TSTP Solution File: SET930+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 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 12:35:34 EDT 2023
% Result : Theorem 0.11s 0.27s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n023.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue May 30 10:30:53 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.5.1
% 0.11/0.27 % Refutation found
% 0.11/0.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.27 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.27 fof(f1,axiom,(
% 0.11/0.27 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f2,axiom,(
% 0.11/0.27 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f4,axiom,(
% 0.11/0.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f7,axiom,(
% 0.11/0.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)<=> ( ~ in(A,C)& ~ in(B,C) ) ) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f8,axiom,(
% 0.11/0.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = empty_set<=> ( in(A,C)& in(B,C) ) ) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f9,conjecture,(
% 0.11/0.27 (! [A,B,C] :~ ( set_difference(unordered_pair(A,B),C) != empty_set& set_difference(unordered_pair(A,B),C) != singleton(A)& set_difference(unordered_pair(A,B),C) != singleton(B)& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) )),
% 0.11/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.27 fof(f10,negated_conjecture,(
% 0.11/0.27 ~((! [A,B,C] :~ ( set_difference(unordered_pair(A,B),C) != empty_set& set_difference(unordered_pair(A,B),C) != singleton(A)& set_difference(unordered_pair(A,B),C) != singleton(B)& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ))),
% 0.11/0.27 inference(negated_conjecture,[status(cth)],[f9])).
% 0.11/0.27 fof(f11,plain,(
% 0.11/0.27 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.11/0.27 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.11/0.27 fof(f12,plain,(
% 0.11/0.27 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f11])).
% 0.11/0.27 fof(f13,plain,(
% 0.11/0.27 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f2])).
% 0.11/0.27 fof(f15,plain,(
% 0.11/0.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B)))&(set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.11/0.27 inference(NNF_transformation,[status(esa)],[f4])).
% 0.11/0.27 fof(f16,plain,(
% 0.11/0.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.11/0.27 inference(miniscoping,[status(esa)],[f15])).
% 0.11/0.27 fof(f19,plain,(
% 0.11/0.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~in(X1,X2))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f16])).
% 0.11/0.27 fof(f20,plain,(
% 0.11/0.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~X0=X1)),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f16])).
% 0.11/0.27 fof(f25,plain,(
% 0.11/0.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(~in(A,C)&~in(B,C)))&(set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(in(A,C)|in(B,C))))),
% 0.11/0.27 inference(NNF_transformation,[status(esa)],[f7])).
% 0.11/0.27 fof(f26,plain,(
% 0.11/0.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(~in(A,C)&~in(B,C))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(in(A,C)|in(B,C))))),
% 0.11/0.27 inference(miniscoping,[status(esa)],[f25])).
% 0.11/0.27 fof(f29,plain,(
% 0.11/0.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=unordered_pair(X0,X1)|in(X0,X2)|in(X1,X2))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f26])).
% 0.11/0.27 fof(f30,plain,(
% 0.11/0.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=empty_set|(in(A,C)&in(B,C)))&(set_difference(unordered_pair(A,B),C)=empty_set|(~in(A,C)|~in(B,C))))),
% 0.11/0.27 inference(NNF_transformation,[status(esa)],[f8])).
% 0.11/0.27 fof(f31,plain,(
% 0.11/0.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=empty_set|(in(A,C)&in(B,C))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=empty_set|(~in(A,C)|~in(B,C))))),
% 0.11/0.27 inference(miniscoping,[status(esa)],[f30])).
% 0.11/0.27 fof(f33,plain,(
% 0.11/0.27 ![X0,X1,X2]: (~set_difference(unordered_pair(X0,X1),X2)=empty_set|in(X1,X2))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f31])).
% 0.11/0.27 fof(f34,plain,(
% 0.11/0.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=empty_set|~in(X0,X2)|~in(X1,X2))),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f31])).
% 0.11/0.27 fof(f35,plain,(
% 0.11/0.27 (?[A,B,C]: (((~set_difference(unordered_pair(A,B),C)=empty_set&~set_difference(unordered_pair(A,B),C)=singleton(A))&~set_difference(unordered_pair(A,B),C)=singleton(B))&~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)))),
% 0.11/0.27 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.11/0.27 fof(f36,plain,(
% 0.11/0.27 (((~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=empty_set&~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=singleton(sk0_2))&~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=singleton(sk0_3))&~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=unordered_pair(sk0_2,sk0_3))),
% 0.11/0.27 inference(skolemization,[status(esa)],[f35])).
