%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT008-1 : 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 : n016.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 06:55:34 AM UTC 2026
% Result : Unsatisfiable 47.65s 7.32s
% Output : CNFRefutation 47.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 19 unt; 0 nHn; 27 RR)
% Number of literals : 61 ( 6 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 46 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ab_defined,hypothesis,
defined(a,b) ).
cnf(prove_domain_of_a_equals_codomain_of_b,negated_conjecture,
domain(a) != codomain(b) ).
cnf(associative_property2,axiom,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom3,axiom,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(domain_is_an_identity_map,axiom,
'identity$umap'(domain(X0)) ).
cnf(codomain_is_an_identity_map,axiom,
'identity$umap'(codomain(X0)) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X0),X0) ).
cnf(product_on_domain,axiom,
product(X0,domain(X0),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,b),
inference(clausification,[status(esa)],[ab_defined]) ).
cnf(c1,plain,
codomain(b) != domain(a),
inference(clausification,[status(esa)],[prove_domain_of_a_equals_codomain_of_b]) ).
cnf(c4,plain,
( defined(X3,X1)
| ~ product(X2,X3,X0)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[associative_property2]) ).
cnf(c7,plain,
( defined(X0,X2)
| ~ product(X2,X3,X1)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[category_theory_axiom3]) ).
cnf(c11,plain,
'identity$umap'(domain(X0)),
inference(clausification,[status(esa)],[domain_is_an_identity_map]) ).
cnf(c12,plain,
'identity$umap'(codomain(X0)),
inference(clausification,[status(esa)],[codomain_is_an_identity_map]) ).
cnf(c14,plain,
defined(codomain(X0),X0),
inference(clausification,[status(esa)],[mapping_from_codomain_of_x_to_x]) ).
cnf(c15,plain,
product(X0,domain(X0),X0),
inference(clausification,[status(esa)],[product_on_domain]) ).
cnf(c17,plain,
( product(X0,X1,X1)
| ~ defined(X0,X1)
| ~ 'identity$umap'(X0) ),
inference(clausification,[status(esa)],[identity1]) ).
cnf(c18,plain,
( product(X1,X0,X1)
| ~ defined(X1,X0)
| ~ 'identity$umap'(X0) ),
inference(clausification,[status(esa)],[identity2]) ).
cnf(c19,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[composition_is_well_defined]) ).
cnf(d0,plain,
( ~ product(X1,X2,X0)
| defined(codomain(X0),X1) ),
inference(resolution,[status(thm)],[c7,c14]) ).
cnf(d1,plain,
( ~ product(X1,X0,a)
| defined(X0,b) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
defined(domain(a),b),
inference(resolution,[status(thm)],[d1,c15]) ).
cnf(d3,plain,
( ~ 'identity$umap'(domain(a))
| product(domain(a),b,b) ),
inference(resolution,[status(thm)],[d2,c17]) ).
cnf(d4,plain,
product(domain(a),b,b),
inference(resolution,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
defined(codomain(b),domain(a)),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ 'identity$umap'(domain(a))
| product(codomain(b),domain(a),codomain(b)) ),
inference(resolution,[status(thm)],[d5,c18]) ).
cnf(d7,plain,
product(codomain(b),domain(a),codomain(b)),
inference(resolution,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
( ~ 'identity$umap'(codomain(b))
| product(codomain(b),domain(a),domain(a)) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d9,plain,
product(codomain(b),domain(a),domain(a)),
inference(resolution,[status(thm)],[c12,d8]) ).
cnf(d10,plain,
( ~ product(codomain(b),domain(a),X0)
| X0 = domain(a) ),
inference(resolution,[status(thm)],[d9,c19]) ).
cnf(d11,plain,
codomain(b) = domain(a),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c1,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 22:53:45 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.65/7.32 % SZS status Unsatisfiable for theBenchmark.p
% 47.65/7.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------