TSTP Solution File: CAT005-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT005-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 00:07:28 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 9 unt; 0 nHn; 19 RR)
% Number of literals : 29 ( 0 equ; 12 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
there_exists(compose(a,d)),
file('CAT005-4.p',unknown),
[] ).
cnf(2,axiom,
( ~ there_exists(compose(u,d))
| equal(compose(u,d),u) ),
file('CAT005-4.p',unknown),
[] ).
cnf(4,axiom,
~ equal(domain__dfg(a),d),
file('CAT005-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ there_exists(domain__dfg(u))
| there_exists(u) ),
file('CAT005-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT005-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT005-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT005-4.p',unknown),
[] ).
cnf(15,axiom,
equal(compose(codomain(u),u),u),
file('CAT005-4.p',unknown),
[] ).
cnf(22,plain,
there_exists(domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(23,plain,
there_exists(a),
inference(res,[status(thm),theory(equality)],[22,8]),
[iquote('0:Res:22.0,8.0')] ).
cnf(39,plain,
( ~ there_exists(d)
| equal(compose(codomain(d),d),codomain(d)) ),
inference(spl,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpL:15.0,2.0')] ).
cnf(40,plain,
equal(compose(a,d),a),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(42,plain,
( ~ there_exists(d)
| equal(codomain(d),d) ),
inference(rew,[status(thm),theory(equality)],[15,39]),
[iquote('0:Rew:15.0,39.1')] ).
cnf(54,plain,
( ~ there_exists(a)
| equal(codomain(d),domain__dfg(a)) ),
inference(spl,[status(thm),theory(equality)],[40,11]),
[iquote('0:SpL:40.0,11.0')] ).
cnf(57,plain,
equal(codomain(d),domain__dfg(a)),
inference(mrr,[status(thm)],[54,23]),
[iquote('0:MRR:54.0,23.0')] ).
cnf(58,plain,
( ~ there_exists(d)
| equal(domain__dfg(a),d) ),
inference(rew,[status(thm),theory(equality)],[57,42]),
[iquote('0:Rew:57.0,42.1')] ).
cnf(59,plain,
~ there_exists(d),
inference(mrr,[status(thm)],[58,4]),
[iquote('0:MRR:58.1,4.0')] ).
cnf(69,plain,
( ~ there_exists(domain__dfg(a))
| there_exists(d) ),
inference(spl,[status(thm),theory(equality)],[57,9]),
[iquote('0:SpL:57.0,9.0')] ).
cnf(70,plain,
$false,
inference(mrr,[status(thm)],[69,22,59]),
[iquote('0:MRR:69.0,69.1,22.0,59.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT005-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 17:47:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 45 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.12/0.41 SPASS allocated 75629 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 3, length 19 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : ad_exists xd_equals_x prove_domain_of_a_is_d domain_has_elements codomain_has_elements composition_implies_domain domain_codomain_composition1 compose_codomain
% 0.12/0.41
%------------------------------------------------------------------------------