%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 12:35:24 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 19:52:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.48 % Refutation found
% 0.08/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.48 fof(f1,axiom,(
% 0.08/0.48 (![X]: (multiply(identity,X) = X ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f2,axiom,(
% 0.08/0.48 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f3,axiom,(
% 0.08/0.48 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f4,axiom,(
% 0.08/0.48 (![X]: (multiply(X,identity) = X ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f5,axiom,(
% 0.08/0.48 (![X]: (multiply(X,inverse(X)) = identity ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f6,hypothesis,(
% 0.08/0.48 (![X]: (multiply(X,multiply(X,X)) = identity ))),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f7,negated_conjecture,(
% 0.08/0.48 multiply(a,b) = c ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f8,negated_conjecture,(
% 0.08/0.48 multiply(c,inverse(a)) = d ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f9,negated_conjecture,(
% 0.08/0.48 multiply(d,inverse(b)) = h ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f10,negated_conjecture,(
% 0.08/0.48 multiply(h,b) = j ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f11,negated_conjecture,(
% 0.08/0.48 multiply(j,inverse(h)) = k ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f12,negated_conjecture,(
% 0.08/0.48 multiply(k,inverse(b)) != identity ),
% 0.08/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.48 fof(f13,plain,(
% 0.08/0.48 ![X0]: (multiply(identity,X0)=X0)),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.48 fof(f14,plain,(
% 0.08/0.48 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.48 fof(f15,plain,(
% 0.08/0.48 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.48 fof(f16,plain,(
% 0.08/0.48 ![X0]: (multiply(X0,identity)=X0)),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.48 fof(f17,plain,(
% 0.08/0.48 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.48 fof(f18,plain,(
% 0.08/0.48 ![X0]: (multiply(X0,multiply(X0,X0))=identity)),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.48 fof(f19,plain,(
% 0.08/0.48 multiply(a,b)=c),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.48 fof(f20,plain,(
% 0.08/0.48 multiply(c,inverse(a))=d),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.08/0.48 fof(f21,plain,(
% 0.08/0.48 multiply(d,inverse(b))=h),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.48 fof(f22,plain,(
% 0.08/0.48 multiply(h,b)=j),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f10])).
% 0.08/0.48 fof(f23,plain,(
% 0.08/0.48 multiply(j,inverse(h))=k),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f11])).
% 0.08/0.48 fof(f24,plain,(
% 0.08/0.48 ~multiply(k,inverse(b))=identity),
% 0.08/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.08/0.48 fof(f36,plain,(
% 0.08/0.48 ![X0,X1]: (identity=multiply(X0,multiply(X1,inverse(multiply(X0,X1)))))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f17,f15])).
% 0.08/0.48 fof(f39,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f14,f15])).
% 0.08/0.48 fof(f42,plain,(
% 0.08/0.48 ![X0]: (multiply(h,X0)=multiply(d,multiply(inverse(b),X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f21,f15])).
% 0.08/0.48 fof(f43,plain,(
% 0.08/0.48 ![X0]: (multiply(d,X0)=multiply(c,multiply(inverse(a),X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f20,f15])).
% 0.08/0.48 fof(f45,plain,(
% 0.08/0.48 ![X0]: (multiply(c,X0)=multiply(a,multiply(b,X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f19,f15])).
% 0.08/0.48 fof(f46,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f17,f15])).
% 0.08/0.48 fof(f52,plain,(
% 0.08/0.48 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f13,f39])).
% 0.08/0.48 fof(f53,plain,(
% 0.08/0.48 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f13,f46])).
% 0.08/0.48 fof(f58,plain,(
% 0.08/0.48 ![X0]: (inverse(inverse(X0))=multiply(X0,identity))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f17,f53])).
% 0.08/0.48 fof(f66,plain,(
% 0.08/0.48 ![X0]: (inverse(inverse(X0))=X0)),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f16,f58])).
% 0.08/0.48 fof(f82,plain,(
% 0.08/0.48 inverse(b)=multiply(inverse(d),h)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f21,f52])).
% 0.08/0.48 fof(f83,plain,(
% 0.08/0.48 inverse(a)=multiply(inverse(c),d)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f20,f52])).
% 0.08/0.48 fof(f85,plain,(
% 0.08/0.48 b=multiply(inverse(a),c)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f19,f52])).
% 0.08/0.48 fof(f119,plain,(
% 0.08/0.48 ![X0]: (multiply(X0,X0)=multiply(inverse(X0),identity))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f18,f52])).
% 0.08/0.48 fof(f127,plain,(
% 0.08/0.48 ![X0]: (multiply(X0,X0)=inverse(X0))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f16,f119])).
% 0.08/0.48 fof(f158,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=multiply(inverse(X1),identity))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f36,f52])).
% 0.08/0.48 fof(f192,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f16,f158])).
% 0.08/0.48 fof(f203,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(inverse(X0),X1)=multiply(X0,multiply(X0,X1)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f127,f15])).
% 0.08/0.48 fof(f214,plain,(
% 0.08/0.48 multiply(h,inverse(inverse(b)))=inverse(inverse(d))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f82,f192])).
% 0.08/0.48 fof(f225,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),inverse(inverse(X0)))=inverse(X1))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f192,f192])).
% 0.08/0.48 fof(f232,plain,(
% 0.08/0.48 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f192,f52])).
% 0.08/0.48 fof(f239,plain,(
% 0.08/0.48 multiply(h,b)=inverse(inverse(d))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f66,f214])).
% 0.08/0.48 fof(f240,plain,(
% 0.08/0.48 j=inverse(inverse(d))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f22,f239])).
% 0.08/0.48 fof(f243,plain,(
% 0.08/0.48 multiply(d,inverse(h))=k),
% 0.08/0.48 inference(backward_demodulation,[status(thm)],[f250,f23])).
