%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU309+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:22:17 PM UTC 2026
% Result : Theorem 0.26s 0.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU309+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 06:10:04 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.17/0.52 % Drodi V4.1.1
% 0.26/0.94 % Refutation found
% 0.26/0.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.94 % SZS output start CNFRefutation for theBenchmark
% 0.26/0.94 fof(f77,axiom,(
% 0.26/0.94 (! [A] :( one_sorted_str(A)=> cast_as_carrier_subset(A) = the_carrier(A) ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f94,axiom,(
% 0.26/0.94 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,B) = set_difference(A,B) ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f130,axiom,(
% 0.26/0.94 (! [A] :( one_sorted_str(A)=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f139,axiom,(
% 0.26/0.94 (! [A,B] :( element(B,powerset(A))=> element(subset_complement(A,B),powerset(A)) ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f235,axiom,(
% 0.26/0.94 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,subset_complement(A,B)) = B ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f291,axiom,(
% 0.26/0.94 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> subset_difference(A,B,C) = set_difference(B,C) ) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f361,lemma,(
% 0.26/0.94 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) )) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f380,conjecture,(
% 0.26/0.94 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) )) )),
% 0.26/0.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.94 fof(f381,negated_conjecture,(
% 0.26/0.94 ~((! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) )) ))),
% 0.26/0.94 inference(negated_conjecture,[status(cth)],[f380])).
% 0.26/0.94 fof(f891,plain,(
% 0.26/0.94 ![A]: (~one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f77])).
% 0.26/0.94 fof(f892,plain,(
% 0.26/0.94 ![X0]: (~one_sorted_str(X0)|cast_as_carrier_subset(X0)=the_carrier(X0))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f891])).
% 0.26/0.94 fof(f1020,plain,(
% 0.26/0.94 ![A,B]: (~element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f94])).
% 0.26/0.94 fof(f1021,plain,(
% 0.26/0.94 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,X0)=set_difference(X1,X0))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f1020])).
% 0.26/0.94 fof(f1140,plain,(
% 0.26/0.94 ![A]: (~one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f130])).
% 0.26/0.94 fof(f1141,plain,(
% 0.26/0.94 ![X0]: (~one_sorted_str(X0)|element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f1140])).
% 0.26/0.94 fof(f1148,plain,(
% 0.26/0.94 ![A,B]: (~element(B,powerset(A))|element(subset_complement(A,B),powerset(A)))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f139])).
% 0.26/0.94 fof(f1149,plain,(
% 0.26/0.94 ![X0,X1]: (~element(X0,powerset(X1))|element(subset_complement(X1,X0),powerset(X1)))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f1148])).
% 0.26/0.94 fof(f1411,plain,(
% 0.26/0.94 ![A,B]: (~element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B)),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f235])).
% 0.26/0.94 fof(f1412,plain,(
% 0.26/0.94 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,subset_complement(X1,X0))=X0)),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f1411])).
% 0.26/0.94 fof(f1625,plain,(
% 0.26/0.94 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|subset_difference(A,B,C)=set_difference(B,C))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f291])).
% 0.26/0.94 fof(f1626,plain,(
% 0.26/0.94 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|subset_difference(X1,X0,X2)=set_difference(X0,X2))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f1625])).
% 0.26/0.94 fof(f2066,plain,(
% 0.26/0.94 ![A]: (~one_sorted_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f361])).
% 0.26/0.94 fof(f2067,plain,(
% 0.26/0.94 ![X0,X1]: (~one_sorted_str(X0)|~element(X1,powerset(the_carrier(X0)))|subset_complement(the_carrier(X0),X1)=subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f2066])).
% 0.26/0.94 fof(f2119,plain,(
% 0.26/0.94 (?[A]: (one_sorted_str(A)&(?[B]: (element(B,powerset(the_carrier(A)))&~subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))=B))))),
% 0.26/0.94 inference(pre_NNF_transformation,[status(thm)],[f381])).
% 0.26/0.94 fof(f2120,plain,(
% 0.26/0.94 (one_sorted_str(sK253_skl)&(element(sK254_skl,powerset(the_carrier(sK253_skl)))&~subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl))),
% 0.26/0.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK253_skl,sK254_skl]),skolemize(A,sK253_skl),skolemize(B,sK254_skl)],[f2119])).
