%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN059+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 : n009.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 03:18:50 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN059+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 : n009.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 10:41:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.38 fof(f1,axiom,(
% 0.08/0.38 (? [X] : big_f(X) )),
% 0.08/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f2,axiom,(
% 0.08/0.38 (? [Y] : big_g(Y) )),
% 0.08/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f3,conjecture,(
% 0.08/0.38 ( ( (! [X] :( big_f(X)=> big_h(X) ))& (! [U] :( big_g(U)=> big_j(U) ) ))<=> (! [W,Y] :( ( big_f(W)& big_g(Y) )=> ( big_h(W)& big_j(Y) ) ) )) ),
% 0.08/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f4,negated_conjecture,(
% 0.08/0.38 ~(( ( (! [X] :( big_f(X)=> big_h(X) ))& (! [U] :( big_g(U)=> big_j(U) ) ))<=> (! [W,Y] :( ( big_f(W)& big_g(Y) )=> ( big_h(W)& big_j(Y) ) ) )) )),
% 0.08/0.38 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.38 fof(f5,plain,(
% 0.08/0.38 big_f(sK0_skl)),
% 0.08/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f1])).
% 0.08/0.38 fof(f6,plain,(
% 0.08/0.38 big_f(sK0_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.38 fof(f7,plain,(
% 0.08/0.38 big_g(sK1_skl)),
% 0.08/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl)],[f2])).
% 0.08/0.38 fof(f8,plain,(
% 0.08/0.38 big_g(sK1_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.38 fof(f9,plain,(
% 0.08/0.38 (((![X]: (~big_f(X)|big_h(X)))&(![U]: (~big_g(U)|big_j(U))))<~>(![W,Y]: ((~big_f(W)|~big_g(Y))|(big_h(W)&big_j(Y)))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.08/0.38 fof(f10,definition,(
% 0.08/0.38 ![X]: (sP0_prd(X)<=>(~big_f(X)|big_h(X)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.08/0.38 fof(f11,definition,(
% 0.08/0.38 ![U]: (sP1_prd(U)<=>(~big_g(U)|big_j(U)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.08/0.38 fof(f12,plain,(
% 0.08/0.38 ((![X]: sP0_prd(X))&(![U]: sP1_prd(U)))<~>(![W,Y]: ((~big_f(W)|~big_g(Y))|(big_h(W)&big_j(Y))))),
% 0.08/0.38 inference(formula_renaming,[status(thm)],[f9,f11,f10])).
% 0.08/0.38 fof(f13,plain,(
% 0.08/0.38 (((![X]: sP0_prd(X))&(![U]: sP1_prd(U)))|(![W,Y]: ((~big_f(W)|~big_g(Y))|(big_h(W)&big_j(Y)))))&(((?[X]: ~sP0_prd(X))|(?[U]: ~sP1_prd(U)))|(?[W,Y]: ((big_f(W)&big_g(Y))&(~big_h(W)|~big_j(Y)))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f12])).
% 0.08/0.38 fof(f14,plain,(
% 0.08/0.38 (((![X]: sP0_prd(X))&(![U]: sP1_prd(U)))|(![W,Y]: ((~big_f(W)|~big_g(Y))|(big_h(W)&big_j(Y)))))&((~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl))|((big_f(sK4_skl)&big_g(sK5_skl))&(~big_h(sK4_skl)|~big_j(sK5_skl))))),
% 0.08/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK2_skl),skolemize(U,sK3_skl),skolemize(W,sK4_skl),skolemize(Y,sK5_skl)],[f13])).
% 0.08/0.38 fof(f15,plain,(
% 0.08/0.38 ![X0,X1,X2]: (sP0_prd(X0)|~big_f(X1)|~big_g(X2)|big_h(X1))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.38 fof(f18,plain,(
% 0.08/0.38 ![X0,X1,X2]: (sP1_prd(X0)|~big_f(X1)|~big_g(X2)|big_j(X2))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.38 fof(f19,plain,(
% 0.08/0.38 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|big_f(sK4_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.38 fof(f20,plain,(
% 0.08/0.38 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|big_g(sK5_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.38 fof(f21,plain,(
% 0.08/0.38 ~sP0_prd(sK2_skl)|~sP1_prd(sK3_skl)|~big_h(sK4_skl)|~big_j(sK5_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.38 fof(f22,plain,(
% 0.08/0.38 ![X]: ((~sP0_prd(X)|(~big_f(X)|big_h(X)))&(sP0_prd(X)|(big_f(X)&~big_h(X))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f10])).
% 0.08/0.38 fof(f23,plain,(
% 0.08/0.38 (![X]: (~sP0_prd(X)|(~big_f(X)|big_h(X))))&(![X]: (sP0_prd(X)|(big_f(X)&~big_h(X))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f22])).
% 0.08/0.38 fof(f24,plain,(
% 0.08/0.38 ![X0]: (~sP0_prd(X0)|~big_f(X0)|big_h(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f23])).
% 0.08/0.38 fof(f25,plain,(
% 0.08/0.38 ![X0]: (sP0_prd(X0)|big_f(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f23])).
