TSTP Solution File: SEU173+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:36:07 EDT 2023
% Result : Theorem 0.15s 0.31s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n006.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 09:10:02 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.15/0.31 % Refutation found
% 0.15/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.31 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.31 fof(f2,axiom,(
% 0.15/0.31 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f3,axiom,(
% 0.15/0.31 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f4,axiom,(
% 0.15/0.31 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f10,axiom,(
% 0.15/0.31 empty(empty_set) ),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f11,conjecture,(
% 0.15/0.31 (! [A,B] :( (! [C] :( in(C,A)=> in(C,B) ))=> element(A,powerset(B)) ) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f12,negated_conjecture,(
% 0.15/0.31 ~((! [A,B] :( (! [C] :( in(C,A)=> in(C,B) ))=> element(A,powerset(B)) ) ))),
% 0.15/0.31 inference(negated_conjecture,[status(cth)],[f11])).
% 0.15/0.31 fof(f18,axiom,(
% 0.15/0.31 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f19,axiom,(
% 0.15/0.31 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.15/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.31 fof(f23,plain,(
% 0.15/0.31 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.15/0.31 inference(NNF_transformation,[status(esa)],[f2])).
% 0.15/0.31 fof(f24,plain,(
% 0.15/0.31 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.15/0.31 inference(miniscoping,[status(esa)],[f23])).
% 0.15/0.31 fof(f25,plain,(
% 0.15/0.31 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sk0_0(B,A),B)|~subset(sk0_0(B,A),A))&(in(sk0_0(B,A),B)|subset(sk0_0(B,A),A)))))),
% 0.15/0.31 inference(skolemization,[status(esa)],[f24])).
% 0.15/0.31 fof(f27,plain,(
% 0.15/0.31 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f25])).
% 0.15/0.31 fof(f30,plain,(
% 0.15/0.31 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 0.15/0.31 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.15/0.31 fof(f31,plain,(
% 0.15/0.31 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 0.15/0.31 inference(NNF_transformation,[status(esa)],[f30])).
% 0.15/0.31 fof(f32,plain,(
% 0.15/0.31 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 0.15/0.31 inference(miniscoping,[status(esa)],[f31])).
% 0.15/0.31 fof(f33,plain,(
% 0.15/0.31 ![X0,X1]: (empty(X0)|~element(X1,X0)|in(X1,X0))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f32])).
% 0.15/0.31 fof(f34,plain,(
% 0.15/0.31 ![X0,X1]: (empty(X0)|element(X1,X0)|~in(X1,X0))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f32])).
% 0.15/0.31 fof(f37,plain,(
% 0.15/0.31 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.15/0.31 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.15/0.31 fof(f38,plain,(
% 0.15/0.31 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.15/0.31 inference(NNF_transformation,[status(esa)],[f37])).
% 0.15/0.31 fof(f39,plain,(
% 0.15/0.31 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.15/0.31 inference(miniscoping,[status(esa)],[f38])).
% 0.15/0.31 fof(f40,plain,(
% 0.15/0.31 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_1(B,A),A)&~in(sk0_1(B,A),B))))),
% 0.15/0.31 inference(skolemization,[status(esa)],[f39])).
% 0.15/0.31 fof(f42,plain,(
% 0.15/0.31 ![X0,X1]: (subset(X0,X1)|in(sk0_1(X1,X0),X0))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f40])).
% 0.15/0.31 fof(f43,plain,(
% 0.15/0.31 ![X0,X1]: (subset(X0,X1)|~in(sk0_1(X1,X0),X1))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f40])).
% 0.15/0.31 fof(f47,plain,(
% 0.15/0.31 empty(empty_set)),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f10])).
% 0.15/0.31 fof(f48,plain,(
% 0.15/0.31 (?[A,B]: ((![C]: (~in(C,A)|in(C,B)))&~element(A,powerset(B))))),
% 0.15/0.31 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.15/0.31 fof(f49,plain,(
% 0.15/0.31 ((![C]: (~in(C,sk0_3)|in(C,sk0_4)))&~element(sk0_3,powerset(sk0_4)))),
% 0.15/0.31 inference(skolemization,[status(esa)],[f48])).
