%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:36:36 PM UTC 2026
% Result : Unsatisfiable 172.51s 22.16s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:13:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 172.51/22.16 % Refutation found
% 172.51/22.16 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 172.51/22.16 % SZS output start CNFRefutation for theBenchmark
% 172.51/22.16 fof(f1,axiom,(
% 172.51/22.16 (![A,B,C]: (inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C ))),
% 172.51/22.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 172.51/22.16 fof(f2,negated_conjecture,(
% 172.51/22.16 multiply(multiply(inverse(b2),b2),a2) != a2 ),
% 172.51/22.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 172.51/22.16 fof(f3,plain,(
% 172.51/22.16 ![X0,X1,X2]: (inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))))=X2)),
% 172.51/22.16 inference(cnf_transformation,[status(thm)],[f1])).
% 172.51/22.16 fof(f4,plain,(
% 172.51/22.16 ~multiply(multiply(inverse(b2),b2),a2)=a2),
% 172.51/22.16 inference(cnf_transformation,[status(thm)],[f2])).
% 172.51/22.16 fof(f10,plain,(
% 172.51/22.16 ![X0,X1,X2,X3,X4]: (inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0))))))=multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X3),X3))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f3,f3])).
% 172.51/22.16 fof(f12,plain,(
% 172.51/22.16 ![X0,X1,X2]: (X0=multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X0))))),inverse(multiply(inverse(X1),X1))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f3,f10])).
% 172.51/22.16 fof(f34,plain,(
% 172.51/22.16 ![X0,X1,X2]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0)))))))=X2)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f10,f3])).
% 172.51/22.16 fof(f50,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0))))))=multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12,f3])).
% 172.51/22.16 fof(f213,plain,(
% 172.51/22.16 ![X0,X1,X2]: (X0=multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X0))))))),inverse(multiply(inverse(X2),X2))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f3,f50])).
% 172.51/22.16 fof(f258,plain,(
% 172.51/22.16 ![X0,X1,X2]: (inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,X2)))))),inverse(multiply(inverse(X1),X1))))=X2)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f50,f34])).
% 172.51/22.16 fof(f283,plain,(
% 172.51/22.16 ![X0,X1,X2]: (X0=multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),inverse(multiply(inverse(X2),X2)))))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f50,f12])).
% 172.51/22.16 fof(f359,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),X0)),X3)),inverse(multiply(inverse(X0),X0))))))=multiply(inverse(X2),X2))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f213,f3])).
% 172.51/22.16 fof(f506,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),X3)),inverse(multiply(inverse(X0),X0)))))))=multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f283,f283])).
% 172.51/22.16 fof(f2814,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0))))))))=multiply(inverse(X0),X0))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f258,f359])).
% 172.51/22.16 fof(f8348,plain,(
% 172.51/22.16 ![X0,X1,X2]: (X0=multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2))))))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f506,f283])).
% 172.51/22.16 fof(f8743,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (multiply(inverse(multiply(X0,X1)),multiply(X0,X2))=multiply(inverse(multiply(X3,X1)),multiply(X3,X2)))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f34,f8348])).
% 172.51/22.16 fof(f8748,plain,(
% 172.51/22.16 ![X0,X1,X2]: (multiply(inverse(X0),X0)=multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f2814,f8348])).
% 172.51/22.16 fof(f12182,plain,(
% 172.51/22.16 ![X0,X1]: (multiply(inverse(X0),X0)=multiply(inverse(X1),X1))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f8748,f8748])).
% 172.51/22.16 fof(f12891,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0)))))))=multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X0)),inverse(multiply(inverse(X3),X3)))))))))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f506])).
% 172.51/22.16 fof(f12921,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(X0)),inverse(X0)))))))=X0)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f3])).
% 172.51/22.16 fof(f12954,plain,(
% 172.51/22.16 ![X0]: (~multiply(multiply(inverse(X0),X0),a2)=a2)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f4])).
% 172.51/22.16 fof(f13084,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (multiply(inverse(multiply(X0,X1)),multiply(X0,X2))=multiply(inverse(multiply(inverse(X2),X1)),multiply(inverse(X3),X3)))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f8743])).
% 172.51/22.16 fof(f13444,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0)))))))=X0)),
% 172.51/22.16 inference(forward_demodulation,[status(thm)],[f283,f12891])).
% 172.51/22.16 fof(f13569,plain,(
% 172.51/22.16 ![X0,X1,X2]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2)))))))=X0)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f13444])).
% 172.51/22.16 fof(f14786,plain,(
% 172.51/22.16 ![X0,X1,X2]: (multiply(inverse(X0),X0)=multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2)))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f13084])).
% 172.51/22.16 fof(f15058,plain,(
% 172.51/22.16 ![X0,X1]: (~multiply(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X1)),a2)=a2)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f13084,f12954])).
% 172.51/22.16 fof(f23539,plain,(
% 172.51/22.16 ![X0,X1,X2]: (inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))))))=X0)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f12182,f12921])).
% 172.51/22.16 fof(f24224,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))))=X0)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f23539,f23539])).
