TSTP Solution File: SEU364+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU364+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:36:39 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 67 ( 21 unt; 29 nHn; 67 RR)
% Number of literals : 239 ( 0 equ; 155 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
transitive_relstr(skc9),
file('SEU364+1.p',unknown),
[] ).
cnf(2,axiom,
rel_str(skc9),
file('SEU364+1.p',unknown),
[] ).
cnf(3,axiom,
finite(skc7),
file('SEU364+1.p',unknown),
[] ).
cnf(7,axiom,
~ empty_carrier(skc9),
file('SEU364+1.p',unknown),
[] ).
cnf(12,axiom,
element(skc7,powerset(skc8)),
file('SEU364+1.p',unknown),
[] ).
cnf(14,axiom,
element(skc8,powerset(the_carrier(skc9))),
file('SEU364+1.p',unknown),
[] ).
cnf(27,axiom,
( in(skf12(u),u)
| in(skf13(v),skc8) ),
file('SEU364+1.p',unknown),
[] ).
cnf(31,axiom,
( in(skf12(u),u)
| in(skf12(u),powerset(skc7)) ),
file('SEU364+1.p',unknown),
[] ).
cnf(32,axiom,
( in(skf12(u),u)
| element(skf13(v),the_carrier(skc9)) ),
file('SEU364+1.p',unknown),
[] ).
cnf(37,axiom,
( in(skf12(u),u)
| relstr_set_smaller(skc9,skf12(u),skf13(u)) ),
file('SEU364+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ equal(skf24(u,v),skf24(u,v))
| skP0(w,x) ),
file('SEU364+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ in(u,v)
| ~ element(u,the_carrier(w))
| ~ in(x,powerset(y))
| ~ relstr_set_smaller(w,x,u)
| in(x,skf22(v,w,y)) ),
file('SEU364+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ in(u,skc8)
| ~ element(u,the_carrier(skc9))
| ~ in(skf12(v),v)
| ~ in(skf12(v),powerset(skc7))
| ~ relstr_set_smaller(skc9,skf12(v),u) ),
file('SEU364+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(v)
| ~ skP0(w,u)
| ~ in(x,skf22(w,u,v))
| ~ element(v,powerset(w))
| ~ element(w,powerset(the_carrier(u)))
| in(x,powerset(v))
| empty_carrier(u) ),
file('SEU364+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(v)
| ~ skP0(w,u)
| ~ in(x,skf22(w,u,v))
| ~ element(v,powerset(w))
| ~ element(w,powerset(the_carrier(u)))
| in(skf23(u,w,y),w)
| empty_carrier(u) ),
file('SEU364+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(v)
| ~ skP0(w,u)
| ~ in(x,skf22(w,u,v))
| ~ element(v,powerset(w))
| ~ element(w,powerset(the_carrier(u)))
| relstr_set_smaller(u,x,skf23(u,w,x))
| empty_carrier(u) ),
file('SEU364+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(v)
| ~ skP0(w,u)
| ~ in(x,skf22(w,u,v))
| ~ element(v,powerset(w))
| ~ element(w,powerset(the_carrier(u)))
| element(skf23(u,y,z),the_carrier(u))
| empty_carrier(u) ),
file('SEU364+1.p',unknown),
[] ).
cnf(48,plain,
skP0(u,v),
inference(obv,[status(thm),theory(equality)],[41]),
[iquote('0:Obv:41.0')] ).
cnf(49,plain,
( ~ finite(u)
| ~ rel_str(v)
| ~ transitive_relstr(v)
| ~ element(u,powerset(w))
| ~ element(w,powerset(the_carrier(v)))
| ~ in(x,skf22(w,v,u))
| empty_carrier(v)
| in(x,powerset(u)) ),
inference(mrr,[status(thm)],[44,48]),
[iquote('0:MRR:44.3,48.0')] ).
