%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT006-1 : 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 : n014.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 15.40s 3.30s
% Output : CNFRefutation 15.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 20 unt; 0 nHn; 32 RR)
% Number of literals : 82 ( 17 equ; 43 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ha_defined,hypothesis,
defined(h,a) ).
cnf(h_is_the_identity_map,hypothesis,
'identity$umap'(h) ).
cnf(prove_codomain_of_a_is_h,negated_conjecture,
codomain(a) != h ).
cnf(closure_of_composition,axiom,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ) ).
cnf(category_theory_axiom3,axiom,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(codomain_is_an_identity_map,axiom,
'identity$umap'(codomain(X0)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X0,domain(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(h,a),
inference(clausification,[status(esa)],[ha_defined]) ).
cnf(c1,plain,
'identity$umap'(h),
inference(clausification,[status(esa)],[h_is_the_identity_map]) ).
cnf(c2,plain,
codomain(a) != h,
inference(clausification,[status(esa)],[prove_codomain_of_a_is_h]) ).
cnf(c3,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[closure_of_composition]) ).
cnf(c8,plain,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom3]) ).
cnf(c13,plain,
'identity$umap'(codomain(X0)),
inference(clausification,[status(esa)],[codomain_is_an_identity_map]) ).
cnf(c14,plain,
defined(X0,domain(X0)),
inference(clausification,[status(esa)],[mapping_from_x_to_its_domain]) ).
cnf(c15,plain,
defined(codomain(X0),X0),
inference(clausification,[status(esa)],[mapping_from_codomain_of_x_to_x]) ).
cnf(c16,plain,
product(X0,domain(X0),X0),
inference(clausification,[status(esa)],[product_on_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(X2,X0)
| ~ defined(X2,X1)
| ~ 'identity$umap'(X0)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d1,plain,
( ~ 'identity$umap'(h)
| defined(X0,h)
| ~ defined(X0,a) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ defined(X0,a)
| defined(X0,h) ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
defined(codomain(a),h),
inference(resolution,[status(thm)],[d2,c15]) ).
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'(h)
| ~ 'identity$umap'(codomain(a))
| h = codomain(a) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ 'identity$umap'(codomain(a))
| h = codomain(a) ),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
h = codomain(a),
inference(resolution,[status(thm)],[c13,d7]) ).
cnf(d9,plain,
h != h,
inference(demodulation,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( ~ product(X1,domain(X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c20,c16]) ).
cnf(d11,plain,
( ~ defined(X0,domain(X0))
| compose(X0,domain(X0)) = X0 ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
compose(X0,domain(X0)) = X0,
inference(resolution,[status(thm)],[c14,d11]) ).
cnf(d13,plain,
( ~ defined(X1,X2)
| ~ product(X1,X2,X0)
| X0 = compose(X1,X2) ),
inference(resolution,[status(thm)],[c20,c3]) ).
cnf(d14,plain,
( ~ defined(X0,domain(X0))
| X0 = compose(X0,domain(X0)) ),
inference(resolution,[status(thm)],[d13,c16]) ).
cnf(d15,plain,
( ~ defined(X0,domain(X0))
| X0 = X0 ),
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
X0 = X0,
inference(resolution,[status(thm)],[c14,d15]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:48:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.40/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 15.40/3.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------