%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Unsatisfiable 8.80s 1.82s
% Output : CNFRefutation 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 15 unt; 0 nHn; 21 RR)
% Number of literals : 51 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
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(square_element,hypothesis,
product(X0,X0,identity) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c) ).
cnf(c0,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c1,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_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,X0,identity),
inference(clausification,[status(esa)],[square_element]) ).
cnf(c5,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c6,plain,
~ product(b,a,c),
inference(clausification,[status(esa)],[prove_b_times_a_is_c]) ).
cnf(d0,plain,
( ~ product(a,X2,X1)
| ~ product(b,X0,X2)
| product(c,X0,X1) ),
inference(resolution,[status(thm)],[c3,c5]) ).
cnf(d1,plain,
( product(c,b,X0)
| ~ product(a,identity,X0) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
product(c,b,a),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( ~ product(X2,b,X1)
| ~ product(X0,c,X2)
| product(X0,a,X1) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ product(X2,b,X1)
| ~ product(X0,a,X2)
| product(X0,c,X1) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d5,plain,
( product(a,c,X0)
| ~ product(identity,b,X0) ),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
product(a,c,b),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ product(a,X2,X1)
| ~ product(c,X0,X2)
| product(b,X0,X1) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( product(b,c,X0)
| ~ product(a,identity,X0) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
product(b,c,a),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( product(b,a,X0)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
product(b,a,c),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c6,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n018.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Fri Sep 25 14:17:21 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.80/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 8.80/1.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------