cnf(50,plain,
( ~ finite(u)
| ~ rel_str(v)
| ~ transitive_relstr(v)
| ~ element(u,powerset(w))
| ~ element(w,powerset(the_carrier(v)))
| ~ in(x,skf22(w,v,u))
| empty_carrier(v)
| in(skf23(v,w,y),w) ),
inference(mrr,[status(thm)],[45,48]),
[iquote('0:MRR:45.3,48.0')] ).
cnf(51,plain,
( ~ finite(u)
| ~ rel_str(v)
| ~ transitive_relstr(v)
| ~ element(u,powerset(w))
| ~ element(w,powerset(the_carrier(v)))
| ~ in(x,skf22(w,v,u))
| empty_carrier(v)
| relstr_set_smaller(v,x,skf23(v,w,x)) ),
inference(mrr,[status(thm)],[46,48]),
[iquote('0:MRR:46.3,48.0')] ).
cnf(52,plain,
( ~ finite(u)
| ~ rel_str(v)
| ~ transitive_relstr(v)
| ~ element(u,powerset(w))
| ~ element(w,powerset(the_carrier(v)))
| ~ in(x,skf22(w,v,u))
| empty_carrier(v)
| element(skf23(v,y,z),the_carrier(v)) ),
inference(mrr,[status(thm)],[47,48]),
[iquote('0:MRR:47.3,48.0')] ).
cnf(74,plain,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(skc7)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| element(skf23(u,w,x),the_carrier(u))
| empty_carrier(u) ),
inference(res,[status(thm),theory(equality)],[12,52]),
[iquote('0:Res:12.0,52.4')] ).
cnf(75,plain,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(skc7)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| relstr_set_smaller(u,v,skf23(u,skc8,v))
| empty_carrier(u) ),
inference(res,[status(thm),theory(equality)],[12,51]),
[iquote('0:Res:12.0,51.4')] ).
cnf(76,plain,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(skc7)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| in(skf23(u,skc8,w),skc8)
| empty_carrier(u) ),
inference(res,[status(thm),theory(equality)],[12,50]),
[iquote('0:Res:12.0,50.4')] ).
cnf(77,plain,
( ~ transitive_relstr(u)
| ~ rel_str(u)
| ~ finite(skc7)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| in(v,powerset(skc7))
| empty_carrier(u) ),
inference(res,[status(thm),theory(equality)],[12,49]),
[iquote('0:Res:12.0,49.4')] ).
cnf(90,plain,
( ~ rel_str(u)
| ~ transitive_relstr(u)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| empty_carrier(u)
| in(v,powerset(skc7)) ),
inference(mrr,[status(thm)],[77,3]),
[iquote('0:MRR:77.2,3.0')] ).
cnf(94,plain,
( ~ rel_str(u)
| ~ transitive_relstr(u)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| empty_carrier(u)
| in(skf23(u,skc8,w),skc8) ),
inference(mrr,[status(thm)],[76,3]),
[iquote('0:MRR:76.2,3.0')] ).
cnf(96,plain,
( ~ rel_str(u)
| ~ transitive_relstr(u)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| empty_carrier(u)
| relstr_set_smaller(u,v,skf23(u,skc8,v)) ),
inference(mrr,[status(thm)],[75,3]),
[iquote('0:MRR:75.2,3.0')] ).
cnf(97,plain,
( ~ rel_str(u)
| ~ transitive_relstr(u)
| ~ in(v,skf22(skc8,u,skc7))
| ~ element(skc8,powerset(the_carrier(u)))
| empty_carrier(u)
| element(skf23(u,w,x),the_carrier(u)) ),
inference(mrr,[status(thm)],[74,3]),
[iquote('0:MRR:74.2,3.0')] ).
cnf(107,plain,
( ~ rel_str(skc9)
| ~ in(u,skf22(skc8,skc9,skc7))
| ~ element(skc8,powerset(the_carrier(skc9)))
| element(skf23(skc9,v,w),the_carrier(skc9))
| empty_carrier(skc9) ),
inference(res,[status(thm),theory(equality)],[1,97]),
[iquote('0:Res:1.0,97.0')] ).
