TSTP Solution File: SEU030+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:33:38 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 14 unt; 0 nHn; 31 RR)
% Number of literals : 89 ( 0 equ; 67 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU030+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc10),
file('SEU030+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc10),
file('SEU030+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc11),
file('SEU030+1.p',unknown),
[] ).
cnf(5,axiom,
one_to_one(skc10),
file('SEU030+1.p',unknown),
[] ).
cnf(35,axiom,
equal(relation_rng(skc10),relation_dom(skc11)),
file('SEU030+1.p',unknown),
[] ).
cnf(36,axiom,
~ equal(function_inverse(skc10),skc11),
file('SEU030+1.p',unknown),
[] ).
cnf(47,axiom,
equal(relation_composition(skc10,skc11),identity_relation(relation_dom(skc10))),
file('SEU030+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU030+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU030+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
file('SEU030+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_composition(function_inverse(u),u),identity_relation(relation_rng(u))) ),
file('SEU030+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ relation(w)
| ~ function(w)
| ~ equal(relation_rng(u),x)
| ~ equal(relation_composition(v,w),identity_relation(x))
| ~ equal(relation_composition(u,v),identity_relation(relation_dom(w)))
| equal(w,u) ),
file('SEU030+1.p',unknown),
[] ).
cnf(76,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_rng(skc10))) ),
inference(res,[status(thm),theory(equality)],[5,72]),
[iquote('0:Res:5.0,72.2')] ).
cnf(78,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(relation_rng(function_inverse(skc10)),relation_dom(skc10)) ),
inference(res,[status(thm),theory(equality)],[5,68]),
[iquote('0:Res:5.0,68.2')] ).
cnf(96,plain,
( ~ relation(skc10)
| relation(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.1')] ).
cnf(97,plain,
( ~ relation(skc10)
| function(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,54]),
[iquote('0:Res:3.0,54.1')] ).
cnf(142,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ function(u)
| ~ relation(u)
| ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ equal(relation_rng(function_inverse(skc10)),v)
| ~ equal(relation_composition(u,skc11),identity_relation(v))
| ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
inference(res,[status(thm),theory(equality)],[73,36]),
[iquote('0:Res:73.9,36.0')] ).
cnf(146,plain,
relation(function_inverse(skc10)),
inference(mrr,[status(thm)],[96,2]),
[iquote('0:MRR:96.0,2.0')] ).
cnf(147,plain,
function(function_inverse(skc10)),
inference(mrr,[status(thm)],[97,2]),
[iquote('0:MRR:97.0,2.0')] ).
cnf(151,plain,
equal(relation_rng(function_inverse(skc10)),relation_dom(skc10)),
inference(mrr,[status(thm)],[78,2,3]),
[iquote('0:MRR:78.0,78.1,2.0,3.0')] ).
cnf(161,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_dom(skc11))) ),
inference(rew,[status(thm),theory(equality)],[35,76]),
[iquote('0:Rew:35.0,76.2')] ).
cnf(162,plain,
equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_dom(skc11))),
inference(mrr,[status(thm)],[161,2,3]),
[iquote('0:MRR:161.0,161.1,2.0,3.0')] ).
cnf(176,plain,
( ~ function(skc11)
| ~ relation(skc11)
| ~ function(u)
| ~ relation(u)
| ~ function(function_inverse(skc10))
| ~ relation(function_inverse(skc10))
| ~ equal(relation_dom(skc10),v)
| ~ equal(relation_composition(u,skc11),identity_relation(v))
| ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
inference(rew,[status(thm),theory(equality)],[151,142]),
[iquote('0:Rew:151.0,142.6')] ).
cnf(177,plain,
( ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(skc10),v)
| ~ equal(relation_composition(u,skc11),identity_relation(v))
| ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
inference(mrr,[status(thm)],[176,4,1,147,146]),
[iquote('0:MRR:176.0,176.1,176.4,176.5,4.0,1.0,147.0,146.0')] ).
cnf(919,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ equal(relation_dom(skc10),u)
| ~ equal(relation_composition(skc10,skc11),identity_relation(u))
| ~ equal(identity_relation(relation_dom(skc11)),identity_relation(relation_dom(skc11))) ),
inference(spl,[status(thm),theory(equality)],[162,177]),
[iquote('0:SpL:162.0,177.4')] ).
cnf(922,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ equal(relation_dom(skc10),u)
| ~ equal(relation_composition(skc10,skc11),identity_relation(u)) ),
inference(obv,[status(thm),theory(equality)],[919]),
[iquote('0:Obv:919.4')] ).
cnf(923,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ equal(relation_dom(skc10),u)
| ~ equal(identity_relation(relation_dom(skc10)),identity_relation(u)) ),
inference(rew,[status(thm),theory(equality)],[47,922]),
[iquote('0:Rew:47.0,922.3')] ).
cnf(924,plain,
( ~ equal(relation_dom(skc10),u)
| ~ equal(identity_relation(relation_dom(skc10)),identity_relation(u)) ),
inference(ssi,[status(thm)],[923,5,3,2]),
[iquote('0:SSi:923.1,923.0,5.0,3.0,2.0,5.0,3.0,2.0')] ).
cnf(1004,plain,
~ equal(relation_dom(skc10),relation_dom(skc10)),
inference(eqr,[status(thm),theory(equality)],[924]),
[iquote('0:EqR:924.1')] ).
cnf(1006,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1004]),
[iquote('0:Obv:1004.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.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 : Sat Jun 18 23:32:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 689 clauses, backtracked 0 clauses, performed 0 splits and kept 325 clauses.
% 0.19/0.51 SPASS allocated 98437 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.05 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 3, length 31 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : t63_funct_1 dt_k2_funct_1 t55_funct_1 t61_funct_1 l72_funct_1
% 0.19/0.51
%------------------------------------------------------------------------------