TSTP Solution File: SEU326+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU326+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:36:17 EDT 2022
% Result : Theorem 85.80s 85.97s
% Output : Refutation 85.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 41 ( 21 unt; 5 nHn; 41 RR)
% Number of literals : 70 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(51,axiom,
empty(skc328),
file('SEU326+2.p',unknown),
[] ).
cnf(151,axiom,
equal(relation_rng(empty_set),empty_set),
file('SEU326+2.p',unknown),
[] ).
cnf(153,axiom,
element(skc32,powerset(powerset(skc31))),
file('SEU326+2.p',unknown),
[] ).
cnf(212,axiom,
equal(set_difference(u,empty_set),u),
file('SEU326+2.p',unknown),
[] ).
cnf(218,axiom,
( skP25(skc31,skc32)
| equal(empty_set,skc32) ),
file('SEU326+2.p',unknown),
[] ).
cnf(283,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU326+2.p',unknown),
[] ).
cnf(378,axiom,
( ~ skP25(u,v)
| ~ equal(v,empty_set) ),
file('SEU326+2.p',unknown),
[] ).
cnf(446,axiom,
( ~ equal(complements_of_subsets(skc31,skc32),empty_set)
| skP25(skc31,skc32) ),
file('SEU326+2.p',unknown),
[] ).
cnf(447,axiom,
( ~ skP25(u,v)
| equal(complements_of_subsets(u,v),empty_set) ),
file('SEU326+2.p',unknown),
[] ).
cnf(713,axiom,
( ~ element(u,powerset(v))
| equal(set_difference(v,u),subset_complement(v,u)) ),
file('SEU326+2.p',unknown),
[] ).
cnf(724,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| in(u,w) ),
file('SEU326+2.p',unknown),
[] ).
cnf(872,axiom,
( ~ element(u,powerset(powerset(v)))
| ~ equal(complements_of_subsets(v,u),empty_set)
| equal(u,empty_set) ),
file('SEU326+2.p',unknown),
[] ).
cnf(873,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| ~ in(u,subset_complement(w,v)) ),
file('SEU326+2.p',unknown),
[] ).
cnf(1268,axiom,
( ~ element(u,powerset(powerset(v)))
| ~ element(w,powerset(powerset(v)))
| equal(u,complements_of_subsets(v,w))
| in(subset_complement(v,skf350(w,u,v)),w)
| in(skf350(w,u,v),u) ),
file('SEU326+2.p',unknown),
[] ).
cnf(1329,plain,
( ~ equal(complements_of_subsets(skc31,skc32),skc32)
| skP25(skc31,skc32) ),
inference(rew,[status(thm),theory(equality)],[218,446]),
[iquote('0:Rew:218.0,446.0')] ).
cnf(1505,plain,
( ~ element(u,powerset(powerset(skc31)))
| equal(complements_of_subsets(skc31,u),skc32)
| in(subset_complement(skc31,skf350(u,skc32,skc31)),u)
| in(skf350(u,skc32,skc31),skc32) ),
inference(res,[status(thm),theory(equality)],[153,1268]),
[iquote('0:Res:153.0,1268.1')] ).
cnf(1540,plain,
( ~ in(u,skc32)
| ~ in(u,subset_complement(powerset(skc31),skc32)) ),
inference(res,[status(thm),theory(equality)],[153,873]),
[iquote('0:Res:153.0,873.0')] ).
cnf(1542,plain,
equal(set_difference(powerset(skc31),skc32),subset_complement(powerset(skc31),skc32)),
inference(res,[status(thm),theory(equality)],[153,713]),
[iquote('0:Res:153.0,713.0')] ).
cnf(1544,plain,
( ~ in(u,skc32)
| in(u,powerset(skc31)) ),
inference(res,[status(thm),theory(equality)],[153,724]),
[iquote('0:Res:153.0,724.0')] ).
cnf(1550,plain,
( ~ equal(complements_of_subsets(skc31,skc32),empty_set)
| equal(empty_set,skc32) ),
inference(res,[status(thm),theory(equality)],[153,872]),
[iquote('0:Res:153.0,872.0')] ).
cnf(1564,plain,
~ skP25(u,relation_rng(empty_set)),
inference(res,[status(thm),theory(equality)],[151,378]),
[iquote('0:Res:151.0,378.0')] ).
cnf(1580,plain,
~ skP25(u,empty_set),
inference(rew,[status(thm),theory(equality)],[151,1564]),
[iquote('0:Rew:151.0,1564.0')] ).
cnf(1603,plain,
( equal(complements_of_subsets(skc31,skc32),skc32)
| in(subset_complement(skc31,skf350(skc32,skc32,skc31)),skc32)
| in(skf350(skc32,skc32,skc31),skc32) ),
inference(res,[status(thm),theory(equality)],[153,1505]),
[iquote('0:Res:153.0,1505.0')] ).
cnf(1622,plain,
equal(empty_set,skc32),
inference(spt,[spt(split,[position(s1)])],[218]),
[iquote('1:Spt:218.1')] ).
