%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:32:23 PM UTC 2026
% Result : Unsatisfiable 33.98s 4.79s
% Output : CNFRefutation 33.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 118 ( 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Z,Y,X] : multiply(Z,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),X)),multiply(inverse(Y),multiply(inverse(Y),Y))))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( 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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( 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,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1)),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f7,plain,
! [X0,X1,X2,X3] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X0))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),X5)),multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2))),multiply(inverse(X5),multiply(inverse(X5),X5)))),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),multiply(inverse(multiply(X3,X4)),X1))),multiply(inverse(X5),multiply(inverse(X5),X5)))),X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f97,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(forward_demodulation,[status(thm)],[f7,f59]) ).
fof(f134,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f97,f31]) ).
fof(f326,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,X3)),
inference(paramodulation,[status(thm)],[f97,f134]) ).
fof(f364,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))))) = multiply(inverse(X1),X3),
inference(paramodulation,[status(thm)],[f134,f31]) ).
fof(f1920,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))),multiply(X0,inverse(multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))))))) = X3,
inference(paramodulation,[status(thm)],[f326,f31]) ).
fof(f2052,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(forward_demodulation,[status(thm)],[f364,f1920]) ).
fof(f2131,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f2052,f326]) ).
fof(f2241,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f2131,f2131]) ).
fof(f2556,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(backward_subsumption_resolution,[status(thm)],[f4,f2241]) ).
fof(f2596,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f2241,f9]) ).
fof(f2797,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(forward_demodulation,[status(thm)],[f31,f2596]) ).
fof(f2829,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))),
inference(paramodulation,[status(thm)],[f134,f2797]) ).
fof(f3109,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f2241,f2829]) ).
fof(f3282,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(X1),X2),
inference(backward_demodulation,[status(thm)],[f3109,f364]) ).
fof(f3293,plain,
! [X0,X1] : multiply(inverse(X0),X0) = inverse(multiply(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f2241,f3109]) ).
fof(f6226,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(X0),multiply(inverse(X1),X1))),
inference(backward_demodulation,[status(thm)],[f3282,f3109]) ).
fof(f7774,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))))) = X1,
inference(paramodulation,[status(thm)],[f6226,f3]) ).
fof(f7910,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f3282,f7774]) ).
fof(f7911,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f6226,f7910]) ).
fof(f8064,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f7911,f7911]) ).
fof(f8161,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f7911,f8064]) ).
fof(f8295,plain,
! [X0,X1] : X0 = multiply(X0,inverse(multiply(inverse(X1),X1))),
inference(paramodulation,[status(thm)],[f3293,f8161]) ).
fof(f8296,plain,
! [X0,X1] : X0 = multiply(X0,multiply(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f2241,f8161]) ).
fof(f8333,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8161,f6226]) ).
fof(f8492,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X0) = multiply(inverse(X1),multiply(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f8296,f3282]) ).
fof(f8506,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8296,f8492]) ).
fof(f8761,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(X0,X1)) = multiply(inverse(inverse(multiply(inverse(X2),X2))),X1),
inference(paramodulation,[status(thm)],[f8295,f3282]) ).
fof(f8796,plain,
! [X0,X1] : X0 = multiply(inverse(inverse(multiply(inverse(X1),X1))),X0),
inference(forward_demodulation,[status(thm)],[f7911,f8761]) ).
fof(f8797,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f8333,f8796]) ).
fof(f8798,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f8797,f2556]) ).
fof(f8831,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f8798]) ).
fof(f8888,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f8506,f8506]) ).
fof(f8913,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8333,f8888]) ).
fof(f11029,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),multiply(X1,X2)) = multiply(inverse(inverse(multiply(X0,X1))),X2),
inference(paramodulation,[status(thm)],[f8913,f3282]) ).
fof(f11108,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(inverse(inverse(multiply(X0,X1))),X2),
inference(forward_demodulation,[status(thm)],[f8333,f11029]) ).
fof(f11109,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f8333,f11108]) ).
fof(f19466,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f11109,f8831]) ).
fof(f19553,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f19466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 19:58:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 33.98/4.79 % Refutation found
% 33.98/4.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 33.98/4.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.39/4.91 % Elapsed time: 4.527129 seconds
% 32.39/4.91 % CPU time: 35.386467 seconds
% 32.39/4.91 % Total memory used: 485.268 MB
% 32.39/4.91 % Net memory used: 483.008 MB
%------------------------------------------------------------------------------