%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP682-11 : TPTP v9.3.1. Released v8.1.0.
% 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 12:37:09 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP682-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 20:32:57 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.48 % Drodi V4.1.1
% 0.20/0.57 % Refutation found
% 0.20/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.57 fof(f1,axiom,(
% 0.20/0.57 (![A]: (ld(A,mult(A,A)) = A ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f2,axiom,(
% 0.20/0.57 (![A]: (rd(mult(A,A),A) = A ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f3,axiom,(
% 0.20/0.57 (![A,B]: (mult(A,ld(A,B)) = ld(A,mult(A,B)) ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f4,axiom,(
% 0.20/0.57 (![A,B]: (mult(rd(A,B),B) = rd(mult(A,B),B) ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f5,axiom,(
% 0.20/0.57 (![A,B,C,D]: (ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f6,axiom,(
% 0.20/0.57 (![A,B,C,D]: (rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f7,axiom,(
% 0.20/0.57 (![A,B]: (ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) ))),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f8,negated_conjecture,(
% 0.20/0.57 ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)) ),
% 0.20/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.57 fof(f9,plain,(
% 0.20/0.57 ![X0]: (ld(X0,mult(X0,X0))=X0)),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f1])).
% 0.20/0.57 fof(f10,plain,(
% 0.20/0.57 ![X0]: (rd(mult(X0,X0),X0)=X0)),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f2])).
% 0.20/0.57 fof(f11,plain,(
% 0.20/0.57 ![X0,X1]: (mult(X0,ld(X0,X1))=ld(X0,mult(X0,X1)))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f3])).
% 0.20/0.57 fof(f12,plain,(
% 0.20/0.57 ![X0,X1]: (mult(rd(X0,X1),X1)=rd(mult(X0,X1),X1))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f4])).
% 0.20/0.57 fof(f13,plain,(
% 0.20/0.57 ![X0,X1,X2,X3]: (ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3)))=mult(ld(X0,mult(X0,X2)),X3))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f5])).
% 0.20/0.57 fof(f14,plain,(
% 0.20/0.57 ![X0,X1,X2,X3]: (rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3))=mult(X0,rd(mult(X1,X3),X3)))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f6])).
% 0.20/0.57 fof(f15,plain,(
% 0.20/0.57 ![X0,X1]: (ld(X0,mult(X0,ld(X1,X1)))=rd(mult(rd(X0,X0),X1),X1))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f7])).
% 0.20/0.57 fof(f16,plain,(
% 0.20/0.57 ~ld(rd(x0,x1),mult(rd(x0,x1),x2))=ld(x0,mult(x0,x2))),
% 0.20/0.57 inference(cnf_transformation,[status(thm)],[f8])).
% 0.20/0.57 fof(f29,plain,(
% 0.20/0.57 ![X0]: (ld(X0,ld(X0,mult(X0,X0)))=rd(mult(rd(X0,X0),X0),X0))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f11,f15])).
% 0.20/0.57 fof(f31,plain,(
% 0.20/0.57 ![X0,X1]: (mult(X0,rd(mult(rd(X0,X0),X1),X1))=ld(X0,mult(X0,mult(X0,ld(X1,X1)))))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f15,f11])).
% 0.20/0.57 fof(f32,plain,(
% 0.20/0.57 ![X0]: (ld(X0,X0)=rd(mult(rd(X0,X0),X0),X0))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f9,f29])).
% 0.20/0.57 fof(f33,plain,(
% 0.20/0.57 ![X0]: (ld(X0,X0)=rd(rd(mult(X0,X0),X0),X0))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f12,f32])).
% 0.20/0.57 fof(f37,plain,(
% 0.20/0.57 ![X0]: (ld(X0,X0)=rd(X0,X0))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f10,f33])).
% 0.20/0.57 fof(f41,plain,(
% 0.20/0.57 ![X0,X1]: (mult(X0,rd(mult(rd(X0,X0),X1),X1))=ld(X0,mult(X0,mult(X0,rd(X1,X1)))))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f37,f31])).
% 0.20/0.57 fof(f48,plain,(
% 0.20/0.57 ![X0]: (mult(X0,rd(X0,X0))=ld(X0,mult(X0,X0)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f37,f11])).
% 0.20/0.57 fof(f49,plain,(
% 0.20/0.57 ![X0]: (mult(X0,rd(X0,X0))=X0)),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f9,f48])).
% 0.20/0.57 fof(f60,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(X0,mult(ld(X0,mult(X0,X0)),mult(X1,X2)))=mult(ld(X0,mult(X0,X1)),X2))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f9,f13])).
% 0.20/0.57 fof(f68,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(ld(X0,X1),mult(ld(X0,X1),X2))=mult(ld(X0,mult(X0,X2)),rd(X2,X2)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f49,f13])).