cnf(108,plain,
( ~ rel_str(skc9)
| ~ in(u,skf22(skc8,skc9,skc7))
| ~ element(skc8,powerset(the_carrier(skc9)))
| relstr_set_smaller(skc9,u,skf23(skc9,skc8,u))
| empty_carrier(skc9) ),
inference(res,[status(thm),theory(equality)],[1,96]),
[iquote('0:Res:1.0,96.0')] ).
cnf(110,plain,
( ~ rel_str(skc9)
| ~ in(u,skf22(skc8,skc9,skc7))
| ~ element(skc8,powerset(the_carrier(skc9)))
| in(skf23(skc9,skc8,v),skc8)
| empty_carrier(skc9) ),
inference(res,[status(thm),theory(equality)],[1,94]),
[iquote('0:Res:1.0,94.0')] ).
cnf(112,plain,
( ~ rel_str(skc9)
| ~ in(u,skf22(skc8,skc9,skc7))
| ~ element(skc8,powerset(the_carrier(skc9)))
| in(u,powerset(skc7))
| empty_carrier(skc9) ),
inference(res,[status(thm),theory(equality)],[1,90]),
[iquote('0:Res:1.0,90.0')] ).
cnf(113,plain,
( ~ in(u,skf22(skc8,skc9,skc7))
| in(u,powerset(skc7)) ),
inference(mrr,[status(thm)],[112,2,14,7]),
[iquote('0:MRR:112.0,112.2,112.4,2.0,14.0,7.0')] ).
cnf(114,plain,
( ~ in(u,skf22(skc8,skc9,skc7))
| in(skf23(skc9,skc8,v),skc8) ),
inference(mrr,[status(thm)],[110,2,14,7]),
[iquote('0:MRR:110.0,110.2,110.4,2.0,14.0,7.0')] ).
cnf(115,plain,
( ~ in(u,skf22(skc8,skc9,skc7))
| relstr_set_smaller(skc9,u,skf23(skc9,skc8,u)) ),
inference(mrr,[status(thm)],[108,2,14,7]),
[iquote('0:MRR:108.0,108.2,108.4,2.0,14.0,7.0')] ).
cnf(116,plain,
( ~ in(u,skf22(skc8,skc9,skc7))
| element(skf23(skc9,v,w),the_carrier(skc9)) ),
inference(mrr,[status(thm)],[107,2,14,7]),
[iquote('0:MRR:107.0,107.2,107.4,2.0,14.0,7.0')] ).
cnf(158,plain,
in(skf12(u),u),
inference(spt,[spt(split,[position(s1)])],[27]),
[iquote('1:Spt:27.0')] ).
cnf(159,plain,
( ~ in(u,skc8)
| ~ element(u,the_carrier(skc9))
| ~ in(skf12(v),powerset(skc7))
| ~ relstr_set_smaller(skc9,skf12(v),u) ),
inference(mrr,[status(thm)],[43,158]),
[iquote('1:MRR:43.2,158.0')] ).
cnf(176,plain,
in(skf23(skc9,skc8,u),skc8),
inference(res,[status(thm),theory(equality)],[158,114]),
[iquote('1:Res:158.0,114.0')] ).
cnf(179,plain,
( ~ in(skf12(u),skf22(skc8,skc9,skc7))
| ~ in(skf23(skc9,skc8,skf12(u)),skc8)
| ~ element(skf23(skc9,skc8,skf12(u)),the_carrier(skc9))
| ~ in(skf12(u),powerset(skc7)) ),
inference(res,[status(thm),theory(equality)],[115,159]),
[iquote('1:Res:115.1,159.3')] ).
cnf(180,plain,
( ~ in(skf12(u),skf22(skc8,skc9,skc7))
| ~ element(skf23(skc9,skc8,skf12(u)),the_carrier(skc9)) ),
inference(mrr,[status(thm)],[179,176,113]),
[iquote('1:MRR:179.1,179.3,176.0,113.1')] ).
