TSTP Solution File: SEU394+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU394+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 : Tue Apr 30 20:42:11 EDT 2024
% Result : Theorem 11.74s 1.95s
% Output : CNFRefutation 11.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU394+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 19:38:17 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % Drodi V3.6.0
% 11.74/1.95 % Refutation found
% 11.74/1.95 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.74/1.95 % SZS output start CNFRefutation for theBenchmark
% 11.74/1.95 fof(f98,axiom,(
% 11.74/1.95 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f138,axiom,(
% 11.74/1.95 (! [A] :( one_sorted_str(A)=> ( empty_carrier(A)<=> empty(the_carrier(A)) ) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f148,axiom,(
% 11.74/1.95 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f173,axiom,(
% 11.74/1.95 (! [A] :( one_sorted_str(A)=> cast_as_carrier_subset(A) = the_carrier(A) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f368,axiom,(
% 11.74/1.95 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f388,axiom,(
% 11.74/1.95 (! [A] :( ~ empty_carrier(boole_POSet(A))& strict_rel_str(boole_POSet(A))& reflexive_relstr(boole_POSet(A))& transitive_relstr(boole_POSet(A))& antisymmetric_relstr(boole_POSet(A))& with_suprema_relstr(boole_POSet(A))& with_infima_relstr(boole_POSet(A))& complete_relstr(boole_POSet(A))& lower_bounded_relstr(boole_POSet(A))& upper_bounded_relstr(boole_POSet(A))& bounded_relstr(boole_POSet(A))& up_complete_relstr(boole_POSet(A))& join_complete_relstr(boole_POSet(A))& distributive_relstr(boole_POSet(A)) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f708,lemma,(
% 11.74/1.95 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( ( ~ empty(B)& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) )=> set_difference(B,singleton(empty_set)) = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) )) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f711,conjecture,(
% 11.74/1.95 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( ( ~ empty(B)& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) )=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) )) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f712,negated_conjecture,(
% 11.74/1.95 ~((! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( ( ~ empty(B)& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))) )=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) )) ))),
% 11.74/1.95 inference(negated_conjecture,[status(cth)],[f711])).
% 11.74/1.95 fof(f737,axiom,(
% 11.74/1.95 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f785,lemma,(
% 11.74/1.95 (! [A] :( ~ empty(A)=> (! [B] :( ( ~ empty(B)& filtered_subset(B,boole_POSet(A))& upper_relstr_subset(B,boole_POSet(A))& proper_element(B,powerset(the_carrier(boole_POSet(A))))& element(B,powerset(the_carrier(boole_POSet(A)))) )=> (! [C] :~ ( in(C,B)& empty(C) ) )) )) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f848,lemma,(
% 11.74/1.95 (! [A] : the_carrier(boole_POSet(A)) = powerset(A) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f879,lemma,(
% 11.74/1.95 (! [A,B] :( set_difference(A,singleton(B)) = A<=> ~ in(B,A) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f892,axiom,(
% 11.74/1.95 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 11.74/1.95 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.74/1.95 fof(f1344,plain,(
% 11.74/1.95 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 11.74/1.95 inference(NNF_transformation,[status(esa)],[f98])).
% 11.74/1.95 fof(f1345,plain,(
% 11.74/1.95 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 11.74/1.95 inference(miniscoping,[status(esa)],[f1344])).
% 11.74/1.95 fof(f1346,plain,(
% 11.74/1.95 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f1345])).
% 11.74/1.95 fof(f1645,plain,(
% 11.74/1.95 ![A]: (~one_sorted_str(A)|(empty_carrier(A)<=>empty(the_carrier(A))))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f138])).
% 11.74/1.95 fof(f1646,plain,(
% 11.74/1.95 ![A]: (~one_sorted_str(A)|((~empty_carrier(A)|empty(the_carrier(A)))&(empty_carrier(A)|~empty(the_carrier(A)))))),
% 11.74/1.95 inference(NNF_transformation,[status(esa)],[f1645])).
% 11.74/1.95 fof(f1648,plain,(
% 11.74/1.95 ![X0]: (~one_sorted_str(X0)|empty_carrier(X0)|~empty(the_carrier(X0)))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f1646])).
% 11.74/1.95 fof(f1706,plain,(
% 11.74/1.95 ![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))))))),
% 11.74/1.95 inference(NNF_transformation,[status(esa)],[f148])).
