TSTP Solution File: SEU221+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:35:11 EDT 2022
% Result : Theorem 1.10s 1.27s
% Output : Refutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 9 unt; 17 nHn; 41 RR)
% Number of literals : 149 ( 0 equ; 92 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU221+3.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU221+3.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU221+3.p',unknown),
[] ).
cnf(28,axiom,
~ one_to_one(function_inverse(skc9)),
file('SEU221+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU221+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU221+3.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf10(u),relation_dom(u)) ),
file('SEU221+3.p',unknown),
[] ).
cnf(63,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf9(u),relation_dom(u)) ),
file('SEU221+3.p',unknown),
[] ).
cnf(64,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf10(u),skf9(u))
| one_to_one(u) ),
file('SEU221+3.p',unknown),
[] ).
cnf(68,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf10(u)),apply(u,skf9(u))) ),
file('SEU221+3.p',unknown),
[] ).
cnf(71,axiom,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(v,relation_rng(u))
| equal(apply(u,apply(function_inverse(u),v)),v) ),
file('SEU221+3.p',unknown),
[] ).
cnf(74,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(v)
| ~ function(v)
| ~ relation(v)
| ~ equal(u,function_inverse(v))
| equal(relation_dom(u),relation_rng(v)) ),
file('SEU221+3.p',unknown),
[] ).
cnf(90,plain,
( ~ function(skc9)
| ~ relation(skc9)
| ~ in(u,relation_rng(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
inference(res,[status(thm),theory(equality)],[3,71]),
[iquote('0:Res:3.0,71.0')] ).
cnf(107,plain,
( ~ relation(skc9)
| relation(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,46]),
[iquote('0:Res:2.0,46.1')] ).
cnf(108,plain,
( ~ relation(skc9)
| function(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,47]),
[iquote('0:Res:2.0,47.1')] ).
cnf(123,plain,
( ~ function(skc9)
| ~ one_to_one(skc9)
| ~ relation(u)
| ~ function(u)
| ~ equal(u,function_inverse(skc9))
| equal(relation_dom(u),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[1,74]),
[iquote('0:Res:1.0,74.0')] ).
cnf(155,plain,
relation(function_inverse(skc9)),
inference(mrr,[status(thm)],[107,1]),
[iquote('0:MRR:107.0,1.0')] ).
cnf(156,plain,
function(function_inverse(skc9)),
inference(mrr,[status(thm)],[108,1]),
[iquote('0:MRR:108.0,1.0')] ).
cnf(159,plain,
( ~ in(u,relation_rng(skc9))
| equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
inference(mrr,[status(thm)],[90,2,1]),
[iquote('0:MRR:90.0,90.1,2.0,1.0')] ).
cnf(164,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| equal(relation_dom(u),relation_rng(skc9)) ),
inference(mrr,[status(thm)],[123,2,3]),
[iquote('0:MRR:123.0,123.1,2.0,3.0')] ).
cnf(554,plain,
( ~ function(function_inverse(u))
| ~ relation(function_inverse(u))
| ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(skf10(function_inverse(u)),relation_rng(u))
| one_to_one(function_inverse(u))
| equal(apply(u,apply(function_inverse(u),skf9(function_inverse(u)))),skf10(function_inverse(u))) ),
inference(spr,[status(thm),theory(equality)],[68,71]),
[iquote('0:SpR:68.3,71.4')] ).
cnf(555,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(skf10(function_inverse(u)),relation_rng(u))
| one_to_one(function_inverse(u))
| equal(apply(u,apply(function_inverse(u),skf9(function_inverse(u)))),skf10(function_inverse(u))) ),
inference(ssi,[status(thm)],[554,47,46]),
[iquote('0:SSi:554.1,554.0,47.2,46.2,47.2,46.2')] ).
cnf(939,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf9(u),relation_rng(skc9)) ),
inference(spr,[status(thm),theory(equality)],[164,63]),
[iquote('0:SpR:164.3,63.3')] ).
cnf(940,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf10(u),relation_rng(skc9)) ),
inference(spr,[status(thm),theory(equality)],[164,62]),
[iquote('0:SpR:164.3,62.3')] ).
cnf(953,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf10(u),relation_rng(skc9)) ),
inference(obv,[status(thm),theory(equality)],[940]),
[iquote('0:Obv:940.1')] ).