cnf(1694,plain,
~ skP25(u,skc32),
inference(rew,[status(thm),theory(equality)],[1622,1580]),
[iquote('1:Rew:1622.0,1580.0')] ).
cnf(1698,plain,
equal(set_difference(u,skc32),u),
inference(rew,[status(thm),theory(equality)],[1622,212]),
[iquote('1:Rew:1622.0,212.0')] ).
cnf(1721,plain,
~ equal(complements_of_subsets(skc31,skc32),skc32),
inference(mrr,[status(thm)],[1329,1694]),
[iquote('1:MRR:1329.1,1694.0')] ).
cnf(1726,plain,
equal(subset_complement(powerset(skc31),skc32),powerset(skc31)),
inference(rew,[status(thm),theory(equality)],[1698,1542]),
[iquote('1:Rew:1698.0,1542.0')] ).
cnf(1731,plain,
( in(subset_complement(skc31,skf350(skc32,skc32,skc31)),skc32)
| in(skf350(skc32,skc32,skc31),skc32) ),
inference(mrr,[status(thm)],[1603,1721]),
[iquote('1:MRR:1603.0,1721.0')] ).
cnf(1733,plain,
( ~ in(u,skc32)
| ~ in(u,powerset(skc31)) ),
inference(rew,[status(thm),theory(equality)],[1726,1540]),
[iquote('1:Rew:1726.0,1540.1')] ).
cnf(1740,plain,
~ in(u,skc32),
inference(mrr,[status(thm)],[1733,1544]),
[iquote('1:MRR:1733.1,1544.1')] ).
cnf(1756,plain,
$false,
inference(mrr,[status(thm)],[1731,1740]),
[iquote('1:MRR:1731.0,1731.1,1740.0,1740.0')] ).
cnf(1766,plain,
~ equal(empty_set,skc32),
inference(spt,[spt(split,[position(sa)])],[1756,1622]),
[iquote('1:Spt:1756.0,218.1,1622.0')] ).
cnf(1767,plain,
skP25(skc31,skc32),
inference(spt,[spt(split,[position(s2)])],[218]),
[iquote('1:Spt:1756.0,218.0')] ).
cnf(1768,plain,
~ equal(complements_of_subsets(skc31,skc32),empty_set),
inference(mrr,[status(thm)],[1550,1766]),
[iquote('1:MRR:1550.1,1766.0')] ).
cnf(1994,plain,
equal(empty_set,skc328),
inference(ems,[status(thm)],[283,51]),
[iquote('0:EmS:283.0,51.0')] ).
cnf(2074,plain,
( ~ skP25(u,v)
| equal(complements_of_subsets(u,v),skc328) ),
inference(rew,[status(thm),theory(equality)],[1994,447]),
[iquote('0:Rew:1994.0,447.1')] ).
cnf(4782,plain,
~ equal(complements_of_subsets(skc31,skc32),skc328),
inference(rew,[status(thm),theory(equality)],[1994,1768]),
[iquote('1:Rew:1994.0,1768.0')] ).
cnf(4916,plain,
( ~ skP25(skc31,skc32)
| ~ equal(skc328,skc328) ),
inference(spl,[status(thm),theory(equality)],[2074,4782]),
[iquote('1:SpL:2074.1,4782.0')] ).
cnf(4917,plain,
~ skP25(skc31,skc32),
inference(obv,[status(thm),theory(equality)],[4916]),
[iquote('1:Obv:4916.1')] ).
cnf(4918,plain,
$false,
inference(mrr,[status(thm)],[4917,1767]),
[iquote('1:MRR:4917.0,1767.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU326+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 09:08:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 85.80/85.97
% 85.80/85.97 SPASS V 3.9
% 85.80/85.97 SPASS beiseite: Proof found.
% 85.80/85.97 % SZS status Theorem
% 85.80/85.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.80/85.97 SPASS derived 3220 clauses, backtracked 364 clauses, performed 25 splits and kept 3564 clauses.
% 85.80/85.97 SPASS allocated 165640 KBytes.
% 85.80/85.97 SPASS spent 0:1:25.56 on the problem.
% 85.80/85.97 0:00:00.04 for the input.
% 85.80/85.97 0:1:23.29 for the FLOTTER CNF translation.
% 85.80/85.97 0:00:00.05 for inferences.
% 85.80/85.97 0:00:00.02 for the backtracking.
% 85.80/85.97 0:00:01.78 for the reduction.
% 85.80/85.97
% 85.80/85.97
% 85.80/85.97 Here is a proof with depth 2, length 41 :
% 85.80/85.97 % SZS output start Refutation
% See solution above
% 85.80/85.97 Formulae used in the proof : rc1_partfun1 t60_relat_1 t10_tops_2 t3_boole t6_boole d5_subset_1 l3_subset_1 t46_setfam_1 t54_subset_1 d8_setfam_1 existence_m1_subset_1
% 85.80/85.97
%------------------------------------------------------------------------------