%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU309+1 : 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 : n011.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 0.92s 0.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:10:10 UTC 2026
% 0.02/0.35 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.92/0.65 % Refutation found
% 0.92/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.92/0.65 % SZS output start CNFRefutation for theBenchmark
% 0.92/0.65 fof(f17,axiom,(
% 0.92/0.65 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f19,axiom,(
% 0.92/0.65 (! [A] :( one_sorted_str(A)=> cast_as_carrier_subset(A) = the_carrier(A) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f22,axiom,(
% 0.92/0.65 (! [A] :( one_sorted_str(A)=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f26,axiom,(
% 0.92/0.65 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> element(subset_difference(A,B,C),powerset(A)) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f54,axiom,(
% 0.92/0.65 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> subset_intersection2(A,B,C) = set_intersection2(B,C) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f55,axiom,(
% 0.92/0.65 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> subset_difference(A,B,C) = set_difference(B,C) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f56,axiom,(
% 0.92/0.65 (! [A,B] : subset(A,A) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f57,axiom,(
% 0.92/0.65 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) )) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f59,conjecture,(
% 0.92/0.65 (! [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 ) )) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f60,negated_conjecture,(
% 0.92/0.65 ~((! [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 ) )) ))),
% 0.92/0.65 inference(negated_conjecture,[status(cth)],[f59])).
% 0.92/0.65 fof(f64,axiom,(
% 0.92/0.65 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f65,axiom,(
% 0.92/0.65 (! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) )),
% 0.92/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.92/0.65 fof(f128,plain,(
% 0.92/0.65 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f17])).
% 0.92/0.65 fof(f131,plain,(
% 0.92/0.65 ![A]: (~one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.92/0.65 fof(f132,plain,(
% 0.92/0.65 ![X0]: (~one_sorted_str(X0)|cast_as_carrier_subset(X0)=the_carrier(X0))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f131])).
% 0.92/0.65 fof(f133,plain,(
% 0.92/0.65 ![A]: (~one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.92/0.65 fof(f134,plain,(
% 0.92/0.65 ![X0]: (~one_sorted_str(X0)|element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f133])).
% 0.92/0.65 fof(f137,plain,(
% 0.92/0.65 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|element(subset_difference(A,B,C),powerset(A)))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.92/0.65 fof(f138,plain,(
% 0.92/0.65 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|element(subset_difference(X1,X0,X2),powerset(X1)))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f137])).
% 0.92/0.65 fof(f244,plain,(
% 0.92/0.65 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|subset_intersection2(A,B,C)=set_intersection2(B,C))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 0.92/0.65 fof(f245,plain,(
% 0.92/0.65 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|subset_intersection2(X1,X0,X2)=set_intersection2(X0,X2))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f244])).
% 0.92/0.65 fof(f246,plain,(
% 0.92/0.65 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|subset_difference(A,B,C)=set_difference(B,C))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f55])).
% 0.92/0.65 fof(f247,plain,(
% 0.92/0.65 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|subset_difference(X1,X0,X2)=set_difference(X0,X2))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f246])).
% 0.92/0.65 fof(f248,plain,(
% 0.92/0.65 ![A]: subset(A,A)),
% 0.92/0.65 inference(miniscoping,[status(thm)],[f56])).
% 0.92/0.65 fof(f249,plain,(
% 0.92/0.65 ![X0]: (subset(X0,X0))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f248])).
% 0.92/0.65 fof(f250,plain,(
% 0.92/0.65 ![A]: (~one_sorted_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A))=B)))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.92/0.65 fof(f251,plain,(
% 0.92/0.65 ![X0,X1]: (~one_sorted_str(X0)|~element(X1,powerset(the_carrier(X0)))|subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0))=X1)),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f250])).
% 0.92/0.65 fof(f254,plain,(
% 0.92/0.65 (?[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))))),
% 0.92/0.65 inference(pre_NNF_transformation,[status(thm)],[f60])).
% 0.92/0.65 fof(f255,plain,(
% 0.92/0.65 (one_sorted_str(sK5_skl)&(element(sK6_skl,powerset(the_carrier(sK5_skl)))&~subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl))=sK6_skl))),
% 0.92/0.65 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f254])).
% 0.92/0.65 fof(f256,plain,(
% 0.92/0.65 one_sorted_str(sK5_skl)),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f255])).
% 0.92/0.65 fof(f257,plain,(
% 0.92/0.65 element(sK6_skl,powerset(the_carrier(sK5_skl)))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f255])).