% 172.51/22.16 fof(f24290,plain,(
% 172.51/22.16 ![X0,X1,X2,X3]: (inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))))))=X0)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f23539,f13569])).
% 172.51/22.16 fof(f24414,plain,(
% 172.51/22.16 ![X0,X1,X2,X3,X4]: (multiply(X0,multiply(inverse(X0),X1))=multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X4),X4)))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f23539,f13084])).
% 172.51/22.16 fof(f24638,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(multiply(inverse(X0),multiply(inverse(X1),X1)))=X0)),
% 172.51/22.16 inference(forward_demodulation,[status(thm)],[f23539,f24224])).
% 172.51/22.16 fof(f24669,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(inverse(multiply(X0,multiply(inverse(X1),X1))))=X0)),
% 172.51/22.16 inference(forward_demodulation,[status(thm)],[f23539,f24290])).
% 172.51/22.16 fof(f24927,plain,(
% 172.51/22.16 ![X0,X1,X2]: (multiply(X0,multiply(inverse(X0),X1))=multiply(X1,multiply(inverse(X2),X2)))),
% 172.51/22.16 inference(forward_demodulation,[status(thm)],[f23539,f24414])).
% 172.51/22.16 fof(f25305,plain,(
% 172.51/22.16 ![X0,X1]: (inverse(multiply(inverse(X0),X0))=multiply(inverse(X1),X1))),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f14786,f24638])).
% 172.51/22.16 fof(f25499,plain,(
% 172.51/22.16 ![X0,X1]: (~multiply(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)),a2)=a2)),
% 172.51/22.16 inference(paramodulation,[status(thm)],[f24638,f15058])).
% 172.51/22.24 fof(f25705,plain,(
% 172.51/22.24 ![X0,X1,X2]: (multiply(inverse(X0),X0)=multiply(X1,multiply(inverse(X1),multiply(inverse(X2),X2))))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f24638,f12182])).
% 172.51/22.24 fof(f27080,plain,(
% 172.51/22.24 ![X0,X1,X2,X3]: (X0=multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),multiply(inverse(X3),X3)))))))))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f25305,f8348])).
% 172.51/22.24 fof(f27832,plain,(
% 172.51/22.24 ![X0,X1,X2]: (X0=multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X0))))))),
% 172.51/22.24 inference(forward_demodulation,[status(thm)],[f24638,f27080])).
% 172.51/22.24 fof(f35458,plain,(
% 172.51/22.24 ![X0,X1,X2]: (multiply(X0,multiply(inverse(X0),X1))=multiply(X2,multiply(inverse(X2),X1)))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f24927,f24927])).
% 172.51/22.24 fof(f35545,plain,(
% 172.51/22.24 ![X0,X1]: (inverse(inverse(multiply(X0,multiply(inverse(X0),X1))))=X1)),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f24927,f24669])).
% 172.51/22.24 fof(f40280,plain,(
% 172.51/22.24 ![X0,X1,X2]: (inverse(inverse(multiply(X0,multiply(inverse(X1),X1))))=multiply(inverse(inverse(X0)),multiply(inverse(X2),X2)))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f25705,f35545])).
% 172.51/22.24 fof(f40330,plain,(
% 172.51/22.24 ![X0,X1]: (X0=multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)))),
% 172.51/22.24 inference(forward_demodulation,[status(thm)],[f24669,f40280])).
% 172.51/22.24 fof(f40338,plain,(
% 172.51/22.24 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),inverse(inverse(X0)))))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f35458,f40330])).
% 172.51/22.24 fof(f42946,plain,(
% 172.51/22.24 ![X0,X1,X2]: (X0=multiply(X1,multiply(inverse(X1),inverse(inverse(multiply(multiply(inverse(X2),X2),X0))))))),
% 172.51/22.24 inference(paramodulation,[status(thm)],[f24638,f27832])).
% 172.51/22.24 fof(f43129,plain,(
% 172.51/22.24 ![X0,X1]: (X0=multiply(multiply(inverse(X1),X1),X0))),
% 172.51/22.24 inference(forward_demodulation,[status(thm)],[f40338,f42946])).
% 172.51/22.24 fof(f43176,plain,(
% 172.51/22.24 ![X0]: (~multiply(multiply(inverse(X0),X0),a2)=a2)),
% 172.51/22.24 inference(backward_demodulation,[status(thm)],[f43129,f25499])).
% 172.51/22.24 fof(f43330,plain,(
% 172.51/22.24 ~a2=a2),
% 172.51/22.24 inference(forward_demodulation,[status(thm)],[f43129,f43176])).
% 172.51/22.24 fof(f43331,plain,(
% 172.51/22.24 $false),
% 172.51/22.24 inference(trivial_equality_resolution,[status(thm)],[f43330])).
% 172.51/22.24 % SZS output end CNFRefutation for theBenchmark.p
% 11.11/22.49 % Elapsed time: 22.110085 seconds
% 11.11/22.49 % CPU time: 174.483077 seconds
% 11.11/22.49 % Total memory used: 2.823 GB
% 11.11/22.49 % Net memory used: 2.811 GB
%------------------------------------------------------------------------------