%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP514-1 : 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 12:34:34 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 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 : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,inverse(multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X3,X2))))))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X0,X3)))),inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f3,f9]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X2,X1)))) = X0,
inference(paramodulation,[status(thm)],[f19,f9]) ).
fof(f38,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),inverse(X1))) = multiply(X0,X2),
inference(paramodulation,[status(thm)],[f19,f10]) ).
fof(f123,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,inverse(multiply(X1,X2)))),multiply(multiply(X3,X2),inverse(X3))) = X0,
inference(paramodulation,[status(thm)],[f30,f30]) ).
fof(f131,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,inverse(multiply(X1,X2)))),X2) = X0,
inference(forward_demodulation,[status(thm)],[f38,f123]) ).
fof(f144,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X0,multiply(X2,inverse(multiply(X2,inverse(X1))))),
inference(paramodulation,[status(thm)],[f131,f38]) ).
fof(f145,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X1,multiply(X2,inverse(multiply(X2,inverse(X0))))),
inference(paramodulation,[status(thm)],[f131,f19]) ).
fof(f157,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(backward_demodulation,[status(thm)],[f162,f4]) ).
fof(f162,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f144,f145]) ).
fof(f167,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(forward_demodulation,[status(thm)],[f162,f157]) ).
fof(f168,plain,
a2 != a2,
inference(forward_demodulation,[status(thm)],[f11,f167]) ).
fof(f169,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP514-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 20:15:20 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.45 % Refutation found
% 0.16/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.47 % Elapsed time: 0.036111 seconds
% 0.16/0.47 % CPU time: 0.086747 seconds
% 0.16/0.47 % Total memory used: 2.838 MB
% 0.16/0.47 % Net memory used: 2.729 MB
%------------------------------------------------------------------------------