%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN398+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 : n008.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 03:19:34 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN398+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
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 10:54:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.40 fof(f1,conjecture,(
% 0.11/0.40 ( (! [X] :( p& f(X) ))<=> ( p& (! [Y] : f(Y) )) ) ),
% 0.11/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.40 fof(f2,negated_conjecture,(
% 0.11/0.40 ~(( (! [X] :( p& f(X) ))<=> ( p& (! [Y] : f(Y) )) ) )),
% 0.11/0.40 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.40 fof(f3,plain,(
% 0.11/0.40 ((![X]: (p&f(X)))<~>(p&(![Y]: f(Y))))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.11/0.40 fof(f4,definition,(
% 0.11/0.40 sP0_prd<=>(p&(![Y]: f(Y)))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.11/0.40 fof(f5,plain,(
% 0.11/0.40 (![X]: (p&f(X)))<~>sP0_prd),
% 0.11/0.40 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.11/0.40 fof(f6,plain,(
% 0.11/0.40 ((![X]: (p&f(X)))|sP0_prd)&((?[X]: (~p|~f(X)))|~sP0_prd)),
% 0.11/0.40 inference(NNF_transformation,[status(thm)],[f5])).
% 0.11/0.40 fof(f7,plain,(
% 0.11/0.40 ((p&(![X]: f(X)))|sP0_prd)&((~p|(?[X]: ~f(X)))|~sP0_prd)),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f6])).
% 0.11/0.40 fof(f8,plain,(
% 0.11/0.40 ((p&(![X]: f(X)))|sP0_prd)&((~p|~f(sK0_skl))|~sP0_prd)),
% 0.11/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f7])).
% 0.11/0.40 fof(f9,plain,(
% 0.11/0.40 p|sP0_prd),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.11/0.40 fof(f10,plain,(
% 0.11/0.40 ![X0]: (f(X0)|sP0_prd)),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.11/0.40 fof(f11,plain,(
% 0.11/0.40 ~p|~f(sK0_skl)|~sP0_prd),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.11/0.40 fof(f12,plain,(
% 0.11/0.40 (~sP0_prd|(p&(![Y]: f(Y))))&(sP0_prd|(~p|(?[Y]: ~f(Y))))),
% 0.11/0.40 inference(NNF_transformation,[status(thm)],[f4])).
% 0.11/0.40 fof(f13,plain,(
% 0.11/0.40 (~sP0_prd|(p&(![Y]: f(Y))))&(sP0_prd|(~p|~f(sK1_skl)))),
% 0.11/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl)],[f12])).
% 0.11/0.40 fof(f14,plain,(
% 0.11/0.40 ~sP0_prd|p),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.11/0.40 fof(f15,plain,(
% 0.11/0.40 ![X0]: (~sP0_prd|f(X0))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.11/0.40 fof(f16,plain,(
% 0.11/0.40 sP0_prd|~p|~f(sK1_skl)),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.11/0.40 fof(f17,definition,(
% 0.11/0.40 sQ0_spl <=> (p)),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f20,definition,(
% 0.11/0.40 sQ1_spl <=> (sP0_prd)),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f23,plain,(
% 0.11/0.40 sQ0_spl|sQ1_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f9,f17,f20])).
% 0.11/0.40 fof(f24,definition,(
% 0.11/0.40 ![X0]: (sQ2_spl <=> (f(X0)))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f25,plain,(
% 0.11/0.40 ![X0]: (f(X0)|~sQ2_spl)),
% 0.11/0.40 inference(component_clause,[status(thm)],[f24])).
% 0.11/0.40 fof(f27,plain,(
% 0.11/0.40 sQ2_spl|sQ1_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f10,f24,f20])).
% 0.11/0.40 fof(f28,definition,(
% 0.11/0.40 sQ3_spl <=> (f(sK0_skl))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f30,plain,(
% 0.11/0.40 ~f(sK0_skl)|sQ3_spl),
% 0.11/0.40 inference(component_clause,[status(thm)],[f28])).
% 0.11/0.40 fof(f31,plain,(
% 0.11/0.40 ~sQ0_spl|~sQ3_spl|~sQ1_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f11,f17,f28,f20])).
% 0.11/0.40 fof(f32,plain,(
% 0.11/0.40 ~sQ1_spl|sQ0_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f14,f20,f17])).
% 0.11/0.40 fof(f33,plain,(
% 0.11/0.40 ~sQ1_spl|sQ2_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f15,f20,f24])).
% 0.11/0.40 fof(f34,definition,(
% 0.11/0.40 sQ4_spl <=> (f(sK1_skl))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f36,plain,(
% 0.11/0.40 ~f(sK1_skl)|sQ4_spl),
% 0.11/0.40 inference(component_clause,[status(thm)],[f34])).
% 0.11/0.40 fof(f37,plain,(
% 0.11/0.40 sQ1_spl|~sQ0_spl|~sQ4_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f16,f20,f17,f34])).
% 0.11/0.40 fof(f38,plain,(
% 0.11/0.40 $false|~sQ2_spl|sQ4_spl),
% 0.11/0.40 inference(forward_subsumption_resolution,[status(thm)],[f36,f25])).
% 0.11/0.40 fof(f39,plain,(
% 0.11/0.40 ~sQ2_spl|sQ4_spl),
% 0.11/0.40 inference(contradiction_clause,[status(thm)],[f38])).
% 0.11/0.40 fof(f40,plain,(
% 0.11/0.40 $false|~sQ2_spl|sQ3_spl),
% 0.11/0.40 inference(forward_subsumption_resolution,[status(thm)],[f30,f25])).
% 0.11/0.40 fof(f41,plain,(
% 0.11/0.40 ~sQ2_spl|sQ3_spl),
% 0.11/0.40 inference(contradiction_clause,[status(thm)],[f40])).
% 0.11/0.40 fof(f42,plain,(
% 0.11/0.40 $false),
% 0.11/0.40 inference(sat_refutation,[status(thm)],[f23,f27,f31,f32,f33,f37,f39,f41])).
% 0.11/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.42 % Elapsed time: 0.047333 seconds
% 0.11/0.42 % CPU time: 0.109692 seconds
% 0.11/0.42 % Total memory used: 16.525 MB
% 0.11/0.42 % Net memory used: 15.935 MB
%------------------------------------------------------------------------------