TSTP Solution File: SET962+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.02/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26 % Computer : n027.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 30 10:30:47 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.10/0.27 % Refutation found
% 0.10/0.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.27 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.27 fof(f5,axiom,(
% 0.10/0.27 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.10/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.27 fof(f8,conjecture,(
% 0.10/0.27 (! [A,B] :( cartesian_product2(A,A) = cartesian_product2(B,B)=> A = B ) )),
% 0.10/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.27 fof(f9,negated_conjecture,(
% 0.10/0.27 ~((! [A,B] :( cartesian_product2(A,A) = cartesian_product2(B,B)=> A = B ) ))),
% 0.10/0.27 inference(negated_conjecture,[status(cth)],[f8])).
% 0.10/0.27 fof(f10,axiom,(
% 0.10/0.27 (! [A,B] :( (! [C] :( in(C,A)<=> in(C,B) ))=> A = B ) )),
% 0.10/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.27 fof(f16,plain,(
% 0.10/0.27 ![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))))),
% 0.10/0.27 inference(NNF_transformation,[status(esa)],[f5])).
% 0.10/0.27 fof(f17,plain,(
% 0.10/0.27 (![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))))),
% 0.10/0.27 inference(miniscoping,[status(esa)],[f16])).
% 0.10/0.27 fof(f19,plain,(
% 0.10/0.27 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f17])).
% 0.10/0.27 fof(f20,plain,(
% 0.10/0.27 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f17])).
% 0.10/0.27 fof(f25,plain,(
% 0.10/0.27 (?[A,B]: (cartesian_product2(A,A)=cartesian_product2(B,B)&~A=B))),
% 0.10/0.27 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.10/0.27 fof(f26,plain,(
% 0.10/0.27 (cartesian_product2(sk0_2,sk0_2)=cartesian_product2(sk0_3,sk0_3)&~sk0_2=sk0_3)),
% 0.10/0.27 inference(skolemization,[status(esa)],[f25])).
% 0.10/0.27 fof(f27,plain,(
% 0.10/0.27 cartesian_product2(sk0_2,sk0_2)=cartesian_product2(sk0_3,sk0_3)),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f26])).
% 0.10/0.27 fof(f28,plain,(
% 0.10/0.27 ~sk0_2=sk0_3),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f26])).
% 0.10/0.27 fof(f29,plain,(
% 0.10/0.27 ![A,B]: ((?[C]: (in(C,A)<~>in(C,B)))|A=B)),
% 0.10/0.27 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.10/0.27 fof(f30,plain,(
% 0.10/0.27 ![A,B]: ((?[C]: ((in(C,A)|in(C,B))&(~in(C,A)|~in(C,B))))|A=B)),
% 0.10/0.27 inference(NNF_transformation,[status(esa)],[f29])).
% 0.10/0.27 fof(f31,plain,(
% 0.10/0.27 ![A,B]: (((in(sk0_4(B,A),A)|in(sk0_4(B,A),B))&(~in(sk0_4(B,A),A)|~in(sk0_4(B,A),B)))|A=B)),
% 0.10/0.27 inference(skolemization,[status(esa)],[f30])).
% 0.10/0.27 fof(f32,plain,(
% 0.10/0.27 ![X0,X1]: (in(sk0_4(X0,X1),X1)|in(sk0_4(X0,X1),X0)|X1=X0)),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f31])).
% 0.10/0.27 fof(f33,plain,(
% 0.10/0.27 ![X0,X1]: (~in(sk0_4(X0,X1),X1)|~in(sk0_4(X0,X1),X0)|X1=X0)),
% 0.10/0.27 inference(cnf_transformation,[status(esa)],[f31])).
% 0.10/0.27 fof(f35,plain,(
% 0.10/0.27 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_2,sk0_2))|in(X1,sk0_3))),
% 0.10/0.27 inference(paramodulation,[status(thm)],[f27,f19])).
% 0.10/0.27 fof(f36,plain,(
% 0.10/0.27 spl0_0 <=> ~in(X0,sk0_2)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f37,plain,(
% 0.10/0.27 ![X0]: (~in(X0,sk0_2)|~spl0_0)),
% 0.10/0.27 inference(component_clause,[status(thm)],[f36])).
% 0.10/0.27 fof(f39,plain,(
% 0.10/0.27 spl0_1 <=> ~in(X1,sk0_2)|in(X1,sk0_3)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f40,plain,(
% 0.10/0.27 ![X0]: (~in(X0,sk0_2)|in(X0,sk0_3)|~spl0_1)),
% 0.10/0.27 inference(component_clause,[status(thm)],[f39])).
% 0.10/0.27 fof(f42,plain,(
% 0.10/0.27 ![X0,X1]: (~in(X0,sk0_2)|~in(X1,sk0_2)|in(X1,sk0_3))),
% 0.10/0.27 inference(resolution,[status(thm)],[f20,f35])).
