%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 03:20:07 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 11:09:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f1,conjecture,(
% 0.09/0.40 ( ( (? [X] : X = f(g(X)))& (! [Y,Z] :( ( Y = f(g(Y))& Z = f(g(Z)) )=> Y = Z ) ))<=> ( (? [X] : X = g(f(X)))& (! [Y,Z] :( ( Y = g(f(Y))& Z = g(f(Z)) )=> Y = Z ) )) ) ),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f2,negated_conjecture,(
% 0.09/0.40 ~(( ( (? [X] : X = f(g(X)))& (! [Y,Z] :( ( Y = f(g(Y))& Z = f(g(Z)) )=> Y = Z ) ))<=> ( (? [X] : X = g(f(X)))& (! [Y,Z] :( ( Y = g(f(Y))& Z = g(f(Z)) )=> Y = Z ) )) ) )),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.40 fof(f3,plain,(
% 0.09/0.40 (((?[X]: X=f(g(X)))&(![Y,Z]: ((~Y=f(g(Y))|~Z=f(g(Z)))|Y=Z)))<~>((?[X]: X=g(f(X)))&(![Y,Z]: ((~Y=g(f(Y))|~Z=g(f(Z)))|Y=Z))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/0.40 fof(f4,definition,(
% 0.09/0.40 sP0_prd<=>((?[X]: X=f(g(X)))&(![Y,Z]: ((~Y=f(g(Y))|~Z=f(g(Z)))|Y=Z)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.40 fof(f5,plain,(
% 0.09/0.40 sP0_prd<~>((?[X]: X=g(f(X)))&(![Y,Z]: ((~Y=g(f(Y))|~Z=g(f(Z)))|Y=Z)))),
% 0.09/0.40 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.09/0.40 fof(f6,plain,(
% 0.09/0.40 (sP0_prd|((?[X]: X=g(f(X)))&(![Y,Z]: ((~Y=g(f(Y))|~Z=g(f(Z)))|Y=Z))))&(~sP0_prd|((![X]: ~X=g(f(X)))|(?[Y,Z]: ((Y=g(f(Y))&Z=g(f(Z)))&~Y=Z))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f5])).
% 0.09/0.40 fof(f7,plain,(
% 0.09/0.40 (sP0_prd|(sK0_skl=g(f(sK0_skl))&(![Y,Z]: ((~Y=g(f(Y))|~Z=g(f(Z)))|Y=Z))))&(~sP0_prd|((![X]: ~X=g(f(X)))|((sK1_skl=g(f(sK1_skl))&sK2_skl=g(f(sK2_skl)))&~sK1_skl=sK2_skl)))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f6])).
% 0.09/0.40 fof(f8,plain,(
% 0.09/0.40 sP0_prd|sK0_skl=g(f(sK0_skl))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f9,plain,(
% 0.09/0.40 ![X0,X1]: (sP0_prd|~X0=g(f(X0))|~X1=g(f(X1))|X0=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f10,plain,(
% 0.09/0.40 ![X0]: (~sP0_prd|~X0=g(f(X0))|sK1_skl=g(f(sK1_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f11,plain,(
% 0.09/0.40 ![X0]: (~sP0_prd|~X0=g(f(X0))|sK2_skl=g(f(sK2_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f12,plain,(
% 0.09/0.40 ![X0]: (~sP0_prd|~X0=g(f(X0))|~sK1_skl=sK2_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f13,plain,(
% 0.09/0.40 (~sP0_prd|((?[X]: X=f(g(X)))&(![Y,Z]: ((~Y=f(g(Y))|~Z=f(g(Z)))|Y=Z))))&(sP0_prd|((![X]: ~X=f(g(X)))|(?[Y,Z]: ((Y=f(g(Y))&Z=f(g(Z)))&~Y=Z))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f4])).
