TSTP Solution File: SET927+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:29:53 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 10 unt; 7 nHn; 28 RR)
% Number of literals : 55 ( 0 equ; 25 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ in(skc5,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
file('SET927+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(u,v)
| ~ equal(set_difference(unordered_pair(u,w),v),singleton(u)) ),
file('SET927+1.p',unknown),
[] ).
cnf(7,axiom,
( equal(skc6,skc5)
| in(skc6,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
file('SET927+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(set_difference(unordered_pair(u,v),w),singleton(u))
| equal(u,v)
| in(v,w) ),
file('SET927+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(u,v)
| in(w,v)
| equal(set_difference(unordered_pair(w,u),v),singleton(w)) ),
file('SET927+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,v)
| in(u,w)
| equal(set_difference(unordered_pair(u,v),w),singleton(u)) ),
file('SET927+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(skc6,skc7)
| ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5))
| in(skc5,skc7) ),
file('SET927+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(skc6,skc5)
| ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5))
| in(skc5,skc7) ),
file('SET927+1.p',unknown),
[] ).
cnf(13,plain,
( ~ equal(skc6,skc5)
| ~ equal(singleton(skc5),singleton(skc5))
| in(skc5,skc7) ),
inference(rew,[status(thm),theory(equality)],[10,12]),
[iquote('0:Rew:10.1,12.1')] ).
cnf(14,plain,
( ~ equal(skc6,skc5)
| in(skc5,skc7) ),
inference(obv,[status(thm),theory(equality)],[13]),
[iquote('0:Obv:13.1')] ).
cnf(15,plain,
( ~ in(skc6,skc7)
| ~ equal(singleton(skc5),singleton(skc5))
| in(skc5,skc7) ),
inference(rew,[status(thm),theory(equality)],[9,11]),
[iquote('0:Rew:9.1,11.1')] ).
cnf(16,plain,
( ~ in(skc6,skc7)
| in(skc5,skc7) ),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('0:Obv:15.1')] ).
cnf(17,plain,
equal(skc6,skc5),
inference(spt,[spt(split,[position(s1)])],[7]),
[iquote('1:Spt:7.0')] ).
cnf(18,plain,
( ~ in(skc5,skc7)
| equal(set_difference(unordered_pair(skc5,skc5),skc7),singleton(skc5)) ),
inference(rew,[status(thm),theory(equality)],[17,5]),
[iquote('1:Rew:17.0,5.1')] ).
cnf(20,plain,
( ~ equal(skc5,skc5)
| in(skc5,skc7) ),
inference(rew,[status(thm),theory(equality)],[17,14]),
[iquote('1:Rew:17.0,14.0')] ).
cnf(21,plain,
in(skc5,skc7),
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('1:Obv:20.0')] ).
cnf(22,plain,
equal(set_difference(unordered_pair(skc5,skc5),skc7),singleton(skc5)),
inference(mrr,[status(thm)],[18,21]),
[iquote('1:MRR:18.0,21.0')] ).
cnf(34,plain,
( ~ in(skc5,skc7)
| ~ equal(singleton(skc5),singleton(skc5)) ),
inference(spl,[status(thm),theory(equality)],[22,6]),
[iquote('1:SpL:22.0,6.1')] ).
cnf(35,plain,
~ in(skc5,skc7),
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('1:Obv:34.1')] ).
cnf(36,plain,
$false,
inference(mrr,[status(thm)],[35,21]),
[iquote('1:MRR:35.0,21.0')] ).
cnf(37,plain,
~ equal(skc6,skc5),
inference(spt,[spt(split,[position(sa)])],[36,17]),
[iquote('1:Spt:36.0,7.0,17.0')] ).
cnf(38,plain,
( in(skc6,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
inference(spt,[spt(split,[position(s2)])],[7]),
[iquote('1:Spt:36.0,7.1,7.2')] ).
cnf(39,plain,
~ in(skc5,skc7),
inference(mrr,[status(thm)],[5,6]),
[iquote('0:MRR:5.1,6.1')] ).
cnf(40,plain,
~ in(skc6,skc7),
inference(mrr,[status(thm)],[16,39]),
[iquote('0:MRR:16.1,39.0')] ).
cnf(41,plain,
equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)),
inference(mrr,[status(thm)],[38,40]),
[iquote('1:MRR:38.0,40.0')] ).
cnf(66,plain,
( ~ equal(singleton(skc5),singleton(skc5))
| equal(skc6,skc5)
| in(skc6,skc7) ),
inference(spl,[status(thm),theory(equality)],[41,8]),
[iquote('1:SpL:41.0,8.0')] ).
cnf(68,plain,
( equal(skc6,skc5)
| in(skc6,skc7) ),
inference(obv,[status(thm),theory(equality)],[66]),
[iquote('1:Obv:66.0')] ).
cnf(69,plain,
$false,
inference(mrr,[status(thm)],[68,37,40]),
[iquote('1:MRR:68.0,68.1,37.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 05:11:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 42 clauses, backtracked 5 clauses, performed 1 splits and kept 30 clauses.
% 0.19/0.45 SPASS allocated 85109 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.00 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 2, length 28 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : t70_zfmisc_1 l39_zfmisc_1
% 0.19/0.45
%------------------------------------------------------------------------------