TSTP Solution File: SEU028+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 14:33:37 EDT 2022
% Result : Theorem 0.12s 0.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 57 ( 16 unt; 8 nHn; 57 RR)
% Number of literals : 194 ( 0 equ; 133 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU028+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU028+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU028+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(relation_composition(u,function_inverse(u))),relation_dom(u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(relation_composition(function_inverse(u),u)),relation_rng(u)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9)))
| ~ equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))) ),
file('SEU028+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),v)
| equal(u,identity_relation(v))
| in(skf7(v,w),v) ),
file('SEU028+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(v,relation_rng(u))
| equal(apply(relation_composition(function_inverse(u),u),v),v) ),
file('SEU028+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(v,relation_dom(u))
| equal(apply(relation_composition(u,function_inverse(u)),v),v) ),
file('SEU028+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ relation(u)
| ~ function(u)
| ~ equal(relation_dom(u),v)
| ~ equal(apply(u,skf7(v,u)),skf7(v,u))
| equal(u,identity_relation(v)) ),
file('SEU028+1.p',unknown),
[] ).
cnf(82,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,65]),
[iquote('0:Res:3.0,65.2')] ).
cnf(84,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,67]),
[iquote('0:Res:3.0,67.2')] ).
cnf(97,plain,
( ~ relation(skc9)
| ~ function(u)
| ~ relation(u)
| function(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[2,64]),
[iquote('0:Res:2.0,64.1')] ).
cnf(99,plain,
( ~ relation(skc9)
| relation(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,48]),
[iquote('0:Res:2.0,48.1')] ).
cnf(100,plain,
( ~ relation(skc9)
| function(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.1')] ).
cnf(101,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(skc9)
| function(relation_composition(u,skc9)) ),
inference(res,[status(thm),theory(equality)],[2,64]),
[iquote('0:Res:2.0,64.2')] ).
cnf(115,plain,
( ~ relation(u)
| relation(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[1,54]),
[iquote('0:Res:1.0,54.0')] ).
cnf(121,plain,
( ~ relation(u)
| relation(relation_composition(u,skc9)) ),
inference(res,[status(thm),theory(equality)],[1,54]),
[iquote('0:Res:1.0,54.1')] ).
cnf(126,plain,
relation(function_inverse(skc9)),
inference(mrr,[status(thm)],[99,1]),
[iquote('0:MRR:99.0,1.0')] ).
cnf(127,plain,
function(function_inverse(skc9)),
inference(mrr,[status(thm)],[100,1]),
[iquote('0:MRR:100.0,1.0')] ).
cnf(129,plain,
( ~ relation(u)
| ~ function(u)
| function(relation_composition(skc9,u)) ),
inference(mrr,[status(thm)],[97,1]),
[iquote('0:MRR:97.0,1.0')] ).
cnf(130,plain,
( ~ function(u)
| ~ relation(u)
| function(relation_composition(u,skc9)) ),
inference(mrr,[status(thm)],[101,1]),
[iquote('0:MRR:101.2,1.0')] ).
cnf(131,plain,
equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)),
inference(mrr,[status(thm)],[82,1,2]),
[iquote('0:MRR:82.0,82.1,1.0,2.0')] ).
cnf(133,plain,
equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)),
inference(mrr,[status(thm)],[84,1,2]),
[iquote('0:MRR:84.0,84.1,1.0,2.0')] ).
cnf(466,plain,
( ~ relation(u)
| ~ function(u)
| equal(identity_relation(relation_dom(u)),u)
| in(skf7(relation_dom(u),v),relation_dom(u)) ),
inference(eqr,[status(thm),theory(equality)],[70]),
[iquote('0:EqR:70.2')] ).
cnf(636,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(function_inverse(u),u))
| ~ function(relation_composition(function_inverse(u),u))
| ~ in(skf7(v,relation_composition(function_inverse(u),u)),relation_rng(u))
| ~ equal(relation_dom(relation_composition(function_inverse(u),u)),v)
| ~ equal(skf7(v,relation_composition(function_inverse(u),u)),skf7(v,relation_composition(function_inverse(u),u)))
| equal(relation_composition(function_inverse(u),u),identity_relation(v)) ),
inference(spl,[status(thm),theory(equality)],[72,76]),
[iquote('0:SpL:72.4,76.3')] ).
cnf(637,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(u,function_inverse(u)))
| ~ function(relation_composition(u,function_inverse(u)))
| ~ in(skf7(v,relation_composition(u,function_inverse(u))),relation_dom(u))
| ~ equal(relation_dom(relation_composition(u,function_inverse(u))),v)
| ~ equal(skf7(v,relation_composition(u,function_inverse(u))),skf7(v,relation_composition(u,function_inverse(u))))
| equal(relation_composition(u,function_inverse(u)),identity_relation(v)) ),
inference(spl,[status(thm),theory(equality)],[74,76]),
[iquote('0:SpL:74.4,76.3')] ).
