%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Tue Jul 19 14:35:28 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of clauses : 76 ( 25 unt; 1 nHn; 76 RR)
% Number of literals : 179 ( 0 equ; 107 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc1),
file('SEU244+1.p',unknown),
[] ).
cnf(3,axiom,
( well_ordering(skc1)
| well_orders(skc1,relation_field(skc1)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ well_ordering(skc1)
| ~ well_orders(skc1,relation_field(skc1)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| reflexive(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| transitive(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| antisymmetric(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| connected(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| well_founded_relation(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ relation(u)
| ~ antisymmetric(u)
| is_antisymmetric_in(u,relation_field(u)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ relation(u)
| ~ is_antisymmetric_in(u,relation_field(u))
| antisymmetric(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ relation(u)
| ~ connected(u)
| is_connected_in(u,relation_field(u)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ relation(u)
| ~ is_connected_in(u,relation_field(u))
| connected(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ relation(u)
| ~ transitive(u)
| is_transitive_in(u,relation_field(u)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ relation(u)
| ~ is_transitive_in(u,relation_field(u))
| transitive(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ relation(u)
| ~ well_orders(u,v)
| is_reflexive_in(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ relation(u)
| ~ well_orders(u,v)
| is_transitive_in(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ relation(u)
| ~ well_orders(u,v)
| is_antisymmetric_in(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ relation(u)
| ~ well_orders(u,v)
| is_connected_in(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ relation(u)
| ~ well_orders(u,v)
| is_well_founded_in(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ relation(u)
| ~ reflexive(u)
| is_reflexive_in(u,relation_field(u)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ relation(u)
| ~ is_reflexive_in(u,relation_field(u))
| reflexive(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| is_well_founded_in(u,relation_field(u)) ),
file('SEU244+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ relation(u)
| ~ is_well_founded_in(u,relation_field(u))
| well_founded_relation(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| ~ connected(u)
| ~ antisymmetric(u)
| ~ transitive(u)
| ~ reflexive(u)
| well_ordering(u) ),
file('SEU244+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ relation(u)
| ~ is_reflexive_in(u,v)
| ~ is_well_founded_in(u,v)
| ~ is_connected_in(u,v)
| ~ is_antisymmetric_in(u,v)
| ~ is_transitive_in(u,v)
| well_orders(u,v) ),
file('SEU244+1.p',unknown),
[] ).
cnf(30,plain,
( ~ well_founded_relation(skc1)
| ~ connected(skc1)
| ~ antisymmetric(skc1)
| ~ transitive(skc1)
| ~ reflexive(skc1)
| well_ordering(skc1) ),
inference(res,[status(thm),theory(equality)],[1,27]),
[iquote('0:Res:1.0,27.5')] ).
cnf(32,plain,
( ~ antisymmetric(skc1)
| is_antisymmetric_in(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.1')] ).
cnf(33,plain,
( ~ is_antisymmetric_in(skc1,relation_field(skc1))
| antisymmetric(skc1) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(34,plain,
( ~ connected(skc1)
| is_connected_in(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[1,13]),
[iquote('0:Res:1.0,13.1')] ).
cnf(35,plain,
( ~ is_connected_in(skc1,relation_field(skc1))
| connected(skc1) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.0')] ).
cnf(36,plain,
( ~ transitive(skc1)
| is_transitive_in(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.1')] ).
cnf(37,plain,
( ~ is_transitive_in(skc1,relation_field(skc1))
| transitive(skc1) ),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.0,16.0')] ).
cnf(39,plain,
( ~ well_orders(skc1,u)
| is_transitive_in(skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(40,plain,
( ~ well_orders(skc1,u)
| is_antisymmetric_in(skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.0')] ).
cnf(41,plain,
( ~ well_orders(skc1,u)
| is_connected_in(skc1,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(43,plain,
( ~ reflexive(skc1)
| is_reflexive_in(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.1')] ).
cnf(45,plain,
( ~ well_founded_relation(skc1)
| is_well_founded_in(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[1,24]),
[iquote('0:Res:1.0,24.1')] ).
