TSTP Solution File: NUM378+1.010.015 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM378+1.010.015 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 : 300s
% DateTime : Fri May 19 11:40:25 EDT 2023
% Result : Unsatisfiable 88.01s 45.72s
% Output : Refutation 88.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 17 ( 1 unt; 14 typ; 0 def)
% Number of atoms : 629 ( 628 equ; 0 cnn)
% Maximal formula atoms : 314 ( 209 avg)
% Number of connectives : 3192 ( 118 ~; 46 |; 580 &;2448 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 384 ( 256 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 184 ( 0 ^; 0 !; 184 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(succ_type,type,
succ: $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(n1_type,type,
n1: $i ).
thf(n2_type,type,
n2: $i ).
thf(n3_type,type,
n3: $i ).
thf(n4_type,type,
n4: $i ).
thf(n5_type,type,
n5: $i ).
thf(n6_type,type,
n6: $i ).
thf(n7_type,type,
n7: $i ).
thf(n8_type,type,
n8: $i ).
thf(n9_type,type,
n9: $i ).
thf(n10_type,type,
n10: $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(1,axiom,
? [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i,ZA: $i,ZB: $i,ZC: $i,ZD: $i,ZE: $i,ZF: $i,ZG: $i,ZH: $i,ZI: $i,ZJ: $i,ZK: $i,ZL: $i,ZM: $i,ZN: $i,ZO: $i,ZP: $i,ZQ: $i,ZR: $i,ZS: $i,ZT: $i,ZU: $i,ZV: $i,ZW: $i,ZX: $i,ZY: $i,ZZ: $i,ZZA: $i,ZZB: $i,ZZC: $i,ZZD: $i,ZZE: $i,ZZF: $i,ZZG: $i,ZZH: $i,ZZI: $i,ZZJ: $i,ZZK: $i,ZZL: $i,ZZM: $i,ZZN: $i,ZZO: $i,ZZP: $i,ZZQ: $i,ZZR: $i,ZZS: $i,ZZT: $i,ZZU: $i,ZZV: $i,ZZW: $i,ZZX: $i,ZZY: $i,ZZZ: $i,ZZZA: $i,ZZZB: $i,ZZZC: $i,ZZZD: $i,ZZZE: $i,ZZZF: $i,ZZZG: $i,ZZZH: $i,ZZZI: $i,ZZZJ: $i,ZZZK: $i,ZZZL: $i,ZZZM: $i,ZZZN: $i] :
( ( ( succ @ n0 )
= n1 )
& ( ( succ @ n1 )
= n2 )
& ( ( succ @ n2 )
= n3 )
& ( ( succ @ n3 )
= n4 )
& ( ( succ @ n4 )
= n5 )
& ( ( succ @ n5 )
= n6 )
& ( ( succ @ n6 )
= n7 )
& ( ( succ @ n7 )
= n8 )
& ( ( succ @ n8 )
= n9 )
& ( ( succ @ n9 )
= n10 )
& ( ( succ @ n10 )
= n0 )
& ( ( pred @ n0 )
= n10 )
& ( ( pred @ n1 )
= n0 )
& ( ( pred @ n2 )
= n1 )
& ( ( pred @ n3 )
= n2 )
& ( ( pred @ n4 )
= n3 )
& ( ( pred @ n5 )
= n4 )
& ( ( pred @ n6 )
= n5 )
& ( ( pred @ n7 )
= n6 )
& ( ( pred @ n8 )
= n7 )
& ( ( pred @ n9 )
= n8 )
& ( ( pred @ n10 )
= n9 )
& ( ( sum @ n0 @ n0 )
= n0 )
& ( ( sum @ n0 @ n1 )
= n1 )
