%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:32:19 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.34s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 19 unt; 0 def)
% Number of atoms : 47 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : product(identity,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : product(inverse(A),A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [A] : ~ product(not_right_identity(A),A,not_right_identity(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] : ~ product(not_right_identity(X0),X0,not_right_identity(X0)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] :
( product(multiply(X3,X0),X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f8,f14]) ).
fof(f20,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f8,f10]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f23,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f22,f8]) ).
fof(f26,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f86,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[f15,f20]) ).
fof(f101,plain,
! [X0,X1] : product(multiply(X0,identity),X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f86,f23]) ).
fof(f117,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(resolution,[status(thm)],[f16,f20]) ).
fof(f133,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f117,f26]) ).
fof(f138,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f86,f133]) ).
fof(f142,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f117,f138]) ).
fof(f350,plain,
! [X0] : product(multiply(inverse(inverse(X0)),identity),identity,X0),
inference(paramodulation,[status(thm)],[f142,f101]) ).
fof(f365,plain,
! [X0] : product(X0,identity,X0),
inference(forward_demodulation,[status(thm)],[f142,f350]) ).
fof(f372,plain,
$false,
inference(resolution,[status(thm)],[f365,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 19:54:38 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.08/0.34 % Refutation found
% 0.08/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.35 % Elapsed time: 0.041416 seconds
% 0.08/0.35 % CPU time: 0.107565 seconds
% 0.08/0.35 % Total memory used: 44.618 MB
% 0.08/0.35 % Net memory used: 44.030 MB
%------------------------------------------------------------------------------