%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:37:18 PM UTC 2026
% Result : Theorem 0.11s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:40:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.51 % Refutation found
% 0.11/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.51 fof(f1,axiom,(
% 0.11/0.51 (! [C,B,A] : product(product(A,B),C) = product(A,product(B,C)) )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f2,axiom,(
% 0.11/0.51 (! [A] : product(A,A) = A )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f3,axiom,(
% 0.11/0.51 (! [X0,X1] :( l(X0,X1)<=> ( product(X0,X1) = X0& product(X1,X0) = X1 ) ) )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f4,axiom,(
% 0.11/0.51 (! [X2,X3] :( r(X2,X3)<=> ( product(X2,X3) = X3& product(X3,X2) = X2 ) ) )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f5,axiom,(
% 0.11/0.51 (! [X4,X5] :( d(X4,X5)<=> (? [X6] :( r(X4,X6)& l(X6,X5) ) )) )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f6,conjecture,(
% 0.11/0.51 (! [X7,X8] :( d(X7,X8)<=> ( product(X7,product(X8,X7)) = X7& product(X8,product(X7,X8)) = X8 ) ) )),
% 0.11/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f7,negated_conjecture,(
% 0.11/0.51 ~((! [X7,X8] :( d(X7,X8)<=> ( product(X7,product(X8,X7)) = X7& product(X8,product(X7,X8)) = X8 ) ) ))),
% 0.11/0.51 inference(negated_conjecture,[status(cth)],[f6])).
% 0.11/0.51 fof(f8,plain,(
% 0.11/0.51 ![X0,X1,X2]: (product(product(X0,X1),X2)=product(X0,product(X1,X2)))),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f1])).
% 0.11/0.51 fof(f9,plain,(
% 0.11/0.51 ![X0]: (product(X0,X0)=X0)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.51 fof(f10,plain,(
% 0.11/0.51 ![X0,X1]: ((~l(X0,X1)|(product(X0,X1)=X0&product(X1,X0)=X1))&(l(X0,X1)|(~product(X0,X1)=X0|~product(X1,X0)=X1)))),
% 0.11/0.51 inference(NNF_transformation,[status(thm)],[f3])).
% 0.11/0.51 fof(f11,plain,(
% 0.11/0.51 (![X0,X1]: (~l(X0,X1)|(product(X0,X1)=X0&product(X1,X0)=X1)))&(![X0,X1]: (l(X0,X1)|(~product(X0,X1)=X0|~product(X1,X0)=X1)))),
% 0.11/0.51 inference(miniscoping,[status(thm)],[f10])).
% 0.11/0.51 fof(f12,plain,(
% 0.11/0.51 ![X0,X1]: (~l(X0,X1)|product(X0,X1)=X0)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f11])).
% 0.11/0.51 fof(f13,plain,(
% 0.11/0.51 ![X0,X1]: (~l(X0,X1)|product(X1,X0)=X1)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f11])).
% 0.11/0.51 fof(f14,plain,(
% 0.11/0.51 ![X0,X1]: (l(X0,X1)|~product(X0,X1)=X0|~product(X1,X0)=X1)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f11])).
% 0.11/0.51 fof(f15,plain,(
% 0.11/0.51 ![X2,X3]: ((~r(X2,X3)|(product(X2,X3)=X3&product(X3,X2)=X2))&(r(X2,X3)|(~product(X2,X3)=X3|~product(X3,X2)=X2)))),
% 0.11/0.51 inference(NNF_transformation,[status(thm)],[f4])).
% 0.11/0.51 fof(f16,plain,(
% 0.11/0.51 (![X2,X3]: (~r(X2,X3)|(product(X2,X3)=X3&product(X3,X2)=X2)))&(![X2,X3]: (r(X2,X3)|(~product(X2,X3)=X3|~product(X3,X2)=X2)))),
% 0.11/0.51 inference(miniscoping,[status(thm)],[f15])).
% 0.11/0.51 fof(f17,plain,(
% 0.11/0.51 ![X0,X1]: (~r(X0,X1)|product(X0,X1)=X1)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.51 fof(f18,plain,(
% 0.11/0.51 ![X0,X1]: (~r(X0,X1)|product(X1,X0)=X0)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.51 fof(f19,plain,(
% 0.11/0.51 ![X0,X1]: (r(X0,X1)|~product(X0,X1)=X1|~product(X1,X0)=X0)),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.51 fof(f20,plain,(
% 0.11/0.51 ![X4,X5]: ((~d(X4,X5)|(?[X6]: (r(X4,X6)&l(X6,X5))))&(d(X4,X5)|(![X6]: (~r(X4,X6)|~l(X6,X5)))))),
% 0.11/0.51 inference(NNF_transformation,[status(thm)],[f5])).
