%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:34:13 PM UTC 2026
% Result : Unsatisfiable 58.87s 8.12s
% Output : CNFRefutation 59.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 17 ( 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 : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = 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] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = 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(f10,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,X5),inverse(multiply(X6,multiply(X0,X5))))))) = X6,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)))) = X4,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f17,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = X2,
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X2,multiply(X6,X8)))))),
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f3035,plain,
! [X0,X1,X2,X3] : X0 = multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X0),multiply(X1,X3)))))),
inference(paramodulation,[status(thm)],[f17,f50]) ).
fof(f3569,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X3,multiply(X0,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(inverse(X2),multiply(inverse(X1),X5)))))))))))) = X3,
inference(paramodulation,[status(thm)],[f3035,f3]) ).
fof(f4434,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(X2,X1)))))) = X2,
inference(paramodulation,[status(thm)],[f3035,f3569]) ).
fof(f4747,plain,
! [X0,X1,X2,X3] : X0 = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(X2,inverse(multiply(X3,X2)))),X3))),
inference(paramodulation,[status(thm)],[f4434,f3035]) ).
fof(f6502,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X0),multiply(X1,multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X5,X4)))),X5)))))))),
inference(paramodulation,[status(thm)],[f4747,f3035]) ).
fof(f6536,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(X2,multiply(X0,multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X5,X4)))),X5))))))))) = X2,
inference(paramodulation,[status(thm)],[f4747,f3]) ).
fof(f6700,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f4747,f6502]) ).
fof(f6734,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X0)))))) = X2,
inference(forward_demodulation,[status(thm)],[f4747,f6536]) ).
fof(f6952,plain,
! [X0,X1,X2,X3,X4] : X0 = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X4)))),X3)),X4))),
inference(paramodulation,[status(thm)],[f6734,f4747]) ).
fof(f7082,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(X0,multiply(X1,inverse(multiply(X2,X1)))),multiply(X3,multiply(inverse(X3),X2))),
inference(paramodulation,[status(thm)],[f4434,f6700]) ).
fof(f7097,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X0))))),multiply(X3,multiply(inverse(X3),X2))),
inference(paramodulation,[status(thm)],[f6734,f6700]) ).
fof(f13767,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : X0 = multiply(X0,multiply(X1,multiply(inverse(X1),multiply(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(X5,multiply(inverse(X5),inverse(multiply(X6,X7)))),X6)),X7)))))),X3)))),
inference(paramodulation,[status(thm)],[f6952,f6952]) ).
fof(f14233,plain,
! [X0,X1,X2,X3] : X0 = multiply(X0,multiply(X1,multiply(inverse(X1),multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3)))),
inference(forward_demodulation,[status(thm)],[f6952,f13767]) ).
fof(f14390,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X0),inverse(multiply(multiply(multiply(X1,multiply(inverse(X1),inverse(X2))),X2),inverse(X3))))) = X3,
inference(paramodulation,[status(thm)],[f7097,f14233]) ).
fof(f15638,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),X0)) = multiply(multiply(X1,multiply(inverse(X1),inverse(X2))),X2),
inference(paramodulation,[status(thm)],[f14390,f6734]) ).
fof(f16701,plain,
! [X0,X1,X2] : X0 = multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(inverse(X2),X2))))),
inference(paramodulation,[status(thm)],[f15638,f14233]) ).
fof(f16920,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)))) = X0,
inference(paramodulation,[status(thm)],[f7082,f16701]) ).
fof(f20891,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f16920,f6700]) ).
fof(f22026,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f4,f20891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n018.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 20:15:28 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 58.87/8.12 % Refutation found
% 58.87/8.12 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 58.87/8.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.85/8.22 % Elapsed time: 7.740098 seconds
% 5.85/8.22 % CPU time: 60.311030 seconds
% 5.85/8.22 % Total memory used: 769.836 MB
% 5.85/8.22 % Net memory used: 752.317 MB
%------------------------------------------------------------------------------