% 11.74/1.95 fof(f1707,plain,(
% 11.74/1.95 (![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))))))),
% 11.74/1.95 inference(miniscoping,[status(esa)],[f1706])).
% 11.74/1.95 fof(f1708,plain,(
% 11.74/1.95 (![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_64(B,A),B)|~subset(sk0_64(B,A),A))&(in(sk0_64(B,A),B)|subset(sk0_64(B,A),A)))))),
% 11.74/1.95 inference(skolemization,[status(esa)],[f1707])).
% 11.74/1.95 fof(f1710,plain,(
% 11.74/1.95 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f1708])).
% 11.74/1.95 fof(f1868,plain,(
% 11.74/1.95 ![A]: (~one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f173])).
% 11.74/1.95 fof(f1869,plain,(
% 11.74/1.95 ![X0]: (~one_sorted_str(X0)|cast_as_carrier_subset(X0)=the_carrier(X0))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f1868])).
% 11.74/1.95 fof(f2560,plain,(
% 11.74/1.95 empty(empty_set)),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f368])).
% 11.74/1.95 fof(f2640,plain,(
% 11.74/1.95 (((((((((((((![A]: ~empty_carrier(boole_POSet(A)))&(![A]: strict_rel_str(boole_POSet(A))))&(![A]: reflexive_relstr(boole_POSet(A))))&(![A]: transitive_relstr(boole_POSet(A))))&(![A]: antisymmetric_relstr(boole_POSet(A))))&(![A]: with_suprema_relstr(boole_POSet(A))))&(![A]: with_infima_relstr(boole_POSet(A))))&(![A]: complete_relstr(boole_POSet(A))))&(![A]: lower_bounded_relstr(boole_POSet(A))))&(![A]: upper_bounded_relstr(boole_POSet(A))))&(![A]: bounded_relstr(boole_POSet(A))))&(![A]: up_complete_relstr(boole_POSet(A))))&(![A]: join_complete_relstr(boole_POSet(A))))&(![A]: distributive_relstr(boole_POSet(A)))),
% 11.74/1.95 inference(miniscoping,[status(esa)],[f388])).
% 11.74/1.95 fof(f2641,plain,(
% 11.74/1.95 ![X0]: (~empty_carrier(boole_POSet(X0)))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f2640])).
% 11.74/1.95 fof(f4533,plain,(
% 11.74/1.95 ![A]: ((empty_carrier(A)|~one_sorted_str(A))|(![B]: ((((empty(B)|~filtered_subset(B,boole_POSet(cast_as_carrier_subset(A))))|~upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A))))|~element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))|set_difference(B,singleton(empty_set))=filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)))))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f708])).
% 11.74/1.95 fof(f4534,plain,(
% 11.74/1.95 ![X0,X1]: (empty_carrier(X0)|~one_sorted_str(X0)|empty(X1)|~filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))|~upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))|~element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))|set_difference(X1,singleton(empty_set))=filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4533])).
% 11.74/1.95 fof(f4540,plain,(
% 11.74/1.95 (?[A]: ((~empty_carrier(A)&one_sorted_str(A))&(?[B]: (((((~empty(B)&filtered_subset(B,boole_POSet(cast_as_carrier_subset(A))))&upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A))))&proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))&element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))))&~B=filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B))))))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f712])).
% 11.74/1.95 fof(f4541,plain,(
% 11.74/1.95 ((~empty_carrier(sk0_465)&one_sorted_str(sk0_465))&(((((~empty(sk0_466)&filtered_subset(sk0_466,boole_POSet(cast_as_carrier_subset(sk0_465))))&upper_relstr_subset(sk0_466,boole_POSet(cast_as_carrier_subset(sk0_465))))&proper_element(sk0_466,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sk0_465))))))&element(sk0_466,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sk0_465))))))&~sk0_466=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),sk0_466))))),
% 11.74/1.95 inference(skolemization,[status(esa)],[f4540])).
% 11.74/1.95 fof(f4542,plain,(
% 11.74/1.95 ~empty_carrier(sk0_465)),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4543,plain,(
% 11.74/1.95 one_sorted_str(sk0_465)),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4544,plain,(
% 11.74/1.95 ~empty(sk0_466)),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4545,plain,(
% 11.74/1.95 filtered_subset(sk0_466,boole_POSet(cast_as_carrier_subset(sk0_465)))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4546,plain,(
% 11.74/1.95 upper_relstr_subset(sk0_466,boole_POSet(cast_as_carrier_subset(sk0_465)))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4547,plain,(
% 11.74/1.95 proper_element(sk0_466,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sk0_465)))))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4548,plain,(
% 11.74/1.95 element(sk0_466,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sk0_465)))))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4549,plain,(
% 11.74/1.95 ~sk0_466=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),sk0_466))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4541])).
