%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN377+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 : 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 03:19:30 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN377+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
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 10:52:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.38 fof(f1,conjecture,(
% 0.12/0.38 ( (! [X] :( big_p(X)<=> (! [Y] : big_p(Y) )))<=> ( (? [X] : big_p(X))<=> (! [Y] : big_p(Y) )) ) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f2,negated_conjecture,(
% 0.12/0.38 ~(( (! [X] :( big_p(X)<=> (! [Y] : big_p(Y) )))<=> ( (? [X] : big_p(X))<=> (! [Y] : big_p(Y) )) ) )),
% 0.12/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.12/0.38 fof(f3,plain,(
% 0.12/0.38 ((![X]: (big_p(X)<=>(![Y]: big_p(Y))))<~>((?[X]: big_p(X))<=>(![Y]: big_p(Y))))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.12/0.38 fof(f4,definition,(
% 0.12/0.38 ![X]: (sP0_prd(X)<=>(big_p(X)<=>(![Y]: big_p(Y))))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.38 fof(f5,plain,(
% 0.12/0.38 (![X]: sP0_prd(X))<~>((?[X]: big_p(X))<=>(![Y]: big_p(Y)))),
% 0.12/0.38 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.12/0.38 fof(f6,plain,(
% 0.12/0.38 ((![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)))))),
% 0.12/0.38 inference(NNF_transformation,[status(thm)],[f5])).
% 0.12/0.38 fof(f7,plain,(
% 0.12/0.38 ((![X]: sP0_prd(X))|(((![X]: ~big_p(X))|(![Y]: big_p(Y)))&(big_p(sK0_skl)|~big_p(sK1_skl))))&(~sP0_prd(sK2_skl)|(((![X]: ~big_p(X))|~big_p(sK3_skl))&(big_p(sK4_skl)|(![Y]: big_p(Y)))))),
% 0.12/0.38 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(Y,sK3_skl),skolemize(X,sK4_skl)],[f6])).
% 0.12/0.38 fof(f8,plain,(
% 0.12/0.38 ![X0,X1,X2]: (sP0_prd(X0)|~big_p(X1)|big_p(X2))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.38 fof(f10,plain,(
% 0.12/0.38 ![X0]: (~sP0_prd(sK2_skl)|~big_p(X0)|~big_p(sK3_skl))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.38 fof(f11,plain,(
% 0.12/0.38 ![X0]: (~sP0_prd(sK2_skl)|big_p(sK4_skl)|big_p(X0))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.38 fof(f12,plain,(
% 0.12/0.38 ![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))))))),
% 0.12/0.38 inference(NNF_transformation,[status(thm)],[f4])).
% 0.12/0.38 fof(f13,plain,(
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f12])).
% 0.12/0.38 fof(f14,plain,(
% 0.12/0.38 (![X]: (~sP0_prd(X)|((~big_p(X)|(![Y]: big_p(Y)))&(big_p(X)|~big_p(sK5_skl(X))))))&(![X]: (sP0_prd(X)|((~big_p(X)|~big_p(sK6_skl(X)))&(big_p(X)|(![Y]: big_p(Y))))))),
% 0.12/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Y,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f13])).
% 0.12/0.38 fof(f15,plain,(
% 0.12/0.38 ![X0,X1]: (~sP0_prd(X0)|~big_p(X0)|big_p(X1))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.12/0.38 fof(f17,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|~big_p(X0)|~big_p(sK6_skl(X0)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.12/0.38 fof(f18,plain,(
% 0.12/0.38 ![X0,X1]: (sP0_prd(X0)|big_p(X0)|big_p(X1))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.12/0.38 fof(f19,definition,(
% 0.12/0.38 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f20,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.12/0.38 inference(component_clause,[status(thm)],[f19])).
% 0.12/0.38 fof(f22,definition,(
% 0.12/0.38 ![X1]: (sQ1_spl <=> (~big_p(X1)))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f23,plain,(
% 0.12/0.38 ![X0]: (~big_p(X0)|~sQ1_spl)),
% 0.12/0.38 inference(component_clause,[status(thm)],[f22])).
% 0.12/0.38 fof(f25,definition,(
% 0.12/0.38 ![X2]: (sQ2_spl <=> (big_p(X2)))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f26,plain,(
% 0.12/0.38 ![X0]: (big_p(X0)|~sQ2_spl)),
% 0.12/0.38 inference(component_clause,[status(thm)],[f25])).
% 0.12/0.38 fof(f28,plain,(
% 0.12/0.38 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f8,f19,f22,f25])).
% 0.12/0.38 fof(f36,definition,(
% 0.12/0.38 sQ5_spl <=> (sP0_prd(sK2_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f38,plain,(
% 0.12/0.38 ~sP0_prd(sK2_skl)|sQ5_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f36])).
% 0.12/0.38 fof(f39,definition,(
% 0.12/0.38 sQ6_spl <=> (big_p(sK3_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f41,plain,(
% 0.12/0.38 ~big_p(sK3_skl)|sQ6_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f39])).
