TSTP Solution File: KLE146+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Sun Jul 17 02:28:45 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 14 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ leq(one,strong_iteration(skc1)),
file('KLE146+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE146+1.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE146+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE146+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE146+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE146+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(136,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(193,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[136,12]),
[iquote('0:SpL:136.0,12.0')] ).
cnf(198,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[193]),
[iquote('0:Obv:193.0')] ).
cnf(240,plain,
leq(one,strong_iteration(u)),
inference(spr,[status(thm),theory(equality)],[21,198]),
[iquote('0:SpR:21.0,198.0')] ).
cnf(244,plain,
$false,
inference(unc,[status(thm)],[240,1]),
[iquote('0:UnC:240.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 16:27:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 182 clauses, backtracked 0 clauses, performed 0 splits and kept 95 clauses.
% 0.18/0.46 SPASS allocated 85295 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.46 0:00:00.04 for the input.
% 0.18/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.00 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.01 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 3, length 12 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : goals idempotence additive_commutativity infty_unfold1 order additive_associativity
% 0.18/0.46
%------------------------------------------------------------------------------