%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.09s 5.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n009.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:34:17 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.40 % Refutation found
% 0.09/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/5.40 fof(f1,axiom,(
% 0.09/5.40 (! [B,A] : mult(A,ld(A,B)) = B )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f5,axiom,(
% 0.09/5.40 (! [A] : mult(A,unit) = A )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f6,axiom,(
% 0.09/5.40 (! [A] : mult(unit,A) = A )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f8,axiom,(
% 0.09/5.40 (! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f9,axiom,(
% 0.09/5.40 (! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f10,axiom,(
% 0.09/5.40 (! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f11,axiom,(
% 0.09/5.40 (! [A] : op_d = ld(A,mult(op_c,A)) )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f14,conjecture,(
% 0.09/5.40 (! [X0,X1] :( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)& mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ) )),
% 0.09/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.40 fof(f15,negated_conjecture,(
% 0.09/5.40 ~((! [X0,X1] :( mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1)& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)& mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1) ) ))),
% 0.09/5.40 inference(negated_conjecture,[status(cth)],[f14])).
% 0.09/5.40 fof(f16,plain,(
% 0.09/5.40 ![X0,X1]: (mult(X0,ld(X0,X1))=X1)),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/5.40 fof(f20,plain,(
% 0.09/5.40 ![X0]: (mult(X0,unit)=X0)),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/5.40 fof(f21,plain,(
% 0.09/5.40 ![X0]: (mult(unit,X0)=X0)),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/5.40 fof(f23,plain,(
% 0.09/5.40 ![X0,X1]: (mult(op_c,mult(X0,X1))=mult(mult(op_c,X0),X1))),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/5.40 fof(f24,plain,(
% 0.09/5.40 ![X0,X1]: (mult(X0,mult(X1,op_c))=mult(mult(X0,X1),op_c))),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/5.40 fof(f25,plain,(
% 0.09/5.40 ![X0,X1]: (mult(X0,mult(op_c,X1))=mult(mult(X0,op_c),X1))),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/5.40 fof(f26,plain,(
% 0.09/5.40 ![X0]: (op_d=ld(X0,mult(op_c,X0)))),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/5.40 fof(f29,plain,(
% 0.09/5.40 (?[X0,X1]: ((~mult(op_d,mult(X0,X1))=mult(mult(op_d,X0),X1)|~mult(X0,mult(X1,op_d))=mult(mult(X0,X1),op_d))|~mult(X0,mult(op_d,X1))=mult(mult(X0,op_d),X1)))),
% 0.09/5.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/5.40 fof(f30,plain,(
% 0.09/5.40 ((?[X0,X1]: ~mult(op_d,mult(X0,X1))=mult(mult(op_d,X0),X1))|(?[X0,X1]: ~mult(X0,mult(X1,op_d))=mult(mult(X0,X1),op_d)))|(?[X0,X1]: ~mult(X0,mult(op_d,X1))=mult(mult(X0,op_d),X1))),
% 0.09/5.40 inference(miniscoping,[status(thm)],[f29])).
% 0.09/5.40 fof(f31,plain,(
% 0.09/5.40 (~mult(op_d,mult(sK0_skl,sK1_skl))=mult(mult(op_d,sK0_skl),sK1_skl)|~mult(sK2_skl,mult(sK3_skl,op_d))=mult(mult(sK2_skl,sK3_skl),op_d))|~mult(sK4_skl,mult(op_d,sK5_skl))=mult(mult(sK4_skl,op_d),sK5_skl)),
% 0.09/5.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl),skolemize(X0,sK4_skl),skolemize(X1,sK5_skl)],[f30])).
% 0.09/5.40 fof(f32,plain,(
% 0.09/5.40 ~mult(op_d,mult(sK0_skl,sK1_skl))=mult(mult(op_d,sK0_skl),sK1_skl)|~mult(sK2_skl,mult(sK3_skl,op_d))=mult(mult(sK2_skl,sK3_skl),op_d)|~mult(sK4_skl,mult(op_d,sK5_skl))=mult(mult(sK4_skl,op_d),sK5_skl)),
% 0.09/5.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/5.40 fof(f33,definition,(
% 0.09/5.40 sQ0_spl <=> (mult(op_d,mult(sK0_skl,sK1_skl))=mult(mult(op_d,sK0_skl),sK1_skl))),
% 0.09/5.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/5.40 fof(f35,plain,(
% 0.09/5.40 ~mult(op_d,mult(sK0_skl,sK1_skl))=mult(mult(op_d,sK0_skl),sK1_skl)|sQ0_spl),
% 0.09/5.40 inference(component_clause,[status(thm)],[f33])).
% 0.09/5.40 fof(f36,definition,(
% 0.09/5.40 sQ1_spl <=> (mult(sK2_skl,mult(sK3_skl,op_d))=mult(mult(sK2_skl,sK3_skl),op_d))),
% 0.09/5.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/5.40 fof(f38,plain,(
% 0.09/5.40 ~mult(sK2_skl,mult(sK3_skl,op_d))=mult(mult(sK2_skl,sK3_skl),op_d)|sQ1_spl),
% 0.09/5.40 inference(component_clause,[status(thm)],[f36])).
% 0.09/5.40 fof(f39,definition,(
% 0.09/5.40 sQ2_spl <=> (mult(sK4_skl,mult(op_d,sK5_skl))=mult(mult(sK4_skl,op_d),sK5_skl))),
% 0.09/5.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/5.40 fof(f41,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(op_d,sK5_skl))=mult(mult(sK4_skl,op_d),sK5_skl)|sQ2_spl),
% 0.09/5.40 inference(component_clause,[status(thm)],[f39])).