% 0.09/0.40 fof(f14,plain,(
% 0.09/0.40 (~sP0_prd|(sK3_skl=f(g(sK3_skl))&(![Y,Z]: ((~Y=f(g(Y))|~Z=f(g(Z)))|Y=Z))))&(sP0_prd|((![X]: ~X=f(g(X)))|((sK4_skl=f(g(sK4_skl))&sK5_skl=f(g(sK5_skl)))&~sK4_skl=sK5_skl)))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK3_skl),skolemize(Y,sK4_skl),skolemize(Z,sK5_skl)],[f13])).
% 0.09/0.40 fof(f15,plain,(
% 0.09/0.40 ~sP0_prd|sK3_skl=f(g(sK3_skl))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f16,plain,(
% 0.09/0.40 ![X0,X1]: (~sP0_prd|~X0=f(g(X0))|~X1=f(g(X1))|X0=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f17,plain,(
% 0.09/0.40 ![X0]: (sP0_prd|~X0=f(g(X0))|sK4_skl=f(g(sK4_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f18,plain,(
% 0.09/0.40 ![X0]: (sP0_prd|~X0=f(g(X0))|sK5_skl=f(g(sK5_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f19,plain,(
% 0.09/0.40 ![X0]: (sP0_prd|~X0=f(g(X0))|~sK4_skl=sK5_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f20,definition,(
% 0.09/0.40 sQ0_spl <=> (sP0_prd)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f23,definition,(
% 0.09/0.40 sQ1_spl <=> (sK0_skl=g(f(sK0_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f24,plain,(
% 0.09/0.40 sK0_skl=g(f(sK0_skl))|~sQ1_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f23])).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 sQ0_spl|sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f8,f20,f23])).
% 0.09/0.40 fof(f27,definition,(
% 0.09/0.40 ![X0,X1]: (sQ2_spl <=> (~X0=g(f(X0))|~X1=g(f(X1))|X0=X1))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 ![X0,X1]: (~X0=g(f(X0))|~X1=g(f(X1))|X0=X1|~sQ2_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f27])).
% 0.09/0.40 fof(f30,plain,(
% 0.09/0.40 sQ0_spl|sQ2_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f9,f20,f27])).
% 0.09/0.40 fof(f31,definition,(
% 0.09/0.40 ![X0]: (sQ3_spl <=> (~X0=g(f(X0))))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 ![X0]: (~X0=g(f(X0))|~sQ3_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f31])).
% 0.09/0.40 fof(f34,definition,(
% 0.09/0.40 sQ4_spl <=> (sK1_skl=g(f(sK1_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f35,plain,(
% 0.09/0.40 sK1_skl=g(f(sK1_skl))|~sQ4_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f34])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 ~sQ0_spl|sQ3_spl|sQ4_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f10,f20,f31,f34])).
% 0.09/0.40 fof(f38,definition,(
% 0.09/0.40 sQ5_spl <=> (sK2_skl=g(f(sK2_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 sK2_skl=g(f(sK2_skl))|~sQ5_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f38])).
% 0.09/0.40 fof(f41,plain,(
% 0.09/0.40 ~sQ0_spl|sQ3_spl|sQ5_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f11,f20,f31,f38])).
% 0.09/0.40 fof(f42,definition,(
% 0.09/0.40 sQ6_spl <=> (sK1_skl=sK2_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 ~sK1_skl=sK2_skl|sQ6_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f42])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 ~sQ0_spl|sQ3_spl|~sQ6_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f12,f20,f31,f42])).
% 0.09/0.40 fof(f46,definition,(
% 0.09/0.40 sQ7_spl <=> (sK3_skl=f(g(sK3_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 sK3_skl=f(g(sK3_skl))|~sQ7_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f46])).
% 0.09/0.40 fof(f49,plain,(
% 0.09/0.40 ~sQ0_spl|sQ7_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f15,f20,f46])).
% 0.09/0.40 fof(f50,definition,(
% 0.09/0.40 ![X0,X1]: (sQ8_spl <=> (~X0=f(g(X0))|~X1=f(g(X1))|X0=X1))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f51,plain,(
% 0.09/0.40 ![X0,X1]: (~X0=f(g(X0))|~X1=f(g(X1))|X0=X1|~sQ8_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f50])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 ~sQ0_spl|sQ8_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f16,f20,f50])).
