TSTP Solution File: SET682+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET682+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:28:04 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 56 ( 14 unt; 9 nHn; 56 RR)
% Number of literals : 133 ( 0 equ; 77 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
ilf_type(u,set_type),
file('SET682+3.p',unknown),
[] ).
cnf(13,axiom,
ilf_type(skc7,relation_type(skc5,skc6)),
file('SET682+3.p',unknown),
[] ).
cnf(15,axiom,
member(skc8,domain__dfg(skc5,skc6,skc7)),
file('SET682+3.p',unknown),
[] ).
cnf(22,axiom,
( ~ ilf_type(u,set_type)
| member(skf12(u),u)
| empty(u) ),
file('SET682+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET682+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ ilf_type(u,member_type(skc6))
| ~ member(u,range__dfg(skc5,skc6,skc7)) ),
file('SET682+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET682+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf14(v,u),u)
| member(u,power_set(v)) ),
file('SET682+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET682+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,binary_relation_type)
| ~ member(u,domain_of(v))
| member(skf9(v),range_of(v)) ),
file('SET682+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET682+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET682+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ ilf_type(u,subset_type(v))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,member_type(power_set(v))) ),
file('SET682+3.p',unknown),
[] ).
cnf(40,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('SET682+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| ilf_type(range__dfg(u,v,w),subset_type(v)) ),
file('SET682+3.p',unknown),
[] ).
cnf(43,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('SET682+3.p',unknown),
[] ).
cnf(45,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('SET682+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ member(u,power_set(v))
| ~ ilf_type(w,set_type)
| ~ member(w,u)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(w,v) ),
file('SET682+3.p',unknown),
[] ).
cnf(53,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[24,6]),
[iquote('0:MRR:24.1,6.0')] ).
cnf(55,plain,
( empty(u)
| member(skf12(u),u) ),
inference(mrr,[status(thm)],[22,6]),
[iquote('0:MRR:22.0,6.0')] ).
cnf(57,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[31,6]),
[iquote('0:MRR:31.1,31.3,6.0,6.0')] ).
cnf(59,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[33,6]),
[iquote('0:MRR:33.0,33.1,6.0,6.0')] ).
cnf(60,plain,
( member(u,power_set(v))
| member(skf14(v,u),u) ),
inference(mrr,[status(thm)],[32,6]),
[iquote('0:MRR:32.0,32.1,6.0,6.0')] ).
cnf(63,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[37,6]),
[iquote('0:MRR:37.1,37.2,6.0,6.0')] ).
cnf(64,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[36,6,57]),
[iquote('0:MRR:36.1,36.2,36.4,6.0,6.0,57.0')] ).
cnf(65,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[35,6]),
[iquote('0:MRR:35.1,35.2,6.0,6.0')] ).
cnf(66,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ member(v,domain_of(u))
| member(skf9(u),range_of(u)) ),
inference(mrr,[status(thm)],[34,6]),
[iquote('0:MRR:34.0,6.0')] ).
cnf(67,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[40,6]),
[iquote('0:MRR:40.1,40.2,6.0,6.0')] ).
cnf(69,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range__dfg(v,w,u),subset_type(w)) ),
inference(mrr,[status(thm)],[42,6]),
[iquote('0:MRR:42.0,42.1,6.0,6.0')] ).
cnf(70,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[43,6]),
[iquote('0:MRR:43.0,43.1,6.0,6.0')] ).
cnf(71,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range_of(u),subset_type(w)) ),
inference(rew,[status(thm),theory(equality)],[70,69]),
[iquote('0:Rew:70.1,69.1')] ).
cnf(73,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[45,6]),
[iquote('0:MRR:45.0,45.1,6.0,6.0')] ).
cnf(77,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[48,6]),
[iquote('0:MRR:48.1,48.3,48.4,6.0,6.0,6.0')] ).
cnf(86,plain,
equal(domain__dfg(skc5,skc6,skc7),domain_of(skc7)),
inference(res,[status(thm),theory(equality)],[13,73]),
[iquote('0:Res:13.0,73.0')] ).
cnf(87,plain,
ilf_type(range_of(skc7),subset_type(skc6)),
inference(res,[status(thm),theory(equality)],[13,71]),
[iquote('0:Res:13.0,71.0')] ).