% 0.08/0.48 fof(f250,plain,(
% 0.08/0.48 j=d),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f66,f240])).
% 0.08/0.48 fof(f264,plain,(
% 0.08/0.48 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),X0)=inverse(X1))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f66,f225])).
% 0.08/0.48 fof(f316,plain,(
% 0.08/0.48 ![X0,X1]: (inverse(multiply(inverse(X0),X1))=multiply(inverse(X1),X0))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f66,f232])).
% 0.08/0.48 fof(f566,plain,(
% 0.08/0.48 multiply(inverse(inverse(c)),d)=multiply(inverse(c),inverse(a))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f83,f203])).
% 0.08/0.48 fof(f577,plain,(
% 0.08/0.48 multiply(inverse(a),b)=multiply(a,c)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f19,f203])).
% 0.08/0.48 fof(f602,plain,(
% 0.08/0.48 multiply(c,d)=multiply(inverse(c),inverse(a))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f66,f566])).
% 0.08/0.48 fof(f603,plain,(
% 0.08/0.48 multiply(c,d)=inverse(multiply(a,c))),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f232,f602])).
% 0.08/0.48 fof(f704,plain,(
% 0.08/0.48 ![X0]: (multiply(d,inverse(X0))=multiply(c,inverse(multiply(X0,a))))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f232,f43])).
% 0.08/0.48 fof(f778,plain,(
% 0.08/0.48 inverse(multiply(a,c))=multiply(inverse(b),a)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f577,f316])).
% 0.08/0.48 fof(f785,plain,(
% 0.08/0.48 multiply(c,d)=multiply(inverse(b),a)),
% 0.08/0.48 inference(forward_demodulation,[status(thm)],[f603,f778])).
% 0.08/0.48 fof(f838,plain,(
% 0.08/0.48 ![X0]: (multiply(b,X0)=multiply(inverse(a),multiply(c,X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f45,f52])).
% 0.08/0.48 fof(f849,plain,(
% 0.08/0.48 multiply(h,a)=multiply(d,multiply(c,d))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f785,f42])).
% 0.08/0.48 fof(f1428,plain,(
% 0.08/0.48 multiply(d,c)=multiply(c,b)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f85,f43])).
% 0.08/0.48 fof(f1495,plain,(
% 0.08/0.48 ![X0]: (multiply(d,multiply(c,X0))=multiply(c,multiply(b,X0)))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f838,f43])).
% 0.08/0.48 fof(f1520,plain,(
% 0.08/0.48 multiply(h,a)=multiply(c,multiply(b,d))),
% 0.08/0.48 inference(backward_demodulation,[status(thm)],[f1495,f849])).
% 0.08/0.48 fof(f1533,plain,(
% 0.08/0.48 multiply(inverse(multiply(c,b)),d)=inverse(c)),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f1428,f264])).
% 0.08/0.48 fof(f1665,plain,(
% 0.08/0.48 multiply(inverse(inverse(multiply(c,b))),d)=multiply(inverse(multiply(c,b)),inverse(c))),
% 0.08/0.48 inference(paramodulation,[status(thm)],[f1533,f203])).
% 0.08/0.49 fof(f1674,plain,(
% 0.08/0.49 multiply(multiply(c,b),d)=multiply(inverse(multiply(c,b)),inverse(c))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f66,f1665])).
% 0.08/0.49 fof(f1675,plain,(
% 0.08/0.49 multiply(c,multiply(b,d))=multiply(inverse(multiply(c,b)),inverse(c))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f15,f1674])).
% 0.08/0.49 fof(f1676,plain,(
% 0.08/0.49 multiply(h,a)=multiply(inverse(multiply(c,b)),inverse(c))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f1520,f1675])).
% 0.08/0.49 fof(f1677,plain,(
% 0.08/0.49 multiply(h,a)=inverse(multiply(c,multiply(c,b)))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f232,f1676])).
% 0.08/0.49 fof(f1678,plain,(
% 0.08/0.49 multiply(h,a)=inverse(multiply(inverse(c),b))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f203,f1677])).
% 0.08/0.49 fof(f1680,plain,(
% 0.08/0.49 multiply(h,a)=multiply(inverse(b),c)),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f316,f1678])).
% 0.08/0.49 fof(f1696,plain,(
% 0.08/0.49 multiply(c,inverse(multiply(h,a)))=inverse(inverse(b))),
% 0.08/0.49 inference(paramodulation,[status(thm)],[f1680,f192])).
% 0.08/0.49 fof(f1704,plain,(
% 0.08/0.49 multiply(d,inverse(h))=inverse(inverse(b))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f704,f1696])).
% 0.08/0.49 fof(f1705,plain,(
% 0.08/0.49 k=inverse(inverse(b))),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f243,f1704])).
% 0.08/0.49 fof(f1747,plain,(
% 0.08/0.49 ~multiply(k,inverse(k))=identity),
% 0.08/0.49 inference(backward_demodulation,[status(thm)],[f1836,f24])).
% 0.08/0.49 fof(f1836,plain,(
% 0.08/0.49 k=b),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f66,f1705])).
% 0.08/0.49 fof(f1883,plain,(
% 0.08/0.49 ~identity=identity),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f17,f1747])).
% 0.08/0.49 fof(f1884,plain,(
% 0.08/0.49 $false),
% 0.08/0.49 inference(trivial_equality_resolution,[status(thm)],[f1883])).
% 0.08/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 51.70/27.84 % Elapsed time: 27.472923 seconds
% 51.70/27.84 % CPU time: 217.354590 seconds
% 51.70/27.84 % Total memory used: 135.131 GB
% 51.70/27.84 % Net memory used: 135.130 GB
%------------------------------------------------------------------------------