% 0.09/0.40 fof(f54,definition,(
% 0.09/0.40 ![X0]: (sQ9_spl <=> (~X0=f(g(X0))))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f55,plain,(
% 0.09/0.40 ![X0]: (~X0=f(g(X0))|~sQ9_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f54])).
% 0.09/0.40 fof(f57,definition,(
% 0.09/0.40 sQ10_spl <=> (sK4_skl=f(g(sK4_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f58,plain,(
% 0.09/0.40 sK4_skl=f(g(sK4_skl))|~sQ10_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f57])).
% 0.09/0.40 fof(f60,plain,(
% 0.09/0.40 sQ0_spl|sQ9_spl|sQ10_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f17,f20,f54,f57])).
% 0.09/0.40 fof(f61,definition,(
% 0.09/0.40 sQ11_spl <=> (sK5_skl=f(g(sK5_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f62,plain,(
% 0.09/0.40 sK5_skl=f(g(sK5_skl))|~sQ11_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f61])).
% 0.09/0.40 fof(f64,plain,(
% 0.09/0.40 sQ0_spl|sQ9_spl|sQ11_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f18,f20,f54,f61])).
% 0.09/0.40 fof(f65,definition,(
% 0.09/0.40 sQ12_spl <=> (sK4_skl=sK5_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f67,plain,(
% 0.09/0.40 ~sK4_skl=sK5_skl|sQ12_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f65])).
% 0.09/0.40 fof(f68,plain,(
% 0.09/0.40 sQ0_spl|sQ9_spl|~sQ12_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f19,f20,f54,f65])).
% 0.09/0.40 fof(f72,plain,(
% 0.09/0.40 ![X0]: (~X0=g(f(X0))|~sK0_skl=sK0_skl|X0=sK0_skl|~sQ2_spl|~sQ1_spl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f24,f28])).
% 0.09/0.40 fof(f73,definition,(
% 0.09/0.40 ![X0]: (sQ13_spl <=> (~X0=g(f(X0))|X0=sK0_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f74,plain,(
% 0.09/0.40 ![X0]: (~X0=g(f(X0))|X0=sK0_skl|~sQ13_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f73])).
% 0.09/0.40 fof(f76,definition,(
% 0.09/0.40 sQ14_spl <=> (sK0_skl=sK0_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f78,plain,(
% 0.09/0.40 ~sK0_skl=sK0_skl|sQ14_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f76])).
% 0.09/0.40 fof(f79,plain,(
% 0.09/0.40 sQ13_spl|~sQ14_spl|~sQ2_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f72,f73,f76,f27,f23])).
% 0.09/0.40 fof(f80,plain,(
% 0.09/0.40 $false|sQ14_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f78])).
% 0.09/0.40 fof(f81,plain,(
% 0.09/0.40 sQ14_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f80])).
% 0.09/0.40 fof(f82,plain,(
% 0.09/0.40 ~g(sK5_skl)=g(sK5_skl)|~sQ3_spl|~sQ11_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f62,f32])).
% 0.09/0.40 fof(f84,plain,(
% 0.09/0.40 $false|~sQ3_spl|~sQ11_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f82])).
% 0.09/0.40 fof(f85,plain,(
% 0.09/0.40 ~sQ3_spl|~sQ11_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f84])).
% 0.09/0.40 fof(f87,plain,(
% 0.09/0.40 ![X0]: (~X0=f(g(X0))|~sK4_skl=sK4_skl|X0=sK4_skl|~sQ8_spl|~sQ10_spl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f58,f51])).
% 0.09/0.40 fof(f88,definition,(
% 0.09/0.40 ![X0]: (sQ15_spl <=> (~X0=f(g(X0))|X0=sK4_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f89,plain,(
% 0.09/0.40 ![X0]: (~X0=f(g(X0))|X0=sK4_skl|~sQ15_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f88])).
