%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP659+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 : n005.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 12:37:06 PM UTC 2026
% Result : Theorem 25.65s 8.89s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n005.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sun Sep 20 20:29:39 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.46 % Drodi V4.1.1
% 25.65/8.89 % Refutation found
% 25.65/8.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 25.65/8.89 % SZS output start CNFRefutation for theBenchmark
% 25.65/8.89 fof(f1,axiom,(
% 25.65/8.89 (! [B,A] : mult(A,ld(A,B)) = B )),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f2,axiom,(
% 25.65/8.89 (! [B,A] : ld(A,mult(A,B)) = B )),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f3,axiom,(
% 25.65/8.89 (! [B,A] : mult(rd(A,B),B) = A )),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f4,axiom,(
% 25.65/8.89 (! [B,A] : rd(mult(A,B),B) = A )),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f5,axiom,(
% 25.65/8.89 (! [C,B,A] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)) )),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f6,conjecture,(
% 25.65/8.89 (? [X0] :(! [X1] :( mult(X1,X0) = X1& mult(X0,X1) = X1 ) ))),
% 25.65/8.89 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.65/8.89 fof(f7,negated_conjecture,(
% 25.65/8.89 ~((? [X0] :(! [X1] :( mult(X1,X0) = X1& mult(X0,X1) = X1 ) )))),
% 25.65/8.89 inference(negated_conjecture,[status(cth)],[f6])).
% 25.65/8.89 fof(f8,plain,(
% 25.65/8.89 ![X0,X1]: (mult(X0,ld(X0,X1))=X1)),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f1])).
% 25.65/8.89 fof(f9,plain,(
% 25.65/8.89 ![X0,X1]: (ld(X0,mult(X0,X1))=X1)),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f2])).
% 25.65/8.89 fof(f10,plain,(
% 25.65/8.89 ![X0,X1]: (mult(rd(X0,X1),X1)=X0)),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f3])).
% 25.65/8.89 fof(f11,plain,(
% 25.65/8.89 ![X0,X1]: (rd(mult(X0,X1),X1)=X0)),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f4])).
% 25.65/8.89 fof(f12,plain,(
% 25.65/8.89 ![X0,X1,X2]: (mult(mult(X0,mult(X1,X2)),X1)=mult(mult(X0,X1),mult(X2,X1)))),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f5])).
% 25.65/8.89 fof(f13,plain,(
% 25.65/8.89 (![X0]: ?[X1]: (~mult(X1,X0)=X1|~mult(X0,X1)=X1))),
% 25.65/8.89 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 25.65/8.89 fof(f14,plain,(
% 25.65/8.89 ![X0]: ((?[X1]: ~mult(X1,X0)=X1)|(?[X1]: ~mult(X0,X1)=X1))),
% 25.65/8.89 inference(miniscoping,[status(thm)],[f13])).
% 25.65/8.89 fof(f15,plain,(
% 25.65/8.89 ![X0]: (~mult(sK0_skl(X0),X0)=sK0_skl(X0)|~mult(X0,sK1_skl(X0))=sK1_skl(X0))),
% 25.65/8.89 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X1,sK0_skl(X0)),skolemize(X1,sK1_skl(X0))],[f14])).
% 25.65/8.89 fof(f16,plain,(
% 25.65/8.89 ![X0]: (~mult(sK0_skl(X0),X0)=sK0_skl(X0)|~mult(X0,sK1_skl(X0))=sK1_skl(X0))),
% 25.65/8.89 inference(cnf_transformation,[status(thm)],[f15])).
% 25.65/8.89 fof(f19,plain,(
% 25.65/8.89 ![X0,X1]: (ld(rd(X0,X1),X0)=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f10,f9])).
% 25.65/8.89 fof(f21,plain,(
% 25.65/8.89 ![X0,X1]: (rd(X0,ld(X1,X0))=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f8,f11])).
% 25.65/8.89 fof(f26,plain,(
% 25.65/8.89 ![X0,X1,X2]: (mult(X0,X1)=mult(mult(rd(X0,mult(X1,X2)),X1),mult(X2,X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f10,f12])).