% 0.26/0.94 fof(f2121,plain,(
% 0.26/0.94 one_sorted_str(sK253_skl)),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f2120])).
% 0.26/0.94 fof(f2122,plain,(
% 0.26/0.94 element(sK254_skl,powerset(the_carrier(sK253_skl)))),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f2120])).
% 0.26/0.94 fof(f2123,plain,(
% 0.26/0.94 ~subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl),
% 0.26/0.94 inference(cnf_transformation,[status(thm)],[f2120])).
% 0.26/0.94 fof(f3290,plain,(
% 0.26/0.94 cast_as_carrier_subset(sK253_skl)=the_carrier(sK253_skl)),
% 0.26/0.94 inference(resolution,[status(thm)],[f892,f2121])).
% 0.26/0.94 fof(f3291,plain,(
% 0.26/0.94 element(sK254_skl,powerset(cast_as_carrier_subset(sK253_skl)))),
% 0.26/0.94 inference(backward_demodulation,[status(thm)],[f3290,f2122])).
% 0.26/0.94 fof(f3292,plain,(
% 0.26/0.94 ~one_sorted_str(sK253_skl)|element(cast_as_carrier_subset(sK253_skl),powerset(cast_as_carrier_subset(sK253_skl)))),
% 0.26/0.94 inference(paramodulation,[status(thm)],[f3290,f1141])).
% 0.26/0.94 fof(f3293,definition,(
% 0.26/0.94 sQ57_spl <=> (one_sorted_str(sK253_skl))),
% 0.26/0.94 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 0.26/0.94 fof(f3295,plain,(
% 0.26/0.94 ~one_sorted_str(sK253_skl)|sQ57_spl),
% 0.26/0.94 inference(component_clause,[status(thm)],[f3293])).
% 0.26/0.94 fof(f3296,definition,(
% 0.26/0.94 sQ58_spl <=> (element(cast_as_carrier_subset(sK253_skl),powerset(cast_as_carrier_subset(sK253_skl))))),
% 0.26/0.94 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 0.26/0.94 fof(f3297,plain,(
% 0.26/0.94 element(cast_as_carrier_subset(sK253_skl),powerset(cast_as_carrier_subset(sK253_skl)))|~sQ58_spl),
% 0.26/0.94 inference(component_clause,[status(thm)],[f3296])).
% 0.26/0.94 fof(f3299,plain,(
% 0.26/0.94 ~sQ57_spl|sQ58_spl),
% 0.26/0.94 inference(split_clause,[status(thm)],[f3292,f3293,f3296])).
% 0.26/0.94 fof(f3300,plain,(
% 0.26/0.94 $false|sQ57_spl),
% 0.26/0.94 inference(forward_subsumption_resolution,[status(thm)],[f3295,f2121])).
% 0.26/0.94 fof(f3301,plain,(
% 0.26/0.94 sQ57_spl),
% 0.26/0.94 inference(contradiction_clause,[status(thm)],[f3300])).
% 0.26/0.94 fof(f3302,plain,(
% 0.26/0.94 ~subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl),
% 0.26/0.94 inference(forward_demodulation,[status(thm)],[f3290,f2123])).
% 0.26/0.94 fof(f3303,plain,(
% 0.26/0.94 ~subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl),
% 0.26/0.94 inference(forward_demodulation,[status(thm)],[f3290,f3302])).
% 0.26/0.94 fof(f3314,plain,(
% 0.26/0.94 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK253_skl)))|subset_difference(cast_as_carrier_subset(sK253_skl),X0,sK254_skl)=set_difference(X0,sK254_skl))),
% 0.26/0.94 inference(resolution,[status(thm)],[f3291,f1626])).
% 0.26/0.94 fof(f3317,plain,(
% 0.26/0.94 ![X0]: (~element(X0,powerset(the_carrier(sK253_skl)))|subset_complement(the_carrier(sK253_skl),X0)=subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),X0))),
% 0.26/0.94 inference(resolution,[status(thm)],[f2067,f2121])).
