TSTP Solution File: SET646+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:27:49 EDT 2022
% Result : Theorem 0.48s 0.67s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 10 unt; 5 nHn; 32 RR)
% Number of literals : 78 ( 0 equ; 45 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
member(skc7,skc5),
file('SET646+3.p',unknown),
[] ).
cnf(6,axiom,
member(skc6,skc4),
file('SET646+3.p',unknown),
[] ).
cnf(7,axiom,
ilf_type(u,set_type),
file('SET646+3.p',unknown),
[] ).
cnf(20,axiom,
~ ilf_type(singleton(ordered_pair(skc6,skc7)),relation_type(skc4,skc5)),
file('SET646+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET646+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf16(v,u),u)
| member(u,power_set(v)) ),
file('SET646+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ ilf_type(u,member_type(power_set(v)))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,subset_type(v)) ),
file('SET646+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(skf16(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET646+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET646+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ilf_type(u,relation_type(v,w)) ),
file('SET646+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ member(u,v)
| ~ equal(v,singleton(w))
| ~ ilf_type(u,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(v,set_type)
| equal(u,w) ),
file('SET646+3.p',unknown),
[] ).
cnf(61,axiom,
( ~ member(u,v)
| ~ member(w,x)
| ~ ilf_type(u,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(x,set_type)
| member(ordered_pair(u,w),cross_product(v,x)) ),
file('SET646+3.p',unknown),
[] ).
cnf(69,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[31,7]),
[iquote('0:MRR:31.1,31.3,7.0,7.0')] ).
cnf(76,plain,
( member(u,power_set(v))
| member(skf16(v,u),u) ),
inference(mrr,[status(thm)],[36,7]),
[iquote('0:MRR:36.0,36.1,7.0,7.0')] ).
cnf(78,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[42,7,69]),
[iquote('0:MRR:42.1,42.2,42.4,7.0,7.0,69.0')] ).
cnf(80,plain,
( ~ member(skf16(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[40,7]),
[iquote('0:MRR:40.1,40.2,7.0,7.0')] ).
cnf(81,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[39,7]),
[iquote('0:MRR:39.1,39.2,7.0,7.0')] ).
cnf(84,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[44,7]),
[iquote('0:MRR:44.1,44.2,7.0,7.0')] ).
cnf(95,plain,
( ~ member(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
inference(mrr,[status(thm)],[56,7]),
[iquote('0:MRR:56.2,56.3,56.4,7.0,7.0,7.0')] ).
cnf(102,plain,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
inference(mrr,[status(thm)],[61,7]),
[iquote('0:MRR:61.2,61.3,61.4,61.5,7.0,7.0,7.0,7.0')] ).
cnf(107,plain,
( ~ member(u,v)
| member(ordered_pair(skc6,u),cross_product(skc4,v)) ),
inference(res,[status(thm),theory(equality)],[6,102]),
[iquote('0:Res:6.0,102.0')] ).
cnf(123,plain,
~ ilf_type(singleton(ordered_pair(skc6,skc7)),subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[84,20]),
[iquote('0:Res:84.1,20.0')] ).
cnf(127,plain,
member(ordered_pair(skc6,skc7),cross_product(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[5,107]),
[iquote('0:Res:5.0,107.0')] ).
cnf(173,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[78,81]),
[iquote('0:Res:78.1,81.0')] ).
cnf(303,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[95]),
[iquote('0:EqR:95.1')] ).
cnf(311,plain,
( member(singleton(u),power_set(v))
| equal(skf16(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[76,303]),
[iquote('0:Res:76.1,303.0')] ).
cnf(1550,plain,
( equal(skf16(u,singleton(v)),v)
| ilf_type(singleton(v),subset_type(u)) ),
inference(res,[status(thm),theory(equality)],[311,173]),
[iquote('0:Res:311.0,173.0')] ).
cnf(1607,plain,
equal(skf16(cross_product(skc4,skc5),singleton(ordered_pair(skc6,skc7))),ordered_pair(skc6,skc7)),
inference(res,[status(thm),theory(equality)],[1550,123]),
[iquote('0:Res:1550.1,123.0')] ).
cnf(1624,plain,
( ~ member(ordered_pair(skc6,skc7),cross_product(skc4,skc5))
| member(singleton(ordered_pair(skc6,skc7)),power_set(cross_product(skc4,skc5))) ),
inference(spl,[status(thm),theory(equality)],[1607,80]),
[iquote('0:SpL:1607.0,80.0')] ).
cnf(1625,plain,
member(singleton(ordered_pair(skc6,skc7)),power_set(cross_product(skc4,skc5))),
inference(mrr,[status(thm)],[1624,127]),
[iquote('0:MRR:1624.0,127.0')] ).
cnf(1637,plain,
ilf_type(singleton(ordered_pair(skc6,skc7)),subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[1625,173]),
[iquote('0:Res:1625.0,173.0')] ).
cnf(1639,plain,
$false,
inference(mrr,[status(thm)],[1637,123]),
[iquote('0:MRR:1637.0,123.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 23:41:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.67
% 0.48/0.67 SPASS V 3.9
% 0.48/0.67 SPASS beiseite: Proof found.
% 0.48/0.67 % SZS status Theorem
% 0.48/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.67 SPASS derived 1459 clauses, backtracked 0 clauses, performed 0 splits and kept 961 clauses.
% 0.48/0.67 SPASS allocated 99160 KBytes.
% 0.48/0.67 SPASS spent 0:00:00.31 on the problem.
% 0.48/0.67 0:00:00.03 for the input.
% 0.48/0.67 0:00:00.04 for the FLOTTER CNF translation.
% 0.48/0.67 0:00:00.02 for inferences.
% 0.48/0.67 0:00:00.00 for the backtracking.
% 0.48/0.67 0:00:00.19 for the reduction.
% 0.48/0.67
% 0.48/0.67
% 0.48/0.67 Here is a proof with depth 6, length 32 :
% 0.48/0.67 % SZS output start Refutation
% See solution above
% 0.48/0.67 Formulae used in the proof : prove_relset_1_8 p25 p21 p17 p12 p19 p3 p5 p2
% 0.48/0.67
%------------------------------------------------------------------------------