% 0.15/0.31 fof(f50,plain,(
% 0.15/0.31 ![X0]: (~in(X0,sk0_3)|in(X0,sk0_4))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f49])).
% 0.15/0.31 fof(f51,plain,(
% 0.15/0.31 ~element(sk0_3,powerset(sk0_4))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f49])).
% 0.15/0.31 fof(f65,plain,(
% 0.15/0.31 ![A]: (~empty(A)|A=empty_set)),
% 0.15/0.31 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.15/0.31 fof(f66,plain,(
% 0.15/0.31 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f65])).
% 0.15/0.31 fof(f67,plain,(
% 0.15/0.31 ![A,B]: (~in(A,B)|~empty(B))),
% 0.15/0.31 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.15/0.31 fof(f68,plain,(
% 0.15/0.31 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.15/0.31 inference(miniscoping,[status(esa)],[f67])).
% 0.15/0.31 fof(f69,plain,(
% 0.15/0.31 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.15/0.31 inference(cnf_transformation,[status(esa)],[f68])).
% 0.15/0.31 fof(f74,plain,(
% 0.15/0.31 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 0.15/0.31 inference(destructive_equality_resolution,[status(esa)],[f27])).
% 0.15/0.31 fof(f76,plain,(
% 0.15/0.31 ![X0,X1]: (element(X0,X1)|~in(X0,X1))),
% 0.15/0.31 inference(forward_subsumption_resolution,[status(thm)],[f34,f69])).
% 0.15/0.31 fof(f77,plain,(
% 0.15/0.31 ![X0]: (element(X0,sk0_4)|~in(X0,sk0_3))),
% 0.15/0.31 inference(resolution,[status(thm)],[f76,f50])).
% 0.15/0.31 fof(f80,plain,(
% 0.15/0.31 ![X0]: (~in(X0,empty_set))),
% 0.15/0.31 inference(resolution,[status(thm)],[f47,f69])).
% 0.15/0.31 fof(f122,plain,(
% 0.15/0.31 ![X0]: (subset(sk0_3,X0)|element(sk0_1(X0,sk0_3),sk0_4))),
% 0.15/0.31 inference(resolution,[status(thm)],[f42,f77])).
% 0.15/0.31 fof(f126,plain,(
% 0.15/0.31 spl0_1 <=> subset(sk0_3,X0)|in(sk0_1(X0,sk0_3),sk0_4)),
% 0.15/0.31 introduced(split_symbol_definition)).
% 0.15/0.31 fof(f127,plain,(
% 0.15/0.31 ![X0]: (subset(sk0_3,X0)|in(sk0_1(X0,sk0_3),sk0_4)|~spl0_1)),
% 0.15/0.31 inference(component_clause,[status(thm)],[f126])).
% 0.15/0.31 fof(f129,plain,(
% 0.15/0.31 spl0_2 <=> empty(sk0_4)),
% 0.15/0.31 introduced(split_symbol_definition)).
% 0.15/0.31 fof(f130,plain,(
% 0.15/0.31 empty(sk0_4)|~spl0_2),
% 0.15/0.31 inference(component_clause,[status(thm)],[f129])).
% 0.15/0.31 fof(f132,plain,(
% 0.15/0.31 ![X0]: (subset(sk0_3,X0)|empty(sk0_4)|in(sk0_1(X0,sk0_3),sk0_4))),
% 0.15/0.31 inference(resolution,[status(thm)],[f122,f33])).
% 0.15/0.31 fof(f133,plain,(
% 0.15/0.31 spl0_1|spl0_2),
% 0.15/0.31 inference(split_clause,[status(thm)],[f132,f126,f129])).
% 0.15/0.31 fof(f145,plain,(
% 0.15/0.31 sk0_4=empty_set|~spl0_2),
% 0.15/0.31 inference(resolution,[status(thm)],[f130,f66])).