% 0.09/5.40 fof(f42,plain,(
% 0.09/5.40 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.09/5.40 inference(split_clause,[status(thm)],[f32,f33,f36,f39])).
% 0.09/5.40 fof(f43,plain,(
% 0.09/5.40 ![X0]: (X0=ld(unit,X0))),
% 0.09/5.40 inference(paramodulation,[status(thm)],[f16,f21])).
% 0.09/5.40 fof(f150,plain,(
% 0.09/5.40 op_d=mult(op_c,unit)),
% 0.09/5.40 inference(paramodulation,[status(thm)],[f43,f26])).
% 0.09/5.40 fof(f157,plain,(
% 0.09/5.40 ![X0]: (mult(X0,op_d)=mult(op_c,X0))),
% 0.09/5.40 inference(paramodulation,[status(thm)],[f26,f16])).
% 0.09/5.40 fof(f159,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(op_d,sK5_skl))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.09/5.40 inference(backward_demodulation,[status(thm)],[f160,f41])).
% 0.09/5.40 fof(f160,plain,(
% 0.09/5.40 op_d=op_c),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f20,f150])).
% 0.09/5.40 fof(f165,plain,(
% 0.09/5.40 ![X0,X1]: (mult(X0,mult(X1,op_c))=mult(op_c,mult(X0,X1)))),
% 0.09/5.40 inference(backward_demodulation,[status(thm)],[f167,f24])).
% 0.09/5.40 fof(f167,plain,(
% 0.09/5.40 ![X0]: (mult(X0,op_c)=mult(op_c,X0))),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f157])).
% 0.09/5.40 fof(f168,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(op_c,sK5_skl))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f159])).
% 0.09/5.40 fof(f169,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(mult(sK4_skl,op_c),sK5_skl)|sQ2_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f167,f168])).
% 0.09/5.40 fof(f170,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(sK4_skl,mult(op_c,sK5_skl))|sQ2_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f25,f169])).
% 0.09/5.40 fof(f171,plain,(
% 0.09/5.40 ~mult(sK4_skl,mult(sK5_skl,op_c))=mult(sK4_skl,mult(sK5_skl,op_c))|sQ2_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f167,f170])).
% 0.09/5.40 fof(f172,plain,(
% 0.09/5.40 $false|sQ2_spl),
% 0.09/5.40 inference(trivial_equality_resolution,[status(thm)],[f171])).
% 0.09/5.40 fof(f173,plain,(
% 0.09/5.40 sQ2_spl),
% 0.09/5.40 inference(contradiction_clause,[status(thm)],[f172])).
% 0.09/5.40 fof(f176,plain,(
% 0.09/5.40 ~mult(op_c,mult(sK0_skl,sK1_skl))=mult(mult(op_d,sK0_skl),sK1_skl)|sQ0_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f35])).
% 0.09/5.40 fof(f177,plain,(
% 0.09/5.40 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(mult(op_d,sK0_skl),sK1_skl)|sQ0_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f165,f176])).
% 0.09/5.40 fof(f178,plain,(
% 0.09/5.40 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(mult(op_c,sK0_skl),sK1_skl)|sQ0_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f177])).
% 0.09/5.40 fof(f179,plain,(
% 0.09/5.40 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(op_c,mult(sK0_skl,sK1_skl))|sQ0_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f23,f178])).
% 0.09/5.40 fof(f180,plain,(
% 0.09/5.40 ~mult(sK0_skl,mult(sK1_skl,op_c))=mult(sK0_skl,mult(sK1_skl,op_c))|sQ0_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f165,f179])).
% 0.09/5.40 fof(f181,plain,(
% 0.09/5.40 $false|sQ0_spl),
% 0.09/5.40 inference(trivial_equality_resolution,[status(thm)],[f180])).
% 0.09/5.40 fof(f182,plain,(
% 0.09/5.40 sQ0_spl),
% 0.09/5.40 inference(contradiction_clause,[status(thm)],[f181])).
% 0.09/5.40 fof(f189,plain,(
% 0.09/5.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(mult(sK2_skl,sK3_skl),op_d)|sQ1_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f38])).
% 0.09/5.40 fof(f190,plain,(
% 0.09/5.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(mult(sK2_skl,sK3_skl),op_c)|sQ1_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f160,f189])).
% 0.09/5.40 fof(f191,plain,(
% 0.09/5.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(op_c,mult(sK2_skl,sK3_skl))|sQ1_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f167,f190])).
% 0.09/5.40 fof(f192,plain,(
% 0.09/5.40 ~mult(sK2_skl,mult(sK3_skl,op_c))=mult(sK2_skl,mult(sK3_skl,op_c))|sQ1_spl),
% 0.09/5.40 inference(forward_demodulation,[status(thm)],[f165,f191])).
% 0.09/5.40 fof(f193,plain,(
% 0.09/5.40 $false|sQ1_spl),
% 0.09/5.40 inference(trivial_equality_resolution,[status(thm)],[f192])).
% 0.09/5.40 fof(f194,plain,(
% 0.09/5.40 sQ1_spl),
% 0.09/5.40 inference(contradiction_clause,[status(thm)],[f193])).
% 0.09/5.40 fof(f195,plain,(
% 0.09/5.40 $false),
% 0.09/5.40 inference(sat_refutation,[status(thm)],[f42,f173,f182,f194])).
% 0.09/5.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.42 % Elapsed time: 0.048844 seconds
% 0.13/5.42 % CPU time: 0.162277 seconds
% 0.13/5.42 % Total memory used: 65.327 MB
% 0.13/5.42 % Net memory used: 64.928 MB
%------------------------------------------------------------------------------