TSTP Solution File: SET681+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:28:03 EDT 2022
% Result : Theorem 18.48s 18.69s
% Output : Refutation 18.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 45 ( 14 unt; 3 nHn; 45 RR)
% Number of literals : 106 ( 0 equ; 73 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
ilf_type(u,set_type),
file('SET681+3.p',unknown),
[] ).
cnf(12,axiom,
ilf_type(skc8,relation_type(skc7,skc6)),
file('SET681+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET681+3.p',unknown),
[] ).
cnf(28,axiom,
( member(ordered_pair(skc10,skc9),skc8)
| member(skc9,range__dfg(skc7,skc6,skc8)) ),
file('SET681+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET681+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET681+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(skc9,range__dfg(skc7,skc6,skc8))
| ~ ilf_type(u,member_type(skc7))
| ~ member(ordered_pair(u,skc9),skc8) ),
file('SET681+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET681+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ ilf_type(u,relation_type(v,w))
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ilf_type(u,subset_type(cross_product(v,w))) ),
file('SET681+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ member(u,range_of(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,binary_relation_type)
| member(ordered_pair(skf10(v,u),u),v) ),
file('SET681+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(range__dfg(u,v,w),range_of(w)) ),
file('SET681+3.p',unknown),
[] ).
cnf(54,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,binary_relation_type)
| ~ member(ordered_pair(u,v),w)
| member(v,range_of(w)) ),
file('SET681+3.p',unknown),
[] ).
cnf(64,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| ~ ilf_type(y,relation_type(u,v))
| ~ member(ordered_pair(w,x),y)
| member(w,u) ),
file('SET681+3.p',unknown),
[] ).
cnf(69,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[26,6]),
[iquote('0:MRR:26.1,6.0')] ).
cnf(74,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[34,6]),
[iquote('0:MRR:34.1,34.3,6.0,6.0')] ).
cnf(76,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[37,6]),
[iquote('0:MRR:37.0,37.1,6.0,6.0')] ).
cnf(81,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[40,6,74]),
[iquote('0:MRR:40.1,40.2,40.4,6.0,6.0,74.0')] ).
cnf(83,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[44,6]),
[iquote('0:MRR:44.1,44.2,6.0,6.0')] ).
cnf(85,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(v,range_of(u))
| member(ordered_pair(skf10(u,v),v),u) ),
inference(mrr,[status(thm)],[46,6]),
[iquote('0:MRR:46.1,6.0')] ).
cnf(87,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[48,6]),
[iquote('0:MRR:48.0,48.1,6.0,6.0')] ).
cnf(95,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(ordered_pair(v,w),u)
| member(w,range_of(u)) ),
inference(mrr,[status(thm)],[54,6]),
[iquote('0:MRR:54.0,54.1,6.0,6.0')] ).
cnf(105,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ member(ordered_pair(x,y),u)
| member(x,v) ),
inference(mrr,[status(thm)],[64,6]),
[iquote('0:MRR:64.0,64.1,64.2,64.3,6.0,6.0,6.0,6.0')] ).
cnf(113,plain,
( ~ member(ordered_pair(u,v),skc8)
| member(u,skc7) ),
inference(res,[status(thm),theory(equality)],[12,105]),
[iquote('0:Res:12.0,105.0')] ).
cnf(118,plain,
equal(range__dfg(skc7,skc6,skc8),range_of(skc8)),
inference(res,[status(thm),theory(equality)],[12,87]),
[iquote('0:Res:12.0,87.0')] ).
cnf(119,plain,
ilf_type(skc8,subset_type(cross_product(skc7,skc6))),
inference(res,[status(thm),theory(equality)],[12,83]),
[iquote('0:Res:12.0,83.0')] ).
cnf(121,plain,
( ~ ilf_type(u,member_type(skc7))
| ~ member(skc9,range_of(skc8))
| ~ member(ordered_pair(u,skc9),skc8) ),
inference(rew,[status(thm),theory(equality)],[118,38]),
[iquote('0:Rew:118.0,38.0')] ).
cnf(122,plain,
( member(skc9,range_of(skc8))
| member(ordered_pair(skc10,skc9),skc8) ),
inference(rew,[status(thm),theory(equality)],[118,28]),
[iquote('0:Rew:118.0,28.1')] ).
cnf(125,plain,
~ member(skc9,range_of(skc8)),
inference(spt,[spt(split,[position(s1)])],[121]),
[iquote('1:Spt:121.1')] ).
