%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP038-3 : 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 : n017.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 07:22:10 AM UTC 2026
% Result : Unsatisfiable 11.93s 2.49s
% Output : CNFRefutation 11.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 14 RR)
% Number of literals : 23 ( 0 equ; 11 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_in_subgroup,hypothesis,
'subgroup$umember'(a) ).
cnf(b_is_in_subgroup,hypothesis,
'subgroup$umember'(b) ).
cnf(a_times_inverse_b_is_c,hypothesis,
product(a,inverse(b),c) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ 'subgroup$umember'(c) ).
cnf(closure_of_product_and_inverse,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c2,plain,
'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_is_in_subgroup]) ).
cnf(c3,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c4,plain,
product(a,inverse(b),c),
inference(clausification,[status(esa)],[a_times_inverse_b_is_c]) ).
cnf(c5,plain,
~ 'subgroup$umember'(c),
inference(clausification,[status(esa)],[prove_c_is_in_subgroup]) ).
cnf(c14,plain,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_product_and_inverse]) ).
cnf(d0,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(a)
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d1,plain,
( 'subgroup$umember'(c)
| ~ 'subgroup$umember'(b) ),
inference(resolution,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
'subgroup$umember'(c),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c5,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:14:17 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.93/2.49 % SZS status Unsatisfiable for theBenchmark.p
% 11.93/2.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------