cnf(47,plain,
( ~ well_ordering(skc1)
| reflexive(skc1) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.1')] ).
cnf(48,plain,
( ~ well_ordering(skc1)
| transitive(skc1) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.1')] ).
cnf(49,plain,
( ~ well_ordering(skc1)
| antisymmetric(skc1) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.1')] ).
cnf(50,plain,
( ~ well_ordering(skc1)
| connected(skc1) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.1')] ).
cnf(51,plain,
( ~ well_ordering(skc1)
| well_founded_relation(skc1) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.1')] ).
cnf(52,plain,
well_ordering(skc1),
inference(spt,[spt(split,[position(s1)])],[3]),
[iquote('1:Spt:3.0')] ).
cnf(53,plain,
well_founded_relation(skc1),
inference(mrr,[status(thm)],[51,52]),
[iquote('1:MRR:51.0,52.0')] ).
cnf(54,plain,
connected(skc1),
inference(mrr,[status(thm)],[50,52]),
[iquote('1:MRR:50.0,52.0')] ).
cnf(55,plain,
antisymmetric(skc1),
inference(mrr,[status(thm)],[49,52]),
[iquote('1:MRR:49.0,52.0')] ).
cnf(56,plain,
transitive(skc1),
inference(mrr,[status(thm)],[48,52]),
[iquote('1:MRR:48.0,52.0')] ).
cnf(57,plain,
reflexive(skc1),
inference(mrr,[status(thm)],[47,52]),
[iquote('1:MRR:47.0,52.0')] ).
cnf(58,plain,
~ well_orders(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[5,52]),
[iquote('1:MRR:5.0,52.0')] ).
cnf(59,plain,
is_well_founded_in(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[45,53]),
[iquote('1:MRR:45.0,53.0')] ).
cnf(60,plain,
is_connected_in(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[34,54]),
[iquote('1:MRR:34.0,54.0')] ).
cnf(61,plain,
is_antisymmetric_in(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[32,55]),
[iquote('1:MRR:32.0,55.0')] ).
cnf(62,plain,
is_transitive_in(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[36,56]),
[iquote('1:MRR:36.0,56.0')] ).
cnf(63,plain,
is_reflexive_in(skc1,relation_field(skc1)),
inference(mrr,[status(thm)],[43,57]),
[iquote('1:MRR:43.0,57.0')] ).
cnf(84,plain,
( ~ relation(u)
| ~ relation(u)
| ~ well_orders(u,relation_field(u))
| well_founded_relation(u) ),
inference(res,[status(thm),theory(equality)],[21,25]),
[iquote('0:Res:21.2,25.1')] ).
cnf(85,plain,
( ~ relation(u)
| ~ well_orders(u,relation_field(u))
| well_founded_relation(u) ),
inference(obv,[status(thm),theory(equality)],[84]),
[iquote('0:Obv:84.0')] ).
cnf(86,plain,
( ~ relation(u)
| ~ relation(u)
| ~ well_orders(u,relation_field(u))
| reflexive(u) ),
inference(res,[status(thm),theory(equality)],[17,23]),
[iquote('0:Res:17.2,23.1')] ).
cnf(87,plain,
( ~ relation(u)
| ~ well_orders(u,relation_field(u))
| reflexive(u) ),
inference(obv,[status(thm),theory(equality)],[86]),
[iquote('0:Obv:86.0')] ).
cnf(90,plain,
( ~ relation(skc1)
| ~ is_reflexive_in(skc1,relation_field(skc1))
| ~ is_connected_in(skc1,relation_field(skc1))
| ~ is_antisymmetric_in(skc1,relation_field(skc1))
| ~ is_transitive_in(skc1,relation_field(skc1))
| well_orders(skc1,relation_field(skc1)) ),
inference(res,[status(thm),theory(equality)],[59,28]),
[iquote('1:Res:59.0,28.2')] ).
