%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET928+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 : 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 02:12:53 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:44:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f2,axiom,(
% 0.09/0.40 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f5,axiom,(
% 0.09/0.40 (! [A,B] :( disjoint(A,B)=> disjoint(B,A) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f6,axiom,(
% 0.09/0.40 (! [A,B,C] :~ ( disjoint(unordered_pair(A,B),C)& in(A,C) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f7,axiom,(
% 0.09/0.40 (! [A,B,C] :~ ( ~ in(A,B)& ~ in(C,B)& ~ disjoint(unordered_pair(A,C),B) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f8,conjecture,(
% 0.09/0.40 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)<=> ( ~ in(A,C)& ~ in(B,C) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f9,negated_conjecture,(
% 0.09/0.40 ~((! [A,B,C] :( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)<=> ( ~ in(A,C)& ~ in(B,C) ) ) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f8])).
% 0.09/0.40 fof(f10,axiom,(
% 0.09/0.40 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f13,plain,(
% 0.09/0.40 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.40 fof(f18,plain,(
% 0.09/0.40 ![A,B]: (~disjoint(A,B)|disjoint(B,A))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.09/0.40 fof(f19,plain,(
% 0.09/0.40 ![X0,X1]: (~disjoint(X0,X1)|disjoint(X1,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.40 fof(f20,plain,(
% 0.09/0.40 ![A,B,C]: (~disjoint(unordered_pair(A,B),C)|~in(A,C))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.09/0.40 fof(f21,plain,(
% 0.09/0.40 ![A,C]: ((![B]: ~disjoint(unordered_pair(A,B),C))|~in(A,C))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.09/0.40 fof(f22,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~disjoint(unordered_pair(X0,X1),X2)|~in(X0,X2))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.40 fof(f23,plain,(
% 0.09/0.40 ![A,B,C]: ((in(A,B)|in(C,B))|disjoint(unordered_pair(A,C),B))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f24,plain,(
% 0.09/0.40 ![X0,X1,X2]: (in(X0,X1)|in(X2,X1)|disjoint(unordered_pair(X0,X2),X1))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f23])).
% 0.09/0.40 fof(f25,plain,(
% 0.09/0.40 (?[A,B,C]: (set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)<~>(~in(A,C)&~in(B,C))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 ?[A,B,C]: ((set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(~in(A,C)&~in(B,C)))&(~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(in(A,C)|in(B,C))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f25])).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ((set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|(~in(sK2_skl,sK4_skl)&~in(sK3_skl,sK4_skl)))&(~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|(in(sK2_skl,sK4_skl)|in(sK3_skl,sK4_skl))))),
% 0.09/0.40 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)],[f26])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|~in(sK2_skl,sK4_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.40 fof(f29,plain,(
% 0.09/0.40 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|~in(sK3_skl,sK4_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.40 fof(f30,plain,(
% 0.09/0.40 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|in(sK2_skl,sK4_skl)|in(sK3_skl,sK4_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.40 fof(f31,plain,(
% 0.09/0.40 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f31])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 ![X0,X1]: (~disjoint(X0,X1)|set_difference(X0,X1)=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/0.40 fof(f35,definition,(
% 0.09/0.40 sQ0_spl <=> (set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|~sQ0_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f35])).
% 0.09/0.40 fof(f38,definition,(
% 0.09/0.40 sQ1_spl <=> (in(sK2_skl,sK4_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 in(sK2_skl,sK4_skl)|~sQ1_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f38])).
% 0.09/0.40 fof(f40,plain,(
% 0.09/0.40 ~in(sK2_skl,sK4_skl)|sQ1_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f38])).
% 0.09/0.40 fof(f41,plain,(
% 0.09/0.40 sQ0_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f28,f35,f38])).
% 0.09/0.40 fof(f42,definition,(
% 0.09/0.40 sQ2_spl <=> (in(sK3_skl,sK4_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 ~in(sK3_skl,sK4_skl)|sQ2_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f42])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 sQ0_spl|~sQ2_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f29,f35,f42])).
% 0.09/0.40 fof(f46,plain,(
% 0.09/0.40 ~sQ0_spl|sQ1_spl|sQ2_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f30,f35,f38,f42])).
% 0.09/0.40 fof(f52,plain,(
% 0.09/0.40 set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|~sQ0_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f13,f36])).
% 0.09/0.40 fof(f54,plain,(
% 0.09/0.40 disjoint(unordered_pair(sK2_skl,sK3_skl),sK4_skl)|~sQ0_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f34,f36])).
% 0.09/0.40 fof(f55,plain,(
% 0.09/0.40 disjoint(unordered_pair(sK3_skl,sK2_skl),sK4_skl)|~unordered_pair(sK2_skl,sK3_skl)=unordered_pair(sK3_skl,sK2_skl)|~sQ0_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f52,f34])).
% 0.09/0.40 fof(f57,definition,(
% 0.09/0.40 sQ3_spl <=> (disjoint(unordered_pair(sK3_skl,sK2_skl),sK4_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f58,plain,(
% 0.09/0.40 disjoint(unordered_pair(sK3_skl,sK2_skl),sK4_skl)|~sQ3_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f57])).
