TSTP Solution File: SET016-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 05:22:34 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 15 unt; 3 nHn; 19 RR)
% Number of literals : 25 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(u,singleton_set(u)),
file('SET016-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,singleton_set(v))
| equal(u,v) ),
file('SET016-1.p',unknown),
[] ).
cnf(3,axiom,
member(u,unordered_pair(u,v)),
file('SET016-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET016-1.p',unknown),
[] ).
cnf(6,axiom,
equal(unordered_pair(singleton_set(u),unordered_pair(u,v)),ordered_pair(u,v)),
file('SET016-1.p',unknown),
[] ).
cnf(7,axiom,
equal(ordered_pair(m2,r2),ordered_pair(m1,r1)),
file('SET016-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(m2,m1),
file('SET016-1.p',unknown),
[] ).
cnf(13,plain,
~ member(m1,singleton_set(m2)),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.1,8.0')] ).
cnf(26,plain,
member(singleton_set(u),ordered_pair(u,v)),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(29,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(spr,[status(thm),theory(equality)],[7,26]),
[iquote('0:SpR:7.0,26.0')] ).
cnf(32,plain,
( ~ member(u,ordered_pair(v,w))
| equal(u,unordered_pair(v,w))
| equal(u,singleton_set(v)) ),
inference(spl,[status(thm),theory(equality)],[6,5]),
[iquote('0:SpL:6.0,5.0')] ).
cnf(56,plain,
( equal(unordered_pair(m1,r1),singleton_set(m2))
| equal(singleton_set(m2),singleton_set(m1)) ),
inference(res,[status(thm),theory(equality)],[29,32]),
[iquote('0:Res:29.0,32.0')] ).
cnf(62,plain,
equal(singleton_set(m2),singleton_set(m1)),
inference(spt,[spt(split,[position(s1)])],[56]),
[iquote('1:Spt:56.1')] ).
cnf(63,plain,
~ member(m1,singleton_set(m1)),
inference(rew,[status(thm),theory(equality)],[62,13]),
[iquote('1:Rew:62.0,13.0')] ).
cnf(71,plain,
$false,
inference(mrr,[status(thm)],[63,1]),
[iquote('1:MRR:63.0,1.0')] ).
cnf(77,plain,
~ equal(singleton_set(m2),singleton_set(m1)),
inference(spt,[spt(split,[position(sa)])],[71,62]),
[iquote('1:Spt:71.0,56.1,62.0')] ).
cnf(78,plain,
equal(unordered_pair(m1,r1),singleton_set(m2)),
inference(spt,[spt(split,[position(s2)])],[56]),
[iquote('1:Spt:71.0,56.0')] ).
cnf(81,plain,
member(m1,singleton_set(m2)),
inference(spr,[status(thm),theory(equality)],[78,3]),
[iquote('1:SpR:78.0,3.0')] ).
cnf(88,plain,
$false,
inference(mrr,[status(thm)],[81,13]),
[iquote('1:MRR:81.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.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 16:41:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 91 clauses, backtracked 10 clauses, performed 1 splits and kept 76 clauses.
% 0.20/0.42 SPASS allocated 63208 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.42 0:00:00.03 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 5, length 19 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : singleton_1 singleton_2 unordered_pair_1 unordered_pair_3 ordered_pair equal_ordered_pairs prove_first_components_equal
% 0.20/0.42
%------------------------------------------------------------------------------