TSTP Solution File: SEU215+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU215+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 14:35:05 EDT 2022
% Result : Theorem 29.79s 29.95s
% Output : Refutation 29.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 9 unt; 9 nHn; 33 RR)
% Number of literals : 120 ( 0 equ; 80 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
function(skc10),
file('SEU215+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc10),
file('SEU215+1.p',unknown),
[] ).
cnf(3,axiom,
function(skc9),
file('SEU215+1.p',unknown),
[] ).
cnf(4,axiom,
relation(skc9),
file('SEU215+1.p',unknown),
[] ).
cnf(21,axiom,
in(skc11,relation_dom(skc9)),
file('SEU215+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU215+1.p',unknown),
[] ).
cnf(44,axiom,
~ equal(apply(relation_composition(skc9,skc10),skc11),apply(skc10,apply(skc9,skc11))),
file('SEU215+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU215+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(v,empty_set)
| in(w,relation_dom(u))
| equal(v,apply(u,w)) ),
file('SEU215+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(relation_composition(v,u)))
| equal(apply(relation_composition(v,u),w),apply(u,apply(v,w))) ),
file('SEU215+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(v))
| ~ in(apply(v,w),relation_dom(u))
| in(w,relation_dom(relation_composition(v,u))) ),
file('SEU215+1.p',unknown),
[] ).
cnf(64,plain,
( ~ function(skc9)
| ~ function(u)
| ~ relation(u)
| function(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[4,46]),
[iquote('0:Res:4.0,46.0')] ).
cnf(65,plain,
( ~ relation(u)
| relation(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[4,39]),
[iquote('0:Res:4.0,39.0')] ).
cnf(77,plain,
( ~ relation(skc9)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(skc9))
| ~ in(apply(skc9,v),relation_dom(u))
| in(v,relation_dom(relation_composition(skc9,u))) ),
inference(res,[status(thm),theory(equality)],[3,54]),
[iquote('0:Res:3.0,54.0')] ).
cnf(78,plain,
( ~ relation(skc9)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.0')] ).
cnf(112,plain,
( ~ relation(u)
| ~ function(u)
| function(relation_composition(skc9,u)) ),
inference(mrr,[status(thm)],[64,3]),
[iquote('0:MRR:64.0,3.0')] ).
cnf(138,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(mrr,[status(thm)],[78,4]),
[iquote('0:MRR:78.0,4.0')] ).
cnf(139,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| ~ in(apply(skc9,v),relation_dom(u))
| in(v,relation_dom(relation_composition(skc9,u))) ),
inference(mrr,[status(thm)],[77,4]),
[iquote('0:MRR:77.0,4.0')] ).
cnf(334,plain,
( ~ function(u)
| ~ relation(u)
| in(v,relation_dom(u))
| equal(apply(u,v),empty_set) ),
inference(eqr,[status(thm),theory(equality)],[48]),
[iquote('0:EqR:48.2')] ).
cnf(1222,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| equal(apply(u,apply(skc9,v)),empty_set)
| in(v,relation_dom(relation_composition(skc9,u))) ),
inference(res,[status(thm),theory(equality)],[334,139]),
[iquote('0:Res:334.2,139.3')] ).
cnf(1228,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| equal(apply(u,apply(skc9,v)),empty_set)
| in(v,relation_dom(relation_composition(skc9,u))) ),
inference(obv,[status(thm),theory(equality)],[1222]),
[iquote('0:Obv:1222.1')] ).
cnf(1335,plain,
( ~ function(relation_composition(skc9,u))
| ~ relation(relation_composition(skc9,u))
| ~ relation(u)
| ~ function(u)
| equal(apply(relation_composition(skc9,u),v),empty_set)
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(res,[status(thm),theory(equality)],[334,138]),
[iquote('0:Res:334.2,138.2')] ).
cnf(1347,plain,
( ~ relation(u)
| ~ function(u)
| equal(apply(relation_composition(skc9,u),v),empty_set)
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(ssi,[status(thm)],[1335,65,112]),
[iquote('0:SSi:1335.1,1335.0,65.2,112.1,65.2,112.1')] ).
cnf(3852,plain,
( ~ relation(u)
| ~ function(u)
| ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| equal(apply(u,apply(skc9,v)),empty_set)
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(res,[status(thm),theory(equality)],[1228,138]),
[iquote('0:Res:1228.4,138.2')] ).
cnf(3879,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(skc9))
| equal(apply(u,apply(skc9,v)),empty_set)
| equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
inference(obv,[status(thm),theory(equality)],[3852]),
[iquote('0:Obv:3852.1')] ).
cnf(4039,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ equal(apply(skc10,apply(skc9,skc11)),apply(skc10,apply(skc9,skc11)))
| equal(apply(relation_composition(skc9,skc10),skc11),empty_set) ),
inference(spl,[status(thm),theory(equality)],[1347,44]),
[iquote('0:SpL:1347.3,44.0')] ).
cnf(4045,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(apply(relation_composition(skc9,skc10),skc11),empty_set) ),
inference(obv,[status(thm),theory(equality)],[4039]),
[iquote('0:Obv:4039.2')] ).
cnf(4046,plain,
equal(apply(relation_composition(skc9,skc10),skc11),empty_set),
inference(ssi,[status(thm)],[4045,1,2]),
[iquote('0:SSi:4045.1,4045.0,1.0,2.0,1.0,2.0')] ).
cnf(4047,plain,
~ equal(apply(skc10,apply(skc9,skc11)),empty_set),
inference(rew,[status(thm),theory(equality)],[4046,44]),
[iquote('0:Rew:4046.0,44.0')] ).
cnf(31520,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(skc11,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,skc11)),empty_set)
| equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
inference(spr,[status(thm),theory(equality)],[3879,4046]),
[iquote('0:SpR:3879.4,4046.0')] ).
cnf(31555,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ in(skc11,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
inference(obv,[status(thm),theory(equality)],[31520]),
[iquote('0:Obv:31520.3')] ).
cnf(31556,plain,
( ~ in(skc11,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
inference(ssi,[status(thm)],[31555,1,2]),
[iquote('0:SSi:31555.1,31555.0,1.0,2.0,1.0,2.0')] ).
cnf(31557,plain,
$false,
inference(mrr,[status(thm)],[31556,21,4047]),
[iquote('0:MRR:31556.0,31556.1,21.0,4047.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU215+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : Mon Jun 20 07:44:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.79/29.95
% 29.79/29.95 SPASS V 3.9
% 29.79/29.95 SPASS beiseite: Proof found.
% 29.79/29.95 % SZS status Theorem
% 29.79/29.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.79/29.95 SPASS derived 21587 clauses, backtracked 0 clauses, performed 15 splits and kept 5184 clauses.
% 29.79/29.95 SPASS allocated 139655 KBytes.
% 29.79/29.95 SPASS spent 0:0:25.69 on the problem.
% 29.79/29.95 0:00:00.03 for the input.
% 29.79/29.95 0:00:00.03 for the FLOTTER CNF translation.
% 29.79/29.95 0:00:00.34 for inferences.
% 29.79/29.95 0:00:01.06 for the backtracking.
% 29.79/29.95 0:0:24.05 for the reduction.
% 29.79/29.95
% 29.79/29.95
% 29.79/29.95 Here is a proof with depth 4, length 33 :
% 29.79/29.95 % SZS output start Refutation
% See solution above
% 29.79/29.95 Formulae used in the proof : t23_funct_1 dt_k5_relat_1 fc1_funct_1 d4_funct_1 t22_funct_1 t21_funct_1
% 29.79/29.95
%------------------------------------------------------------------------------