TSTP Solution File: SET975+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:35:38 EDT 2023
% Result : Theorem 0.06s 0.26s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n029.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 10:32:06 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.06/0.26 % Refutation found
% 0.06/0.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.26 % SZS output start CNFRefutation for theBenchmark
% 0.06/0.26 fof(f3,axiom,(
% 0.06/0.26 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.06/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.06/0.26 fof(f6,axiom,(
% 0.06/0.26 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.06/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.06/0.26 fof(f9,conjecture,(
% 0.06/0.26 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<=> ( A = C& in(B,D) ) ) )),
% 0.06/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.06/0.26 fof(f10,negated_conjecture,(
% 0.06/0.26 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<=> ( A = C& in(B,D) ) ) ))),
% 0.06/0.26 inference(negated_conjecture,[status(cth)],[f9])).
% 0.06/0.26 fof(f14,plain,(
% 0.06/0.26 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.06/0.26 inference(NNF_transformation,[status(esa)],[f3])).
% 0.06/0.26 fof(f15,plain,(
% 0.06/0.27 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.06/0.27 inference(miniscoping,[status(esa)],[f14])).
% 0.06/0.27 fof(f16,plain,(
% 0.06/0.27 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_0(B,A),B)|~sk0_0(B,A)=A)&(in(sk0_0(B,A),B)|sk0_0(B,A)=A))))),
% 0.06/0.27 inference(skolemization,[status(esa)],[f15])).
% 0.06/0.27 fof(f17,plain,(
% 0.06/0.27 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f16])).
% 0.06/0.27 fof(f18,plain,(
% 0.06/0.27 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f16])).
% 0.06/0.27 fof(f23,plain,(
% 0.06/0.27 ![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))))),
% 0.06/0.27 inference(NNF_transformation,[status(esa)],[f6])).
% 0.06/0.27 fof(f24,plain,(
% 0.06/0.27 (![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))))),
% 0.06/0.27 inference(miniscoping,[status(esa)],[f23])).
% 0.06/0.27 fof(f25,plain,(
% 0.06/0.27 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f24])).
% 0.06/0.27 fof(f26,plain,(
% 0.06/0.27 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f24])).
% 0.06/0.27 fof(f27,plain,(
% 0.06/0.27 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f24])).
% 0.06/0.27 fof(f32,plain,(
% 0.06/0.27 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<~>(A=C&in(B,D))))),
% 0.06/0.27 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.06/0.27 fof(f33,plain,(
% 0.06/0.27 ?[A,B,C,D]: ((in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(A=C&in(B,D)))&(~in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(~A=C|~in(B,D))))),
% 0.06/0.27 inference(NNF_transformation,[status(esa)],[f32])).
% 0.06/0.27 fof(f34,plain,(
% 0.06/0.27 ((in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|(sk0_3=sk0_5&in(sk0_4,sk0_6)))&(~in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|(~sk0_3=sk0_5|~in(sk0_4,sk0_6))))),
% 0.06/0.27 inference(skolemization,[status(esa)],[f33])).
% 0.06/0.27 fof(f35,plain,(
% 0.06/0.27 in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|sk0_3=sk0_5),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f34])).
% 0.06/0.27 fof(f36,plain,(
% 0.06/0.27 in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|in(sk0_4,sk0_6)),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f34])).
% 0.06/0.27 fof(f37,plain,(
% 0.06/0.27 ~in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|~sk0_3=sk0_5|~in(sk0_4,sk0_6)),
% 0.06/0.27 inference(cnf_transformation,[status(esa)],[f34])).
% 0.06/0.27 fof(f38,plain,(
% 0.06/0.27 spl0_0 <=> in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f39,plain,(
% 0.06/0.27 in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|~spl0_0),
% 0.06/0.27 inference(component_clause,[status(thm)],[f38])).
% 0.06/0.27 fof(f40,plain,(
% 0.06/0.27 ~in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_5),sk0_6))|spl0_0),
% 0.06/0.27 inference(component_clause,[status(thm)],[f38])).
% 0.06/0.27 fof(f41,plain,(
% 0.06/0.27 spl0_1 <=> sk0_3=sk0_5),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f42,plain,(
% 0.06/0.27 sk0_3=sk0_5|~spl0_1),
% 0.06/0.27 inference(component_clause,[status(thm)],[f41])).
% 0.06/0.27 fof(f43,plain,(
% 0.06/0.27 ~sk0_3=sk0_5|spl0_1),
% 0.06/0.27 inference(component_clause,[status(thm)],[f41])).
% 0.06/0.27 fof(f44,plain,(
% 0.06/0.27 spl0_0|spl0_1),
% 0.06/0.27 inference(split_clause,[status(thm)],[f35,f38,f41])).
% 0.06/0.27 fof(f45,plain,(
% 0.06/0.27 spl0_2 <=> in(sk0_4,sk0_6)),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f48,plain,(
% 0.06/0.27 spl0_0|spl0_2),
% 0.06/0.27 inference(split_clause,[status(thm)],[f36,f38,f45])).