% 0.08/0.38 fof(f26,plain,(
% 0.08/0.38 ![X0]: (sP0_prd(X0)|~big_h(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f23])).
% 0.08/0.38 fof(f27,plain,(
% 0.08/0.38 ![U]: ((~sP1_prd(U)|(~big_g(U)|big_j(U)))&(sP1_prd(U)|(big_g(U)&~big_j(U))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f11])).
% 0.08/0.38 fof(f28,plain,(
% 0.08/0.38 (![U]: (~sP1_prd(U)|(~big_g(U)|big_j(U))))&(![U]: (sP1_prd(U)|(big_g(U)&~big_j(U))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f27])).
% 0.08/0.38 fof(f29,plain,(
% 0.08/0.38 ![X0]: (~sP1_prd(X0)|~big_g(X0)|big_j(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f28])).
% 0.08/0.38 fof(f30,plain,(
% 0.08/0.38 ![X0]: (sP1_prd(X0)|big_g(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f28])).
% 0.08/0.38 fof(f31,plain,(
% 0.08/0.38 ![X0]: (sP1_prd(X0)|~big_j(X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f28])).
% 0.08/0.38 fof(f32,definition,(
% 0.08/0.38 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f33,plain,(
% 0.08/0.38 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f32])).
% 0.08/0.38 fof(f35,definition,(
% 0.08/0.38 ![X1]: (sQ1_spl <=> (~big_f(X1)|big_h(X1)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f36,plain,(
% 0.08/0.38 ![X0]: (~big_f(X0)|big_h(X0)|~sQ1_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f35])).
% 0.08/0.38 fof(f38,definition,(
% 0.08/0.38 ![X2]: (sQ2_spl <=> (~big_g(X2)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f39,plain,(
% 0.08/0.38 ![X0]: (~big_g(X0)|~sQ2_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f38])).
% 0.08/0.38 fof(f41,plain,(
% 0.08/0.38 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.08/0.38 inference(split_clause,[status(thm)],[f15,f32,f35,f38])).
% 0.08/0.38 fof(f42,definition,(
% 0.08/0.38 ![X1]: (sQ3_spl <=> (~big_f(X1)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f43,plain,(
% 0.08/0.38 ![X0]: (~big_f(X0)|~sQ3_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f42])).
% 0.08/0.38 fof(f45,definition,(
% 0.08/0.38 ![X2]: (sQ4_spl <=> (~big_g(X2)|big_j(X2)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f46,plain,(
% 0.08/0.38 ![X0]: (~big_g(X0)|big_j(X0)|~sQ4_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f45])).
% 0.08/0.38 fof(f49,definition,(
% 0.08/0.38 ![X0]: (sQ5_spl <=> (sP1_prd(X0)))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f50,plain,(
% 0.08/0.38 ![X0]: (sP1_prd(X0)|~sQ5_spl)),
% 0.08/0.38 inference(component_clause,[status(thm)],[f49])).
% 0.08/0.38 fof(f53,plain,(
% 0.08/0.38 sQ5_spl|sQ3_spl|sQ4_spl),
% 0.08/0.38 inference(split_clause,[status(thm)],[f18,f49,f42,f45])).
% 0.08/0.38 fof(f54,definition,(
% 0.08/0.38 sQ6_spl <=> (sP0_prd(sK2_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f56,plain,(
% 0.08/0.38 ~sP0_prd(sK2_skl)|sQ6_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f54])).
% 0.08/0.38 fof(f57,definition,(
% 0.08/0.38 sQ7_spl <=> (sP1_prd(sK3_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f59,plain,(
% 0.08/0.38 ~sP1_prd(sK3_skl)|sQ7_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f57])).
% 0.08/0.38 fof(f60,definition,(
% 0.08/0.38 sQ8_spl <=> (big_f(sK4_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f61,plain,(
% 0.08/0.38 big_f(sK4_skl)|~sQ8_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f60])).
% 0.08/0.38 fof(f63,plain,(
% 0.08/0.38 ~sQ6_spl|~sQ7_spl|sQ8_spl),
% 0.08/0.38 inference(split_clause,[status(thm)],[f19,f54,f57,f60])).
% 0.08/0.38 fof(f64,definition,(
% 0.08/0.38 sQ9_spl <=> (big_g(sK5_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f65,plain,(
% 0.08/0.38 big_g(sK5_skl)|~sQ9_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f64])).
% 0.08/0.38 fof(f67,plain,(
% 0.08/0.38 ~sQ6_spl|~sQ7_spl|sQ9_spl),
% 0.08/0.38 inference(split_clause,[status(thm)],[f20,f54,f57,f64])).
% 0.08/0.38 fof(f68,definition,(
% 0.08/0.38 sQ10_spl <=> (big_h(sK4_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f70,plain,(
% 0.08/0.38 ~big_h(sK4_skl)|sQ10_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f68])).
% 0.08/0.38 fof(f71,definition,(
% 0.08/0.38 sQ11_spl <=> (big_j(sK5_skl))),
% 0.08/0.38 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.08/0.38 fof(f73,plain,(
% 0.08/0.38 ~big_j(sK5_skl)|sQ11_spl),
% 0.08/0.38 inference(component_clause,[status(thm)],[f71])).