% 0.10/0.27 fof(f43,plain,(
% 0.10/0.27 spl0_0|spl0_1),
% 0.10/0.27 inference(split_clause,[status(thm)],[f42,f36,f39])).
% 0.10/0.27 fof(f46,plain,(
% 0.10/0.27 spl0_2 <=> ~in(X0,X1)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f47,plain,(
% 0.10/0.27 ![X0,X1]: (~in(X0,X1)|~spl0_2)),
% 0.10/0.27 inference(component_clause,[status(thm)],[f46])).
% 0.10/0.27 fof(f49,plain,(
% 0.10/0.27 spl0_3 <=> ~in(X2,X3)|in(X2,X3)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f52,plain,(
% 0.10/0.27 ![X0,X1,X2,X3]: (~in(X0,X1)|~in(X2,X3)|in(X2,X3))),
% 0.10/0.27 inference(resolution,[status(thm)],[f20,f19])).
% 0.10/0.27 fof(f53,plain,(
% 0.10/0.27 spl0_2|spl0_3),
% 0.10/0.27 inference(split_clause,[status(thm)],[f52,f46,f49])).
% 0.10/0.27 fof(f56,plain,(
% 0.10/0.27 ![X0,X1]: (in(ordered_pair(X0,X1),cartesian_product2(sk0_2,sk0_2))|~in(X0,sk0_3)|~in(X1,sk0_3))),
% 0.10/0.27 inference(paramodulation,[status(thm)],[f27,f20])).
% 0.10/0.27 fof(f57,plain,(
% 0.10/0.27 spl0_4 <=> ~in(X0,sk0_3)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f58,plain,(
% 0.10/0.27 ![X0]: (~in(X0,sk0_3)|~spl0_4)),
% 0.10/0.27 inference(component_clause,[status(thm)],[f57])).
% 0.10/0.27 fof(f67,plain,(
% 0.10/0.27 spl0_6 <=> ~in(X1,sk0_3)|in(X1,sk0_2)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f68,plain,(
% 0.10/0.27 ![X0]: (~in(X0,sk0_3)|in(X0,sk0_2)|~spl0_6)),
% 0.10/0.27 inference(component_clause,[status(thm)],[f67])).
% 0.10/0.27 fof(f70,plain,(
% 0.10/0.27 ![X0,X1]: (~in(X0,sk0_3)|~in(X1,sk0_3)|in(X1,sk0_2))),
% 0.10/0.27 inference(resolution,[status(thm)],[f56,f19])).
% 0.10/0.27 fof(f71,plain,(
% 0.10/0.27 spl0_4|spl0_6),
% 0.10/0.27 inference(split_clause,[status(thm)],[f70,f57,f67])).
% 0.10/0.27 fof(f74,plain,(
% 0.10/0.27 ![X0,X1]: (~in(ordered_pair(X0,X1),cartesian_product2(sk0_2,sk0_2))|~spl0_4)),
% 0.10/0.27 inference(backward_subsumption_resolution,[status(thm)],[f35,f58])).
% 0.10/0.27 fof(f76,plain,(
% 0.10/0.27 ![X0,X1]: (~in(X0,sk0_2)|~in(X1,sk0_2)|~spl0_4)),
% 0.10/0.27 inference(resolution,[status(thm)],[f74,f20])).
% 0.10/0.27 fof(f77,plain,(
% 0.10/0.27 spl0_0|~spl0_4),
% 0.10/0.27 inference(split_clause,[status(thm)],[f76,f36,f57])).
% 0.10/0.27 fof(f89,plain,(
% 0.10/0.27 ![X0,X1]: (in(sk0_4(X0,X1),X0)|X1=X0|~spl0_2)),
% 0.10/0.27 inference(forward_subsumption_resolution,[status(thm)],[f32,f47])).
% 0.10/0.27 fof(f90,plain,(
% 0.10/0.27 ![X0,X1]: (X0=X1|~spl0_2)),
% 0.10/0.27 inference(resolution,[status(thm)],[f89,f47])).
% 0.10/0.27 fof(f91,plain,(
% 0.10/0.27 $false|~spl0_2),
% 0.10/0.27 inference(backward_subsumption_resolution,[status(thm)],[f28,f90])).
% 0.10/0.27 fof(f92,plain,(
% 0.10/0.27 ~spl0_2),
% 0.10/0.27 inference(contradiction_clause,[status(thm)],[f91])).
% 0.10/0.27 fof(f110,plain,(
% 0.10/0.27 ![X0]: (in(sk0_4(X0,sk0_2),X0)|sk0_2=X0|~spl0_0)),
% 0.10/0.27 inference(resolution,[status(thm)],[f32,f37])).