cnf(94,plain,
( ~ is_reflexive_in(skc1,relation_field(skc1))
| ~ is_connected_in(skc1,relation_field(skc1))
| ~ is_antisymmetric_in(skc1,relation_field(skc1))
| ~ is_transitive_in(skc1,relation_field(skc1))
| well_orders(skc1,relation_field(skc1)) ),
inference(ssi,[status(thm)],[90,52,1,53,54,55,56,57]),
[iquote('1:SSi:90.0,52.0,1.0,53.0,54.0,55.0,56.0,57.0')] ).
cnf(95,plain,
$false,
inference(mrr,[status(thm)],[94,63,60,61,62,58]),
[iquote('1:MRR:94.0,94.1,94.2,94.3,94.4,63.0,60.0,61.0,62.0,58.0')] ).
cnf(97,plain,
~ well_ordering(skc1),
inference(spt,[spt(split,[position(sa)])],[95,52]),
[iquote('1:Spt:95.0,3.0,52.0')] ).
cnf(98,plain,
well_orders(skc1,relation_field(skc1)),
inference(spt,[spt(split,[position(s2)])],[3]),
[iquote('1:Spt:95.0,3.1')] ).
cnf(99,plain,
( ~ well_founded_relation(skc1)
| ~ connected(skc1)
| ~ antisymmetric(skc1)
| ~ transitive(skc1)
| ~ reflexive(skc1) ),
inference(mrr,[status(thm)],[30,97]),
[iquote('1:MRR:30.5,97.0')] ).
cnf(100,plain,
is_transitive_in(skc1,relation_field(skc1)),
inference(res,[status(thm),theory(equality)],[98,39]),
[iquote('1:Res:98.0,39.0')] ).
cnf(101,plain,
is_antisymmetric_in(skc1,relation_field(skc1)),
inference(res,[status(thm),theory(equality)],[98,40]),
[iquote('1:Res:98.0,40.0')] ).
cnf(102,plain,
is_connected_in(skc1,relation_field(skc1)),
inference(res,[status(thm),theory(equality)],[98,41]),
[iquote('1:Res:98.0,41.0')] ).
cnf(106,plain,
( ~ relation(skc1)
| reflexive(skc1) ),
inference(res,[status(thm),theory(equality)],[98,87]),
[iquote('1:Res:98.0,87.1')] ).
cnf(107,plain,
( ~ relation(skc1)
| well_founded_relation(skc1) ),
inference(res,[status(thm),theory(equality)],[98,85]),
[iquote('1:Res:98.0,85.1')] ).
cnf(108,plain,
transitive(skc1),
inference(mrr,[status(thm)],[37,100]),
[iquote('1:MRR:37.0,100.0')] ).
cnf(109,plain,
( ~ well_founded_relation(skc1)
| ~ connected(skc1)
| ~ antisymmetric(skc1)
| ~ reflexive(skc1) ),
inference(mrr,[status(thm)],[99,108]),
[iquote('1:MRR:99.3,108.0')] ).
cnf(110,plain,
antisymmetric(skc1),
inference(mrr,[status(thm)],[33,101]),
[iquote('1:MRR:33.0,101.0')] ).
cnf(111,plain,
connected(skc1),
inference(mrr,[status(thm)],[35,102]),
[iquote('1:MRR:35.0,102.0')] ).
cnf(112,plain,
reflexive(skc1),
inference(ssi,[status(thm)],[106,1]),
[iquote('1:SSi:106.0,1.0')] ).
cnf(114,plain,
well_founded_relation(skc1),
inference(ssi,[status(thm)],[107,1]),
[iquote('1:SSi:107.0,1.0')] ).
cnf(116,plain,
$false,
inference(mrr,[status(thm)],[109,114,111,110,112]),
[iquote('1:MRR:109.0,109.1,109.2,109.3,114.0,111.0,110.0,112.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 10:14:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 77 clauses, backtracked 21 clauses, performed 1 splits and kept 96 clauses.
% 0.21/0.45 SPASS allocated 97654 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 2, length 76 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : t8_wellord1 d4_wellord1 d12_relat_2 d14_relat_2 d16_relat_2 d5_wellord1 d9_relat_2 t5_wellord1
% 0.21/0.45
%------------------------------------------------------------------------------