% 11.74/1.95 fof(f4637,plain,(
% 11.74/1.95 ![A,B]: (~in(A,B)|element(A,B))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f737])).
% 11.74/1.95 fof(f4638,plain,(
% 11.74/1.95 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4637])).
% 11.74/1.95 fof(f4791,plain,(
% 11.74/1.95 ![A]: (empty(A)|(![B]: (((((empty(B)|~filtered_subset(B,boole_POSet(A)))|~upper_relstr_subset(B,boole_POSet(A)))|~proper_element(B,powerset(the_carrier(boole_POSet(A)))))|~element(B,powerset(the_carrier(boole_POSet(A)))))|(![C]: (~in(C,B)|~empty(C))))))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f785])).
% 11.74/1.95 fof(f4792,plain,(
% 11.74/1.95 ![X0,X1,X2]: (empty(X0)|empty(X1)|~filtered_subset(X1,boole_POSet(X0))|~upper_relstr_subset(X1,boole_POSet(X0))|~proper_element(X1,powerset(the_carrier(boole_POSet(X0))))|~element(X1,powerset(the_carrier(boole_POSet(X0))))|~in(X2,X1)|~empty(X2))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f4791])).
% 11.74/1.95 fof(f5012,plain,(
% 11.74/1.95 ![X0]: (the_carrier(boole_POSet(X0))=powerset(X0))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f848])).
% 11.74/1.95 fof(f5111,plain,(
% 11.74/1.95 ![A,B]: ((~set_difference(A,singleton(B))=A|~in(B,A))&(set_difference(A,singleton(B))=A|in(B,A)))),
% 11.74/1.95 inference(NNF_transformation,[status(esa)],[f879])).
% 11.74/1.95 fof(f5112,plain,(
% 11.74/1.95 (![A,B]: (~set_difference(A,singleton(B))=A|~in(B,A)))&(![A,B]: (set_difference(A,singleton(B))=A|in(B,A)))),
% 11.74/1.95 inference(miniscoping,[status(esa)],[f5111])).
% 11.74/1.95 fof(f5114,plain,(
% 11.74/1.95 ![X0,X1]: (set_difference(X0,singleton(X1))=X0|in(X1,X0))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f5112])).
% 11.74/1.95 fof(f5157,plain,(
% 11.74/1.95 ![A,B]: (~in(A,B)|~empty(B))),
% 11.74/1.95 inference(pre_NNF_transformation,[status(esa)],[f892])).
% 11.74/1.95 fof(f5158,plain,(
% 11.74/1.95 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 11.74/1.95 inference(miniscoping,[status(esa)],[f5157])).
% 11.74/1.95 fof(f5159,plain,(
% 11.74/1.95 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 11.74/1.95 inference(cnf_transformation,[status(esa)],[f5158])).
% 11.74/1.95 fof(f5799,plain,(
% 11.74/1.95 ![X0]: (subset(X0,X0))),
% 11.74/1.95 inference(destructive_equality_resolution,[status(esa)],[f1346])).
% 11.74/1.95 fof(f5861,plain,(
% 11.74/1.95 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 11.74/1.95 inference(destructive_equality_resolution,[status(esa)],[f1710])).
% 11.74/1.95 fof(f6099,plain,(
% 11.74/1.95 element(sk0_466,powerset(powerset(cast_as_carrier_subset(sk0_465))))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f5012,f4548])).
% 11.74/1.95 fof(f6100,plain,(
% 11.74/1.95 proper_element(sk0_466,powerset(powerset(cast_as_carrier_subset(sk0_465))))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f5012,f4547])).
% 11.74/1.95 fof(f6103,plain,(
% 11.74/1.95 cast_as_carrier_subset(sk0_465)=the_carrier(sk0_465)),
% 11.74/1.95 inference(resolution,[status(thm)],[f1869,f4543])).
% 11.74/1.95 fof(f6104,plain,(
% 11.74/1.95 proper_element(sk0_466,powerset(powerset(the_carrier(sk0_465))))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f6103,f6100])).
