TSTP Solution File: SEU081+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU081+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:33:52 EDT 2022
% Result : Theorem 14.14s 14.36s
% Output : Refutation 14.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of clauses : 73 ( 29 unt; 15 nHn; 73 RR)
% Number of literals : 146 ( 0 equ; 66 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
empty(empty_set),
file('SEU081+1.p',unknown),
[] ).
cnf(22,axiom,
relation(identity_relation(u)),
file('SEU081+1.p',unknown),
[] ).
cnf(23,axiom,
function(identity_relation(u)),
file('SEU081+1.p',unknown),
[] ).
cnf(25,axiom,
empty(skf10(u)),
file('SEU081+1.p',unknown),
[] ).
cnf(28,axiom,
element(skc11,powerset(skc10)),
file('SEU081+1.p',unknown),
[] ).
cnf(29,axiom,
element(skf8(u),u),
file('SEU081+1.p',unknown),
[] ).
cnf(33,axiom,
element(skf9(u),powerset(u)),
file('SEU081+1.p',unknown),
[] ).
cnf(34,axiom,
element(skf10(u),powerset(u)),
file('SEU081+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ empty(skf9(u))
| empty(u) ),
file('SEU081+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU081+1.p',unknown),
[] ).
cnf(39,axiom,
~ equal(relation_image(identity_relation(skc10),skc11),skc11),
file('SEU081+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU081+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ skP0(u,v,w)
| in(skf7(v,x,y),v) ),
file('SEU081+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| element(u,w) ),
file('SEU081+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU081+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ skP0(u,v,w)
| equal(apply(w,skf7(v,w,u)),u) ),
file('SEU081+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(skf6(u,v,w),w)
| ~ skP0(skf6(u,v,w),v,u) ),
file('SEU081+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ relation(u)
| ~ function(u)
| ~ equal(u,identity_relation(v))
| equal(relation_dom(u),v) ),
file('SEU081+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ in(u,v)
| ~ in(u,relation_dom(w))
| ~ equal(x,apply(w,u))
| skP0(x,v,w) ),
file('SEU081+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ relation(u)
| ~ function(u)
| ~ in(v,w)
| ~ equal(u,identity_relation(w))
| equal(apply(u,v),v) ),
file('SEU081+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_image(u,w))
| in(skf6(u,w,v),v)
| skP0(skf6(u,w,v),w,u) ),
file('SEU081+1.p',unknown),
[] ).
cnf(64,plain,
( ~ empty(skc10)
| ~ in(u,skc11) ),
inference(res,[status(thm),theory(equality)],[28,52]),
[iquote('0:Res:28.0,52.1')] ).
cnf(66,plain,
( ~ in(u,skc11)
| element(u,skc10) ),
inference(res,[status(thm),theory(equality)],[28,51]),
[iquote('0:Res:28.0,51.1')] ).
cnf(70,plain,
( ~ relation(identity_relation(skc10))
| ~ function(identity_relation(skc10))
| in(skf6(identity_relation(skc10),skc11,skc11),skc11)
| skP0(skf6(identity_relation(skc10),skc11,skc11),skc11,identity_relation(skc10)) ),
inference(res,[status(thm),theory(equality)],[61,39]),
[iquote('0:Res:61.4,39.0')] ).
cnf(72,plain,
( in(skf6(identity_relation(skc10),skc11,skc11),skc11)
| skP0(skf6(identity_relation(skc10),skc11,skc11),skc11,identity_relation(skc10)) ),
inference(mrr,[status(thm)],[70,22,23]),
[iquote('0:MRR:70.0,70.1,22.0,23.0')] ).
cnf(73,plain,
equal(skf10(u),empty_set),
inference(ems,[status(thm)],[38,25]),
[iquote('0:EmS:38.0,25.0')] ).
cnf(85,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[73,34]),
[iquote('0:Rew:73.0,34.0')] ).
