TSTP Solution File: SET961+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:35:37 EDT 2023
% Result : Theorem 0.14s 0.34s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:21:38 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.34 % Refutation found
% 0.14/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.34 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.34 fof(f3,axiom,(
% 0.14/0.34 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.14/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f7,axiom,(
% 0.14/0.34 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.14/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f10,conjecture,(
% 0.14/0.34 (! [A,B] :( cartesian_product2(A,B) = cartesian_product2(B,A)=> ( A = empty_set| B = empty_set| A = B ) ) )),
% 0.14/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f11,negated_conjecture,(
% 0.14/0.34 ~((! [A,B] :( cartesian_product2(A,B) = cartesian_product2(B,A)=> ( A = empty_set| B = empty_set| A = B ) ) ))),
% 0.14/0.34 inference(negated_conjecture,[status(cth)],[f10])).
% 0.14/0.34 fof(f12,axiom,(
% 0.14/0.34 (! [A,B] :( (! [C] :( in(C,A)<=> in(C,B) ))=> A = B ) )),
% 0.14/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.34 fof(f16,plain,(
% 0.14/0.34 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.14/0.34 inference(NNF_transformation,[status(esa)],[f3])).
% 0.14/0.34 fof(f17,plain,(
% 0.14/0.34 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.14/0.34 inference(miniscoping,[status(esa)],[f16])).
% 0.14/0.34 fof(f18,plain,(
% 0.14/0.34 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_0(A),A)))),
% 0.14/0.34 inference(skolemization,[status(esa)],[f17])).
% 0.14/0.34 fof(f20,plain,(
% 0.14/0.34 ![X0]: (X0=empty_set|in(sk0_0(X0),X0))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f18])).
% 0.14/0.34 fof(f24,plain,(
% 0.14/0.34 ![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))))),
% 0.14/0.34 inference(NNF_transformation,[status(esa)],[f7])).
% 0.14/0.34 fof(f25,plain,(
% 0.14/0.34 (![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))))),
% 0.14/0.34 inference(miniscoping,[status(esa)],[f24])).
% 0.14/0.34 fof(f26,plain,(
% 0.14/0.34 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f25])).
% 0.14/0.34 fof(f27,plain,(
% 0.14/0.34 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f25])).
% 0.14/0.34 fof(f28,plain,(
% 0.14/0.34 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f25])).
% 0.14/0.34 fof(f33,plain,(
% 0.14/0.34 (?[A,B]: (cartesian_product2(A,B)=cartesian_product2(B,A)&((~A=empty_set&~B=empty_set)&~A=B)))),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.14/0.34 fof(f34,plain,(
% 0.14/0.34 (cartesian_product2(sk0_3,sk0_4)=cartesian_product2(sk0_4,sk0_3)&((~sk0_3=empty_set&~sk0_4=empty_set)&~sk0_3=sk0_4))),
% 0.14/0.34 inference(skolemization,[status(esa)],[f33])).
% 0.14/0.34 fof(f35,plain,(
% 0.14/0.34 cartesian_product2(sk0_3,sk0_4)=cartesian_product2(sk0_4,sk0_3)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f34])).
% 0.14/0.34 fof(f36,plain,(
% 0.14/0.34 ~sk0_3=empty_set),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f34])).
% 0.14/0.34 fof(f37,plain,(
% 0.14/0.34 ~sk0_4=empty_set),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f34])).
% 0.14/0.34 fof(f38,plain,(
% 0.14/0.34 ~sk0_3=sk0_4),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f34])).
% 0.14/0.34 fof(f39,plain,(
% 0.14/0.34 ![A,B]: ((?[C]: (in(C,A)<~>in(C,B)))|A=B)),
% 0.14/0.34 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.14/0.34 fof(f40,plain,(
% 0.14/0.34 ![A,B]: ((?[C]: ((in(C,A)|in(C,B))&(~in(C,A)|~in(C,B))))|A=B)),
% 0.14/0.34 inference(NNF_transformation,[status(esa)],[f39])).
