TSTP Solution File: SEU014+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU014+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 14:33:33 EDT 2022
% Result : Theorem 2.83s 3.00s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 41 ( 13 unt; 6 nHn; 41 RR)
% Number of literals : 139 ( 0 equ; 94 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU014+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc8),
file('SEU014+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc8),
file('SEU014+1.p',unknown),
[] ).
cnf(4,axiom,
function(skc9),
file('SEU014+1.p',unknown),
[] ).
cnf(19,axiom,
~ one_to_one(skc9),
file('SEU014+1.p',unknown),
[] ).
cnf(24,axiom,
one_to_one(relation_composition(skc9,skc8)),
file('SEU014+1.p',unknown),
[] ).
cnf(27,axiom,
subset(relation_rng(skc9),relation_dom(skc8)),
file('SEU014+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU014+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf6(u),relation_dom(u)) ),
file('SEU014+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf5(u),relation_dom(u)) ),
file('SEU014+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf6(u),skf5(u))
| one_to_one(u) ),
file('SEU014+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU014+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| equal(apply(u,skf6(u)),apply(u,skf5(u))) ),
file('SEU014+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ relation(u)
| ~ relation(v)
| ~ subset(relation_rng(v),relation_dom(u))
| equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
file('SEU014+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(u))
| equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
file('SEU014+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| ~ one_to_one(u)
| ~ in(v,relation_dom(u))
| ~ in(w,relation_dom(u))
| ~ equal(apply(u,v),apply(u,w))
| equal(v,w) ),
file('SEU014+1.p',unknown),
[] ).
cnf(65,plain,
( ~ relation(skc9)
| equal(apply(skc9,skf6(skc9)),apply(skc9,skf5(skc9)))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[4,59]),
[iquote('0:Res:4.0,59.1')] ).
cnf(67,plain,
( ~ relation(skc9)
| ~ equal(skf6(skc9),skf5(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[4,56]),
[iquote('0:Res:4.0,56.1')] ).
cnf(68,plain,
( ~ relation(skc9)
| in(skf6(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[4,54]),
[iquote('0:Res:4.0,54.1')] ).
cnf(69,plain,
( ~ relation(skc9)
| in(skf5(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[4,55]),
[iquote('0:Res:4.0,55.1')] ).
cnf(102,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)],[1,60]),
[iquote('0:Res:1.0,60.0')] ).
cnf(108,plain,
( ~ relation(u)
| relation(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[1,47]),
[iquote('0:Res:1.0,47.0')] ).
cnf(111,plain,
( ~ function(u)
| ~ relation(u)
| ~ function(skc9)
| ~ in(v,relation_dom(skc9))
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(res,[status(thm),theory(equality)],[1,61]),
[iquote('0:Res:1.0,61.3')] ).
cnf(123,plain,
in(skf6(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[68,1,19]),
[iquote('0:MRR:68.0,68.2,1.0,19.0')] ).
cnf(124,plain,
in(skf5(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[69,1,19]),
[iquote('0:MRR:69.0,69.2,1.0,19.0')] ).
cnf(127,plain,
~ equal(skf6(skc9),skf5(skc9)),
inference(mrr,[status(thm)],[67,1,19]),
[iquote('0:MRR:67.0,67.2,1.0,19.0')] ).
cnf(133,plain,
equal(apply(skc9,skf6(skc9)),apply(skc9,skf5(skc9))),
inference(mrr,[status(thm)],[65,1,19]),
[iquote('0:MRR:65.0,65.2,1.0,19.0')] ).
cnf(135,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(mrr,[status(thm)],[111,4]),
[iquote('0:MRR:111.2,4.0')] ).
cnf(739,plain,
( ~ relation(skc8)
| equal(relation_dom(relation_composition(skc9,skc8)),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[27,102]),
[iquote('0:Res:27.0,102.1')] ).
cnf(923,plain,
( ~ relation(u)
| ~ function(u)
| ~ function(relation_composition(skc9,u))
| ~ relation(relation_composition(skc9,u))
| ~ one_to_one(relation_composition(skc9,u))
| ~ in(v,relation_dom(skc9))
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| ~ in(w,relation_dom(relation_composition(skc9,u)))
| ~ equal(apply(u,apply(skc9,v)),apply(relation_composition(skc9,u),w))
| equal(v,w) ),
inference(spl,[status(thm),theory(equality)],[135,62]),
[iquote('0:SpL:135.3,62.5')] ).
cnf(926,plain,
( ~ relation(u)
| ~ function(u)
| ~ one_to_one(relation_composition(skc9,u))
| ~ in(v,relation_dom(skc9))
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| ~ in(w,relation_dom(relation_composition(skc9,u)))
| ~ equal(apply(u,apply(skc9,v)),apply(relation_composition(skc9,u),w))
| equal(v,w) ),
inference(ssi,[status(thm)],[923,58,4,1,108]),
[iquote('0:SSi:923.3,923.2,58.1,4.0,1.0,108.4,58.1,4.0,1.0,108.4')] ).
