%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN375+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 : 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 03:19:30 PM UTC 2026
% Result : Theorem 0.09s 5.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN375+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
% 0.09/5.53 % Computer : n020.cluster.edu
% 0.09/5.53 % Model : x86_64 x86_64
% 0.09/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.53 % Memory : 8046.5625MB
% 0.09/5.53 % OS : Linux 6.8.0-71-generic
% 0.09/5.53 % CPULimit : 300
% 0.09/5.53 % WCLimit : 300
% 0.09/5.53 % DateTime : Mon Sep 21 10:53:08 UTC 2026
% 0.09/5.53 % CPUTime :
% 0.09/5.54 % Drodi V4.1.1
% 0.09/5.55 % Refutation found
% 0.09/5.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.55 % SZS output start CNFRefutation for theBenchmark
% 0.09/5.55 fof(f1,conjecture,(
% 0.09/5.55 ( (! [X] :( big_p(X)<=> (? [Y] : big_p(Y) )))<=> ( (! [X] : big_p(X))<=> (? [Y] : big_p(Y) )) ) ),
% 0.09/5.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.55 fof(f2,negated_conjecture,(
% 0.09/5.55 ~(( (! [X] :( big_p(X)<=> (? [Y] : big_p(Y) )))<=> ( (! [X] : big_p(X))<=> (? [Y] : big_p(Y) )) ) )),
% 0.09/5.55 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/5.55 fof(f3,plain,(
% 0.09/5.55 ((![X]: (big_p(X)<=>(?[Y]: big_p(Y))))<~>((![X]: big_p(X))<=>(?[Y]: big_p(Y))))),
% 0.09/5.55 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/5.55 fof(f4,definition,(
% 0.09/5.55 ![X]: (sP0_prd(X)<=>(big_p(X)<=>(?[Y]: big_p(Y))))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/5.55 fof(f5,plain,(
% 0.09/5.55 (![X]: sP0_prd(X))<~>((![X]: big_p(X))<=>(?[Y]: big_p(Y)))),
% 0.09/5.55 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.09/5.55 fof(f6,plain,(
% 0.09/5.55 ((![X]: sP0_prd(X))|(((?[X]: ~big_p(X))|(?[Y]: big_p(Y)))&((![X]: big_p(X))|(![Y]: ~big_p(Y)))))&((?[X]: ~sP0_prd(X))|(((?[X]: ~big_p(X))|(![Y]: ~big_p(Y)))&((![X]: big_p(X))|(?[Y]: big_p(Y)))))),
% 0.09/5.55 inference(NNF_transformation,[status(thm)],[f5])).
% 0.09/5.55 fof(f7,plain,(
% 0.09/5.55 ((![X]: sP0_prd(X))|((~big_p(sK0_skl)|big_p(sK1_skl))&((![X]: big_p(X))|(![Y]: ~big_p(Y)))))&(~sP0_prd(sK2_skl)|((~big_p(sK3_skl)|(![Y]: ~big_p(Y)))&((![X]: big_p(X))|big_p(sK4_skl))))),
% 0.09/5.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(Y,sK4_skl)],[f6])).
% 0.09/5.55 fof(f9,plain,(
% 0.09/5.55 ![X0,X1,X2]: (sP0_prd(X0)|big_p(X1)|~big_p(X2))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/5.55 fof(f10,plain,(
% 0.09/5.55 ![X0]: (~sP0_prd(sK2_skl)|~big_p(sK3_skl)|~big_p(X0))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/5.55 fof(f11,plain,(
% 0.09/5.55 ![X0]: (~sP0_prd(sK2_skl)|big_p(X0)|big_p(sK4_skl))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/5.55 fof(f12,plain,(
% 0.09/5.55 ![X]: ((~sP0_prd(X)|((~big_p(X)|(?[Y]: big_p(Y)))&(big_p(X)|(![Y]: ~big_p(Y)))))&(sP0_prd(X)|((~big_p(X)|(![Y]: ~big_p(Y)))&(big_p(X)|(?[Y]: big_p(Y))))))),
% 0.09/5.55 inference(NNF_transformation,[status(thm)],[f4])).
% 0.09/5.55 fof(f13,plain,(
% 0.09/5.55 (![X]: (~sP0_prd(X)|((~big_p(X)|(?[Y]: big_p(Y)))&(big_p(X)|(![Y]: ~big_p(Y))))))&(![X]: (sP0_prd(X)|((~big_p(X)|(![Y]: ~big_p(Y)))&(big_p(X)|(?[Y]: big_p(Y))))))),
% 0.09/5.55 inference(miniscoping,[status(thm)],[f12])).