% 0.09/0.40 fof(f60,definition,(
% 0.09/0.40 sQ4_spl <=> (unordered_pair(sK2_skl,sK3_skl)=unordered_pair(sK3_skl,sK2_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f62,plain,(
% 0.09/0.40 ~unordered_pair(sK2_skl,sK3_skl)=unordered_pair(sK3_skl,sK2_skl)|sQ4_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f60])).
% 0.09/0.40 fof(f63,plain,(
% 0.09/0.40 sQ3_spl|~sQ4_spl|~sQ0_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f55,f57,f60,f35])).
% 0.09/0.40 fof(f90,plain,(
% 0.09/0.40 ~in(sK3_skl,sK4_skl)|~sQ3_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f22,f58])).
% 0.09/0.40 fof(f91,plain,(
% 0.09/0.40 ~in(sK2_skl,sK4_skl)|~sQ0_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f22,f54])).
% 0.09/0.40 fof(f94,plain,(
% 0.09/0.40 $false|~sQ1_spl|~sQ0_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f91,f39])).
% 0.09/0.40 fof(f95,plain,(
% 0.09/0.40 ~sQ1_spl|~sQ0_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f94])).
% 0.09/0.40 fof(f100,plain,(
% 0.09/0.40 ![X0,X1,X2]: (in(X0,X1)|in(X2,X1)|disjoint(X1,unordered_pair(X0,X2)))),
% 0.09/0.40 inference(resolution,[status(thm)],[f24,f19])).
% 0.09/0.40 fof(f107,plain,(
% 0.09/0.40 ![X0,X1,X2]: (in(X0,X1)|in(X2,X1)|set_difference(X1,unordered_pair(X0,X2))=X1)),
% 0.09/0.40 inference(resolution,[status(thm)],[f100,f33])).
% 0.09/0.40 fof(f112,plain,(
% 0.09/0.40 set_difference(sK4_skl,unordered_pair(sK3_skl,sK3_skl))=sK4_skl|sQ2_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f107,f44])).
% 0.09/0.40 fof(f115,plain,(
% 0.09/0.40 ![X0]: (in(X0,sK4_skl)|set_difference(sK4_skl,unordered_pair(sK2_skl,X0))=sK4_skl|sQ1_spl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f107,f40])).
% 0.09/0.40 fof(f122,plain,(
% 0.09/0.40 disjoint(sK4_skl,unordered_pair(sK3_skl,sK3_skl))|~sK4_skl=sK4_skl|sQ2_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f112,f34])).
% 0.09/0.40 fof(f123,definition,(
% 0.09/0.40 sQ8_spl <=> (disjoint(sK4_skl,unordered_pair(sK3_skl,sK3_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f124,plain,(
% 0.09/0.40 disjoint(sK4_skl,unordered_pair(sK3_skl,sK3_skl))|~sQ8_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f123])).
% 0.09/0.40 fof(f126,definition,(
% 0.09/0.40 sQ9_spl <=> (sK4_skl=sK4_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f128,plain,(
% 0.09/0.40 ~sK4_skl=sK4_skl|sQ9_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f126])).
% 0.09/0.40 fof(f129,plain,(
% 0.09/0.40 sQ8_spl|~sQ9_spl|sQ2_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f122,f123,f126,f42])).
% 0.09/0.40 fof(f130,plain,(
% 0.09/0.40 ~sQ2_spl|~sQ3_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f90,f42,f57])).
% 0.09/0.40 fof(f135,plain,(
% 0.09/0.40 disjoint(unordered_pair(sK3_skl,sK3_skl),sK4_skl)|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f124,f19])).
% 0.09/0.40 fof(f149,plain,(
% 0.09/0.40 ~in(sK3_skl,sK4_skl)|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f135,f22])).
% 0.09/0.40 fof(f158,plain,(
% 0.09/0.40 $false|sQ9_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f128])).
% 0.09/0.40 fof(f159,plain,(
% 0.09/0.40 sQ9_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f158])).
% 0.09/0.40 fof(f160,plain,(
% 0.09/0.40 $false|sQ4_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f62,f13])).
% 0.09/0.40 fof(f161,plain,(
% 0.09/0.40 sQ4_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f160])).
% 0.09/0.40 fof(f203,plain,(
% 0.09/0.40 set_difference(sK4_skl,unordered_pair(sK2_skl,sK3_skl))=sK4_skl|sQ1_spl|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f115,f149])).
% 0.09/0.40 fof(f208,plain,(
% 0.09/0.40 disjoint(sK4_skl,unordered_pair(sK2_skl,sK3_skl))|sQ1_spl|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f203,f34])).
% 0.09/0.40 fof(f216,plain,(
% 0.09/0.40 disjoint(unordered_pair(sK2_skl,sK3_skl),sK4_skl)|sQ1_spl|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f208,f19])).
% 0.09/0.40 fof(f223,plain,(
% 0.09/0.40 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)|sQ1_spl|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f216,f33])).
% 0.09/0.40 fof(f226,plain,(
% 0.09/0.40 sQ0_spl|sQ1_spl|~sQ8_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f223,f35,f38,f123])).
% 0.09/0.40 fof(f227,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f41,f45,f46,f63,f95,f129,f130,f159,f161,f226])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.053040 seconds
% 0.09/0.43 % CPU time: 0.169537 seconds
% 0.09/0.43 % Total memory used: 101.695 MB
% 0.09/0.43 % Net memory used: 101.276 MB
%------------------------------------------------------------------------------