% 0.09/0.40 fof(f91,definition,(
% 0.09/0.40 sQ16_spl <=> (sK4_skl=sK4_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f93,plain,(
% 0.09/0.40 ~sK4_skl=sK4_skl|sQ16_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f91])).
% 0.09/0.40 fof(f94,plain,(
% 0.09/0.40 sQ15_spl|~sQ16_spl|~sQ8_spl|~sQ10_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f87,f88,f91,f50,f57])).
% 0.09/0.40 fof(f95,plain,(
% 0.09/0.40 $false|sQ16_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f93])).
% 0.09/0.40 fof(f96,plain,(
% 0.09/0.40 sQ16_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f95])).
% 0.09/0.40 fof(f97,plain,(
% 0.09/0.40 ![X0]: (~X0=f(g(X0))|X0=sK3_skl|~sQ7_spl|~sQ8_spl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f47,f51])).
% 0.09/0.40 fof(f102,definition,(
% 0.09/0.40 sQ18_spl <=> (sK3_skl=sK3_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f104,plain,(
% 0.09/0.40 ~sK3_skl=sK3_skl|sQ18_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f102])).
% 0.09/0.40 fof(f106,plain,(
% 0.09/0.40 $false|sQ18_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f104])).
% 0.09/0.40 fof(f107,plain,(
% 0.09/0.40 sQ18_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f106])).
% 0.09/0.40 fof(f112,definition,(
% 0.09/0.40 sQ20_spl <=> (f(sK1_skl)=f(sK1_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f114,plain,(
% 0.09/0.40 ~f(sK1_skl)=f(sK1_skl)|sQ20_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f112])).
% 0.09/0.40 fof(f116,plain,(
% 0.09/0.40 $false|sQ20_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f114])).
% 0.09/0.40 fof(f117,plain,(
% 0.09/0.40 sQ20_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f116])).
% 0.09/0.40 fof(f123,plain,(
% 0.09/0.40 ~g(sK3_skl)=g(sK3_skl)|~sQ3_spl|~sQ7_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f47,f32])).
% 0.09/0.40 fof(f125,plain,(
% 0.09/0.40 $false|~sQ3_spl|~sQ7_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f123])).
% 0.09/0.40 fof(f126,plain,(
% 0.09/0.40 ~sQ3_spl|~sQ7_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f125])).
% 0.09/0.40 fof(f127,plain,(
% 0.09/0.40 ~f(sK0_skl)=f(sK0_skl)|~sQ9_spl|~sQ1_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f24,f55])).
% 0.09/0.40 fof(f128,plain,(
% 0.09/0.40 $false|~sQ9_spl|~sQ1_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f127])).
% 0.09/0.40 fof(f129,plain,(
% 0.09/0.40 ~sQ9_spl|~sQ1_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f128])).
% 0.09/0.40 fof(f138,definition,(
% 0.09/0.40 sQ22_spl <=> (f(sK2_skl)=f(sK2_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f140,plain,(
% 0.09/0.40 ~f(sK2_skl)=f(sK2_skl)|sQ22_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f138])).
% 0.09/0.40 fof(f143,plain,(
% 0.09/0.40 ![X0]: (~X0=f(g(X0))|~f(sK0_skl)=f(sK0_skl)|X0=f(sK0_skl)|~sQ8_spl|~sQ1_spl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f24,f51])).
% 0.09/0.40 fof(f144,definition,(
% 0.09/0.40 ![X0]: (sQ23_spl <=> (~X0=f(g(X0))|X0=f(sK0_skl)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f147,definition,(
% 0.09/0.40 sQ24_spl <=> (f(sK0_skl)=f(sK0_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f149,plain,(
% 0.09/0.40 ~f(sK0_skl)=f(sK0_skl)|sQ24_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f147])).
% 0.09/0.40 fof(f150,plain,(
% 0.09/0.40 sQ23_spl|~sQ24_spl|~sQ8_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f143,f144,f147,f50,f23])).
