%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:35:37 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of clauses : 51 ( 19 unt; 0 nHn; 51 RR)
% Number of literals : 163 ( 0 equ; 119 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc6),
file('SEU261+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc5),
file('SEU261+1.p',unknown),
[] ).
cnf(3,axiom,
relation(skc4),
file('SEU261+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc6),
file('SEU261+1.p',unknown),
[] ).
cnf(5,axiom,
well_ordering(skc4),
file('SEU261+1.p',unknown),
[] ).
cnf(8,axiom,
~ well_ordering(skc5),
file('SEU261+1.p',unknown),
[] ).
cnf(9,axiom,
relation_isomorphism(skc4,skc5,skc6),
file('SEU261+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| reflexive(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| transitive(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| antisymmetric(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| connected(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ relation(u)
| ~ well_ordering(u)
| well_founded_relation(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ relation(u)
| ~ well_founded_relation(u)
| ~ connected(u)
| ~ antisymmetric(u)
| ~ transitive(u)
| ~ reflexive(u)
| well_ordering(u) ),
file('SEU261+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ well_founded_relation(w)
| ~ relation_isomorphism(w,v,u)
| well_founded_relation(v) ),
file('SEU261+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ antisymmetric(w)
| ~ relation_isomorphism(w,v,u)
| antisymmetric(v) ),
file('SEU261+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ connected(w)
| ~ relation_isomorphism(w,v,u)
| connected(v) ),
file('SEU261+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ transitive(w)
| ~ relation_isomorphism(w,v,u)
| transitive(v) ),
file('SEU261+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation(w)
| ~ reflexive(w)
| ~ relation_isomorphism(w,v,u)
| reflexive(v) ),
file('SEU261+1.p',unknown),
[] ).
cnf(21,plain,
( ~ relation(skc4)
| reflexive(skc4) ),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(22,plain,
( ~ relation(skc4)
| transitive(skc4) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(23,plain,
( ~ relation(skc4)
| antisymmetric(skc4) ),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.0,12.0')] ).
cnf(24,plain,
( ~ relation(skc4)
| connected(skc4) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.0')] ).
cnf(25,plain,
( ~ relation(skc4)
| well_founded_relation(skc4) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.0,14.0')] ).
cnf(33,plain,
( ~ connected(skc4)
| ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ relation_isomorphism(skc4,u,v)
| connected(u) ),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.0,18.1')] ).
cnf(34,plain,
( ~ antisymmetric(skc4)
| ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ relation_isomorphism(skc4,u,v)
| antisymmetric(u) ),
inference(res,[status(thm),theory(equality)],[3,17]),
[iquote('0:Res:3.0,17.1')] ).
cnf(35,plain,
( ~ well_founded_relation(skc4)
| ~ relation(u)
| ~ relation(v)
| ~ function(v)
| ~ relation_isomorphism(skc4,u,v)
| well_founded_relation(u) ),
inference(res,[status(thm),theory(equality)],[3,16]),
[iquote('0:Res:3.0,16.1')] ).
cnf(52,plain,
reflexive(skc4),
inference(mrr,[status(thm)],[21,3]),
[iquote('0:MRR:21.0,3.0')] ).
cnf(53,plain,
transitive(skc4),
inference(mrr,[status(thm)],[22,3]),
[iquote('0:MRR:22.0,3.0')] ).
cnf(54,plain,
antisymmetric(skc4),
inference(mrr,[status(thm)],[23,3]),
[iquote('0:MRR:23.0,3.0')] ).
cnf(55,plain,
connected(skc4),
inference(mrr,[status(thm)],[24,3]),
[iquote('0:MRR:24.0,3.0')] ).
cnf(56,plain,
well_founded_relation(skc4),
inference(mrr,[status(thm)],[25,3]),
[iquote('0:MRR:25.0,3.0')] ).
cnf(64,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation_isomorphism(skc4,v,u)
| connected(v) ),
inference(mrr,[status(thm)],[33,55]),
[iquote('0:MRR:33.0,55.0')] ).
cnf(65,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation_isomorphism(skc4,v,u)
| antisymmetric(v) ),
inference(mrr,[status(thm)],[34,54]),
[iquote('0:MRR:34.0,54.0')] ).
cnf(66,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(v)
| ~ relation_isomorphism(skc4,v,u)
| well_founded_relation(v) ),
inference(mrr,[status(thm)],[35,56]),
[iquote('0:MRR:35.0,56.0')] ).
cnf(100,plain,
( ~ relation(skc5)
| ~ well_founded_relation(skc5)
| ~ connected(skc5)
| ~ antisymmetric(skc5)
| ~ transitive(skc5)
| ~ reflexive(skc5) ),
inference(res,[status(thm),theory(equality)],[15,8]),
[iquote('0:Res:15.6,8.0')] ).
