%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:32:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 42 ( 37 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 105 ( 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1),X3),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f6,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X1),X2),multiply(multiply(inverse(multiply(X0,X3)),X1),X3))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(X1,multiply(multiply(inverse(multiply(X0,X2)),X3),X2))) = multiply(multiply(inverse(multiply(inverse(X3),X4)),X1),X4),
inference(paramodulation,[status(thm)],[f3,f5]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X2,X1))) = X2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),X2) = X0,
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(X0),multiply(X1,X2))),X1) = inverse(multiply(inverse(multiply(X0,X3)),multiply(X2,X3))),
inference(paramodulation,[status(thm)],[f20,f20]) ).
fof(f35,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(X0),multiply(X1,multiply(X2,multiply(X0,X3))))),X1) = inverse(multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f11,f20]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X2,multiply(X3,X1))) = multiply(multiply(inverse(X0),X2),X3),
inference(paramodulation,[status(thm)],[f20,f5]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2))) = X3,
inference(paramodulation,[status(thm)],[f20,f11]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2)) = multiply(multiply(inverse(multiply(inverse(X0),X4)),X3),X4),
inference(paramodulation,[status(thm)],[f20,f5]) ).
fof(f50,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(backward_demodulation,[status(thm)],[f43,f11]) ).
fof(f51,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f50,f4]) ).
fof(f52,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(paramodulation,[status(thm)],[f3,f6]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(X1,multiply(multiply(inverse(multiply(X0,X2)),multiply(inverse(multiply(X1,X3)),multiply(X4,X3))),X2))) = X4,
inference(paramodulation,[status(thm)],[f20,f6]) ).
fof(f95,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(X0),multiply(X1,X0))),X1) = multiply(inverse(X2),X2),
inference(paramodulation,[status(thm)],[f50,f20]) ).
fof(f96,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(X0),X0),multiply(X1,X2)) = multiply(multiply(inverse(multiply(inverse(X2),X3)),X1),X3),
inference(paramodulation,[status(thm)],[f50,f5]) ).
fof(f109,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2)) = multiply(X3,X0),
inference(backward_demodulation,[status(thm)],[f112,f48]) ).
fof(f111,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(multiply(inverse(multiply(X0,X2)),X3),X2))) = multiply(X1,X3),
inference(backward_demodulation,[status(thm)],[f112,f10]) ).
fof(f112,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(inverse(multiply(inverse(X1),X2)),X0),X2),
inference(forward_demodulation,[status(thm)],[f50,f96]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f109,f47]) ).
fof(f119,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X2,X1))) = X2,
inference(backward_demodulation,[status(thm)],[f111,f54]) ).
fof(f123,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f116,f95]) ).
fof(f125,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f123]) ).
fof(f131,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(X0),multiply(X1,X2))),X1) = multiply(inverse(X2),X0),
inference(paramodulation,[status(thm)],[f53,f20]) ).
fof(f137,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,multiply(X1,X2))),X1) = inverse(multiply(X0,X2)),
inference(backward_demodulation,[status(thm)],[f131,f35]) ).
fof(f138,plain,
! [X0,X1,X2] : multiply(inverse(X0),X1) = inverse(multiply(inverse(multiply(X1,X2)),multiply(X0,X2))),
inference(backward_demodulation,[status(thm)],[f131,f34]) ).
fof(f152,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(backward_demodulation,[status(thm)],[f137,f131]) ).
fof(f169,plain,
! [X0,X1,X2] : multiply(inverse(X0),X1) = multiply(inverse(multiply(X0,X2)),multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f152,f138]) ).
fof(f175,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f169,f119]) ).
fof(f208,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f116,f175]) ).
fof(f211,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f116,f175]) ).
fof(f215,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(inverse(inverse(multiply(X0,X2))),X1),
inference(paramodulation,[status(thm)],[f175,f3]) ).
fof(f223,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f125,f211]) ).
fof(f241,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f208,f215]) ).
fof(f246,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f241,f223]) ).
fof(f430,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f211,f246]) ).
fof(f432,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 19:56:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.054639 seconds
% 0.14/0.42 % CPU time: 0.215651 seconds
% 0.14/0.42 % Total memory used: 68.370 MB
% 0.14/0.42 % Net memory used: 67.741 MB
%------------------------------------------------------------------------------