%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN078+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 : n005.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 03:18:54 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN078+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
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 10:41:49 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.37 fof(f1,conjecture,(
% 0.07/0.37 ( (! [X] :( (? [Y] :( big_p(Y)& X = f(Y) ))=> big_p(X) ))<=> (! [U] :( big_p(U)=> big_p(f(U)) ) )) ),
% 0.07/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.37 fof(f2,negated_conjecture,(
% 0.07/0.37 ~(( (! [X] :( (? [Y] :( big_p(Y)& X = f(Y) ))=> big_p(X) ))<=> (! [U] :( big_p(U)=> big_p(f(U)) ) )) )),
% 0.07/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.37 fof(f3,plain,(
% 0.07/0.37 ((![X]: ((![Y]: (~big_p(Y)|~X=f(Y)))|big_p(X)))<~>(![U]: (~big_p(U)|big_p(f(U)))))),
% 0.07/0.37 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.07/0.37 fof(f4,definition,(
% 0.07/0.37 ![X]: (sP0_prd(X)<=>((![Y]: (~big_p(Y)|~X=f(Y)))|big_p(X)))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.07/0.37 fof(f5,plain,(
% 0.07/0.37 (![X]: sP0_prd(X))<~>(![U]: (~big_p(U)|big_p(f(U))))),
% 0.07/0.37 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.07/0.37 fof(f6,plain,(
% 0.07/0.37 ((![X]: sP0_prd(X))|(![U]: (~big_p(U)|big_p(f(U)))))&((?[X]: ~sP0_prd(X))|(?[U]: (big_p(U)&~big_p(f(U)))))),
% 0.07/0.37 inference(NNF_transformation,[status(thm)],[f5])).
% 0.07/0.37 fof(f7,plain,(
% 0.07/0.37 ((![X]: sP0_prd(X))|(![U]: (~big_p(U)|big_p(f(U)))))&(~sP0_prd(sK0_skl)|(big_p(sK1_skl)&~big_p(f(sK1_skl))))),
% 0.07/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl)],[f6])).
% 0.07/0.37 fof(f8,plain,(
% 0.07/0.37 ![X0,X1]: (sP0_prd(X0)|~big_p(X1)|big_p(f(X1)))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f7])).
% 0.07/0.37 fof(f9,plain,(
% 0.07/0.37 ~sP0_prd(sK0_skl)|big_p(sK1_skl)),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f7])).
% 0.07/0.37 fof(f10,plain,(
% 0.07/0.37 ~sP0_prd(sK0_skl)|~big_p(f(sK1_skl))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f7])).
% 0.07/0.37 fof(f11,plain,(
% 0.07/0.37 ![X]: ((~sP0_prd(X)|((![Y]: (~big_p(Y)|~X=f(Y)))|big_p(X)))&(sP0_prd(X)|((?[Y]: (big_p(Y)&X=f(Y)))&~big_p(X))))),
% 0.07/0.37 inference(NNF_transformation,[status(thm)],[f4])).
% 0.07/0.37 fof(f12,plain,(
% 0.07/0.37 (![X]: (~sP0_prd(X)|((![Y]: (~big_p(Y)|~X=f(Y)))|big_p(X))))&(![X]: (sP0_prd(X)|((?[Y]: (big_p(Y)&X=f(Y)))&~big_p(X))))),
% 0.07/0.37 inference(miniscoping,[status(thm)],[f11])).
% 0.07/0.37 fof(f13,plain,(
% 0.07/0.37 (![X]: (~sP0_prd(X)|((![Y]: (~big_p(Y)|~X=f(Y)))|big_p(X))))&(![X]: (sP0_prd(X)|((big_p(sK2_skl(X))&X=f(sK2_skl(X)))&~big_p(X))))),
% 0.07/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f12])).
% 0.07/0.37 fof(f14,plain,(
% 0.07/0.37 ![X0,X1]: (~sP0_prd(X0)|~big_p(X1)|~X0=f(X1)|big_p(X0))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.07/0.37 fof(f15,plain,(
% 0.07/0.37 ![X0]: (sP0_prd(X0)|big_p(sK2_skl(X0)))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.07/0.37 fof(f16,plain,(
% 0.07/0.37 ![X0]: (sP0_prd(X0)|X0=f(sK2_skl(X0)))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.07/0.37 fof(f17,plain,(
% 0.07/0.37 ![X0]: (sP0_prd(X0)|~big_p(X0))),
% 0.07/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.07/0.37 fof(f18,definition,(
% 0.07/0.37 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.07/0.37 fof(f19,plain,(
% 0.07/0.37 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.07/0.37 inference(component_clause,[status(thm)],[f18])).
% 0.07/0.37 fof(f21,definition,(
% 0.07/0.37 ![X1]: (sQ1_spl <=> (~big_p(X1)|big_p(f(X1))))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.07/0.37 fof(f22,plain,(
% 0.07/0.37 ![X0]: (~big_p(X0)|big_p(f(X0))|~sQ1_spl)),
% 0.07/0.37 inference(component_clause,[status(thm)],[f21])).