% 11.74/1.95 fof(f6105,plain,(
% 11.74/1.95 element(sk0_466,powerset(powerset(the_carrier(sk0_465))))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f6103,f6099])).
% 11.74/1.95 fof(f6106,plain,(
% 11.74/1.95 ~sk0_466=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,the_carrier(sk0_465),sk0_466))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f6103,f4549])).
% 11.74/1.95 fof(f6107,plain,(
% 11.74/1.95 upper_relstr_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f6103,f4546])).
% 11.74/1.95 fof(f6108,plain,(
% 11.74/1.95 filtered_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))),
% 11.74/1.95 inference(backward_demodulation,[status(thm)],[f6103,f4545])).
% 11.74/1.95 fof(f6112,plain,(
% 11.74/1.95 spl0_53 <=> empty(sk0_466)),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6113,plain,(
% 11.74/1.95 empty(sk0_466)|~spl0_53),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6112])).
% 11.74/1.95 fof(f6122,plain,(
% 11.74/1.95 $false|~spl0_53),
% 11.74/1.95 inference(forward_subsumption_resolution,[status(thm)],[f6113,f4544])).
% 11.74/1.95 fof(f6123,plain,(
% 11.74/1.95 ~spl0_53),
% 11.74/1.95 inference(contradiction_clause,[status(thm)],[f6122])).
% 11.74/1.95 fof(f6143,plain,(
% 11.74/1.95 spl0_57 <=> empty_carrier(sk0_465)),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6144,plain,(
% 11.74/1.95 empty_carrier(sk0_465)|~spl0_57),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6143])).
% 11.74/1.95 fof(f6152,plain,(
% 11.74/1.95 spl0_60 <=> empty(the_carrier(sk0_465))),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6153,plain,(
% 11.74/1.95 empty(the_carrier(sk0_465))|~spl0_60),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6152])).
% 11.74/1.95 fof(f6194,plain,(
% 11.74/1.95 spl0_67 <=> upper_relstr_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6196,plain,(
% 11.74/1.95 ~upper_relstr_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|spl0_67),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6194])).
% 11.74/1.95 fof(f6202,plain,(
% 11.74/1.95 $false|spl0_67),
% 11.74/1.95 inference(forward_subsumption_resolution,[status(thm)],[f6196,f6107])).
% 11.74/1.95 fof(f6203,plain,(
% 11.74/1.95 spl0_67),
% 11.74/1.95 inference(contradiction_clause,[status(thm)],[f6202])).
% 11.74/1.95 fof(f6240,plain,(
% 11.74/1.95 spl0_72 <=> one_sorted_str(sk0_465)),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6242,plain,(
% 11.74/1.95 ~one_sorted_str(sk0_465)|spl0_72),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6240])).
% 11.74/1.95 fof(f6243,plain,(
% 11.74/1.95 ~one_sorted_str(sk0_465)|empty_carrier(sk0_465)|~spl0_60),
% 11.74/1.95 inference(resolution,[status(thm)],[f6153,f1648])).
% 11.74/1.95 fof(f6244,plain,(
% 11.74/1.95 ~spl0_72|spl0_57|~spl0_60),
% 11.74/1.95 inference(split_clause,[status(thm)],[f6243,f6240,f6143,f6152])).
% 11.74/1.95 fof(f6248,plain,(
% 11.74/1.95 $false|spl0_72),
% 11.74/1.95 inference(forward_subsumption_resolution,[status(thm)],[f6242,f4543])).
% 11.74/1.95 fof(f6249,plain,(
% 11.74/1.95 spl0_72),
% 11.74/1.95 inference(contradiction_clause,[status(thm)],[f6248])).
% 11.74/1.95 fof(f6276,plain,(
% 11.74/1.95 ![X0,X1,X2]: (empty(X0)|empty(X1)|~filtered_subset(X1,boole_POSet(X0))|~upper_relstr_subset(X1,boole_POSet(X0))|~proper_element(X1,powerset(powerset(X0)))|~element(X1,powerset(the_carrier(boole_POSet(X0))))|~in(X2,X1)|~empty(X2))),
% 11.74/1.95 inference(forward_demodulation,[status(thm)],[f5012,f4792])).
