%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP013-1 : 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 : n005.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 16.21s 2.54s
% Output : CNFRefutation 16.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 35 ( 8 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(squareness,hypothesis,
product(X0,X0,identity) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(inverse_a_times_inverse_b_is_d,hypothesis,
product(inverse(a),inverse(b),d) ).
cnf(inverses_have_property,hypothesis,
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ) ).
cnf(prove_c_times_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(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(X0,X0,identity),
inference(clausification,[status(esa)],[squareness]) ).
cnf(c1,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c2,plain,
product(inverse(a),inverse(b),d),
inference(clausification,[status(esa)],[inverse_a_times_inverse_b_is_d]) ).
cnf(c3,plain,
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ),
inference(clausification,[status(esa)],[inverses_have_property]) ).
cnf(c4,plain,
~ product(c,d,identity),
inference(clausification,[status(esa)],[prove_c_times_d_is_identity]) ).
cnf(c6,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c8,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c10,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(d0,plain,
product(X0,identity,inverse(X0)),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d1,plain,
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(d2,plain,
inverse(X0) = X0,
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ product(inverse(a),inverse(b),X0)
| X0 = d ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d4,plain,
( ~ product(a,inverse(b),X0)
| X0 = d ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ product(a,b,X0)
| X0 = d ),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
c = d,
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
~ product(c,c,identity),
inference(demodulation,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c0,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n005.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 14:16:18 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.21/2.54 % SZS status Unsatisfiable for theBenchmark.p
% 16.21/2.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------