% 0.07/0.37 fof(f24,plain,(
% 0.07/0.37 sQ0_spl|sQ1_spl),
% 0.07/0.37 inference(split_clause,[status(thm)],[f8,f18,f21])).
% 0.07/0.37 fof(f25,definition,(
% 0.07/0.37 sQ2_spl <=> (sP0_prd(sK0_skl))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.07/0.37 fof(f27,plain,(
% 0.07/0.37 ~sP0_prd(sK0_skl)|sQ2_spl),
% 0.07/0.37 inference(component_clause,[status(thm)],[f25])).
% 0.07/0.37 fof(f28,definition,(
% 0.07/0.37 sQ3_spl <=> (big_p(sK1_skl))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.07/0.37 fof(f29,plain,(
% 0.07/0.37 big_p(sK1_skl)|~sQ3_spl),
% 0.07/0.37 inference(component_clause,[status(thm)],[f28])).
% 0.07/0.37 fof(f31,plain,(
% 0.07/0.37 ~sQ2_spl|sQ3_spl),
% 0.07/0.37 inference(split_clause,[status(thm)],[f9,f25,f28])).
% 0.07/0.37 fof(f32,definition,(
% 0.07/0.37 sQ4_spl <=> (big_p(f(sK1_skl)))),
% 0.07/0.37 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.07/0.38 fof(f34,plain,(
% 0.07/0.38 ~big_p(f(sK1_skl))|sQ4_spl),
% 0.07/0.38 inference(component_clause,[status(thm)],[f32])).
% 0.07/0.38 fof(f35,plain,(
% 0.07/0.38 ~sQ2_spl|~sQ4_spl),
% 0.07/0.38 inference(split_clause,[status(thm)],[f10,f25,f32])).
% 0.07/0.38 fof(f36,plain,(
% 0.07/0.38 ![X0]: (~sP0_prd(f(X0))|~big_p(X0)|big_p(f(X0)))),
% 0.07/0.38 inference(destructive_equality_resolution,[status(thm)],[f14])).
% 0.07/0.38 fof(f38,plain,(
% 0.07/0.38 ![X0]: (~big_p(X0)|big_p(f(X0))|~sQ0_spl)),
% 0.07/0.38 inference(backward_subsumption_resolution,[status(thm)],[f36,f19])).
% 0.07/0.38 fof(f40,plain,(
% 0.07/0.38 big_p(f(sK1_skl))|~sQ1_spl|~sQ3_spl),
% 0.07/0.38 inference(resolution,[status(thm)],[f22,f29])).
% 0.07/0.38 fof(f41,plain,(
% 0.07/0.38 $false|sQ4_spl|~sQ1_spl|~sQ3_spl),
% 0.07/0.38 inference(forward_subsumption_resolution,[status(thm)],[f40,f34])).
% 0.07/0.38 fof(f42,plain,(
% 0.07/0.38 sQ4_spl|~sQ1_spl|~sQ3_spl),
% 0.07/0.38 inference(contradiction_clause,[status(thm)],[f41])).
% 0.07/0.38 fof(f43,plain,(
% 0.07/0.38 sK0_skl=f(sK2_skl(sK0_skl))|sQ2_spl),
% 0.07/0.38 inference(resolution,[status(thm)],[f16,f27])).
% 0.07/0.38 fof(f45,plain,(
% 0.07/0.38 ![X0]: (sP0_prd(X0)|big_p(f(sK2_skl(X0)))|~sQ1_spl)),
% 0.07/0.38 inference(resolution,[status(thm)],[f15,f22])).
% 0.07/0.38 fof(f50,plain,(
% 0.07/0.38 ![X0]: (sP0_prd(X0)|sP0_prd(f(sK2_skl(X0)))|~sQ1_spl)),
% 0.07/0.38 inference(resolution,[status(thm)],[f45,f17])).
% 0.07/0.38 fof(f59,plain,(
% 0.07/0.38 sP0_prd(sK0_skl)|sP0_prd(sK0_skl)|~sQ1_spl|sQ2_spl),
% 0.07/0.38 inference(paramodulation,[status(thm)],[f43,f50])).
% 0.07/0.38 fof(f60,plain,(
% 0.07/0.38 sQ2_spl|~sQ1_spl),
% 0.07/0.38 inference(split_clause,[status(thm)],[f59,f25,f21])).
% 0.07/0.38 fof(f61,plain,(
% 0.07/0.38 sQ1_spl|~sQ0_spl),
% 0.07/0.38 inference(split_clause,[status(thm)],[f38,f21,f18])).
% 0.07/0.38 fof(f64,plain,(
% 0.07/0.38 $false),
% 0.07/0.38 inference(sat_refutation,[status(thm)],[f24,f31,f35,f42,f60,f61])).
% 0.07/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.40 % Elapsed time: 0.049880 seconds
% 0.13/0.40 % CPU time: 0.140607 seconds
% 0.13/0.40 % Total memory used: 79.841 MB
% 0.13/0.40 % Net memory used: 79.287 MB
%------------------------------------------------------------------------------