TSTP Solution File: SET929+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:29:54 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 11 unt; 2 nHn; 24 RR)
% Number of literals : 40 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ equal(set_difference(u,v),empty_set)
| subset(u,v) ),
file('SET929+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(u,v)
| equal(set_difference(u,v),empty_set) ),
file('SET929+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(unordered_pair(u,v),w)
| in(u,w) ),
file('SET929+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ subset(unordered_pair(u,v),w)
| in(v,w) ),
file('SET929+1.p',unknown),
[] ).
cnf(11,axiom,
( in(skc5,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set) ),
file('SET929+1.p',unknown),
[] ).
cnf(12,axiom,
( in(skc6,skc7)
| equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set) ),
file('SET929+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(u,v)
| ~ in(w,v)
| subset(unordered_pair(u,w),v) ),
file('SET929+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7)
| ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set) ),
file('SET929+1.p',unknown),
[] ).
cnf(15,plain,
equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set),
inference(spt,[spt(split,[position(s1)])],[12]),
[iquote('1:Spt:12.1')] ).
cnf(16,plain,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7)
| ~ equal(empty_set,empty_set) ),
inference(rew,[status(thm),theory(equality)],[15,14]),
[iquote('1:Rew:15.0,14.2')] ).
cnf(17,plain,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('1:Obv:16.2')] ).
cnf(25,plain,
( ~ equal(empty_set,empty_set)
| subset(unordered_pair(skc5,skc6),skc7) ),
inference(spl,[status(thm),theory(equality)],[15,7]),
[iquote('1:SpL:15.0,7.0')] ).
cnf(27,plain,
subset(unordered_pair(skc5,skc6),skc7),
inference(obv,[status(thm),theory(equality)],[25]),
[iquote('1:Obv:25.0')] ).
cnf(31,plain,
in(skc6,skc7),
inference(res,[status(thm),theory(equality)],[27,10]),
[iquote('1:Res:27.0,10.0')] ).
cnf(32,plain,
~ in(skc5,skc7),
inference(mrr,[status(thm)],[17,31]),
[iquote('1:MRR:17.0,31.0')] ).
cnf(37,plain,
in(skc5,skc7),
inference(res,[status(thm),theory(equality)],[27,9]),
[iquote('1:Res:27.0,9.0')] ).
cnf(38,plain,
$false,
inference(mrr,[status(thm)],[37,32]),
[iquote('1:MRR:37.0,32.0')] ).
cnf(39,plain,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set),
inference(spt,[spt(split,[position(sa)])],[38,15]),
[iquote('1:Spt:38.0,12.1,15.0')] ).
cnf(40,plain,
in(skc6,skc7),
inference(spt,[spt(split,[position(s2)])],[12]),
[iquote('1:Spt:38.0,12.0')] ).
cnf(41,plain,
in(skc5,skc7),
inference(mrr,[status(thm)],[11,39]),
[iquote('1:MRR:11.1,39.0')] ).
cnf(47,plain,
( ~ subset(unordered_pair(skc5,skc6),skc7)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[8,39]),
[iquote('1:SpL:8.1,39.0')] ).
cnf(48,plain,
~ subset(unordered_pair(skc5,skc6),skc7),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('1:Obv:47.1')] ).
cnf(60,plain,
( ~ in(skc5,skc7)
| ~ in(skc6,skc7) ),
inference(res,[status(thm),theory(equality)],[13,48]),
[iquote('1:Res:13.2,48.0')] ).
cnf(61,plain,
$false,
inference(mrr,[status(thm)],[60,41,40]),
[iquote('1:MRR:60.0,60.1,41.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 21:55:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 39 clauses, backtracked 4 clauses, performed 1 splits and kept 32 clauses.
% 0.21/0.45 SPASS allocated 85133 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 3, length 24 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : t37_xboole_1 t38_zfmisc_1 t73_zfmisc_1
% 0.21/0.45
%------------------------------------------------------------------------------