% 0.06/0.27 fof(f49,plain,(
% 0.06/0.27 ~spl0_0|~spl0_1|~spl0_2),
% 0.06/0.27 inference(split_clause,[status(thm)],[f37,f38,f41,f45])).
% 0.06/0.27 fof(f50,plain,(
% 0.06/0.27 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.06/0.27 inference(destructive_equality_resolution,[status(esa)],[f17])).
% 0.06/0.27 fof(f51,plain,(
% 0.06/0.27 ![X0]: (in(X0,singleton(X0)))),
% 0.06/0.27 inference(destructive_equality_resolution,[status(esa)],[f18])).
% 0.06/0.27 fof(f54,plain,(
% 0.06/0.27 in(sk0_3,singleton(sk0_5))|~spl0_0),
% 0.06/0.27 inference(resolution,[status(thm)],[f25,f39])).
% 0.06/0.27 fof(f55,plain,(
% 0.06/0.27 sk0_3=sk0_5|~spl0_0),
% 0.06/0.27 inference(resolution,[status(thm)],[f54,f50])).
% 0.06/0.27 fof(f56,plain,(
% 0.06/0.27 $false|spl0_1|~spl0_0),
% 0.06/0.27 inference(forward_subsumption_resolution,[status(thm)],[f55,f43])).
% 0.06/0.27 fof(f57,plain,(
% 0.06/0.27 spl0_1|~spl0_0),
% 0.06/0.27 inference(contradiction_clause,[status(thm)],[f56])).
% 0.06/0.27 fof(f59,plain,(
% 0.06/0.27 ~in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_3),sk0_6))|~spl0_1|spl0_0),
% 0.06/0.27 inference(backward_demodulation,[status(thm)],[f42,f40])).
% 0.06/0.27 fof(f60,plain,(
% 0.06/0.27 spl0_3 <=> in(sk0_3,singleton(sk0_3))),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f62,plain,(
% 0.06/0.27 ~in(sk0_3,singleton(sk0_3))|spl0_3),
% 0.06/0.27 inference(component_clause,[status(thm)],[f60])).
% 0.06/0.27 fof(f63,plain,(
% 0.06/0.27 ~in(sk0_3,singleton(sk0_3))|~in(sk0_4,sk0_6)|~spl0_1|spl0_0),
% 0.06/0.27 inference(resolution,[status(thm)],[f27,f59])).
% 0.06/0.27 fof(f64,plain,(
% 0.06/0.27 ~spl0_3|~spl0_2|~spl0_1|spl0_0),
% 0.06/0.27 inference(split_clause,[status(thm)],[f63,f60,f45,f41,f38])).
% 0.06/0.27 fof(f65,plain,(
% 0.06/0.27 spl0_4 <=> ~in(X0,X1)),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f68,plain,(
% 0.06/0.27 spl0_5 <=> ~in(X2,X3)|in(X2,X3)),
% 0.06/0.27 introduced(split_symbol_definition)).
% 0.06/0.27 fof(f71,plain,(
% 0.06/0.27 ![X0,X1,X2,X3]: (~in(X0,X1)|~in(X2,X3)|in(X2,X3))),
% 0.06/0.27 inference(resolution,[status(thm)],[f27,f26])).
% 0.06/0.27 fof(f72,plain,(
% 0.06/0.27 spl0_4|spl0_5),
% 0.06/0.27 inference(split_clause,[status(thm)],[f71,f65,f68])).
% 0.06/0.27 fof(f76,plain,(
% 0.06/0.27 in(ordered_pair(sk0_3,sk0_4),cartesian_product2(singleton(sk0_3),sk0_6))|~spl0_1|~spl0_0),
% 0.06/0.27 inference(forward_demodulation,[status(thm)],[f42,f39])).
% 0.06/0.27 fof(f81,plain,(
% 0.06/0.27 in(sk0_4,sk0_6)|~spl0_1|~spl0_0),
% 0.06/0.27 inference(resolution,[status(thm)],[f76,f26])).
% 0.06/0.27 fof(f82,plain,(
% 0.06/0.27 spl0_2|~spl0_1|~spl0_0),
% 0.06/0.27 inference(split_clause,[status(thm)],[f81,f45,f41,f38])).
% 0.06/0.27 fof(f85,plain,(
% 0.06/0.27 $false|spl0_3),
% 0.06/0.27 inference(forward_subsumption_resolution,[status(thm)],[f62,f51])).
% 0.06/0.27 fof(f86,plain,(
% 0.06/0.27 spl0_3),
% 0.06/0.27 inference(contradiction_clause,[status(thm)],[f85])).
% 0.06/0.27 fof(f87,plain,(
% 0.06/0.27 $false),
% 0.06/0.27 inference(sat_refutation,[status(thm)],[f44,f48,f49,f57,f64,f72,f82,f86])).
% 0.06/0.27 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.48 % Elapsed time: 0.014190 seconds
% 0.10/0.48 % CPU time: 0.033664 seconds
% 0.10/0.48 % Memory used: 14.647 MB
%------------------------------------------------------------------------------