cnf(181,plain,
~ in(skf12(u),skf22(skc8,skc9,skc7)),
inference(mrr,[status(thm)],[180,116]),
[iquote('1:MRR:180.1,116.1')] ).
cnf(182,plain,
$false,
inference(unc,[status(thm)],[181,158]),
[iquote('1:UnC:181.0,158.0')] ).
cnf(183,plain,
in(skf13(u),skc8),
inference(spt,[spt(split,[position(s2)])],[27]),
[iquote('1:Spt:182.0,27.1')] ).
cnf(185,plain,
in(skf12(u),u),
inference(spt,[spt(split,[position(s2s1)])],[32]),
[iquote('2:Spt:32.0')] ).
cnf(186,plain,
( ~ in(u,skc8)
| ~ element(u,the_carrier(skc9))
| ~ in(skf12(v),powerset(skc7))
| ~ relstr_set_smaller(skc9,skf12(v),u) ),
inference(mrr,[status(thm)],[43,185]),
[iquote('2:MRR:43.2,185.0')] ).
cnf(190,plain,
( ~ in(skf12(u),skf22(skc8,skc9,skc7))
| ~ in(skf23(skc9,skc8,skf12(u)),skc8)
| ~ element(skf23(skc9,skc8,skf12(u)),the_carrier(skc9))
| ~ in(skf12(u),powerset(skc7)) ),
inference(res,[status(thm),theory(equality)],[115,186]),
[iquote('2:Res:115.1,186.3')] ).
cnf(191,plain,
( ~ in(skf12(u),skf22(skc8,skc9,skc7))
| ~ in(skf23(skc9,skc8,skf12(u)),skc8)
| ~ element(skf23(skc9,skc8,skf12(u)),the_carrier(skc9)) ),
inference(mrr,[status(thm)],[190,113]),
[iquote('2:MRR:190.3,113.1')] ).
cnf(192,plain,
~ in(skf12(u),skf22(skc8,skc9,skc7)),
inference(mrr,[status(thm)],[191,114,116]),
[iquote('2:MRR:191.1,191.2,114.1,116.1')] ).
cnf(193,plain,
$false,
inference(unc,[status(thm)],[192,185]),
[iquote('2:UnC:192.0,185.0')] ).
cnf(194,plain,
element(skf13(u),the_carrier(skc9)),
inference(spt,[spt(split,[position(s2s2)])],[32]),
[iquote('2:Spt:193.0,32.1')] ).
cnf(195,plain,
( ~ in(skf13(u),v)
| ~ in(w,powerset(x))
| ~ relstr_set_smaller(skc9,w,skf13(u))
| in(w,skf22(v,skc9,x)) ),
inference(res,[status(thm),theory(equality)],[194,42]),
[iquote('2:Res:194.0,42.1')] ).
cnf(198,plain,
( in(skf12(skf22(skc8,skc9,skc7)),powerset(skc7))
| in(skf12(skf22(skc8,skc9,skc7)),powerset(skc7)) ),
inference(res,[status(thm),theory(equality)],[31,113]),
[iquote('0:Res:31.0,113.0')] ).
cnf(201,plain,
in(skf12(skf22(skc8,skc9,skc7)),powerset(skc7)),
inference(obv,[status(thm),theory(equality)],[198]),
[iquote('0:Obv:198.0')] ).
cnf(207,plain,
( ~ in(u,skc8)
| ~ element(u,the_carrier(skc9))
| ~ in(skf12(skf22(skc8,skc9,skc7)),skf22(skc8,skc9,skc7))
| ~ relstr_set_smaller(skc9,skf12(skf22(skc8,skc9,skc7)),u) ),
inference(res,[status(thm),theory(equality)],[201,43]),
[iquote('0:Res:201.0,43.3')] ).
