TSTP Solution File: SEU094+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:35:48 EDT 2023
% Result : Theorem 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 08:42:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.41 % Refutation found
% 0.20/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.41 fof(f20,axiom,(
% 0.20/0.41 ~ empty(positive_rationals) ),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f21,axiom,(
% 0.20/0.41 (! [A] :( ( finite(A)& (! [B] :( in(B,A)=> finite(B) ) ))=> finite(union(A)) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f31,axiom,(
% 0.20/0.41 (? [A] :( element(A,positive_rationals)& ~ empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f39,axiom,(
% 0.20/0.41 (? [A] :( element(A,positive_rationals)& empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A)& natural(A) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f48,axiom,(
% 0.20/0.41 (! [A] : subset(A,powerset(union(A))) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f49,axiom,(
% 0.20/0.41 (! [A,B] :( ( subset(A,B)& finite(B) )=> finite(A) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f51,axiom,(
% 0.20/0.41 (! [A] :( finite(A)<=> finite(powerset(A)) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f52,conjecture,(
% 0.20/0.41 (! [A] :( ( finite(A)& (! [B] :( in(B,A)=> finite(B) ) ))<=> finite(union(A)) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f53,negated_conjecture,(
% 0.20/0.41 ~((! [A] :( ( finite(A)& (! [B] :( in(B,A)=> finite(B) ) ))<=> finite(union(A)) ) ))),
% 0.20/0.41 inference(negated_conjecture,[status(cth)],[f52])).
% 0.20/0.41 fof(f54,axiom,(
% 0.20/0.41 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f58,axiom,(
% 0.20/0.41 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f61,axiom,(
% 0.20/0.41 (! [A,B] :( in(A,B)=> subset(A,union(B)) ) )),
% 0.20/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.41 fof(f120,plain,(
% 0.20/0.41 ~empty(positive_rationals)),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f20])).
% 0.20/0.41 fof(f121,plain,(
% 0.20/0.41 ![A]: ((~finite(A)|(?[B]: (in(B,A)&~finite(B))))|finite(union(A)))),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f21])).
% 0.20/0.41 fof(f122,plain,(
% 0.20/0.41 ![A]: ((~finite(A)|(in(sk0_1(A),A)&~finite(sk0_1(A))))|finite(union(A)))),
% 0.20/0.41 inference(skolemization,[status(esa)],[f121])).
% 0.20/0.41 fof(f123,plain,(
% 0.20/0.41 ![X0]: (~finite(X0)|in(sk0_1(X0),X0)|finite(union(X0)))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f122])).
% 0.20/0.41 fof(f124,plain,(
% 0.20/0.41 ![X0]: (~finite(X0)|~finite(sk0_1(X0))|finite(union(X0)))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f122])).
% 0.20/0.41 fof(f159,plain,(
% 0.20/0.41 ((((element(sk0_11,positive_rationals)&~empty(sk0_11))&epsilon_transitive(sk0_11))&epsilon_connected(sk0_11))&ordinal(sk0_11))),
% 0.20/0.41 inference(skolemization,[status(esa)],[f31])).
% 0.20/0.41 fof(f160,plain,(
% 0.20/0.41 element(sk0_11,positive_rationals)),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f159])).
% 0.20/0.41 fof(f201,plain,(
% 0.20/0.41 (((((element(sk0_19,positive_rationals)&empty(sk0_19))&epsilon_transitive(sk0_19))&epsilon_connected(sk0_19))&ordinal(sk0_19))&natural(sk0_19))),
% 0.20/0.41 inference(skolemization,[status(esa)],[f39])).
% 0.20/0.41 fof(f202,plain,(
% 0.20/0.41 element(sk0_19,positive_rationals)),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f201])).
% 0.20/0.41 fof(f203,plain,(
% 0.20/0.41 empty(sk0_19)),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f201])).
% 0.20/0.41 fof(f239,plain,(
% 0.20/0.41 ![X0]: (subset(X0,powerset(union(X0))))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f48])).
% 0.20/0.41 fof(f240,plain,(
% 0.20/0.41 ![A,B]: ((~subset(A,B)|~finite(B))|finite(A))),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f49])).
% 0.20/0.41 fof(f241,plain,(
% 0.20/0.41 ![A]: ((![B]: (~subset(A,B)|~finite(B)))|finite(A))),
% 0.20/0.41 inference(miniscoping,[status(esa)],[f240])).
