TSTP Solution File: CAT005-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT005-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 20 RR)
% Number of literals : 30 ( 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('CAT005-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ there_exists(compose(u,d))
| equal(compose(u,d),u) ),
file('CAT005-3.p',unknown),
[] ).
cnf(4,axiom,
~ equal(domain__dfg(a),d),
file('CAT005-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT005-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ there_exists(compose(u,v))
| there_exists(domain__dfg(u)) ),
file('CAT005-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT005-3.p',unknown),
[] ).
cnf(15,axiom,
equal(compose(codomain(u),u),u),
file('CAT005-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ there_exists(compose(u,v))
| there_exists(codomain(u)) ),
file('CAT005-3.p',unknown),
[] ).
cnf(34,plain,
there_exists(codomain(a)),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(35,plain,
there_exists(a),
inference(res,[status(thm),theory(equality)],[34,9]),
[iquote('0:Res:34.0,9.0')] ).
cnf(38,plain,
there_exists(domain__dfg(a)),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(58,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(59,plain,
equal(compose(a,d),a),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(61,plain,
( ~ there_exists(d)
| equal(codomain(d),d) ),
inference(rew,[status(thm),theory(equality)],[15,58]),
[iquote('0:Rew:15.0,58.1')] ).
cnf(76,plain,
( ~ there_exists(a)
| equal(codomain(d),domain__dfg(a)) ),
inference(spl,[status(thm),theory(equality)],[59,11]),
[iquote('0:SpL:59.0,11.0')] ).
cnf(79,plain,
equal(codomain(d),domain__dfg(a)),
inference(mrr,[status(thm)],[76,35]),
[iquote('0:MRR:76.0,35.0')] ).
cnf(80,plain,
( ~ there_exists(d)
| equal(domain__dfg(a),d) ),
inference(rew,[status(thm),theory(equality)],[79,61]),
[iquote('0:Rew:79.0,61.1')] ).
cnf(81,plain,
~ there_exists(d),
inference(mrr,[status(thm)],[80,4]),
[iquote('0:MRR:80.1,4.0')] ).
cnf(93,plain,
( ~ there_exists(domain__dfg(a))
| there_exists(d) ),
inference(spl,[status(thm),theory(equality)],[79,9]),
[iquote('0:SpL:79.0,9.0')] ).
cnf(94,plain,
$false,
inference(mrr,[status(thm)],[93,38,81]),
[iquote('0:MRR:93.0,93.1,38.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT005-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 20:42:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.19/0.40 SPASS allocated 75643 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.04 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 3, length 20 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : ad_exists xd_equals_x prove_domain_of_a_is_d codomain_has_elements composition_implies_domain domain_codomain_composition1 compose_codomain composition_implies_codomain
% 0.19/0.40
%------------------------------------------------------------------------------