& ( ( sum @ n0 @ n2 )
= n2 )
& ( ( sum @ n0 @ n3 )
= n3 )
& ( ( sum @ n0 @ n4 )
= n4 )
& ( ( sum @ n0 @ n5 )
= n5 )
& ( ( sum @ n0 @ n6 )
= n6 )
& ( ( sum @ n0 @ n7 )
= n7 )
& ( ( sum @ n0 @ n8 )
= n8 )
& ( ( sum @ n0 @ n9 )
= n9 )
& ( ( sum @ n0 @ n10 )
= n10 )
& ( ( sum @ n1 @ n0 )
= n1 )
& ( ( sum @ n1 @ n1 )
= n2 )
& ( ( sum @ n1 @ n2 )
= n3 )
& ( ( sum @ n1 @ n3 )
= n4 )
& ( ( sum @ n1 @ n4 )
= n5 )
& ( ( sum @ n1 @ n5 )
= n6 )
& ( ( sum @ n1 @ n6 )
= n7 )
& ( ( sum @ n1 @ n7 )
= n8 )
& ( ( sum @ n1 @ n8 )
= n9 )
& ( ( sum @ n1 @ n9 )
= n10 )
& ( ( sum @ n1 @ n10 )
= n0 )
& ( ( sum @ n2 @ n0 )
= n2 )
& ( ( sum @ n2 @ n1 )
= n3 )
& ( ( sum @ n2 @ n2 )
= n4 )
& ( ( sum @ n2 @ n3 )
= n5 )
& ( ( sum @ n2 @ n4 )
= n6 )
& ( ( sum @ n2 @ n5 )
= n7 )
& ( ( sum @ n2 @ n6 )
= n8 )
& ( ( sum @ n2 @ n7 )
= n9 )
& ( ( sum @ n2 @ n8 )
= n10 )
& ( ( sum @ n2 @ n9 )
= n0 )
& ( ( sum @ n2 @ n10 )
= n1 )
& ( ( sum @ n3 @ n0 )
= n3 )
& ( ( sum @ n3 @ n1 )
= n4 )
& ( ( sum @ n3 @ n2 )
= n5 )
& ( ( sum @ n3 @ n3 )
= n6 )
& ( ( sum @ n3 @ n4 )
= n7 )
& ( ( sum @ n3 @ n5 )
= n8 )
& ( ( sum @ n3 @ n6 )
= n9 )
& ( ( sum @ n3 @ n7 )
= n10 )
& ( ( sum @ n3 @ n8 )
= n0 )
& ( ( sum @ n3 @ n9 )
= n1 )
& ( ( sum @ n3 @ n10 )
= n2 )
& ( ( sum @ n4 @ n0 )
= n4 )
& ( ( sum @ n4 @ n1 )
= n5 )
& ( ( sum @ n4 @ n2 )
= n6 )
& ( ( sum @ n4 @ n3 )
= n7 )
& ( ( sum @ n4 @ n4 )
= n8 )
& ( ( sum @ n4 @ n5 )
= n9 )
& ( ( sum @ n4 @ n6 )
= n10 )
& ( ( sum @ n4 @ n7 )
= n0 )
& ( ( sum @ n4 @ n8 )
= n1 )
& ( ( sum @ n4 @ n9 )
= n2 )
& ( ( sum @ n4 @ n10 )
= n3 )
& ( ( sum @ n5 @ n0 )
= n5 )
& ( ( sum @ n5 @ n1 )
= n6 )
& ( ( sum @ n5 @ n2 )
= n7 )
& ( ( sum @ n5 @ n3 )
= n8 )
& ( ( sum @ n5 @ n4 )
= n9 )
& ( ( sum @ n5 @ n5 )
= n10 )
& ( ( sum @ n5 @ n6 )
= n0 )
& ( ( sum @ n5 @ n7 )
= n1 )
& ( ( sum @ n5 @ n8 )
= n2 )
& ( ( sum @ n5 @ n9 )
= n3 )
& ( ( sum @ n5 @ n10 )
= n4 )
& ( ( sum @ n6 @ n0 )
= n6 )
& ( ( sum @ n6 @ n1 )
= n7 )
& ( ( sum @ n6 @ n2 )
= n8 )
& ( ( sum @ n6 @ n3 )
= n9 )
& ( ( sum @ n6 @ n4 )
= n10 )
& ( ( sum @ n6 @ n5 )
= n0 )
& ( ( sum @ n6 @ n6 )
= n1 )
& ( ( sum @ n6 @ n7 )
= n2 )
& ( ( sum @ n6 @ n8 )
= n3 )
& ( ( sum @ n6 @ n9 )
= n4 )
& ( ( sum @ n6 @ n10 )
= n5 )
& ( ( sum @ n7 @ n0 )
= n7 )
& ( ( sum @ n7 @ n1 )
= n8 )
& ( ( sum @ n7 @ n2 )
= n9 )
& ( ( sum @ n7 @ n3 )
