%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP028-1 : 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 : n008.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 07:22:08 AM UTC 2026
% Result : Unsatisfiable 9.23s 1.54s
% Output : CNFRefutation 9.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 7 RR)
% Number of literals : 21 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(left_soln,hypothesis,
product('left$usolution'(X0,X1),X0,X1) ).
cnf(right_soln,hypothesis,
product(X0,'right$usolution'(X0,X1),X1) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product('not$uidentity'(X0),X0,'not$uidentity'(X0)) ).
cnf(c0,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c1,plain,
product('left$usolution'(X0,X1),X0,X1),
inference(clausification,[status(esa)],[left_soln]) ).
cnf(c2,plain,
product(X0,'right$usolution'(X0,X1),X1),
inference(clausification,[status(esa)],[right_soln]) ).
cnf(c3,plain,
~ product('not$uidentity'(X0),X0,'not$uidentity'(X0)),
inference(clausification,[status(esa)],[prove_there_is_a_right_identity]) ).
cnf(d0,plain,
( ~ product(X4,X1,X0)
| ~ product(X4,X2,X3)
| product(X0,'right$usolution'(X1,X2),X3) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
( product(X1,'right$usolution'(X0,X2),X3)
| ~ product('left$usolution'(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
product(X0,'right$usolution'(X1,X1),X0),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:18:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.23/1.54 % SZS status Unsatisfiable for theBenchmark.p
% 9.23/1.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------