% 11.74/1.95 fof(f6277,plain,(
% 11.74/1.95 ![X0,X1,X2]: (empty(X0)|empty(X1)|~filtered_subset(X1,boole_POSet(X0))|~upper_relstr_subset(X1,boole_POSet(X0))|~proper_element(X1,powerset(powerset(X0)))|~element(X1,powerset(powerset(X0)))|~in(X2,X1)|~empty(X2))),
% 11.74/1.95 inference(forward_demodulation,[status(thm)],[f5012,f6276])).
% 11.74/1.95 fof(f6278,plain,(
% 11.74/1.95 ![X0,X1,X2]: (empty(X0)|~filtered_subset(X1,boole_POSet(X0))|~upper_relstr_subset(X1,boole_POSet(X0))|~proper_element(X1,powerset(powerset(X0)))|~element(X1,powerset(powerset(X0)))|~in(X2,X1)|~empty(X2))),
% 11.74/1.95 inference(forward_subsumption_resolution,[status(thm)],[f6277,f5159])).
% 11.74/1.95 fof(f6279,plain,(
% 11.74/1.95 spl0_75 <=> filtered_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6281,plain,(
% 11.74/1.95 ~filtered_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|spl0_75),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6279])).
% 11.74/1.95 fof(f6282,plain,(
% 11.74/1.95 spl0_76 <=> element(sk0_466,powerset(powerset(the_carrier(sk0_465))))),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6284,plain,(
% 11.74/1.95 ~element(sk0_466,powerset(powerset(the_carrier(sk0_465))))|spl0_76),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6282])).
% 11.74/1.95 fof(f6285,plain,(
% 11.74/1.95 spl0_77 <=> ~in(X0,sk0_466)|~empty(X0)),
% 11.74/1.95 introduced(split_symbol_definition)).
% 11.74/1.95 fof(f6286,plain,(
% 11.74/1.95 ![X0]: (~in(X0,sk0_466)|~empty(X0)|~spl0_77)),
% 11.74/1.95 inference(component_clause,[status(thm)],[f6285])).
% 11.74/1.95 fof(f6288,plain,(
% 11.74/1.95 ![X0]: (empty(the_carrier(sk0_465))|~filtered_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|~upper_relstr_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|~element(sk0_466,powerset(powerset(the_carrier(sk0_465))))|~in(X0,sk0_466)|~empty(X0))),
% 11.74/1.95 inference(resolution,[status(thm)],[f6278,f6104])).
% 11.74/1.95 fof(f6289,plain,(
% 11.74/1.95 spl0_60|~spl0_75|~spl0_67|~spl0_76|spl0_77),
% 11.74/1.95 inference(split_clause,[status(thm)],[f6288,f6152,f6279,f6194,f6282,f6285])).
% 11.74/1.96 fof(f6290,plain,(
% 11.74/1.96 $false|spl0_76),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f6284,f6105])).
% 11.74/1.96 fof(f6291,plain,(
% 11.74/1.96 spl0_76),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f6290])).
% 11.74/1.96 fof(f6292,plain,(
% 11.74/1.96 $false|spl0_75),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f6281,f6108])).
% 11.74/1.96 fof(f6293,plain,(
% 11.74/1.96 spl0_75),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f6292])).
% 11.74/1.96 fof(f6294,plain,(
% 11.74/1.96 $false|~spl0_57),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f6144,f4542])).
% 11.74/1.96 fof(f6295,plain,(
% 11.74/1.96 ~spl0_57),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f6294])).
% 11.74/1.96 fof(f6848,plain,(
% 11.74/1.96 spl0_169 <=> empty(empty_set)),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f6850,plain,(
% 11.74/1.96 ~empty(empty_set)|spl0_169),
% 11.74/1.96 inference(component_clause,[status(thm)],[f6848])).
% 11.74/1.96 fof(f7038,plain,(
% 11.74/1.96 ![X0,X1]: (empty_carrier(X0)|~one_sorted_str(X0)|empty(X1)|~filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))|~upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))|~element(X1,powerset(powerset(cast_as_carrier_subset(X0))))|set_difference(X1,singleton(empty_set))=filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))),
% 11.74/1.96 inference(forward_demodulation,[status(thm)],[f5012,f4534])).
% 11.74/1.96 fof(f7086,plain,(
% 11.74/1.96 spl0_204 <=> empty(X0)|~filtered_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),X0))),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f7087,plain,(
% 11.74/1.96 ![X0]: (empty(X0)|~filtered_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),X0))|~spl0_204)),
% 11.74/1.96 inference(component_clause,[status(thm)],[f7086])).
