%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 10:52:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.38 fof(f1,conjecture,(
% 0.13/0.38 ( (? [X] :(! [Y] :( big_p(X)<=> big_p(Y) )))<=> ( (? [X] : big_p(X))<=> (! [Y] : big_p(Y) )) ) ),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f2,negated_conjecture,(
% 0.13/0.38 ~(( (? [X] :(! [Y] :( big_p(X)<=> big_p(Y) )))<=> ( (? [X] : big_p(X))<=> (! [Y] : big_p(Y) )) ) )),
% 0.13/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.13/0.38 fof(f3,plain,(
% 0.13/0.38 ((?[X]: ![Y]: (big_p(X)<=>big_p(Y)))<~>((?[X]: big_p(X))<=>(![Y]: big_p(Y))))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.38 fof(f4,definition,(
% 0.13/0.38 ![X,Y]: (sP0_prd(Y,X)<=>(big_p(X)<=>big_p(Y)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.38 fof(f5,plain,(
% 0.13/0.38 (?[X]: ![Y]: sP0_prd(Y,X))<~>((?[X]: big_p(X))<=>(![Y]: big_p(Y)))),
% 0.13/0.38 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.13/0.38 fof(f6,plain,(
% 0.13/0.38 ((?[X]: ![Y]: sP0_prd(Y,X))|(((![X]: ~big_p(X))|(![Y]: big_p(Y)))&((?[X]: big_p(X))|(?[Y]: ~big_p(Y)))))&((![X]: ?[Y]: ~sP0_prd(Y,X))|(((![X]: ~big_p(X))|(?[Y]: ~big_p(Y)))&((?[X]: big_p(X))|(![Y]: big_p(Y)))))),
% 0.13/0.38 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.38 fof(f7,plain,(
% 0.13/0.38 (![Y]: sP0_prd(Y,sK0_skl)|(((![X]: ~big_p(X))|(![Y]: big_p(Y)))&(big_p(sK1_skl)|~big_p(sK2_skl))))&((![X]: ~sP0_prd(sK3_skl(X),X))|(((![X]: ~big_p(X))|~big_p(sK4_skl))&(big_p(sK5_skl)|(![Y]: big_p(Y)))))),
% 0.13/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(Y,sK2_skl),skolemize(Y,sK3_skl(X)),skolemize(Y,sK4_skl),skolemize(X,sK5_skl)],[f6])).
% 0.13/0.38 fof(f8,plain,(
% 0.13/0.38 ![X0,X1,X2]: (sP0_prd(X0,sK0_skl)|~big_p(X1)|big_p(X2))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.38 fof(f10,plain,(
% 0.13/0.38 ![X0,X1]: (~sP0_prd(sK3_skl(X0),X0)|~big_p(X1)|~big_p(sK4_skl))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.38 fof(f11,plain,(
% 0.13/0.38 ![X0,X1]: (~sP0_prd(sK3_skl(X0),X0)|big_p(sK5_skl)|big_p(X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.38 fof(f12,plain,(
% 0.13/0.38 ![X,Y]: ((~sP0_prd(Y,X)|((~big_p(X)|big_p(Y))&(big_p(X)|~big_p(Y))))&(sP0_prd(Y,X)|((~big_p(X)|~big_p(Y))&(big_p(X)|big_p(Y)))))),
% 0.13/0.38 inference(NNF_transformation,[status(thm)],[f4])).
% 0.13/0.38 fof(f13,plain,(
% 0.13/0.38 (![X,Y]: (~sP0_prd(Y,X)|((~big_p(X)|big_p(Y))&(big_p(X)|~big_p(Y)))))&(![X,Y]: (sP0_prd(Y,X)|((~big_p(X)|~big_p(Y))&(big_p(X)|big_p(Y)))))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f12])).
