%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP116-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:32:33 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(identity,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),X2)),multiply(identity,multiply(X2,X2)))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(identity,a) != a,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))),X2)) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),multiply(identity,X2)),
inference(paramodulation,[status(thm)],[f3,f10]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(X2,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),X3)),multiply(identity,multiply(X3,X3)))))))),multiply(multiply(identity,multiply(multiply(identity,X2),X3)),multiply(identity,multiply(X3,X3))))) = X1,
inference(paramodulation,[status(thm)],[f3,f10]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,multiply(X2,X2))))),X2)) = X1,
inference(backward_demodulation,[status(thm)],[f12,f10]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X2),multiply(X2,X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f12,f3]) ).
fof(f39,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,multiply(X2,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),X3)),multiply(identity,multiply(X3,X3)))))))),multiply(multiply(identity,multiply(multiply(identity,X2),X3)),multiply(identity,multiply(X3,X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f17]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,multiply(X2,X2)))),multiply(multiply(identity,multiply(multiply(identity,X2),X3)),multiply(identity,multiply(X3,X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f3,f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,multiply(X2,X2)))),multiply(identity,multiply(multiply(multiply(identity,X2),X3),multiply(X3,X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,multiply(X2,X2))),multiply(multiply(multiply(identity,X2),X3),multiply(X3,X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f41]) ).
fof(f60,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,multiply(identity,multiply(X2,X2))))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f23]) ).
fof(f66,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),multiply(multiply(identity,X2),X3)) = multiply(multiply(X0,multiply(X1,X2)),multiply(identity,X3)),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f68,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),multiply(multiply(identity,X2),X3)) = multiply(X0,multiply(multiply(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f12,f66]) ).
fof(f70,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity)))) = X1,
inference(paramodulation,[status(thm)],[f12,f24]) ).
fof(f71,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,X2)),multiply(multiply(identity,X2),multiply(identity,X2))))) = X1,
inference(paramodulation,[status(thm)],[f12,f24]) ).
fof(f78,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(X1,identity)))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f70]) ).
fof(f79,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(multiply(X1,X2),X2),multiply(identity,X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f68,f71]) ).
fof(f80,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,X2),multiply(X2,X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f79]) ).
fof(f86,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,multiply(X2,multiply(X3,X3))))),X3)) = multiply(X1,X2),
inference(paramodulation,[status(thm)],[f12,f60]) ).
fof(f87,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(X0,X1)),multiply(multiply(identity,X1),multiply(identity,X1)))) = identity,
inference(paramodulation,[status(thm)],[f24,f60]) ).
fof(f95,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f86,f60]) ).
fof(f96,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X1),multiply(identity,X1)))) = identity,
inference(forward_demodulation,[status(thm)],[f68,f87]) ).
fof(f97,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(X1,X1)))) = identity,
inference(forward_demodulation,[status(thm)],[f12,f96]) ).
fof(f99,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(backward_demodulation,[status(thm)],[f95,f78]) ).
fof(f100,plain,
! [X0,X1] : multiply(multiply(X0,X1),multiply(X1,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f99,f80]) ).
fof(f103,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,multiply(X2,X2))),multiply(identity,X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f100,f42]) ).
fof(f109,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(backward_demodulation,[status(thm)],[f100,f97]) ).
fof(f114,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,multiply(X2,X2)),X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f103]) ).
fof(f115,plain,
! [X0,X1] : multiply(multiply(X0,multiply(X1,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f99,f114]) ).
fof(f149,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f109,f115]) ).
fof(f160,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f149,f4]) ).
fof(f177,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP116-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 19:57:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.028471 seconds
% 0.12/0.38 % CPU time: 0.069452 seconds
% 0.12/0.38 % Total memory used: 3.804 MB
% 0.12/0.38 % Net memory used: 3.584 MB
%------------------------------------------------------------------------------