cnf(642,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(u,function_inverse(u)))
| ~ function(relation_composition(u,function_inverse(u)))
| ~ in(skf7(v,relation_composition(u,function_inverse(u))),relation_dom(u))
| ~ equal(relation_dom(relation_composition(u,function_inverse(u))),v)
| equal(relation_composition(u,function_inverse(u)),identity_relation(v)) ),
inference(obv,[status(thm),theory(equality)],[637]),
[iquote('0:Obv:637.7')] ).
cnf(643,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(u,function_inverse(u)))
| ~ function(relation_composition(u,function_inverse(u)))
| ~ in(skf7(v,relation_composition(u,function_inverse(u))),relation_dom(u))
| ~ equal(relation_dom(u),v)
| equal(relation_composition(u,function_inverse(u)),identity_relation(v)) ),
inference(rew,[status(thm),theory(equality)],[65,642]),
[iquote('0:Rew:65.3,642.6')] ).
cnf(644,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(skf7(v,relation_composition(u,function_inverse(u))),relation_dom(u))
| ~ equal(relation_dom(u),v)
| equal(relation_composition(u,function_inverse(u)),identity_relation(v)) ),
inference(ssi,[status(thm)],[643,54,49,48,64]),
[iquote('0:SSi:643.4,643.3,54.2,49.2,48.4,64.2,49.2,48.2,54.2,49.2,48.4,64.2,49.2,48.2')] ).
cnf(645,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(function_inverse(u),u))
| ~ function(relation_composition(function_inverse(u),u))
| ~ in(skf7(v,relation_composition(function_inverse(u),u)),relation_rng(u))
| ~ equal(relation_dom(relation_composition(function_inverse(u),u)),v)
| equal(relation_composition(function_inverse(u),u),identity_relation(v)) ),
inference(obv,[status(thm),theory(equality)],[636]),
[iquote('0:Obv:636.7')] ).
cnf(646,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ relation(relation_composition(function_inverse(u),u))
| ~ function(relation_composition(function_inverse(u),u))
| ~ in(skf7(v,relation_composition(function_inverse(u),u)),relation_rng(u))
| ~ equal(relation_rng(u),v)
| equal(relation_composition(function_inverse(u),u),identity_relation(v)) ),
inference(rew,[status(thm),theory(equality)],[67,645]),
[iquote('0:Rew:67.3,645.6')] ).
cnf(647,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(u)
| ~ in(skf7(v,relation_composition(function_inverse(u),u)),relation_rng(u))
| ~ equal(relation_rng(u),v)
| equal(relation_composition(function_inverse(u),u),identity_relation(v)) ),
inference(ssi,[status(thm)],[646,54,49,48,64]),
[iquote('0:SSi:646.4,646.3,54.2,49.2,48.4,64.2,49.2,48.2,54.2,49.2,48.4,64.2,49.2,48.2')] ).
cnf(1095,plain,
( ~ relation(relation_composition(function_inverse(skc9),skc9))
| ~ function(relation_composition(function_inverse(skc9),skc9))
| equal(identity_relation(relation_dom(relation_composition(function_inverse(skc9),skc9))),relation_composition(function_inverse(skc9),skc9))
| in(skf7(relation_rng(skc9),u),relation_rng(skc9)) ),
inference(spr,[status(thm),theory(equality)],[133,466]),
[iquote('0:SpR:133.0,466.3')] ).
cnf(1097,plain,
( ~ relation(relation_composition(skc9,function_inverse(skc9)))
| ~ function(relation_composition(skc9,function_inverse(skc9)))
| equal(identity_relation(relation_dom(relation_composition(skc9,function_inverse(skc9)))),relation_composition(skc9,function_inverse(skc9)))
| in(skf7(relation_dom(skc9),u),relation_dom(skc9)) ),
inference(spr,[status(thm),theory(equality)],[131,466]),
[iquote('0:SpR:131.0,466.3')] ).
cnf(1116,plain,
( ~ relation(relation_composition(skc9,function_inverse(skc9)))
| ~ function(relation_composition(skc9,function_inverse(skc9)))
| equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9)))
| in(skf7(relation_dom(skc9),u),relation_dom(skc9)) ),
inference(rew,[status(thm),theory(equality)],[131,1097]),
[iquote('0:Rew:131.0,1097.2')] ).
cnf(1117,plain,
( equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9)))
| in(skf7(relation_dom(skc9),u),relation_dom(skc9)) ),
inference(ssi,[status(thm)],[1116,115,127,126,129]),
[iquote('0:SSi:1116.1,1116.0,115.0,127.0,126.2,129.0,127.0,126.1,115.0,127.0,126.2,129.0,127.0,126.1')] ).
cnf(1118,plain,
( ~ relation(relation_composition(function_inverse(skc9),skc9))
| ~ function(relation_composition(function_inverse(skc9),skc9))
| equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9)))
| in(skf7(relation_rng(skc9),u),relation_rng(skc9)) ),
inference(rew,[status(thm),theory(equality)],[133,1095]),
[iquote('0:Rew:133.0,1095.2')] ).
