%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP436-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:34:12 PM UTC 2026
% Result : Unsatisfiable 44.34s 6.14s
% Output : CNFRefutation 44.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 196 ( 196 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X0))))) = X3,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))),multiply(X4,multiply(X2,X0))))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X4)))),multiply(X5,multiply(multiply(inverse(X5),inverse(X3)),X0))))) = X4,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(multiply(X1,multiply(X2,inverse(X3))),multiply(X3,multiply(X4,X0))))) = multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X2,X4))),inverse(X1))),
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f17,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(X0,inverse(multiply(multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(X3))),multiply(X3,multiply(X4,X0))))) = inverse(multiply(multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X6,X2))),inverse(X7))),multiply(X7,multiply(X6,X4)))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f51,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X0),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))),inverse(X1))) = X3,
inference(paramodulation,[status(thm)],[f16,f11]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X0,multiply(X3,inverse(X4))),multiply(X4,multiply(X1,X2)))))))) = X3,
inference(paramodulation,[status(thm)],[f16,f3]) ).
fof(f87,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X0,multiply(X3,inverse(X1)))))),X2))) = X3,
inference(paramodulation,[status(thm)],[f3,f58]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))) = multiply(inverse(X0),inverse(multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4))),
inference(paramodulation,[status(thm)],[f51,f87]) ).
fof(f128,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,multiply(X2,multiply(X3,X0))))) = multiply(inverse(X4),inverse(multiply(X1,multiply(X2,multiply(X3,inverse(X4)))))),
inference(paramodulation,[status(thm)],[f87,f3]) ).
fof(f196,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X0,multiply(X3,X1))))),X2))) = X3,
inference(paramodulation,[status(thm)],[f128,f87]) ).
fof(f200,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(multiply(X1,multiply(X2,inverse(X3))),multiply(X3,multiply(multiply(X4,inverse(multiply(X5,multiply(X1,multiply(X2,X4))))),X0))))) = X5,
inference(paramodulation,[status(thm)],[f128,f3]) ).
fof(f305,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(multiply(inverse(X0),inverse(multiply(X1,multiply(X2,inverse(multiply(X3,multiply(X4,multiply(X1,X2)))))))),inverse(X4))) = X3,
inference(paramodulation,[status(thm)],[f196,f51]) ).
fof(f717,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(X0,multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))))),inverse(X5))) = multiply(X6,multiply(multiply(inverse(X6),inverse(X4)),inverse(X5))),
inference(paramodulation,[status(thm)],[f12,f51]) ).
fof(f747,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X0),inverse(X1)),inverse(X2))) = multiply(X3,multiply(multiply(inverse(X3),inverse(X1)),inverse(X2))),
inference(forward_demodulation,[status(thm)],[f3,f717]) ).
fof(f2349,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(X0,multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,multiply(X0,X1)))))) = multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(multiply(inverse(X6),inverse(multiply(X7,X3))),X7))),inverse(X6))),
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f2420,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,multiply(X0,X1)))))) = X3,
inference(forward_demodulation,[status(thm)],[f51,f2349]) ).
fof(f3052,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(X0,multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(multiply(inverse(X3),inverse(multiply(X4,X5))),X4))),inverse(X6))),multiply(X6,multiply(X0,X1)))))) = multiply(multiply(inverse(X3),inverse(multiply(X7,X5))),X7),
inference(paramodulation,[status(thm)],[f117,f2420]) ).
fof(f3205,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(X0),inverse(multiply(X1,X2))),X1) = multiply(multiply(inverse(X0),inverse(multiply(X3,X2))),X3),
inference(forward_demodulation,[status(thm)],[f2420,f3052]) ).
fof(f3626,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X3))))) = X0,
inference(paramodulation,[status(thm)],[f3205,f3]) ).
fof(f4178,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(inverse(X0),inverse(X1))) = multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(X5,X3))),X5))))),inverse(X1))),
inference(paramodulation,[status(thm)],[f3626,f747]) ).
