%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP012-1 : 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 : n007.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 : Unsatisfiable 10.45s 8.08s
% Output : CNFRefutation 10.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 39 ( 0 equ; 20 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d) ).
cnf(prove_c_multiply_d_is_identity,negated_conjecture,
~ product(c,d,identity) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
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(c0,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_multiply_b_is_c]) ).
cnf(c1,plain,
product(inverse(b),inverse(a),d),
inference(clausification,[status(esa)],[inverse_b_multiply_inverse_a_is_d]) ).
cnf(c2,plain,
~ product(c,d,identity),
inference(clausification,[status(esa)],[prove_c_multiply_d_is_identity]) ).
cnf(c4,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c6,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c9,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(d0,plain,
( ~ product(X3,X0,X1)
| product(X3,X2,identity)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d1,plain,
( ~ product(X0,inverse(b),a)
| product(X0,d,identity) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ product(X2,X3,X0)
| ~ product(X3,X1,identity)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d3,plain,
( product(c,X0,a)
| ~ product(b,X0,identity) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
product(c,inverse(b),a),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
product(c,d,identity),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c2,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n007.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 14:14:14 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.45/8.08 % SZS status Unsatisfiable for theBenchmark.p
% 10.45/8.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------