TSTP Solution File: SEU291+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU291+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:35:54 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of clauses : 112 ( 60 unt; 13 nHn; 112 RR)
% Number of literals : 188 ( 0 equ; 77 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
function(skc14),
file('SEU291+1.p',unknown),
[] ).
cnf(4,axiom,
relation_empty_yielding(empty_set),
file('SEU291+1.p',unknown),
[] ).
cnf(6,axiom,
empty(empty_set),
file('SEU291+1.p',unknown),
[] ).
cnf(7,axiom,
relation(empty_set),
file('SEU291+1.p',unknown),
[] ).
cnf(11,axiom,
function(skc19),
file('SEU291+1.p',unknown),
[] ).
cnf(12,axiom,
one_to_one(skc19),
file('SEU291+1.p',unknown),
[] ).
cnf(13,axiom,
empty(skc19),
file('SEU291+1.p',unknown),
[] ).
cnf(29,axiom,
subset(skc16,skc15),
file('SEU291+1.p',unknown),
[] ).
cnf(31,axiom,
empty(skf13(u)),
file('SEU291+1.p',unknown),
[] ).
cnf(34,axiom,
quasi_total(skc14,skc17,skc16),
file('SEU291+1.p',unknown),
[] ).
cnf(35,axiom,
relation_of2_as_subset(skc14,skc17,skc16),
file('SEU291+1.p',unknown),
[] ).
cnf(36,axiom,
element(skf8(u),u),
file('SEU291+1.p',unknown),
[] ).
cnf(38,axiom,
relation(skf10(u,v)),
file('SEU291+1.p',unknown),
[] ).
cnf(39,axiom,
function(skf10(u,v)),
file('SEU291+1.p',unknown),
[] ).
cnf(44,axiom,
element(skf11(u),powerset(u)),
file('SEU291+1.p',unknown),
[] ).
cnf(45,axiom,
element(skf13(u),powerset(u)),
file('SEU291+1.p',unknown),
[] ).
cnf(46,axiom,
( skP0(u,v)
| equal(v,empty_set) ),
file('SEU291+1.p',unknown),
[] ).
cnf(51,axiom,
relation_of2(skf10(u,v),v,u),
file('SEU291+1.p',unknown),
[] ).
cnf(52,axiom,
quasi_total(skf10(u,v),v,u),
file('SEU291+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ empty(skf11(u))
| empty(u) ),
file('SEU291+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU291+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ equal(skc16,empty_set)
| equal(skc17,empty_set) ),
file('SEU291+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
file('SEU291+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ element(u,powerset(v))
| subset(u,v) ),
file('SEU291+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU291+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ element(u,powerset(cartesian_product2(v,w)))
| relation(u) ),
file('SEU291+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ relation(u)
| ~ empty(relation_dom(u))
| empty(u) ),
file('SEU291+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU291+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU291+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation_of2_as_subset(u,v,w)
| element(u,powerset(cartesian_product2(v,w))) ),
file('SEU291+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ relation_of2(u,v,w)
| element(relation_dom_as_subset(v,w,u),powerset(v)) ),
file('SEU291+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ relation_of2(u,v,w)
| equal(relation_dom_as_subset(v,w,u),relation_dom(u)) ),
file('SEU291+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| element(u,w) ),
file('SEU291+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU291+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ function(skc14)
| ~ quasi_total(skc14,skc17,skc15)
| ~ relation_of2_as_subset(skc14,skc17,skc15) ),
file('SEU291+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ subset(u,v)
| ~ relation_of2_as_subset(w,x,u)
| relation_of2_as_subset(w,x,v) ),
file('SEU291+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ skP0(u,v)
| ~ equal(relation_dom_as_subset(u,v,w),u)
| ~ relation_of2_as_subset(w,u,v)
| quasi_total(w,u,v) ),
file('SEU291+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ skP0(u,v)
| ~ relation_of2_as_subset(w,u,v)
| ~ quasi_total(w,u,v)
| equal(relation_dom_as_subset(u,v,w),u) ),
file('SEU291+1.p',unknown),
[] ).