% 0.15/0.31 fof(f155,plain,(
% 0.15/0.31 ![X0]: (~in(X0,sk0_3)|in(X0,empty_set)|~spl0_2)),
% 0.15/0.31 inference(backward_demodulation,[status(thm)],[f145,f50])).
% 0.15/0.31 fof(f156,plain,(
% 0.15/0.31 ![X0]: (~in(X0,sk0_3)|~spl0_2)),
% 0.15/0.31 inference(forward_subsumption_resolution,[status(thm)],[f155,f80])).
% 0.15/0.31 fof(f157,plain,(
% 0.15/0.31 ~element(sk0_3,powerset(empty_set))|~spl0_2),
% 0.15/0.31 inference(backward_demodulation,[status(thm)],[f145,f51])).
% 0.15/0.31 fof(f159,plain,(
% 0.15/0.31 ![X0]: (subset(sk0_3,X0)|~spl0_2)),
% 0.15/0.31 inference(resolution,[status(thm)],[f156,f42])).
% 0.15/0.31 fof(f162,plain,(
% 0.15/0.31 ![X0]: (in(sk0_3,powerset(X0))|~spl0_2)),
% 0.15/0.31 inference(resolution,[status(thm)],[f159,f74])).
% 0.15/0.31 fof(f164,plain,(
% 0.15/0.31 ![X0]: (element(sk0_3,powerset(X0))|~spl0_2)),
% 0.15/0.31 inference(resolution,[status(thm)],[f162,f76])).
% 0.15/0.31 fof(f169,plain,(
% 0.15/0.31 $false|~spl0_2),
% 0.15/0.31 inference(forward_subsumption_resolution,[status(thm)],[f157,f164])).
% 0.15/0.31 fof(f170,plain,(
% 0.15/0.31 ~spl0_2),
% 0.15/0.31 inference(contradiction_clause,[status(thm)],[f169])).
% 0.15/0.31 fof(f261,plain,(
% 0.15/0.31 spl0_9 <=> subset(sk0_3,sk0_4)),
% 0.15/0.31 introduced(split_symbol_definition)).
% 0.15/0.31 fof(f262,plain,(
% 0.15/0.31 subset(sk0_3,sk0_4)|~spl0_9),
% 0.15/0.31 inference(component_clause,[status(thm)],[f261])).
% 0.15/0.31 fof(f264,plain,(
% 0.15/0.31 subset(sk0_3,sk0_4)|subset(sk0_3,sk0_4)|~spl0_1),
% 0.15/0.31 inference(resolution,[status(thm)],[f43,f127])).
% 0.15/0.31 fof(f265,plain,(
% 0.15/0.31 spl0_9|~spl0_1),
% 0.15/0.31 inference(split_clause,[status(thm)],[f264,f261,f126])).
% 0.15/0.31 fof(f310,plain,(
% 0.15/0.31 in(sk0_3,powerset(sk0_4))|~spl0_9),
% 0.15/0.31 inference(resolution,[status(thm)],[f262,f74])).
% 0.15/0.31 fof(f318,plain,(
% 0.15/0.31 element(sk0_3,powerset(sk0_4))|~spl0_9),
% 0.15/0.31 inference(resolution,[status(thm)],[f310,f76])).
% 0.15/0.31 fof(f360,plain,(
% 0.15/0.31 $false|~spl0_9),
% 0.15/0.31 inference(forward_subsumption_resolution,[status(thm)],[f51,f318])).
% 0.15/0.31 fof(f361,plain,(
% 0.15/0.31 ~spl0_9),
% 0.15/0.31 inference(contradiction_clause,[status(thm)],[f360])).
% 0.15/0.31 fof(f362,plain,(
% 0.15/0.31 $false),
% 0.15/0.31 inference(sat_refutation,[status(thm)],[f133,f170,f265,f361])).
% 0.15/0.31 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.55 % Elapsed time: 0.037317 seconds
% 0.16/0.55 % CPU time: 0.020342 seconds
% 0.16/0.55 % Memory used: 3.047 MB
%------------------------------------------------------------------------------