%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT017-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 00:07:32 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 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(a),
file('CAT017-4.p',unknown),
[] ).
cnf(2,axiom,
~ there_exists(codomain(a)),
file('CAT017-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT017-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT017-4.p',unknown),
[] ).
cnf(13,axiom,
equal(compose(codomain(u),u),u),
file('CAT017-4.p',unknown),
[] ).
cnf(19,plain,
( ~ there_exists(u)
| there_exists(domain__dfg(codomain(u))) ),
inference(spl,[status(thm),theory(equality)],[13,8]),
[iquote('0:SpL:13.0,8.0')] ).
cnf(22,plain,
( ~ there_exists(u)
| there_exists(codomain(u)) ),
inference(res,[status(thm),theory(equality)],[19,6]),
[iquote('0:Res:19.1,6.0')] ).
cnf(23,plain,
~ there_exists(a),
inference(res,[status(thm),theory(equality)],[22,2]),
[iquote('0:Res:22.1,2.0')] ).
cnf(25,plain,
$false,
inference(mrr,[status(thm)],[23,1]),
[iquote('0:MRR:23.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT017-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 17:11:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.19/0.41 SPASS allocated 75593 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 3, length 9 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : assume_a_exists prove_codomain_of_a_exists domain_has_elements composition_implies_domain compose_codomain
% 0.19/0.41
%------------------------------------------------------------------------------