TSTP Solution File: SEU072+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU072+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:33:49 EDT 2022
% Result : Theorem 4.64s 4.86s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of clauses : 84 ( 27 unt; 20 nHn; 84 RR)
% Number of literals : 199 ( 0 equ; 107 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
relation(skc9),
file('SEU072+1.p',unknown),
[] ).
cnf(2,axiom,
function(skc9),
file('SEU072+1.p',unknown),
[] ).
cnf(7,axiom,
empty(empty_set),
file('SEU072+1.p',unknown),
[] ).
cnf(23,axiom,
~ one_to_one(skc9),
file('SEU072+1.p',unknown),
[] ).
cnf(27,axiom,
subset(u,u),
file('SEU072+1.p',unknown),
[] ).
cnf(28,axiom,
element(skf14(u),u),
file('SEU072+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ empty(u)
| function(u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ empty(u)
| relation(u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(41,axiom,
subset(relation_inverse_image(skc9,relation_image(skc9,u)),u),
file('SEU072+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(48,axiom,
equal(apply(u,skf13(u)),apply(u,skf12(u))),
file('SEU072+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ relation(u)
| ~ empty(relation_rng(u))
| empty(u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU072+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ subset(singleton(u),singleton(v))
| equal(u,v) ),
file('SEU072+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ relation(u)
| ~ empty(u)
| ~ function(u)
| one_to_one(u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ subset(u,singleton(v))
| equal(u,empty_set)
| equal(u,singleton(v)) ),
file('SEU072+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf13(u),relation_dom(u)) ),
file('SEU072+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ function(u)
| ~ relation(u)
| one_to_one(u)
| in(skf12(u),relation_dom(u)) ),
file('SEU072+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ relation(u)
| in(v,relation_rng(u))
| equal(relation_inverse_image(u,singleton(v)),empty_set) ),
file('SEU072+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ function(u)
| ~ relation(u)
| ~ equal(skf13(u),skf12(u))
| one_to_one(u) ),
file('SEU072+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ relation(u)
| ~ in(v,relation_rng(u))
| ~ equal(relation_inverse_image(u,singleton(v)),empty_set) ),
file('SEU072+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ relation(u)
| ~ function(u)
| ~ in(v,relation_dom(u))
| equal(relation_image(u,singleton(v)),singleton(apply(u,v))) ),
file('SEU072+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ function(u)
| ~ relation(u)
| equal(v,relation_rng(u))
| in(skf10(u,v),v)
| in(skf11(u,w),relation_dom(u)) ),
file('SEU072+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf8(u,x),relation_dom(u)) ),
file('SEU072+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf8(u,v)),v) ),
file('SEU072+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_rng(u))
| ~ equal(x,apply(u,v))
| in(x,w) ),
file('SEU072+1.p',unknown),
[] ).
cnf(72,plain,
( ~ empty(u)
| one_to_one(u) ),
inference(mrr,[status(thm)],[55,32,31]),
[iquote('0:MRR:55.0,55.2,32.1,31.1')] ).
cnf(77,plain,
( ~ relation(skc9)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc9))
| in(skf8(skc9,w),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.1')] ).
cnf(78,plain,
( ~ relation(skc9)
| in(skf11(skc9,u),relation_dom(skc9))
| in(skf10(skc9,v),v)
| equal(v,relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[2,66]),
[iquote('0:Res:2.0,66.1')] ).
cnf(80,plain,
( ~ relation(skc9)
| ~ equal(skf13(skc9),skf12(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,62]),
[iquote('0:Res:2.0,62.1')] ).
cnf(81,plain,
( ~ relation(skc9)
| in(skf13(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,59]),
[iquote('0:Res:2.0,59.1')] ).
cnf(82,plain,
( ~ relation(skc9)
| in(skf12(skc9),relation_dom(skc9))
| one_to_one(skc9) ),
inference(res,[status(thm),theory(equality)],[2,60]),
[iquote('0:Res:2.0,60.1')] ).
cnf(90,plain,
( ~ in(u,relation_rng(skc9))
| ~ equal(relation_inverse_image(skc9,singleton(u)),empty_set) ),
inference(res,[status(thm),theory(equality)],[1,63]),
[iquote('0:Res:1.0,63.0')] ).
cnf(94,plain,
( in(u,relation_rng(skc9))
| equal(relation_inverse_image(skc9,singleton(u)),empty_set) ),
inference(res,[status(thm),theory(equality)],[1,61]),
[iquote('0:Res:1.0,61.0')] ).
cnf(96,plain,
( ~ empty(relation_rng(skc9))
| empty(skc9) ),
inference(res,[status(thm),theory(equality)],[1,50]),
[iquote('0:Res:1.0,50.0')] ).