% 0.13/0.38 fof(f14,plain,(
% 0.13/0.38 ![X0,X1]: (~sP0_prd(X0,X1)|~big_p(X1)|big_p(X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.38 fof(f15,plain,(
% 0.13/0.38 ![X0,X1]: (~sP0_prd(X0,X1)|big_p(X1)|~big_p(X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.38 fof(f16,plain,(
% 0.13/0.38 ![X0,X1]: (sP0_prd(X0,X1)|~big_p(X1)|~big_p(X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.38 fof(f17,plain,(
% 0.13/0.38 ![X0,X1]: (sP0_prd(X0,X1)|big_p(X1)|big_p(X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.38 fof(f18,definition,(
% 0.13/0.38 ![X0]: (sQ0_spl <=> (sP0_prd(X0,sK0_skl)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f19,plain,(
% 0.13/0.38 ![X0]: (sP0_prd(X0,sK0_skl)|~sQ0_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f18])).
% 0.13/0.38 fof(f21,definition,(
% 0.13/0.38 ![X1]: (sQ1_spl <=> (~big_p(X1)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f22,plain,(
% 0.13/0.38 ![X0]: (~big_p(X0)|~sQ1_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f21])).
% 0.13/0.38 fof(f24,definition,(
% 0.13/0.38 ![X2]: (sQ2_spl <=> (big_p(X2)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f25,plain,(
% 0.13/0.38 ![X0]: (big_p(X0)|~sQ2_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f24])).
% 0.13/0.38 fof(f27,plain,(
% 0.13/0.38 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f8,f18,f21,f24])).
% 0.13/0.38 fof(f35,definition,(
% 0.13/0.38 ![X0]: (sQ5_spl <=> (~sP0_prd(sK3_skl(X0),X0)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f36,plain,(
% 0.13/0.38 ![X0]: (~sP0_prd(sK3_skl(X0),X0)|~sQ5_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f35])).
% 0.13/0.38 fof(f38,definition,(
% 0.13/0.38 sQ6_spl <=> (big_p(sK4_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f40,plain,(
% 0.13/0.38 ~big_p(sK4_skl)|sQ6_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f38])).
% 0.13/0.38 fof(f41,plain,(
% 0.13/0.38 sQ5_spl|sQ1_spl|~sQ6_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f10,f35,f21,f38])).
% 0.13/0.38 fof(f42,definition,(
% 0.13/0.38 sQ7_spl <=> (big_p(sK5_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f43,plain,(
% 0.13/0.38 big_p(sK5_skl)|~sQ7_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f42])).
% 0.13/0.38 fof(f45,plain,(
% 0.13/0.38 sQ5_spl|sQ7_spl|sQ2_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f11,f35,f42,f24])).
% 0.13/0.38 fof(f46,plain,(
% 0.13/0.38 $false|~sQ2_spl|~sQ1_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f22,f25])).
% 0.13/0.38 fof(f47,plain,(
% 0.13/0.38 ~sQ2_spl|~sQ1_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f46])).
% 0.13/0.38 fof(f48,plain,(
% 0.13/0.38 $false|~sQ5_spl|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f36,f19])).
% 0.13/0.38 fof(f49,plain,(
% 0.13/0.38 ~sQ5_spl|~sQ0_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f48])).
% 0.13/0.38 fof(f50,plain,(
% 0.13/0.38 $false|~sQ1_spl|~sQ7_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f43,f22])).
% 0.13/0.38 fof(f51,plain,(
% 0.13/0.38 ~sQ1_spl|~sQ7_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f50])).
% 0.13/0.38 fof(f52,plain,(
% 0.13/0.38 $false|~sQ2_spl|sQ6_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f40,f25])).
% 0.13/0.38 fof(f53,plain,(
% 0.13/0.38 ~sQ2_spl|sQ6_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f52])).
% 0.13/0.38 fof(f55,plain,(
% 0.13/0.38 ![X0]: (~sP0_prd(sK5_skl,X0)|big_p(X0)|~sQ7_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f43,f15])).
% 0.13/0.38 fof(f57,plain,(
% 0.13/0.38 big_p(sK0_skl)|~sQ7_spl|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f55,f19])).
% 0.13/0.38 fof(f60,plain,(
% 0.13/0.38 ![X0]: (~sP0_prd(sK0_skl,X0)|big_p(X0)|~sQ7_spl|~sQ0_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f57,f15])).