% 0.09/0.40 fof(f154,plain,(
% 0.09/0.40 ~f(sK2_skl)=f(sK2_skl)|f(sK2_skl)=sK3_skl|~sQ7_spl|~sQ8_spl|~sQ5_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f39,f97])).
% 0.09/0.40 fof(f155,plain,(
% 0.09/0.40 ~f(sK1_skl)=f(sK1_skl)|f(sK1_skl)=sK3_skl|~sQ7_spl|~sQ8_spl|~sQ4_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f35,f97])).
% 0.09/0.40 fof(f161,definition,(
% 0.09/0.40 sQ26_spl <=> (f(sK2_skl)=sK3_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f162,plain,(
% 0.09/0.40 f(sK2_skl)=sK3_skl|~sQ26_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f161])).
% 0.09/0.40 fof(f164,plain,(
% 0.09/0.40 ~sQ22_spl|sQ26_spl|~sQ7_spl|~sQ8_spl|~sQ5_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f154,f138,f161,f46,f50,f38])).
% 0.09/0.40 fof(f165,definition,(
% 0.09/0.40 sQ27_spl <=> (f(sK1_skl)=sK3_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f166,plain,(
% 0.09/0.40 f(sK1_skl)=sK3_skl|~sQ27_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f165])).
% 0.09/0.40 fof(f168,plain,(
% 0.09/0.40 ~sQ20_spl|sQ27_spl|~sQ7_spl|~sQ8_spl|~sQ4_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f155,f112,f165,f46,f50,f34])).
% 0.09/0.40 fof(f169,plain,(
% 0.09/0.40 $false|sQ22_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f140])).
% 0.09/0.40 fof(f170,plain,(
% 0.09/0.40 sQ22_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f169])).
% 0.09/0.40 fof(f171,plain,(
% 0.09/0.40 $false|sQ24_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f149])).
% 0.09/0.40 fof(f172,plain,(
% 0.09/0.40 sQ24_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f171])).
% 0.09/0.40 fof(f173,plain,(
% 0.09/0.40 sK1_skl=g(sK3_skl)|~sQ27_spl|~sQ4_spl),
% 0.09/0.40 inference(backward_demodulation,[status(thm)],[f166,f35])).
% 0.09/0.40 fof(f175,plain,(
% 0.09/0.40 sK2_skl=g(sK3_skl)|~sQ26_spl|~sQ5_spl),
% 0.09/0.40 inference(backward_demodulation,[status(thm)],[f162,f39])).
% 0.09/0.40 fof(f180,plain,(
% 0.09/0.40 sK2_skl=sK1_skl|~sQ27_spl|~sQ4_spl|~sQ26_spl|~sQ5_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f173,f175])).
% 0.09/0.40 fof(f181,plain,(
% 0.09/0.40 $false|sQ6_spl|~sQ27_spl|~sQ4_spl|~sQ26_spl|~sQ5_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f180,f44])).
% 0.09/0.40 fof(f182,plain,(
% 0.09/0.40 sQ6_spl|~sQ27_spl|~sQ4_spl|~sQ26_spl|~sQ5_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f181])).
% 0.09/0.40 fof(f191,definition,(
% 0.09/0.40 sQ29_spl <=> (g(sK4_skl)=g(sK4_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f193,plain,(
% 0.09/0.40 ~g(sK4_skl)=g(sK4_skl)|sQ29_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f191])).
% 0.09/0.40 fof(f195,plain,(
% 0.09/0.40 $false|sQ29_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f193])).
% 0.09/0.40 fof(f196,plain,(
% 0.09/0.40 sQ29_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f195])).
% 0.09/0.40 fof(f201,definition,(
% 0.09/0.40 sQ31_spl <=> (g(sK5_skl)=g(sK5_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f203,plain,(
% 0.09/0.40 ~g(sK5_skl)=g(sK5_skl)|sQ31_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f201])).
% 0.09/0.40 fof(f205,plain,(
% 0.09/0.40 $false|sQ31_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f203])).
% 0.09/0.40 fof(f206,plain,(
% 0.09/0.40 sQ31_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f205])).