% 0.20/0.41 fof(f242,plain,(
% 0.20/0.41 ![X0,X1]: (~subset(X0,X1)|~finite(X1)|finite(X0))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f241])).
% 0.20/0.41 fof(f245,plain,(
% 0.20/0.41 ![A]: ((~finite(A)|finite(powerset(A)))&(finite(A)|~finite(powerset(A))))),
% 0.20/0.41 inference(NNF_transformation,[status(esa)],[f51])).
% 0.20/0.41 fof(f246,plain,(
% 0.20/0.41 (![A]: (~finite(A)|finite(powerset(A))))&(![A]: (finite(A)|~finite(powerset(A))))),
% 0.20/0.41 inference(miniscoping,[status(esa)],[f245])).
% 0.20/0.41 fof(f247,plain,(
% 0.20/0.41 ![X0]: (~finite(X0)|finite(powerset(X0)))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f246])).
% 0.20/0.41 fof(f249,plain,(
% 0.20/0.41 (?[A]: ((finite(A)&(![B]: (~in(B,A)|finite(B))))<~>finite(union(A))))),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 0.20/0.41 fof(f250,plain,(
% 0.20/0.41 ?[A]: (((finite(A)&(![B]: (~in(B,A)|finite(B))))|finite(union(A)))&((~finite(A)|(?[B]: (in(B,A)&~finite(B))))|~finite(union(A))))),
% 0.20/0.41 inference(NNF_transformation,[status(esa)],[f249])).
% 0.20/0.41 fof(f251,plain,(
% 0.20/0.41 (((finite(sk0_27)&(![B]: (~in(B,sk0_27)|finite(B))))|finite(union(sk0_27)))&((~finite(sk0_27)|(in(sk0_28,sk0_27)&~finite(sk0_28)))|~finite(union(sk0_27))))),
% 0.20/0.41 inference(skolemization,[status(esa)],[f250])).
% 0.20/0.41 fof(f252,plain,(
% 0.20/0.41 finite(sk0_27)|finite(union(sk0_27))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f251])).
% 0.20/0.41 fof(f253,plain,(
% 0.20/0.41 ![X0]: (~in(X0,sk0_27)|finite(X0)|finite(union(sk0_27)))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f251])).
% 0.20/0.41 fof(f254,plain,(
% 0.20/0.41 ~finite(sk0_27)|in(sk0_28,sk0_27)|~finite(union(sk0_27))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f251])).
% 0.20/0.41 fof(f255,plain,(
% 0.20/0.41 ~finite(sk0_27)|~finite(sk0_28)|~finite(union(sk0_27))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f251])).
% 0.20/0.41 fof(f256,plain,(
% 0.20/0.41 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f54])).
% 0.20/0.41 fof(f257,plain,(
% 0.20/0.41 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f256])).
% 0.20/0.41 fof(f268,plain,(
% 0.20/0.41 ![A]: (~empty(A)|A=empty_set)),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f58])).
% 0.20/0.41 fof(f269,plain,(
% 0.20/0.41 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f268])).
% 0.20/0.41 fof(f276,plain,(
% 0.20/0.41 ![A,B]: (~in(A,B)|subset(A,union(B)))),
% 0.20/0.41 inference(pre_NNF_transformation,[status(esa)],[f61])).
% 0.20/0.41 fof(f277,plain,(
% 0.20/0.41 ![X0,X1]: (~in(X0,X1)|subset(X0,union(X1)))),
% 0.20/0.41 inference(cnf_transformation,[status(esa)],[f276])).
% 0.20/0.41 fof(f278,plain,(
% 0.20/0.41 spl0_0 <=> finite(sk0_27)),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f280,plain,(
% 0.20/0.41 ~finite(sk0_27)|spl0_0),
% 0.20/0.41 inference(component_clause,[status(thm)],[f278])).
% 0.20/0.41 fof(f281,plain,(
% 0.20/0.41 spl0_1 <=> finite(union(sk0_27))),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f282,plain,(
% 0.20/0.41 finite(union(sk0_27))|~spl0_1),
% 0.20/0.41 inference(component_clause,[status(thm)],[f281])).
% 0.20/0.41 fof(f283,plain,(
% 0.20/0.41 ~finite(union(sk0_27))|spl0_1),
% 0.20/0.41 inference(component_clause,[status(thm)],[f281])).
% 0.20/0.41 fof(f284,plain,(
% 0.20/0.41 spl0_0|spl0_1),
% 0.20/0.41 inference(split_clause,[status(thm)],[f252,f278,f281])).
