TSTP Solution File: SEU009+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:33:32 EDT 2022
% Result : Theorem 0.48s 0.65s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 14 unt; 2 nHn; 33 RR)
% Number of literals : 90 ( 0 equ; 60 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU009+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU009+1.p',unknown),
[] ).
cnf(18,axiom,
relation(identity_relation(u)),
file('SEU009+1.p',unknown),
[] ).
cnf(19,axiom,
function(identity_relation(u)),
file('SEU009+1.p',unknown),
[] ).
cnf(47,axiom,
( in(skc10,relation_dom(skc9))
| in(skc10,relation_dom(relation_composition(skc9,identity_relation(skc11)))) ),
file('SEU009+1.p',unknown),
[] ).
cnf(48,axiom,
( in(skc10,relation_dom(relation_composition(skc9,identity_relation(skc11))))
| in(apply(skc9,skc10),skc11) ),
file('SEU009+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,identity_relation(v))
| equal(relation_dom(u),v) ),
file('SEU009+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(skc10,relation_dom(skc9))
| ~ in(skc10,relation_dom(relation_composition(skc9,identity_relation(skc11))))
| ~ in(apply(skc9,skc10),skc11) ),
file('SEU009+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(relation_composition(v,u)))
| in(w,relation_dom(v)) ),
file('SEU009+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ relation(u)
| ~ function(u)
| ~ relation(v)
| ~ function(v)
| ~ in(w,relation_dom(relation_composition(v,u)))
| in(apply(v,w),relation_dom(u)) ),
file('SEU009+1.p',unknown),
[] ).
cnf(60,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('SEU009+1.p',unknown),
[] ).
cnf(73,plain,
( ~ function(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)],[1,60]),
[iquote('0:Res:1.0,60.1')] ).
cnf(74,plain,
( ~ function(skc9)
| ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| in(apply(skc9,v),relation_dom(u)) ),
inference(res,[status(thm),theory(equality)],[1,59]),
[iquote('0:Res:1.0,59.1')] ).
cnf(101,plain,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(relation_composition(skc9,u)))
| in(apply(skc9,v),relation_dom(u)) ),
inference(mrr,[status(thm)],[74,2]),
[iquote('0:MRR:74.0,2.0')] ).
cnf(103,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)],[73,2]),
[iquote('0:MRR:73.0,2.0')] ).
cnf(126,plain,
in(skc10,relation_dom(relation_composition(skc9,identity_relation(skc11)))),
inference(spt,[spt(split,[position(s1)])],[47]),
[iquote('1:Spt:47.1')] ).
cnf(127,plain,
( ~ in(skc10,relation_dom(skc9))
| ~ in(apply(skc9,skc10),skc11) ),
inference(mrr,[status(thm)],[54,126]),
[iquote('1:MRR:54.1,126.0')] ).
cnf(269,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| equal(relation_dom(identity_relation(u)),u) ),
inference(eqr,[status(thm),theory(equality)],[51]),
[iquote('0:EqR:51.2')] ).
cnf(270,plain,
equal(relation_dom(identity_relation(u)),u),
inference(ssi,[status(thm)],[269,19,18]),
[iquote('0:SSi:269.1,269.0,19.0,18.0,19.0,18.0')] ).
cnf(350,plain,
( ~ relation(identity_relation(skc11))
| ~ function(identity_relation(skc11))
| ~ relation(skc9)
| ~ function(skc9)
| in(skc10,relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[126,57]),
[iquote('1:Res:126.0,57.4')] ).
cnf(353,plain,
in(skc10,relation_dom(skc9)),
inference(ssi,[status(thm)],[350,2,1,19,18]),
[iquote('1:SSi:350.3,350.2,350.1,350.0,2.0,1.0,2.0,1.0,19.0,18.0,19.0,18.0')] ).
cnf(354,plain,
~ in(apply(skc9,skc10),skc11),
inference(mrr,[status(thm)],[127,353]),
[iquote('1:MRR:127.0,353.0')] ).
