%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN415+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 : n001.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 03:19:35 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 10:59:14 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.47 fof(f1,conjecture,(
% 0.16/0.47 ( ( (? [X] : f(X))& (! [Y,Z] :( ( f(Y)& f(Z) )=> Y = Z ) ))<=> (? [U] :( f(U)& (! [V] :( f(V)=> U = V ) )) )) ),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f2,negated_conjecture,(
% 0.16/0.47 ~(( ( (? [X] : f(X))& (! [Y,Z] :( ( f(Y)& f(Z) )=> Y = Z ) ))<=> (? [U] :( f(U)& (! [V] :( f(V)=> U = V ) )) )) )),
% 0.16/0.47 inference(negated_conjecture,[status(cth)],[f1])).
% 0.16/0.47 fof(f3,plain,(
% 0.16/0.47 (((?[X]: f(X))&(![Y,Z]: ((~f(Y)|~f(Z))|Y=Z)))<~>(?[U]: (f(U)&(![V]: (~f(V)|U=V)))))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.16/0.47 fof(f4,definition,(
% 0.16/0.47 sP0_prd<=>((?[X]: f(X))&(![Y,Z]: ((~f(Y)|~f(Z))|Y=Z)))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.16/0.47 fof(f5,plain,(
% 0.16/0.47 sP0_prd<~>(?[U]: (f(U)&(![V]: (~f(V)|U=V))))),
% 0.16/0.47 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.16/0.47 fof(f6,plain,(
% 0.16/0.47 (sP0_prd|(?[U]: (f(U)&(![V]: (~f(V)|U=V)))))&(~sP0_prd|(![U]: (~f(U)|(?[V]: (f(V)&~U=V)))))),
% 0.16/0.47 inference(NNF_transformation,[status(thm)],[f5])).
% 0.16/0.47 fof(f7,plain,(
% 0.16/0.47 (sP0_prd|(f(sK0_skl)&(![V]: (~f(V)|sK0_skl=V))))&(~sP0_prd|(![U]: (~f(U)|(f(sK1_skl(U))&~U=sK1_skl(U)))))),
% 0.16/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl(U))],[f6])).
% 0.16/0.47 fof(f8,plain,(
% 0.16/0.47 sP0_prd|f(sK0_skl)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.16/0.47 fof(f9,plain,(
% 0.16/0.47 ![X0]: (sP0_prd|~f(X0)|sK0_skl=X0)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.16/0.47 fof(f10,plain,(
% 0.16/0.47 ![X0]: (~sP0_prd|~f(X0)|f(sK1_skl(X0)))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.16/0.47 fof(f11,plain,(
% 0.16/0.47 ![X0]: (~sP0_prd|~f(X0)|~X0=sK1_skl(X0))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.16/0.47 fof(f12,plain,(
% 0.16/0.47 (~sP0_prd|((?[X]: f(X))&(![Y,Z]: ((~f(Y)|~f(Z))|Y=Z))))&(sP0_prd|((![X]: ~f(X))|(?[Y,Z]: ((f(Y)&f(Z))&~Y=Z))))),
% 0.16/0.47 inference(NNF_transformation,[status(thm)],[f4])).
% 0.16/0.47 fof(f13,plain,(
% 0.16/0.47 (~sP0_prd|(f(sK2_skl)&(![Y,Z]: ((~f(Y)|~f(Z))|Y=Z))))&(sP0_prd|((![X]: ~f(X))|((f(sK3_skl)&f(sK4_skl))&~sK3_skl=sK4_skl)))),
% 0.16/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Z,sK4_skl)],[f12])).
% 0.16/0.47 fof(f14,plain,(
% 0.16/0.47 ~sP0_prd|f(sK2_skl)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f15,plain,(
% 0.16/0.47 ![X0,X1]: (~sP0_prd|~f(X0)|~f(X1)|X0=X1)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f16,plain,(
% 0.16/0.47 ![X0]: (sP0_prd|~f(X0)|f(sK3_skl))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f17,plain,(
% 0.16/0.47 ![X0]: (sP0_prd|~f(X0)|f(sK4_skl))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f18,plain,(
% 0.16/0.47 ![X0]: (sP0_prd|~f(X0)|~sK3_skl=sK4_skl)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f19,definition,(
% 0.16/0.47 sQ0_spl <=> (sP0_prd)),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f22,definition,(
% 0.16/0.47 sQ1_spl <=> (f(sK0_skl))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f23,plain,(
% 0.16/0.47 f(sK0_skl)|~sQ1_spl),
% 0.16/0.47 inference(component_clause,[status(thm)],[f22])).
