%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT014-1 : 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 : n006.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 06:55:36 AM UTC 2026
% Result : Unsatisfiable 11.23s 1.90s
% Output : CNFRefutation 11.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 29 ( 8 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_codomain_is_idempotent,negated_conjecture,
codomain(codomain(a)) != codomain(a) ).
cnf(codomain_is_an_identity_map,axiom,
'identity$umap'(codomain(X0)) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X0),X0) ).
cnf(product_on_codomain,axiom,
product(codomain(X0),X0,X0) ).
cnf(identity2,axiom,
( product(X0,X1,X0)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ) ).
cnf(composition_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
codomain(codomain(a)) != codomain(a),
inference(clausification,[status(esa)],[prove_codomain_is_idempotent]) ).
cnf(c11,plain,
'identity$umap'(codomain(X0)),
inference(clausification,[status(esa)],[codomain_is_an_identity_map]) ).
cnf(c13,plain,
defined(codomain(X0),X0),
inference(clausification,[status(esa)],[mapping_from_codomain_of_x_to_x]) ).
cnf(c15,plain,
product(codomain(X0),X0,X0),
inference(clausification,[status(esa)],[product_on_codomain]) ).
cnf(c17,plain,
( product(X0,X1,X0)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[identity2]) ).
cnf(c18,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[composition_is_well_defined]) ).
cnf(d0,plain,
( ~ product(codomain(X1),X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c18,c15]) ).
cnf(d1,plain,
( ~ 'identity$umap'(X0)
| ~ defined(codomain(X0),X0)
| codomain(X0) = X0 ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( ~ 'identity$umap'(X0)
| codomain(X0) = X0 ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d3,plain,
codomain(codomain(X0)) = codomain(X0),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[d3,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 22:49:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.23/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 11.23/1.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------