%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT009-4 : 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 : n009.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 11.31s 1.90s
% Output : CNFRefutation 11.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 21 RR)
% Number of literals : 35 ( 15 equ; 12 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ab_exists,hypothesis,
'there$uexists'(compose(a,b)) ).
cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
domain(compose(a,b)) != domain(b) ).
cnf(codomain_has_elements,axiom,
( 'there$uexists'(X0)
| ~ 'there$uexists'(codomain(X0)) ) ).
cnf(composition_implies_domain,axiom,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(domain_codomain_composition1,axiom,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(associativity_of_compose,axiom,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ).
cnf(compose_domain,axiom,
compose(X0,domain(X0)) = X0 ).
cnf(c0,plain,
'there$uexists'(compose(a,b)),
inference(clausification,[status(esa)],[ab_exists]) ).
cnf(c1,plain,
domain(compose(a,b)) != domain(b),
inference(clausification,[status(esa)],[prove_domain_of_ab_equals_domain_of_b]) ).
cnf(c6,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(codomain(X0)) ),
inference(clausification,[status(esa)],[codomain_has_elements]) ).
cnf(c7,plain,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[composition_implies_domain]) ).
cnf(c8,plain,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c10,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_compose]) ).
cnf(c11,plain,
compose(X0,domain(X0)) = X0,
inference(clausification,[status(esa)],[compose_domain]) ).
cnf(d0,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d1,plain,
( 'there$uexists'(b)
| ~ 'there$uexists'(domain(a)) ),
inference(superposition,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
'there$uexists'(domain(a)),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d3,plain,
'there$uexists'(b),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( domain(X0) = codomain(domain(X0))
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c11,c8]) ).
cnf(d5,plain,
domain(b) = codomain(domain(b)),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( domain(compose(X0,X1)) = codomain(X2)
| ~ 'there$uexists'(compose(X0,compose(X1,X2))) ),
inference(superposition,[status(thm)],[c10,c8]) ).
cnf(d7,plain,
( domain(compose(X1,X0)) = codomain(domain(X0))
| ~ 'there$uexists'(compose(X1,X0)) ),
inference(superposition,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
domain(compose(a,b)) = domain(b),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c1,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.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 22:49:14 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.31/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 11.31/1.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------