%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP685+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 : n012.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 12:37:10 PM UTC 2026
% Result : Theorem 0.08s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 20:33:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.08/0.35 % Refutation found
% 0.08/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.35 fof(f1,axiom,(
% 0.08/0.35 (! [A] : ld(A,mult(A,A)) = A )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f2,axiom,(
% 0.08/0.35 (! [A] : rd(mult(A,A),A) = A )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f3,axiom,(
% 0.08/0.35 (! [B,A] : mult(A,ld(A,B)) = ld(A,mult(A,B)) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f4,axiom,(
% 0.08/0.35 (! [B,A] : mult(rd(A,B),B) = rd(mult(A,B),B) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f5,axiom,(
% 0.08/0.35 (! [D,C,B,A] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f6,axiom,(
% 0.08/0.35 (! [D,C,B,A] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f7,axiom,(
% 0.08/0.35 (! [B,A] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f8,conjecture,(
% 0.08/0.35 (! [X6,X7,X8] :( rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8)& rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8) ) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f9,negated_conjecture,(
% 0.08/0.35 ~((! [X6,X7,X8] :( rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8)& rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8) ) ))),
% 0.08/0.35 inference(negated_conjecture,[status(cth)],[f8])).
% 0.08/0.35 fof(f10,plain,(
% 0.08/0.35 ![X0]: (ld(X0,mult(X0,X0))=X0)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.35 fof(f11,plain,(
% 0.08/0.35 ![X0]: (rd(mult(X0,X0),X0)=X0)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.35 fof(f12,plain,(
% 0.08/0.35 ![X0,X1]: (mult(X0,ld(X0,X1))=ld(X0,mult(X0,X1)))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.35 fof(f13,plain,(
% 0.08/0.35 ![X0,X1]: (mult(rd(X0,X1),X1)=rd(mult(X0,X1),X1))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.35 fof(f14,plain,(
% 0.08/0.35 ![X0,X1,X2,X3]: (ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3)))=mult(ld(X0,mult(X0,X2)),X3))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.35 fof(f15,plain,(
% 0.08/0.35 ![X0,X1,X2,X3]: (rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3))=mult(X0,rd(mult(X1,X3),X3)))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.35 fof(f16,plain,(
% 0.08/0.35 ![X0,X1]: (ld(X0,mult(X0,ld(X1,X1)))=rd(mult(rd(X0,X0),X1),X1))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.35 fof(f17,plain,(
% 0.08/0.35 (?[X6,X7,X8]: (~rd(mult(X6,ld(X7,X8)),ld(X7,X8))=rd(mult(X6,X8),X8)|~rd(mult(X6,rd(X7,X8)),rd(X7,X8))=rd(mult(X6,X8),X8)))),
% 0.08/0.35 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.08/0.35 fof(f18,plain,(
% 0.08/0.35 (?[X6,X7,X8]: ~rd(mult(X6,ld(X7,X8)),ld(X7,X8))=rd(mult(X6,X8),X8))|(?[X6,X7,X8]: ~rd(mult(X6,rd(X7,X8)),rd(X7,X8))=rd(mult(X6,X8),X8))),
% 0.08/0.35 inference(miniscoping,[status(thm)],[f17])).
% 0.08/0.35 fof(f19,plain,(
% 0.08/0.35 ~rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl))=rd(mult(sK0_skl,sK2_skl),sK2_skl)|~rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl))=rd(mult(sK3_skl,sK5_skl),sK5_skl)),
% 0.08/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X6,sK0_skl),skolemize(X7,sK1_skl),skolemize(X8,sK2_skl),skolemize(X6,sK3_skl),skolemize(X7,sK4_skl),skolemize(X8,sK5_skl)],[f18])).
% 0.08/0.35 fof(f20,plain,(
% 0.08/0.35 ~rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl))=rd(mult(sK0_skl,sK2_skl),sK2_skl)|~rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl))=rd(mult(sK3_skl,sK5_skl),sK5_skl)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f19])).
