%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:32:23 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 39 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
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(f6,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(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,negated_conjecture,
~ equalish(multiply(a,c),multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [Z,W] :
( equalish(Z,W)
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,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)],[f6]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
~ equalish(multiply(a,c),multiply(b,c)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0,X1] :
( ~ product(X0,X1,multiply(b,c))
| ~ product(X0,X1,multiply(a,c)) ),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f24,plain,
~ product(b,c,multiply(a,c)),
inference(resolution,[status(thm)],[f23,f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,multiply(a,c))
| ~ product(X1,c,X2)
| ~ product(X0,X1,b) ),
inference(resolution,[status(thm)],[f18,f24]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ product(X2,X0,X3)
| ~ equalish(X3,b)
| ~ product(X2,X1,multiply(a,c))
| ~ product(X0,c,X1) ),
inference(resolution,[status(thm)],[f30,f20]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ product(X2,X0,a)
| ~ product(X2,X1,multiply(a,c))
| ~ product(X0,c,X1) ),
inference(resolution,[status(thm)],[f58,f21]) ).
fof(f158,plain,
! [X0] :
( ~ product(identity,X0,multiply(a,c))
| ~ product(a,c,X0) ),
inference(resolution,[status(thm)],[f155,f10]) ).
fof(f162,plain,
~ product(identity,multiply(a,c),multiply(a,c)),
inference(resolution,[status(thm)],[f158,f12]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f162,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.097164 seconds
% 0.14/0.47 % CPU time: 0.473635 seconds
% 0.14/0.47 % Total memory used: 60.033 MB
% 0.14/0.47 % Net memory used: 58.833 MB
%------------------------------------------------------------------------------