TSTP Solution File: SEU261+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:35:38 EDT 2022
% Result : Theorem 41.34s 41.58s
% Output : Refutation 41.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of clauses : 51 ( 21 unt; 0 nHn; 51 RR)
% Number of literals : 148 ( 0 equ; 105 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc17),
file('SEU261+2.p',unknown),
[] ).
cnf(2,axiom,
relation(skc16),
file('SEU261+2.p',unknown),
[] ).
cnf(3,axiom,
relation(skc15),
file('SEU261+2.p',unknown),
[] ).
cnf(4,axiom,
function(skc17),
file('SEU261+2.p',unknown),
[] ).
cnf(5,axiom,
well_ordering(skc15),
file('SEU261+2.p',unknown),
[] ).
cnf(50,axiom,
~ well_ordering(skc16),
file('SEU261+2.p',unknown),
[] ).
cnf(63,axiom,
relation_isomorphism(skc15,skc16,skc17),
file('SEU261+2.p',unknown),
[] ).
cnf(163,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| reflexive(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(164,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| transitive(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(165,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| antisymmetric(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(166,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| connected(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(167,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| well_founded_relation(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(291,axiom,
( ~ relation(u)
| ~ well_orders(u,relation_field(u))
| well_ordering(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(292,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| well_orders(u,relation_field(u)) ),
file('SEU261+2.p',unknown),
[] ).
cnf(538,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| ~ connected(u)
| ~ antisymmetric(u)
| ~ transitive(u)
| ~ reflexive(u)
| well_ordering(u) ),
file('SEU261+2.p',unknown),
[] ).
cnf(579,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ well_founded_relation(w)
| ~ relation_isomorphism(w,v,u)
| well_founded_relation(v) ),
file('SEU261+2.p',unknown),
[] ).
cnf(580,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ antisymmetric(w)
| ~ relation_isomorphism(w,v,u)
| antisymmetric(v) ),
file('SEU261+2.p',unknown),
[] ).
cnf(581,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ connected(w)
| ~ relation_isomorphism(w,v,u)
| connected(v) ),
file('SEU261+2.p',unknown),
[] ).
cnf(582,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ transitive(w)
| ~ relation_isomorphism(w,v,u)
| transitive(v) ),
file('SEU261+2.p',unknown),
[] ).
cnf(583,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ reflexive(w)
| ~ relation_isomorphism(w,v,u)
| reflexive(v) ),
file('SEU261+2.p',unknown),
[] ).
cnf(723,plain,
( ~ relation(skc15)
| reflexive(skc15) ),
inference(res,[status(thm),theory(equality)],[5,163]),
[iquote('0:Res:5.0,163.0')] ).
cnf(724,plain,
( ~ relation(skc15)
| transitive(skc15) ),
inference(res,[status(thm),theory(equality)],[5,164]),
[iquote('0:Res:5.0,164.0')] ).
cnf(725,plain,
( ~ relation(skc15)
| antisymmetric(skc15) ),
inference(res,[status(thm),theory(equality)],[5,165]),
[iquote('0:Res:5.0,165.0')] ).
cnf(726,plain,
( ~ relation(skc15)
| connected(skc15) ),
inference(res,[status(thm),theory(equality)],[5,166]),
[iquote('0:Res:5.0,166.0')] ).
cnf(727,plain,
( ~ relation(skc15)
| well_founded_relation(skc15) ),
inference(res,[status(thm),theory(equality)],[5,167]),
[iquote('0:Res:5.0,167.0')] ).
cnf(1304,plain,
( ~ reflexive(skc16)
| ~ transitive(skc16)
| ~ antisymmetric(skc16)
| ~ connected(skc16)
| ~ well_founded_relation(skc16)
| well_ordering(skc16) ),
inference(res,[status(thm),theory(equality)],[2,538]),
[iquote('0:Res:2.0,538.5')] ).
cnf(1445,plain,
( ~ well_orders(skc16,relation_field(skc16))
| well_ordering(skc16) ),
inference(res,[status(thm),theory(equality)],[2,291]),
[iquote('0:Res:2.0,291.0')] ).
cnf(1446,plain,
( ~ well_ordering(skc16)
| well_orders(skc16,relation_field(skc16)) ),
inference(res,[status(thm),theory(equality)],[2,292]),
[iquote('0:Res:2.0,292.1')] ).
cnf(1552,plain,
reflexive(skc15),
inference(mrr,[status(thm)],[723,3]),
[iquote('0:MRR:723.0,3.0')] ).
cnf(1553,plain,
transitive(skc15),
inference(mrr,[status(thm)],[724,3]),
[iquote('0:MRR:724.0,3.0')] ).
cnf(1554,plain,
antisymmetric(skc15),
inference(mrr,[status(thm)],[725,3]),
[iquote('0:MRR:725.0,3.0')] ).
cnf(1555,plain,
connected(skc15),
inference(mrr,[status(thm)],[726,3]),
[iquote('0:MRR:726.0,3.0')] ).
cnf(1556,plain,
well_founded_relation(skc15),
inference(mrr,[status(thm)],[727,3]),
[iquote('0:MRR:727.0,3.0')] ).
cnf(1573,plain,
~ well_orders(skc16,relation_field(skc16)),
inference(mrr,[status(thm)],[1445,50]),
[iquote('0:MRR:1445.1,50.0')] ).
cnf(1574,plain,
~ well_ordering(skc16),
inference(mrr,[status(thm)],[1446,1573]),
[iquote('0:MRR:1446.1,1573.0')] ).