% 11.74/1.96 fof(f7089,plain,(
% 11.74/1.96 ![X0]: (empty_carrier(sk0_465)|~one_sorted_str(sk0_465)|empty(X0)|~filtered_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),X0)))),
% 11.74/1.96 inference(paramodulation,[status(thm)],[f6103,f7038])).
% 11.74/1.96 fof(f7090,plain,(
% 11.74/1.96 spl0_57|~spl0_72|spl0_204),
% 11.74/1.96 inference(split_clause,[status(thm)],[f7089,f6143,f6240,f7086])).
% 11.74/1.96 fof(f7091,plain,(
% 11.74/1.96 ![X0]: (empty(X0)|~filtered_subset(X0,boole_POSet(the_carrier(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(cast_as_carrier_subset(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),X0))|~spl0_204)),
% 11.74/1.96 inference(forward_demodulation,[status(thm)],[f6103,f7087])).
% 11.74/1.96 fof(f7092,plain,(
% 11.74/1.96 ![X0]: (empty(X0)|~filtered_subset(X0,boole_POSet(the_carrier(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(the_carrier(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,cast_as_carrier_subset(sk0_465),X0))|~spl0_204)),
% 11.74/1.96 inference(forward_demodulation,[status(thm)],[f6103,f7091])).
% 11.74/1.96 fof(f7093,plain,(
% 11.74/1.96 ![X0]: (empty(X0)|~filtered_subset(X0,boole_POSet(the_carrier(sk0_465)))|~upper_relstr_subset(X0,boole_POSet(the_carrier(sk0_465)))|~element(X0,powerset(powerset(the_carrier(sk0_465))))|set_difference(X0,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,the_carrier(sk0_465),X0))|~spl0_204)),
% 11.74/1.96 inference(forward_demodulation,[status(thm)],[f6103,f7092])).
% 11.74/1.96 fof(f7558,plain,(
% 11.74/1.96 spl0_286 <=> set_difference(sk0_466,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,the_carrier(sk0_465),sk0_466))),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f7559,plain,(
% 11.74/1.96 set_difference(sk0_466,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,the_carrier(sk0_465),sk0_466))|~spl0_286),
% 11.74/1.96 inference(component_clause,[status(thm)],[f7558])).
% 11.74/1.96 fof(f7561,plain,(
% 11.74/1.96 empty(sk0_466)|~filtered_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|~upper_relstr_subset(sk0_466,boole_POSet(the_carrier(sk0_465)))|set_difference(sk0_466,singleton(empty_set))=filter_of_net_str(sk0_465,net_of_bool_filter(sk0_465,the_carrier(sk0_465),sk0_466))|~spl0_204),
% 11.74/1.96 inference(resolution,[status(thm)],[f7093,f6105])).
% 11.74/1.96 fof(f7562,plain,(
% 11.74/1.96 spl0_53|~spl0_75|~spl0_67|spl0_286|~spl0_204),
% 11.74/1.96 inference(split_clause,[status(thm)],[f7561,f6112,f6279,f6194,f7558,f7086])).
% 11.74/1.96 fof(f7567,plain,(
% 11.74/1.96 ~sk0_466=set_difference(sk0_466,singleton(empty_set))|~spl0_286),
% 11.74/1.96 inference(backward_demodulation,[status(thm)],[f7559,f6106])).
% 11.74/1.96 fof(f9358,plain,(
% 11.74/1.96 spl0_556 <=> in(empty_set,sk0_466)),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f9359,plain,(
% 11.74/1.96 in(empty_set,sk0_466)|~spl0_556),
% 11.74/1.96 inference(component_clause,[status(thm)],[f9358])).
% 11.74/1.96 fof(f9360,plain,(
% 11.74/1.96 ~in(empty_set,sk0_466)|spl0_556),
% 11.74/1.96 inference(component_clause,[status(thm)],[f9358])).
% 11.74/1.96 fof(f9866,plain,(
% 11.74/1.96 spl0_600 <=> empty_carrier(boole_POSet(the_carrier(sk0_465)))),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f9867,plain,(
% 11.74/1.96 empty_carrier(boole_POSet(the_carrier(sk0_465)))|~spl0_600),
% 11.74/1.96 inference(component_clause,[status(thm)],[f9866])).
% 11.74/1.96 fof(f11342,plain,(
% 11.74/1.96 ![X0]: (in(X0,powerset(X0)))),
% 11.74/1.96 inference(resolution,[status(thm)],[f5861,f5799])).
