TSTP Solution File: SEU025+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 0.34s 0.53s
% Output : Refutation 0.34s
% 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('SEU025+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU025+1.p',unknown),
[] ).
cnf(3,axiom,
one_to_one(skc9),
file('SEU025+1.p',unknown),
[] ).
cnf(27,axiom,
subset(u,u),
file('SEU025+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU025+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU025+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU025+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
file('SEU025+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9))
| ~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
file('SEU025+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('SEU025+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('SEU025+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(75,plain,
( ~ relation(u)
| ~ subset(relation_rng(skc9),relation_dom(u))
| equal(relation_dom(relation_composition(skc9,u)),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[1,64]),
[iquote('0:Res:1.0,64.0')] ).
cnf(86,plain,
( ~ relation(u)
| ~ subset(relation_dom(u),relation_rng(skc9))
| equal(relation_rng(relation_composition(skc9,u)),relation_rng(u)) ),
inference(res,[status(thm),theory(equality)],[1,65]),
[iquote('0:Res:1.0,65.1')] ).
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(665,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_rng(skc9),relation_rng(skc9))
| equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(spl,[status(thm),theory(equality)],[95,75]),
[iquote('0:SpL:95.0,75.1')] ).
cnf(671,plain,
( ~ subset(relation_rng(skc9),relation_rng(skc9))
| equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(ssi,[status(thm)],[665,94,93]),
[iquote('0:SSi:665.0,94.0,93.0')] ).
cnf(672,plain,
equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)),
inference(mrr,[status(thm)],[671,27]),
[iquote('0:MRR:671.0,27.0')] ).
cnf(673,plain,
( ~ equal(relation_dom(skc9),relation_dom(skc9))
| ~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(rew,[status(thm),theory(equality)],[672,63]),
[iquote('0:Rew:672.0,63.0')] ).
cnf(674,plain,
~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)),
inference(obv,[status(thm),theory(equality)],[673]),
[iquote('0:Obv:673.0')] ).
cnf(741,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_rng(skc9),relation_rng(skc9))
| equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_rng(function_inverse(skc9))) ),
inference(spl,[status(thm),theory(equality)],[95,86]),
[iquote('0:SpL:95.0,86.1')] ).
cnf(750,plain,
( ~ relation(function_inverse(skc9))
| ~ subset(relation_rng(skc9),relation_rng(skc9))
| equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(rew,[status(thm),theory(equality)],[96,741]),
[iquote('0:Rew:96.0,741.2')] ).
cnf(751,plain,
( ~ subset(relation_rng(skc9),relation_rng(skc9))
| equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
inference(ssi,[status(thm)],[750,94,93]),
[iquote('0:SSi:750.0,94.0,93.0')] ).
cnf(752,plain,
$false,
inference(mrr,[status(thm)],[751,27,674]),
[iquote('0:MRR:751.0,751.1,27.0,674.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.36 % Computer : n003.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Sun Jun 19 16:05:59 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.34/0.53
% 0.34/0.53 SPASS V 3.9
% 0.34/0.53 SPASS beiseite: Proof found.
% 0.34/0.53 % SZS status Theorem
% 0.34/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/0.53 SPASS derived 523 clauses, backtracked 0 clauses, performed 0 splits and kept 271 clauses.
% 0.34/0.53 SPASS allocated 98180 KBytes.
% 0.34/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.34/0.53 0:00:00.03 for the input.
% 0.34/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.34/0.53 0:00:00.01 for inferences.
% 0.34/0.53 0:00:00.00 for the backtracking.
% 0.34/0.53 0:00:00.05 for the reduction.
% 0.34/0.53
% 0.34/0.53
% 0.34/0.53 Here is a proof with depth 2, length 30 :
% 0.34/0.53 % SZS output start Refutation
% See solution above
% 0.34/0.53 Formulae used in the proof : t58_funct_1 reflexivity_r1_tarski dt_k2_funct_1 t55_funct_1 t46_relat_1 t47_relat_1
% 0.34/0.53
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