% 0.11/0.51 fof(f21,plain,(
% 0.11/0.51 (![X4,X5]: (~d(X4,X5)|(?[X6]: (r(X4,X6)&l(X6,X5)))))&(![X4,X5]: (d(X4,X5)|(![X6]: (~r(X4,X6)|~l(X6,X5)))))),
% 0.11/0.51 inference(miniscoping,[status(thm)],[f20])).
% 0.11/0.51 fof(f22,plain,(
% 0.11/0.51 (![X4,X5]: (~d(X4,X5)|(r(X4,sK0_skl(X5,X4))&l(sK0_skl(X5,X4),X5))))&(![X4,X5]: (d(X4,X5)|(![X6]: (~r(X4,X6)|~l(X6,X5)))))),
% 0.11/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X6,sK0_skl(X5,X4))],[f21])).
% 0.11/0.51 fof(f23,plain,(
% 0.11/0.51 ![X0,X1]: (~d(X0,X1)|r(X0,sK0_skl(X1,X0)))),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.51 fof(f24,plain,(
% 0.11/0.51 ![X0,X1]: (~d(X0,X1)|l(sK0_skl(X1,X0),X1))),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.51 fof(f25,plain,(
% 0.11/0.51 ![X0,X1,X2]: (d(X0,X1)|~r(X0,X2)|~l(X2,X1))),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.51 fof(f26,plain,(
% 0.11/0.51 (?[X7,X8]: (d(X7,X8)<~>(product(X7,product(X8,X7))=X7&product(X8,product(X7,X8))=X8)))),
% 0.11/0.51 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.11/0.51 fof(f27,plain,(
% 0.11/0.51 ?[X7,X8]: ((d(X7,X8)|(product(X7,product(X8,X7))=X7&product(X8,product(X7,X8))=X8))&(~d(X7,X8)|(~product(X7,product(X8,X7))=X7|~product(X8,product(X7,X8))=X8)))),
% 0.11/0.51 inference(NNF_transformation,[status(thm)],[f26])).
% 0.11/0.51 fof(f28,plain,(
% 0.11/0.51 ((d(sK1_skl,sK2_skl)|(product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl&product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl))&(~d(sK1_skl,sK2_skl)|(~product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl|~product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl)))),
% 0.11/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X7,sK1_skl),skolemize(X8,sK2_skl)],[f27])).
% 0.11/0.51 fof(f29,plain,(
% 0.11/0.51 d(sK1_skl,sK2_skl)|product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.51 fof(f30,plain,(
% 0.11/0.51 d(sK1_skl,sK2_skl)|product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.51 fof(f31,plain,(
% 0.11/0.51 ~d(sK1_skl,sK2_skl)|~product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl|~product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl),
% 0.11/0.51 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.51 fof(f32,definition,(
% 0.11/0.51 sQ0_spl <=> (d(sK1_skl,sK2_skl))),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f33,plain,(
% 0.11/0.51 d(sK1_skl,sK2_skl)|~sQ0_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f32])).
% 0.11/0.51 fof(f34,plain,(
% 0.11/0.51 ~d(sK1_skl,sK2_skl)|sQ0_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f32])).
% 0.11/0.51 fof(f35,definition,(
% 0.11/0.51 sQ1_spl <=> (product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl)),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f36,plain,(
% 0.11/0.51 product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl|~sQ1_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f35])).
% 0.11/0.51 fof(f37,plain,(
% 0.11/0.51 ~product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl|sQ1_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f35])).
% 0.11/0.51 fof(f38,plain,(
% 0.11/0.51 sQ0_spl|sQ1_spl),
% 0.11/0.51 inference(split_clause,[status(thm)],[f29,f32,f35])).
% 0.11/0.51 fof(f39,definition,(
% 0.11/0.51 sQ2_spl <=> (product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl)),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f42,plain,(
% 0.11/0.51 sQ0_spl|sQ2_spl),
% 0.11/0.51 inference(split_clause,[status(thm)],[f30,f32,f39])).
% 0.11/0.51 fof(f43,plain,(
% 0.11/0.51 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.11/0.51 inference(split_clause,[status(thm)],[f31,f32,f35,f39])).