% 11.74/1.96 fof(f11353,plain,(
% 11.74/1.96 ![X0]: (element(X0,powerset(X0)))),
% 11.74/1.96 inference(resolution,[status(thm)],[f11342,f4638])).
% 11.74/1.96 fof(f12968,plain,(
% 11.74/1.96 $false|spl0_169),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f6850,f2560])).
% 11.74/1.96 fof(f12969,plain,(
% 11.74/1.96 spl0_169),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f12968])).
% 11.74/1.96 fof(f13233,plain,(
% 11.74/1.96 spl0_799 <=> element(sk0_466,powerset(the_carrier(boole_POSet(the_carrier(sk0_465)))))),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f13235,plain,(
% 11.74/1.96 ~element(sk0_466,powerset(the_carrier(boole_POSet(the_carrier(sk0_465)))))|spl0_799),
% 11.74/1.96 inference(component_clause,[status(thm)],[f13233])).
% 11.74/1.96 fof(f13236,plain,(
% 11.74/1.96 spl0_800 <=> element(powerset(sk0_466),powerset(powerset(sk0_466)))),
% 11.74/1.96 introduced(split_symbol_definition)).
% 11.74/1.96 fof(f13238,plain,(
% 11.74/1.96 ~element(powerset(sk0_466),powerset(powerset(sk0_466)))|spl0_800),
% 11.74/1.96 inference(component_clause,[status(thm)],[f13236])).
% 11.74/1.96 fof(f13254,plain,(
% 11.74/1.96 $false|spl0_800),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f13238,f11353])).
% 11.74/1.96 fof(f13255,plain,(
% 11.74/1.96 spl0_800),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f13254])).
% 11.74/1.96 fof(f13256,plain,(
% 11.74/1.96 ~element(sk0_466,powerset(powerset(the_carrier(sk0_465))))|spl0_799),
% 11.74/1.96 inference(forward_demodulation,[status(thm)],[f5012,f13235])).
% 11.74/1.96 fof(f13257,plain,(
% 11.74/1.96 $false|spl0_799),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f13256,f6105])).
% 11.74/1.96 fof(f13258,plain,(
% 11.74/1.96 spl0_799),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f13257])).
% 11.74/1.96 fof(f13259,plain,(
% 11.74/1.96 $false|~spl0_600),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f9867,f2641])).
% 11.74/1.96 fof(f13260,plain,(
% 11.74/1.96 ~spl0_600),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f13259])).
% 11.74/1.96 fof(f13650,plain,(
% 11.74/1.96 set_difference(sk0_466,singleton(empty_set))=sk0_466|spl0_556),
% 11.74/1.96 inference(resolution,[status(thm)],[f5114,f9360])).
% 11.74/1.96 fof(f13651,plain,(
% 11.74/1.96 $false|~spl0_286|spl0_556),
% 11.74/1.96 inference(forward_subsumption_resolution,[status(thm)],[f13650,f7567])).
% 11.74/1.96 fof(f13652,plain,(
% 11.74/1.96 ~spl0_286|spl0_556),
% 11.74/1.96 inference(contradiction_clause,[status(thm)],[f13651])).
% 11.74/1.96 fof(f13680,plain,(
% 11.74/1.96 ~empty(empty_set)|~spl0_556|~spl0_77),
% 11.74/1.96 inference(resolution,[status(thm)],[f9359,f6286])).
% 11.74/1.96 fof(f13681,plain,(
% 11.74/1.96 ~spl0_169|~spl0_556|~spl0_77),
% 11.74/1.96 inference(split_clause,[status(thm)],[f13680,f6848,f9358,f6285])).
% 11.74/1.96 fof(f13697,plain,(
% 11.74/1.96 $false),
% 11.74/1.96 inference(sat_refutation,[status(thm)],[f6123,f6203,f6244,f6249,f6289,f6291,f6293,f6295,f7090,f7562,f12969,f13255,f13258,f13260,f13652,f13681])).
% 11.74/1.96 % SZS output end CNFRefutation for theBenchmark.p
% 11.74/1.97 % Elapsed time: 1.614871 seconds
% 11.74/1.97 % CPU time: 11.931086 seconds
% 11.74/1.97 % Total memory used: 263.754 MB
% 11.74/1.97 % Net memory used: 261.517 MB
%------------------------------------------------------------------------------