%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:12:53 PM UTC 2026
% Result : Theorem 0.02s 0.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 05:43:52 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.32 % Refutation found
% 0.02/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% 0.02/0.32 fof(f2,axiom,(
% 0.02/0.32 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.02/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.32 fof(f6,axiom,(
% 0.02/0.32 (! [A,B] : subset(A,A) )),
% 0.02/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.32 fof(f7,axiom,(
% 0.02/0.32 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 0.02/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.32 fof(f8,axiom,(
% 0.02/0.32 (! [A,B,C] :( subset(unordered_pair(A,B),C)<=> ( in(A,C)& in(B,C) ) ) )),
% 0.02/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.32 fof(f9,conjecture,(
% 0.02/0.32 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = empty_set<=> ( in(A,C)& in(B,C) ) ) )),
% 0.02/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.32 fof(f10,negated_conjecture,(
% 0.02/0.32 ~((! [A,B,C] :( set_difference(unordered_pair(A,B),C) = empty_set<=> ( in(A,C)& in(B,C) ) ) ))),
% 0.02/0.32 inference(negated_conjecture,[status(cth)],[f9])).
% 0.02/0.32 fof(f13,plain,(
% 0.02/0.32 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f2])).
% 0.02/0.32 fof(f19,plain,(
% 0.02/0.32 ![A]: subset(A,A)),
% 0.02/0.32 inference(miniscoping,[status(thm)],[f6])).
% 0.02/0.32 fof(f20,plain,(
% 0.02/0.32 ![X0]: (subset(X0,X0))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f19])).
% 0.02/0.32 fof(f21,plain,(
% 0.02/0.32 ![A,B]: ((~set_difference(A,B)=empty_set|subset(A,B))&(set_difference(A,B)=empty_set|~subset(A,B)))),
% 0.02/0.32 inference(NNF_transformation,[status(thm)],[f7])).
% 0.02/0.32 fof(f22,plain,(
% 0.02/0.32 (![A,B]: (~set_difference(A,B)=empty_set|subset(A,B)))&(![A,B]: (set_difference(A,B)=empty_set|~subset(A,B)))),
% 0.02/0.32 inference(miniscoping,[status(thm)],[f21])).
% 0.02/0.32 fof(f23,plain,(
% 0.02/0.32 ![X0,X1]: (~set_difference(X0,X1)=empty_set|subset(X0,X1))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f22])).
% 0.02/0.32 fof(f24,plain,(
% 0.02/0.32 ![X0,X1]: (set_difference(X0,X1)=empty_set|~subset(X0,X1))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f22])).
% 0.02/0.32 fof(f25,plain,(
% 0.02/0.32 ![A,B,C]: ((~subset(unordered_pair(A,B),C)|(in(A,C)&in(B,C)))&(subset(unordered_pair(A,B),C)|(~in(A,C)|~in(B,C))))),
% 0.02/0.32 inference(NNF_transformation,[status(thm)],[f8])).
% 0.02/0.32 fof(f26,plain,(
% 0.02/0.32 (![A,B,C]: (~subset(unordered_pair(A,B),C)|(in(A,C)&in(B,C))))&(![A,B,C]: (subset(unordered_pair(A,B),C)|(~in(A,C)|~in(B,C))))),
% 0.02/0.32 inference(miniscoping,[status(thm)],[f25])).
% 0.02/0.32 fof(f27,plain,(
% 0.02/0.32 ![X0,X1,X2]: (~subset(unordered_pair(X0,X1),X2)|in(X0,X2))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f26])).
% 0.02/0.32 fof(f29,plain,(
% 0.02/0.32 ![X0,X1,X2]: (subset(unordered_pair(X0,X1),X2)|~in(X0,X2)|~in(X1,X2))),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f26])).
% 0.02/0.32 fof(f30,plain,(
% 0.02/0.32 (?[A,B,C]: (set_difference(unordered_pair(A,B),C)=empty_set<~>(in(A,C)&in(B,C))))),
% 0.02/0.32 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.02/0.32 fof(f31,plain,(
% 0.02/0.32 ?[A,B,C]: ((set_difference(unordered_pair(A,B),C)=empty_set|(in(A,C)&in(B,C)))&(~set_difference(unordered_pair(A,B),C)=empty_set|(~in(A,C)|~in(B,C))))),
% 0.02/0.32 inference(NNF_transformation,[status(thm)],[f30])).
% 0.02/0.32 fof(f32,plain,(
% 0.02/0.32 ((set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|(in(sK2_skl,sK4_skl)&in(sK3_skl,sK4_skl)))&(~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|(~in(sK2_skl,sK4_skl)|~in(sK3_skl,sK4_skl))))),
% 0.02/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f31])).
% 0.02/0.32 fof(f33,plain,(
% 0.02/0.32 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|in(sK2_skl,sK4_skl)),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f32])).
% 0.02/0.32 fof(f34,plain,(
% 0.02/0.32 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|in(sK3_skl,sK4_skl)),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f32])).
% 0.02/0.32 fof(f35,plain,(
% 0.02/0.32 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|~in(sK2_skl,sK4_skl)|~in(sK3_skl,sK4_skl)),
% 0.02/0.32 inference(cnf_transformation,[status(thm)],[f32])).
% 0.02/0.32 fof(f36,definition,(
% 0.02/0.32 sQ0_spl <=> (set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set)),
% 0.02/0.32 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.02/0.32 fof(f37,plain,(
% 0.02/0.32 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|~sQ0_spl),
% 0.02/0.32 inference(component_clause,[status(thm)],[f36])).
% 0.02/0.32 fof(f39,definition,(
% 0.02/0.32 sQ1_spl <=> (in(sK2_skl,sK4_skl))),
% 0.02/0.32 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.02/0.32 fof(f40,plain,(
% 0.02/0.32 in(sK2_skl,sK4_skl)|~sQ1_spl),
% 0.02/0.32 inference(component_clause,[status(thm)],[f39])).
