TSTP Solution File: SEU032+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:33:39 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 28 ( 12 unt; 0 nHn; 28 RR)
% Number of literals : 80 ( 0 equ; 53 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU032+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU032+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU032+1.p',unknown),
[] ).
cnf(37,axiom,
~ equal(function_inverse(function_inverse(skc9)),skc9),
file('SEU032+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| one_to_one(function_inverse(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_composition(function_inverse(u),u),identity_relation(relation_rng(u))) ),
file('SEU032+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ one_to_one(u)
| ~ function(v)
| ~ relation(v)
| ~ function(u)
| ~ relation(u)
| ~ equal(relation_rng(u),relation_dom(v))
| ~ equal(relation_composition(u,v),identity_relation(relation_dom(u)))
| equal(v,function_inverse(u)) ),
file('SEU032+1.p',unknown),
[] ).
cnf(74,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))) ),
inference(res,[status(thm),theory(equality)],[3,69]),
[iquote('0:Res:3.0,69.2')] ).
cnf(75,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,64]),
[iquote('0:Res:3.0,64.2')] ).
cnf(76,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,65]),
[iquote('0:Res:3.0,65.2')] ).
cnf(77,plain,
( ~ relation(skc9)
| ~ function(skc9)
| one_to_one(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,63]),
[iquote('0:Res:3.0,63.2')] ).
cnf(85,plain,
( ~ relation(skc9)
| relation(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.1')] ).
cnf(86,plain,
( ~ relation(skc9)
| function(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,50]),
[iquote('0:Res:2.0,50.1')] ).
cnf(111,plain,
relation(function_inverse(skc9)),
inference(mrr,[status(thm)],[85,1]),
[iquote('0:MRR:85.0,1.0')] ).
cnf(112,plain,
function(function_inverse(skc9)),
inference(mrr,[status(thm)],[86,1]),
[iquote('0:MRR:86.0,1.0')] ).
cnf(113,plain,
one_to_one(function_inverse(skc9)),
inference(mrr,[status(thm)],[77,1,2]),
[iquote('0:MRR:77.0,77.1,1.0,2.0')] ).
cnf(114,plain,
equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)),
inference(mrr,[status(thm)],[75,1,2]),
[iquote('0:MRR:75.0,75.1,1.0,2.0')] ).
cnf(115,plain,
equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)),
inference(mrr,[status(thm)],[76,1,2]),
[iquote('0:MRR:76.0,76.1,1.0,2.0')] ).
cnf(119,plain,
equal(relation_composition(function_inverse(skc9),skc9),identity_relation(relation_rng(skc9))),
inference(mrr,[status(thm)],[74,1,2]),
[iquote('0:MRR:74.0,74.1,1.0,2.0')] ).
cnf(498,plain,
( ~ one_to_one(function_inverse(skc9))
| ~ function(skc9)
| ~ relation(skc9)
| ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(relation_rng(function_inverse(skc9)),relation_dom(skc9))
| ~ equal(identity_relation(relation_dom(function_inverse(skc9))),identity_relation(relation_rng(skc9)))
| equal(function_inverse(function_inverse(skc9)),skc9) ),
inference(spl,[status(thm),theory(equality)],[119,70]),
[iquote('0:SpL:119.0,70.6')] ).
cnf(515,plain,
( ~ one_to_one(function_inverse(skc9))
| ~ function(skc9)
| ~ relation(skc9)
| ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| ~ equal(relation_dom(skc9),relation_dom(skc9))
| ~ equal(identity_relation(relation_rng(skc9)),identity_relation(relation_rng(skc9)))
| equal(function_inverse(function_inverse(skc9)),skc9) ),
inference(rew,[status(thm),theory(equality)],[114,498,115]),
[iquote('0:Rew:114.0,498.6,115.0,498.5')] ).
cnf(516,plain,
( ~ one_to_one(function_inverse(skc9))
| ~ function(skc9)
| ~ relation(skc9)
| ~ function(function_inverse(skc9))
| ~ relation(function_inverse(skc9))
| equal(function_inverse(function_inverse(skc9)),skc9) ),
inference(obv,[status(thm),theory(equality)],[515]),
[iquote('0:Obv:515.6')] ).
cnf(517,plain,
equal(function_inverse(function_inverse(skc9)),skc9),
inference(ssi,[status(thm)],[516,113,112,111,3,2,1]),
[iquote('0:SSi:516.4,516.3,516.2,516.1,516.0,113.0,112.0,111.0,113.0,112.0,111.0,3.0,2.0,1.0,3.0,2.0,1.0,113.0,112.0,111.0')] ).
cnf(518,plain,
$false,
inference(mrr,[status(thm)],[517,37]),
[iquote('0:MRR:517.0,37.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.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 18:52:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 342 clauses, backtracked 0 clauses, performed 0 splits and kept 188 clauses.
% 0.20/0.48 SPASS allocated 98002 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.02 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 2, length 28 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : t65_funct_1 dt_k2_funct_1 t62_funct_1 t55_funct_1 t61_funct_1 t63_funct_1
% 0.20/0.48
%------------------------------------------------------------------------------