference(forward_subsumption_resolution,[status(thm)],[f389,f363])).
% 0.19/0.54 fof(f396,plain,(
% 0.19/0.54 empty_set=sk0_4|~spl0_18|~spl0_6|~spl0_9),
% 0.19/0.54 inference(resolution,[status(thm)],[f390,f363])).
% 0.19/0.54 fof(f397,plain,(
% 0.19/0.54 spl0_21|~spl0_18|~spl0_6|~spl0_9),
% 0.19/0.54 inference(split_clause,[status(thm)],[f396,f297,f243,f76,f129])).
% 0.19/0.54 fof(f398,plain,(
% 0.19/0.54 cartesian_product2(sk0_3,sk0_4)=cartesian_product2(empty_set,sk0_6)|~spl0_5),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f74,f41])).
% 0.19/0.54 fof(f400,plain,(
% 0.19/0.54 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(empty_set,sk0_6))|in(X0,sk0_5)|~spl0_5)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f398,f98])).
% 0.19/0.54 fof(f401,plain,(
% 0.19/0.54 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(empty_set,sk0_6))|in(X0,empty_set)|~spl0_5)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f74,f400])).
% 0.19/0.54 fof(f403,plain,(
% 0.19/0.54 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(empty_set,sk0_6))|~in(X0,sk0_5)|~in(X1,sk0_6)|~spl0_5)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f398,f154])).
% 0.19/0.54 fof(f404,plain,(
% 0.19/0.54 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(empty_set,sk0_6))|~in(X0,empty_set)|~in(X1,sk0_6)|~spl0_5)),
% 0.19/0.54 inference(forward_demodulation,[status(thm)],[f74,f403])).
% 0.19/0.54 fof(f410,plain,(
% 0.19/0.54 spl0_28 <=> ~in(X0,empty_set)|in(X0,empty_set)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f413,plain,(
% 0.19/0.54 ![X0,X1]: (~in(X0,empty_set)|~in(X1,sk0_6)|in(X0,empty_set)|~spl0_5)),
% 0.19/0.54 inference(resolution,[status(thm)],[f404,f401])).
% 0.19/0.54 fof(f414,plain,(
% 0.19/0.54 spl0_28|spl0_17|~spl0_5),
% 0.19/0.54 inference(split_clause,[status(thm)],[f413,f410,f238,f73])).
% 0.19/0.54 fof(f475,plain,(
% 0.19/0.54 ![X0]: (~in(sk0_7(X0,sk0_6),X0)|sk0_6=X0|~in(sk0_7(X0,sk0_6),sk0_4)|~spl0_9)),
% 0.19/0.54 inference(resolution,[status(thm)],[f49,f130])).
% 0.19/0.54 fof(f540,plain,(
% 0.19/0.54 ![X0]: (~in(sk0_7(X0,sk0_5),sk0_3)|~in(sk0_7(X0,sk0_5),X0)|sk0_5=X0|~spl0_10)),
% 0.19/0.54 inference(resolution,[status(thm)],[f135,f49])).
% 0.19/0.54 fof(f541,plain,(
% 0.19/0.54 ![X0]: (~in(X0,sk0_3)|~in(sk0_5,X0)|~spl0_10)),
% 0.19/0.54 inference(resolution,[status(thm)],[f135,f15])).
% 0.19/0.54 fof(f550,plain,(
% 0.19/0.54 spl0_31 <=> in(sk0_6,sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f553,plain,(
% 0.19/0.54 ~in(sk0_6,sk0_4)|~in(sk0_6,sk0_4)|~spl0_9),
% 0.19/0.54 inference(resolution,[status(thm)],[f334,f130])).
% 0.19/0.54 fof(f554,plain,(
% 0.19/0.54 ~spl0_31|~spl0_9),
% 0.19/0.54 inference(split_clause,[status(thm)],[f553,f550,f129])).
% 0.19/0.54 fof(f562,plain,(
% 0.19/0.54 spl0_32 <=> in(sk0_5,sk0_3)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f565,plain,(
% 0.19/0.54 ~in(sk0_5,sk0_3)|~in(sk0_5,sk0_3)|~spl0_10),
% 0.19/0.54 inference(resolution,[status(thm)],[f541,f135])).