% 25.65/8.89 fof(f29,plain,(
% 25.65/8.89 ![X0,X1,X2]: (mult(mult(X0,X1),X2)=mult(mult(X0,X2),mult(ld(X2,X1),X2)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f8,f12])).
% 25.65/8.89 fof(f30,plain,(
% 25.65/8.89 ![X0,X1,X2]: (rd(mult(mult(X0,X1),mult(X2,X1)),X1)=mult(X0,mult(X1,X2)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f12,f11])).
% 25.65/8.89 fof(f31,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(mult(X0,mult(X1,X2)),mult(mult(X0,X1),mult(X2,X1)))=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f12,f9])).
% 25.65/8.89 fof(f47,plain,(
% 25.65/8.89 ![X0,X1,X2]: (rd(mult(X0,X1),mult(X2,X1))=mult(rd(X0,mult(X1,X2)),X1))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f26,f11])).
% 25.65/8.89 fof(f70,plain,(
% 25.65/8.89 ![X0,X1,X2]: (mult(mult(rd(X0,X1),X2),X1)=mult(X0,mult(ld(X1,X2),X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f10,f29])).
% 25.65/8.89 fof(f190,plain,(
% 25.65/8.89 ![X0,X1,X2]: (rd(rd(mult(X0,X1),mult(X2,X1)),X1)=rd(X0,mult(X1,X2)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f47,f11])).
% 25.65/8.89 fof(f191,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(rd(X0,mult(X1,X2)),rd(mult(X0,X1),mult(X2,X1)))=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f47,f9])).
% 25.65/8.89 fof(f202,plain,(
% 25.65/8.89 ![X0,X1]: (mult(X0,X1)=mult(X0,mult(ld(X1,X1),X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f10,f70])).
% 25.65/8.89 fof(f222,plain,(
% 25.65/8.89 ![X0,X1,X2]: (rd(mult(X0,mult(ld(X1,X2),X1)),X1)=mult(rd(X0,X1),X2))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f70,f11])).
% 25.65/8.89 fof(f223,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(mult(rd(X0,X1),X2),mult(X0,mult(ld(X1,X2),X1)))=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f70,f9])).
% 25.65/8.89 fof(f250,plain,(
% 25.65/8.89 ![X0,X1]: (mult(mult(X0,X1),ld(X1,X1))=mult(mult(X0,ld(X1,X1)),mult(X1,ld(X1,X1))))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f202,f12])).
% 25.65/8.89 fof(f260,plain,(
% 25.65/8.89 ![X0,X1]: (ld(X0,mult(X0,X1))=mult(ld(X1,X1),X1))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f202,f9])).
% 25.65/8.89 fof(f290,plain,(
% 25.65/8.89 ![X0,X1]: (mult(mult(X0,X1),ld(X1,X1))=mult(mult(X0,ld(X1,X1)),X1))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f8,f250])).
% 25.65/8.89 fof(f318,plain,(
% 25.65/8.89 ![X0]: (X0=mult(ld(X0,X0),X0))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f9,f260])).
% 25.65/8.89 fof(f337,plain,(
% 25.65/8.89 ![X0]: (rd(X0,X0)=ld(X0,X0))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f318,f11])).
% 25.65/8.89 fof(f649,plain,(
% 25.65/8.89 ![X0,X1]: (rd(ld(mult(X0,X1),mult(X0,X1)),X1)=rd(X0,mult(X1,X0)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f337,f190])).
% 25.65/8.89 fof(f720,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(rd(X0,mult(X1,rd(X2,X1))),rd(mult(X0,X1),X2))=X1)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f10,f191])).
% 25.65/8.89 fof(f736,plain,(
% 25.65/8.89 ![X0,X1]: (rd(mult(X0,mult(X1,X0)),X0)=mult(ld(X0,X0),mult(X0,X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f318,f30])).
% 25.65/8.89 fof(f899,plain,(
% 25.65/8.89 ![X0,X1]: (ld(mult(ld(X0,X0),X1),mult(X0,mult(ld(X0,X1),X0)))=X0)),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f337,f223])).