cnf(84,plain,
( ~ relation_of2(u,v,w)
| element(relation_dom(u),powerset(v)) ),
inference(rew,[status(thm),theory(equality)],[74,73]),
[iquote('0:Rew:74.1,73.1')] ).
cnf(85,plain,
( ~ quasi_total(skc14,skc17,skc15)
| ~ relation_of2_as_subset(skc14,skc17,skc15) ),
inference(mrr,[status(thm)],[77,1]),
[iquote('0:MRR:77.0,1.0')] ).
cnf(86,plain,
element(skc16,powerset(skc15)),
inference(res,[status(thm),theory(equality)],[29,63]),
[iquote('0:Res:29.0,63.0')] ).
cnf(88,plain,
( ~ quasi_total(skc14,skc17,skc16)
| ~ skP0(skc17,skc16)
| equal(relation_dom_as_subset(skc17,skc16,skc14),skc17) ),
inference(res,[status(thm),theory(equality)],[35,82]),
[iquote('0:Res:35.0,82.2')] ).
cnf(90,plain,
( ~ subset(skc16,u)
| relation_of2_as_subset(skc14,skc17,u) ),
inference(res,[status(thm),theory(equality)],[35,78]),
[iquote('0:Res:35.0,78.0')] ).
cnf(91,plain,
element(skc14,powerset(cartesian_product2(skc17,skc16))),
inference(res,[status(thm),theory(equality)],[35,72]),
[iquote('0:Res:35.0,72.0')] ).
cnf(92,plain,
relation_of2(skc14,skc17,skc16),
inference(res,[status(thm),theory(equality)],[35,67]),
[iquote('0:Res:35.0,67.0')] ).
cnf(97,plain,
( ~ skP0(skc17,skc16)
| equal(relation_dom_as_subset(skc17,skc16,skc14),skc17) ),
inference(mrr,[status(thm)],[88,34]),
[iquote('0:MRR:88.0,34.0')] ).
cnf(98,plain,
relation_of2_as_subset(skc14,skc17,skc15),
inference(res,[status(thm),theory(equality)],[29,90]),
[iquote('0:Res:29.0,90.0')] ).
cnf(100,plain,
~ quasi_total(skc14,skc17,skc15),
inference(mrr,[status(thm)],[85,98]),
[iquote('0:MRR:85.1,98.0')] ).
cnf(101,plain,
equal(skc17,empty_set),
inference(spt,[spt(split,[position(s1)])],[56]),
[iquote('1:Spt:56.1')] ).
cnf(102,plain,
relation_of2(skc14,empty_set,skc16),
inference(rew,[status(thm),theory(equality)],[101,92]),
[iquote('1:Rew:101.0,92.0')] ).
cnf(106,plain,
~ quasi_total(skc14,empty_set,skc15),
inference(rew,[status(thm),theory(equality)],[101,100]),
[iquote('1:Rew:101.0,100.0')] ).
cnf(107,plain,
element(skc14,powerset(cartesian_product2(empty_set,skc16))),
inference(rew,[status(thm),theory(equality)],[101,91]),
[iquote('1:Rew:101.0,91.0')] ).
cnf(112,plain,
equal(skf13(u),empty_set),
inference(ems,[status(thm)],[55,31]),
[iquote('0:EmS:55.0,31.0')] ).
cnf(114,plain,
equal(skc19,empty_set),
inference(ems,[status(thm)],[55,13]),
[iquote('0:EmS:55.0,13.0')] ).
cnf(118,plain,
one_to_one(empty_set),
inference(rew,[status(thm),theory(equality)],[114,12]),
[iquote('0:Rew:114.0,12.0')] ).
cnf(119,plain,
function(empty_set),
inference(rew,[status(thm),theory(equality)],[114,11]),
[iquote('0:Rew:114.0,11.0')] ).
cnf(129,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[112,45]),
[iquote('0:Rew:112.0,45.0')] ).
cnf(161,plain,
relation(skc14),
inference(res,[status(thm),theory(equality)],[107,64]),
[iquote('1:Res:107.0,64.0')] ).