% 0.11/0.27 fof(f37,plain,(
% 0.11/0.27 ~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=empty_set),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.27 fof(f38,plain,(
% 0.11/0.27 ~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=singleton(sk0_2)),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.27 fof(f39,plain,(
% 0.11/0.27 ~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=singleton(sk0_3)),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.27 fof(f40,plain,(
% 0.11/0.27 ~set_difference(unordered_pair(sk0_2,sk0_3),sk0_4)=unordered_pair(sk0_2,sk0_3)),
% 0.11/0.27 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.27 fof(f41,plain,(
% 0.11/0.27 ![X0,X1]: (set_difference(unordered_pair(X0,X0),X1)=singleton(X0)|in(X0,X1))),
% 0.11/0.27 inference(destructive_equality_resolution,[status(esa)],[f20])).
% 0.11/0.27 fof(f48,plain,(
% 0.11/0.27 ![X0,X1]: (~singleton(X0)=empty_set|in(X0,X1)|in(X0,X1))),
% 0.11/0.27 inference(paramodulation,[status(thm)],[f41,f33])).
% 0.11/0.27 fof(f49,plain,(
% 0.11/0.27 ![X0,X1]: (~singleton(X0)=empty_set|in(X0,X1))),
% 0.11/0.27 inference(duplicate_literals_removal,[status(esa)],[f48])).
% 0.11/0.27 fof(f64,plain,(
% 0.11/0.27 spl0_0 <=> in(sk0_2,sk0_4)),
% 0.11/0.27 introduced(split_symbol_definition)).
% 0.11/0.27 fof(f67,plain,(
% 0.11/0.27 spl0_1 <=> in(sk0_3,sk0_4)),
% 0.11/0.27 introduced(split_symbol_definition)).
% 0.11/0.27 fof(f70,plain,(
% 0.11/0.27 in(sk0_2,sk0_4)|~in(sk0_3,sk0_4)),
% 0.11/0.27 inference(resolution,[status(thm)],[f19,f38])).
% 0.11/0.27 fof(f71,plain,(
% 0.11/0.27 spl0_0|~spl0_1),
% 0.11/0.27 inference(split_clause,[status(thm)],[f70,f64,f67])).
% 0.11/0.27 fof(f72,plain,(
% 0.11/0.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X1)|in(X1,X2)|~in(X0,X2))),
% 0.11/0.27 inference(paramodulation,[status(thm)],[f13,f19])).
% 0.11/0.27 fof(f74,plain,(
% 0.11/0.27 in(sk0_2,sk0_4)|in(sk0_3,sk0_4)),
% 0.11/0.27 inference(resolution,[status(thm)],[f29,f40])).
% 0.11/0.27 fof(f75,plain,(
% 0.11/0.27 spl0_0|spl0_1),
% 0.11/0.27 inference(split_clause,[status(thm)],[f74,f64,f67])).
% 0.11/0.27 fof(f108,plain,(
% 0.11/0.27 ![X0,X1]: (~in(X0,X1)|~singleton(X1)=empty_set)),
% 0.11/0.27 inference(resolution,[status(thm)],[f12,f49])).
% 0.11/0.27 fof(f109,plain,(
% 0.11/0.27 spl0_6 <=> ~singleton(X0)=empty_set),
% 0.11/0.27 introduced(split_symbol_definition)).
% 0.11/0.27 fof(f112,plain,(
% 0.11/0.27 ![X0,X1]: (~singleton(X0)=empty_set|~singleton(X1)=empty_set)),
% 0.11/0.27 inference(resolution,[status(thm)],[f108,f49])).
% 0.11/0.27 fof(f113,plain,(
% 0.11/0.27 spl0_6),
% 0.11/0.27 inference(split_clause,[status(thm)],[f112,f109])).
% 0.11/0.27 fof(f132,plain,(
% 0.11/0.27 ~in(sk0_2,sk0_4)|~in(sk0_3,sk0_4)),
% 0.11/0.27 inference(resolution,[status(thm)],[f34,f37])).
% 0.11/0.27 fof(f133,plain,(
% 0.11/0.27 ~spl0_0|~spl0_1),
% 0.11/0.27 inference(split_clause,[status(thm)],[f132,f64,f67])).
% 0.11/0.27 fof(f143,plain,(
% 0.11/0.27 in(sk0_3,sk0_4)|~in(sk0_2,sk0_4)),
% 0.11/0.27 inference(resolution,[status(thm)],[f72,f39])).
% 0.11/0.27 fof(f144,plain,(
% 0.11/0.27 spl0_1|~spl0_0),
% 0.11/0.27 inference(split_clause,[status(thm)],[f143,f67,f64])).
% 0.11/0.27 fof(f147,plain,(
% 0.11/0.27 $false),
% 0.11/0.27 inference(sat_refutation,[status(thm)],[f71,f75,f113,f133,f144])).
% 0.11/0.27 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.28 % Elapsed time: 0.016109 seconds
% 0.11/0.28 % CPU time: 0.031850 seconds
% 0.11/0.28 % Memory used: 19.787 MB
%------------------------------------------------------------------------------