%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT012-4 : 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 : n010.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 10.02s 12.65s
% Output : CNFRefutation 10.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 13 RR)
% Number of literals : 20 ( 9 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(assume_domain_exists,hypothesis,
'there$uexists'(domain(a)) ).
cnf(prove_codomain_of_domain_is_domain,negated_conjecture,
codomain(domain(a)) != domain(a) ).
cnf(domain_has_elements,axiom,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ) ).
cnf(domain_codomain_composition1,axiom,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(compose_domain,axiom,
compose(X0,domain(X0)) = X0 ).
cnf(c0,plain,
'there$uexists'(domain(a)),
inference(clausification,[status(esa)],[assume_domain_exists]) ).
cnf(c1,plain,
codomain(domain(a)) != domain(a),
inference(clausification,[status(esa)],[prove_codomain_of_domain_is_domain]) ).
cnf(c5,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ),
inference(clausification,[status(esa)],[domain_has_elements]) ).
cnf(c8,plain,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c11,plain,
compose(X0,domain(X0)) = X0,
inference(clausification,[status(esa)],[compose_domain]) ).
cnf(d0,plain,
'there$uexists'(a),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d1,plain,
( domain(X0) = codomain(domain(X0))
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c11,c8]) ).
cnf(d2,plain,
domain(a) = codomain(domain(a)),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
domain(a) != domain(a),
inference(demodulation,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
$false,
inference(equality_resolution,[status(thm)],[d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n010.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Sat Sep 26 22:50:01 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.02/12.65 % SZS status Unsatisfiable for theBenchmark.p
% 10.02/12.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------