%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:37:12 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:34:22 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f1,axiom,(
% 0.12/0.39 (! [B,A] : mult(A,ld(A,B)) = B )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f5,axiom,(
% 0.12/0.39 (! [A] : mult(A,unit) = A )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f6,axiom,(
% 0.12/0.39 (! [A] : mult(unit,A) = A )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f8,axiom,(
% 0.12/0.39 (! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f9,axiom,(
% 0.12/0.39 (! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f10,axiom,(
% 0.12/0.39 (! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f11,axiom,(
% 0.12/0.39 (! [A] : op_d = ld(A,mult(op_c,A)) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f13,axiom,(
% 0.12/0.39 (! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f14,conjecture,(
% 0.12/0.39 (! [X4,X5] :( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)& mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f15,negated_conjecture,(
% 0.12/0.39 ~((! [X4,X5] :( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)& mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f14])).
% 0.12/0.39 fof(f16,plain,(
% 0.12/0.39 ![X0,X1]: (mult(X0,ld(X0,X1))=X1)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.39 fof(f20,plain,(
% 0.12/0.39 ![X0]: (mult(X0,unit)=X0)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.39 fof(f21,plain,(
% 0.12/0.39 ![X0]: (mult(unit,X0)=X0)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f23,plain,(
% 0.12/0.39 ![X0,X1]: (mult(op_c,mult(X0,X1))=mult(mult(op_c,X0),X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.39 fof(f24,plain,(
% 0.12/0.39 ![X0,X1]: (mult(X0,mult(X1,op_c))=mult(mult(X0,X1),op_c))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.39 fof(f25,plain,(
% 0.12/0.39 ![X0,X1]: (mult(X0,mult(op_c,X1))=mult(mult(X0,op_c),X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.12/0.39 fof(f26,plain,(
% 0.12/0.39 ![X0]: (op_d=ld(X0,mult(op_c,X0)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.12/0.39 fof(f28,plain,(
% 0.12/0.39 ![X0,X1]: (op_f=mult(X0,mult(X1,ld(mult(X0,X1),op_c))))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.12/0.39 fof(f29,plain,(
% 0.12/0.39 (?[X4,X5]: ((~mult(op_f,mult(X4,X5))=mult(mult(op_f,X4),X5)|~mult(X4,mult(X5,op_f))=mult(mult(X4,X5),op_f))|~mult(X4,mult(op_f,X5))=mult(mult(X4,op_f),X5)))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.12/0.39 fof(f30,plain,(
% 0.12/0.39 ((?[X4,X5]: ~mult(op_f,mult(X4,X5))=mult(mult(op_f,X4),X5))|(?[X4,X5]: ~mult(X4,mult(X5,op_f))=mult(mult(X4,X5),op_f)))|(?[X4,X5]: ~mult(X4,mult(op_f,X5))=mult(mult(X4,op_f),X5))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.12/0.39 fof(f31,plain,(
% 0.12/0.39 (~mult(op_f,mult(sK0_skl,sK1_skl))=mult(mult(op_f,sK0_skl),sK1_skl)|~mult(sK2_skl,mult(sK3_skl,op_f))=mult(mult(sK2_skl,sK3_skl),op_f))|~mult(sK4_skl,mult(op_f,sK5_skl))=mult(mult(sK4_skl,op_f),sK5_skl)),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X4,sK0_skl),skolemize(X5,sK1_skl),skolemize(X4,sK2_skl),skolemize(X5,sK3_skl),skolemize(X4,sK4_skl),skolemize(X5,sK5_skl)],[f30])).
% 0.12/0.39 fof(f32,plain,(
% 0.12/0.39 ~mult(op_f,mult(sK0_skl,sK1_skl))=mult(mult(op_f,sK0_skl),sK1_skl)|~mult(sK2_skl,mult(sK3_skl,op_f))=mult(mult(sK2_skl,sK3_skl),op_f)|~mult(sK4_skl,mult(op_f,sK5_skl))=mult(mult(sK4_skl,op_f),sK5_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f31])).
% 0.12/0.39 fof(f33,definition,(
% 0.12/0.39 sQ0_spl <=> (mult(op_f,mult(sK0_skl,sK1_skl))=mult(mult(op_f,sK0_skl),sK1_skl))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f35,plain,(
% 0.12/0.39 ~mult(op_f,mult(sK0_skl,sK1_skl))=mult(mult(op_f,sK0_skl),sK1_skl)|sQ0_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f33])).
% 0.12/0.39 fof(f36,definition,(
% 0.12/0.39 sQ1_spl <=> (mult(sK2_skl,mult(sK3_skl,op_f))=mult(mult(sK2_skl,sK3_skl),op_f))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f38,plain,(
% 0.12/0.39 ~mult(sK2_skl,mult(sK3_skl,op_f))=mult(mult(sK2_skl,sK3_skl),op_f)|sQ1_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f36])).
% 0.12/0.39 fof(f39,definition,(
% 0.12/0.39 sQ2_spl <=> (mult(sK4_skl,mult(op_f,sK5_skl))=mult(mult(sK4_skl,op_f),sK5_skl))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f41,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(op_f,sK5_skl))=mult(mult(sK4_skl,op_f),sK5_skl)|sQ2_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f39])).
% 0.12/0.39 fof(f42,plain,(
% 0.12/0.39 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f32,f33,f36,f39])).
