TSTP Solution File: SET903+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET903+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 05:29:41 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 12 unt; 5 nHn; 20 RR)
% Number of literals : 34 ( 0 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc6,empty_set),
file('SET903+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(skc6,skc5),
file('SET903+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(skc5,empty_set),
file('SET903+1.p',unknown),
[] ).
cnf(8,axiom,
equal(set_union2(skc6,skc5),singleton(skc7)),
file('SET903+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET903+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ skP1(u,v,w)
| equal(w,empty_set) ),
file('SET903+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ skP0(u,v,w)
| equal(w,singleton(v)) ),
file('SET903+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ skP0(u,v,w)
| equal(u,singleton(v)) ),
file('SET903+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(singleton(u),set_union2(v,w))
| equal(w,empty_set)
| skP1(u,w,v)
| skP0(w,u,v) ),
file('SET903+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(singleton(u),set_union2(v,w))
| equal(v,singleton(u))
| skP0(w,u,v)
| skP1(u,w,v) ),
file('SET903+1.p',unknown),
[] ).
cnf(18,plain,
equal(set_union2(skc5,skc6),singleton(skc7)),
inference(rew,[status(thm),theory(equality)],[9,8]),
[iquote('0:Rew:9.0,8.0')] ).
cnf(19,plain,
( ~ equal(singleton(u),set_union2(v,w))
| equal(v,singleton(u))
| skP1(u,w,v) ),
inference(mrr,[status(thm)],[17,13]),
[iquote('0:MRR:17.2,13.0')] ).
cnf(21,plain,
~ skP1(u,v,skc5),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.1,6.0')] ).
cnf(24,plain,
( equal(singleton(skc7),skc5)
| skP1(skc7,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[18,19]),
[iquote('0:Res:18.0,19.0')] ).
cnf(25,plain,
( equal(skc6,empty_set)
| skP0(skc6,skc7,skc5)
| skP1(skc7,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[18,16]),
[iquote('0:Res:18.0,16.0')] ).
cnf(26,plain,
equal(singleton(skc7),skc5),
inference(mrr,[status(thm)],[24,21]),
[iquote('0:MRR:24.1,21.0')] ).
cnf(28,plain,
skP0(skc6,skc7,skc5),
inference(mrr,[status(thm)],[25,4,21]),
[iquote('0:MRR:25.0,25.2,4.0,21.0')] ).
cnf(46,plain,
equal(singleton(skc7),skc6),
inference(res,[status(thm),theory(equality)],[28,14]),
[iquote('0:Res:28.0,14.0')] ).
cnf(47,plain,
equal(skc6,skc5),
inference(rew,[status(thm),theory(equality)],[26,46]),
[iquote('0:Rew:26.0,46.0')] ).
cnf(48,plain,
$false,
inference(mrr,[status(thm)],[47,5]),
[iquote('0:MRR:47.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n025.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 : Sat Jul 9 17:50:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.20/0.45 SPASS allocated 85118 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 2, length 20 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : t44_zfmisc_1 commutativity_k2_xboole_0 t43_zfmisc_1
% 0.20/0.45
%------------------------------------------------------------------------------