% 0.11/0.51 fof(f47,plain,(
% 0.11/0.51 ![X0,X1]: (product(X0,product(X1,product(X0,X1)))=product(X0,X1))),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f8,f9])).
% 0.11/0.51 fof(f49,plain,(
% 0.11/0.51 ![X0,X1]: (product(X0,X1)=product(X0,product(X0,X1)))),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f9,f8])).
% 0.11/0.51 fof(f56,plain,(
% 0.11/0.51 ![X0,X1,X2]: (product(product(X0,X1),X2)=product(X0,product(product(X1,product(X0,X1)),X2)))),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f47,f8])).
% 0.11/0.51 fof(f65,plain,(
% 0.11/0.51 ![X0,X1,X2]: (product(X0,product(X1,X2))=product(X0,product(product(X1,product(X0,X1)),X2)))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f8,f56])).
% 0.11/0.51 fof(f66,plain,(
% 0.11/0.51 ![X0,X1,X2]: (product(X0,product(X1,X2))=product(X0,product(X1,product(product(X0,X1),X2))))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f8,f65])).
% 0.11/0.51 fof(f67,plain,(
% 0.11/0.51 ![X0,X1,X2]: (product(X0,product(X1,X2))=product(X0,product(X1,product(X0,product(X1,X2)))))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f8,f66])).
% 0.11/0.51 fof(f254,plain,(
% 0.11/0.51 r(sK1_skl,sK0_skl(sK2_skl,sK1_skl))|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f23,f33])).
% 0.11/0.51 fof(f255,plain,(
% 0.11/0.51 l(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f24,f33])).
% 0.11/0.51 fof(f256,plain,(
% 0.11/0.51 ![X0,X1,X2]: (d(X0,X1)|~r(X0,X2)|~product(X2,X1)=X2|~product(X1,X2)=X1)),
% 0.11/0.51 inference(resolution,[status(thm)],[f25,f14])).
% 0.11/0.51 fof(f257,plain,(
% 0.11/0.51 product(sK0_skl(sK2_skl,sK1_skl),sK1_skl)=sK1_skl|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f254,f18])).
% 0.11/0.51 fof(f258,plain,(
% 0.11/0.51 product(sK1_skl,sK0_skl(sK2_skl,sK1_skl))=sK0_skl(sK2_skl,sK1_skl)|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f254,f17])).
% 0.11/0.51 fof(f260,plain,(
% 0.11/0.51 product(sK2_skl,sK0_skl(sK2_skl,sK1_skl))=sK2_skl|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f255,f13])).
% 0.11/0.51 fof(f261,plain,(
% 0.11/0.51 product(sK0_skl(sK2_skl,sK1_skl),sK2_skl)=sK0_skl(sK2_skl,sK1_skl)|~sQ0_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f255,f12])).
% 0.11/0.51 fof(f263,plain,(
% 0.11/0.51 ![X0,X1,X2]: (d(X0,X1)|~product(X2,X1)=X2|~product(X1,X2)=X1|~product(X0,X2)=X2|~product(X2,X0)=X0)),
% 0.11/0.51 inference(resolution,[status(thm)],[f256,f19])).
% 0.11/0.51 fof(f268,plain,(
% 0.11/0.51 ![X0]: (product(sK1_skl,X0)=product(sK0_skl(sK2_skl,sK1_skl),product(sK1_skl,X0))|~sQ0_spl)),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f257,f8])).
% 0.11/0.51 fof(f271,plain,(
% 0.11/0.51 ![X0]: (product(X0,product(sK1_skl,sK0_skl(sK2_skl,sK1_skl)))=product(X0,product(sK1_skl,product(X0,sK0_skl(sK2_skl,sK1_skl))))|~sQ0_spl)),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f258,f67])).
% 0.11/0.51 fof(f276,plain,(
% 0.11/0.51 ![X0]: (product(X0,sK0_skl(sK2_skl,sK1_skl))=product(X0,product(sK1_skl,product(X0,sK0_skl(sK2_skl,sK1_skl))))|~sQ0_spl)),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f258,f271])).
% 0.11/0.51 fof(f293,plain,(
% 0.11/0.51 ![X0]: (product(sK0_skl(sK2_skl,sK1_skl),X0)=product(sK0_skl(sK2_skl,sK1_skl),product(sK2_skl,X0))|~sQ0_spl)),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f261,f8])).