% 0.14/0.34 fof(f41,plain,(
% 0.14/0.34 ![A,B]: (((in(sk0_5(B,A),A)|in(sk0_5(B,A),B))&(~in(sk0_5(B,A),A)|~in(sk0_5(B,A),B)))|A=B)),
% 0.14/0.34 inference(skolemization,[status(esa)],[f40])).
% 0.14/0.34 fof(f42,plain,(
% 0.14/0.34 ![X0,X1]: (in(sk0_5(X0,X1),X1)|in(sk0_5(X0,X1),X0)|X1=X0)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f41])).
% 0.14/0.34 fof(f43,plain,(
% 0.14/0.34 ![X0,X1]: (~in(sk0_5(X0,X1),X1)|~in(sk0_5(X0,X1),X0)|X1=X0)),
% 0.14/0.34 inference(cnf_transformation,[status(esa)],[f41])).
% 0.14/0.34 fof(f44,plain,(
% 0.14/0.34 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_3,sk0_4))|in(X0,sk0_4))),
% 0.14/0.34 inference(paramodulation,[status(thm)],[f35,f26])).
% 0.14/0.34 fof(f45,plain,(
% 0.14/0.34 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_3,sk0_4))|in(X1,sk0_3))),
% 0.14/0.34 inference(paramodulation,[status(thm)],[f35,f27])).
% 0.14/0.34 fof(f46,plain,(
% 0.14/0.34 spl0_0 <=> ~in(X0,sk0_3)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f47,plain,(
% 0.14/0.34 ![X0]: (~in(X0,sk0_3)|~spl0_0)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f46])).
% 0.14/0.34 fof(f49,plain,(
% 0.14/0.34 spl0_1 <=> ~in(X1,sk0_4)|in(X1,sk0_3)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f50,plain,(
% 0.14/0.34 ![X0]: (~in(X0,sk0_4)|in(X0,sk0_3)|~spl0_1)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f49])).
% 0.14/0.34 fof(f52,plain,(
% 0.14/0.34 ![X0,X1]: (~in(X0,sk0_3)|~in(X1,sk0_4)|in(X1,sk0_3))),
% 0.14/0.34 inference(resolution,[status(thm)],[f28,f45])).
% 0.14/0.34 fof(f53,plain,(
% 0.14/0.34 spl0_0|spl0_1),
% 0.14/0.34 inference(split_clause,[status(thm)],[f52,f46,f49])).
% 0.14/0.34 fof(f54,plain,(
% 0.14/0.34 spl0_2 <=> ~in(X0,sk0_3)|in(X0,sk0_4)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f55,plain,(
% 0.14/0.34 ![X0]: (~in(X0,sk0_3)|in(X0,sk0_4)|~spl0_2)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f54])).
% 0.14/0.34 fof(f57,plain,(
% 0.14/0.34 spl0_3 <=> ~in(X1,sk0_4)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f58,plain,(
% 0.14/0.34 ![X0]: (~in(X0,sk0_4)|~spl0_3)),
% 0.14/0.34 inference(component_clause,[status(thm)],[f57])).
% 0.14/0.34 fof(f60,plain,(
% 0.14/0.34 ![X0,X1]: (~in(X0,sk0_3)|~in(X1,sk0_4)|in(X0,sk0_4))),
% 0.14/0.34 inference(resolution,[status(thm)],[f28,f44])).
% 0.14/0.34 fof(f61,plain,(
% 0.14/0.34 spl0_2|spl0_3),
% 0.14/0.34 inference(split_clause,[status(thm)],[f60,f54,f57])).
% 0.14/0.34 fof(f146,plain,(
% 0.14/0.34 sk0_3=empty_set|~spl0_0),
% 0.14/0.34 inference(resolution,[status(thm)],[f47,f20])).
% 0.14/0.34 fof(f147,plain,(
% 0.14/0.34 $false|~spl0_0),
% 0.14/0.34 inference(forward_subsumption_resolution,[status(thm)],[f146,f36])).
% 0.14/0.34 fof(f148,plain,(
% 0.14/0.34 ~spl0_0),
% 0.14/0.34 inference(contradiction_clause,[status(thm)],[f147])).
