TSTP Solution File: SEU215+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 13.68s 13.92s
% Output : Refutation 13.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 9 unt; 9 nHn; 34 RR)
% Number of literals : 121 ( 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+3.p',unknown),
[] ).
cnf(2,axiom,
relation(skc10),
file('SEU215+3.p',unknown),
[] ).
cnf(3,axiom,
function(skc9),
file('SEU215+3.p',unknown),
[] ).
cnf(4,axiom,
relation(skc9),
file('SEU215+3.p',unknown),
[] ).
cnf(23,axiom,
in(skc11,relation_dom(skc9)),
file('SEU215+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ relation(u)
| ~ relation(v)
| relation(relation_composition(v,u)) ),
file('SEU215+3.p',unknown),
[] ).
cnf(52,axiom,
~ equal(apply(relation_composition(skc9,skc10),skc11),apply(skc10,apply(skc9,skc11))),
file('SEU215+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ relation(u)
| ~ function(u)
| ~ function(v)
| ~ relation(v)
| function(relation_composition(v,u)) ),
file('SEU215+3.p',unknown),
[] ).
cnf(58,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(v,empty_set)
| in(w,relation_dom(u))
| equal(v,apply(u,w)) ),
file('SEU215+3.p',unknown),
[] ).
cnf(63,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+3.p',unknown),
[] ).
cnf(64,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+3.p',unknown),
[] ).
cnf(74,plain,
( ~ function(skc9)
| ~ function(u)
| ~ relation(u)
| function(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[4,56]),
[iquote('0:Res:4.0,56.0')] ).
cnf(75,plain,
( ~ relation(u)
| relation(relation_composition(skc9,u)) ),
inference(res,[status(thm),theory(equality)],[4,47]),
[iquote('0:Res:4.0,47.0')] ).
cnf(87,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)],[3,64]),
[iquote('0:Res:3.0,64.0')] ).
cnf(88,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)],[3,63]),
[iquote('0:Res:3.0,63.0')] ).
cnf(132,plain,
( ~ function(u)
| ~ relation(u)
| ~ relation(skc10)
| ~ in(v,relation_dom(relation_composition(u,skc10)))
| equal(apply(relation_composition(u,skc10),v),apply(skc10,apply(u,v))) ),
inference(res,[status(thm),theory(equality)],[1,63]),
[iquote('0:Res:1.0,63.2')] ).
cnf(136,plain,
( ~ relation(u)
| ~ function(u)
| function(relation_composition(skc9,u)) ),
inference(mrr,[status(thm)],[74,3]),
[iquote('0:MRR:74.0,3.0')] ).
cnf(156,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(relation_composition(u,skc10)))
| equal(apply(relation_composition(u,skc10),v),apply(skc10,apply(u,v))) ),
inference(mrr,[status(thm)],[132,2]),
[iquote('0:MRR:132.2,2.0')] ).
cnf(162,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)],[88,4]),
[iquote('0:MRR:88.0,4.0')] ).
cnf(163,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)],[87,4]),
[iquote('0:MRR:87.0,4.0')] ).
cnf(406,plain,
( ~ function(u)
| ~ relation(u)
| in(v,relation_dom(u))
| equal(apply(u,v),empty_set) ),
inference(eqr,[status(thm),theory(equality)],[58]),
[iquote('0:EqR:58.2')] ).
cnf(1469,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)],[406,163]),
[iquote('0:Res:406.2,163.3')] ).
cnf(1471,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)],[1469]),
[iquote('0:Obv:1469.1')] ).
cnf(1505,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)],[406,162]),
[iquote('0:Res:406.2,162.2')] ).
cnf(1510,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)],[1505,75,136]),
[iquote('0:SSi:1505.1,1505.0,75.2,136.1,75.2,136.1')] ).
cnf(3816,plain,
( ~ relation(skc10)
| ~ function(skc10)
| ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,u)),empty_set)
| equal(apply(relation_composition(skc9,skc10),u),apply(skc10,apply(skc9,u))) ),
inference(res,[status(thm),theory(equality)],[1471,156]),
[iquote('0:Res:1471.4,156.2')] ).
cnf(3827,plain,
( ~ in(u,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,u)),empty_set)
| equal(apply(relation_composition(skc9,skc10),u),apply(skc10,apply(skc9,u))) ),
inference(ssi,[status(thm)],[3816,3,4,1,2]),
[iquote('0:SSi:3816.3,3816.2,3816.1,3816.0,3.0,4.0,3.0,4.0,1.0,2.0,1.0,2.0')] ).
cnf(3910,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)],[1510,52]),
[iquote('0:SpL:1510.3,52.0')] ).
cnf(3915,plain,
( ~ relation(skc10)
| ~ function(skc10)
| equal(apply(relation_composition(skc9,skc10),skc11),empty_set) ),
inference(obv,[status(thm),theory(equality)],[3910]),
[iquote('0:Obv:3910.2')] ).
cnf(3916,plain,
equal(apply(relation_composition(skc9,skc10),skc11),empty_set),
inference(ssi,[status(thm)],[3915,1,2]),
[iquote('0:SSi:3915.1,3915.0,1.0,2.0,1.0,2.0')] ).
cnf(3917,plain,
~ equal(apply(skc10,apply(skc9,skc11)),empty_set),
inference(rew,[status(thm),theory(equality)],[3916,52]),
[iquote('0:Rew:3916.0,52.0')] ).
cnf(11971,plain,
( ~ 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)],[3827,3916]),
[iquote('0:SpR:3827.2,3916.0')] ).
cnf(11991,plain,
( ~ in(skc11,relation_dom(skc9))
| equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
inference(obv,[status(thm),theory(equality)],[11971]),
[iquote('0:Obv:11971.1')] ).
cnf(11992,plain,
$false,
inference(mrr,[status(thm)],[11991,23,3917]),
[iquote('0:MRR:11991.0,11991.1,23.0,3917.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n017.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 : Sun Jun 19 10:03:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 13.68/13.92
% 13.68/13.92 SPASS V 3.9
% 13.68/13.92 SPASS beiseite: Proof found.
% 13.68/13.92 % SZS status Theorem
% 13.68/13.92 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.68/13.92 SPASS derived 9131 clauses, backtracked 0 clauses, performed 2 splits and kept 4738 clauses.
% 13.68/13.92 SPASS allocated 116102 KBytes.
% 13.68/13.92 SPASS spent 0:0:12.92 on the problem.
% 13.68/13.92 0:00:00.04 for the input.
% 13.68/13.92 0:00:00.03 for the FLOTTER CNF translation.
% 13.68/13.92 0:00:00.15 for inferences.
% 13.68/13.92 0:00:00.02 for the backtracking.
% 13.68/13.92 0:0:12.57 for the reduction.
% 13.68/13.92
% 13.68/13.92
% 13.68/13.92 Here is a proof with depth 4, length 34 :
% 13.68/13.92 % SZS output start Refutation
% See solution above
% 13.68/13.92 Formulae used in the proof : t23_funct_1 dt_k5_relat_1 fc1_funct_1 d4_funct_1 t22_funct_1 t21_funct_1
% 13.68/13.92
%------------------------------------------------------------------------------