cnf(868,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| ~ in(v,relation_dom(relation_composition(skc9,identity_relation(u))))
| in(apply(skc9,v),u) ),
inference(spr,[status(thm),theory(equality)],[270,101]),
[iquote('0:SpR:270.0,101.3')] ).
cnf(879,plain,
( ~ in(u,relation_dom(relation_composition(skc9,identity_relation(v))))
| in(apply(skc9,u),v) ),
inference(ssi,[status(thm)],[868,19,18]),
[iquote('0:SSi:868.1,868.0,19.0,18.0,19.0,18.0')] ).
cnf(1016,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| ~ in(v,relation_dom(skc9))
| ~ in(apply(skc9,v),u)
| in(v,relation_dom(relation_composition(skc9,identity_relation(u)))) ),
inference(spl,[status(thm),theory(equality)],[270,103]),
[iquote('0:SpL:270.0,103.3')] ).
cnf(1021,plain,
( ~ in(u,relation_dom(skc9))
| ~ in(apply(skc9,u),v)
| in(u,relation_dom(relation_composition(skc9,identity_relation(v)))) ),
inference(ssi,[status(thm)],[1016,19,18]),
[iquote('0:SSi:1016.1,1016.0,19.0,18.0,19.0,18.0')] ).
cnf(1251,plain,
in(apply(skc9,skc10),skc11),
inference(res,[status(thm),theory(equality)],[126,879]),
[iquote('1:Res:126.0,879.0')] ).
cnf(1263,plain,
$false,
inference(mrr,[status(thm)],[1251,354]),
[iquote('1:MRR:1251.0,354.0')] ).
cnf(1272,plain,
~ in(skc10,relation_dom(relation_composition(skc9,identity_relation(skc11)))),
inference(spt,[spt(split,[position(sa)])],[1263,126]),
[iquote('1:Spt:1263.0,47.1,126.0')] ).
cnf(1273,plain,
in(skc10,relation_dom(skc9)),
inference(spt,[spt(split,[position(s2)])],[47]),
[iquote('1:Spt:1263.0,47.0')] ).
cnf(1279,plain,
in(apply(skc9,skc10),skc11),
inference(mrr,[status(thm)],[48,879]),
[iquote('0:MRR:48.0,879.0')] ).
cnf(1772,plain,
( ~ in(skc10,relation_dom(skc9))
| ~ in(apply(skc9,skc10),skc11) ),
inference(res,[status(thm),theory(equality)],[1021,1272]),
[iquote('1:Res:1021.2,1272.0')] ).
cnf(1779,plain,
$false,
inference(mrr,[status(thm)],[1772,1273,1279]),
[iquote('1:MRR:1772.0,1772.1,1273.0,1279.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 05:59:29 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.48/0.65
% 0.48/0.65 SPASS V 3.9
% 0.48/0.65 SPASS beiseite: Proof found.
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.65 SPASS derived 1346 clauses, backtracked 59 clauses, performed 3 splits and kept 674 clauses.
% 0.48/0.65 SPASS allocated 99241 KBytes.
% 0.48/0.65 SPASS spent 0:00:00.26 on the problem.
% 0.48/0.65 0:00:00.04 for the input.
% 0.48/0.65 0:00:00.03 for the FLOTTER CNF translation.
% 0.48/0.65 0:00:00.02 for inferences.
% 0.48/0.65 0:00:00.00 for the backtracking.
% 0.48/0.65 0:00:00.14 for the reduction.
% 0.48/0.65
% 0.48/0.65
% 0.48/0.65 Here is a proof with depth 3, length 33 :
% 0.48/0.65 % SZS output start Refutation
% See solution above
% 0.48/0.65 Formulae used in the proof : t40_funct_1 fc2_funct_1 t34_funct_1 t21_funct_1
% 0.48/0.65
%------------------------------------------------------------------------------