%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP034-4 : 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 : 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 07:22:09 AM UTC 2026
% Result : Unsatisfiable 9.70s 2.68s
% Output : CNFRefutation 9.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 27 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(closure_of_subgroup,axiom,
( 'subgroup$umember'(X2)
| ~ product(X1,inverse(X0),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(a_is_in_subgroup,hypothesis,
'subgroup$umember'(a) ).
cnf(prove_inverse_is_in_subgroup,negated_conjecture,
~ 'subgroup$umember'(inverse(a)) ).
cnf(c1,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c3,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c6,plain,
( 'subgroup$umember'(X2)
| ~ product(X1,inverse(X0),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_subgroup]) ).
cnf(c7,plain,
'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_is_in_subgroup]) ).
cnf(c8,plain,
~ 'subgroup$umember'(inverse(a)),
inference(clausification,[status(esa)],[prove_inverse_is_in_subgroup]) ).
cnf(d0,plain,
( ~ 'subgroup$umember'(identity)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(inverse(X0)) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(identity) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d2,plain,
'subgroup$umember'(identity),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ 'subgroup$umember'(a),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c7,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP034-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:21:05 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.70/2.68 % SZS status Unsatisfiable for theBenchmark.p
% 9.70/2.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------