%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:35 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 15 unt; 4 nHn; 25 RR)
% Number of literals : 43 ( 0 equ; 20 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ equal(skc8,skc6),
file('SET887+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(skc7,skc6),
file('SET887+1.p',unknown),
[] ).
cnf(7,axiom,
subset(unordered_pair(skc6,skc9),unordered_pair(skc8,skc7)),
file('SET887+1.p',unknown),
[] ).
cnf(8,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET887+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SET887+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ equal(singleton(u),unordered_pair(v,w))
| equal(u,v) ),
file('SET887+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET887+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ equal(unordered_pair(u,v),unordered_pair(w,x))
| equal(u,x)
| equal(u,w) ),
file('SET887+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(u,unordered_pair(v,w))
| equal(u,empty_set)
| equal(u,singleton(v))
| equal(u,singleton(w))
| equal(u,unordered_pair(v,w)) ),
file('SET887+1.p',unknown),
[] ).
cnf(25,plain,
subset(unordered_pair(skc6,skc9),unordered_pair(skc7,skc8)),
inference(rew,[status(thm),theory(equality)],[8,7]),
[iquote('0:Rew:8.0,7.0')] ).
cnf(26,plain,
~ equal(unordered_pair(skc6,u),singleton(skc7)),
inference(res,[status(thm),theory(equality)],[15,6]),
[iquote('0:Res:15.1,6.0')] ).
cnf(35,plain,
( ~ equal(unordered_pair(skc6,u),unordered_pair(v,skc7))
| equal(skc6,v) ),
inference(res,[status(thm),theory(equality)],[19,6]),
[iquote('0:Res:19.2,6.0')] ).
cnf(36,plain,
~ equal(unordered_pair(skc6,u),singleton(skc8)),
inference(res,[status(thm),theory(equality)],[15,5]),
[iquote('0:Res:15.1,5.0')] ).
cnf(46,plain,
( equal(unordered_pair(skc6,skc9),singleton(skc8))
| equal(unordered_pair(skc7,skc8),unordered_pair(skc6,skc9))
| equal(unordered_pair(skc6,skc9),singleton(skc7))
| equal(unordered_pair(skc6,skc9),empty_set) ),
inference(res,[status(thm),theory(equality)],[25,24]),
[iquote('0:Res:25.0,24.0')] ).
cnf(47,plain,
( equal(unordered_pair(skc6,skc9),empty_set)
| equal(unordered_pair(skc7,skc8),unordered_pair(skc6,skc9)) ),
inference(mrr,[status(thm)],[46,36,26]),
[iquote('0:MRR:46.0,46.2,36.0,26.0')] ).
cnf(58,plain,
~ equal(unordered_pair(skc6,u),unordered_pair(skc8,skc7)),
inference(res,[status(thm),theory(equality)],[35,5]),
[iquote('0:Res:35.1,5.0')] ).
cnf(60,plain,
~ equal(unordered_pair(skc6,u),unordered_pair(skc7,skc8)),
inference(rew,[status(thm),theory(equality)],[8,58]),
[iquote('0:Rew:8.0,58.0')] ).
cnf(62,plain,
equal(unordered_pair(skc7,skc8),unordered_pair(skc6,skc9)),
inference(spt,[spt(split,[position(s1)])],[47]),
[iquote('1:Spt:47.1')] ).
cnf(63,plain,
$false,
inference(unc,[status(thm)],[62,60]),
[iquote('1:UnC:62.0,60.0')] ).
cnf(64,plain,
~ equal(unordered_pair(skc7,skc8),unordered_pair(skc6,skc9)),
inference(spt,[spt(split,[position(sa)])],[63,62]),
[iquote('1:Spt:63.0,47.1,62.0')] ).
cnf(65,plain,
equal(unordered_pair(skc6,skc9),empty_set),
inference(spt,[spt(split,[position(s2)])],[47]),
[iquote('1:Spt:63.0,47.0')] ).
cnf(154,plain,
( ~ equal(u,skc9)
| ~ equal(v,empty_set)
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[65,18]),
[iquote('1:SpL:65.0,18.1')] ).
cnf(157,plain,
( ~ equal(u,skc9)
| ~ equal(v,empty_set) ),
inference(mrr,[status(thm)],[154,11]),
[iquote('1:MRR:154.2,11.0')] ).
cnf(158,plain,
~ equal(u,empty_set),
inference(eqr,[status(thm),theory(equality)],[157]),
[iquote('1:EqR:157.0')] ).
cnf(159,plain,
$false,
inference(obv,[status(thm),theory(equality)],[158]),
[iquote('1:Obv:158.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 16:42:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 124 clauses, backtracked 2 clauses, performed 1 splits and kept 81 clauses.
% 0.19/0.41 SPASS allocated 85249 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.02 for the input.
% 0.19/0.41 0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 4, length 25 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : t28_zfmisc_1 commutativity_k2_tarski d1_xboole_0 t8_zfmisc_1 d2_tarski t10_zfmisc_1 l46_zfmisc_1
% 0.19/0.41
%------------------------------------------------------------------------------