%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT014-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:07:31 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 6 unt; 0 nHn; 13 RR)
% Number of literals : 21 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(codomain(a)),
file('CAT014-4.p',unknown),
[] ).
cnf(2,axiom,
~ equal(codomain(codomain(a)),codomain(a)),
file('CAT014-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT014-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT014-4.p',unknown),
[] ).
cnf(12,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT014-4.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(codomain(u),u),u),
file('CAT014-4.p',unknown),
[] ).
cnf(23,plain,
( ~ there_exists(u)
| equal(domain__dfg(codomain(u)),codomain(u)) ),
inference(spl,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpL:13.0,9.0')] ).
cnf(24,plain,
( ~ there_exists(u)
| equal(codomain(domain__dfg(u)),domain__dfg(u)) ),
inference(spl,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpL:12.0,9.0')] ).
cnf(35,plain,
( ~ there_exists(u)
| ~ there_exists(codomain(u))
| equal(codomain(codomain(u)),codomain(u)) ),
inference(spr,[status(thm),theory(equality)],[23,24]),
[iquote('0:SpR:23.1,24.1')] ).
cnf(38,plain,
( ~ there_exists(codomain(u))
| equal(codomain(codomain(u)),codomain(u)) ),
inference(mrr,[status(thm)],[35,7]),
[iquote('0:MRR:35.0,7.1')] ).
cnf(58,plain,
( ~ there_exists(codomain(a))
| ~ equal(codomain(a),codomain(a)) ),
inference(spl,[status(thm),theory(equality)],[38,2]),
[iquote('0:SpL:38.1,2.0')] ).
cnf(61,plain,
~ there_exists(codomain(a)),
inference(obv,[status(thm),theory(equality)],[58]),
[iquote('0:Obv:58.1')] ).
cnf(62,plain,
$false,
inference(mrr,[status(thm)],[61,1]),
[iquote('0:MRR:61.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT014-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 17:43:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 44 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.20/0.42 SPASS allocated 75631 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.00 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 3, length 13 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : assume_codomain_exists prove_codomain_is_idempotent codomain_has_elements domain_codomain_composition1 compose_domain compose_codomain
% 0.20/0.42
%------------------------------------------------------------------------------