%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT018-1 : 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 : n026.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 06:55:37 AM UTC 2026
% Result : Unsatisfiable 13.91s 12.71s
% Output : CNFRefutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 13 unt; 0 nHn; 23 RR)
% Number of literals : 57 ( 0 equ; 35 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(assume_ab_exists,hypothesis,
defined(a,b) ).
cnf(assume_bc_exists,hypothesis,
defined(b,c) ).
cnf(prove_a_bc_exists,negated_conjecture,
~ defined(a,compose(b,c)) ).
cnf(closure_of_composition,axiom,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ) ).
cnf(category_theory_axiom1,axiom,
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom3,axiom,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom6,axiom,
( defined(X0,X2)
| ~ 'identity$umap'(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ) ).
cnf(codomain_is_an_identity_map,axiom,
'identity$umap'(codomain(X0)) ).
cnf(product_on_codomain,axiom,
product(codomain(X0),X0,X0) ).
cnf(c0,plain,
defined(a,b),
inference(clausification,[status(esa)],[assume_ab_exists]) ).
cnf(c1,plain,
defined(b,c),
inference(clausification,[status(esa)],[assume_bc_exists]) ).
cnf(c2,plain,
~ defined(a,compose(b,c)),
inference(clausification,[status(esa)],[prove_a_bc_exists]) ).
cnf(c3,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[closure_of_composition]) ).
cnf(c6,plain,
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom1]) ).
cnf(c8,plain,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom3]) ).
cnf(c11,plain,
( defined(X0,X2)
| ~ 'identity$umap'(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[category_theory_axiom6]) ).
cnf(c13,plain,
'identity$umap'(codomain(X0)),
inference(clausification,[status(esa)],[codomain_is_an_identity_map]) ).
cnf(c17,plain,
product(codomain(X0),X0,X0),
inference(clausification,[status(esa)],[product_on_codomain]) ).
cnf(d0,plain,
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(d1,plain,
( ~ defined(X3,X1)
| ~ product(X2,X3,X0)
| defined(X2,compose(X3,X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d2,plain,
( ~ defined(X0,X1)
| defined(codomain(X0),compose(X0,X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[d1,c17]) ).
cnf(d3,plain,
( ~ 'identity$umap'(codomain(X0))
| ~ defined(X2,codomain(X0))
| defined(X2,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
( ~ defined(X1,X2)
| ~ defined(X0,codomain(X1))
| defined(X0,compose(X1,X2)) ),
inference(resolution,[status(thm)],[c13,d3]) ).
cnf(d5,plain,
( ~ defined(a,codomain(b))
| ~ defined(b,c) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
~ defined(a,codomain(b)),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
~ defined(a,b),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c0,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.36 % Computer : n026.cluster.edu
% 0.09/10.36 % Model : x86_64 x86_64
% 0.09/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.36 % Memory : 8046.5625MB
% 0.09/10.36 % OS : Linux 6.8.0-71-generic
% 0.09/10.36 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 22:53:06 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.91/12.71 % SZS status Unsatisfiable for theBenchmark.p
% 13.91/12.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------