% 0.12/0.38 fof(f42,plain,(
% 0.12/0.38 ~sQ5_spl|sQ1_spl|~sQ6_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f10,f36,f22,f39])).
% 0.12/0.38 fof(f43,definition,(
% 0.12/0.38 sQ7_spl <=> (big_p(sK4_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f44,plain,(
% 0.12/0.38 big_p(sK4_skl)|~sQ7_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f43])).
% 0.12/0.38 fof(f46,plain,(
% 0.12/0.38 ~sQ5_spl|sQ7_spl|sQ2_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f11,f36,f43,f25])).
% 0.12/0.38 fof(f47,definition,(
% 0.12/0.38 ![X0]: (sQ8_spl <=> (~sP0_prd(X0)|~big_p(X0)))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f48,plain,(
% 0.12/0.38 ![X0]: (~sP0_prd(X0)|~big_p(X0)|~sQ8_spl)),
% 0.12/0.38 inference(component_clause,[status(thm)],[f47])).
% 0.12/0.38 fof(f50,plain,(
% 0.12/0.38 sQ8_spl|sQ2_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f15,f47,f25])).
% 0.12/0.38 fof(f51,definition,(
% 0.12/0.38 ![X0]: (sQ9_spl <=> (sP0_prd(X0)|big_p(X0)))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f52,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|big_p(X0)|~sQ9_spl)),
% 0.12/0.38 inference(component_clause,[status(thm)],[f51])).
% 0.12/0.38 fof(f54,plain,(
% 0.12/0.38 sQ9_spl|sQ2_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f18,f51,f25])).
% 0.12/0.38 fof(f55,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|~big_p(X0)|~sQ2_spl)),
% 0.12/0.38 inference(backward_subsumption_resolution,[status(thm)],[f17,f26])).
% 0.12/0.38 fof(f56,plain,(
% 0.12/0.38 $false|~sQ2_spl|~sQ1_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f23,f26])).
% 0.12/0.38 fof(f57,plain,(
% 0.12/0.38 ~sQ2_spl|~sQ1_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f56])).
% 0.12/0.38 fof(f58,plain,(
% 0.12/0.38 $false|~sQ0_spl|sQ5_spl),
% 0.12/0.38 inference(backward_subsumption_resolution,[status(thm)],[f38,f20])).
% 0.12/0.38 fof(f59,plain,(
% 0.12/0.38 ![X0]: (~big_p(X0)|~sQ0_spl|~sQ8_spl)),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f48,f20])).
% 0.12/0.38 fof(f60,plain,(
% 0.12/0.38 ~sQ0_spl|sQ5_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f58])).
% 0.12/0.38 fof(f61,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|~sQ2_spl)),
% 0.12/0.38 inference(backward_subsumption_resolution,[status(thm)],[f55,f26])).
% 0.12/0.38 fof(f62,plain,(
% 0.12/0.38 sQ0_spl|~sQ2_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f61,f19,f25])).
% 0.12/0.38 fof(f63,plain,(
% 0.12/0.38 $false|~sQ0_spl|~sQ8_spl|~sQ7_spl),
% 0.12/0.38 inference(backward_subsumption_resolution,[status(thm)],[f44,f59])).
% 0.12/0.38 fof(f65,plain,(
% 0.12/0.38 ~sQ0_spl|~sQ8_spl|~sQ7_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f63])).
% 0.12/0.38 fof(f67,plain,(
% 0.12/0.38 ![X0]: (sP0_prd(X0)|~sQ1_spl|~sQ9_spl)),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f52,f23])).
% 0.12/0.38 fof(f68,plain,(
% 0.12/0.38 $false|~sQ1_spl|~sQ9_spl|sQ5_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f38,f67])).
% 0.12/0.38 fof(f69,plain,(
% 0.12/0.38 ~sQ1_spl|~sQ9_spl|sQ5_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f68])).
% 0.12/0.38 fof(f71,plain,(
% 0.12/0.38 $false|~sQ2_spl|sQ6_spl),
% 0.12/0.38 inference(backward_subsumption_resolution,[status(thm)],[f41,f26])).
% 0.12/0.38 fof(f73,plain,(
% 0.12/0.38 ~sQ2_spl|sQ6_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f71])).
% 0.12/0.38 fof(f76,plain,(
% 0.12/0.38 $false|~sQ1_spl|~sQ7_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f44,f23])).
% 0.12/0.38 fof(f77,plain,(
% 0.12/0.38 ~sQ1_spl|~sQ7_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f76])).
% 0.12/0.38 fof(f78,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(sat_refutation,[status(thm)],[f28,f42,f46,f50,f54,f57,f60,f62,f65,f69,f73,f77])).
% 0.12/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.041554 seconds
% 0.12/0.41 % CPU time: 0.114014 seconds
% 0.12/0.41 % Total memory used: 16.673 MB
% 0.12/0.41 % Net memory used: 16.129 MB
%------------------------------------------------------------------------------