% 0.92/0.65 fof(f258,plain,(
% 0.92/0.65 ~subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl))=sK6_skl),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f255])).
% 0.92/0.65 fof(f263,plain,(
% 0.92/0.65 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 0.92/0.65 inference(NNF_transformation,[status(thm)],[f64])).
% 0.92/0.65 fof(f264,plain,(
% 0.92/0.65 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 0.92/0.65 inference(miniscoping,[status(thm)],[f263])).
% 0.92/0.65 fof(f266,plain,(
% 0.92/0.65 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f264])).
% 0.92/0.65 fof(f267,plain,(
% 0.92/0.65 ![X0,X1]: (set_difference(X0,set_difference(X0,X1))=set_intersection2(X0,X1))),
% 0.92/0.65 inference(cnf_transformation,[status(thm)],[f65])).
% 0.92/0.65 fof(f283,plain,(
% 0.92/0.65 cast_as_carrier_subset(sK5_skl)=the_carrier(sK5_skl)),
% 0.92/0.65 inference(resolution,[status(thm)],[f132,f256])).
% 0.92/0.65 fof(f284,plain,(
% 0.92/0.65 element(sK6_skl,powerset(cast_as_carrier_subset(sK5_skl)))),
% 0.92/0.65 inference(backward_demodulation,[status(thm)],[f283,f257])).
% 0.92/0.65 fof(f285,plain,(
% 0.92/0.65 ~subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl))=sK6_skl),
% 0.92/0.65 inference(backward_demodulation,[status(thm)],[f283,f258])).
% 0.92/0.65 fof(f286,plain,(
% 0.92/0.65 ~subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl))=sK6_skl),
% 0.92/0.65 inference(forward_demodulation,[status(thm)],[f283,f285])).
% 0.92/0.65 fof(f287,plain,(
% 0.92/0.65 element(cast_as_carrier_subset(sK5_skl),powerset(the_carrier(sK5_skl)))),
% 0.92/0.65 inference(resolution,[status(thm)],[f134,f256])).
% 0.92/0.65 fof(f288,plain,(
% 0.92/0.65 element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl)))),
% 0.92/0.65 inference(forward_demodulation,[status(thm)],[f283,f287])).
% 0.92/0.65 fof(f293,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|element(subset_difference(cast_as_carrier_subset(sK5_skl),X0,sK6_skl),powerset(cast_as_carrier_subset(sK5_skl))))),
% 0.92/0.65 inference(resolution,[status(thm)],[f284,f138])).
% 0.92/0.65 fof(f311,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_difference(cast_as_carrier_subset(sK5_skl),X0,sK6_skl)=set_difference(X0,sK6_skl))),
% 0.92/0.65 inference(resolution,[status(thm)],[f247,f284])).
% 0.92/0.65 fof(f314,plain,(
% 0.92/0.65 ![X0]: (~one_sorted_str(sK5_skl)|~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_intersection2(the_carrier(sK5_skl),X0,cast_as_carrier_subset(sK5_skl))=X0)),
% 0.92/0.65 inference(paramodulation,[status(thm)],[f283,f251])).
% 0.92/0.65 fof(f322,definition,(
% 0.92/0.65 sQ5_spl <=> (one_sorted_str(sK5_skl))),
% 0.92/0.65 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.92/0.65 fof(f324,plain,(
% 0.92/0.65 ~one_sorted_str(sK5_skl)|sQ5_spl),
% 0.92/0.65 inference(component_clause,[status(thm)],[f322])).
% 0.92/0.65 fof(f325,definition,(
% 0.92/0.65 ![X0]: (sQ6_spl <=> (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_intersection2(the_carrier(sK5_skl),X0,cast_as_carrier_subset(sK5_skl))=X0))),
% 0.92/0.65 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.92/0.65 fof(f326,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_intersection2(the_carrier(sK5_skl),X0,cast_as_carrier_subset(sK5_skl))=X0|~sQ6_spl)),
% 0.92/0.65 inference(component_clause,[status(thm)],[f325])).
% 0.92/0.65 fof(f328,plain,(
% 0.92/0.65 ~sQ5_spl|sQ6_spl),
% 0.92/0.65 inference(split_clause,[status(thm)],[f314,f322,f325])).
% 0.92/0.65 fof(f329,plain,(
% 0.92/0.65 $false|sQ5_spl),
% 0.92/0.65 inference(forward_subsumption_resolution,[status(thm)],[f324,f256])).