cnf(108,plain,
( empty(u)
| in(skf8(u),u) ),
inference(res,[status(thm),theory(equality)],[29,46]),
[iquote('0:Res:29.0,46.0')] ).
cnf(109,plain,
( ~ in(u,skc11)
| empty(skc10)
| in(u,skc10) ),
inference(res,[status(thm),theory(equality)],[66,46]),
[iquote('0:Res:66.1,46.0')] ).
cnf(114,plain,
( ~ in(u,skc11)
| in(u,skc10) ),
inference(mrr,[status(thm)],[109,64]),
[iquote('0:MRR:109.1,64.0')] ).
cnf(127,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[85,52]),
[iquote('0:Res:85.0,52.2')] ).
cnf(135,plain,
( ~ in(u,skf9(v))
| element(u,v) ),
inference(res,[status(thm),theory(equality)],[33,51]),
[iquote('0:Res:33.0,51.1')] ).
cnf(140,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[127,5]),
[iquote('0:EmS:127.0,5.0')] ).
cnf(163,plain,
( empty(skf9(u))
| element(skf8(skf9(u)),u) ),
inference(res,[status(thm),theory(equality)],[108,135]),
[iquote('0:Res:108.1,135.0')] ).
cnf(168,plain,
( empty(skf9(u))
| empty(u)
| in(skf8(skf9(u)),u) ),
inference(res,[status(thm),theory(equality)],[163,46]),
[iquote('0:Res:163.1,46.0')] ).
cnf(171,plain,
( empty(u)
| in(skf8(skf9(u)),u) ),
inference(mrr,[status(thm)],[168,37]),
[iquote('0:MRR:168.0,37.0')] ).
cnf(174,plain,
( empty(skc11)
| in(skf8(skf9(skc11)),skc10) ),
inference(res,[status(thm),theory(equality)],[171,114]),
[iquote('0:Res:171.1,114.0')] ).
cnf(181,plain,
empty(skc11),
inference(spt,[spt(split,[position(s1)])],[174]),
[iquote('1:Spt:174.0')] ).
cnf(184,plain,
equal(skc11,empty_set),
inference(ems,[status(thm)],[38,181]),
[iquote('1:EmS:38.0,181.0')] ).
cnf(195,plain,
( in(skf6(identity_relation(skc10),empty_set,empty_set),empty_set)
| skP0(skf6(identity_relation(skc10),skc11,skc11),skc11,identity_relation(skc10)) ),
inference(rew,[status(thm),theory(equality)],[184,72]),
[iquote('1:Rew:184.0,72.0')] ).
cnf(198,plain,
( in(skf6(identity_relation(skc10),empty_set,empty_set),empty_set)
| skP0(skf6(identity_relation(skc10),empty_set,empty_set),empty_set,identity_relation(skc10)) ),
inference(rew,[status(thm),theory(equality)],[184,195]),
[iquote('1:Rew:184.0,195.1')] ).
cnf(199,plain,
skP0(skf6(identity_relation(skc10),empty_set,empty_set),empty_set,identity_relation(skc10)),
inference(mrr,[status(thm)],[198,140]),
[iquote('1:MRR:198.0,140.0')] ).
cnf(203,plain,
in(skf7(empty_set,u,v),empty_set),
inference(res,[status(thm),theory(equality)],[199,49]),
[iquote('1:Res:199.0,49.0')] ).
cnf(204,plain,
$false,
inference(mrr,[status(thm)],[203,140]),
[iquote('1:MRR:203.0,140.0')] ).
cnf(205,plain,
~ empty(skc11),
inference(spt,[spt(split,[position(sa)])],[204,181]),
[iquote('1:Spt:204.0,174.0,181.0')] ).
cnf(206,plain,
in(skf8(skf9(skc11)),skc10),
inference(spt,[spt(split,[position(s2)])],[174]),
[iquote('1:Spt:204.0,174.1')] ).
cnf(223,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| equal(relation_dom(identity_relation(u)),u) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.2')] ).