% 0.08/0.38 fof(f74,plain,(
% 0.08/0.38 ~sQ6_spl|~sQ7_spl|~sQ10_spl|~sQ11_spl),
% 0.08/0.38 inference(split_clause,[status(thm)],[f21,f54,f57,f68,f71])).
% 0.08/0.38 fof(f75,plain,(
% 0.08/0.38 $false|~sQ5_spl|sQ7_spl),
% 0.08/0.38 inference(forward_subsumption_resolution,[status(thm)],[f59,f50])).
% 0.08/0.38 fof(f76,plain,(
% 0.08/0.38 ~sQ5_spl|sQ7_spl),
% 0.08/0.38 inference(contradiction_clause,[status(thm)],[f75])).
% 0.08/0.38 fof(f90,plain,(
% 0.08/0.39 ![X0]: (~big_g(X0)|sP1_prd(X0)|~sQ4_spl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f46,f31])).
% 0.08/0.39 fof(f91,plain,(
% 0.08/0.39 ![X0]: (sP1_prd(X0)|~sQ4_spl)),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f90,f30])).
% 0.08/0.39 fof(f93,plain,(
% 0.08/0.39 $false|~sQ4_spl|sQ7_spl),
% 0.08/0.39 inference(backward_subsumption_resolution,[status(thm)],[f59,f91])).
% 0.08/0.39 fof(f95,plain,(
% 0.08/0.39 ![X0]: (~big_f(X0)|big_h(X0)|~sQ0_spl)),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f24,f33])).
% 0.08/0.39 fof(f96,plain,(
% 0.08/0.39 $false|~sQ0_spl|sQ6_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f56,f33])).
% 0.08/0.39 fof(f97,plain,(
% 0.08/0.39 ~sQ0_spl|sQ6_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f96])).
% 0.08/0.39 fof(f99,plain,(
% 0.08/0.39 sQ5_spl|~sQ4_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f91,f49,f45])).
% 0.08/0.39 fof(f100,plain,(
% 0.08/0.39 ~sQ4_spl|sQ7_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f93])).
% 0.08/0.39 fof(f102,plain,(
% 0.08/0.39 $false|~sQ3_spl),
% 0.08/0.39 inference(backward_subsumption_resolution,[status(thm)],[f6,f43])).
% 0.08/0.39 fof(f103,plain,(
% 0.08/0.39 ~sQ3_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f102])).
% 0.08/0.39 fof(f104,plain,(
% 0.08/0.39 ![X0]: (~big_g(X0)|big_j(X0)|~sQ5_spl)),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f29,f50])).
% 0.08/0.39 fof(f105,plain,(
% 0.08/0.39 ~big_f(sK4_skl)|~sQ0_spl|sQ10_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f95,f70])).
% 0.08/0.39 fof(f106,plain,(
% 0.08/0.39 $false|~sQ8_spl|~sQ0_spl|sQ10_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f105,f61])).
% 0.08/0.39 fof(f107,plain,(
% 0.08/0.39 ~sQ8_spl|~sQ0_spl|sQ10_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f106])).
% 0.08/0.39 fof(f108,plain,(
% 0.08/0.39 ~big_g(sK5_skl)|sQ11_spl|~sQ5_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f73,f104])).
% 0.08/0.39 fof(f109,plain,(
% 0.08/0.39 $false|~sQ9_spl|sQ11_spl|~sQ5_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f108,f65])).
% 0.08/0.39 fof(f110,plain,(
% 0.08/0.39 ~sQ9_spl|sQ11_spl|~sQ5_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f109])).
% 0.08/0.39 fof(f111,plain,(
% 0.08/0.39 ![X0]: (sP0_prd(X0)|~big_f(X0)|~sQ1_spl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f26,f36])).
% 0.08/0.39 fof(f113,plain,(
% 0.08/0.39 ![X0]: (sP0_prd(X0)|~sQ1_spl)),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f111,f25])).
% 0.08/0.39 fof(f115,plain,(
% 0.08/0.39 $false|~sQ2_spl),
% 0.08/0.39 inference(backward_subsumption_resolution,[status(thm)],[f8,f39])).
% 0.08/0.39 fof(f116,plain,(
% 0.08/0.39 ~sQ2_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f115])).
% 0.08/0.39 fof(f117,plain,(
% 0.08/0.39 sQ0_spl|~sQ1_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f113,f32,f35])).
% 0.08/0.39 fof(f118,plain,(
% 0.08/0.39 $false),
% 0.08/0.39 inference(sat_refutation,[status(thm)],[f41,f53,f63,f67,f74,f76,f97,f99,f100,f103,f107,f110,f116,f117])).
% 0.08/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.40 % Elapsed time: 0.032175 seconds
% 0.08/0.40 % CPU time: 0.077256 seconds
% 0.08/0.40 % Total memory used: 8.950 MB
% 0.08/0.40 % Net memory used: 8.760 MB
%------------------------------------------------------------------------------