%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT006-3 : 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 : n012.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 4.57s 3.04s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 16 unt; 0 nHn; 30 RR)
% Number of literals : 52 ( 25 equ; 21 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(da_exists,hypothesis,
'there$uexists'(compose(d,a)) ).
cnf(xd_equals_x,hypothesis,
( compose(X0,d) = X0
| ~ 'there$uexists'(compose(X0,d)) ) ).
cnf(dx_equals_x,hypothesis,
( compose(d,X0) = X0
| ~ 'there$uexists'(compose(d,X0)) ) ).
cnf(prove_codomain_of_a_is_d,negated_conjecture,
codomain(a) != d ).
cnf(domain_has_elements,axiom,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ) ).
cnf(composition_implies_domain,axiom,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(domain_codomain_composition1,axiom,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ) ).
cnf(compose_domain,axiom,
compose(X0,domain(X0)) = X0 ).
cnf(compose_codomain,axiom,
compose(codomain(X0),X0) = X0 ).
cnf(c0,plain,
'there$uexists'(compose(d,a)),
inference(clausification,[status(esa)],[da_exists]) ).
cnf(c1,plain,
( compose(X0,d) = X0
| ~ 'there$uexists'(compose(X0,d)) ),
inference(clausification,[status(esa)],[xd_equals_x]) ).
cnf(c2,plain,
( compose(d,X0) = X0
| ~ 'there$uexists'(compose(d,X0)) ),
inference(clausification,[status(esa)],[dx_equals_x]) ).
cnf(c3,plain,
codomain(a) != d,
inference(clausification,[status(esa)],[prove_codomain_of_a_is_d]) ).
cnf(c7,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ),
inference(clausification,[status(esa)],[domain_has_elements]) ).
cnf(c9,plain,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[composition_implies_domain]) ).
cnf(c10,plain,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c13,plain,
compose(X0,domain(X0)) = X0,
inference(clausification,[status(esa)],[compose_domain]) ).
cnf(c14,plain,
compose(codomain(X0),X0) = X0,
inference(clausification,[status(esa)],[compose_codomain]) ).
cnf(d0,plain,
( ~ 'there$uexists'(compose(d,domain(d)))
| domain(d) = d ),
inference(superposition,[status(thm)],[c2,c13]) ).
cnf(d1,plain,
( ~ 'there$uexists'(d)
| domain(d) = d ),
inference(demodulation,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
'there$uexists'(domain(d)),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d3,plain,
'there$uexists'(d),
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
domain(d) = d,
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'there$uexists'(compose(d,X0))
| d = codomain(X0) ),
inference(superposition,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
d = codomain(a),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
d != d,
inference(demodulation,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
( ~ 'there$uexists'(compose(codomain(d),d))
| d = codomain(d) ),
inference(superposition,[status(thm)],[c14,c1]) ).
cnf(d9,plain,
( ~ 'there$uexists'(d)
| d = codomain(d) ),
inference(demodulation,[status(thm)],[d8,c14]) ).
cnf(d10,plain,
d = codomain(d),
inference(resolution,[status(thm)],[d3,d9]) ).
cnf(d11,plain,
( ~ 'there$uexists'(compose(codomain(d),d))
| codomain(d) = d ),
inference(superposition,[status(thm)],[c1,c14]) ).
cnf(d12,plain,
( ~ 'there$uexists'(compose(codomain(d),d))
| d = d ),
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ 'there$uexists'(d)
| d = d ),
inference(demodulation,[status(thm)],[d12,c14]) ).
cnf(d14,plain,
d = d,
inference(resolution,[status(thm)],[d3,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 22:48:34 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/3.04 % SZS status Unsatisfiable for theBenchmark.p
% 4.57/3.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------