cnf(170,plain,
( empty(u)
| in(skf8(u),u) ),
inference(res,[status(thm),theory(equality)],[36,69]),
[iquote('0:Res:36.0,69.0')] ).
cnf(200,plain,
element(relation_dom(skc14),powerset(empty_set)),
inference(res,[status(thm),theory(equality)],[102,84]),
[iquote('1:Res:102.0,84.0')] ).
cnf(202,plain,
element(relation_dom(skf10(u,v)),powerset(v)),
inference(res,[status(thm),theory(equality)],[51,84]),
[iquote('0:Res:51.0,84.0')] ).
cnf(206,plain,
subset(relation_dom(skc14),empty_set),
inference(res,[status(thm),theory(equality)],[200,62]),
[iquote('1:Res:200.0,62.0')] ).
cnf(210,plain,
equal(relation_dom(skc14),empty_set),
inference(res,[status(thm),theory(equality)],[206,59]),
[iquote('1:Res:206.0,59.0')] ).
cnf(216,plain,
( ~ relation(skc14)
| ~ empty(empty_set)
| empty(skc14) ),
inference(spl,[status(thm),theory(equality)],[210,66]),
[iquote('1:SpL:210.0,66.1')] ).
cnf(217,plain,
( ~ empty(empty_set)
| empty(skc14) ),
inference(ssi,[status(thm)],[216,1,161]),
[iquote('1:SSi:216.0,1.0,161.0')] ).
cnf(218,plain,
empty(skc14),
inference(mrr,[status(thm)],[217,6]),
[iquote('1:MRR:217.0,6.0')] ).
cnf(220,plain,
equal(skc14,empty_set),
inference(ems,[status(thm)],[55,218]),
[iquote('1:EmS:55.0,218.0')] ).
cnf(227,plain,
~ quasi_total(empty_set,empty_set,skc15),
inference(rew,[status(thm),theory(equality)],[220,106]),
[iquote('1:Rew:220.0,106.0')] ).
cnf(281,plain,
( ~ empty(skc15)
| ~ in(u,skc16) ),
inference(res,[status(thm),theory(equality)],[86,76]),
[iquote('0:Res:86.0,76.2')] ).
cnf(283,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[129,76]),
[iquote('0:Res:129.0,76.2')] ).
cnf(292,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[283,6]),
[iquote('0:EmS:283.0,6.0')] ).
cnf(293,plain,
( ~ in(u,skc16)
| element(u,skc15) ),
inference(res,[status(thm),theory(equality)],[86,75]),
[iquote('0:Res:86.0,75.1')] ).
cnf(294,plain,
( ~ in(u,skf11(v))
| element(u,v) ),
inference(res,[status(thm),theory(equality)],[44,75]),
[iquote('0:Res:44.0,75.1')] ).
cnf(302,plain,
( ~ in(u,skc16)
| empty(skc15)
| in(u,skc15) ),
inference(res,[status(thm),theory(equality)],[293,69]),
[iquote('0:Res:293.1,69.0')] ).
cnf(303,plain,
( ~ in(u,skc16)
| in(u,skc15) ),
inference(mrr,[status(thm)],[302,281]),
[iquote('0:MRR:302.1,281.0')] ).
cnf(310,plain,
subset(relation_dom(skf10(u,v)),v),
inference(res,[status(thm),theory(equality)],[202,62]),
[iquote('0:Res:202.0,62.0')] ).
cnf(316,plain,
equal(relation_dom(skf10(u,empty_set)),empty_set),
inference(res,[status(thm),theory(equality)],[310,59]),
[iquote('0:Res:310.0,59.0')] ).
cnf(326,plain,
( ~ relation(skf10(u,empty_set))
| ~ empty(empty_set)
| empty(skf10(u,empty_set)) ),
inference(spl,[status(thm),theory(equality)],[316,66]),
[iquote('0:SpL:316.0,66.1')] ).
