%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT005-1 : 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 : n001.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 06:55:33 AM UTC 2026
% Result : Unsatisfiable 18.36s 3.44s
% Output : CNFRefutation 18.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 60 ( 9 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 38 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ad_defined,hypothesis,
defined(a,d) ).
cnf(d_is_identity_map,hypothesis,
'identity$umap'(d) ).
cnf(prove_domain_of_a_is_d,negated_conjecture,
domain(a) != d ).
cnf(associative_property2,axiom,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(domain_is_an_identity_map,axiom,
'identity$umap'(domain(X0)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X0,domain(X0)) ).
cnf(identity1,axiom,
( product(X0,X1,X1)
| ~ 'identity$umap'(X0)
| ~ defined(X0,X1) ) ).
cnf(identity2,axiom,
( product(X0,X1,X0)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ) ).
cnf(composition_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a,d),
inference(clausification,[status(esa)],[ad_defined]) ).
cnf(c1,plain,
'identity$umap'(d),
inference(clausification,[status(esa)],[d_is_identity_map]) ).
cnf(c2,plain,
domain(a) != d,
inference(clausification,[status(esa)],[prove_domain_of_a_is_d]) ).
cnf(c5,plain,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associative_property2]) ).
cnf(c12,plain,
'identity$umap'(domain(X0)),
inference(clausification,[status(esa)],[domain_is_an_identity_map]) ).
cnf(c14,plain,
defined(X0,domain(X0)),
inference(clausification,[status(esa)],[mapping_from_x_to_its_domain]) ).
cnf(c18,plain,
( product(X0,X1,X1)
| ~ 'identity$umap'(X0)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[identity1]) ).
cnf(c19,plain,
( product(X0,X1,X0)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[identity2]) ).
cnf(c20,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[composition_is_well_defined]) ).
cnf(d0,plain,
( ~ defined(X0,X2)
| defined(X1,X2)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[c19,c5]) ).
cnf(d1,plain,
( ~ 'identity$umap'(d)
| ~ defined(a,X0)
| defined(d,X0) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( defined(d,X0)
| ~ defined(a,X0) ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
defined(d,domain(a)),
inference(resolution,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
( ~ 'identity$umap'(X2)
| ~ defined(X1,X2)
| ~ product(X1,X2,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c20,c19]) ).
cnf(d5,plain,
( ~ 'identity$umap'(X1)
| ~ defined(X1,X0)
| ~ 'identity$umap'(X0)
| ~ defined(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[d4,c18]) ).
cnf(d6,plain,
( ~ 'identity$umap'(domain(a))
| ~ 'identity$umap'(d)
| domain(a) = d ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ 'identity$umap'(domain(a))
| domain(a) = d ),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
domain(a) = d,
inference(resolution,[status(thm)],[c12,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c2,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 22:54:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.36/3.44 % SZS status Unsatisfiable for theBenchmark.p
% 18.36/3.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------