cnf(1119,plain,
( equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9)))
| in(skf7(relation_rng(skc9),u),relation_rng(skc9)) ),
inference(ssi,[status(thm)],[1118,121,127,126,130]),
[iquote('0:SSi:1118.1,1118.0,121.0,127.0,126.2,130.0,127.0,126.1,121.0,127.0,126.2,130.0,127.0,126.1')] ).
cnf(1452,plain,
equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9))),
inference(spt,[spt(split,[position(s1)])],[1117]),
[iquote('1:Spt:1117.0')] ).
cnf(1455,plain,
( ~ equal(identity_relation(relation_dom(skc9)),identity_relation(relation_dom(skc9)))
| ~ equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))) ),
inference(rew,[status(thm),theory(equality)],[1452,69]),
[iquote('1:Rew:1452.0,69.0')] ).
cnf(1462,plain,
~ equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))),
inference(obv,[status(thm),theory(equality)],[1455]),
[iquote('1:Obv:1455.0')] ).
cnf(1463,plain,
in(skf7(relation_rng(skc9),u),relation_rng(skc9)),
inference(mrr,[status(thm)],[1119,1462]),
[iquote('1:MRR:1119.0,1462.0')] ).
cnf(1498,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ one_to_one(skc9)
| ~ equal(relation_rng(skc9),relation_rng(skc9))
| equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))) ),
inference(res,[status(thm),theory(equality)],[1463,647]),
[iquote('1:Res:1463.0,647.3')] ).
cnf(1499,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ one_to_one(skc9)
| equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))) ),
inference(obv,[status(thm),theory(equality)],[1498]),
[iquote('1:Obv:1498.3')] ).
cnf(1500,plain,
equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))),
inference(ssi,[status(thm)],[1499,3,2,1]),
[iquote('1:SSi:1499.2,1499.1,1499.0,3.0,2.0,1.0,3.0,2.0,1.0,3.0,2.0,1.0')] ).
cnf(1501,plain,
$false,
inference(mrr,[status(thm)],[1500,1462]),
[iquote('1:MRR:1500.0,1462.0')] ).
cnf(1502,plain,
~ equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9))),
inference(spt,[spt(split,[position(sa)])],[1501,1452]),
[iquote('1:Spt:1501.0,1117.0,1452.0')] ).
cnf(1503,plain,
in(skf7(relation_dom(skc9),u),relation_dom(skc9)),
inference(spt,[spt(split,[position(s2)])],[1117]),
[iquote('1:Spt:1501.0,1117.1')] ).
cnf(1509,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ one_to_one(skc9)
| ~ equal(relation_dom(skc9),relation_dom(skc9))
| equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9))) ),
inference(res,[status(thm),theory(equality)],[1503,644]),
[iquote('1:Res:1503.0,644.3')] ).
cnf(1510,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ one_to_one(skc9)
| equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9))) ),
inference(obv,[status(thm),theory(equality)],[1509]),
[iquote('1:Obv:1509.3')] ).
cnf(1511,plain,
equal(relation_composition(skc9,function_inverse(skc9)),identity_relation(relation_dom(skc9))),
inference(ssi,[status(thm)],[1510,3,2,1]),
[iquote('1:SSi:1510.2,1510.1,1510.0,3.0,2.0,1.0,3.0,2.0,1.0,3.0,2.0,1.0')] ).
cnf(1512,plain,
$false,
inference(mrr,[status(thm)],[1511,1502]),
[iquote('1:MRR:1511.0,1502.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Mon Jun 20 09:21:03 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.12/0.48
% 0.12/0.48 SPASS V 3.9
% 0.12/0.48 SPASS beiseite: Proof found.
% 0.12/0.48 % SZS status Theorem
% 0.12/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.48 SPASS derived 1090 clauses, backtracked 12 clauses, performed 1 splits and kept 552 clauses.
% 0.12/0.48 SPASS allocated 98972 KBytes.
% 0.12/0.48 SPASS spent 0:00:00.20 on the problem.
% 0.12/0.48 0:00:00.03 for the input.
% 0.12/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.12/0.48 0:00:00.01 for inferences.
% 0.12/0.48 0:00:00.00 for the backtracking.
% 0.12/0.48 0:00:00.09 for the reduction.
% 0.12/0.48
% 0.12/0.48
% 0.12/0.48 Here is a proof with depth 4, length 57 :
% 0.12/0.48 % SZS output start Refutation
% See solution above
% 0.12/0.49 Formulae used in the proof : t61_funct_1 dt_k2_funct_1 dt_k5_relat_1 fc1_funct_1 t58_funct_1 t59_funct_1 t34_funct_1 t57_funct_1 t56_funct_1
% 0.12/0.49
%------------------------------------------------------------------------------