%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP036-3 : 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 : n026.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 15.54s 7.44s
% Output : CNFRefutation 15.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 16 RR)
% Number of literals : 36 ( 6 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(another_left_identity,hypothesis,
( product('another$uidentity',X0,X0)
| ~ 'subgroup$umember'(X0) ) ).
cnf(another_identity_in_subgroup,hypothesis,
'subgroup$umember'('another$uidentity') ).
cnf(prove_identity_equals_another_identity,negated_conjecture,
identity != 'another$uidentity' ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(closure_of_product_and_inverse,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c0,plain,
( product('another$uidentity',X0,X0)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[another_left_identity]) ).
cnf(c5,plain,
'subgroup$umember'('another$uidentity'),
inference(clausification,[status(esa)],[another_identity_in_subgroup]) ).
cnf(c6,plain,
identity != 'another$uidentity',
inference(clausification,[status(esa)],[prove_identity_equals_another_identity]) ).
cnf(c8,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c10,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c12,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c15,plain,
( 'subgroup$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,
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d1,plain,
( ~ 'subgroup$umember'(identity)
| identity = 'another$uidentity' ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
~ 'subgroup$umember'(identity),
inference(resolution,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(identity) ),
inference(resolution,[status(thm)],[c15,c10]) ).
cnf(d4,plain,
'subgroup$umember'(identity),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n026.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Fri Sep 25 14:21:46 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.54/7.44 % SZS status Unsatisfiable for theBenchmark.p
% 15.54/7.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------