%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP731-1 : 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 12:37:15 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 20:36:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.53 fof(f1,axiom,(
% 0.10/0.53 (![A]: (mult(unit,A) = A ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f2,axiom,(
% 0.10/0.53 (![A]: (mult(A,unit) = A ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f3,axiom,(
% 0.10/0.53 (![A]: (mult(A,i(A)) = unit ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f4,axiom,(
% 0.10/0.53 (![A]: (mult(i(A),A) = unit ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f5,axiom,(
% 0.10/0.53 (![A,B]: (i(mult(A,B)) = mult(i(A),i(B)) ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f6,axiom,(
% 0.10/0.53 (![A,B]: (mult(i(A),mult(A,B)) = B ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f7,axiom,(
% 0.10/0.53 (![A,B]: (rd(mult(A,B),B) = A ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f10,axiom,(
% 0.10/0.53 (![A,B,C]: (mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f11,axiom,(
% 0.10/0.53 (![A,B]: (mult(A,B) = mult(mult(B,A),op_k(A,B)) ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f13,axiom,(
% 0.10/0.53 (![A,B,C]: (op_r(A,B,C) = rd(mult(mult(A,B),C),mult(B,C)) ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f21,axiom,(
% 0.10/0.53 (![A,B,C,D,E]: (asoc(asoc(A,B,C),D,E) = unit ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f22,axiom,(
% 0.10/0.53 (![A,B,C,D,E]: (asoc(A,B,asoc(C,D,E)) = unit ))),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f23,negated_conjecture,(
% 0.10/0.53 op_k(asoc(a,b,c),d) != unit ),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f24,plain,(
% 0.10/0.53 ![X0]: (mult(unit,X0)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.53 fof(f25,plain,(
% 0.10/0.53 ![X0]: (mult(X0,unit)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.53 fof(f26,plain,(
% 0.10/0.53 ![X0]: (mult(X0,i(X0))=unit)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.53 fof(f27,plain,(
% 0.10/0.53 ![X0]: (mult(i(X0),X0)=unit)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.53 fof(f28,plain,(
% 0.10/0.53 ![X0,X1]: (i(mult(X0,X1))=mult(i(X0),i(X1)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.53 fof(f29,plain,(
% 0.10/0.53 ![X0,X1]: (mult(i(X0),mult(X0,X1))=X1)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.53 fof(f30,plain,(
% 0.10/0.53 ![X0,X1]: (rd(mult(X0,X1),X1)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.53 fof(f33,plain,(
% 0.10/0.53 ![X0,X1,X2]: (mult(mult(X0,X1),X2)=mult(mult(X0,mult(X1,X2)),asoc(X0,X1,X2)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f10])).
% 0.10/0.53 fof(f34,plain,(
% 0.10/0.53 ![X0,X1]: (mult(X0,X1)=mult(mult(X1,X0),op_k(X0,X1)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f11])).
% 0.10/0.53 fof(f36,plain,(
% 0.10/0.53 ![X0,X1,X2]: (op_r(X0,X1,X2)=rd(mult(mult(X0,X1),X2),mult(X1,X2)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f13])).
% 0.10/0.53 fof(f44,plain,(
% 0.10/0.53 ![X0,X1,X2,X3,X4]: (asoc(asoc(X0,X1,X2),X3,X4)=unit)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f21])).
% 0.10/0.53 fof(f45,plain,(
% 0.10/0.53 ![X0,X1,X2,X3,X4]: (asoc(X0,X1,asoc(X2,X3,X4))=unit)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f22])).
% 0.10/0.53 fof(f46,plain,(
% 0.10/0.53 ~op_k(asoc(a,b,c),d)=unit),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f23])).
% 0.10/0.53 fof(f47,definition,(
% 0.10/0.53 sF1_fnc=asoc(a,b,c)),
% 0.10/0.53 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.10/0.53 fof(f48,definition,(
% 0.10/0.53 sF0_fnc=op_k(sF1_fnc,d)),
% 0.10/0.53 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.10/0.53 fof(f49,plain,(
% 0.10/0.53 ~sF0_fnc=unit),
% 0.10/0.53 inference(definition_folding,[],[f46,f48,f47])).