% 0.20/0.41 fof(f285,plain,(
% 0.20/0.41 spl0_2 <=> ~in(X0,sk0_27)|finite(X0)),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f286,plain,(
% 0.20/0.41 ![X0]: (~in(X0,sk0_27)|finite(X0)|~spl0_2)),
% 0.20/0.41 inference(component_clause,[status(thm)],[f285])).
% 0.20/0.41 fof(f288,plain,(
% 0.20/0.41 spl0_2|spl0_1),
% 0.20/0.41 inference(split_clause,[status(thm)],[f253,f285,f281])).
% 0.20/0.41 fof(f289,plain,(
% 0.20/0.41 spl0_3 <=> in(sk0_28,sk0_27)),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f290,plain,(
% 0.20/0.41 in(sk0_28,sk0_27)|~spl0_3),
% 0.20/0.41 inference(component_clause,[status(thm)],[f289])).
% 0.20/0.41 fof(f292,plain,(
% 0.20/0.41 ~spl0_0|spl0_3|~spl0_1),
% 0.20/0.41 inference(split_clause,[status(thm)],[f254,f278,f289,f281])).
% 0.20/0.41 fof(f293,plain,(
% 0.20/0.41 spl0_4 <=> finite(sk0_28)),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f295,plain,(
% 0.20/0.41 ~finite(sk0_28)|spl0_4),
% 0.20/0.41 inference(component_clause,[status(thm)],[f293])).
% 0.20/0.41 fof(f296,plain,(
% 0.20/0.41 ~spl0_0|~spl0_4|~spl0_1),
% 0.20/0.41 inference(split_clause,[status(thm)],[f255,f278,f293,f281])).
% 0.20/0.41 fof(f297,plain,(
% 0.20/0.41 ~in(sk0_28,sk0_27)|~spl0_2|spl0_4),
% 0.20/0.41 inference(resolution,[status(thm)],[f286,f295])).
% 0.20/0.41 fof(f298,plain,(
% 0.20/0.41 $false|~spl0_3|~spl0_2|spl0_4),
% 0.20/0.41 inference(forward_subsumption_resolution,[status(thm)],[f297,f290])).
% 0.20/0.41 fof(f299,plain,(
% 0.20/0.41 ~spl0_3|~spl0_2|spl0_4),
% 0.20/0.41 inference(contradiction_clause,[status(thm)],[f298])).
% 0.20/0.41 fof(f332,plain,(
% 0.20/0.41 sk0_19=empty_set),
% 0.20/0.41 inference(resolution,[status(thm)],[f269,f203])).
% 0.20/0.41 fof(f388,plain,(
% 0.20/0.41 ![X0]: (~subset(sk0_27,X0)|~finite(X0)|spl0_0)),
% 0.20/0.41 inference(resolution,[status(thm)],[f242,f280])).
% 0.20/0.41 fof(f400,plain,(
% 0.20/0.41 spl0_5 <=> empty(positive_rationals)),
% 0.20/0.41 introduced(split_symbol_definition)).
% 0.20/0.41 fof(f401,plain,(
% 0.20/0.41 empty(positive_rationals)|~spl0_5),
% 0.20/0.41 inference(component_clause,[status(thm)],[f400])).
% 0.20/0.42 fof(f403,plain,(
% 0.20/0.42 spl0_6 <=> in(sk0_11,positive_rationals)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f406,plain,(
% 0.20/0.42 empty(positive_rationals)|in(sk0_11,positive_rationals)),
% 0.20/0.42 inference(resolution,[status(thm)],[f160,f257])).
% 0.20/0.42 fof(f407,plain,(
% 0.20/0.42 spl0_5|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f406,f400,f403])).
% 0.20/0.42 fof(f408,plain,(
% 0.20/0.42 $false|~spl0_5),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f401,f120])).
% 0.20/0.42 fof(f409,plain,(
% 0.20/0.42 ~spl0_5),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f408])).
% 0.20/0.42 fof(f411,plain,(
% 0.20/0.42 element(empty_set,positive_rationals)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f332,f202])).
% 0.20/0.42 fof(f412,plain,(
% 0.20/0.42 spl0_7 <=> in(empty_set,positive_rationals)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f415,plain,(
% 0.20/0.42 empty(positive_rationals)|in(empty_set,positive_rationals)),
% 0.20/0.42 inference(resolution,[status(thm)],[f411,f257])).
% 0.20/0.42 fof(f416,plain,(
% 0.20/0.42 spl0_5|spl0_7),
% 0.20/0.42 inference(split_clause,[status(thm)],[f415,f400,f412])).
