%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:12:33 PM UTC 2026
% Result : Theorem 0.26s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET762+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:39:08 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.26/0.51 % Refutation found
% 0.26/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.26/0.51 fof(f1,axiom,(
% 0.26/0.51 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.26/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.26/0.51 fof(f2,axiom,(
% 0.26/0.51 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.26/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.26/0.51 fof(f6,axiom,(
% 0.26/0.51 (! [X] : ~ member(X,empty_set) )),
% 0.26/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.26/0.51 fof(f22,axiom,(
% 0.26/0.51 (! [F,A,Y] :( member(Y,image2(F,A))<=> (? [X] :( member(X,A)& apply(F,X,Y) ) )) )),
% 0.26/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.26/0.51 fof(f29,conjecture,(
% 0.26/0.51 (! [F,A,B] :( maps(F,A,B)=> equal_set(image2(F,empty_set),empty_set) ) )),
% 0.26/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.26/0.51 fof(f30,negated_conjecture,(
% 0.26/0.51 ~((! [F,A,B] :( maps(F,A,B)=> equal_set(image2(F,empty_set),empty_set) ) ))),
% 0.26/0.51 inference(negated_conjecture,[status(cth)],[f29])).
% 0.26/0.51 fof(f31,plain,(
% 0.26/0.51 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.26/0.51 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.26/0.51 fof(f32,plain,(
% 0.26/0.51 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.26/0.51 inference(NNF_transformation,[status(thm)],[f31])).
% 0.26/0.51 fof(f33,plain,(
% 0.26/0.51 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.26/0.51 inference(miniscoping,[status(thm)],[f32])).
% 0.26/0.51 fof(f34,plain,(
% 0.26/0.51 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 0.26/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f33])).
% 0.26/0.51 fof(f36,plain,(
% 0.26/0.51 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.26/0.51 inference(cnf_transformation,[status(thm)],[f34])).
% 0.26/0.51 fof(f38,plain,(
% 0.26/0.51 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.26/0.51 inference(NNF_transformation,[status(thm)],[f2])).
% 0.26/0.51 fof(f39,plain,(
% 0.26/0.51 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.26/0.51 inference(miniscoping,[status(thm)],[f38])).
% 0.26/0.51 fof(f42,plain,(
% 0.26/0.51 ![X0,X1]: (equal_set(X0,X1)|~subset(X0,X1)|~subset(X1,X0))),
% 0.26/0.51 inference(cnf_transformation,[status(thm)],[f39])).
% 0.26/0.51 fof(f57,plain,(
% 0.26/0.51 ![X0]: (~member(X0,empty_set))),
% 0.26/0.51 inference(cnf_transformation,[status(thm)],[f6])).
% 0.26/0.51 fof(f176,plain,(
% 0.26/0.51 ![F,A,Y]: ((~member(Y,image2(F,A))|(?[X]: (member(X,A)&apply(F,X,Y))))&(member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 0.26/0.51 inference(NNF_transformation,[status(thm)],[f22])).
% 0.26/0.51 fof(f177,plain,(
% 0.26/0.51 (![F,A,Y]: (~member(Y,image2(F,A))|(?[X]: (member(X,A)&apply(F,X,Y)))))&(![F,A,Y]: (member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 0.26/0.51 inference(miniscoping,[status(thm)],[f176])).
% 0.26/0.51 fof(f178,plain,(
% 0.26/0.51 (![F,A,Y]: (~member(Y,image2(F,A))|(member(sK23_skl(Y,A,F),A)&apply(F,sK23_skl(Y,A,F),Y))))&(![F,A,Y]: (member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 0.26/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(X,sK23_skl(Y,A,F))],[f177])).
% 0.26/0.51 fof(f179,plain,(
% 0.26/0.51 ![X0,X1,X2]: (~member(X0,image2(X1,X2))|member(sK23_skl(X0,X2,X1),X2))),
% 0.26/0.51 inference(cnf_transformation,[status(thm)],[f178])).
% 0.26/0.51 fof(f244,plain,(
% 0.26/0.51 (?[F,A,B]: (maps(F,A,B)&~equal_set(image2(F,empty_set),empty_set)))),
% 0.26/0.51 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.26/0.51 fof(f245,plain,(
% 0.26/0.51 ?[F]: ((?[A,B]: maps(F,A,B))&~equal_set(image2(F,empty_set),empty_set))),
% 0.26/0.51 inference(miniscoping,[status(thm)],[f244])).
% 0.26/0.51 fof(f246,plain,(
% 0.26/0.51 (maps(sK39_skl,sK40_skl,sK41_skl)&~equal_set(image2(sK39_skl,empty_set),empty_set))),
% 0.26/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl]),skolemize(F,sK39_skl),skolemize(A,sK40_skl),skolemize(B,sK41_skl)],[f245])).
% 0.26/0.51 fof(f248,plain,(
% 0.26/0.51 ~equal_set(image2(sK39_skl,empty_set),empty_set)),
% 0.26/0.51 inference(cnf_transformation,[status(thm)],[f246])).
% 0.26/0.51 fof(f274,plain,(
% 0.26/0.51 ![X0]: (subset(empty_set,X0))),
% 0.26/0.51 inference(resolution,[status(thm)],[f36,f57])).
% 0.26/0.52 fof(f276,plain,(
% 0.26/0.52 ![X0]: (equal_set(X0,empty_set)|~subset(X0,empty_set))),
% 0.26/0.52 inference(resolution,[status(thm)],[f274,f42])).
% 0.26/0.52 fof(f512,plain,(
% 0.26/0.52 ![X0,X1]: (~member(X0,image2(X1,empty_set)))),
% 0.26/0.52 inference(resolution,[status(thm)],[f179,f57])).
% 0.26/0.52 fof(f525,plain,(
% 0.26/0.52 ![X0,X1]: (subset(image2(X0,empty_set),X1))),
% 0.26/0.52 inference(resolution,[status(thm)],[f512,f36])).
% 0.26/0.52 fof(f529,plain,(
% 0.26/0.52 ![X0]: (equal_set(image2(X0,empty_set),empty_set))),
% 0.26/0.52 inference(resolution,[status(thm)],[f525,f276])).
% 0.26/0.52 fof(f533,plain,(
% 0.26/0.52 $false),
% 0.26/0.52 inference(backward_subsumption_resolution,[status(thm)],[f248,f529])).
% 0.26/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/0.54 % Elapsed time: 0.092347 seconds
% 0.26/0.54 % CPU time: 0.333967 seconds
% 0.26/0.54 % Total memory used: 88.573 MB
% 0.26/0.54 % Net memory used: 88.306 MB
%------------------------------------------------------------------------------