% 0.10/0.53 fof(f59,plain,(
% 0.10/0.53 ![X0,X1]: (asoc(sF1_fnc,X0,X1)=unit)),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f47,f44])).
% 0.10/0.53 fof(f90,plain,(
% 0.10/0.53 ![X0,X1]: (mult(mult(i(mult(X0,X1)),X0),X1)=mult(unit,asoc(i(mult(X0,X1)),X0,X1)))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f27,f33])).
% 0.10/0.53 fof(f97,plain,(
% 0.10/0.53 ![X0,X1]: (mult(mult(sF1_fnc,X0),X1)=mult(mult(sF1_fnc,mult(X0,X1)),unit))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f59,f33])).
% 0.10/0.53 fof(f104,plain,(
% 0.10/0.53 ![X0,X1]: (mult(mult(i(mult(X0,X1)),X0),X1)=asoc(i(mult(X0,X1)),X0,X1))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f90])).
% 0.10/0.54 fof(f114,plain,(
% 0.10/0.54 ![X0,X1]: (mult(mult(sF1_fnc,X0),X1)=mult(sF1_fnc,mult(X0,X1)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f25,f97])).
% 0.10/0.54 fof(f128,plain,(
% 0.10/0.54 mult(sF1_fnc,d)=mult(mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f48,f34])).
% 0.10/0.54 fof(f138,plain,(
% 0.10/0.54 ![X0]: (rd(unit,X0)=i(X0))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f27,f30])).
% 0.10/0.54 fof(f140,plain,(
% 0.10/0.54 ![X0]: (rd(unit,i(X0))=X0)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f26,f30])).
% 0.10/0.54 fof(f168,plain,(
% 0.10/0.54 ![X0]: (i(i(X0))=X0)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f138,f140])).
% 0.10/0.54 fof(f214,plain,(
% 0.10/0.54 ![X0,X1]: (mult(X0,mult(i(X0),X1))=X1)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f168,f29])).
% 0.10/0.54 fof(f226,plain,(
% 0.10/0.54 ![X0,X1]: (mult(mult(i(X0),X0),X1)=mult(X1,asoc(i(X0),X0,X1)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f29,f33])).
% 0.10/0.54 fof(f235,plain,(
% 0.10/0.54 ![X0,X1]: (mult(unit,X0)=mult(X0,asoc(i(X1),X1,X0)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f27,f226])).
% 0.10/0.54 fof(f236,plain,(
% 0.10/0.54 ![X0,X1]: (X0=mult(X0,asoc(i(X1),X1,X0)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f235])).
% 0.10/0.54 fof(f376,plain,(
% 0.10/0.54 ![X0]: (unit=mult(sF1_fnc,mult(X0,i(mult(sF1_fnc,X0)))))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f26,f114])).
% 0.10/0.54 fof(f521,plain,(
% 0.10/0.54 ![X0,X1]: (mult(X0,i(mult(X0,X1)))=i(X1))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f28,f214])).
% 0.10/0.54 fof(f543,plain,(
% 0.10/0.54 ![X0,X1]: (rd(X0,mult(i(X1),X0))=X1)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f214,f30])).
% 0.10/0.54 fof(f565,plain,(
% 0.10/0.54 ![X0,X1]: (rd(X0,mult(X1,X0))=i(X1))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f168,f543])).
% 0.10/0.54 fof(f857,plain,(
% 0.10/0.54 ![X0,X1]: (mult(mult(i(X0),X0),asoc(i(X1),X1,X0))=asoc(i(mult(X0,asoc(i(X1),X1,X0))),X0,asoc(i(X1),X1,X0)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f236,f104])).
% 0.10/0.54 fof(f878,plain,(
% 0.10/0.54 ![X0,X1]: (mult(unit,asoc(i(X0),X0,X1))=asoc(i(mult(X1,asoc(i(X0),X0,X1))),X1,asoc(i(X0),X0,X1)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f27,f857])).
% 0.10/0.54 fof(f879,plain,(
% 0.10/0.54 ![X0,X1]: (asoc(i(X0),X0,X1)=asoc(i(mult(X1,asoc(i(X0),X0,X1))),X1,asoc(i(X0),X0,X1)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f878])).