cnf(100,plain,
~ empty(skc9),
inference(res,[status(thm),theory(equality)],[72,23]),
[iquote('0:Res:72.1,23.0')] ).
cnf(104,plain,
~ empty(relation_rng(skc9)),
inference(mrr,[status(thm)],[96,100]),
[iquote('0:MRR:96.1,100.0')] ).
cnf(105,plain,
in(skf13(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[81,1,23]),
[iquote('0:MRR:81.0,81.2,1.0,23.0')] ).
cnf(106,plain,
in(skf12(skc9),relation_dom(skc9)),
inference(mrr,[status(thm)],[82,1,23]),
[iquote('0:MRR:82.0,82.2,1.0,23.0')] ).
cnf(107,plain,
~ equal(skf13(skc9),skf12(skc9)),
inference(mrr,[status(thm)],[80,1,23]),
[iquote('0:MRR:80.0,80.2,1.0,23.0')] ).
cnf(109,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc9))
| in(skf8(skc9,w),relation_dom(skc9)) ),
inference(mrr,[status(thm)],[77,1]),
[iquote('0:MRR:77.0,1.0')] ).
cnf(110,plain,
( equal(u,relation_rng(skc9))
| in(skf10(skc9,u),u)
| in(skf11(skc9,v),relation_dom(skc9)) ),
inference(mrr,[status(thm)],[78,1]),
[iquote('0:MRR:78.0,1.0')] ).
cnf(115,plain,
( equal(u,relation_rng(skc9))
| in(skf10(skc9,u),u) ),
inference(spt,[spt(split,[position(s1)])],[110]),
[iquote('1:Spt:110.0,110.1')] ).
cnf(148,plain,
( ~ empty(u)
| equal(u,relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[115,43]),
[iquote('1:Res:115.1,43.1')] ).
cnf(174,plain,
( ~ empty(u)
| ~ empty(u) ),
inference(spl,[status(thm),theory(equality)],[148,104]),
[iquote('1:SpL:148.1,104.0')] ).
cnf(175,plain,
~ empty(u),
inference(obv,[status(thm),theory(equality)],[174]),
[iquote('1:Obv:174.0')] ).
cnf(176,plain,
$false,
inference(unc,[status(thm)],[175,7]),
[iquote('1:UnC:175.0,7.0')] ).
cnf(178,plain,
in(skf11(skc9,u),relation_dom(skc9)),
inference(spt,[spt(split,[position(s2)])],[110]),
[iquote('1:Spt:176.0,110.2')] ).
cnf(201,plain,
( empty(u)
| in(skf14(u),u) ),
inference(res,[status(thm),theory(equality)],[28,51]),
[iquote('0:Res:28.0,51.0')] ).
cnf(360,plain,
( ~ relation(skc9)
| ~ function(skc9)
| ~ in(u,relation_dom(skc9))
| subset(relation_inverse_image(skc9,singleton(apply(skc9,u))),singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[65,41]),
[iquote('0:SpR:65.3,41.0')] ).
cnf(365,plain,
( ~ in(u,relation_dom(skc9))
| subset(relation_inverse_image(skc9,singleton(apply(skc9,u))),singleton(u)) ),
inference(ssi,[status(thm)],[360,2,1]),
[iquote('0:SSi:360.1,360.0,2.0,1.0,2.0,1.0')] ).
cnf(465,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_rng(u))
| equal(apply(u,skf8(u,v)),v) ),
inference(eqr,[status(thm),theory(equality)],[68]),
[iquote('0:EqR:68.3')] ).
cnf(510,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(v,relation_dom(u))
| ~ equal(w,relation_rng(u))
| in(apply(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[70]),
[iquote('0:EqR:70.4')] ).
cnf(774,plain,
( ~ in(skf13(skc9),relation_dom(skc9))
| subset(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),singleton(skf13(skc9))) ),
inference(spr,[status(thm),theory(equality)],[48,365]),
[iquote('0:SpR:48.0,365.1')] ).
cnf(779,plain,
( ~ in(u,relation_dom(skc9))
| equal(relation_inverse_image(skc9,singleton(apply(skc9,u))),empty_set)
| equal(relation_inverse_image(skc9,singleton(apply(skc9,u))),singleton(u)) ),
inference(res,[status(thm),theory(equality)],[365,56]),
[iquote('0:Res:365.1,56.0')] ).
cnf(781,plain,
subset(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),singleton(skf13(skc9))),
inference(mrr,[status(thm)],[774,105]),
[iquote('0:MRR:774.0,105.0')] ).