% 0.10/0.27 fof(f121,plain,(
% 0.10/0.27 sk0_2=sk0_3|~spl0_0|~spl0_4),
% 0.10/0.27 inference(resolution,[status(thm)],[f110,f58])).
% 0.10/0.27 fof(f122,plain,(
% 0.10/0.27 $false|~spl0_0|~spl0_4),
% 0.10/0.27 inference(forward_subsumption_resolution,[status(thm)],[f121,f28])).
% 0.10/0.27 fof(f123,plain,(
% 0.10/0.27 ~spl0_0|~spl0_4),
% 0.10/0.27 inference(contradiction_clause,[status(thm)],[f122])).
% 0.10/0.27 fof(f128,plain,(
% 0.10/0.27 ![X0]: (~in(sk0_4(X0,sk0_3),sk0_2)|~in(sk0_4(X0,sk0_3),X0)|sk0_3=X0|~spl0_1)),
% 0.10/0.27 inference(resolution,[status(thm)],[f40,f33])).
% 0.10/0.27 fof(f130,plain,(
% 0.10/0.27 ![X0]: (in(sk0_4(X0,sk0_3),sk0_2)|in(sk0_4(X0,sk0_3),X0)|sk0_3=X0|~spl0_6)),
% 0.10/0.27 inference(resolution,[status(thm)],[f68,f32])).
% 0.10/0.27 fof(f137,plain,(
% 0.10/0.27 ![X0]: (~in(X0,sk0_3)|~spl0_0|~spl0_6)),
% 0.10/0.27 inference(backward_subsumption_resolution,[status(thm)],[f68,f37])).
% 0.10/0.27 fof(f138,plain,(
% 0.10/0.27 spl0_4|~spl0_0|~spl0_6),
% 0.10/0.27 inference(split_clause,[status(thm)],[f137,f57,f36,f67])).
% 0.10/0.27 fof(f159,plain,(
% 0.10/0.27 spl0_10 <=> sk0_3=sk0_2),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f160,plain,(
% 0.10/0.27 sk0_3=sk0_2|~spl0_10),
% 0.10/0.27 inference(component_clause,[status(thm)],[f159])).
% 0.10/0.27 fof(f165,plain,(
% 0.10/0.27 spl0_12 <=> in(sk0_4(sk0_2,sk0_3),sk0_2)),
% 0.10/0.27 introduced(split_symbol_definition)).
% 0.10/0.27 fof(f166,plain,(
% 0.10/0.27 in(sk0_4(sk0_2,sk0_3),sk0_2)|~spl0_12),
% 0.10/0.27 inference(component_clause,[status(thm)],[f165])).
% 0.10/0.27 fof(f167,plain,(
% 0.10/0.27 ~in(sk0_4(sk0_2,sk0_3),sk0_2)|spl0_12),
% 0.10/0.27 inference(component_clause,[status(thm)],[f165])).
% 0.10/0.27 fof(f192,plain,(
% 0.10/0.27 in(sk0_4(sk0_2,sk0_3),sk0_2)|sk0_3=sk0_2|spl0_12|~spl0_6),
% 0.10/0.27 inference(resolution,[status(thm)],[f167,f130])).
% 0.10/0.27 fof(f193,plain,(
% 0.10/0.27 spl0_12|spl0_10|~spl0_6),
% 0.10/0.27 inference(split_clause,[status(thm)],[f192,f165,f159,f67])).
% 0.10/0.27 fof(f196,plain,(
% 0.10/0.27 $false|~spl0_10),
% 0.10/0.27 inference(forward_subsumption_resolution,[status(thm)],[f160,f28])).
% 0.10/0.27 fof(f197,plain,(
% 0.10/0.27 ~spl0_10),
% 0.10/0.27 inference(contradiction_clause,[status(thm)],[f196])).
% 0.10/0.27 fof(f198,plain,(
% 0.10/0.27 ~in(sk0_4(sk0_2,sk0_3),sk0_2)|sk0_3=sk0_2|~spl0_12|~spl0_1),
% 0.10/0.27 inference(resolution,[status(thm)],[f166,f128])).
% 0.10/0.27 fof(f199,plain,(
% 0.10/0.27 ~spl0_12|spl0_10|~spl0_1),
% 0.10/0.27 inference(split_clause,[status(thm)],[f198,f165,f159,f39])).
% 0.10/0.27 fof(f200,plain,(
% 0.10/0.27 $false),
% 0.10/0.27 inference(sat_refutation,[status(thm)],[f43,f53,f71,f77,f92,f123,f138,f193,f197,f199])).
% 0.10/0.27 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.28 % Elapsed time: 0.018051 seconds
% 0.10/0.28 % CPU time: 0.054161 seconds
% 0.10/0.28 % Memory used: 16.758 MB
%------------------------------------------------------------------------------