%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:33:38 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 14 unt; 0 nHn; 29 RR)
% Number of literals : 88 ( 0 equ; 60 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc11),
file('SEU031+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc10),
file('SEU031+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc10),
file('SEU031+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc11),
file('SEU031+1.p',unknown),
[] ).
cnf(5,axiom,
one_to_one(skc10),
file('SEU031+1.p',unknown),
[] ).
cnf(35,axiom,
equal(relation_rng(skc11),relation_dom(skc10)),
file('SEU031+1.p',unknown),
[] ).
cnf(36,axiom,
~ equal(function_inverse(skc10),skc11),
file('SEU031+1.p',unknown),
[] ).
cnf(47,axiom,
equal(relation_composition(skc11,skc10),identity_relation(relation_rng(skc10))),
file('SEU031+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU031+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU031+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU031+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_composition(u,function_inverse(u)),identity_relation(relation_dom(u))) ),
file('SEU031+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ relation(w)
| ~ function(w)
| ~ equal(relation_rng(u),x)
| ~ equal(relation_composition(v,w),identity_relation(x))
| ~ equal(relation_composition(u,v),identity_relation(relation_dom(w)))
| equal(w,u) ),
file('SEU031+1.p',unknown),
[] ).
cnf(75,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(relation_composition(skc10,function_inverse(skc10)),identity_relation(relation_dom(skc10))) ),
inference(res,[status(thm),theory(equality)],[5,71]),
[iquote('0:Res:5.0,71.2')] ).
cnf(77,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)) ),
inference(res,[status(thm),theory(equality)],[5,67]),
[iquote('0:Res:5.0,67.2')] ).
cnf(96,plain,
( ~ relation(skc10)
| relation(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.1')] ).
cnf(97,plain,
( ~ relation(skc10)
| function(function_inverse(skc10)) ),
inference(res,[status(thm),theory(equality)],[3,54]),
[iquote('0:Res:3.0,54.1')] ).
cnf(143,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ function(skc11)
| ~ relation(skc11)
| ~ equal(relation_composition(v,u),identity_relation(relation_dom(skc10)))
| ~ equal(relation_composition(skc11,v),identity_relation(relation_dom(u)))
| equal(u,skc11) ),
inference(res,[status(thm),theory(equality)],[35,73]),
[iquote('0:Res:35.0,73.6')] ).
cnf(146,plain,
relation(function_inverse(skc10)),
inference(mrr,[status(thm)],[96,2]),
[iquote('0:MRR:96.0,2.0')] ).
cnf(147,plain,
function(function_inverse(skc10)),
inference(mrr,[status(thm)],[97,2]),
[iquote('0:MRR:97.0,2.0')] ).
cnf(149,plain,
equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)),
inference(mrr,[status(thm)],[77,2,3]),
[iquote('0:MRR:77.0,77.1,2.0,3.0')] ).
cnf(159,plain,
equal(relation_composition(skc10,function_inverse(skc10)),identity_relation(relation_dom(skc10))),
inference(mrr,[status(thm)],[75,2,3]),
[iquote('0:MRR:75.0,75.1,2.0,3.0')] ).
cnf(165,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ equal(relation_composition(u,v),identity_relation(relation_dom(skc10)))
| ~ equal(relation_composition(skc11,u),identity_relation(relation_dom(v)))
| equal(v,skc11) ),
inference(mrr,[status(thm)],[143,4,1]),
[iquote('0:MRR:143.4,143.5,4.0,1.0')] ).
cnf(993,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ equal(identity_relation(relation_dom(skc10)),identity_relation(relation_dom(skc10)))
| ~ equal(identity_relation(relation_dom(function_inverse(skc10))),relation_composition(skc11,skc10))
| equal(function_inverse(skc10),skc11) ),
inference(spl,[status(thm),theory(equality)],[159,165]),
[iquote('0:SpL:159.0,165.4')] ).
cnf(1029,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ equal(identity_relation(relation_dom(function_inverse(skc10))),relation_composition(skc11,skc10))
| equal(function_inverse(skc10),skc11) ),
inference(obv,[status(thm),theory(equality)],[993]),
[iquote('0:Obv:993.4')] ).
cnf(1030,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| ~ equal(identity_relation(relation_rng(skc10)),identity_relation(relation_rng(skc10)))
| equal(function_inverse(skc10),skc11) ),
inference(rew,[status(thm),theory(equality)],[149,1029,47]),
[iquote('0:Rew:149.0,1029.4,47.0,1029.4')] ).
cnf(1031,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(function_inverse(skc10))
| ~ function(function_inverse(skc10))
| equal(function_inverse(skc10),skc11) ),
inference(obv,[status(thm),theory(equality)],[1030]),
[iquote('0:Obv:1030.4')] ).
cnf(1032,plain,
equal(function_inverse(skc10),skc11),
inference(ssi,[status(thm)],[1031,147,146,5,3,2]),
[iquote('0:SSi:1031.3,1031.2,1031.1,1031.0,147.0,146.0,147.0,146.0,5.0,3.0,2.0,5.0,3.0,2.0')] ).
cnf(1033,plain,
$false,
inference(mrr,[status(thm)],[1032,36]),
[iquote('0:MRR:1032.0,36.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 19:56:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 701 clauses, backtracked 0 clauses, performed 0 splits and kept 332 clauses.
% 0.20/0.53 SPASS allocated 98481 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.53 0:00:00.04 for the input.
% 0.20/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.05 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 2, length 29 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : t64_funct_1 dt_k2_funct_1 t55_funct_1 t61_funct_1 l72_funct_1
% 0.20/0.53
%------------------------------------------------------------------------------