%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 03:19:35 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 10:53:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.39 fof(f1,conjecture,(
% 0.14/0.39 ( (! [X] : f(X))<=> (! [Y,Z] :( f(Y)& f(Z) ) )) ),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f2,negated_conjecture,(
% 0.14/0.39 ~(( (! [X] : f(X))<=> (! [Y,Z] :( f(Y)& f(Z) ) )) )),
% 0.14/0.39 inference(negated_conjecture,[status(cth)],[f1])).
% 0.14/0.39 fof(f3,plain,(
% 0.14/0.39 ((![X]: f(X))<~>(![Y,Z]: (f(Y)&f(Z))))),
% 0.14/0.39 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.14/0.39 fof(f4,plain,(
% 0.14/0.39 ((![X]: f(X))|(![Y,Z]: (f(Y)&f(Z))))&((?[X]: ~f(X))|(?[Y,Z]: (~f(Y)|~f(Z))))),
% 0.14/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.14/0.39 fof(f5,plain,(
% 0.14/0.39 ((![X]: f(X))|((![Y]: f(Y))&(![Z]: f(Z))))&((?[X]: ~f(X))|((?[Y]: ~f(Y))|(?[Z]: ~f(Z))))),
% 0.14/0.39 inference(miniscoping,[status(thm)],[f4])).
% 0.14/0.39 fof(f6,plain,(
% 0.14/0.39 ((![X]: f(X))|((![Y]: f(Y))&(![Z]: f(Z))))&(~f(sK0_skl)|(~f(sK1_skl)|~f(sK2_skl)))),
% 0.14/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f5])).
% 0.14/0.39 fof(f7,plain,(
% 0.14/0.39 ![X0,X1]: (f(X0)|f(X1))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.39 fof(f9,plain,(
% 0.14/0.39 ~f(sK0_skl)|~f(sK1_skl)|~f(sK2_skl)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.39 fof(f10,definition,(
% 0.14/0.39 ![X0]: (sQ0_spl <=> (f(X0)))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f11,plain,(
% 0.14/0.39 ![X0]: (f(X0)|~sQ0_spl)),
% 0.14/0.39 inference(component_clause,[status(thm)],[f10])).
% 0.14/0.39 fof(f13,plain,(
% 0.14/0.39 sQ0_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f7,f10])).
% 0.14/0.39 fof(f15,definition,(
% 0.14/0.39 sQ1_spl <=> (f(sK0_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f17,plain,(
% 0.14/0.39 ~f(sK0_skl)|sQ1_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f15])).
% 0.14/0.39 fof(f18,definition,(
% 0.14/0.39 sQ2_spl <=> (f(sK1_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f20,plain,(
% 0.14/0.39 ~f(sK1_skl)|sQ2_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f18])).
% 0.14/0.39 fof(f21,definition,(
% 0.14/0.39 sQ3_spl <=> (f(sK2_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f23,plain,(
% 0.14/0.39 ~f(sK2_skl)|sQ3_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f21])).
% 0.14/0.39 fof(f24,plain,(
% 0.14/0.39 ~sQ1_spl|~sQ2_spl|~sQ3_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f9,f15,f18,f21])).
% 0.14/0.39 fof(f25,plain,(
% 0.14/0.39 $false|~sQ0_spl|sQ3_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f23,f11])).
% 0.14/0.39 fof(f26,plain,(
% 0.14/0.39 ~sQ0_spl|sQ3_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f25])).
% 0.14/0.39 fof(f27,plain,(
% 0.14/0.39 $false|~sQ0_spl|sQ1_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f17,f11])).
% 0.14/0.39 fof(f28,plain,(
% 0.14/0.39 ~sQ0_spl|sQ1_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f27])).
% 0.14/0.39 fof(f29,plain,(
% 0.14/0.39 $false|~sQ0_spl|sQ2_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f20,f11])).
% 0.14/0.39 fof(f30,plain,(
% 0.14/0.39 ~sQ0_spl|sQ2_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f29])).
% 0.14/0.39 fof(f31,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(sat_refutation,[status(thm)],[f13,f24,f26,f28,f30])).
% 0.14/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.41 % Elapsed time: 0.041358 seconds
% 0.14/0.41 % CPU time: 0.108058 seconds
% 0.14/0.41 % Total memory used: 16.493 MB
% 0.14/0.41 % Net memory used: 15.853 MB
%------------------------------------------------------------------------------