%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT009-1 : 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 : n018.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 38.63s 6.21s
% Output : CNFRefutation 38.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 59 ( 38 unt; 0 nHn; 34 RR)
% Number of literals : 88 ( 19 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 66 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ba_defined,hypothesis,
defined(b,a) ).
cnf(prove_domain_of_ba_equals_domain_of_a,negated_conjecture,
domain(compose(b,a)) != domain(a) ).
cnf(closure_of_composition,axiom,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ) ).
cnf(associative_property2,axiom,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(domain_is_an_identity_map,axiom,
'identity$umap'(domain(X0)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X0,domain(X0)) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X0),X0) ).
cnf(product_on_domain,axiom,
product(X0,domain(X0),X0) ).
cnf(product_on_codomain,axiom,
product(codomain(X0),X0,X0) ).
cnf(identity1,axiom,
( product(X0,X1,X1)
| ~ 'identity$umap'(X0)
| ~ defined(X0,X1) ) ).
cnf(identity2,axiom,
( product(X0,X1,X0)
| ~ 'identity$umap'(X1)
| ~ defined(X0,X1) ) ).
cnf(composition_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
defined(b,a),
inference(clausification,[status(esa)],[ba_defined]) ).
cnf(c1,plain,
domain(a) != domain(compose(b,a)),
inference(clausification,[status(esa)],[prove_domain_of_ba_equals_domain_of_a]) ).
cnf(c2,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[closure_of_composition]) ).
cnf(c4,plain,
( defined(X3,X1)
| ~ product(X2,X3,X0)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[associative_property2]) ).
cnf(c11,plain,
'identity$umap'(domain(X0)),
inference(clausification,[status(esa)],[domain_is_an_identity_map]) ).
cnf(c13,plain,
defined(X0,domain(X0)),
inference(clausification,[status(esa)],[mapping_from_x_to_its_domain]) ).
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(c16,plain,
product(codomain(X0),X0,X0),
inference(clausification,[status(esa)],[product_on_codomain]) ).
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(X2,X0,X1)
| defined(X0,domain(X1)) ),
inference(resolution,[status(thm)],[c4,c13]) ).
cnf(d1,plain,
product(b,a,compose(b,a)),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
defined(a,domain(compose(b,a))),
inference(resolution,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
( ~ 'identity$umap'(domain(compose(b,a)))
| product(a,domain(compose(b,a)),a) ),
inference(resolution,[status(thm)],[d2,c18]) ).
cnf(d4,plain,
product(a,domain(compose(b,a)),a),
inference(resolution,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
defined(domain(compose(b,a)),domain(a)),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ 'identity$umap'(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a)) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
product(domain(compose(b,a)),domain(a),domain(a)),
inference(resolution,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
( ~ product(domain(compose(b,a)),domain(a),X0)
| X0 = domain(a) ),
inference(resolution,[status(thm)],[d7,c19]) ).
cnf(d9,plain,
( ~ 'identity$umap'(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ),
inference(resolution,[status(thm)],[d5,c18]) ).
cnf(d10,plain,
product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
inference(resolution,[status(thm)],[c11,d9]) ).
cnf(d11,plain,
domain(compose(b,a)) = domain(a),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
domain(a) != domain(a),
inference(demodulation,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
product(X0,domain(X0),compose(X0,domain(X0))),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d14,plain,
( ~ product(X1,domain(X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c19,c15]) ).
cnf(d15,plain,
compose(X0,domain(X0)) = X0,
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
( ~ 'identity$umap'(X0)
| product(X0,domain(X0),domain(X0)) ),
inference(resolution,[status(thm)],[c17,c13]) ).
cnf(d17,plain,
product(domain(X0),domain(domain(X0)),domain(domain(X0))),
inference(resolution,[status(thm)],[d16,c11]) ).
cnf(d18,plain,
domain(domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
defined(domain(X0),domain(X0)),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d20,plain,
( ~ 'identity$umap'(domain(X0))
| product(domain(X0),domain(X0),domain(X0)) ),
inference(resolution,[status(thm)],[d19,c17]) ).
cnf(d21,plain,
product(domain(X0),domain(X0),domain(X0)),
inference(resolution,[status(thm)],[c11,d20]) ).
cnf(d22,plain,
product(domain(X0),domain(X0),compose(domain(X0),domain(X0))),
inference(resolution,[status(thm)],[d19,c2]) ).
cnf(d23,plain,
( ~ product(domain(X1),domain(X1),X0)
| X0 = compose(domain(X1),domain(X1)) ),
inference(resolution,[status(thm)],[d22,c19]) ).
cnf(d24,plain,
domain(X0) = compose(domain(X0),domain(X0)),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( ~ product(codomain(X1),X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c19,c16]) ).
cnf(d26,plain,
( ~ 'identity$umap'(X0)
| product(codomain(X0),X0,codomain(X0)) ),
inference(resolution,[status(thm)],[c18,c14]) ).
cnf(d27,plain,
product(codomain(domain(X0)),domain(X0),codomain(domain(X0))),
inference(resolution,[status(thm)],[d26,c11]) ).
cnf(d28,plain,
codomain(domain(X0)) = domain(X0),
inference(resolution,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
codomain(domain(X0)) = domain(domain(X0)),
inference(superposition,[status(thm)],[d18,d28]) ).
cnf(d30,plain,
domain(X0) = domain(domain(X0)),
inference(demodulation,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
domain(domain(X0)) = compose(domain(X0),domain(domain(X0))),
inference(superposition,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
domain(X0) = compose(domain(X0),domain(domain(X0))),
inference(demodulation,[status(thm)],[d31,d18]) ).
cnf(d33,plain,
domain(X0) = domain(X0),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 22:51:07 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.63/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 38.63/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------