%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:12:28 PM UTC 2026
% Result : Theorem 0.19s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n003.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 05:34:00 UTC 2026
% 0.19/0.41 % CPUTime :
% 0.19/0.42 % Drodi V4.1.1
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.44 fof(f1,axiom,(
% 0.19/0.44 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f2,axiom,(
% 0.19/0.44 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f6,axiom,(
% 0.19/0.44 (! [X] : ~ member(X,empty_set) )),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f12,conjecture,(
% 0.19/0.44 (! [A] :( subset(A,empty_set)<=> equal_set(A,empty_set) ) )),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f13,negated_conjecture,(
% 0.19/0.44 ~((! [A] :( subset(A,empty_set)<=> equal_set(A,empty_set) ) ))),
% 0.19/0.44 inference(negated_conjecture,[status(cth)],[f12])).
% 0.19/0.44 fof(f14,plain,(
% 0.19/0.44 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.19/0.44 fof(f15,plain,(
% 0.19/0.44 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.19/0.44 inference(NNF_transformation,[status(thm)],[f14])).
% 0.19/0.44 fof(f16,plain,(
% 0.19/0.44 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.19/0.44 inference(miniscoping,[status(thm)],[f15])).
% 0.19/0.44 fof(f17,plain,(
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16])).
% 0.19/0.44 fof(f19,plain,(
% 0.19/0.44 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.19/0.44 fof(f21,plain,(
% 0.19/0.44 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.19/0.44 inference(NNF_transformation,[status(thm)],[f2])).
% 0.19/0.44 fof(f22,plain,(
% 0.19/0.44 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.19/0.44 inference(miniscoping,[status(thm)],[f21])).
% 0.19/0.44 fof(f23,plain,(
% 0.19/0.44 ![X0,X1]: (~equal_set(X0,X1)|subset(X0,X1))),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f22])).
% 0.19/0.44 fof(f25,plain,(
% 0.19/0.44 ![X0,X1]: (equal_set(X0,X1)|~subset(X0,X1)|~subset(X1,X0))),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f22])).
% 0.19/0.44 fof(f40,plain,(
% 0.19/0.44 ![X0]: (~member(X0,empty_set))),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f6])).
% 0.19/0.44 fof(f68,plain,(
% 0.19/0.44 (?[A]: (subset(A,empty_set)<~>equal_set(A,empty_set)))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.19/0.44 fof(f69,plain,(
% 0.19/0.44 ?[A]: ((subset(A,empty_set)|equal_set(A,empty_set))&(~subset(A,empty_set)|~equal_set(A,empty_set)))),
% 0.19/0.44 inference(NNF_transformation,[status(thm)],[f68])).
% 0.19/0.44 fof(f70,plain,(
% 0.19/0.44 ((subset(sK3_skl,empty_set)|equal_set(sK3_skl,empty_set))&(~subset(sK3_skl,empty_set)|~equal_set(sK3_skl,empty_set)))),
% 0.19/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f69])).
% 0.19/0.44 fof(f71,plain,(
% 0.19/0.44 subset(sK3_skl,empty_set)|equal_set(sK3_skl,empty_set)),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f70])).
% 0.19/0.44 fof(f72,plain,(
% 0.19/0.44 ~subset(sK3_skl,empty_set)|~equal_set(sK3_skl,empty_set)),
% 0.19/0.44 inference(cnf_transformation,[status(thm)],[f70])).
% 0.19/0.44 fof(f73,definition,(
% 0.19/0.44 sQ0_spl <=> (subset(sK3_skl,empty_set))),
% 0.19/0.44 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.19/0.44 fof(f74,plain,(
% 0.19/0.44 subset(sK3_skl,empty_set)|~sQ0_spl),
% 0.19/0.44 inference(component_clause,[status(thm)],[f73])).
% 0.19/0.44 fof(f75,plain,(
% 0.19/0.44 ~subset(sK3_skl,empty_set)|sQ0_spl),
% 0.19/0.44 inference(component_clause,[status(thm)],[f73])).
% 0.19/0.44 fof(f76,definition,(
% 0.19/0.44 sQ1_spl <=> (equal_set(sK3_skl,empty_set))),
% 0.19/0.44 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.19/0.44 fof(f77,plain,(
% 0.19/0.44 equal_set(sK3_skl,empty_set)|~sQ1_spl),
% 0.19/0.44 inference(component_clause,[status(thm)],[f76])).