% 0.11/0.51 fof(f675,plain,(
% 0.11/0.51 product(sK2_skl,sK0_skl(sK2_skl,sK1_skl))=product(sK2_skl,product(sK1_skl,sK2_skl))|~sQ0_spl),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f260,f276])).
% 0.11/0.51 fof(f703,plain,(
% 0.11/0.51 sK2_skl=product(sK2_skl,product(sK1_skl,sK2_skl))|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f260,f675])).
% 0.11/0.51 fof(f1660,plain,(
% 0.11/0.51 product(sK0_skl(sK2_skl,sK1_skl),product(sK1_skl,product(sK2_skl,sK0_skl(sK2_skl,sK1_skl))))=product(sK0_skl(sK2_skl,sK1_skl),product(sK2_skl,sK0_skl(sK2_skl,sK1_skl)))|~sQ0_spl),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f276,f293])).
% 0.11/0.51 fof(f1711,plain,(
% 0.11/0.51 product(sK1_skl,product(sK2_skl,sK0_skl(sK2_skl,sK1_skl)))=product(sK0_skl(sK2_skl,sK1_skl),product(sK2_skl,sK0_skl(sK2_skl,sK1_skl)))|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f268,f1660])).
% 0.11/0.51 fof(f1712,plain,(
% 0.11/0.51 product(sK1_skl,sK2_skl)=product(sK0_skl(sK2_skl,sK1_skl),product(sK2_skl,sK0_skl(sK2_skl,sK1_skl)))|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f260,f1711])).
% 0.11/0.51 fof(f1713,plain,(
% 0.11/0.51 product(sK1_skl,sK2_skl)=product(sK0_skl(sK2_skl,sK1_skl),sK0_skl(sK2_skl,sK1_skl))|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f293,f1712])).
% 0.11/0.51 fof(f1714,plain,(
% 0.11/0.51 product(sK1_skl,sK2_skl)=sK0_skl(sK2_skl,sK1_skl)|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f9,f1713])).
% 0.11/0.51 fof(f2309,plain,(
% 0.11/0.51 product(product(sK1_skl,sK2_skl),sK1_skl)=sK1_skl|~sQ0_spl),
% 0.11/0.51 inference(backward_demodulation,[status(thm)],[f1714,f257])).
% 0.11/0.51 fof(f2334,plain,(
% 0.11/0.51 product(sK1_skl,product(sK2_skl,sK1_skl))=sK1_skl|~sQ0_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f8,f2309])).
% 0.11/0.51 fof(f2335,plain,(
% 0.11/0.51 $false|sQ1_spl|~sQ0_spl),
% 0.11/0.51 inference(forward_subsumption_resolution,[status(thm)],[f2334,f37])).
% 0.11/0.51 fof(f2336,plain,(
% 0.11/0.51 sQ1_spl|~sQ0_spl),
% 0.11/0.51 inference(contradiction_clause,[status(thm)],[f2335])).
% 0.11/0.51 fof(f2360,plain,(
% 0.11/0.51 ![X0]: (~product(X0,sK2_skl)=X0|~product(sK2_skl,X0)=sK2_skl|~product(sK1_skl,X0)=X0|~product(X0,sK1_skl)=sK1_skl|sQ0_spl)),
% 0.11/0.51 inference(resolution,[status(thm)],[f34,f263])).
% 0.11/0.51 fof(f2388,plain,(
% 0.11/0.51 ![X0,X1]: (~product(product(X0,X1),sK2_skl)=product(X0,X1)|~product(sK2_skl,product(X0,X1))=sK2_skl|~product(sK1_skl,product(X0,X1))=product(X0,X1)|~product(X0,product(X1,sK1_skl))=sK1_skl|sQ0_spl)),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f8,f2360])).
% 0.11/0.51 fof(f2396,definition,(
% 0.11/0.51 sQ6_spl <=> (product(sK1_skl,sK1_skl)=sK1_skl)),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f2398,plain,(
% 0.11/0.51 ~product(sK1_skl,sK1_skl)=sK1_skl|sQ6_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f2396])).
% 0.11/0.51 fof(f2400,plain,(
% 0.11/0.51 ![X0,X1]: (~product(X0,product(X1,sK2_skl))=product(X0,X1)|~product(sK2_skl,product(X0,X1))=sK2_skl|~product(sK1_skl,product(X0,X1))=product(X0,X1)|~product(X0,product(X1,sK1_skl))=sK1_skl|sQ0_spl)),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f8,f2388])).