% 0.09/5.55 fof(f14,plain,(
% 0.09/5.55 (![X]: (~sP0_prd(X)|((~big_p(X)|big_p(sK5_skl(X)))&(big_p(X)|(![Y]: ~big_p(Y))))))&(![X]: (sP0_prd(X)|((~big_p(X)|(![Y]: ~big_p(Y)))&(big_p(X)|big_p(sK6_skl(X))))))),
% 0.09/5.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Y,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f13])).
% 0.09/5.55 fof(f16,plain,(
% 0.09/5.55 ![X0,X1]: (~sP0_prd(X0)|big_p(X0)|~big_p(X1))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/5.55 fof(f17,plain,(
% 0.09/5.55 ![X0,X1]: (sP0_prd(X0)|~big_p(X0)|~big_p(X1))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/5.55 fof(f18,plain,(
% 0.09/5.55 ![X0]: (sP0_prd(X0)|big_p(X0)|big_p(sK6_skl(X0)))),
% 0.09/5.55 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/5.55 fof(f19,definition,(
% 0.09/5.55 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f20,plain,(
% 0.09/5.55 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.09/5.55 inference(component_clause,[status(thm)],[f19])).
% 0.09/5.55 fof(f29,definition,(
% 0.09/5.55 ![X1]: (sQ3_spl <=> (big_p(X1)))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f30,plain,(
% 0.09/5.55 ![X0]: (big_p(X0)|~sQ3_spl)),
% 0.09/5.55 inference(component_clause,[status(thm)],[f29])).
% 0.09/5.55 fof(f32,definition,(
% 0.09/5.55 ![X2]: (sQ4_spl <=> (~big_p(X2)))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f33,plain,(
% 0.09/5.55 ![X0]: (~big_p(X0)|~sQ4_spl)),
% 0.09/5.55 inference(component_clause,[status(thm)],[f32])).
% 0.09/5.55 fof(f35,plain,(
% 0.09/5.55 sQ0_spl|sQ3_spl|sQ4_spl),
% 0.09/5.55 inference(split_clause,[status(thm)],[f9,f19,f29,f32])).
% 0.09/5.55 fof(f36,definition,(
% 0.09/5.55 sQ5_spl <=> (sP0_prd(sK2_skl))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f38,plain,(
% 0.09/5.55 ~sP0_prd(sK2_skl)|sQ5_spl),
% 0.09/5.55 inference(component_clause,[status(thm)],[f36])).
% 0.09/5.55 fof(f39,definition,(
% 0.09/5.55 sQ6_spl <=> (big_p(sK3_skl))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f41,plain,(
% 0.09/5.55 ~big_p(sK3_skl)|sQ6_spl),
% 0.09/5.55 inference(component_clause,[status(thm)],[f39])).
% 0.09/5.55 fof(f42,plain,(
% 0.09/5.55 ~sQ5_spl|~sQ6_spl|sQ4_spl),
% 0.09/5.55 inference(split_clause,[status(thm)],[f10,f36,f39,f32])).
% 0.09/5.55 fof(f43,definition,(
% 0.09/5.55 sQ7_spl <=> (big_p(sK4_skl))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f44,plain,(
% 0.09/5.55 big_p(sK4_skl)|~sQ7_spl),
% 0.09/5.55 inference(component_clause,[status(thm)],[f43])).
% 0.09/5.55 fof(f46,plain,(
% 0.09/5.55 ~sQ5_spl|sQ3_spl|sQ7_spl),
% 0.09/5.55 inference(split_clause,[status(thm)],[f11,f36,f29,f43])).
% 0.09/5.55 fof(f47,definition,(
% 0.09/5.55 ![X0]: (sQ8_spl <=> (~sP0_prd(X0)|big_p(X0)))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f48,plain,(
% 0.09/5.55 ![X0]: (~sP0_prd(X0)|big_p(X0)|~sQ8_spl)),
% 0.09/5.55 inference(component_clause,[status(thm)],[f47])).
% 0.09/5.55 fof(f50,plain,(
% 0.09/5.55 sQ8_spl|sQ4_spl),
% 0.09/5.55 inference(split_clause,[status(thm)],[f16,f47,f32])).