% 0.19/0.44 fof(f79,plain,(
% 0.19/0.44 sQ0_spl|sQ1_spl),
% 0.19/0.44 inference(split_clause,[status(thm)],[f71,f73,f76])).
% 0.19/0.44 fof(f80,plain,(
% 0.19/0.44 ~sQ0_spl|~sQ1_spl),
% 0.19/0.44 inference(split_clause,[status(thm)],[f72,f73,f76])).
% 0.19/0.44 fof(f87,plain,(
% 0.19/0.44 subset(sK3_skl,empty_set)|~sQ1_spl),
% 0.19/0.44 inference(resolution,[status(thm)],[f23,f77])).
% 0.19/0.44 fof(f88,plain,(
% 0.19/0.44 $false|sQ0_spl|~sQ1_spl),
% 0.19/0.44 inference(forward_subsumption_resolution,[status(thm)],[f87,f75])).
% 0.19/0.44 fof(f89,plain,(
% 0.19/0.44 sQ0_spl|~sQ1_spl),
% 0.19/0.44 inference(contradiction_clause,[status(thm)],[f88])).
% 0.19/0.44 fof(f90,plain,(
% 0.19/0.44 equal_set(empty_set,sK3_skl)|~subset(empty_set,sK3_skl)|~sQ0_spl),
% 0.19/0.44 inference(resolution,[status(thm)],[f74,f25])).
% 0.19/0.44 fof(f91,definition,(
% 0.19/0.44 sQ2_spl <=> (equal_set(empty_set,sK3_skl))),
% 0.19/0.44 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.44 fof(f92,plain,(
% 0.19/0.44 equal_set(empty_set,sK3_skl)|~sQ2_spl),
% 0.19/0.44 inference(component_clause,[status(thm)],[f91])).
% 0.19/0.44 fof(f94,definition,(
% 0.19/0.44 sQ3_spl <=> (subset(empty_set,sK3_skl))),
% 0.19/0.44 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.44 fof(f96,plain,(
% 0.19/0.44 ~subset(empty_set,sK3_skl)|sQ3_spl),
% 0.19/0.44 inference(component_clause,[status(thm)],[f94])).
% 0.19/0.44 fof(f97,plain,(
% 0.19/0.44 sQ2_spl|~sQ3_spl|~sQ0_spl),
% 0.19/0.44 inference(split_clause,[status(thm)],[f90,f91,f94,f73])).
% 0.19/0.44 fof(f100,plain,(
% 0.19/0.44 subset(empty_set,sK3_skl)|~sQ2_spl),
% 0.19/0.44 inference(resolution,[status(thm)],[f92,f23])).
% 0.19/0.44 fof(f101,plain,(
% 0.19/0.44 equal_set(sK3_skl,empty_set)|~subset(sK3_skl,empty_set)|~sQ2_spl),
% 0.19/0.44 inference(resolution,[status(thm)],[f100,f25])).
% 0.19/0.44 fof(f102,plain,(
% 0.19/0.44 sQ1_spl|~sQ0_spl|~sQ2_spl),
% 0.19/0.44 inference(split_clause,[status(thm)],[f101,f76,f73,f91])).
% 0.19/0.44 fof(f103,plain,(
% 0.19/0.44 ![X0]: (subset(empty_set,X0))),
% 0.19/0.44 inference(resolution,[status(thm)],[f19,f40])).
% 0.19/0.44 fof(f105,plain,(
% 0.19/0.44 $false|sQ3_spl),
% 0.19/0.44 inference(backward_subsumption_resolution,[status(thm)],[f96,f103])).
% 0.19/0.44 fof(f106,plain,(
% 0.19/0.44 sQ3_spl),
% 0.19/0.44 inference(contradiction_clause,[status(thm)],[f105])).
% 0.19/0.44 fof(f107,plain,(
% 0.19/0.44 $false),
% 0.19/0.44 inference(sat_refutation,[status(thm)],[f79,f80,f89,f97,f102,f106])).
% 0.19/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.47 % Elapsed time: 0.057465 seconds
% 0.19/0.47 % CPU time: 0.158550 seconds
% 0.19/0.47 % Total memory used: 52.880 MB
% 0.19/0.47 % Net memory used: 52.698 MB
%------------------------------------------------------------------------------