% 0.10/0.54 fof(f880,plain,(
% 0.10/0.54 ![X0,X1]: (asoc(i(X0),X0,X1)=unit)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f45,f879])).
% 0.10/0.54 fof(f1061,plain,(
% 0.10/0.54 ![X0,X1]: (op_r(sF1_fnc,X0,X1)=rd(mult(sF1_fnc,mult(X0,X1)),mult(X0,X1)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f114,f36])).
% 0.10/0.54 fof(f1108,plain,(
% 0.10/0.54 ![X0,X1]: (op_r(sF1_fnc,X0,X1)=sF1_fnc)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f30,f1061])).
% 0.10/0.54 fof(f2011,plain,(
% 0.10/0.54 ![X0,X1]: (op_r(sF1_fnc,mult(X0,i(mult(sF1_fnc,X0))),X1)=rd(mult(unit,X1),mult(mult(X0,i(mult(sF1_fnc,X0))),X1)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f376,f36])).
% 0.10/0.54 fof(f2055,plain,(
% 0.10/0.54 ![X0,X1]: (sF1_fnc=rd(mult(unit,X0),mult(mult(X1,i(mult(sF1_fnc,X1))),X0)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f1108,f2011])).
% 0.10/0.54 fof(f2056,plain,(
% 0.10/0.54 ![X0,X1]: (sF1_fnc=rd(X0,mult(mult(X1,i(mult(sF1_fnc,X1))),X0)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f2055])).
% 0.10/0.54 fof(f2057,plain,(
% 0.10/0.54 ![X0]: (sF1_fnc=i(mult(X0,i(mult(sF1_fnc,X0)))))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f565,f2056])).
% 0.10/0.54 fof(f2095,plain,(
% 0.10/0.54 ![X0]: (mult(X0,sF1_fnc)=i(i(mult(sF1_fnc,X0))))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f2057,f521])).
% 0.10/0.54 fof(f2136,plain,(
% 0.10/0.54 ![X0]: (mult(X0,sF1_fnc)=mult(sF1_fnc,X0))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f168,f2095])).
% 0.10/0.54 fof(f2181,plain,(
% 0.10/0.54 mult(d,sF1_fnc)=mult(mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.54 inference(backward_demodulation,[status(thm)],[f2136,f128])).
% 0.10/0.54 fof(f3556,plain,(
% 0.10/0.54 mult(mult(i(mult(d,sF1_fnc)),mult(d,sF1_fnc)),sF0_fnc)=asoc(i(mult(mult(d,sF1_fnc),sF0_fnc)),mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f2181,f104])).
% 0.10/0.54 fof(f3567,plain,(
% 0.10/0.54 mult(unit,sF0_fnc)=asoc(i(mult(mult(d,sF1_fnc),sF0_fnc)),mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f27,f3556])).
% 0.10/0.54 fof(f3568,plain,(
% 0.10/0.54 sF0_fnc=asoc(i(mult(mult(d,sF1_fnc),sF0_fnc)),mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f3567])).
% 0.10/0.57 fof(f3569,plain,(
% 0.10/0.57 sF0_fnc=asoc(i(mult(d,sF1_fnc)),mult(d,sF1_fnc),sF0_fnc)),
% 0.10/0.57 inference(forward_demodulation,[status(thm)],[f2181,f3568])).
% 0.10/0.57 fof(f3570,plain,(
% 0.10/0.57 sF0_fnc=unit),
% 0.10/0.57 inference(forward_demodulation,[status(thm)],[f880,f3569])).
% 0.10/0.57 fof(f3571,plain,(
% 0.10/0.57 $false),
% 0.10/0.57 inference(forward_subsumption_resolution,[status(thm)],[f3570,f49])).
% 0.10/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.57 % Elapsed time: 0.169854 seconds
% 0.10/0.57 % CPU time: 1.159775 seconds
% 0.10/0.57 % Total memory used: 40.585 MB
% 0.10/0.57 % Net memory used: 39.999 MB
%------------------------------------------------------------------------------