%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP012+5 : 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 : n026.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 07:22:05 AM UTC 2026
% Result : Theorem 34.93s 6.68s
% Output : CNFRefutation 34.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 68 ( 20 ~; 18 |; 22 &)
% ( 0 <=>; 8 =>; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 85 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_distribution,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) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ) ).
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) )
=> ! [X4,X5,X6,X1] :
( ( product(X5,X4,X1)
& product(inverse(X4),inverse(X5),X6) )
=> product(inverse(X6),inverse(X1),X0) ) ),
inference(negate_conjecture,[status(cth)],[prove_distribution]) ).
cnf(c0,plain,
( product(X5,X2,X4)
| ~ product(X5,X0,X3)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1,plain,
product(X0,sK0,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2,plain,
product(X0,inverse(X0),sK0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
product(sK0,X0,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
product(sK21,sK20,sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
product(inverse(sK20),inverse(sK21),sK22),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
~ product(inverse(sK22),inverse(sK23),sK0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ product(X3,sK0,X0)
| ~ product(X3,X1,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d1,plain,
( product(X1,inverse(X0),sK0)
| ~ product(X0,sK0,X1) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( ~ product(X3,X2,X1)
| ~ product(X0,X3,sK0)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d3,plain,
( product(X0,sK0,inverse(X1))
| ~ product(X0,X1,sK0) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ product(X2,inverse(X3),X1)
| ~ product(X0,X2,X3)
| product(X0,X1,sK0) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d5,plain,
( product(X0,sK22,sK0)
| ~ product(X0,inverse(sK20),sK21) ),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( ~ product(X3,X1,X0)
| ~ product(X3,sK0,X2)
| product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d7,plain,
( product(sK23,inverse(sK20),X0)
| ~ product(sK21,sK0,X0) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
product(sK23,inverse(sK20),sK21),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
product(sK23,sK22,sK0),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
product(sK23,sK0,inverse(sK22)),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
product(inverse(sK22),inverse(sK23),sK0),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c9,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.74 % Computer : n026.cluster.edu
% 0.09/0.74 % Model : x86_64 x86_64
% 0.09/0.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.74 % Memory : 8046.5625MB
% 0.09/0.74 % OS : Linux 6.8.0-71-generic
% 0.09/0.75 % CPULimit : 300
% 0.09/0.75 % WCLimit : 300
% 0.09/0.75 % DateTime : Fri Sep 25 14:19:12 UTC 2026
% 0.09/0.75 % CPUTime :
% 0.09/0.75 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.93/6.68 % SZS status Theorem for theBenchmark.p
% 34.93/6.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------