% 0.20/0.57 fof(f82,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(X0,mult(X0,mult(X1,X2)))=mult(ld(X0,mult(X0,X1)),X2))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f9,f60])).
% 0.20/0.57 fof(f100,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(ld(X0,X1),mult(ld(X0,X1),X2))=ld(X0,mult(X0,mult(X2,rd(X2,X2)))))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f82,f68])).
% 0.20/0.57 fof(f103,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(ld(X0,X1),mult(ld(X0,X1),X2))=ld(X0,mult(X0,X2)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f49,f100])).
% 0.20/0.57 fof(f119,plain,(
% 0.20/0.57 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=mult(X0,rd(mult(rd(X0,X0),X2),X2)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f49,f14])).
% 0.20/0.57 fof(f125,plain,(
% 0.20/0.57 ![X0,X1,X2]: (rd(mult(mult(X0,X1),X2),rd(mult(X2,X2),X2))=mult(X0,rd(mult(X1,X2),X2)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f10,f14])).
% 0.20/0.57 fof(f144,plain,(
% 0.20/0.57 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=rd(mult(mult(X0,rd(X0,X0)),X2),X2))),
% 0.20/0.57 inference(backward_demodulation,[status(thm)],[f150,f119])).
% 0.20/0.57 fof(f145,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(mult(X0,rd(X0,X0)),X1),X1)=ld(X0,mult(X0,mult(X0,rd(X1,X1)))))),
% 0.20/0.57 inference(backward_demodulation,[status(thm)],[f150,f41])).
% 0.20/0.57 fof(f150,plain,(
% 0.20/0.57 ![X0,X1,X2]: (rd(mult(mult(X0,X1),X2),X2)=mult(X0,rd(mult(X1,X2),X2)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f10,f125])).
% 0.20/0.57 fof(f177,plain,(
% 0.20/0.57 ![X0,X1,X2]: (rd(mult(X0,rd(X1,X2)),rd(X1,X2))=rd(mult(X0,X2),X2))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f49,f144])).
% 0.20/0.57 fof(f178,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(X0,X1),X1)=ld(X0,mult(X0,mult(X0,rd(X1,X1)))))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f49,f145])).
% 0.20/0.57 fof(f200,plain,(
% 0.20/0.57 ![X0,X1]: (ld(X0,mult(X0,mult(X0,X1)))=mult(X0,X1))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f9,f82])).
% 0.20/0.57 fof(f221,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(X0,X1),X1)=mult(X0,rd(X1,X1)))),
% 0.20/0.57 inference(backward_demodulation,[status(thm)],[f200,f178])).
% 0.20/0.57 fof(f266,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(X0,mult(X0,mult(mult(X0,X1),X2)))=mult(mult(X0,X1),X2))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f200,f82])).
% 0.20/0.57 fof(f295,plain,(
% 0.20/0.57 ![X0]: (rd(rd(mult(rd(X0,X0),X0),X0),rd(X0,X0))=rd(X0,X0))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f221,f10])).
% 0.20/0.57 fof(f372,plain,(
% 0.20/0.57 ![X0]: (rd(rd(rd(mult(X0,X0),X0),X0),rd(X0,X0))=rd(X0,X0))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f12,f295])).
% 0.20/0.57 fof(f377,plain,(
% 0.20/0.57 ![X0]: (rd(rd(X0,X0),rd(X0,X0))=rd(X0,X0))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f10,f372])).
% 0.20/0.57 fof(f403,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(mult(X0,X1),mult(ld(X0,mult(X0,mult(X0,X1))),X2))=ld(X0,mult(X0,X2)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f200,f103])).
% 0.20/0.57 fof(f428,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(mult(X0,X1),ld(X0,mult(X0,mult(mult(X0,X1),X2))))=ld(X0,mult(X0,X2)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f82,f403])).
% 0.20/0.57 fof(f431,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(mult(X0,X1),mult(mult(X0,X1),X2))=ld(X0,mult(X0,X2)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f266,f428])).
% 0.20/0.57 fof(f471,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(mult(X0,X1),X1),X1)=mult(X0,X1))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f10,f150])).
% 0.20/0.57 fof(f570,plain,(
% 0.20/0.57 ![X0,X1]: (rd(X0,X1)=rd(mult(rd(X0,X1),X1),X1))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f10,f177])).
% 0.20/0.57 fof(f579,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(X0,rd(rd(X1,X1),rd(X1,X1))),rd(X1,X1))=rd(mult(X0,rd(X1,X1)),rd(X1,X1)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f377,f177])).