% 0.16/0.47 fof(f25,plain,(
% 0.16/0.47 sQ0_spl|sQ1_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f8,f19,f22])).
% 0.16/0.47 fof(f26,definition,(
% 0.16/0.47 ![X0]: (sQ2_spl <=> (~f(X0)|sK0_skl=X0))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f27,plain,(
% 0.16/0.47 ![X0]: (~f(X0)|sK0_skl=X0|~sQ2_spl)),
% 0.16/0.47 inference(component_clause,[status(thm)],[f26])).
% 0.16/0.47 fof(f29,plain,(
% 0.16/0.47 sQ0_spl|sQ2_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f9,f19,f26])).
% 0.16/0.47 fof(f30,definition,(
% 0.16/0.47 ![X0]: (sQ3_spl <=> (~f(X0)|f(sK1_skl(X0))))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f31,plain,(
% 0.16/0.47 ![X0]: (~f(X0)|f(sK1_skl(X0))|~sQ3_spl)),
% 0.16/0.47 inference(component_clause,[status(thm)],[f30])).
% 0.16/0.47 fof(f33,plain,(
% 0.16/0.47 ~sQ0_spl|sQ3_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f10,f19,f30])).
% 0.16/0.47 fof(f34,definition,(
% 0.16/0.47 ![X0]: (sQ4_spl <=> (~f(X0)|~X0=sK1_skl(X0)))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f35,plain,(
% 0.16/0.47 ![X0]: (~f(X0)|~X0=sK1_skl(X0)|~sQ4_spl)),
% 0.16/0.47 inference(component_clause,[status(thm)],[f34])).
% 0.16/0.47 fof(f37,plain,(
% 0.16/0.47 ~sQ0_spl|sQ4_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f11,f19,f34])).
% 0.16/0.47 fof(f38,definition,(
% 0.16/0.47 sQ5_spl <=> (f(sK2_skl))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f39,plain,(
% 0.16/0.47 f(sK2_skl)|~sQ5_spl),
% 0.16/0.47 inference(component_clause,[status(thm)],[f38])).
% 0.16/0.47 fof(f41,plain,(
% 0.16/0.47 ~sQ0_spl|sQ5_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f14,f19,f38])).
% 0.16/0.47 fof(f42,definition,(
% 0.16/0.47 ![X0,X1]: (sQ6_spl <=> (~f(X0)|~f(X1)|X0=X1))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f43,plain,(
% 0.16/0.47 ![X0,X1]: (~f(X0)|~f(X1)|X0=X1|~sQ6_spl)),
% 0.16/0.47 inference(component_clause,[status(thm)],[f42])).
% 0.16/0.47 fof(f45,plain,(
% 0.16/0.47 ~sQ0_spl|sQ6_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f15,f19,f42])).
% 0.16/0.47 fof(f46,definition,(
% 0.16/0.47 ![X0]: (sQ7_spl <=> (~f(X0)))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f47,plain,(
% 0.16/0.47 ![X0]: (~f(X0)|~sQ7_spl)),
% 0.16/0.47 inference(component_clause,[status(thm)],[f46])).
% 0.16/0.47 fof(f49,definition,(
% 0.16/0.47 sQ8_spl <=> (f(sK3_skl))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f50,plain,(
% 0.16/0.47 f(sK3_skl)|~sQ8_spl),
% 0.16/0.47 inference(component_clause,[status(thm)],[f49])).
% 0.16/0.47 fof(f52,plain,(
% 0.16/0.47 sQ0_spl|sQ7_spl|sQ8_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f16,f19,f46,f49])).
% 0.16/0.47 fof(f53,definition,(
% 0.16/0.47 sQ9_spl <=> (f(sK4_skl))),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f54,plain,(
% 0.16/0.47 f(sK4_skl)|~sQ9_spl),
% 0.16/0.47 inference(component_clause,[status(thm)],[f53])).
% 0.16/0.47 fof(f56,plain,(
% 0.16/0.47 sQ0_spl|sQ7_spl|sQ9_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f17,f19,f46,f53])).