cnf(954,plain,
( ~ function(u)
| ~ relation(u)
| ~ equal(u,function_inverse(skc9))
| one_to_one(u)
| in(skf9(u),relation_rng(skc9)) ),
inference(obv,[status(thm),theory(equality)],[939]),
[iquote('0:Obv:939.1')] ).
cnf(1339,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ one_to_one(skc9)
| ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
| ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(spr,[status(thm),theory(equality)],[555,159]),
[iquote('0:SpR:555.5,159.1')] ).
cnf(1350,plain,
( ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
| ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[1339,3,2,1]),
[iquote('0:SSi:1339.2,1339.1,1339.0,3.0,2.0,1.0,3.0,2.0,1.0,3.0,2.0,1.0')] ).
cnf(1351,plain,
( ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
| ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(mrr,[status(thm)],[1350,28]),
[iquote('0:MRR:1350.2,28.0')] ).
cnf(2742,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(function_inverse(skc9),function_inverse(skc9))
| ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(res,[status(thm),theory(equality)],[953,1351]),
[iquote('0:Res:953.4,1351.0')] ).
cnf(2744,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(obv,[status(thm),theory(equality)],[2742]),
[iquote('0:Obv:2742.2')] ).
cnf(2745,plain,
( ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[2744,155,156]),
[iquote('0:SSi:2744.1,2744.0,155.0,156.0,155.0,156.0')] ).
cnf(2746,plain,
( ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(mrr,[status(thm)],[2745,28]),
[iquote('0:MRR:2745.1,28.0')] ).
cnf(2753,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(function_inverse(skc9),function_inverse(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(res,[status(thm),theory(equality)],[954,2746]),
[iquote('0:Res:954.4,2746.0')] ).
cnf(2755,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(obv,[status(thm),theory(equality)],[2753]),
[iquote('0:Obv:2753.2')] ).
cnf(2756,plain,
( one_to_one(function_inverse(skc9))
| equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
inference(ssi,[status(thm)],[2755,155,156]),
[iquote('0:SSi:2755.1,2755.0,155.0,156.0,155.0,156.0')] ).
cnf(2757,plain,
equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))),
inference(mrr,[status(thm)],[2756,28]),
[iquote('0:MRR:2756.0,28.0')] ).
cnf(2779,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(skf9(function_inverse(skc9)),skf9(function_inverse(skc9)))
| one_to_one(function_inverse(skc9)) ),
inference(spl,[status(thm),theory(equality)],[2757,64]),
[iquote('0:SpL:2757.0,64.2')] ).
cnf(2782,plain,
( ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| one_to_one(function_inverse(skc9)) ),
inference(obv,[status(thm),theory(equality)],[2779]),
[iquote('0:Obv:2779.2')] ).
cnf(2783,plain,
one_to_one(function_inverse(skc9)),
inference(ssi,[status(thm)],[2782,155,156]),
[iquote('0:SSi:2782.1,2782.0,155.0,156.0,155.0,156.0')] ).
cnf(2784,plain,
$false,
inference(mrr,[status(thm)],[2783,28]),
[iquote('0:MRR:2783.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 11:35:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.10/1.27
% 1.10/1.27 SPASS V 3.9
% 1.10/1.27 SPASS beiseite: Proof found.
% 1.10/1.27 % SZS status Theorem
% 1.10/1.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/1.27 SPASS derived 2217 clauses, backtracked 19 clauses, performed 2 splits and kept 1320 clauses.
% 1.10/1.27 SPASS allocated 100713 KBytes.
% 1.10/1.27 SPASS spent 0:00:00.92 on the problem.
% 1.10/1.27 0:00:00.03 for the input.
% 1.10/1.27 0:00:00.08 for the FLOTTER CNF translation.
% 1.10/1.27 0:00:00.05 for inferences.
% 1.10/1.27 0:00:00.00 for the backtracking.
% 1.10/1.27 0:00:00.71 for the reduction.
% 1.10/1.27
% 1.10/1.27
% 1.10/1.27 Here is a proof with depth 5, length 41 :
% 1.10/1.27 % SZS output start Refutation
% See solution above
% 1.10/1.27 Formulae used in the proof : t62_funct_1 dt_k2_funct_1 d8_funct_1 t57_funct_1 t54_funct_1
% 1.10/1.27
%------------------------------------------------------------------------------