% 0.20/0.57 fof(f591,plain,(
% 0.20/0.57 ![X0,X1]: (rd(X0,X1)=rd(rd(mult(X0,X1),X1),X1))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f12,f570])).
% 0.20/0.57 fof(f610,plain,(
% 0.20/0.57 ![X0,X1]: (rd(rd(mult(X0,rd(X1,X1)),rd(X1,X1)),rd(X1,X1))=rd(mult(X0,rd(X1,X1)),rd(X1,X1)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f221,f579])).
% 0.20/0.57 fof(f611,plain,(
% 0.20/0.57 ![X0,X1]: (rd(X0,rd(X1,X1))=rd(mult(X0,rd(X1,X1)),rd(X1,X1)))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f591,f610])).
% 0.20/0.57 fof(f612,plain,(
% 0.20/0.57 ![X0,X1]: (rd(mult(X0,X1),rd(X1,X1))=mult(X0,X1))),
% 0.20/0.57 inference(backward_demodulation,[status(thm)],[f641,f471])).
% 0.20/0.57 fof(f616,plain,(
% 0.20/0.57 ![X0,X1]: (mult(rd(X0,X1),X1)=rd(X0,rd(X1,X1)))),
% 0.20/0.57 inference(backward_demodulation,[status(thm)],[f641,f12])).
% 0.20/0.57 fof(f641,plain,(
% 0.20/0.57 ![X0,X1]: (rd(X0,rd(X1,X1))=rd(mult(X0,X1),X1))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f177,f611])).
% 0.20/0.57 fof(f766,plain,(
% 0.20/0.57 ![X0,X1]: (mult(rd(X0,rd(X1,X1)),X1)=rd(mult(X0,X1),rd(X1,X1)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f641,f616])).
% 0.20/0.57 fof(f797,plain,(
% 0.20/0.57 ![X0,X1]: (mult(rd(X0,rd(X1,X1)),X1)=mult(X0,X1))),
% 0.20/0.57 inference(forward_demodulation,[status(thm)],[f612,f766])).
% 0.20/0.57 fof(f1131,plain,(
% 0.20/0.57 ![X0,X1,X2]: (ld(mult(X0,X1),mult(mult(rd(X0,rd(X1,X1)),X1),X2))=ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2)))),
% 0.20/0.57 inference(paramodulation,[status(thm)],[f797,f431])).
% 0.20/0.58 fof(f1132,plain,(
% 0.20/0.58 ![X0,X1,X2]: (ld(rd(X0,rd(X1,X1)),mult(mult(rd(X0,X1),X1),X2))=ld(rd(X0,X1),mult(rd(X0,X1),X2)))),
% 0.20/0.58 inference(paramodulation,[status(thm)],[f616,f431])).
% 0.20/0.58 fof(f1154,plain,(
% 0.20/0.58 ![X0,X1,X2]: (ld(mult(X0,X1),mult(mult(X0,X1),X2))=ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2)))),
% 0.20/0.58 inference(forward_demodulation,[status(thm)],[f797,f1131])).
% 0.20/0.58 fof(f1159,plain,(
% 0.20/0.58 ![X0,X1,X2]: (ld(X0,mult(X0,X1))=ld(rd(X0,rd(X2,X2)),mult(rd(X0,rd(X2,X2)),X1)))),
% 0.20/0.58 inference(forward_demodulation,[status(thm)],[f431,f1154])).
% 0.20/0.58 fof(f1160,plain,(
% 0.20/0.58 ![X0,X1,X2]: (ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2))=ld(rd(X0,X1),mult(rd(X0,X1),X2)))),
% 0.20/0.58 inference(forward_demodulation,[status(thm)],[f616,f1132])).
% 0.20/0.58 fof(f1161,plain,(
% 0.20/0.58 ~ld(x0,mult(x0,x2))=ld(x0,mult(x0,x2))),
% 0.20/0.58 inference(backward_demodulation,[status(thm)],[f1168,f16])).
% 0.20/0.58 fof(f1168,plain,(
% 0.20/0.58 ![X0,X1,X2]: (ld(X0,mult(X0,X1))=ld(rd(X0,X2),mult(rd(X0,X2),X1)))),
% 0.20/0.58 inference(forward_demodulation,[status(thm)],[f1159,f1160])).
% 0.20/0.58 fof(f1199,plain,(
% 0.20/0.58 $false),
% 0.20/0.58 inference(trivial_equality_resolution,[status(thm)],[f1161])).
% 0.20/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 12.72/9.98 % Elapsed time: 9.296284 seconds
% 12.72/9.98 % CPU time: 64.680414 seconds
% 12.72/9.98 % Total memory used: 32.680 GB
% 12.72/9.98 % Net memory used: 32.679 GB
%------------------------------------------------------------------------------