%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET927+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 : n020.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 02:12:52 PM UTC 2026
% Result : Theorem 0.09s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+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
% 0.09/0.53 % Computer : n020.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Mon Sep 21 05:45:03 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.09/0.56 % Refutation found
% 0.09/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.56 fof(f5,conjecture,(
% 0.09/0.56 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) )),
% 0.09/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.56 fof(f6,negated_conjecture,(
% 0.09/0.56 ~((! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) ))),
% 0.09/0.56 inference(negated_conjecture,[status(cth)],[f5])).
% 0.09/0.56 fof(f7,axiom,(
% 0.09/0.56 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) )),
% 0.09/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.56 fof(f15,plain,(
% 0.09/0.56 (?[A,B,C]: (set_difference(unordered_pair(A,B),C)=singleton(A)<~>(~in(A,C)&(in(B,C)|A=B))))),
% 0.09/0.56 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.09/0.56 fof(f16,plain,(
% 0.09/0.56 ?[A,B,C]: ((set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B)))&(~set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.09/0.56 inference(NNF_transformation,[status(thm)],[f15])).
% 0.09/0.56 fof(f17,plain,(
% 0.09/0.56 ((set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|(~in(sK2_skl,sK4_skl)&(in(sK3_skl,sK4_skl)|sK2_skl=sK3_skl)))&(~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|(in(sK2_skl,sK4_skl)|(~in(sK3_skl,sK4_skl)&~sK2_skl=sK3_skl))))),
% 0.09/0.56 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)],[f16])).
% 0.09/0.56 fof(f18,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~in(sK2_skl,sK4_skl)),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.56 fof(f19,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|in(sK3_skl,sK4_skl)|sK2_skl=sK3_skl),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.56 fof(f20,plain,(
% 0.09/0.56 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|in(sK2_skl,sK4_skl)|~in(sK3_skl,sK4_skl)),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.56 fof(f21,plain,(
% 0.09/0.56 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|in(sK2_skl,sK4_skl)|~sK2_skl=sK3_skl),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.56 fof(f22,plain,(
% 0.09/0.56 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B)))&(set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.09/0.56 inference(NNF_transformation,[status(thm)],[f7])).
% 0.09/0.56 fof(f23,plain,(
% 0.09/0.56 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.09/0.56 inference(miniscoping,[status(thm)],[f22])).
% 0.09/0.56 fof(f24,plain,(
% 0.09/0.56 ![X0,X1,X2]: (~set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|~in(X0,X2))),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.09/0.56 fof(f25,plain,(
% 0.09/0.56 ![X0,X1,X2]: (~set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X1,X2)|X0=X1)),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.09/0.56 fof(f26,plain,(
% 0.09/0.56 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~in(X1,X2))),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.09/0.56 fof(f27,plain,(
% 0.09/0.56 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~X0=X1)),
% 0.09/0.56 inference(cnf_transformation,[status(thm)],[f23])).
% 0.09/0.56 fof(f28,definition,(
% 0.09/0.56 sQ0_spl <=> (set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl))),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f29,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~sQ0_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f28])).
% 0.09/0.56 fof(f30,plain,(
% 0.09/0.56 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|sQ0_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f28])).
% 0.09/0.56 fof(f31,definition,(
% 0.09/0.56 sQ1_spl <=> (in(sK2_skl,sK4_skl))),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f33,plain,(
% 0.09/0.56 ~in(sK2_skl,sK4_skl)|sQ1_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f31])).
% 0.09/0.56 fof(f34,plain,(
% 0.09/0.56 sQ0_spl|~sQ1_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f18,f28,f31])).
% 0.09/0.56 fof(f35,definition,(
% 0.09/0.56 sQ2_spl <=> (in(sK3_skl,sK4_skl))),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f36,plain,(
% 0.09/0.56 in(sK3_skl,sK4_skl)|~sQ2_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f35])).
% 0.09/0.56 fof(f38,definition,(
% 0.09/0.56 sQ3_spl <=> (sK2_skl=sK3_skl)),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f39,plain,(
% 0.09/0.56 sK2_skl=sK3_skl|~sQ3_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f38])).
% 0.09/0.56 fof(f41,plain,(
% 0.09/0.56 sQ0_spl|sQ2_spl|sQ3_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f19,f28,f35,f38])).
% 0.09/0.56 fof(f42,plain,(
% 0.09/0.56 ~sQ0_spl|sQ1_spl|~sQ2_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f20,f28,f31,f35])).
% 0.09/0.56 fof(f43,plain,(
% 0.09/0.56 ~sQ0_spl|sQ1_spl|~sQ3_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f21,f28,f31,f38])).
% 0.09/0.56 fof(f44,plain,(
% 0.09/0.56 ![X0,X1]: (set_difference(unordered_pair(X0,X0),X1)=singleton(X0)|in(X0,X1))),
% 0.09/0.56 inference(destructive_equality_resolution,[status(thm)],[f27])).
% 0.09/0.56 fof(f55,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK2_skl,sK2_skl),sK4_skl)=singleton(sK2_skl)|sQ1_spl),
% 0.09/0.56 inference(resolution,[status(thm)],[f44,f33])).
% 0.09/0.56 fof(f63,definition,(
% 0.09/0.56 sQ4_spl <=> (singleton(sK4_skl)=singleton(sK4_skl))),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f65,plain,(
% 0.09/0.56 ~singleton(sK4_skl)=singleton(sK4_skl)|sQ4_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f63])).