% 25.65/8.89 fof(f943,plain,(
% 25.65/8.89 ![X0]: (mult(mult(X0,X0),ld(X0,X0))=mult(X0,X0))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f8,f290])).
% 25.65/8.89 fof(f1005,plain,(
% 25.65/8.89 ![X0,X1]: (ld(mult(X0,mult(X1,X1)),mult(mult(X0,mult(X1,X1)),mult(ld(X1,X1),mult(X1,X1))))=mult(X1,X1))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f943,f31])).
% 25.65/8.89 fof(f1009,plain,(
% 25.65/8.89 ![X0]: (ld(mult(X0,X0),mult(X0,X0))=ld(X0,X0))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f943,f9])).
% 25.65/8.89 fof(f1033,plain,(
% 25.65/8.89 ![X0]: (mult(ld(X0,X0),mult(X0,X0))=mult(X0,X0))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f9,f1005])).
% 25.65/8.89 fof(f1041,plain,(
% 25.65/8.89 ![X0]: (rd(mult(X0,mult(X0,X0)),X0)=mult(X0,X0))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f736,f1033])).
% 25.65/8.89 fof(f1297,plain,(
% 25.65/8.89 ![X0]: (rd(ld(mult(X0,X0),mult(mult(X0,X0),ld(X0,X0))),ld(X0,X0))=rd(mult(X0,X0),mult(ld(X0,X0),mult(X0,X0))))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f943,f649])).
% 25.65/8.89 fof(f1301,plain,(
% 25.65/8.89 ![X0,X1]: (rd(ld(X0,mult(X1,ld(X1,X0))),ld(X1,X0))=rd(X1,mult(ld(X1,X0),X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f8,f649])).
% 25.65/8.89 fof(f1333,plain,(
% 25.65/8.89 ![X0]: (rd(ld(X0,X0),ld(X0,X0))=rd(mult(X0,X0),mult(ld(X0,X0),mult(X0,X0))))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f9,f1297])).
% 25.65/8.89 fof(f1334,plain,(
% 25.65/8.89 ![X0]: (ld(ld(X0,X0),ld(X0,X0))=rd(mult(X0,X0),mult(ld(X0,X0),mult(X0,X0))))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f337,f1333])).
% 25.65/8.89 fof(f1335,plain,(
% 25.65/8.89 ![X0]: (ld(ld(X0,X0),ld(X0,X0))=rd(mult(X0,X0),rd(mult(X0,mult(X0,X0)),X0)))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f736,f1334])).
% 25.65/8.89 fof(f1336,plain,(
% 25.65/8.89 ![X0]: (ld(ld(X0,X0),ld(X0,X0))=rd(mult(X0,X0),mult(X0,X0)))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f1041,f1335])).
% 25.65/8.89 fof(f1337,plain,(
% 25.65/8.89 ![X0]: (ld(ld(X0,X0),ld(X0,X0))=ld(mult(X0,X0),mult(X0,X0)))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f337,f1336])).
% 25.65/8.89 fof(f1341,plain,(
% 25.65/8.89 ![X0]: (ld(ld(X0,X0),ld(X0,X0))=ld(X0,X0))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f1009,f1337])).
% 25.65/8.89 fof(f1345,plain,(
% 25.65/8.89 ![X0,X1]: (rd(ld(X0,X0),ld(X1,X0))=rd(X1,mult(ld(X1,X0),X1)))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f8,f1301])).
% 25.65/8.89 fof(f2689,plain,(
% 25.65/8.89 ![X0,X1]: (rd(ld(X0,X0),ld(X1,ld(X0,X0)))=rd(X1,mult(ld(X1,ld(X0,X0)),X1)))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f1341,f1345])).
% 25.65/8.89 fof(f2732,plain,(
% 25.65/8.89 ![X0,X1]: (X0=rd(X0,mult(ld(X0,ld(X1,X1)),X0)))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f21,f2689])).