cnf(101,plain,
( ~ well_founded_relation(skc5)
| ~ connected(skc5)
| ~ antisymmetric(skc5)
| ~ transitive(skc5)
| ~ reflexive(skc5) ),
inference(ssi,[status(thm)],[100,2]),
[iquote('0:SSi:100.0,2.0')] ).
cnf(106,plain,
( ~ function(skc6)
| ~ relation(skc6)
| ~ relation(skc5)
| well_founded_relation(skc5) ),
inference(res,[status(thm),theory(equality)],[9,66]),
[iquote('0:Res:9.0,66.3')] ).
cnf(107,plain,
well_founded_relation(skc5),
inference(ssi,[status(thm)],[106,2,4,1]),
[iquote('0:SSi:106.2,106.1,106.0,2.0,4.0,1.0,4.0,1.0')] ).
cnf(108,plain,
( ~ connected(skc5)
| ~ antisymmetric(skc5)
| ~ transitive(skc5)
| ~ reflexive(skc5) ),
inference(mrr,[status(thm)],[101,107]),
[iquote('0:MRR:101.0,107.0')] ).
cnf(109,plain,
( ~ function(skc6)
| ~ relation(skc6)
| ~ relation(skc5)
| ~ relation(skc4)
| ~ reflexive(skc4)
| reflexive(skc5) ),
inference(res,[status(thm),theory(equality)],[9,20]),
[iquote('0:Res:9.0,20.5')] ).
cnf(110,plain,
reflexive(skc5),
inference(ssi,[status(thm)],[109,5,3,56,55,54,53,52,2,107,4,1]),
[iquote('0:SSi:109.4,109.3,109.2,109.1,109.0,5.0,3.0,56.0,55.0,54.0,53.0,52.0,5.0,3.0,56.0,55.0,54.0,53.0,52.0,2.0,107.0,4.0,1.0,4.0,1.0')] ).
cnf(111,plain,
( ~ connected(skc5)
| ~ antisymmetric(skc5)
| ~ transitive(skc5) ),
inference(mrr,[status(thm)],[108,110]),
[iquote('0:MRR:108.3,110.0')] ).
cnf(114,plain,
( ~ function(skc6)
| ~ relation(skc6)
| ~ relation(skc5)
| antisymmetric(skc5) ),
inference(res,[status(thm),theory(equality)],[9,65]),
[iquote('0:Res:9.0,65.3')] ).
cnf(115,plain,
antisymmetric(skc5),
inference(ssi,[status(thm)],[114,2,107,110,4,1]),
[iquote('0:SSi:114.2,114.1,114.0,2.0,107.0,110.0,4.0,1.0,4.0,1.0')] ).
cnf(116,plain,
( ~ connected(skc5)
| ~ transitive(skc5) ),
inference(mrr,[status(thm)],[111,115]),
[iquote('0:MRR:111.1,115.0')] ).
cnf(117,plain,
( ~ function(skc6)
| ~ relation(skc6)
| ~ relation(skc5)
| ~ relation(skc4)
| ~ transitive(skc4)
| transitive(skc5) ),
inference(res,[status(thm),theory(equality)],[9,19]),
[iquote('0:Res:9.0,19.5')] ).
cnf(118,plain,
transitive(skc5),
inference(ssi,[status(thm)],[117,5,3,56,55,54,53,52,2,107,110,115,4,1]),
[iquote('0:SSi:117.4,117.3,117.2,117.1,117.0,5.0,3.0,56.0,55.0,54.0,53.0,52.0,5.0,3.0,56.0,55.0,54.0,53.0,52.0,2.0,107.0,110.0,115.0,4.0,1.0,4.0,1.0')] ).
cnf(119,plain,
~ connected(skc5),
inference(mrr,[status(thm)],[116,118]),
[iquote('0:MRR:116.1,118.0')] ).
cnf(121,plain,
( ~ function(skc6)
| ~ relation(skc6)
| ~ relation(skc5)
| connected(skc5) ),
inference(res,[status(thm),theory(equality)],[9,64]),
[iquote('0:Res:9.0,64.3')] ).
cnf(122,plain,
connected(skc5),
inference(ssi,[status(thm)],[121,2,107,110,115,118,4,1]),
[iquote('0:SSi:121.2,121.1,121.0,2.0,107.0,110.0,115.0,118.0,4.0,1.0,4.0,1.0')] ).
cnf(123,plain,
$false,
inference(mrr,[status(thm)],[122,119]),
[iquote('0:MRR:122.0,119.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.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 16:24:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 45 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.19/0.44 SPASS allocated 97716 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 2, length 51 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : t54_wellord1 d4_wellord1 t53_wellord1
% 0.19/0.44
%------------------------------------------------------------------------------