% 0.16/0.47 fof(f57,definition,(
% 0.16/0.47 sQ10_spl <=> (sK3_skl=sK4_skl)),
% 0.16/0.47 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.16/0.47 fof(f59,plain,(
% 0.16/0.47 ~sK3_skl=sK4_skl|sQ10_spl),
% 0.16/0.47 inference(component_clause,[status(thm)],[f57])).
% 0.16/0.47 fof(f60,plain,(
% 0.16/0.47 sQ0_spl|sQ7_spl|~sQ10_spl),
% 0.16/0.47 inference(split_clause,[status(thm)],[f18,f19,f46,f57])).
% 0.16/0.47 fof(f61,plain,(
% 0.16/0.47 $false|~sQ7_spl|~sQ1_spl),
% 0.16/0.47 inference(forward_subsumption_resolution,[status(thm)],[f23,f47])).
% 0.16/0.47 fof(f62,plain,(
% 0.16/0.47 ~sQ7_spl|~sQ1_spl),
% 0.16/0.47 inference(contradiction_clause,[status(thm)],[f61])).
% 0.16/0.47 fof(f63,plain,(
% 0.16/0.47 f(sK1_skl(sK2_skl))|~sQ5_spl|~sQ3_spl),
% 0.16/0.47 inference(resolution,[status(thm)],[f39,f31])).
% 0.16/0.47 fof(f66,plain,(
% 0.16/0.47 ![X0]: (~f(X0)|X0=sK2_skl|~sQ6_spl|~sQ5_spl)),
% 0.16/0.47 inference(resolution,[status(thm)],[f43,f39])).
% 0.16/0.47 fof(f67,plain,(
% 0.16/0.47 sK1_skl(sK2_skl)=sK2_skl|~sQ6_spl|~sQ5_spl|~sQ3_spl),
% 0.16/0.47 inference(resolution,[status(thm)],[f66,f63])).
% 0.16/0.47 fof(f73,plain,(
% 0.16/0.47 ~f(sK2_skl)|~sQ6_spl|~sQ5_spl|~sQ3_spl|~sQ4_spl),
% 0.16/0.47 inference(resolution,[status(thm)],[f67,f35])).
% 0.16/0.47 fof(f75,plain,(
% 0.16/0.47 $false|~sQ6_spl|~sQ5_spl|~sQ3_spl|~sQ4_spl),
% 0.16/0.47 inference(forward_subsumption_resolution,[status(thm)],[f73,f39])).
% 0.16/0.47 fof(f76,plain,(
% 0.16/0.47 ~sQ6_spl|~sQ5_spl|~sQ3_spl|~sQ4_spl),
% 0.16/0.47 inference(contradiction_clause,[status(thm)],[f75])).
% 0.16/0.47 fof(f77,plain,(
% 0.16/0.47 sK0_skl=sK3_skl|~sQ8_spl|~sQ2_spl),
% 0.16/0.47 inference(resolution,[status(thm)],[f50,f27])).
% 0.16/0.47 fof(f80,plain,(
% 0.16/0.47 ~sK0_skl=sK4_skl|~sQ8_spl|~sQ2_spl|sQ10_spl),
% 0.16/0.47 inference(backward_demodulation,[status(thm)],[f77,f59])).
% 0.16/0.47 fof(f82,plain,(
% 0.16/0.47 sK0_skl=sK4_skl|~sQ9_spl|~sQ2_spl),
% 0.16/0.47 inference(resolution,[status(thm)],[f54,f27])).
% 0.16/0.47 fof(f84,plain,(
% 0.16/0.47 $false|~sQ8_spl|sQ10_spl|~sQ9_spl|~sQ2_spl),
% 0.16/0.47 inference(forward_subsumption_resolution,[status(thm)],[f82,f80])).
% 0.16/0.47 fof(f85,plain,(
% 0.16/0.47 ~sQ8_spl|sQ10_spl|~sQ9_spl|~sQ2_spl),
% 0.16/0.47 inference(contradiction_clause,[status(thm)],[f84])).
% 0.16/0.47 fof(f86,plain,(
% 0.16/0.47 $false),
% 0.16/0.47 inference(sat_refutation,[status(thm)],[f25,f29,f33,f37,f41,f45,f52,f56,f60,f62,f76,f85])).
% 0.16/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.50 % Elapsed time: 0.064327 seconds
% 0.16/0.50 % CPU time: 0.164918 seconds
% 0.16/0.50 % Total memory used: 59.877 MB
% 0.16/0.50 % Net memory used: 59.476 MB
%------------------------------------------------------------------------------