% 0.13/0.38 fof(f63,definition,(
% 0.13/0.38 sQ8_spl <=> (big_p(sK0_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f64,plain,(
% 0.13/0.38 big_p(sK0_skl)|~sQ8_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f63])).
% 0.13/0.38 fof(f67,plain,(
% 0.13/0.38 ![X0]: (big_p(X0)|big_p(sK0_skl)|big_p(X0)|~sQ7_spl|~sQ0_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f17,f60])).
% 0.13/0.38 fof(f69,definition,(
% 0.13/0.38 ![X0]: (sQ9_spl <=> (big_p(X0)|big_p(X0)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f70,plain,(
% 0.13/0.38 ![X0]: (big_p(X0)|big_p(X0)|~sQ9_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f69])).
% 0.13/0.38 fof(f72,plain,(
% 0.13/0.38 sQ9_spl|sQ8_spl|~sQ7_spl|~sQ0_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f67,f69,f63,f42,f18])).
% 0.13/0.38 fof(f74,plain,(
% 0.13/0.38 ![X0]: (big_p(X0)|~sQ9_spl)),
% 0.13/0.38 inference(duplicate_literals_removal,[status(thm)],[f70])).
% 0.13/0.38 fof(f77,plain,(
% 0.13/0.38 $false|~sQ9_spl|sQ6_spl),
% 0.13/0.38 inference(backward_subsumption_resolution,[status(thm)],[f40,f74])).
% 0.13/0.38 fof(f79,plain,(
% 0.13/0.38 ~sQ9_spl|sQ6_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f77])).
% 0.13/0.38 fof(f96,plain,(
% 0.13/0.38 ![X0]: (~sP0_prd(X0,sK0_skl)|big_p(X0)|~sQ8_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f14,f64])).
% 0.13/0.38 fof(f97,plain,(
% 0.13/0.38 ![X0]: (big_p(X0)|~sQ0_spl|~sQ8_spl)),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f96,f19])).
% 0.13/0.38 fof(f99,plain,(
% 0.13/0.38 $false|~sQ0_spl|~sQ8_spl|sQ6_spl),
% 0.13/0.38 inference(backward_subsumption_resolution,[status(thm)],[f40,f97])).
% 0.13/0.38 fof(f102,plain,(
% 0.13/0.38 ~sQ0_spl|~sQ8_spl|sQ6_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f99])).
% 0.13/0.38 fof(f107,plain,(
% 0.13/0.38 ![X0,X1]: (sP0_prd(X0,X1)|~big_p(X0)|~sQ2_spl)),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f16,f25])).
% 0.13/0.38 fof(f108,plain,(
% 0.13/0.38 ![X0,X1]: (sP0_prd(X0,X1)|~sQ2_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f107,f25])).
% 0.13/0.38 fof(f109,plain,(
% 0.13/0.38 $false|~sQ2_spl|~sQ5_spl),
% 0.13/0.38 inference(backward_subsumption_resolution,[status(thm)],[f36,f108])).
% 0.13/0.38 fof(f110,plain,(
% 0.13/0.38 ~sQ2_spl|~sQ5_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f109])).
% 0.13/0.38 fof(f111,plain,(
% 0.13/0.38 ![X0,X1]: (sP0_prd(X0,X1)|big_p(X0)|~sQ1_spl)),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f17,f22])).
% 0.13/0.38 fof(f112,plain,(
% 0.13/0.38 ![X0]: (big_p(sK3_skl(X0))|~sQ1_spl|~sQ5_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f111,f36])).
% 0.13/0.38 fof(f113,plain,(
% 0.13/0.38 $false|~sQ1_spl|~sQ5_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f112,f22])).
% 0.13/0.38 fof(f114,plain,(
% 0.13/0.38 ~sQ1_spl|~sQ5_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f113])).
% 0.13/0.38 fof(f115,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f27,f41,f45,f47,f49,f51,f53,f72,f79,f102,f110,f114])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.40 % Elapsed time: 0.035653 seconds
% 0.13/0.40 % CPU time: 0.065334 seconds
% 0.13/0.40 % Total memory used: 6.793 MB
% 0.13/0.40 % Net memory used: 6.631 MB
%------------------------------------------------------------------------------