%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP001+6 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 06:26:35 PM UTC 2025
% Result : Theorem 56.96s 7.47s
% Output : CNFRefutation 56.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 63 ( 18 ~; 15 |; 20 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 63 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity,plain,
! [E] :
( ( ! [X,Y] :
? [Z] : product(X,Y,Z)
& ! [X,Y,Z,U,V,W] :
( ( product(X,Y,U)
& product(Y,Z,V)
& product(U,Z,W) )
=> product(X,V,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(X,Y,U)
& product(Y,Z,V)
& product(X,V,W) )
=> product(U,Z,W) )
& ! [X] : product(X,E,X)
& ! [X] : product(E,X,X)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(inverse(X),X,E) )
=> ( ! [X] : product(X,X,E)
=> ! [U,V,W] :
( product(U,V,W)
=> product(V,U,W) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
fof(commutativity_negated,plain,
~ ! [E] :
( ( ! [X,Y] :
? [Z] : product(X,Y,Z)
& ! [X,Y,Z,U,V,W] :
( ( product(X,Y,U)
& product(Y,Z,V)
& product(U,Z,W) )
=> product(X,V,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(X,Y,U)
& product(Y,Z,V)
& product(X,V,W) )
=> product(U,Z,W) )
& ! [X] : product(X,E,X)
& ! [X] : product(E,X,X)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(inverse(X),X,E) )
=> ( ! [X] : product(X,X,E)
=> ! [U,V,W] :
( product(U,V,W)
=> product(V,U,W) ) ) ),
inference(negate_conjecture,[status(cth)],[commutativity]) ).
cnf(3,plain,
product(X0,sK1,X0),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l0,plain,
product(sK3,sK1,sK3),
inference(instantiation,[status(thm)],[3]) ).
cnf(2,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X5,X3)
| product(X2,X5,X4) ),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l1,plain,
( ~ product(sK3,sK5,sK4)
| ~ product(sK3,sK1,sK3)
| ~ product(sK5,sK5,sK1)
| product(sK4,sK5,sK3) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(1,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l3,plain,
( ~ product(sK4,sK4,sK1)
| ~ product(sK4,sK5,sK3)
| ~ product(sK1,sK5,sK5)
| product(sK4,sK3,sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(7,plain,
product(X0,X0,sK1),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l9,plain,
product(sK4,sK4,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(4,plain,
product(sK1,X0,X0),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l5,plain,
product(sK1,sK5,sK5),
inference(instantiation,[status(thm)],[4]) ).
cnf(l15,plain,
( ~ product(sK3,sK3,sK1)
| ~ product(sK3,sK4,sK5)
| ~ product(sK1,sK4,sK4)
| product(sK3,sK5,sK4) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(9,plain,
~ product(sK4,sK3,sK5),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l6,plain,
~ product(sK4,sK3,sK5),
inference(instantiation,[status(thm)],[9]) ).
cnf(l17,plain,
product(sK1,sK4,sK4),
inference(instantiation,[status(thm)],[4]) ).
cnf(l18,plain,
product(sK3,sK3,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(8,plain,
product(sK3,sK4,sK5),
inference(cnf,[status(esa)],[commutativity_negated]) ).
cnf(l16,plain,
product(sK3,sK4,sK5),
inference(instantiation,[status(thm)],[8]) ).
cnf(l2,plain,
product(sK5,sK5,sK1),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l9,l5,l15,l6,l17,l18,l16,l2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001+6 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.33 % Computer : n031.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun Jul 20 13:23:34 EDT 2025
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % launching worker at depth: 2
% 0.14/0.34 % launching worker at depth: 3
% 0.14/0.34 % launching worker at depth: 5
% 0.14/0.34 % launching worker at depth: 1
% 0.14/0.34 % launching worker at depth: 4
% 0.14/0.34 % launching worker at depth: 6
% 0.14/0.34 % launching worker at depth: 7
% 0.14/0.34 % launching worker at depth: 8
% 0.14/0.34 % launching worker at depth: 9
% 0.20/0.36 % launching worker at depth: 10
% 56.96/7.47 % SZS status Theorem for theBenchmark
% 56.96/7.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------