% 0.12/0.39 fof(f43,plain,(
% 0.12/0.39 ![X0]: (X0=ld(unit,X0))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f16,f21])).
% 0.12/0.39 fof(f150,plain,(
% 0.12/0.39 op_d=mult(op_c,unit)),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f43,f26])).
% 0.12/0.39 fof(f157,plain,(
% 0.12/0.39 ![X0]: (mult(X0,op_d)=mult(op_c,X0))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f26,f16])).
% 0.12/0.39 fof(f159,plain,(
% 0.12/0.39 op_d=op_c),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f20,f150])).
% 0.12/0.39 fof(f164,plain,(
% 0.12/0.39 ![X0,X1]: (mult(X0,mult(X1,op_c))=mult(op_c,mult(X0,X1)))),
% 0.12/0.39 inference(backward_demodulation,[status(thm)],[f166,f24])).
% 0.12/0.39 fof(f166,plain,(
% 0.12/0.39 ![X0]: (mult(X0,op_c)=mult(op_c,X0))),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f159,f157])).
% 0.12/0.39 fof(f217,plain,(
% 0.12/0.39 ![X0]: (op_f=mult(X0,ld(mult(unit,X0),op_c)))),
% 0.12/0.39 inference(paramodulation,[status(thm)],[f21,f28])).
% 0.12/0.39 fof(f236,plain,(
% 0.12/0.39 ![X0]: (op_f=mult(X0,ld(X0,op_c)))),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f21,f217])).
% 0.12/0.39 fof(f240,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(op_f,sK5_skl))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.12/0.39 inference(backward_demodulation,[status(thm)],[f241,f41])).
% 0.12/0.39 fof(f241,plain,(
% 0.12/0.39 op_f=op_c),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f16,f236])).
% 0.12/0.39 fof(f273,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(op_c,sK5_skl))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f241,f240])).
% 0.12/0.39 fof(f274,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f166,f273])).
% 0.12/0.39 fof(f275,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(sK4_skl,mult(op_c,sK5_skl))|sQ2_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f25,f274])).
% 0.12/0.39 fof(f276,plain,(
% 0.12/0.39 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(sK4_skl,mult(sK5_skl,op_c))|sQ2_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f166,f275])).
% 0.12/0.39 fof(f277,plain,(
% 0.12/0.39 $false|sQ2_spl),
% 0.12/0.39 inference(trivial_equality_resolution,[status(thm)],[f276])).
% 0.12/0.39 fof(f278,plain,(
% 0.12/0.39 sQ2_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f277])).
% 0.12/0.39 fof(f279,plain,(
% 0.12/0.39 ~mult(op_c,mult(sK0_skl,sK1_skl))=mult(mult(op_f,sK0_skl),sK1_skl)|sQ0_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f241,f35])).
% 0.12/0.39 fof(f280,plain,(
% 0.12/0.39 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(mult(op_f,sK0_skl),sK1_skl)|sQ0_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f164,f279])).
% 0.12/0.39 fof(f281,plain,(
% 0.12/0.39 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(mult(op_c,sK0_skl),sK1_skl)|sQ0_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f241,f280])).
% 0.12/0.39 fof(f282,plain,(
% 0.12/0.39 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(op_c,mult(sK0_skl,sK1_skl))|sQ0_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f23,f281])).
% 0.12/0.39 fof(f283,plain,(
% 0.12/0.39 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(sK0_skl,mult(sK1_skl,op_c))|sQ0_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f164,f282])).
% 0.12/0.39 fof(f284,plain,(
% 0.12/0.39 $false|sQ0_spl),
% 0.12/0.39 inference(trivial_equality_resolution,[status(thm)],[f283])).
% 0.12/0.39 fof(f285,plain,(
% 0.12/0.39 sQ0_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f284])).
% 0.12/0.39 fof(f290,plain,(
% 0.12/0.39 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(mult(sK2_skl,sK3_skl),op_f)|sQ1_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f241,f38])).
% 0.12/0.39 fof(f291,plain,(
% 0.12/0.39 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(mult(sK2_skl,sK3_skl),op_c)|sQ1_spl),
% 0.12/0.39 inference(forward_demodulation,[status(thm)],[f241,f290])).
% 0.12/0.39 fof(f292,plain,(
% 0.12/0.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(op_c,mult(sK2_skl,sK3_skl))|sQ1_spl),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f166,f291])).
% 0.12/0.40 fof(f293,plain,(
% 0.12/0.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(sK2_skl,mult(sK3_skl,op_c))|sQ1_spl),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f164,f292])).
% 0.12/0.40 fof(f294,plain,(
% 0.12/0.40 $false|sQ1_spl),
% 0.12/0.40 inference(trivial_equality_resolution,[status(thm)],[f293])).
% 0.12/0.40 fof(f295,plain,(
% 0.12/0.40 sQ1_spl),
% 0.12/0.40 inference(contradiction_clause,[status(thm)],[f294])).
% 0.12/0.40 fof(f296,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(sat_refutation,[status(thm)],[f42,f278,f285,f295])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.056523 seconds
% 0.12/0.42 % CPU time: 0.176413 seconds
% 0.12/0.42 % Total memory used: 68.151 MB
% 0.12/0.42 % Net memory used: 67.728 MB
%------------------------------------------------------------------------------