% 0.02/0.32 fof(f41,plain,(
% 0.02/0.32 ~in(sK2_skl,sK4_skl)|sQ1_spl),
% 0.02/0.32 inference(component_clause,[status(thm)],[f39])).
% 0.02/0.32 fof(f42,plain,(
% 0.02/0.32 sQ0_spl|sQ1_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f33,f36,f39])).
% 0.02/0.32 fof(f43,definition,(
% 0.02/0.32 sQ2_spl <=> (in(sK3_skl,sK4_skl))),
% 0.02/0.32 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.02/0.32 fof(f44,plain,(
% 0.02/0.32 in(sK3_skl,sK4_skl)|~sQ2_spl),
% 0.02/0.32 inference(component_clause,[status(thm)],[f43])).
% 0.02/0.32 fof(f46,plain,(
% 0.02/0.32 sQ0_spl|sQ2_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f34,f36,f43])).
% 0.02/0.32 fof(f47,plain,(
% 0.02/0.32 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f35,f36,f39,f43])).
% 0.02/0.32 fof(f52,plain,(
% 0.02/0.32 set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=empty_set|~sQ0_spl),
% 0.02/0.32 inference(paramodulation,[status(thm)],[f13,f37])).
% 0.02/0.32 fof(f54,plain,(
% 0.02/0.32 subset(unordered_pair(sK3_skl,sK2_skl),sK4_skl)|~sQ0_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f23,f52])).
% 0.02/0.32 fof(f55,plain,(
% 0.02/0.32 subset(unordered_pair(sK2_skl,sK3_skl),sK4_skl)|~sQ0_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f23,f37])).
% 0.02/0.32 fof(f58,definition,(
% 0.02/0.32 sQ3_spl <=> (empty_set=empty_set)),
% 0.02/0.32 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.02/0.32 fof(f60,plain,(
% 0.02/0.32 ~empty_set=empty_set|sQ3_spl),
% 0.02/0.32 inference(component_clause,[status(thm)],[f58])).
% 0.02/0.32 fof(f69,plain,(
% 0.02/0.32 $false|sQ3_spl),
% 0.02/0.32 inference(trivial_equality_resolution,[status(thm)],[f60])).
% 0.02/0.32 fof(f70,plain,(
% 0.02/0.32 sQ3_spl),
% 0.02/0.32 inference(contradiction_clause,[status(thm)],[f69])).
% 0.02/0.32 fof(f75,plain,(
% 0.02/0.32 ![X0]: (set_difference(X0,X0)=empty_set)),
% 0.02/0.32 inference(resolution,[status(thm)],[f20,f24])).
% 0.02/0.32 fof(f77,plain,(
% 0.02/0.32 ![X0]: (~empty_set=empty_set|subset(X0,X0))),
% 0.02/0.32 inference(paramodulation,[status(thm)],[f75,f23])).
% 0.02/0.32 fof(f78,definition,(
% 0.02/0.32 ![X0]: (sQ6_spl <=> (subset(X0,X0)))),
% 0.02/0.32 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.02/0.32 fof(f81,plain,(
% 0.02/0.32 ~sQ3_spl|sQ6_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f77,f58,f78])).
% 0.02/0.32 fof(f82,plain,(
% 0.02/0.32 in(sK2_skl,sK4_skl)|~sQ0_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f27,f55])).
% 0.02/0.32 fof(f83,plain,(
% 0.02/0.32 in(sK3_skl,sK4_skl)|~sQ0_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f27,f54])).
% 0.02/0.32 fof(f87,plain,(
% 0.02/0.32 $false|sQ1_spl|~sQ0_spl),
% 0.02/0.32 inference(forward_subsumption_resolution,[status(thm)],[f82,f41])).
% 0.02/0.32 fof(f88,plain,(
% 0.02/0.32 sQ1_spl|~sQ0_spl),
% 0.02/0.32 inference(contradiction_clause,[status(thm)],[f87])).
% 0.02/0.32 fof(f106,plain,(
% 0.02/0.32 ![X0]: (subset(unordered_pair(X0,sK3_skl),sK4_skl)|~in(X0,sK4_skl)|~sQ2_spl)),
% 0.02/0.32 inference(resolution,[status(thm)],[f29,f44])).
% 0.02/0.32 fof(f111,plain,(
% 0.02/0.32 subset(unordered_pair(sK2_skl,sK3_skl),sK4_skl)|~sQ2_spl|~sQ1_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f106,f40])).
% 0.02/0.32 fof(f117,plain,(
% 0.02/0.32 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set|~sQ2_spl|~sQ1_spl),
% 0.02/0.32 inference(resolution,[status(thm)],[f111,f24])).
% 0.02/0.32 fof(f120,plain,(
% 0.02/0.32 sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f117,f36,f43,f39])).
% 0.02/0.32 fof(f121,plain,(
% 0.02/0.32 sQ2_spl|~sQ0_spl),
% 0.02/0.32 inference(split_clause,[status(thm)],[f83,f43,f36])).
% 0.02/0.32 fof(f122,plain,(
% 0.02/0.32 $false),
% 0.02/0.32 inference(sat_refutation,[status(thm)],[f42,f46,f47,f70,f81,f88,f120,f121])).
% 0.02/0.32 % SZS output end CNFRefutation for theBenchmark.p
% 0.07/0.34 % Elapsed time: 0.040195 seconds
% 0.07/0.34 % CPU time: 0.084488 seconds
% 0.07/0.34 % Total memory used: 101.543 MB
% 0.07/0.34 % Net memory used: 101.113 MB
%------------------------------------------------------------------------------