%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT018-4 : 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 : n002.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 06:55:38 AM UTC 2026
% Result : Unsatisfiable 26.97s 16.39s
% Output : CNFRefutation 26.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 49 ( 26 unt; 0 nHn; 43 RR)
% Number of literals : 78 ( 32 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(assume_ab_exists,hypothesis,
'there$uexists'(compose(a,b)) ).
cnf(assume_bc_exists,hypothesis,
'there$uexists'(compose(b,c)) ).
cnf(prove_a_bc_exists,negated_conjecture,
~ 'there$uexists'(compose(a,compose(b,c))) ).
cnf(domain_has_elements,axiom,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ) ).
cnf(codomain_has_elements,axiom,
( 'there$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(domain_codomain_composition2,axiom,
( 'there$uexists'(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ 'there$uexists'(domain(X0)) ) ).
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(compose_codomain,axiom,
compose(codomain(X0),X0) = X0 ).
cnf(c0,plain,
'there$uexists'(compose(a,b)),
inference(clausification,[status(esa)],[assume_ab_exists]) ).
cnf(c1,plain,
'there$uexists'(compose(b,c)),
inference(clausification,[status(esa)],[assume_bc_exists]) ).
cnf(c2,plain,
~ 'there$uexists'(compose(a,compose(b,c))),
inference(clausification,[status(esa)],[prove_a_bc_exists]) ).
cnf(c6,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(domain(X0)) ),
inference(clausification,[status(esa)],[domain_has_elements]) ).
cnf(c7,plain,
( 'there$uexists'(X0)
| ~ 'there$uexists'(codomain(X0)) ),
inference(clausification,[status(esa)],[codomain_has_elements]) ).
cnf(c8,plain,
( 'there$uexists'(domain(X0))
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[composition_implies_domain]) ).
cnf(c9,plain,
( domain(X0) = codomain(X1)
| ~ 'there$uexists'(compose(X0,X1)) ),
inference(clausification,[status(esa)],[domain_codomain_composition1]) ).
cnf(c10,plain,
( 'there$uexists'(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ 'there$uexists'(domain(X0)) ),
inference(clausification,[status(esa)],[domain_codomain_composition2]) ).
cnf(c11,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_compose]) ).
cnf(c12,plain,
compose(X0,domain(X0)) = X0,
inference(clausification,[status(esa)],[compose_domain]) ).
cnf(c13,plain,
compose(codomain(X0),X0) = X0,
inference(clausification,[status(esa)],[compose_codomain]) ).
cnf(d0,plain,
'there$uexists'(domain(b)),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d1,plain,
'there$uexists'(b),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( domain(X0) = codomain(domain(X0))
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c12,c9]) ).
cnf(d3,plain,
domain(b) = codomain(domain(b)),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( domain(compose(X0,X1)) = codomain(X2)
| ~ 'there$uexists'(compose(X0,compose(X1,X2))) ),
inference(superposition,[status(thm)],[c11,c9]) ).
cnf(d5,plain,
( domain(compose(X1,X0)) = codomain(domain(X0))
| ~ 'there$uexists'(compose(X1,X0)) ),
inference(superposition,[status(thm)],[c12,d4]) ).
cnf(d6,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
domain(compose(a,b)) = domain(b),
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
domain(b) = codomain(c),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d9,plain,
( ~ 'there$uexists'(domain(X0))
| 'there$uexists'(compose(X0,c))
| domain(X0) != domain(b) ),
inference(superposition,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
( ~ 'there$uexists'(domain(compose(a,b)))
| 'there$uexists'(compose(compose(a,b),c))
| domain(b) != domain(b) ),
inference(superposition,[status(thm)],[d7,d9]) ).
cnf(d11,plain,
( ~ 'there$uexists'(domain(compose(a,b)))
| 'there$uexists'(compose(a,compose(b,c)))
| domain(b) != domain(b) ),
inference(demodulation,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
( ~ 'there$uexists'(domain(b))
| 'there$uexists'(compose(a,compose(b,c)))
| domain(b) != domain(b) ),
inference(demodulation,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
( ~ 'there$uexists'(domain(b))
| domain(b) != domain(b) ),
inference(resolution,[status(thm)],[c2,d12]) ).
cnf(d14,plain,
domain(b) != domain(b),
inference(resolution,[status(thm)],[d0,d13]) ).
cnf(d15,plain,
( 'there$uexists'(c)
| ~ 'there$uexists'(domain(b)) ),
inference(superposition,[status(thm)],[d8,c7]) ).
cnf(d16,plain,
'there$uexists'(c),
inference(resolution,[status(thm)],[d0,d15]) ).
cnf(d17,plain,
( domain(codomain(X0)) = codomain(X0)
| ~ 'there$uexists'(X0) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d18,plain,
domain(codomain(c)) = codomain(c),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
domain(domain(b)) = codomain(c),
inference(demodulation,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
domain(domain(b)) = domain(b),
inference(demodulation,[status(thm)],[d19,d8]) ).
cnf(d21,plain,
compose(domain(b),c) = c,
inference(superposition,[status(thm)],[d8,c13]) ).
cnf(d22,plain,
( domain(domain(b)) = codomain(c)
| ~ 'there$uexists'(c) ),
inference(superposition,[status(thm)],[d21,c9]) ).
cnf(d23,plain,
( ~ 'there$uexists'(c)
| domain(b) = codomain(c) ),
inference(demodulation,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( ~ 'there$uexists'(c)
| domain(b) = domain(b) ),
inference(demodulation,[status(thm)],[d23,d8]) ).
cnf(d25,plain,
domain(b) = domain(b),
inference(resolution,[status(thm)],[d16,d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.45 % Computer : n002.cluster.edu
% 0.19/10.45 % Model : x86_64 x86_64
% 0.19/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.45 % Memory : 8046.5625MB
% 0.19/10.45 % OS : Linux 6.8.0-71-generic
% 0.19/10.45 % CPULimit : 300
% 0.19/10.45 % WCLimit : 300
% 0.19/10.45 % DateTime : Sat Sep 26 22:53:01 UTC 2026
% 0.19/10.46 % CPUTime :
% 0.19/10.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.97/16.39 % SZS status Unsatisfiable for theBenchmark.p
% 26.97/16.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------