cnf(327,plain,
( ~ empty(empty_set)
| empty(skf10(u,empty_set)) ),
inference(ssi,[status(thm)],[326,39,4,7,6,118,119,38]),
[iquote('0:SSi:326.0,39.0,4.0,7.0,6.0,118.0,119.0,38.0,4.0,7.0,6.0,118.0,119.0')] ).
cnf(328,plain,
empty(skf10(u,empty_set)),
inference(mrr,[status(thm)],[327,6]),
[iquote('0:MRR:327.0,6.0')] ).
cnf(330,plain,
equal(skf10(u,empty_set),empty_set),
inference(ems,[status(thm)],[55,328]),
[iquote('0:EmS:55.0,328.0')] ).
cnf(338,plain,
quasi_total(empty_set,empty_set,u),
inference(spr,[status(thm),theory(equality)],[330,52]),
[iquote('0:SpR:330.0,52.0')] ).
cnf(344,plain,
$false,
inference(unc,[status(thm)],[338,227]),
[iquote('1:UnC:338.0,227.0')] ).
cnf(347,plain,
~ equal(skc17,empty_set),
inference(spt,[spt(split,[position(sa)])],[344,101]),
[iquote('1:Spt:344.0,56.1,101.0')] ).
cnf(348,plain,
~ equal(skc16,empty_set),
inference(spt,[spt(split,[position(s2)])],[56]),
[iquote('1:Spt:344.0,56.0')] ).
cnf(396,plain,
( ~ relation_of2(u,v,w)
| ~ skP0(v,w)
| ~ equal(relation_dom(u),v)
| ~ relation_of2_as_subset(u,v,w)
| quasi_total(u,v,w) ),
inference(spl,[status(thm),theory(equality)],[74,81]),
[iquote('0:SpL:74.1,81.1')] ).
cnf(397,plain,
( ~ skP0(u,v)
| ~ equal(relation_dom(w),u)
| ~ relation_of2_as_subset(w,u,v)
| quasi_total(w,u,v) ),
inference(mrr,[status(thm)],[396,67]),
[iquote('0:MRR:396.0,67.1')] ).
cnf(507,plain,
( empty(skf11(u))
| element(skf8(skf11(u)),u) ),
inference(res,[status(thm),theory(equality)],[170,294]),
[iquote('0:Res:170.1,294.0')] ).
cnf(514,plain,
( empty(skf11(u))
| empty(u)
| in(skf8(skf11(u)),u) ),
inference(res,[status(thm),theory(equality)],[507,69]),
[iquote('0:Res:507.1,69.0')] ).
cnf(516,plain,
( empty(u)
| in(skf8(skf11(u)),u) ),
inference(mrr,[status(thm)],[514,53]),
[iquote('0:MRR:514.0,53.0')] ).
cnf(522,plain,
( empty(skc16)
| in(skf8(skf11(skc16)),skc15) ),
inference(res,[status(thm),theory(equality)],[516,303]),
[iquote('0:Res:516.1,303.0')] ).
cnf(525,plain,
( empty(skf11(u))
| element(skf8(skf11(skf11(u))),u) ),
inference(res,[status(thm),theory(equality)],[516,294]),
[iquote('0:Res:516.1,294.0')] ).
cnf(543,plain,
empty(skc16),
inference(spt,[spt(split,[position(s2s1)])],[522]),
[iquote('2:Spt:522.0')] ).
cnf(545,plain,
equal(skc16,empty_set),
inference(ems,[status(thm)],[55,543]),
[iquote('2:EmS:55.0,543.0')] ).
cnf(547,plain,
$false,
inference(mrr,[status(thm)],[545,348]),
[iquote('2:MRR:545.0,348.0')] ).
cnf(548,plain,
~ empty(skc16),
inference(spt,[spt(split,[position(s2sa)])],[547,543]),
[iquote('2:Spt:547.0,522.0,543.0')] ).
cnf(549,plain,
in(skf8(skf11(skc16)),skc15),
inference(spt,[spt(split,[position(s2s2)])],[522]),
[iquote('2:Spt:547.0,522.1')] ).