% 0.09/0.40 fof(f211,definition,(
% 0.09/0.40 sQ33_spl <=> (g(sK3_skl)=g(sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f213,plain,(
% 0.09/0.40 ~g(sK3_skl)=g(sK3_skl)|sQ33_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f211])).
% 0.09/0.40 fof(f215,plain,(
% 0.09/0.40 $false|sQ33_spl),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f213])).
% 0.09/0.40 fof(f216,plain,(
% 0.09/0.40 sQ33_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f215])).
% 0.09/0.40 fof(f220,plain,(
% 0.09/0.40 sK5_skl=sK4_skl|~sQ15_spl|~sQ11_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f89,f62])).
% 0.09/0.40 fof(f225,plain,(
% 0.09/0.40 $false|sQ12_spl|~sQ15_spl|~sQ11_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f220,f67])).
% 0.09/0.40 fof(f226,plain,(
% 0.09/0.40 sQ12_spl|~sQ15_spl|~sQ11_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f225])).
% 0.09/0.40 fof(f229,plain,(
% 0.09/0.40 ~g(sK5_skl)=g(sK5_skl)|g(sK5_skl)=sK0_skl|~sQ13_spl|~sQ11_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f62,f74])).
% 0.09/0.40 fof(f230,plain,(
% 0.09/0.40 ~g(sK4_skl)=g(sK4_skl)|g(sK4_skl)=sK0_skl|~sQ13_spl|~sQ10_spl),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f58,f74])).
% 0.09/0.40 fof(f232,definition,(
% 0.09/0.40 sQ34_spl <=> (g(sK5_skl)=sK0_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f233,plain,(
% 0.09/0.40 g(sK5_skl)=sK0_skl|~sQ34_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f232])).
% 0.09/0.40 fof(f235,plain,(
% 0.09/0.40 ~sQ31_spl|sQ34_spl|~sQ13_spl|~sQ11_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f229,f201,f232,f73,f61])).
% 0.09/0.40 fof(f236,definition,(
% 0.09/0.40 sQ35_spl <=> (g(sK4_skl)=sK0_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f237,plain,(
% 0.09/0.40 g(sK4_skl)=sK0_skl|~sQ35_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f236])).
% 0.09/0.40 fof(f239,plain,(
% 0.09/0.40 ~sQ29_spl|sQ35_spl|~sQ13_spl|~sQ10_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f230,f191,f236,f73,f57])).
% 0.09/0.40 fof(f240,plain,(
% 0.09/0.40 sK4_skl=f(sK0_skl)|~sQ35_spl|~sQ10_spl),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f237,f58])).
% 0.09/0.41 fof(f242,plain,(
% 0.09/0.41 sK5_skl=f(sK0_skl)|~sQ34_spl|~sQ11_spl),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f233,f62])).
% 0.09/0.41 fof(f247,plain,(
% 0.09/0.41 sK5_skl=sK4_skl|~sQ35_spl|~sQ10_spl|~sQ34_spl|~sQ11_spl),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f240,f242])).
% 0.09/0.41 fof(f248,plain,(
% 0.09/0.41 $false|sQ12_spl|~sQ35_spl|~sQ10_spl|~sQ34_spl|~sQ11_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f247,f67])).
% 0.09/0.41 fof(f249,plain,(
% 0.09/0.41 sQ12_spl|~sQ35_spl|~sQ10_spl|~sQ34_spl|~sQ11_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f248])).
% 0.09/0.41 fof(f250,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(sat_refutation,[status(thm)],[f26,f30,f37,f41,f45,f49,f53,f60,f64,f68,f79,f81,f85,f94,f96,f107,f117,f126,f129,f150,f164,f168,f170,f172,f182,f196,f206,f216,f226,f235,f239,f249])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.058252 seconds
% 0.09/0.43 % CPU time: 0.152200 seconds
% 0.09/0.43 % Total memory used: 80.162 MB
% 0.09/0.43 % Net memory used: 79.656 MB
%------------------------------------------------------------------------------