% 25.65/8.89 fof(f2811,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(rd(X0,mult(mult(ld(X1,ld(X2,X2)),X1),X1)),rd(mult(X0,mult(ld(X1,ld(X2,X2)),X1)),X1))=mult(ld(X1,ld(X2,X2)),X1))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f2732,f720])).
% 25.65/8.89 fof(f2816,plain,(
% 25.65/8.89 ![X0,X1]: (ld(X0,X0)=mult(ld(X0,ld(X1,X1)),X0))),
% 25.65/8.89 inference(paramodulation,[status(thm)],[f2732,f19])).
% 25.65/8.89 fof(f2846,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(rd(X0,mult(mult(ld(X1,ld(X2,X2)),X1),X1)),mult(rd(X0,X1),ld(X2,X2)))=mult(ld(X1,ld(X2,X2)),X1))),
% 25.65/8.89 inference(forward_demodulation,[status(thm)],[f222,f2811])).
% 25.65/8.89 fof(f2856,plain,(
% 25.65/8.89 ![X0,X1,X2]: (ld(rd(X0,mult(mult(ld(X1,ld(X2,X2)),X1),X1)),mult(rd(X0,X1),ld(X2,X2)))=ld(X1,X1))),
% 8.17/8.98 inference(backward_demodulation,[status(thm)],[f2816,f2846])).
% 8.17/8.98 fof(f2864,plain,(
% 8.17/8.98 ![X0,X1,X2]: (ld(rd(X0,mult(ld(X1,X1),X1)),mult(rd(X0,X1),ld(X2,X2)))=ld(X1,X1))),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f2816,f2856])).
% 8.17/8.98 fof(f2865,plain,(
% 8.17/8.98 ![X0,X1,X2]: (ld(rd(X0,X1),mult(rd(X0,X1),ld(X2,X2)))=ld(X1,X1))),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f318,f2864])).
% 8.17/8.98 fof(f2866,plain,(
% 8.17/8.98 ![X0,X1]: (ld(X0,X0)=ld(X1,X1))),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f9,f2865])).
% 8.17/8.98 fof(f2875,plain,(
% 8.17/8.98 ![X0,X1]: (ld(mult(ld(X0,X0),X0),mult(X0,mult(ld(X1,X1),X0)))=X0)),
% 8.17/8.98 inference(paramodulation,[status(thm)],[f2866,f899])).
% 8.17/8.98 fof(f2891,plain,(
% 8.17/8.98 ![X0,X1]: (mult(X0,ld(X1,X1))=X0)),
% 8.17/8.98 inference(paramodulation,[status(thm)],[f2866,f8])).
% 8.17/8.98 fof(f2928,plain,(
% 8.17/8.98 ![X0,X1]: (ld(X0,mult(X0,mult(ld(X1,X1),X0)))=X0)),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f318,f2875])).
% 8.17/8.98 fof(f2987,plain,(
% 8.17/8.98 ![X0,X1]: (mult(ld(X0,X0),X1)=X1)),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f9,f2928])).
% 8.17/8.98 fof(f3839,plain,(
% 8.17/8.98 ![X0]: (~mult(sK0_skl(ld(X0,X0)),ld(X0,X0))=sK0_skl(ld(X0,X0)))),
% 8.17/8.98 inference(resolution,[status(thm)],[f2987,f16])).
% 8.17/8.98 fof(f3876,plain,(
% 8.17/8.98 ![X0]: (~sK0_skl(ld(X0,X0))=sK0_skl(ld(X0,X0)))),
% 8.17/8.98 inference(forward_demodulation,[status(thm)],[f2891,f3839])).
% 8.17/8.98 fof(f3877,plain,(
% 8.17/8.98 $false),
% 8.17/8.98 inference(trivial_equality_resolution,[status(thm)],[f3876])).
% 8.17/8.98 % SZS output end CNFRefutation for theBenchmark.p
% 6.59/9.01 % Elapsed time: 3.533363 seconds
% 6.59/9.01 % CPU time: 26.422878 seconds
% 6.59/9.01 % Total memory used: 396.105 MB
% 6.59/9.01 % Net memory used: 392.977 MB
%------------------------------------------------------------------------------