cnf(1937,plain,
( ~ relation(skc8)
| ~ function(skc8)
| ~ in(u,relation_dom(skc9))
| ~ in(u,relation_dom(relation_composition(skc9,skc8)))
| ~ in(v,relation_dom(relation_composition(skc9,skc8)))
| ~ equal(apply(skc8,apply(skc9,u)),apply(relation_composition(skc9,skc8),v))
| equal(u,v) ),
inference(sor,[status(thm)],[926,24]),
[iquote('0:SoR:926.2,24.0')] ).
cnf(2737,plain,
equal(relation_dom(relation_composition(skc9,skc8)),relation_dom(skc9)),
inference(ssi,[status(thm)],[739,3,2]),
[iquote('0:SSi:739.0,3.0,2.0')] ).
cnf(2741,plain,
( ~ relation(skc8)
| ~ function(skc8)
| ~ in(u,relation_dom(skc9))
| ~ in(u,relation_dom(skc9))
| ~ in(v,relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(relation_composition(skc9,skc8),v))
| equal(u,v) ),
inference(rew,[status(thm),theory(equality)],[2737,1937]),
[iquote('0:Rew:2737.0,1937.4,2737.0,1937.3')] ).
cnf(2742,plain,
( ~ relation(skc8)
| ~ function(skc8)
| ~ in(u,relation_dom(skc9))
| ~ in(v,relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(relation_composition(skc9,skc8),v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[2741]),
[iquote('0:Obv:2741.2')] ).
cnf(2743,plain,
( ~ relation(skc8)
| ~ function(skc8)
| ~ in(u,relation_dom(skc9))
| ~ in(v,relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(skc8,apply(skc9,v)))
| equal(u,v) ),
inference(rew,[status(thm),theory(equality)],[135,2742]),
[iquote('0:Rew:135.3,2742.4')] ).
cnf(2744,plain,
( ~ in(u,relation_dom(skc9))
| ~ in(v,relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(skc8,apply(skc9,v)))
| equal(u,v) ),
inference(ssi,[status(thm)],[2743,3,2]),
[iquote('0:SSi:2743.1,2743.0,3.0,2.0,3.0,2.0')] ).
cnf(3274,plain,
( ~ in(u,relation_dom(skc9))
| ~ in(skf6(skc9),relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(skc8,apply(skc9,skf5(skc9))))
| equal(u,skf6(skc9)) ),
inference(spl,[status(thm),theory(equality)],[133,2744]),
[iquote('0:SpL:133.0,2744.2')] ).
cnf(3291,plain,
( ~ in(u,relation_dom(skc9))
| ~ equal(apply(skc8,apply(skc9,u)),apply(skc8,apply(skc9,skf5(skc9))))
| equal(u,skf6(skc9)) ),
inference(mrr,[status(thm)],[3274,123]),
[iquote('0:MRR:3274.1,123.0')] ).
cnf(6990,plain,
( ~ in(skf5(skc9),relation_dom(skc9))
| equal(skf6(skc9),skf5(skc9)) ),
inference(eqr,[status(thm),theory(equality)],[3291]),
[iquote('0:EqR:3291.1')] ).
cnf(7034,plain,
$false,
inference(mrr,[status(thm)],[6990,124,127]),
[iquote('0:MRR:6990.0,6990.1,124.0,127.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU014+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 00:25:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.83/3.00
% 2.83/3.00 SPASS V 3.9
% 2.83/3.00 SPASS beiseite: Proof found.
% 2.83/3.00 % SZS status Theorem
% 2.83/3.00 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.83/3.00 SPASS derived 4690 clauses, backtracked 33 clauses, performed 9 splits and kept 1822 clauses.
% 2.83/3.00 SPASS allocated 109054 KBytes.
% 2.83/3.00 SPASS spent 0:00:02.41 on the problem.
% 2.83/3.00 0:00:00.04 for the input.
% 2.83/3.00 0:00:00.04 for the FLOTTER CNF translation.
% 2.83/3.00 0:00:00.12 for inferences.
% 2.83/3.00 0:00:00.01 for the backtracking.
% 2.83/3.00 0:00:02.16 for the reduction.
% 2.83/3.00
% 2.83/3.00
% 2.83/3.00 Here is a proof with depth 5, length 41 :
% 2.83/3.00 % SZS output start Refutation
% See solution above
% 2.83/3.00 Formulae used in the proof : t47_funct_1 dt_k5_relat_1 d8_funct_1 fc1_funct_1 t46_relat_1 t23_funct_1
% 2.83/3.00
%------------------------------------------------------------------------------