%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : 10
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 8 unt; 0 nHn; 21 RR)
% Number of literals : 81 ( 0 equ; 61 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(22,axiom,
relation(identity_relation(u)),
file('SEU034+1.p',unknown),
[] ).
cnf(23,axiom,
function(identity_relation(u)),
file('SEU034+1.p',unknown),
[] ).
cnf(28,axiom,
one_to_one(identity_relation(u)),
file('SEU034+1.p',unknown),
[] ).
cnf(35,axiom,
equal(relation_dom(identity_relation(u)),u),
file('SEU034+1.p',unknown),
[] ).
cnf(36,axiom,
equal(relation_rng(identity_relation(u)),u),
file('SEU034+1.p',unknown),
[] ).
cnf(43,axiom,
~ equal(function_inverse(identity_relation(skc9)),identity_relation(skc9)),
file('SEU034+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ function(u)
| ~ relation(u)
| relation(function_inverse(u)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ function(u)
| ~ relation(u)
| function(function_inverse(u)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
file('SEU034+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| equal(relation_composition(u,function_inverse(u)),identity_relation(relation_dom(u))) ),
file('SEU034+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ function(u)
| ~ relation(u)
| ~ function(v)
| ~ relation(v)
| ~ equal(relation_rng(v),relation_dom(u))
| ~ equal(relation_composition(v,u),v)
| equal(identity_relation(relation_dom(u)),u) ),
file('SEU034+1.p',unknown),
[] ).
cnf(323,plain,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| ~ function(function_inverse(u))
| ~ relation(function_inverse(u))
| ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(function_inverse(u)),relation_rng(u))
| ~ equal(identity_relation(relation_dom(u)),u)
| equal(identity_relation(relation_dom(function_inverse(u))),function_inverse(u)) ),
inference(spl,[status(thm),theory(equality)],[67,69]),
[iquote('0:SpL:67.3,69.5')] ).
cnf(328,plain,
( ~ one_to_one(u)
| ~ function(function_inverse(u))
| ~ relation(function_inverse(u))
| ~ function(u)
| ~ relation(u)
| ~ equal(relation_dom(function_inverse(u)),relation_rng(u))
| ~ equal(identity_relation(relation_dom(u)),u)
| equal(identity_relation(relation_dom(function_inverse(u))),function_inverse(u)) ),
inference(obv,[status(thm),theory(equality)],[323]),
[iquote('0:Obv:323.2')] ).
cnf(329,plain,
( ~ one_to_one(u)
| ~ function(function_inverse(u))
| ~ relation(function_inverse(u))
| ~ function(u)
| ~ relation(u)
| ~ equal(relation_rng(u),relation_rng(u))
| ~ equal(identity_relation(relation_dom(u)),u)
| equal(identity_relation(relation_rng(u)),function_inverse(u)) ),
inference(rew,[status(thm),theory(equality)],[63,328]),
[iquote('0:Rew:63.3,328.7,63.3,328.5')] ).
cnf(330,plain,
( ~ one_to_one(u)
| ~ function(function_inverse(u))
| ~ relation(function_inverse(u))
| ~ function(u)
| ~ relation(u)
| ~ equal(identity_relation(relation_dom(u)),u)
| equal(identity_relation(relation_rng(u)),function_inverse(u)) ),
inference(obv,[status(thm),theory(equality)],[329]),
[iquote('0:Obv:329.5')] ).
cnf(331,plain,
( ~ one_to_one(u)
| ~ function(u)
| ~ relation(u)
| ~ equal(identity_relation(relation_dom(u)),u)
| equal(identity_relation(relation_rng(u)),function_inverse(u)) ),
inference(ssi,[status(thm)],[330,50,49]),
[iquote('0:SSi:330.2,330.1,50.2,49.2,50.2,49.2')] ).
cnf(651,plain,
( ~ one_to_one(identity_relation(u))
| ~ function(identity_relation(u))
| ~ relation(identity_relation(u))
| ~ equal(identity_relation(relation_dom(identity_relation(u))),identity_relation(u))
| equal(function_inverse(identity_relation(u)),identity_relation(u)) ),
inference(spr,[status(thm),theory(equality)],[36,331]),
[iquote('0:SpR:36.0,331.4')] ).
cnf(662,plain,
( ~ one_to_one(identity_relation(u))
| ~ function(identity_relation(u))
| ~ relation(identity_relation(u))
| ~ equal(identity_relation(u),identity_relation(u))
| equal(function_inverse(identity_relation(u)),identity_relation(u)) ),
inference(rew,[status(thm),theory(equality)],[35,651]),
[iquote('0:Rew:35.0,651.3')] ).
cnf(663,plain,
( ~ one_to_one(identity_relation(u))
| ~ function(identity_relation(u))
| ~ relation(identity_relation(u))
| equal(function_inverse(identity_relation(u)),identity_relation(u)) ),
inference(obv,[status(thm),theory(equality)],[662]),
[iquote('0:Obv:662.3')] ).
cnf(664,plain,
equal(function_inverse(identity_relation(u)),identity_relation(u)),
inference(ssi,[status(thm)],[663,28,23,22]),
[iquote('0:SSi:663.2,663.1,663.0,28.0,23.0,22.0,28.0,23.0,22.0,28.0,23.0,22.0')] ).
cnf(665,plain,
$false,
inference(unc,[status(thm)],[664,43]),
[iquote('0:UnC:664.0,43.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 03:17:33 EDT 2022
% 0.13/0.33 % 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 462 clauses, backtracked 0 clauses, performed 0 splits and kept 246 clauses.
% 0.20/0.48 SPASS allocated 98109 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.48 0:00:00.04 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 0:00:00.04 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 2, length 21 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : fc2_funct_1 t52_funct_1 t71_relat_1 t67_funct_1 dt_k2_funct_1 t55_funct_1 t61_funct_1 t44_funct_1
% 0.20/0.48
%------------------------------------------------------------------------------