% 0.09/0.56 fof(f76,definition,(
% 0.09/0.56 sQ6_spl <=> (singleton(sK2_skl)=singleton(sK2_skl))),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f78,plain,(
% 0.09/0.56 ~singleton(sK2_skl)=singleton(sK2_skl)|sQ6_spl),
% 0.09/0.56 inference(component_clause,[status(thm)],[f76])).
% 0.09/0.56 fof(f81,plain,(
% 0.09/0.56 in(sK2_skl,sK4_skl)|sK2_skl=sK2_skl|sQ1_spl),
% 0.09/0.56 inference(resolution,[status(thm)],[f25,f55])).
% 0.09/0.56 fof(f85,definition,(
% 0.09/0.56 sQ7_spl <=> (sK2_skl=sK2_skl)),
% 0.09/0.56 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.56 fof(f88,plain,(
% 0.09/0.56 sQ1_spl|sQ7_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f81,f31,f85])).
% 0.09/0.56 fof(f90,plain,(
% 0.09/0.56 $false|sQ6_spl),
% 0.09/0.56 inference(trivial_equality_resolution,[status(thm)],[f78])).
% 0.09/0.56 fof(f91,plain,(
% 0.09/0.56 sQ6_spl),
% 0.09/0.56 inference(contradiction_clause,[status(thm)],[f90])).
% 0.09/0.56 fof(f99,plain,(
% 0.09/0.56 in(sK3_skl,sK4_skl)|sK2_skl=sK3_skl|~sQ0_spl),
% 0.09/0.56 inference(resolution,[status(thm)],[f29,f25])).
% 0.09/0.56 fof(f105,plain,(
% 0.09/0.56 ~singleton(sK2_skl)=singleton(sK2_skl)|~in(sK2_skl,sK4_skl)|~sQ0_spl),
% 0.09/0.56 inference(paramodulation,[status(thm)],[f29,f24])).
% 0.09/0.56 fof(f106,plain,(
% 0.09/0.56 sQ2_spl|sQ3_spl|~sQ0_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f99,f35,f38,f28])).
% 0.09/0.56 fof(f113,plain,(
% 0.09/0.56 ~sQ6_spl|~sQ1_spl|~sQ0_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f105,f76,f31,f28])).
% 0.09/0.56 fof(f132,plain,(
% 0.09/0.56 $false|sQ4_spl),
% 0.09/0.56 inference(trivial_equality_resolution,[status(thm)],[f65])).
% 0.09/0.56 fof(f133,plain,(
% 0.09/0.56 sQ4_spl),
% 0.09/0.56 inference(contradiction_clause,[status(thm)],[f132])).
% 0.09/0.56 fof(f135,plain,(
% 0.09/0.56 ~set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~sQ3_spl|sQ0_spl),
% 0.09/0.56 inference(forward_demodulation,[status(thm)],[f39,f30])).
% 0.09/0.56 fof(f136,plain,(
% 0.09/0.56 ~set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|~sQ3_spl|sQ0_spl),
% 0.09/0.56 inference(forward_demodulation,[status(thm)],[f39,f135])).
% 0.09/0.56 fof(f139,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=singleton(sK2_skl)|~sQ3_spl|sQ1_spl),
% 0.09/0.56 inference(forward_demodulation,[status(thm)],[f39,f55])).
% 0.09/0.56 fof(f140,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~sQ3_spl|sQ1_spl),
% 0.09/0.56 inference(forward_demodulation,[status(thm)],[f39,f139])).
% 0.09/0.56 fof(f141,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|~sQ3_spl|sQ1_spl),
% 0.09/0.56 inference(forward_demodulation,[status(thm)],[f39,f140])).
% 0.09/0.56 fof(f142,plain,(
% 0.09/0.56 $false|sQ0_spl|~sQ3_spl|sQ1_spl),
% 0.09/0.56 inference(forward_subsumption_resolution,[status(thm)],[f141,f136])).
% 0.09/0.56 fof(f143,plain,(
% 0.09/0.56 sQ0_spl|~sQ3_spl|sQ1_spl),
% 0.09/0.56 inference(contradiction_clause,[status(thm)],[f142])).
% 0.09/0.56 fof(f148,plain,(
% 0.09/0.56 ![X0]: (set_difference(unordered_pair(X0,sK3_skl),sK4_skl)=singleton(X0)|in(X0,sK4_skl)|~sQ2_spl)),
% 0.09/0.56 inference(resolution,[status(thm)],[f36,f26])).
% 0.09/0.56 fof(f180,plain,(
% 0.09/0.56 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~sQ2_spl|sQ1_spl),
% 0.09/0.56 inference(resolution,[status(thm)],[f148,f33])).
% 0.09/0.56 fof(f184,plain,(
% 0.09/0.56 sQ0_spl|~sQ2_spl|sQ1_spl),
% 0.09/0.56 inference(split_clause,[status(thm)],[f180,f28,f35,f31])).
% 0.09/0.56 fof(f185,plain,(
% 0.09/0.56 $false),
% 0.09/0.56 inference(sat_refutation,[status(thm)],[f34,f41,f42,f43,f88,f91,f106,f113,f133,f143,f184])).
% 0.09/0.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.59 % Elapsed time: 0.053588 seconds
% 0.12/0.59 % CPU time: 0.144479 seconds
% 0.12/0.59 % Total memory used: 101.617 MB
% 0.12/0.59 % Net memory used: 101.115 MB
%------------------------------------------------------------------------------