%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 07:22:02 AM UTC 2026
% Result : Theorem 14.06s 2.38s
% Output : CNFRefutation 14.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 56 ( 14 ~; 12 |; 20 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 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 : 77 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity,conjecture,
! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
inference(negate_conjecture,[status(cth)],[commutativity]) ).
cnf(c1,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c3,plain,
product(X0,sK0,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
product(sK0,X0,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
product(X0,X0,sK0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
product(sK21,sK22,sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
~ product(sK22,sK21,sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( product(X2,X3,X1)
| ~ product(X2,X0,X3)
| ~ product(sK0,X0,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d1,plain,
( ~ product(X0,X2,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ product(X3,X1,X0)
| ~ product(X3,sK0,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d3,plain,
( product(X2,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
product(sK21,sK23,sK22),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d5,plain,
product(sK22,sK23,sK21),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
product(sK22,sK21,sK23),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c9,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n011.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Fri Sep 25 14:15:13 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.06/2.38 % SZS status Theorem for theBenchmark.p
% 14.06/2.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------