TSTP Solution File: CAT006-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 00:07:29 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 25 ( 0 equ; 9 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(d,a)),
file('CAT006-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ there_exists(compose(d,u))
| equal(compose(d,u),u) ),
file('CAT006-3.p',unknown),
[] ).
cnf(4,axiom,
~ equal(codomain(a),d),
file('CAT006-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ there_exists(codomain(u))
| there_exists(u) ),
file('CAT006-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ there_exists(compose(u,v))
| equal(domain__dfg(u),codomain(v)) ),
file('CAT006-3.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(u,domain__dfg(u)),u),
file('CAT006-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ there_exists(compose(u,v))
| there_exists(codomain(u)) ),
file('CAT006-3.p',unknown),
[] ).
cnf(34,plain,
there_exists(codomain(d)),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(35,plain,
there_exists(d),
inference(res,[status(thm),theory(equality)],[34,9]),
[iquote('0:Res:34.0,9.0')] ).
cnf(42,plain,
( ~ there_exists(d)
| equal(compose(d,domain__dfg(d)),domain__dfg(d)) ),
inference(spl,[status(thm),theory(equality)],[14,3]),
[iquote('0:SpL:14.0,3.0')] ).
cnf(43,plain,
equal(compose(d,a),a),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(44,plain,
there_exists(a),
inference(rew,[status(thm),theory(equality)],[43,1]),
[iquote('0:Rew:43.0,1.0')] ).
cnf(45,plain,
( ~ there_exists(d)
| equal(domain__dfg(d),d) ),
inference(rew,[status(thm),theory(equality)],[14,42]),
[iquote('0:Rew:14.0,42.1')] ).
cnf(46,plain,
equal(domain__dfg(d),d),
inference(mrr,[status(thm)],[45,35]),
[iquote('0:MRR:45.0,35.0')] ).
cnf(76,plain,
( ~ there_exists(a)
| equal(domain__dfg(d),codomain(a)) ),
inference(spl,[status(thm),theory(equality)],[43,11]),
[iquote('0:SpL:43.0,11.0')] ).
cnf(78,plain,
( ~ there_exists(a)
| equal(codomain(a),d) ),
inference(rew,[status(thm),theory(equality)],[46,76]),
[iquote('0:Rew:46.0,76.1')] ).
cnf(79,plain,
$false,
inference(mrr,[status(thm)],[78,44,4]),
[iquote('0:MRR:78.0,78.1,44.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 17:23:09 EDT 2022
% 0.12/0.33 % 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 46 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.19/0.41 SPASS allocated 75632 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 2, length 17 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : da_exists dx_equals_x prove_codomain_of_a_is_d codomain_has_elements domain_codomain_composition1 compose_domain composition_implies_codomain
% 0.19/0.41
%------------------------------------------------------------------------------