%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP037-3 : 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 : n002.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 12.79s 2.00s
% Output : CNFRefutation 12.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 14 unt; 0 nHn; 23 RR)
% Number of literals : 44 ( 14 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(another_right_identity,hypothesis,
( product(X0,'another$uidentity',X0)
| ~ 'subgroup$umember'(X0) ) ).
cnf(another_left_inverse,hypothesis,
( product('another$uinverse'(X0),X0,'another$uidentity')
| ~ 'subgroup$umember'(X0) ) ).
cnf(product_right_cancellation,hypothesis,
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,hypothesis,
( X3 = X0
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ) ).
cnf(a_is_in_subgroup,hypothesis,
'subgroup$umember'(a) ).
cnf(another_identity_in_subgroup,hypothesis,
'subgroup$umember'('another$uidentity') ).
cnf(prove_two_inverses_are_equal,negated_conjecture,
inverse(a) != 'another$uinverse'(a) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(c1,plain,
( product(X0,'another$uidentity',X0)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[another_right_identity]) ).
cnf(c3,plain,
( product('another$uinverse'(X0),X0,'another$uidentity')
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[another_left_inverse]) ).
cnf(c5,plain,
( X3 = X1
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_right_cancellation]) ).
cnf(c6,plain,
( X3 = X0
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c7,plain,
'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_is_in_subgroup]) ).
cnf(c8,plain,
'subgroup$umember'('another$uidentity'),
inference(clausification,[status(esa)],[another_identity_in_subgroup]) ).
cnf(c9,plain,
inverse(a) != 'another$uinverse'(a),
inference(clausification,[status(esa)],[prove_two_inverses_are_equal]) ).
cnf(c11,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c12,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(d0,plain,
( ~ product(X1,X0,X1)
| identity = X0 ),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(d1,plain,
( ~ 'subgroup$umember'(X0)
| identity = 'another$uidentity' ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
identity = 'another$uidentity',
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( ~ product(X0,X1,identity)
| X0 = inverse(X1) ),
inference(resolution,[status(thm)],[c12,c6]) ).
cnf(d4,plain,
( ~ product(X0,X1,'another$uidentity')
| X0 = inverse(X1) ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'subgroup$umember'(X0)
| 'another$uinverse'(X0) = inverse(X0) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'another$uinverse'(a) = inverse(a),
inference(resolution,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
'another$uinverse'(a) != 'another$uinverse'(a),
inference(demodulation,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:21:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.79/2.00 % SZS status Unsatisfiable for theBenchmark.p
% 12.79/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------