cnf(224,plain,
equal(relation_dom(identity_relation(u)),u),
inference(ssi,[status(thm)],[223,23,22]),
[iquote('0:SSi:223.1,223.0,23.0,22.0,23.0,22.0')] ).
cnf(248,plain,
( ~ in(u,v)
| ~ in(u,relation_dom(w))
| skP0(apply(w,u),v,w) ),
inference(eqr,[status(thm),theory(equality)],[56]),
[iquote('0:EqR:56.2')] ).
cnf(279,plain,
( ~ relation(identity_relation(u))
| ~ function(identity_relation(u))
| ~ in(v,u)
| equal(apply(identity_relation(u),v),v) ),
inference(eqr,[status(thm),theory(equality)],[58]),
[iquote('0:EqR:58.3')] ).
cnf(281,plain,
( ~ in(u,v)
| equal(apply(identity_relation(v),u),u) ),
inference(ssi,[status(thm)],[279,23,22]),
[iquote('0:SSi:279.1,279.0,23.0,22.0,23.0,22.0')] ).
cnf(357,plain,
( ~ in(skf7(u,identity_relation(v),w),v)
| ~ skP0(w,u,identity_relation(v))
| equal(skf7(u,identity_relation(v),w),w) ),
inference(spr,[status(thm),theory(equality)],[281,53]),
[iquote('0:SpR:281.1,53.1')] ).
cnf(461,plain,
( ~ in(u,v)
| ~ in(u,w)
| ~ in(u,relation_dom(identity_relation(v)))
| skP0(u,w,identity_relation(v)) ),
inference(spr,[status(thm),theory(equality)],[281,248]),
[iquote('0:SpR:281.1,248.2')] ).
cnf(464,plain,
( ~ in(u,v)
| ~ in(u,w)
| ~ in(u,v)
| skP0(u,w,identity_relation(v)) ),
inference(rew,[status(thm),theory(equality)],[224,461]),
[iquote('0:Rew:224.0,461.2')] ).
cnf(465,plain,
( ~ in(u,v)
| ~ in(u,w)
| skP0(u,v,identity_relation(w)) ),
inference(obv,[status(thm),theory(equality)],[464]),
[iquote('0:Obv:464.0')] ).
cnf(508,plain,
( in(skf6(identity_relation(skc10),skc11,skc11),skc11)
| in(skf7(skc11,u,v),skc11) ),
inference(res,[status(thm),theory(equality)],[72,49]),
[iquote('0:Res:72.1,49.0')] ).
cnf(853,plain,
in(skf6(identity_relation(skc10),skc11,skc11),skc11),
inference(spt,[spt(split,[position(s2s1)])],[508]),
[iquote('2:Spt:508.0')] ).
cnf(859,plain,
in(skf6(identity_relation(skc10),skc11,skc11),skc10),
inference(res,[status(thm),theory(equality)],[853,114]),
[iquote('2:Res:853.0,114.0')] ).
cnf(869,plain,
( ~ in(u,v)
| ~ in(u,w)
| in(skf7(v,x,y),v) ),
inference(res,[status(thm),theory(equality)],[465,49]),
[iquote('0:Res:465.2,49.0')] ).
cnf(870,plain,
( ~ in(skf6(identity_relation(u),v,w),v)
| ~ in(skf6(identity_relation(u),v,w),u)
| ~ in(skf6(identity_relation(u),v,w),w) ),
inference(res,[status(thm),theory(equality)],[465,54]),
[iquote('0:Res:465.2,54.1')] ).
cnf(871,plain,
( ~ in(u,v)
| in(skf7(v,w,x),v) ),
inference(con,[status(thm)],[869]),
[iquote('0:Con:869.1')] ).
cnf(1126,plain,
( empty(u)
| in(skf7(u,v,w),u) ),
inference(res,[status(thm),theory(equality)],[108,871]),
[iquote('0:Res:108.1,871.0')] ).