cnf(228,plain,
( ~ in(skf13(u),v)
| ~ in(skf12(u),powerset(w))
| in(skf12(u),u)
| in(skf12(u),skf22(v,skc9,w)) ),
inference(res,[status(thm),theory(equality)],[37,195]),
[iquote('2:Res:37.1,195.2')] ).
cnf(230,plain,
( ~ in(skf13(u),v)
| in(skf12(u),u)
| in(skf12(u),u)
| in(skf12(u),skf22(v,skc9,skc7)) ),
inference(res,[status(thm),theory(equality)],[31,228]),
[iquote('2:Res:31.1,228.1')] ).
cnf(235,plain,
( ~ in(skf13(u),v)
| in(skf12(u),u)
| in(skf12(u),skf22(v,skc9,skc7)) ),
inference(obv,[status(thm),theory(equality)],[230]),
[iquote('2:Obv:230.1')] ).
cnf(238,plain,
( in(skf12(u),u)
| in(skf12(u),skf22(skc8,skc9,skc7)) ),
inference(res,[status(thm),theory(equality)],[183,235]),
[iquote('2:Res:183.0,235.0')] ).
cnf(239,plain,
in(skf12(skf22(skc8,skc9,skc7)),skf22(skc8,skc9,skc7)),
inference(fac,[status(thm)],[238]),
[iquote('2:Fac:238.0,238.1')] ).
cnf(267,plain,
( ~ in(u,skc8)
| ~ element(u,the_carrier(skc9))
| ~ relstr_set_smaller(skc9,skf12(skf22(skc8,skc9,skc7)),u) ),
inference(mrr,[status(thm)],[207,239]),
[iquote('2:MRR:207.2,239.0')] ).
cnf(274,plain,
element(skf23(skc9,u,v),the_carrier(skc9)),
inference(res,[status(thm),theory(equality)],[239,116]),
[iquote('2:Res:239.0,116.0')] ).
cnf(275,plain,
in(skf23(skc9,skc8,u),skc8),
inference(res,[status(thm),theory(equality)],[239,114]),
[iquote('2:Res:239.0,114.0')] ).
cnf(296,plain,
( ~ in(skf12(skf22(skc8,skc9,skc7)),skf22(skc8,skc9,skc7))
| ~ in(skf23(skc9,skc8,skf12(skf22(skc8,skc9,skc7))),skc8)
| ~ element(skf23(skc9,skc8,skf12(skf22(skc8,skc9,skc7))),the_carrier(skc9)) ),
inference(res,[status(thm),theory(equality)],[115,267]),
[iquote('2:Res:115.1,267.2')] ).
cnf(299,plain,
$false,
inference(mrr,[status(thm)],[296,239,275,274]),
[iquote('2:MRR:296.0,296.1,296.2,239.0,275.0,274.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU364+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jun 19 03:14:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.54
% 0.19/0.54 SPASS V 3.9
% 0.19/0.54 SPASS beiseite: Proof found.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54 SPASS derived 168 clauses, backtracked 11 clauses, performed 3 splits and kept 171 clauses.
% 0.19/0.54 SPASS allocated 99492 KBytes.
% 0.19/0.54 SPASS spent 0:00:00.21 on the problem.
% 0.19/0.54 0:00:00.03 for the input.
% 0.19/0.54 0:00:00.13 for the FLOTTER CNF translation.
% 0.19/0.54 0:00:00.00 for inferences.
% 0.19/0.54 0:00:00.00 for the backtracking.
% 0.19/0.54 0:00:00.01 for the reduction.
% 0.19/0.54
% 0.19/0.54
% 0.19/0.54 Here is a proof with depth 7, length 67 :
% 0.19/0.54 % SZS output start Refutation
% See solution above
% 0.19/0.54 Formulae used in the proof : s1_xboole_0__e11_2_1__waybel_0__1 s1_tarski__e11_2_1__waybel_0__1
% 0.19/0.54
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