%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:32:22 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,W] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
equalish(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ equalish(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [Z,W] :
( equalish(Z,W)
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f20,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
equalish(b,c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
~ equalish(a,c),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f11,f21]) ).
fof(f26,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f11,f15]) ).
fof(f27,plain,
product(identity,b,c),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f28,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[f25,f22]) ).
fof(f30,plain,
! [X0] :
( equalish(X0,c)
| ~ product(identity,b,X0) ),
inference(resolution,[status(thm)],[f27,f15]) ).
fof(f33,plain,
equalish(b,a),
inference(resolution,[status(thm)],[f26,f28]) ).
fof(f37,plain,
product(identity,b,a),
inference(resolution,[status(thm)],[f33,f25]) ).
fof(f49,plain,
equalish(a,c),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f53,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f49,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 19:55:54 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % 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: 0.061122 seconds
% 0.14/0.42 % CPU time: 0.151493 seconds
% 0.14/0.42 % Total memory used: 55.551 MB
% 0.14/0.42 % Net memory used: 55.029 MB
%------------------------------------------------------------------------------