cnf(88,plain,
equal(range__dfg(skc5,skc6,skc7),range_of(skc7)),
inference(res,[status(thm),theory(equality)],[13,70]),
[iquote('0:Res:13.0,70.0')] ).
cnf(89,plain,
ilf_type(skc7,subset_type(cross_product(skc5,skc6))),
inference(res,[status(thm),theory(equality)],[13,67]),
[iquote('0:Res:13.0,67.0')] ).
cnf(95,plain,
member(skc8,domain_of(skc7)),
inference(rew,[status(thm),theory(equality)],[86,15]),
[iquote('0:Rew:86.0,15.0')] ).
cnf(96,plain,
( ~ member(u,range_of(skc7))
| ~ ilf_type(u,member_type(skc6)) ),
inference(rew,[status(thm),theory(equality)],[88,27]),
[iquote('0:Rew:88.0,27.1')] ).
cnf(119,plain,
relation_like(skc7),
inference(res,[status(thm),theory(equality)],[89,59]),
[iquote('0:Res:89.0,59.0')] ).
cnf(120,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[60,57]),
[iquote('0:Res:60.1,57.1')] ).
cnf(121,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[120,57]),
[iquote('0:Res:120.1,57.1')] ).
cnf(123,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[121]),
[iquote('0:Con:121.0')] ).
cnf(124,plain,
( ~ ilf_type(skf12(range_of(skc7)),member_type(skc6))
| empty(range_of(skc7)) ),
inference(res,[status(thm),theory(equality)],[55,96]),
[iquote('0:Res:55.1,96.0')] ).
cnf(127,plain,
( ~ member(skf12(range_of(skc7)),skc6)
| empty(range_of(skc7)) ),
inference(res,[status(thm),theory(equality)],[64,124]),
[iquote('0:Res:64.1,124.0')] ).
cnf(151,plain,
( ~ ilf_type(u,subset_type(v))
| empty(power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[63,65]),
[iquote('0:Res:63.1,65.0')] ).
cnf(153,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[151,123]),
[iquote('0:MRR:151.1,123.0')] ).
cnf(202,plain,
( ~ ilf_type(u,subset_type(v))
| ~ member(w,u)
| member(w,v) ),
inference(res,[status(thm),theory(equality)],[153,77]),
[iquote('0:Res:153.1,77.1')] ).
cnf(234,plain,
( ~ ilf_type(skc7,binary_relation_type)
| member(skf9(skc7),range_of(skc7)) ),
inference(res,[status(thm),theory(equality)],[95,66]),
[iquote('0:Res:95.0,66.1')] ).
cnf(239,plain,
( ~ empty(range_of(skc7))
| ~ ilf_type(skc7,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[234,57]),
[iquote('0:Res:234.1,57.1')] ).
cnf(495,plain,
( ~ member(u,range_of(skc7))
| member(u,skc6) ),
inference(res,[status(thm),theory(equality)],[87,202]),
[iquote('0:Res:87.0,202.0')] ).
cnf(542,plain,
( empty(range_of(skc7))
| member(skf12(range_of(skc7)),skc6) ),
inference(res,[status(thm),theory(equality)],[55,495]),
[iquote('0:Res:55.1,495.0')] ).
cnf(555,plain,
empty(range_of(skc7)),
inference(mrr,[status(thm)],[542,127]),
[iquote('0:MRR:542.1,127.0')] ).
cnf(556,plain,
~ ilf_type(skc7,binary_relation_type),
inference(mrr,[status(thm)],[239,555]),
[iquote('0:MRR:239.0,555.0')] ).
cnf(561,plain,
~ relation_like(skc7),
inference(res,[status(thm),theory(equality)],[53,556]),
[iquote('0:Res:53.1,556.0')] ).
cnf(562,plain,
$false,
inference(ssi,[status(thm)],[561,119]),
[iquote('0:SSi:561.0,119.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET682+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 08:42:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 472 clauses, backtracked 0 clauses, performed 1 splits and kept 415 clauses.
% 0.18/0.51 SPASS allocated 98274 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.05 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 4, length 56 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : p24 prove_relset_1_49 p6 p10 p14 p18 p1 p4 p12 p2 p23 p22 p20
% 0.18/0.51
%------------------------------------------------------------------------------