cnf(127,plain,
member(ordered_pair(skc10,skc9),skc8),
inference(mrr,[status(thm)],[122,125]),
[iquote('1:MRR:122.0,125.0')] ).
cnf(156,plain,
relation_like(skc8),
inference(res,[status(thm),theory(equality)],[119,76]),
[iquote('0:Res:119.0,76.0')] ).
cnf(303,plain,
( ~ ilf_type(skc8,binary_relation_type)
| member(skc9,range_of(skc8)) ),
inference(res,[status(thm),theory(equality)],[127,95]),
[iquote('1:Res:127.0,95.1')] ).
cnf(307,plain,
~ ilf_type(skc8,binary_relation_type),
inference(mrr,[status(thm)],[303,125]),
[iquote('1:MRR:303.1,125.0')] ).
cnf(308,plain,
~ relation_like(skc8),
inference(res,[status(thm),theory(equality)],[69,307]),
[iquote('1:Res:69.1,307.0')] ).
cnf(309,plain,
$false,
inference(ssi,[status(thm)],[308,156]),
[iquote('1:SSi:308.0,156.0')] ).
cnf(310,plain,
member(skc9,range_of(skc8)),
inference(spt,[spt(split,[position(sa)])],[309,125]),
[iquote('1:Spt:309.0,121.1,125.0')] ).
cnf(311,plain,
( ~ ilf_type(u,member_type(skc7))
| ~ member(ordered_pair(u,skc9),skc8) ),
inference(spt,[spt(split,[position(s2)])],[121]),
[iquote('1:Spt:309.0,121.0,121.2')] ).
cnf(817,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(u,range_of(skc8))
| member(skf10(skc8,u),skc7) ),
inference(res,[status(thm),theory(equality)],[85,113]),
[iquote('0:Res:85.2,113.0')] ).
cnf(819,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(skc9,range_of(skc8))
| ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
inference(res,[status(thm),theory(equality)],[85,311]),
[iquote('1:Res:85.2,311.1')] ).
cnf(828,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
inference(mrr,[status(thm)],[819,310]),
[iquote('1:MRR:819.1,310.0')] ).
cnf(989,plain,
( ~ member(skf10(skc8,skc9),skc7)
| ~ ilf_type(skc8,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[81,828]),
[iquote('1:Res:81.1,828.1')] ).
cnf(15827,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(skc9,range_of(skc8))
| ~ ilf_type(skc8,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[817,989]),
[iquote('1:Res:817.2,989.0')] ).
cnf(15828,plain,
( ~ member(skc9,range_of(skc8))
| ~ ilf_type(skc8,binary_relation_type) ),
inference(obv,[status(thm),theory(equality)],[15827]),
[iquote('1:Obv:15827.0')] ).
cnf(15829,plain,
~ ilf_type(skc8,binary_relation_type),
inference(mrr,[status(thm)],[15828,310]),
[iquote('1:MRR:15828.0,310.0')] ).
cnf(15830,plain,
~ relation_like(skc8),
inference(res,[status(thm),theory(equality)],[69,15829]),
[iquote('1:Res:69.1,15829.0')] ).
cnf(15831,plain,
$false,
inference(ssi,[status(thm)],[15830,156]),
[iquote('1:SSi:15830.0,156.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 Jul 10 18:18:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 18.48/18.69
% 18.48/18.69 SPASS V 3.9
% 18.48/18.69 SPASS beiseite: Proof found.
% 18.48/18.69 % SZS status Theorem
% 18.48/18.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.48/18.69 SPASS derived 15207 clauses, backtracked 175 clauses, performed 7 splits and kept 12654 clauses.
% 18.48/18.69 SPASS allocated 112306 KBytes.
% 18.48/18.69 SPASS spent 0:0:18.11 on the problem.
% 18.48/18.69 0:00:00.03 for the input.
% 18.48/18.69 0:00:00.05 for the FLOTTER CNF translation.
% 18.48/18.69 0:00:00.13 for inferences.
% 18.48/18.69 0:00:00.57 for the backtracking.
% 18.48/18.69 0:0:17.23 for the reduction.
% 18.48/18.69
% 18.48/18.69
% 18.48/18.69 Here is a proof with depth 5, length 45 :
% 18.48/18.69 % SZS output start Refutation
% See solution above
% 18.48/18.69 Formulae used in the proof : p31 prove_relset_1_48 p17 p10 p26 p8 p6 p1 p29 p2 p3
% 18.48/18.69
%------------------------------------------------------------------------------