% 0.08/0.35 fof(f21,definition,(
% 0.08/0.35 sQ0_spl <=> (rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl))=rd(mult(sK0_skl,sK2_skl),sK2_skl))),
% 0.08/0.35 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.35 fof(f23,plain,(
% 0.08/0.35 ~rd(mult(sK0_skl,ld(sK1_skl,sK2_skl)),ld(sK1_skl,sK2_skl))=rd(mult(sK0_skl,sK2_skl),sK2_skl)|sQ0_spl),
% 0.08/0.35 inference(component_clause,[status(thm)],[f21])).
% 0.08/0.35 fof(f24,definition,(
% 0.08/0.35 sQ1_spl <=> (rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl))=rd(mult(sK3_skl,sK5_skl),sK5_skl))),
% 0.08/0.35 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.35 fof(f26,plain,(
% 0.08/0.35 ~rd(mult(sK3_skl,rd(sK4_skl,sK5_skl)),rd(sK4_skl,sK5_skl))=rd(mult(sK3_skl,sK5_skl),sK5_skl)|sQ1_spl),
% 0.08/0.35 inference(component_clause,[status(thm)],[f24])).
% 0.08/0.35 fof(f27,plain,(
% 0.08/0.35 ~sQ0_spl|~sQ1_spl),
% 0.08/0.35 inference(split_clause,[status(thm)],[f20,f21,f24])).
% 0.08/0.35 fof(f34,plain,(
% 0.08/0.35 ![X0,X1,X2]: (ld(X0,mult(ld(X0,mult(X0,X0)),mult(X1,X2)))=mult(ld(X0,mult(X0,X1)),X2))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f10,f14])).
% 0.08/0.35 fof(f48,plain,(
% 0.08/0.35 ![X0,X1,X2]: (ld(X0,mult(X0,mult(X1,X2)))=mult(ld(X0,mult(X0,X1)),X2))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f10,f34])).
% 0.08/0.35 fof(f72,plain,(
% 0.08/0.35 ![X0]: (ld(X0,mult(X0,ld(X0,X0)))=rd(rd(mult(X0,X0),X0),X0))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f13,f16])).
% 0.08/0.35 fof(f75,plain,(
% 0.08/0.35 ![X0,X1]: (mult(ld(X0,mult(X0,ld(X1,X1))),X1)=rd(mult(mult(rd(X0,X0),X1),X1),X1))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f16,f13])).
% 0.08/0.35 fof(f76,plain,(
% 0.08/0.35 ![X0]: (ld(X0,ld(X0,mult(X0,X0)))=rd(rd(mult(X0,X0),X0),X0))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f12,f72])).
% 0.08/0.35 fof(f77,plain,(
% 0.08/0.35 ![X0]: (ld(X0,X0)=rd(rd(mult(X0,X0),X0),X0))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f10,f76])).
% 0.08/0.35 fof(f80,plain,(
% 0.08/0.35 ![X0]: (ld(X0,X0)=rd(X0,X0))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f11,f77])).
% 0.08/0.35 fof(f89,plain,(
% 0.08/0.35 ![X0,X1]: (ld(X0,mult(X0,mult(ld(X1,X1),X1)))=rd(mult(mult(rd(X0,X0),X1),X1),X1))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f48,f75])).
% 0.08/0.35 fof(f90,plain,(
% 0.08/0.35 ![X0,X1]: (ld(X0,mult(X0,mult(ld(X1,X1),X1)))=rd(mult(mult(ld(X0,X0),X1),X1),X1))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f80,f89])).
% 0.08/0.35 fof(f93,plain,(
% 0.08/0.35 ![X0]: (mult(ld(X0,X0),X0)=rd(mult(X0,X0),X0))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f80,f13])).
% 0.08/0.35 fof(f94,plain,(
% 0.08/0.35 ![X0,X1]: (ld(X0,mult(X0,X1))=rd(mult(mult(ld(X0,X0),X1),X1),X1))),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f95,f90])).
% 0.08/0.35 fof(f95,plain,(
% 0.08/0.35 ![X0]: (mult(ld(X0,X0),X0)=X0)),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f11,f93])).
% 0.08/0.35 fof(f129,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=mult(ld(X0,X0),rd(mult(X0,X2),X2)))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f95,f15])).