% 0.20/0.42 fof(f423,plain,(
% 0.20/0.42 ~finite(powerset(union(sk0_27)))|spl0_0),
% 0.20/0.42 inference(resolution,[status(thm)],[f388,f239])).
% 0.20/0.42 fof(f426,plain,(
% 0.20/0.42 ~finite(union(sk0_27))|spl0_0),
% 0.20/0.42 inference(resolution,[status(thm)],[f423,f247])).
% 0.20/0.42 fof(f427,plain,(
% 0.20/0.42 $false|~spl0_1|spl0_0),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f426,f282])).
% 0.20/0.42 fof(f428,plain,(
% 0.20/0.42 ~spl0_1|spl0_0),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f427])).
% 0.20/0.42 fof(f429,plain,(
% 0.20/0.42 spl0_8 <=> finite(sk0_1(sk0_27))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f431,plain,(
% 0.20/0.42 ~finite(sk0_1(sk0_27))|spl0_8),
% 0.20/0.42 inference(component_clause,[status(thm)],[f429])).
% 0.20/0.42 fof(f432,plain,(
% 0.20/0.42 ~finite(sk0_27)|~finite(sk0_1(sk0_27))|spl0_1),
% 0.20/0.42 inference(resolution,[status(thm)],[f283,f124])).
% 0.20/0.42 fof(f433,plain,(
% 0.20/0.42 ~spl0_0|~spl0_8|spl0_1),
% 0.20/0.42 inference(split_clause,[status(thm)],[f432,f278,f429,f281])).
% 0.20/0.42 fof(f434,plain,(
% 0.20/0.42 spl0_9 <=> in(sk0_1(sk0_27),sk0_27)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f435,plain,(
% 0.20/0.42 in(sk0_1(sk0_27),sk0_27)|~spl0_9),
% 0.20/0.42 inference(component_clause,[status(thm)],[f434])).
% 0.20/0.42 fof(f437,plain,(
% 0.20/0.42 ~finite(sk0_27)|in(sk0_1(sk0_27),sk0_27)|spl0_1),
% 0.20/0.42 inference(resolution,[status(thm)],[f283,f123])).
% 0.20/0.42 fof(f438,plain,(
% 0.20/0.42 ~spl0_0|spl0_9|spl0_1),
% 0.20/0.42 inference(split_clause,[status(thm)],[f437,f278,f434,f281])).
% 0.20/0.42 fof(f454,plain,(
% 0.20/0.42 ~in(sk0_1(sk0_27),sk0_27)|spl0_8|~spl0_2),
% 0.20/0.42 inference(resolution,[status(thm)],[f431,f286])).
% 0.20/0.42 fof(f455,plain,(
% 0.20/0.42 $false|~spl0_9|spl0_8|~spl0_2),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f454,f435])).
% 0.20/0.42 fof(f456,plain,(
% 0.20/0.42 ~spl0_9|spl0_8|~spl0_2),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f455])).
% 0.20/0.42 fof(f457,plain,(
% 0.20/0.42 ![X0]: (~subset(sk0_28,X0)|~finite(X0)|spl0_4)),
% 0.20/0.42 inference(resolution,[status(thm)],[f295,f242])).
% 0.20/0.42 fof(f467,plain,(
% 0.20/0.42 ![X0]: (~finite(union(X0))|~in(sk0_28,X0)|spl0_4)),
% 0.20/0.42 inference(resolution,[status(thm)],[f457,f277])).
% 0.20/0.42 fof(f528,plain,(
% 0.20/0.42 ~finite(union(sk0_27))|spl0_4|~spl0_3),
% 0.20/0.42 inference(resolution,[status(thm)],[f467,f290])).
% 0.20/0.42 fof(f529,plain,(
% 0.20/0.42 ~spl0_1|spl0_4|~spl0_3),
% 0.20/0.42 inference(split_clause,[status(thm)],[f528,f281,f293,f289])).
% 0.20/0.42 fof(f530,plain,(
% 0.20/0.42 $false),
% 0.20/0.42 inference(sat_refutation,[status(thm)],[f284,f288,f292,f296,f299,f407,f409,f416,f428,f433,f438,f456,f529])).
% 0.20/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.73/0.64 % Elapsed time: 0.077344 seconds
% 0.73/0.64 % CPU time: 0.467042 seconds
% 0.73/0.64 % Memory used: 36.420 MB
%------------------------------------------------------------------------------