TSTP Solution File: NUM412+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 : Mon Jul 18 14:25:57 EDT 2022
% Result : Theorem 0.16s 0.44s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 11 unt; 0 nHn; 22 RR)
% Number of literals : 43 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ordinal(skc19),
file('NUM412+1.p',unknown),
[] ).
cnf(52,axiom,
transfinite_sequence_of(skc18,skc17),
file('NUM412+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ ordinal(u)
| epsilon_transitive(u) ),
file('NUM412+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ ordinal(u)
| epsilon_connected(u) ),
file('NUM412+1.p',unknown),
[] ).
cnf(66,axiom,
~ transfinite_sequence_of(tseq_dom_restriction(skc18,skc19),skc17),
file('NUM412+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ transfinite_sequence_of(u,v)
| relation(u) ),
file('NUM412+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ transfinite_sequence_of(u,v)
| function(u) ),
file('NUM412+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ transfinite_sequence_of(u,v)
| transfinite_sequence(u) ),
file('NUM412+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ transfinite_sequence_of(u,v)
| ~ subset(v,w)
| transfinite_sequence_of(u,w) ),
file('NUM412+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ transfinite_sequence(u)
| ~ function(u)
| ~ relation(u)
| ~ transfinite_sequence_of(u,v)
| subset(relation_rng(u),v) ),
file('NUM412+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ ordinal(u)
| ~ transfinite_sequence(v)
| ~ function(v)
| ~ relation(v)
| transfinite_sequence_of(tseq_dom_restriction(v,u),relation_rng(v)) ),
file('NUM412+1.p',unknown),
[] ).
cnf(97,plain,
( ~ transfinite_sequence_of(u,v)
| subset(relation_rng(u),v) ),
inference(mrr,[status(thm)],[92,69,68,67]),
[iquote('0:MRR:92.0,92.1,92.2,69.1,68.1,67.1')] ).
cnf(98,plain,
epsilon_transitive(skc19),
inference(res,[status(thm),theory(equality)],[1,60]),
[iquote('0:Res:1.0,60.0')] ).
cnf(99,plain,
epsilon_connected(skc19),
inference(res,[status(thm),theory(equality)],[1,61]),
[iquote('0:Res:1.0,61.0')] ).
cnf(103,plain,
subset(relation_rng(skc18),skc17),
inference(res,[status(thm),theory(equality)],[52,97]),
[iquote('0:Res:52.0,97.0')] ).
cnf(104,plain,
relation(skc18),
inference(res,[status(thm),theory(equality)],[52,67]),
[iquote('0:Res:52.0,67.0')] ).
cnf(105,plain,
function(skc18),
inference(res,[status(thm),theory(equality)],[52,68]),
[iquote('0:Res:52.0,68.0')] ).
cnf(106,plain,
transfinite_sequence(skc18),
inference(res,[status(thm),theory(equality)],[52,69]),
[iquote('0:Res:52.0,69.0')] ).
cnf(108,plain,
( ~ subset(u,skc17)
| ~ transfinite_sequence_of(tseq_dom_restriction(skc18,skc19),u) ),
inference(res,[status(thm),theory(equality)],[88,66]),
[iquote('0:Res:88.2,66.0')] ).
cnf(205,plain,
( ~ ordinal(skc19)
| ~ transfinite_sequence(skc18)
| ~ function(skc18)
| ~ relation(skc18)
| ~ subset(relation_rng(skc18),skc17) ),
inference(res,[status(thm),theory(equality)],[94,108]),
[iquote('0:Res:94.4,108.1')] ).
cnf(211,plain,
~ subset(relation_rng(skc18),skc17),
inference(ssi,[status(thm)],[205,106,105,104,1,99,98]),
[iquote('0:SSi:205.3,205.2,205.1,205.0,106.0,105.0,104.0,106.0,105.0,104.0,106.0,105.0,104.0,1.0,99.0,98.0')] ).
cnf(212,plain,
$false,
inference(mrr,[status(thm)],[211,103]),
[iquote('0:MRR:211.0,103.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n016.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jul 6 19:31:35 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.44
% 0.16/0.44 SPASS V 3.9
% 0.16/0.44 SPASS beiseite: Proof found.
% 0.16/0.44 % SZS status Theorem
% 0.16/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 SPASS derived 105 clauses, backtracked 0 clauses, performed 0 splits and kept 141 clauses.
% 0.16/0.44 SPASS allocated 97760 KBytes.
% 0.16/0.44 SPASS spent 0:00:00.11 on the problem.
% 0.16/0.44 0:00:00.04 for the input.
% 0.16/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.16/0.44 0:00:00.00 for inferences.
% 0.16/0.44 0:00:00.00 for the backtracking.
% 0.16/0.44 0:00:00.01 for the reduction.
% 0.16/0.44
% 0.16/0.44
% 0.16/0.44 Here is a proof with depth 2, length 22 :
% 0.16/0.44 % SZS output start Refutation
% See solution above
% 0.16/0.44 Formulae used in the proof : t48_ordinal1 cc1_ordinal1 dt_m1_ordinal1 t47_ordinal1 d8_ordinal1 dt_k2_ordinal1
% 0.16/0.44
%------------------------------------------------------------------------------