% 0.08/0.35 fof(f134,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(mult(X0,X1),X2),rd(mult(X2,X2),X2))=mult(X0,rd(mult(X1,X2),X2)))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f11,f15])).
% 0.08/0.35 fof(f151,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=rd(mult(mult(ld(X0,X0),X0),X2),X2))),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f156,f129])).
% 0.08/0.35 fof(f156,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(mult(X0,X1),X2),X2)=mult(X0,rd(mult(X1,X2),X2)))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f11,f134])).
% 0.08/0.35 fof(f185,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=rd(mult(X0,X2),X2))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f95,f151])).
% 0.08/0.35 fof(f240,plain,(
% 0.08/0.35 ![X0,X1]: (rd(mult(mult(X0,X1),X1),X1)=mult(X0,X1))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f11,f156])).
% 0.08/0.35 fof(f267,plain,(
% 0.08/0.35 ![X0,X1]: (ld(X0,mult(X0,X1))=mult(ld(X0,X0),X1))),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f240,f94])).
% 0.08/0.35 fof(f388,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,mult(X1,X2)),rd(mult(mult(X1,X2),X2),X2))=rd(mult(X0,X2),X2))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f240,f185])).
% 0.08/0.35 fof(f417,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,mult(X1,X2)),mult(X1,X2))=rd(mult(X0,X2),X2))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f240,f388])).
% 0.08/0.35 fof(f594,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,ld(X1,mult(X1,X2))),mult(ld(X1,X1),X2))=rd(mult(X0,X2),X2))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f267,f417])).
% 0.08/0.35 fof(f597,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,ld(X1,mult(X1,X2))),mult(X1,ld(X1,X2)))=rd(mult(X0,ld(X1,X2)),ld(X1,X2)))),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f12,f417])).
% 0.08/0.35 fof(f622,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,ld(X1,mult(X1,X2))),ld(X1,mult(X1,X2)))=rd(mult(X0,X2),X2))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f267,f594])).
% 0.08/0.35 fof(f630,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,ld(X1,mult(X1,X2))),ld(X1,mult(X1,X2)))=rd(mult(X0,ld(X1,X2)),ld(X1,X2)))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f12,f597])).
% 0.08/0.35 fof(f631,plain,(
% 0.08/0.35 ~rd(mult(sK0_skl,sK2_skl),sK2_skl)=rd(mult(sK0_skl,sK2_skl),sK2_skl)|sQ0_spl),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f636,f23])).
% 0.08/0.35 fof(f636,plain,(
% 0.08/0.35 ![X0,X1,X2]: (rd(mult(X0,X1),X1)=rd(mult(X0,ld(X2,X1)),ld(X2,X1)))),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f622,f630])).
% 0.08/0.35 fof(f658,plain,(
% 0.08/0.35 $false|sQ0_spl),
% 0.08/0.35 inference(trivial_equality_resolution,[status(thm)],[f631])).
% 0.08/0.35 fof(f659,plain,(
% 0.08/0.35 sQ0_spl),
% 0.08/0.35 inference(contradiction_clause,[status(thm)],[f658])).
% 0.08/0.35 fof(f661,plain,(
% 0.08/0.35 ~rd(mult(sK3_skl,sK5_skl),sK5_skl)=rd(mult(sK3_skl,sK5_skl),sK5_skl)|sQ1_spl),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f185,f26])).
% 0.08/0.35 fof(f662,plain,(
% 0.08/0.35 $false|sQ1_spl),
% 0.08/0.35 inference(trivial_equality_resolution,[status(thm)],[f661])).
% 0.08/0.35 fof(f663,plain,(
% 0.08/0.35 sQ1_spl),
% 0.08/0.35 inference(contradiction_clause,[status(thm)],[f662])).
% 0.08/0.35 fof(f664,plain,(
% 0.08/0.35 $false),
% 0.08/0.35 inference(sat_refutation,[status(thm)],[f27,f659,f663])).
% 0.08/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.36 % Elapsed time: 0.059265 seconds
% 0.08/0.36 % CPU time: 0.262046 seconds
% 0.08/0.36 % Total memory used: 74.940 MB
% 0.08/0.36 % Net memory used: 74.189 MB
%------------------------------------------------------------------------------