% 0.92/0.65 fof(f330,plain,(
% 0.92/0.65 sQ5_spl),
% 0.92/0.65 inference(contradiction_clause,[status(thm)],[f329])).
% 0.92/0.65 fof(f333,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_intersection2(cast_as_carrier_subset(sK5_skl),X0,cast_as_carrier_subset(sK5_skl))=X0|~sQ6_spl)),
% 0.92/0.65 inference(forward_demodulation,[status(thm)],[f283,f326])).
% 0.92/0.65 fof(f350,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),X0)=set_difference(cast_as_carrier_subset(sK5_skl),X0))),
% 0.92/0.65 inference(resolution,[status(thm)],[f288,f247])).
% 0.92/0.65 fof(f408,plain,(
% 0.92/0.65 element(subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),powerset(cast_as_carrier_subset(sK5_skl)))),
% 0.92/0.65 inference(resolution,[status(thm)],[f293,f288])).
% 0.92/0.65 fof(f534,plain,(
% 0.92/0.65 subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl)=set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl)),
% 0.92/0.65 inference(resolution,[status(thm)],[f311,f288])).
% 0.92/0.65 fof(f537,plain,(
% 0.92/0.65 ~subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl))=sK6_skl),
% 0.92/0.65 inference(backward_demodulation,[status(thm)],[f534,f286])).
% 0.92/0.65 fof(f538,plain,(
% 0.92/0.65 element(set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl),powerset(cast_as_carrier_subset(sK5_skl)))),
% 0.92/0.65 inference(backward_demodulation,[status(thm)],[f534,f408])).
% 0.92/0.65 fof(f541,plain,(
% 0.92/0.65 subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl))=sK6_skl|~sQ6_spl),
% 0.92/0.65 inference(resolution,[status(thm)],[f333,f284])).
% 0.92/0.65 fof(f775,plain,(
% 0.92/0.65 subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl))=set_difference(cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl))),
% 0.92/0.65 inference(resolution,[status(thm)],[f538,f350])).
% 0.92/0.65 fof(f806,plain,(
% 0.92/0.65 ~set_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl)=sK6_skl),
% 0.92/0.65 inference(backward_demodulation,[status(thm)],[f807,f537])).
% 0.92/0.65 fof(f807,plain,(
% 0.92/0.65 subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl))=set_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl)),
% 0.92/0.65 inference(forward_demodulation,[status(thm)],[f267,f775])).
% 0.92/0.65 fof(f1505,plain,(
% 0.92/0.65 ~set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl))=sK6_skl),
% 0.92/0.65 inference(paramodulation,[status(thm)],[f128,f806])).
% 0.92/0.65 fof(f2093,plain,(
% 0.92/0.65 ![X0]: (~element(X0,powerset(cast_as_carrier_subset(sK5_skl)))|subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,X0)=set_intersection2(sK6_skl,X0))),
% 0.92/0.65 inference(resolution,[status(thm)],[f284,f245])).
% 0.92/0.65 fof(f2165,plain,(
% 0.92/0.66 ![X0]: (element(X0,powerset(X0)))),
% 0.92/0.66 inference(resolution,[status(thm)],[f266,f249])).
% 0.92/0.66 fof(f2595,plain,(
% 0.92/0.66 subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl))=set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl))),
% 0.92/0.66 inference(resolution,[status(thm)],[f2165,f2093])).
% 0.92/0.66 fof(f2646,plain,(
% 0.92/0.66 sK6_skl=set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl))|~sQ6_spl),
% 0.92/0.66 inference(forward_demodulation,[status(thm)],[f541,f2595])).
% 0.92/0.66 fof(f2647,plain,(
% 0.92/0.66 $false|~sQ6_spl),
% 0.92/0.66 inference(forward_subsumption_resolution,[status(thm)],[f2646,f1505])).
% 0.92/0.66 fof(f2648,plain,(
% 0.92/0.66 ~sQ6_spl),
% 0.92/0.66 inference(contradiction_clause,[status(thm)],[f2647])).
% 0.92/0.66 fof(f2649,plain,(
% 0.92/0.66 $false),
% 0.92/0.66 inference(sat_refutation,[status(thm)],[f328,f330,f2648])).
% 0.92/0.66 % SZS output end CNFRefutation for theBenchmark.p
% 0.92/0.67 % Elapsed time: 0.308642 seconds
% 0.92/0.67 % CPU time: 2.103966 seconds
% 0.92/0.67 % Total memory used: 152.782 MB
% 0.92/0.67 % Net memory used: 150.062 MB
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