cnf(1600,plain,
( ~ well_founded_relation(skc16)
| ~ connected(skc16)
| ~ antisymmetric(skc16)
| ~ transitive(skc16)
| ~ reflexive(skc16) ),
inference(mrr,[status(thm)],[1304,1574]),
[iquote('0:MRR:1304.5,1574.0')] ).
cnf(28769,plain,
( ~ function(skc17)
| ~ relation(skc17)
| ~ relation(skc16)
| ~ relation(skc15)
| ~ reflexive(skc15)
| reflexive(skc16) ),
inference(res,[status(thm),theory(equality)],[63,583]),
[iquote('0:Res:63.0,583.5')] ).
cnf(28783,plain,
( ~ function(skc17)
| ~ relation(skc17)
| ~ relation(skc16)
| ~ relation(skc15)
| ~ antisymmetric(skc15)
| antisymmetric(skc16) ),
inference(res,[status(thm),theory(equality)],[63,580]),
[iquote('0:Res:63.0,580.5')] ).
cnf(28788,plain,
( ~ function(skc17)
| ~ relation(skc17)
| ~ relation(skc16)
| ~ relation(skc15)
| ~ transitive(skc15)
| transitive(skc16) ),
inference(res,[status(thm),theory(equality)],[63,582]),
[iquote('0:Res:63.0,582.5')] ).
cnf(28793,plain,
( ~ function(skc17)
| ~ relation(skc17)
| ~ relation(skc16)
| ~ relation(skc15)
| ~ well_founded_relation(skc15)
| well_founded_relation(skc16) ),
inference(res,[status(thm),theory(equality)],[63,579]),
[iquote('0:Res:63.0,579.5')] ).
cnf(29157,plain,
( ~ function(skc17)
| ~ relation(skc17)
| ~ relation(skc16)
| ~ relation(skc15)
| ~ connected(skc15)
| connected(skc16) ),
inference(res,[status(thm),theory(equality)],[63,581]),
[iquote('0:Res:63.0,581.5')] ).
cnf(29167,plain,
connected(skc16),
inference(ssi,[status(thm)],[29157,1556,5,1555,1554,1553,1552,3,2,4,1]),
[iquote('0:SSi:29157.4,29157.3,29157.2,29157.1,29157.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(29170,plain,
( ~ well_founded_relation(skc16)
| ~ antisymmetric(skc16)
| ~ transitive(skc16)
| ~ reflexive(skc16) ),
inference(mrr,[status(thm)],[1600,29167]),
[iquote('0:MRR:1600.1,29167.0')] ).
cnf(29171,plain,
transitive(skc16),
inference(ssi,[status(thm)],[28788,1556,5,1555,1554,1553,1552,3,2,4,1]),
[iquote('0:SSi:28788.4,28788.3,28788.2,28788.1,28788.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(29174,plain,
( ~ well_founded_relation(skc16)
| ~ antisymmetric(skc16)
| ~ reflexive(skc16) ),
inference(mrr,[status(thm)],[29170,29171]),
[iquote('0:MRR:29170.2,29171.0')] ).
cnf(29175,plain,
reflexive(skc16),
inference(ssi,[status(thm)],[28769,1556,5,1555,1554,1553,1552,3,2,4,1]),
[iquote('0:SSi:28769.4,28769.3,28769.2,28769.1,28769.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(29179,plain,
( ~ well_founded_relation(skc16)
| ~ antisymmetric(skc16) ),
inference(mrr,[status(thm)],[29174,29175]),
[iquote('0:MRR:29174.2,29175.0')] ).
cnf(29180,plain,
antisymmetric(skc16),
inference(ssi,[status(thm)],[28783,1556,5,1555,1554,1553,1552,3,2,4,1]),
[iquote('0:SSi:28783.4,28783.3,28783.2,28783.1,28783.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(29183,plain,
~ well_founded_relation(skc16),
inference(mrr,[status(thm)],[29179,29180]),
[iquote('0:MRR:29179.1,29180.0')] ).
cnf(29211,plain,
well_founded_relation(skc16),
inference(ssi,[status(thm)],[28793,1556,5,1555,1554,1553,1552,3,2,4,1]),
[iquote('0:SSi:28793.4,28793.3,28793.2,28793.1,28793.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,1556.0,5.0,1555.0,1554.0,1553.0,1552.0,3.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(29212,plain,
$false,
inference(mrr,[status(thm)],[29211,29183]),
[iquote('0:MRR:29211.0,29183.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 14:10:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 41.34/41.58
% 41.34/41.58 SPASS V 3.9
% 41.34/41.58 SPASS beiseite: Proof found.
% 41.34/41.58 % SZS status Theorem
% 41.34/41.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.34/41.58 SPASS derived 21742 clauses, backtracked 4709 clauses, performed 34 splits and kept 14952 clauses.
% 41.34/41.58 SPASS allocated 123770 KBytes.
% 41.34/41.58 SPASS spent 0:0:40.51 on the problem.
% 41.34/41.58 0:00:00.04 for the input.
% 41.34/41.58 0:0:12.09 for the FLOTTER CNF translation.
% 41.34/41.58 0:00:00.32 for inferences.
% 41.34/41.58 0:00:00.63 for the backtracking.
% 41.34/41.58 0:0:26.38 for the reduction.
% 41.34/41.58
% 41.34/41.58
% 41.34/41.58 Here is a proof with depth 1, length 51 :
% 41.34/41.58 % SZS output start Refutation
% See solution above
% 41.34/41.58 Formulae used in the proof : t54_wellord1 d4_wellord1 t8_wellord1 t53_wellord1
% 41.34/41.58
%------------------------------------------------------------------------------