fof(f4205,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X4))))))),X1) = multiply(multiply(inverse(X0),inverse(X5)),X5),
inference(paramodulation,[status(thm)],[f3626,f3205]) ).
fof(f4249,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),inverse(X1)),X1) = multiply(multiply(inverse(X0),inverse(X2)),X2),
inference(forward_demodulation,[status(thm)],[f3626,f4205]) ).
fof(f4252,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),inverse(X1))) = multiply(X2,multiply(inverse(X2),inverse(X1))),
inference(forward_demodulation,[status(thm)],[f3626,f4178]) ).
fof(f4312,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(inverse(X0),inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X3)))))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f3626,f4252]) ).
fof(f4491,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f3626,f4312]) ).
fof(f4500,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(X0)) = multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),X3))),
inference(paramodulation,[status(thm)],[f3626,f4491]) ).
fof(f4527,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = multiply(X1,multiply(X2,inverse(X2))),
inference(paramodulation,[status(thm)],[f4491,f4252]) ).
fof(f4675,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(X1))) = multiply(X0,multiply(X2,inverse(X2))),
inference(paramodulation,[status(thm)],[f4491,f4527]) ).
fof(f6408,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),inverse(X1)),X1) = multiply(multiply(X2,inverse(X2)),inverse(X0)),
inference(paramodulation,[status(thm)],[f4491,f4249]) ).
fof(f6711,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(X0,inverse(X0))),inverse(X1)),X1) = multiply(X2,inverse(X2)),
inference(paramodulation,[status(thm)],[f4491,f6408]) ).
fof(f9365,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(X5,X3))),X5))))),X0))))) = X1,
inference(paramodulation,[status(thm)],[f4500,f3]) ).
fof(f9384,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(paramodulation,[status(thm)],[f4500,f200]) ).
fof(f9518,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(X1),multiply(X2,multiply(inverse(X2),X0))))) = X1,
inference(forward_demodulation,[status(thm)],[f3626,f9365]) ).
fof(f10458,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X0),multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X2))))))) = multiply(X3,inverse(X3)),
inference(paramodulation,[status(thm)],[f9518,f6711]) ).
fof(f10584,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f9384,f10458]) ).
fof(f10985,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X0),inverse(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X2))))))),inverse(inverse(X3)))) = X3,
inference(paramodulation,[status(thm)],[f10584,f305]) ).
fof(f11212,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))),inverse(inverse(X2)))) = X2,
inference(forward_demodulation,[status(thm)],[f9384,f10985]) ).
fof(f11213,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f9384,f11212]) ).
fof(f11467,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f11213,f4675]) ).
fof(f11610,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = multiply(multiply(X2,inverse(X2)),inverse(X0)),
inference(paramodulation,[status(thm)],[f11467,f6408]) ).
fof(f11766,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(X1,inverse(X1)),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f9384,f11610]) ).
fof(f13580,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(X0)) = multiply(inverse(X1),multiply(X2,multiply(multiply(inverse(X2),inverse(inverse(X1))),multiply(X3,inverse(X3))))),
inference(paramodulation,[status(thm)],[f11766,f4500]) ).
fof(f13717,plain,
! [X0,X1,X2] : multiply(X0,inverse(X0)) = multiply(inverse(X1),multiply(X2,multiply(inverse(X2),inverse(inverse(X1))))),
inference(forward_demodulation,[status(thm)],[f11467,f13580]) ).
fof(f13718,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f11213,f13717]) ).
fof(f19765,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(X0,inverse(X0)),
inference(paramodulation,[status(thm)],[f13718,f4]) ).
fof(f20330,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19765,f13718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP436-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n019.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
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 20:13:19 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 44.34/6.14 % Refutation found
% 44.34/6.14 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.34/6.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.24/6.29 % Elapsed time: 5.808039 seconds
% 14.24/6.29 % CPU time: 45.144902 seconds
% 14.24/6.29 % Total memory used: 567.894 MB
% 14.24/6.29 % Net memory used: 559.482 MB
%------------------------------------------------------------------------------