cnf(1216,plain,
( empty(skc11)
| in(skf7(skc11,u,v),skc10) ),
inference(res,[status(thm),theory(equality)],[1126,114]),
[iquote('0:Res:1126.1,114.0')] ).
cnf(12369,plain,
( ~ in(skf6(identity_relation(skc10),skc11,skc11),skc10)
| ~ in(skf6(identity_relation(skc10),skc11,skc11),skc11) ),
inference(res,[status(thm),theory(equality)],[853,870]),
[iquote('2:Res:853.0,870.0')] ).
cnf(12390,plain,
$false,
inference(mrr,[status(thm)],[12369,859,853]),
[iquote('2:MRR:12369.0,12369.1,859.0,853.0')] ).
cnf(12401,plain,
~ in(skf6(identity_relation(skc10),skc11,skc11),skc11),
inference(spt,[spt(split,[position(s2sa)])],[12390,853]),
[iquote('2:Spt:12390.0,508.0,853.0')] ).
cnf(12402,plain,
in(skf7(skc11,u,v),skc11),
inference(spt,[spt(split,[position(s2s2)])],[508]),
[iquote('2:Spt:12390.0,508.1')] ).
cnf(12403,plain,
in(skf7(skc11,u,v),skc10),
inference(mrr,[status(thm)],[1216,205]),
[iquote('1:MRR:1216.0,205.0')] ).
cnf(12425,plain,
skP0(skf6(identity_relation(skc10),skc11,skc11),skc11,identity_relation(skc10)),
inference(mrr,[status(thm)],[72,12401]),
[iquote('2:MRR:72.0,12401.0')] ).
cnf(12482,plain,
( ~ skP0(u,skc11,identity_relation(skc10))
| equal(skf7(skc11,identity_relation(skc10),u),u) ),
inference(res,[status(thm),theory(equality)],[12403,357]),
[iquote('1:Res:12403.0,357.0')] ).
cnf(15690,plain,
( ~ skP0(u,skc11,identity_relation(skc10))
| in(u,skc11) ),
inference(spr,[status(thm),theory(equality)],[12482,12402]),
[iquote('2:SpR:12482.1,12402.0')] ).
cnf(15929,plain,
in(skf6(identity_relation(skc10),skc11,skc11),skc11),
inference(res,[status(thm),theory(equality)],[12425,15690]),
[iquote('2:Res:12425.0,15690.0')] ).
cnf(15931,plain,
$false,
inference(mrr,[status(thm)],[15929,12401]),
[iquote('2:MRR:15929.0,12401.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU081+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 06:03:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 14.14/14.36
% 14.14/14.36 SPASS V 3.9
% 14.14/14.36 SPASS beiseite: Proof found.
% 14.14/14.36 % SZS status Theorem
% 14.14/14.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.14/14.36 SPASS derived 12506 clauses, backtracked 221 clauses, performed 9 splits and kept 6106 clauses.
% 14.14/14.36 SPASS allocated 112779 KBytes.
% 14.14/14.36 SPASS spent 0:0:13.59 on the problem.
% 14.14/14.36 0:00:00.04 for the input.
% 14.14/14.36 0:00:00.04 for the FLOTTER CNF translation.
% 14.14/14.36 0:00:00.23 for inferences.
% 14.14/14.36 0:00:00.32 for the backtracking.
% 14.14/14.36 0:0:12.84 for the reduction.
% 14.14/14.36
% 14.14/14.36
% 14.14/14.36 Here is a proof with depth 8, length 73 :
% 14.14/14.36 % SZS output start Refutation
% See solution above
% 14.14/14.36 Formulae used in the proof : fc4_relat_1 fc2_funct_1 rc2_subset_1 t162_funct_1 existence_m1_subset_1 rc1_subset_1 t6_boole t2_subset d12_funct_1 antisymmetry_r2_hidden t4_subset t5_subset t34_funct_1
% 14.14/14.36
%------------------------------------------------------------------------------