TSTP Solution File: SET921+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:29:49 EDT 2022
% Result : Theorem 0.10s 0.32s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 3 nHn; 28 RR)
% Number of literals : 51 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( in(skc5,skc6)
| in(skc5,set_difference(skc6,singleton(skc7))) ),
file('SET921+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(skc7,skc5)
| in(skc5,set_difference(skc6,singleton(skc7))) ),
file('SET921+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET921+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SET921+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(u,v)
| ~ equal(v,set_difference(w,x))
| in(u,w) ),
file('SET921+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(skc5,skc6)
| ~ in(skc5,set_difference(skc6,singleton(skc7)))
| equal(skc7,skc5) ),
file('SET921+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(v,set_difference(x,w)) ),
file('SET921+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(u,v)
| ~ equal(w,set_difference(v,x))
| in(u,w)
| in(u,x) ),
file('SET921+1.p',unknown),
[] ).
cnf(17,plain,
~ in(skc5,set_difference(skc6,singleton(skc7))),
inference(spt,[spt(split,[position(s1)])],[10]),
[iquote('1:Spt:10.1')] ).
cnf(18,plain,
in(skc5,skc6),
inference(mrr,[status(thm)],[4,17]),
[iquote('1:MRR:4.1,17.0')] ).
cnf(19,plain,
~ equal(skc7,skc5),
inference(mrr,[status(thm)],[5,17]),
[iquote('1:MRR:5.1,17.0')] ).
cnf(21,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[8]),
[iquote('0:EqR:8.1')] ).
cnf(24,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[7]),
[iquote('0:EqR:7.1')] ).
cnf(28,plain,
( ~ in(u,set_difference(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[9]),
[iquote('0:EqR:9.1')] ).
cnf(29,plain,
( ~ in(u,set_difference(v,w))
| ~ in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.2')] ).
cnf(35,plain,
( ~ in(u,v)
| in(u,set_difference(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.1')] ).
cnf(36,plain,
( ~ in(skc5,skc6)
| in(skc5,singleton(skc7)) ),
inference(res,[status(thm),theory(equality)],[35,17]),
[iquote('1:Res:35.1,17.0')] ).
cnf(42,plain,
in(skc5,singleton(skc7)),
inference(mrr,[status(thm)],[36,18]),
[iquote('1:MRR:36.0,18.0')] ).
cnf(44,plain,
equal(skc7,skc5),
inference(res,[status(thm),theory(equality)],[42,24]),
[iquote('1:Res:42.0,24.0')] ).
cnf(45,plain,
$false,
inference(mrr,[status(thm)],[44,19]),
[iquote('1:MRR:44.0,19.0')] ).
cnf(46,plain,
in(skc5,set_difference(skc6,singleton(skc7))),
inference(spt,[spt(split,[position(sa)])],[45,17]),
[iquote('1:Spt:45.0,10.1,17.0')] ).
cnf(47,plain,
( ~ in(skc5,skc6)
| equal(skc7,skc5) ),
inference(spt,[spt(split,[position(s2)])],[10]),
[iquote('1:Spt:45.0,10.0,10.2')] ).
cnf(49,plain,
~ in(skc5,singleton(skc7)),
inference(res,[status(thm),theory(equality)],[46,29]),
[iquote('1:Res:46.0,29.0')] ).
cnf(50,plain,
in(skc5,skc6),
inference(res,[status(thm),theory(equality)],[46,28]),
[iquote('1:Res:46.0,28.0')] ).
cnf(51,plain,
equal(skc7,skc5),
inference(mrr,[status(thm)],[47,50]),
[iquote('1:MRR:47.0,50.0')] ).
cnf(53,plain,
~ in(skc5,singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[51,49]),
[iquote('1:Rew:51.0,49.0')] ).
cnf(57,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[21,53]),
[iquote('1:Res:21.1,53.0')] ).
cnf(58,plain,
$false,
inference(obv,[status(thm),theory(equality)],[57]),
[iquote('1:Obv:57.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.07 % Command : run_spass %d %s
% 0.07/0.26 % Computer : n009.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Sun Jul 10 20:56:07 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.10/0.32
% 0.10/0.32 SPASS V 3.9
% 0.10/0.32 SPASS beiseite: Proof found.
% 0.10/0.32 % SZS status Theorem
% 0.10/0.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 SPASS derived 35 clauses, backtracked 4 clauses, performed 1 splits and kept 48 clauses.
% 0.10/0.32 SPASS allocated 85245 KBytes.
% 0.10/0.32 SPASS spent 0:00:00.06 on the problem.
% 0.10/0.32 0:00:00.02 for the input.
% 0.10/0.32 0:00:00.02 for the FLOTTER CNF translation.
% 0.10/0.32 0:00:00.00 for inferences.
% 0.10/0.32 0:00:00.00 for the backtracking.
% 0.10/0.32 0:00:00.00 for the reduction.
% 0.10/0.32
% 0.10/0.32
% 0.10/0.32 Here is a proof with depth 3, length 28 :
% 0.10/0.32 % SZS output start Refutation
% See solution above
% 0.10/0.32 Formulae used in the proof : t64_zfmisc_1 d1_tarski antisymmetry_r2_hidden d4_xboole_0
% 0.10/0.32
%------------------------------------------------------------------------------