% 0.09/5.55 fof(f51,definition,(
% 0.09/5.55 ![X0]: (sQ9_spl <=> (sP0_prd(X0)|~big_p(X0)))),
% 0.09/5.55 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/5.55 fof(f52,plain,(
% 0.09/5.55 ![X0]: (sP0_prd(X0)|~big_p(X0)|~sQ9_spl)),
% 0.09/5.55 inference(component_clause,[status(thm)],[f51])).
% 0.09/5.55 fof(f54,plain,(
% 0.09/5.55 sQ9_spl|sQ4_spl),
% 0.09/5.55 inference(split_clause,[status(thm)],[f17,f51,f32])).
% 0.09/5.55 fof(f55,plain,(
% 0.09/5.55 $false|~sQ4_spl|~sQ3_spl),
% 0.09/5.55 inference(forward_subsumption_resolution,[status(thm)],[f30,f33])).
% 0.09/5.55 fof(f56,plain,(
% 0.09/5.55 ~sQ4_spl|~sQ3_spl),
% 0.09/5.55 inference(contradiction_clause,[status(thm)],[f55])).
% 0.09/5.55 fof(f58,plain,(
% 0.09/5.55 $false|~sQ0_spl|sQ5_spl),
% 0.09/5.55 inference(forward_subsumption_resolution,[status(thm)],[f38,f20])).
% 0.09/5.55 fof(f59,plain,(
% 0.09/5.55 ~sQ0_spl|sQ5_spl),
% 0.09/5.55 inference(contradiction_clause,[status(thm)],[f58])).
% 0.09/5.55 fof(f60,plain,(
% 0.09/5.55 ![X0]: (sP0_prd(X0)|big_p(sK6_skl(X0))|~sQ4_spl)),
% 0.09/5.55 inference(forward_subsumption_resolution,[status(thm)],[f18,f33])).
% 0.09/5.56 fof(f61,plain,(
% 0.09/5.56 ![X0]: (sP0_prd(X0)|~sQ4_spl)),
% 0.09/5.56 inference(resolution,[status(thm)],[f60,f33])).
% 0.09/5.56 fof(f62,plain,(
% 0.09/5.56 sQ0_spl|~sQ4_spl),
% 0.09/5.56 inference(split_clause,[status(thm)],[f61,f19,f32])).
% 0.09/5.56 fof(f63,plain,(
% 0.09/5.56 $false|~sQ4_spl|~sQ7_spl),
% 0.09/5.56 inference(forward_subsumption_resolution,[status(thm)],[f44,f33])).
% 0.09/5.56 fof(f64,plain,(
% 0.09/5.56 ~sQ4_spl|~sQ7_spl),
% 0.09/5.56 inference(contradiction_clause,[status(thm)],[f63])).
% 0.09/5.56 fof(f67,plain,(
% 0.09/5.56 $false|~sQ0_spl|~sQ8_spl|sQ6_spl),
% 0.09/5.56 inference(backward_subsumption_resolution,[status(thm)],[f41,f68])).
% 0.09/5.56 fof(f68,plain,(
% 0.09/5.56 ![X0]: (big_p(X0)|~sQ0_spl|~sQ8_spl)),
% 0.09/5.56 inference(forward_subsumption_resolution,[status(thm)],[f48,f20])).
% 0.09/5.56 fof(f69,plain,(
% 0.09/5.56 ~sQ0_spl|~sQ8_spl|sQ6_spl),
% 0.09/5.56 inference(contradiction_clause,[status(thm)],[f67])).
% 0.09/5.56 fof(f72,plain,(
% 0.09/5.56 ![X0]: (sP0_prd(X0)|~sQ3_spl|~sQ9_spl)),
% 0.09/5.56 inference(backward_subsumption_resolution,[status(thm)],[f52,f30])).
% 0.09/5.56 fof(f73,plain,(
% 0.09/5.56 sQ0_spl|~sQ3_spl|~sQ9_spl),
% 0.09/5.56 inference(split_clause,[status(thm)],[f72,f19,f29,f51])).
% 0.09/5.56 fof(f74,plain,(
% 0.09/5.56 $false),
% 0.09/5.56 inference(sat_refutation,[status(thm)],[f35,f42,f46,f50,f54,f56,f59,f62,f64,f69,f73])).
% 0.09/5.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/5.58 % Elapsed time: 0.038955 seconds
% 0.09/5.58 % CPU time: 0.099344 seconds
% 0.09/5.58 % Total memory used: 14.602 MB
% 0.09/5.58 % Net memory used: 14.130 MB
%------------------------------------------------------------------------------