% 0.11/0.51 fof(f2410,plain,(
% 0.11/0.51 sQ2_spl|~sQ0_spl),
% 0.11/0.51 inference(split_clause,[status(thm)],[f703,f39,f32])).
% 0.11/0.51 fof(f2419,plain,(
% 0.11/0.51 ~sK1_skl=sK1_skl|sQ6_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f9,f2398])).
% 0.11/0.51 fof(f2420,plain,(
% 0.11/0.51 $false|sQ6_spl),
% 0.11/0.51 inference(trivial_equality_resolution,[status(thm)],[f2419])).
% 0.11/0.51 fof(f2421,plain,(
% 0.11/0.51 sQ6_spl),
% 0.11/0.51 inference(contradiction_clause,[status(thm)],[f2420])).
% 0.11/0.51 fof(f2746,plain,(
% 0.11/0.51 ~product(sK1_skl,product(sK2_skl,sK2_skl))=product(sK1_skl,sK2_skl)|~product(sK2_skl,product(sK1_skl,sK2_skl))=sK2_skl|~product(sK1_skl,product(sK1_skl,sK2_skl))=product(sK1_skl,sK2_skl)|sQ0_spl|~sQ1_spl),
% 0.11/0.51 inference(resolution,[status(thm)],[f2400,f36])).
% 0.11/0.51 fof(f2753,definition,(
% 0.11/0.51 sQ16_spl <=> (product(sK1_skl,product(sK2_skl,sK2_skl))=product(sK1_skl,sK2_skl))),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f2755,plain,(
% 0.11/0.51 ~product(sK1_skl,product(sK2_skl,sK2_skl))=product(sK1_skl,sK2_skl)|sQ16_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f2753])).
% 0.11/0.51 fof(f2756,definition,(
% 0.11/0.51 sQ17_spl <=> (product(sK1_skl,product(sK1_skl,sK2_skl))=product(sK1_skl,sK2_skl))),
% 0.11/0.51 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.11/0.51 fof(f2758,plain,(
% 0.11/0.51 ~product(sK1_skl,product(sK1_skl,sK2_skl))=product(sK1_skl,sK2_skl)|sQ17_spl),
% 0.11/0.51 inference(component_clause,[status(thm)],[f2756])).
% 0.11/0.51 fof(f2759,plain,(
% 0.11/0.51 ~sQ16_spl|~sQ2_spl|~sQ17_spl|sQ0_spl|~sQ1_spl),
% 0.11/0.51 inference(split_clause,[status(thm)],[f2746,f2753,f39,f2756,f32,f35])).
% 0.11/0.51 fof(f2778,plain,(
% 0.11/0.51 ~product(sK1_skl,sK2_skl)=product(sK1_skl,sK2_skl)|sQ16_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f9,f2755])).
% 0.11/0.51 fof(f2779,plain,(
% 0.11/0.51 $false|sQ16_spl),
% 0.11/0.51 inference(trivial_equality_resolution,[status(thm)],[f2778])).
% 0.11/0.51 fof(f2780,plain,(
% 0.11/0.51 sQ16_spl),
% 0.11/0.51 inference(contradiction_clause,[status(thm)],[f2779])).
% 0.11/0.51 fof(f2781,plain,(
% 0.11/0.51 ~product(sK1_skl,sK2_skl)=product(sK1_skl,sK2_skl)|sQ17_spl),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f49,f2758])).
% 0.11/0.51 fof(f2782,plain,(
% 0.11/0.51 $false|sQ17_spl),
% 0.11/0.51 inference(trivial_equality_resolution,[status(thm)],[f2781])).
% 0.11/0.51 fof(f2783,plain,(
% 0.11/0.51 sQ17_spl),
% 0.11/0.51 inference(contradiction_clause,[status(thm)],[f2782])).
% 0.11/0.51 fof(f2784,plain,(
% 0.11/0.51 $false),
% 0.11/0.51 inference(sat_refutation,[status(thm)],[f38,f42,f43,f2336,f2410,f2421,f2759,f2780,f2783])).
% 0.11/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.55 % Elapsed time: 0.162502 seconds
% 0.11/0.55 % CPU time: 1.025297 seconds
% 0.11/0.55 % Total memory used: 117.926 MB
% 0.11/0.55 % Net memory used: 117.330 MB
%------------------------------------------------------------------------------