% 0.19/0.54 fof(f566,plain,(
% 0.19/0.54 ~spl0_32|~spl0_10),
% 0.19/0.54 inference(split_clause,[status(thm)],[f565,f562,f134])).
% 0.19/0.54 fof(f593,plain,(
% 0.19/0.54 spl0_38 <=> in(sk0_7(sk0_4,sk0_6),sk0_4)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f594,plain,(
% 0.19/0.54 in(sk0_7(sk0_4,sk0_6),sk0_4)|~spl0_38),
% 0.19/0.54 inference(component_clause,[status(thm)],[f593])).
% 0.19/0.54 fof(f595,plain,(
% 0.19/0.54 ~in(sk0_7(sk0_4,sk0_6),sk0_4)|spl0_38),
% 0.19/0.54 inference(component_clause,[status(thm)],[f593])).
% 0.19/0.54 fof(f601,plain,(
% 0.19/0.54 in(sk0_7(sk0_4,sk0_6),sk0_4)|sk0_6=sk0_4|spl0_38|~spl0_18),
% 0.19/0.54 inference(resolution,[status(thm)],[f595,f355])).
% 0.19/0.54 fof(f602,plain,(
% 0.19/0.54 spl0_38|spl0_1|~spl0_18),
% 0.19/0.54 inference(split_clause,[status(thm)],[f601,f593,f53,f243])).
% 0.19/0.54 fof(f1296,plain,(
% 0.19/0.54 ~in(sk0_7(sk0_4,sk0_6),sk0_4)|sk0_6=sk0_4|~spl0_9|~spl0_38),
% 0.19/0.54 inference(resolution,[status(thm)],[f475,f594])).
% 0.19/0.54 fof(f1297,plain,(
% 0.19/0.54 ~spl0_38|spl0_1|~spl0_9),
% 0.19/0.54 inference(split_clause,[status(thm)],[f1296,f593,f53,f129])).
% 0.19/0.54 fof(f2097,plain,(
% 0.19/0.54 spl0_46 <=> in(sk0_7(sk0_3,sk0_5),sk0_3)),
% 0.19/0.54 introduced(split_symbol_definition)).
% 0.19/0.54 fof(f2098,plain,(
% 0.19/0.54 in(sk0_7(sk0_3,sk0_5),sk0_3)|~spl0_46),
% 0.19/0.54 inference(component_clause,[status(thm)],[f2097])).
% 0.19/0.54 fof(f2099,plain,(
% 0.19/0.54 ~in(sk0_7(sk0_3,sk0_5),sk0_3)|spl0_46),
% 0.19/0.54 inference(component_clause,[status(thm)],[f2097])).
% 0.19/0.54 fof(f2105,plain,(
% 0.19/0.54 in(sk0_7(sk0_3,sk0_5),sk0_3)|sk0_5=sk0_3|spl0_46|~spl0_19),
% 0.19/0.54 inference(resolution,[status(thm)],[f2099,f341])).
% 0.19/0.54 fof(f2106,plain,(
% 0.19/0.54 spl0_46|spl0_0|~spl0_19),
% 0.19/0.54 inference(split_clause,[status(thm)],[f2105,f2097,f50,f248])).
% 0.19/0.54 fof(f2109,plain,(
% 0.19/0.54 ~in(sk0_7(sk0_3,sk0_5),sk0_3)|sk0_5=sk0_3|~spl0_46|~spl0_10),
% 0.19/0.54 inference(resolution,[status(thm)],[f2098,f540])).
% 0.19/0.54 fof(f2110,plain,(
% 0.19/0.54 ~spl0_46|spl0_0|~spl0_10),
% 0.19/0.54 inference(split_clause,[status(thm)],[f2109,f2097,f50,f134])).
% 0.19/0.54 fof(f2112,plain,(
% 0.19/0.54 $false),
% 0.19/0.54 inference(sat_refutation,[status(thm)],[f56,f80,f133,f141,f149,f234,f242,f247,f252,f284,f301,f310,f312,f322,f328,f353,f360,f369,f397,f414,f554,f566,f602,f1297,f2106,f2110])).
% 0.19/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.55 % Elapsed time: 0.176288 seconds
% 0.19/0.55 % CPU time: 1.239800 seconds
% 0.19/0.55 % Total memory used: 82.018 MB
% 0.19/0.55 % Net memory used: 81.275 MB
%------------------------------------------------------------------------------