% 0.26/0.94 fof(f3318,plain,(
% 0.26/0.96 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK253_skl)))|subset_complement(the_carrier(sK253_skl),X0)=subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),X0))),
% 0.26/0.96 inference(forward_demodulation,[status(thm)],[f3290,f3317])).
% 0.26/0.96 fof(f3319,plain,(
% 0.26/0.96 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK253_skl)))|subset_complement(cast_as_carrier_subset(sK253_skl),X0)=subset_difference(the_carrier(sK253_skl),cast_as_carrier_subset(sK253_skl),X0))),
% 0.26/0.96 inference(forward_demodulation,[status(thm)],[f3290,f3318])).
% 0.26/0.96 fof(f3320,plain,(
% 0.26/0.96 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK253_skl)))|subset_complement(cast_as_carrier_subset(sK253_skl),X0)=subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),X0))),
% 0.26/0.96 inference(forward_demodulation,[status(thm)],[f3290,f3319])).
% 0.26/0.96 fof(f3331,plain,(
% 0.26/0.96 subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl)=set_difference(cast_as_carrier_subset(sK253_skl),sK254_skl)|~sQ58_spl),
% 0.26/0.96 inference(resolution,[status(thm)],[f3297,f3314])).
% 0.26/0.96 fof(f3354,plain,(
% 0.26/0.96 subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl)=set_difference(cast_as_carrier_subset(sK253_skl),sK254_skl)),
% 0.26/0.96 inference(resolution,[status(thm)],[f1021,f3291])).
% 0.26/0.96 fof(f3368,plain,(
% 0.26/0.96 ~subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl|~sQ58_spl),
% 0.26/0.96 inference(backward_demodulation,[status(thm)],[f3369,f3303])).
% 0.26/0.96 fof(f3369,plain,(
% 0.26/0.96 subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),sK254_skl)=subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl)|~sQ58_spl),
% 0.26/0.96 inference(forward_demodulation,[status(thm)],[f3354,f3331])).
% 0.26/0.96 fof(f3410,plain,(
% 0.26/0.96 element(subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl),powerset(cast_as_carrier_subset(sK253_skl)))),
% 0.26/0.96 inference(resolution,[status(thm)],[f1149,f3291])).
% 0.26/0.96 fof(f3420,plain,(
% 0.26/0.96 subset_complement(cast_as_carrier_subset(sK253_skl),subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl))=subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl))),
% 0.26/0.96 inference(resolution,[status(thm)],[f3410,f3320])).
% 0.26/0.96 fof(f3549,plain,(
% 0.26/0.96 subset_complement(cast_as_carrier_subset(sK253_skl),subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl))=sK254_skl),
% 0.26/0.96 inference(resolution,[status(thm)],[f1412,f3291])).
% 0.26/0.96 fof(f3627,plain,(
% 0.26/0.96 sK254_skl=subset_difference(cast_as_carrier_subset(sK253_skl),cast_as_carrier_subset(sK253_skl),subset_complement(cast_as_carrier_subset(sK253_skl),sK254_skl))),
% 0.26/0.96 inference(forward_demodulation,[status(thm)],[f3549,f3420])).
% 0.26/0.96 fof(f3628,plain,(
% 0.26/0.96 $false|~sQ58_spl),
% 0.26/0.96 inference(forward_subsumption_resolution,[status(thm)],[f3627,f3368])).
% 0.26/0.96 fof(f3629,plain,(
% 0.26/0.96 ~sQ58_spl),
% 0.26/0.96 inference(contradiction_clause,[status(thm)],[f3628])).
% 0.26/0.96 fof(f3630,plain,(
% 0.26/0.96 $false),
% 0.26/0.96 inference(sat_refutation,[status(thm)],[f3299,f3301,f3629])).
% 0.26/0.96 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/1.00 % Elapsed time: 0.568312 seconds
% 0.26/1.00 % CPU time: 3.230143 seconds
% 0.26/1.00 % Total memory used: 193.759 MB
% 0.26/1.00 % Net memory used: 190.689 MB
%------------------------------------------------------------------------------