cnf(609,plain,
( ~ skP0(skc17,skc16)
| ~ relation_of2(skc14,skc17,skc16)
| equal(relation_dom(skc14),skc17) ),
inference(spr,[status(thm),theory(equality)],[97,74]),
[iquote('0:SpR:97.1,74.1')] ).
cnf(613,plain,
( ~ skP0(skc17,skc16)
| equal(relation_dom(skc14),skc17) ),
inference(mrr,[status(thm)],[609,92]),
[iquote('0:MRR:609.1,92.0')] ).
cnf(616,plain,
( equal(skc16,empty_set)
| equal(relation_dom(skc14),skc17) ),
inference(res,[status(thm),theory(equality)],[46,613]),
[iquote('0:Res:46.0,613.0')] ).
cnf(617,plain,
equal(relation_dom(skc14),skc17),
inference(mrr,[status(thm)],[616,348]),
[iquote('1:MRR:616.0,348.0')] ).
cnf(750,plain,
( empty(skf11(u))
| empty(u)
| in(skf8(skf11(skf11(u))),u) ),
inference(res,[status(thm),theory(equality)],[525,69]),
[iquote('0:Res:525.1,69.0')] ).
cnf(752,plain,
( empty(u)
| in(skf8(skf11(skf11(u))),u) ),
inference(mrr,[status(thm)],[750,53]),
[iquote('0:MRR:750.0,53.0')] ).
cnf(759,plain,
( empty(skc16)
| in(skf8(skf11(skf11(skc16))),skc15) ),
inference(res,[status(thm),theory(equality)],[752,303]),
[iquote('0:Res:752.1,303.0')] ).
cnf(764,plain,
in(skf8(skf11(skf11(skc16))),skc15),
inference(mrr,[status(thm)],[759,548]),
[iquote('2:MRR:759.0,548.0')] ).
cnf(940,plain,
( ~ skP0(skc17,skc15)
| ~ equal(relation_dom(skc14),skc17)
| ~ relation_of2_as_subset(skc14,skc17,skc15) ),
inference(res,[status(thm),theory(equality)],[397,100]),
[iquote('0:Res:397.3,100.0')] ).
cnf(941,plain,
( ~ skP0(skc17,skc15)
| ~ equal(skc17,skc17)
| ~ relation_of2_as_subset(skc14,skc17,skc15) ),
inference(rew,[status(thm),theory(equality)],[617,940]),
[iquote('1:Rew:617.0,940.1')] ).
cnf(942,plain,
( ~ skP0(skc17,skc15)
| ~ relation_of2_as_subset(skc14,skc17,skc15) ),
inference(obv,[status(thm),theory(equality)],[941]),
[iquote('1:Obv:941.1')] ).
cnf(943,plain,
~ skP0(skc17,skc15),
inference(mrr,[status(thm)],[942,98]),
[iquote('1:MRR:942.1,98.0')] ).
cnf(946,plain,
equal(skc15,empty_set),
inference(res,[status(thm),theory(equality)],[46,943]),
[iquote('1:Res:46.0,943.0')] ).
cnf(970,plain,
in(skf8(skf11(skf11(skc16))),empty_set),
inference(rew,[status(thm),theory(equality)],[946,764]),
[iquote('2:Rew:946.0,764.0')] ).
cnf(988,plain,
$false,
inference(mrr,[status(thm)],[970,292]),
[iquote('2:MRR:970.0,292.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU291+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.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 13:18:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 766 clauses, backtracked 24 clauses, performed 2 splits and kept 412 clauses.
% 0.19/0.49 SPASS allocated 98268 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.03 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 6, length 112 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : t9_funct_2 fc12_relat_1 fc4_relat_1 rc1_partfun1 rc2_subset_1 existence_m1_subset_1 rc1_funct_2 rc1_subset_1 d1_funct_2 t6_boole t3_xboole_1 t3_subset cc1_relset_1 fc5_relat_1 redefinition_m2_relset_1 t2_subset dt_m2_relset_1 dt_k4_relset_1 redefinition_k4_relset_1 t4_subset t5_subset t16_relset_1
% 0.19/0.49
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