%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP009-1 : 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 : n014.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 07:22:04 AM UTC 2026
% Result : Unsatisfiable 15.12s 2.42s
% Output : CNFRefutation 15.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 18 unt; 0 nHn; 24 RR)
% Number of literals : 54 ( 8 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_an_inverse_of_b,hypothesis,
product(a,b,identity) ).
cnf(c_is_an_inverse_of_b,hypothesis,
product(c,b,identity) ).
cnf(prove_a_equals_c,negated_conjecture,
a != c ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
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,identity),
inference(clausification,[status(esa)],[a_is_an_inverse_of_b]) ).
cnf(c1,plain,
product(c,b,identity),
inference(clausification,[status(esa)],[c_is_an_inverse_of_b]) ).
cnf(c2,plain,
a != c,
inference(clausification,[status(esa)],[prove_a_equals_c]) ).
cnf(c3,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c5,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c8,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
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(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d1,plain,
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d2,plain,
( ~ product(X3,X0,identity)
| product(X3,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d3,plain,
( ~ product(X0,a,identity)
| product(X0,identity,b) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
product(inverse(a),identity,b),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
inverse(a) = b,
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
product(b,a,identity),
inference(superposition,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( ~ product(X2,X3,X0)
| ~ product(X3,X1,identity)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d8,plain,
( product(identity,X0,c)
| ~ product(b,X0,identity) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
product(identity,a,c),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
a = c,
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c2,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:16:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.12/2.42 % SZS status Unsatisfiable for theBenchmark.p
% 15.12/2.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------