TSTP Solution File: SET680+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET680+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 23.26s 23.43s
% Output : Refutation 23.26s
% 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('SET680+3.p',unknown),
[] ).
cnf(12,axiom,
ilf_type(skc8,relation_type(skc6,skc7)),
file('SET680+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET680+3.p',unknown),
[] ).
cnf(28,axiom,
( member(ordered_pair(skc9,skc10),skc8)
| member(skc9,domain__dfg(skc6,skc7,skc8)) ),
file('SET680+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET680+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('SET680+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(skc9,domain__dfg(skc6,skc7,skc8))
| ~ ilf_type(u,member_type(skc7))
| ~ member(ordered_pair(skc9,u),skc8) ),
file('SET680+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('SET680+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('SET680+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ member(u,domain_of(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,binary_relation_type)
| member(ordered_pair(u,skf10(v,u)),v) ),
file('SET680+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(domain__dfg(u,v,w),domain_of(w)) ),
file('SET680+3.p',unknown),
[] ).
cnf(55,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,binary_relation_type)
| ~ member(ordered_pair(u,v),w)
| member(u,domain_of(w)) ),
file('SET680+3.p',unknown),
[] ).
cnf(63,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(x,v) ),
file('SET680+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,domain_of(u))
| member(ordered_pair(v,skf10(u,v)),u) ),
inference(mrr,[status(thm)],[46,6]),
[iquote('0:MRR:46.1,6.0')] ).
cnf(90,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[50,6]),
[iquote('0:MRR:50.0,50.1,6.0,6.0')] ).
cnf(96,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(ordered_pair(v,w),u)
| member(v,domain_of(u)) ),
inference(mrr,[status(thm)],[55,6]),
[iquote('0:MRR:55.0,55.1,6.0,6.0')] ).
cnf(104,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ member(ordered_pair(x,y),u)
| member(y,w) ),
inference(mrr,[status(thm)],[63,6]),
[iquote('0:MRR:63.0,63.1,63.2,63.3,6.0,6.0,6.0,6.0')] ).
cnf(114,plain,
( ~ member(ordered_pair(u,v),skc8)
| member(v,skc7) ),
inference(res,[status(thm),theory(equality)],[12,104]),
[iquote('0:Res:12.0,104.0')] ).
cnf(116,plain,
equal(domain__dfg(skc6,skc7,skc8),domain_of(skc8)),
inference(res,[status(thm),theory(equality)],[12,90]),
[iquote('0:Res:12.0,90.0')] ).
cnf(119,plain,
ilf_type(skc8,subset_type(cross_product(skc6,skc7))),
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,domain_of(skc8))
| ~ member(ordered_pair(skc9,u),skc8) ),
inference(rew,[status(thm),theory(equality)],[116,38]),
[iquote('0:Rew:116.0,38.0')] ).
cnf(122,plain,
( member(skc9,domain_of(skc8))
| member(ordered_pair(skc9,skc10),skc8) ),
inference(rew,[status(thm),theory(equality)],[116,28]),
[iquote('0:Rew:116.0,28.1')] ).
cnf(125,plain,
~ member(skc9,domain_of(skc8)),
inference(spt,[spt(split,[position(s1)])],[121]),
[iquote('1:Spt:121.1')] ).
cnf(127,plain,
member(ordered_pair(skc9,skc10),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(320,plain,
( ~ ilf_type(skc8,binary_relation_type)
| member(skc9,domain_of(skc8)) ),
inference(res,[status(thm),theory(equality)],[127,96]),
[iquote('1:Res:127.0,96.1')] ).
cnf(324,plain,
~ ilf_type(skc8,binary_relation_type),
inference(mrr,[status(thm)],[320,125]),
[iquote('1:MRR:320.1,125.0')] ).
cnf(325,plain,
~ relation_like(skc8),
inference(res,[status(thm),theory(equality)],[69,324]),
[iquote('1:Res:69.1,324.0')] ).
cnf(326,plain,
$false,
inference(ssi,[status(thm)],[325,156]),
[iquote('1:SSi:325.0,156.0')] ).
cnf(327,plain,
member(skc9,domain_of(skc8)),
inference(spt,[spt(split,[position(sa)])],[326,125]),
[iquote('1:Spt:326.0,121.1,125.0')] ).
cnf(328,plain,
( ~ ilf_type(u,member_type(skc7))
| ~ member(ordered_pair(skc9,u),skc8) ),
inference(spt,[spt(split,[position(s2)])],[121]),
[iquote('1:Spt:326.0,121.0,121.2')] ).
cnf(809,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(u,domain_of(skc8))
| member(skf10(skc8,u),skc7) ),
inference(res,[status(thm),theory(equality)],[85,114]),
[iquote('0:Res:85.2,114.0')] ).
cnf(810,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(skc9,domain_of(skc8))
| ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
inference(res,[status(thm),theory(equality)],[85,328]),
[iquote('1:Res:85.2,328.1')] ).
cnf(819,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ ilf_type(skf10(skc8,skc9),member_type(skc7)) ),
inference(mrr,[status(thm)],[810,327]),
[iquote('1:MRR:810.1,327.0')] ).
cnf(982,plain,
( ~ member(skf10(skc8,skc9),skc7)
| ~ ilf_type(skc8,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[81,819]),
[iquote('1:Res:81.1,819.1')] ).
cnf(18566,plain,
( ~ ilf_type(skc8,binary_relation_type)
| ~ member(skc9,domain_of(skc8))
| ~ ilf_type(skc8,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[809,982]),
[iquote('1:Res:809.2,982.0')] ).
cnf(18567,plain,
( ~ member(skc9,domain_of(skc8))
| ~ ilf_type(skc8,binary_relation_type) ),
inference(obv,[status(thm),theory(equality)],[18566]),
[iquote('1:Obv:18566.0')] ).
cnf(18568,plain,
~ ilf_type(skc8,binary_relation_type),
inference(mrr,[status(thm)],[18567,327]),
[iquote('1:MRR:18567.0,327.0')] ).
cnf(18569,plain,
~ relation_like(skc8),
inference(res,[status(thm),theory(equality)],[69,18568]),
[iquote('1:Res:69.1,18568.0')] ).
cnf(18570,plain,
$false,
inference(ssi,[status(thm)],[18569,156]),
[iquote('1:SSi:18569.0,156.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET680+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 23:07:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 23.26/23.43
% 23.26/23.43 SPASS V 3.9
% 23.26/23.43 SPASS beiseite: Proof found.
% 23.26/23.43 % SZS status Theorem
% 23.26/23.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.26/23.43 SPASS derived 17797 clauses, backtracked 172 clauses, performed 8 splits and kept 14129 clauses.
% 23.26/23.43 SPASS allocated 114916 KBytes.
% 23.26/23.43 SPASS spent 0:0:22.61 on the problem.
% 23.26/23.43 0:00:00.04 for the input.
% 23.26/23.43 0:00:00.05 for the FLOTTER CNF translation.
% 23.26/23.43 0:00:00.18 for inferences.
% 23.26/23.43 0:00:00.72 for the backtracking.
% 23.26/23.43 0:0:21.47 for the reduction.
% 23.26/23.43
% 23.26/23.43
% 23.26/23.43 Here is a proof with depth 5, length 45 :
% 23.26/23.43 % SZS output start Refutation
% See solution above
% 23.26/23.43 Formulae used in the proof : p31 prove_relset_1_47 p17 p10 p26 p8 p6 p1 p27 p2 p3
% 23.26/23.43
%------------------------------------------------------------------------------