cnf(788,plain,
( equal(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),empty_set)
| equal(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),singleton(skf13(skc9))) ),
inference(res,[status(thm),theory(equality)],[781,56]),
[iquote('0:Res:781.0,56.0')] ).
cnf(842,plain,
( ~ in(u,relation_rng(skc9))
| in(skf8(skc9,v),relation_dom(skc9)) ),
inference(eqr,[status(thm),theory(equality)],[109]),
[iquote('0:EqR:109.1')] ).
cnf(845,plain,
( empty(relation_rng(skc9))
| in(skf8(skc9,u),relation_dom(skc9)) ),
inference(res,[status(thm),theory(equality)],[201,842]),
[iquote('0:Res:201.1,842.0')] ).
cnf(853,plain,
in(skf8(skc9,u),relation_dom(skc9)),
inference(mrr,[status(thm)],[845,104]),
[iquote('0:MRR:845.0,104.0')] ).
cnf(1000,plain,
( ~ function(skc9)
| ~ relation(skc9)
| ~ in(u,relation_rng(skc9))
| ~ in(skf8(skc9,u),relation_dom(skc9))
| subset(relation_inverse_image(skc9,singleton(u)),singleton(skf8(skc9,u))) ),
inference(spr,[status(thm),theory(equality)],[465,365]),
[iquote('0:SpR:465.3,365.1')] ).
cnf(1005,plain,
( ~ in(u,relation_rng(skc9))
| ~ in(skf8(skc9,u),relation_dom(skc9))
| subset(relation_inverse_image(skc9,singleton(u)),singleton(skf8(skc9,u))) ),
inference(ssi,[status(thm)],[1000,2,1]),
[iquote('0:SSi:1000.1,1000.0,2.0,1.0,2.0,1.0')] ).
cnf(1006,plain,
( ~ in(u,relation_rng(skc9))
| subset(relation_inverse_image(skc9,singleton(u)),singleton(skf8(skc9,u))) ),
inference(mrr,[status(thm)],[1005,853]),
[iquote('0:MRR:1005.1,853.0')] ).
cnf(1137,plain,
( ~ function(u)
| ~ relation(u)
| ~ in(skf13(u),relation_dom(u))
| ~ equal(v,relation_rng(u))
| in(apply(u,skf12(u)),v) ),
inference(spr,[status(thm),theory(equality)],[48,510]),
[iquote('0:SpR:48.0,510.4')] ).
cnf(1594,plain,
( ~ in(u,relation_rng(skc9))
| equal(relation_inverse_image(skc9,singleton(u)),empty_set)
| equal(relation_inverse_image(skc9,singleton(u)),singleton(skf8(skc9,u))) ),
inference(res,[status(thm),theory(equality)],[1006,56]),
[iquote('0:Res:1006.1,56.0')] ).
cnf(1596,plain,
( equal(relation_inverse_image(skc9,singleton(u)),empty_set)
| equal(relation_inverse_image(skc9,singleton(u)),singleton(skf8(skc9,u))) ),
inference(mrr,[status(thm)],[1594,94]),
[iquote('0:MRR:1594.0,94.0')] ).
cnf(1598,plain,
( equal(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),empty_set)
| equal(singleton(skf8(skc9,apply(skc9,skf12(skc9)))),singleton(skf13(skc9))) ),
inference(rew,[status(thm),theory(equality)],[1596,788]),
[iquote('0:Rew:1596.1,788.1')] ).
cnf(1599,plain,
( ~ in(u,relation_dom(skc9))
| equal(relation_inverse_image(skc9,singleton(apply(skc9,u))),empty_set)
| equal(singleton(skf8(skc9,apply(skc9,u))),singleton(u)) ),
inference(rew,[status(thm),theory(equality)],[1596,779]),
[iquote('0:Rew:1596.1,779.2')] ).
cnf(9681,plain,
equal(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),empty_set),
inference(spt,[spt(split,[position(s2s1)])],[1598]),
[iquote('2:Spt:1598.0')] ).
cnf(9752,plain,
( ~ in(apply(skc9,skf12(skc9)),relation_rng(skc9))
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[9681,90]),
[iquote('2:SpL:9681.0,90.1')] ).
cnf(9754,plain,
~ in(apply(skc9,skf12(skc9)),relation_rng(skc9)),
inference(obv,[status(thm),theory(equality)],[9752]),
[iquote('2:Obv:9752.1')] ).
cnf(9762,plain,
( ~ function(skc9)
| ~ relation(skc9)
| ~ in(skf13(skc9),relation_dom(skc9))
| ~ equal(relation_rng(skc9),relation_rng(skc9)) ),
inference(res,[status(thm),theory(equality)],[1137,9754]),
[iquote('2:Res:1137.4,9754.0')] ).
