TSTP Solution File: NUM409+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:25:56 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 37 ( 21 unt; 0 nHn; 37 RR)
% Number of literals : 67 ( 0 equ; 33 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
relation_empty_yielding(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(7,axiom,
function(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(8,axiom,
one_to_one(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(10,axiom,
epsilon_transitive(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(11,axiom,
epsilon_connected(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(12,axiom,
ordinal(empty_set),
file('NUM409+1.p',unknown),
[] ).
cnf(20,axiom,
empty(skc22),
file('NUM409+1.p',unknown),
[] ).
cnf(21,axiom,
relation(skc22),
file('NUM409+1.p',unknown),
[] ).
cnf(55,axiom,
subset(empty_set,u),
file('NUM409+1.p',unknown),
[] ).
cnf(56,axiom,
~ transfinite_sequence_of(empty_set,skc15),
file('NUM409+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ empty(u)
| function(u) ),
file('NUM409+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ empty(u)
| relation(u) ),
file('NUM409+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ empty(u)
| empty(relation_dom(u)) ),
file('NUM409+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ empty(u)
| empty(relation_rng(u)) ),
file('NUM409+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('NUM409+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ function(u)
| ~ relation(u)
| ~ ordinal(relation_dom(u))
| transfinite_sequence(u) ),
file('NUM409+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ relation(u)
| ~ function(u)
| ~ transfinite_sequence(u)
| ~ subset(relation_rng(u),v)
| transfinite_sequence_of(u,v) ),
file('NUM409+1.p',unknown),
[] ).
cnf(107,plain,
equal(empty_set,skc22),
inference(ems,[status(thm)],[74,20]),
[iquote('0:EmS:74.0,20.0')] ).
cnf(111,plain,
relation_empty_yielding(skc22),
inference(rew,[status(thm),theory(equality)],[107,6]),
[iquote('0:Rew:107.0,6.0')] ).
cnf(112,plain,
one_to_one(skc22),
inference(rew,[status(thm),theory(equality)],[107,8]),
[iquote('0:Rew:107.0,8.0')] ).
cnf(113,plain,
epsilon_connected(skc22),
inference(rew,[status(thm),theory(equality)],[107,11]),
[iquote('0:Rew:107.0,11.0')] ).
cnf(114,plain,
epsilon_transitive(skc22),
inference(rew,[status(thm),theory(equality)],[107,10]),
[iquote('0:Rew:107.0,10.0')] ).
cnf(115,plain,
ordinal(skc22),
inference(rew,[status(thm),theory(equality)],[107,12]),
[iquote('0:Rew:107.0,12.0')] ).
cnf(116,plain,
function(skc22),
inference(rew,[status(thm),theory(equality)],[107,7]),
[iquote('0:Rew:107.0,7.0')] ).
cnf(119,plain,
subset(skc22,u),
inference(rew,[status(thm),theory(equality)],[107,55]),
[iquote('0:Rew:107.0,55.0')] ).
cnf(120,plain,
~ transfinite_sequence_of(skc22,skc15),
inference(rew,[status(thm),theory(equality)],[107,56]),
[iquote('0:Rew:107.0,56.0')] ).
cnf(121,plain,
( ~ empty(u)
| equal(u,skc22) ),
inference(rew,[status(thm),theory(equality)],[107,74]),
[iquote('0:Rew:107.0,74.1')] ).
cnf(145,plain,
( ~ empty(u)
| equal(relation_dom(u),skc22) ),
inference(ems,[status(thm)],[121,70]),
[iquote('0:EmS:121.0,70.1')] ).
cnf(146,plain,
( ~ empty(u)
| equal(relation_rng(u),skc22) ),
inference(ems,[status(thm)],[121,72]),
[iquote('0:EmS:121.0,72.1')] ).
cnf(206,plain,
( ~ empty(u)
| ~ function(u)
| ~ relation(u)
| ~ ordinal(skc22)
| transfinite_sequence(u) ),
inference(spl,[status(thm),theory(equality)],[145,89]),
[iquote('0:SpL:145.1,89.2')] ).
cnf(210,plain,
( ~ empty(u)
| ~ ordinal(skc22)
| transfinite_sequence(u) ),
inference(ssi,[status(thm)],[206,62,59]),
[iquote('0:SSi:206.2,206.1,62.1,59.1')] ).
cnf(211,plain,
( ~ empty(u)
| transfinite_sequence(u) ),
inference(mrr,[status(thm)],[210,115]),
[iquote('0:MRR:210.1,115.0')] ).
cnf(259,plain,
( ~ empty(u)
| ~ relation(u)
| ~ function(u)
| ~ transfinite_sequence(u)
| ~ subset(skc22,v)
| transfinite_sequence_of(u,v) ),
inference(spl,[status(thm),theory(equality)],[146,98]),
[iquote('0:SpL:146.1,98.3')] ).
cnf(262,plain,
( ~ empty(u)
| ~ subset(skc22,v)
| transfinite_sequence_of(u,v) ),
inference(ssi,[status(thm)],[259,211,59,62]),
[iquote('0:SSi:259.3,259.2,259.1,211.1,59.1,62.1')] ).
cnf(263,plain,
( ~ empty(u)
| transfinite_sequence_of(u,v) ),
inference(mrr,[status(thm)],[262,119]),
[iquote('0:MRR:262.1,119.0')] ).
cnf(266,plain,
~ empty(skc22),
inference(res,[status(thm),theory(equality)],[263,120]),
[iquote('0:Res:263.1,120.0')] ).
cnf(270,plain,
$false,
inference(ssi,[status(thm)],[266,21,20,111,112,113,114,115,116]),
[iquote('0:SSi:266.0,21.0,20.0,111.0,112.0,113.0,114.0,115.0,116.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 23:14:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 139 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.21/0.47 SPASS allocated 97836 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.03 for the input.
% 0.21/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.01 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 3, length 37 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : fc2_ordinal1 rc1_relat_1 t2_xboole_1 t45_ordinal1 cc1_funct_1 cc1_relat_1 fc7_relat_1 fc8_relat_1 t6_boole d7_ordinal1 d8_ordinal1
% 0.21/0.47
%------------------------------------------------------------------------------