%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:22:09 AM UTC 2026
% Result : Unsatisfiable 12.18s 2.47s
% Output : CNFRefutation 12.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 35 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(right_inverse,hypothesis,
product(X0,inverse(X0),identity) ).
cnf(right_identity,hypothesis,
product(X0,identity,X0) ).
cnf(prove_a_has_a_left_inverse,negated_conjecture,
~ product(X0,a,identity) ).
cnf(c2,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c3,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c4,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c5,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c6,plain,
~ product(X0,a,identity),
inference(clausification,[status(esa)],[prove_a_has_a_left_inverse]) ).
cnf(d0,plain,
( ~ product(X2,inverse(X3),X1)
| ~ product(X0,X2,X3)
| product(X0,X1,identity) ),
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d1,plain,
( ~ product(X2,X3,X0)
| ~ product(X3,X1,identity)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c3,c5]) ).
cnf(d2,plain,
( product(identity,X1,X0)
| ~ product(inverse(X0),X1,identity) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
product(identity,inverse(inverse(X0)),X0),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( product(X0,X1,identity)
| ~ product(X0,identity,inverse(X1)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
product(inverse(X0),X0,identity),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 14:18:20 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.18/2.47 % SZS status Unsatisfiable for theBenchmark.p
% 12.18/2.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------