%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.57s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 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(multiply(a,b),c) != multiply(a,multiply(b,c)),
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(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,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(f15,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),multiply(identity,X2)),
inference(paramodulation,[status(thm)],[f3,f13]) ).
fof(f20,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,f13]) ).
fof(f26,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)],[f15,f13]) ).
fof(f27,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X2),multiply(X2,X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f15,f3]) ).
fof(f42,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)],[f15,f20]) ).
fof(f43,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,f42]) ).
fof(f44,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)],[f15,f43]) ).
fof(f45,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)],[f15,f44]) ).
fof(f63,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)],[f15,f26]) ).
fof(f69,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)],[f15,f15]) ).
fof(f71,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)],[f15,f69]) ).
fof(f73,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity)))) = X1,
inference(paramodulation,[status(thm)],[f15,f27]) ).
fof(f74,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)],[f15,f27]) ).
fof(f81,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(X1,identity)))) = X1,
inference(forward_demodulation,[status(thm)],[f15,f73]) ).
fof(f82,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)],[f71,f74]) ).
fof(f83,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,X2),multiply(X2,X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f15,f82]) ).
fof(f89,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)],[f15,f63]) ).
fof(f90,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(X0,X1)),multiply(multiply(identity,X1),multiply(identity,X1)))) = identity,
inference(paramodulation,[status(thm)],[f27,f63]) ).
fof(f98,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f89,f63]) ).
fof(f99,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X1),multiply(identity,X1)))) = identity,
inference(forward_demodulation,[status(thm)],[f71,f90]) ).
fof(f100,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(X1,X1)))) = identity,
inference(forward_demodulation,[status(thm)],[f15,f99]) ).
fof(f102,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(backward_demodulation,[status(thm)],[f98,f81]) ).
fof(f103,plain,
! [X0,X1] : multiply(multiply(X0,X1),multiply(X1,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f102,f83]) ).
fof(f106,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)],[f103,f45]) ).
fof(f112,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(backward_demodulation,[status(thm)],[f103,f100]) ).
fof(f117,plain,
! [X0,X1,X2] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,multiply(X2,X2)),X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f15,f106]) ).
fof(f118,plain,
! [X0,X1] : multiply(multiply(X0,multiply(X1,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f102,f117]) ).
fof(f152,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f112,f118]) ).
fof(f163,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f152,f15]) ).
fof(f179,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(b,c)),
inference(backward_demodulation,[status(thm)],[f163,f4]) ).
fof(f204,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n007.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sun Sep 20 19:55:51 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 0.08/0.57 % Refutation found
% 0.08/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.60 % Elapsed time: 0.035024 seconds
% 0.08/0.60 % CPU time: 0.069464 seconds
% 0.08/0.60 % Total memory used: 3.082 MB
% 0.08/0.60 % Net memory used: 2.865 MB
%------------------------------------------------------------------------------