% 0.14/0.34 fof(f153,plain,(
% 0.14/0.34 sk0_4=empty_set|~spl0_3),
% 0.14/0.34 inference(resolution,[status(thm)],[f58,f20])).
% 0.14/0.34 fof(f154,plain,(
% 0.14/0.34 $false|~spl0_3),
% 0.14/0.34 inference(forward_subsumption_resolution,[status(thm)],[f153,f37])).
% 0.14/0.34 fof(f155,plain,(
% 0.14/0.34 ~spl0_3),
% 0.14/0.34 inference(contradiction_clause,[status(thm)],[f154])).
% 0.14/0.34 fof(f159,plain,(
% 0.14/0.34 ![X0]: (~in(sk0_5(X0,sk0_4),sk0_3)|~in(sk0_5(X0,sk0_4),X0)|sk0_4=X0|~spl0_2)),
% 0.14/0.34 inference(resolution,[status(thm)],[f55,f43])).
% 0.14/0.34 fof(f167,plain,(
% 0.14/0.34 ![X0]: (in(sk0_5(X0,sk0_4),sk0_3)|in(sk0_5(X0,sk0_4),X0)|sk0_4=X0|~spl0_1)),
% 0.14/0.34 inference(resolution,[status(thm)],[f50,f42])).
% 0.14/0.34 fof(f173,plain,(
% 0.14/0.34 spl0_9 <=> in(sk0_5(sk0_3,sk0_4),sk0_3)),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f174,plain,(
% 0.14/0.34 in(sk0_5(sk0_3,sk0_4),sk0_3)|~spl0_9),
% 0.14/0.34 inference(component_clause,[status(thm)],[f173])).
% 0.14/0.34 fof(f175,plain,(
% 0.14/0.34 ~in(sk0_5(sk0_3,sk0_4),sk0_3)|spl0_9),
% 0.14/0.34 inference(component_clause,[status(thm)],[f173])).
% 0.14/0.34 fof(f176,plain,(
% 0.14/0.34 spl0_10 <=> sk0_4=sk0_3),
% 0.14/0.34 introduced(split_symbol_definition)).
% 0.14/0.34 fof(f177,plain,(
% 0.14/0.34 sk0_4=sk0_3|~spl0_10),
% 0.14/0.34 inference(component_clause,[status(thm)],[f176])).
% 0.14/0.34 fof(f233,plain,(
% 0.14/0.34 in(sk0_5(sk0_3,sk0_4),sk0_3)|sk0_4=sk0_3|spl0_9|~spl0_1),
% 0.14/0.34 inference(resolution,[status(thm)],[f175,f167])).
% 0.14/0.34 fof(f234,plain,(
% 0.14/0.34 spl0_9|spl0_10|~spl0_1),
% 0.14/0.34 inference(split_clause,[status(thm)],[f233,f173,f176,f49])).
% 0.14/0.34 fof(f237,plain,(
% 0.14/0.34 $false|~spl0_10),
% 0.14/0.34 inference(forward_subsumption_resolution,[status(thm)],[f177,f38])).
% 0.14/0.34 fof(f238,plain,(
% 0.14/0.34 ~spl0_10),
% 0.14/0.34 inference(contradiction_clause,[status(thm)],[f237])).
% 0.14/0.34 fof(f239,plain,(
% 0.14/0.34 ~in(sk0_5(sk0_3,sk0_4),sk0_3)|sk0_4=sk0_3|~spl0_9|~spl0_2),
% 0.14/0.34 inference(resolution,[status(thm)],[f174,f159])).
% 0.14/0.34 fof(f240,plain,(
% 0.14/0.34 ~spl0_9|spl0_10|~spl0_2),
% 0.14/0.34 inference(split_clause,[status(thm)],[f239,f173,f176,f54])).
% 0.14/0.34 fof(f243,plain,(
% 0.14/0.34 $false),
% 0.14/0.34 inference(sat_refutation,[status(thm)],[f53,f61,f148,f155,f234,f238,f240])).
% 0.14/0.34 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.36 % Elapsed time: 0.059781 seconds
% 0.14/0.36 % CPU time: 0.081856 seconds
% 0.14/0.36 % Memory used: 13.656 MB
%------------------------------------------------------------------------------