cnf(9771,plain,
( ~ function(skc9)
| ~ relation(skc9)
| ~ in(skf13(skc9),relation_dom(skc9)) ),
inference(obv,[status(thm),theory(equality)],[9762]),
[iquote('2:Obv:9762.3')] ).
cnf(9772,plain,
~ in(skf13(skc9),relation_dom(skc9)),
inference(ssi,[status(thm)],[9771,2,1]),
[iquote('2:SSi:9771.1,9771.0,2.0,1.0,2.0,1.0')] ).
cnf(9773,plain,
$false,
inference(mrr,[status(thm)],[9772,105]),
[iquote('2:MRR:9772.0,105.0')] ).
cnf(9774,plain,
~ equal(relation_inverse_image(skc9,singleton(apply(skc9,skf12(skc9)))),empty_set),
inference(spt,[spt(split,[position(s2sa)])],[9773,9681]),
[iquote('2:Spt:9773.0,1598.0,9681.0')] ).
cnf(9775,plain,
equal(singleton(skf8(skc9,apply(skc9,skf12(skc9)))),singleton(skf13(skc9))),
inference(spt,[spt(split,[position(s2s2)])],[1598]),
[iquote('2:Spt:9773.0,1598.1')] ).
cnf(9873,plain,
( ~ in(skf12(skc9),relation_dom(skc9))
| ~ equal(empty_set,empty_set)
| equal(singleton(skf8(skc9,apply(skc9,skf12(skc9)))),singleton(skf12(skc9))) ),
inference(spl,[status(thm),theory(equality)],[1599,9774]),
[iquote('2:SpL:1599.1,9774.0')] ).
cnf(9876,plain,
( ~ in(skf12(skc9),relation_dom(skc9))
| equal(singleton(skf8(skc9,apply(skc9,skf12(skc9)))),singleton(skf12(skc9))) ),
inference(obv,[status(thm),theory(equality)],[9873]),
[iquote('2:Obv:9873.1')] ).
cnf(9877,plain,
( ~ in(skf12(skc9),relation_dom(skc9))
| equal(singleton(skf13(skc9)),singleton(skf12(skc9))) ),
inference(rew,[status(thm),theory(equality)],[9775,9876]),
[iquote('2:Rew:9775.0,9876.1')] ).
cnf(9878,plain,
equal(singleton(skf13(skc9)),singleton(skf12(skc9))),
inference(mrr,[status(thm)],[9877,106]),
[iquote('2:MRR:9877.0,106.0')] ).
cnf(9994,plain,
( ~ subset(singleton(skf12(skc9)),singleton(u))
| equal(skf13(skc9),u) ),
inference(spl,[status(thm),theory(equality)],[9878,53]),
[iquote('2:SpL:9878.0,53.0')] ).
cnf(10145,plain,
equal(skf13(skc9),skf12(skc9)),
inference(res,[status(thm),theory(equality)],[27,9994]),
[iquote('2:Res:27.0,9994.0')] ).
cnf(10148,plain,
$false,
inference(mrr,[status(thm)],[10145,107]),
[iquote('2:MRR:10145.0,107.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU072+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 02:44:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.64/4.86
% 4.64/4.86 SPASS V 3.9
% 4.64/4.86 SPASS beiseite: Proof found.
% 4.64/4.86 % SZS status Theorem
% 4.64/4.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.64/4.86 SPASS derived 8106 clauses, backtracked 64 clauses, performed 7 splits and kept 4060 clauses.
% 4.64/4.86 SPASS allocated 107974 KBytes.
% 4.64/4.86 SPASS spent 0:00:04.50 on the problem.
% 4.64/4.86 0:00:00.04 for the input.
% 4.64/4.86 0:00:00.05 for the FLOTTER CNF translation.
% 4.64/4.86 0:00:00.12 for inferences.
% 4.64/4.86 0:00:00.18 for the backtracking.
% 4.64/4.86 0:00:04.03 for the reduction.
% 4.64/4.86
% 4.64/4.86
% 4.64/4.86 Here is a proof with depth 6, length 84 :
% 4.64/4.86 % SZS output start Refutation
% See solution above
% 4.83/5.01 Formulae used in the proof : t153_funct_1 fc4_relat_1 reflexivity_r1_tarski existence_m1_subset_1 cc1_funct_1 cc1_relat_1 t7_boole d8_funct_1 t6_zfmisc_1 fc6_relat_1 t2_subset cc2_funct_1 t39_zfmisc_1 t142_funct_1 t117_funct_1 d5_funct_1 antisymmetry_r2_hidden
% 4.83/5.01
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