TSTP Solution File: SEU026+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU026+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 14:33:36 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 11 unt; 0 nHn; 30 RR)
% Number of literals : 66 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU026+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU026+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU026+1.p',unknown),
[] ).
cnf(27,axiom,
subset(u,u),
file('SEU026+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ equal(relation_rng(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9))
| ~ equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ subset(relation_rng(v),relation_dom(u))
| equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ subset(relation_dom(v),relation_rng(u))
| equal(relation_rng(relation_composition(u,v)),relation_rng(v)) ),
file('SEU026+1.p',unknown),
[] ).
cnf(67,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,59]),
[iquote('0:Res:3.0,59.2')] ).
cnf(68,plain,
( ~ relation(skc9)
| ~ function(skc9)
| equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[3,60]),
[iquote('0:Res:3.0,60.2')] ).
cnf(72,plain,
( ~ relation(skc9)
| relation(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,45]),
[iquote('0:Res:2.0,45.1')] ).
cnf(73,plain,
( ~ relation(skc9)
| function(function_inverse(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,46]),
[iquote('0:Res:2.0,46.1')] ).
cnf(76,plain,
( ~ relation(u)
| ~ subset(relation_dom(skc9),relation_rng(u))
| equal(relation_rng(relation_composition(u,skc9)),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[1,65]),
[iquote('0:Res:1.0,65.0')] ).
cnf(85,plain,
( ~ relation(u)
| ~ subset(relation_rng(u),relation_dom(skc9))
| equal(relation_dom(relation_composition(u,skc9)),relation_dom(u)) ),
inference(res,[status(thm),theory(equality)],[1,64]),
[iquote('0:Res:1.0,64.1')] ).
cnf(93,plain,
relation(function_inverse(skc9)),
inference(mrr,[status(thm)],[72,1]),
[iquote('0:MRR:72.0,1.0')] ).
cnf(94,plain,
function(function_inverse(skc9)),
inference(mrr,[status(thm)],[73,1]),
[iquote('0:MRR:73.0,1.0')] ).
cnf(95,plain,
equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)),
inference(mrr,[status(thm)],[67,1,2]),
[iquote('0:MRR:67.0,67.1,1.0,2.0')] ).
cnf(96,plain,
equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)),
inference(mrr,[status(thm)],[68,1,2]),
[iquote('0:MRR:68.0,68.1,1.0,2.0')] ).
cnf(710,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_dom(skc9),relation_dom(skc9))
| equal(relation_rng(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(spl,[status(thm),theory(equality)],[96,76]),
[iquote('0:SpL:96.0,76.1')] ).
cnf(716,plain,
( ~ subset(relation_dom(skc9),relation_dom(skc9))
| equal(relation_rng(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(ssi,[status(thm)],[710,94,93]),
[iquote('0:SSi:710.0,94.0,93.0')] ).
cnf(717,plain,
equal(relation_rng(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)),
inference(mrr,[status(thm)],[716,27]),
[iquote('0:MRR:716.0,27.0')] ).
cnf(718,plain,
( ~ equal(relation_rng(skc9),relation_rng(skc9))
| ~ equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(rew,[status(thm),theory(equality)],[717,63]),
[iquote('0:Rew:717.0,63.0')] ).
cnf(719,plain,
~ equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)),
inference(obv,[status(thm),theory(equality)],[718]),
[iquote('0:Obv:718.0')] ).
cnf(817,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_dom(skc9),relation_dom(skc9))
| equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_dom(function_inverse(skc9))) ),
inference(spl,[status(thm),theory(equality)],[96,85]),
[iquote('0:SpL:96.0,85.1')] ).
cnf(827,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_dom(skc9),relation_dom(skc9))
| equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(rew,[status(thm),theory(equality)],[95,817]),
[iquote('0:Rew:95.0,817.2')] ).
cnf(828,plain,
( ~ subset(relation_dom(skc9),relation_dom(skc9))
| equal(relation_dom(relation_composition(function_inverse(skc9),skc9)),relation_rng(skc9)) ),
inference(ssi,[status(thm)],[827,94,93]),
[iquote('0:SSi:827.0,94.0,93.0')] ).
cnf(829,plain,
$false,
inference(mrr,[status(thm)],[828,27,719]),
[iquote('0:MRR:828.0,828.1,27.0,719.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU026+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 09:27:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 572 clauses, backtracked 0 clauses, performed 0 splits and kept 286 clauses.
% 0.21/0.50 SPASS allocated 98240 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.50 0:00:00.04 for the input.
% 0.21/0.50 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.03 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 2, length 30 :
% 0.21/0.50 % SZS output start Refutation
% See solution above
% 0.21/0.50 Formulae used in the proof : t59_funct_1 reflexivity_r1_tarski dt_k2_funct_1 t55_funct_1 t46_relat_1 t47_relat_1
% 0.21/0.50
%------------------------------------------------------------------------------