= n10 )
& ( ( sum @ n7 @ n4 )
= n0 )
& ( ( sum @ n7 @ n5 )
= n1 )
& ( ( sum @ n7 @ n6 )
= n2 )
& ( ( sum @ n7 @ n7 )
= n3 )
& ( ( sum @ n7 @ n8 )
= n4 )
& ( ( sum @ n7 @ n9 )
= n5 )
& ( ( sum @ n7 @ n10 )
= n6 )
& ( ( sum @ n8 @ n0 )
= n8 )
& ( ( sum @ n8 @ n1 )
= n9 )
& ( ( sum @ n8 @ n2 )
= n10 )
& ( ( sum @ n8 @ n3 )
= n0 )
& ( ( sum @ n8 @ n4 )
= n1 )
& ( ( sum @ n8 @ n5 )
= n2 )
& ( ( sum @ n8 @ n6 )
= n3 )
& ( ( sum @ n8 @ n7 )
= n4 )
& ( ( sum @ n8 @ n8 )
= n5 )
& ( ( sum @ n8 @ n9 )
= n6 )
& ( ( sum @ n8 @ n10 )
= n7 )
& ( ( sum @ n9 @ n0 )
= n9 )
& ( ( sum @ n9 @ n1 )
= n10 )
& ( ( sum @ n9 @ n2 )
= n0 )
& ( ( sum @ n9 @ n3 )
= n1 )
& ( ( sum @ n9 @ n4 )
= n2 )
& ( ( sum @ n9 @ n5 )
= n3 )
& ( ( sum @ n9 @ n6 )
= n4 )
& ( ( sum @ n9 @ n7 )
= n5 )
& ( ( sum @ n9 @ n8 )
= n6 )
& ( ( sum @ n9 @ n9 )
= n7 )
& ( ( sum @ n9 @ n10 )
= n8 )
& ( ( sum @ n10 @ n0 )
= n10 )
& ( ( sum @ n10 @ n1 )
= n0 )
& ( ( sum @ n10 @ n2 )
= n1 )
& ( ( sum @ n10 @ n3 )
= n2 )
& ( ( sum @ n10 @ n4 )
= n3 )
& ( ( sum @ n10 @ n5 )
= n4 )
& ( ( sum @ n10 @ n6 )
= n5 )
& ( ( sum @ n10 @ n7 )
= n6 )
& ( ( sum @ n10 @ n8 )
= n7 )
& ( ( sum @ n10 @ n9 )
= n8 )
& ( ( sum @ n10 @ n10 )
= n9 )
& ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 )
| ( A = n6 )
| ( A = n7 )
| ( A = n8 )
| ( A = n9 )
| ( A = n10 ) )
& ( ( B = n0 )
| ( B = n1 )
| ( B = n2 )
| ( B = n3 )
| ( B = n4 )
| ( B = n5 )
| ( B = n6 )
| ( B = n7 )
| ( B = n8 )
| ( B = n9 )
| ( B = n10 ) )
& ( ZG
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ A ) ) ) ) ) ) ) ) ) ) ) )
& ( ZI
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ) ) ) ) ) ) )
& ( ZH
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ B ) ) ) ) ) ) ) ) ) ) ) )
& ( ZJ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ B ) ) ) ) ) ) ) ) ) ) ) )
& ( ZK
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ C ) ) ) ) ) ) ) ) ) ) ) )
& ( ZM
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ C ) ) ) ) ) ) ) ) ) ) ) )
& ( ZL
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ D ) ) ) ) ) ) ) ) ) ) ) )
& ( ZN
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ D ) ) ) ) ) ) ) ) ) ) ) )
& ( ZO
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ E ) ) ) ) ) ) ) ) ) ) ) )
& ( ZQ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ E ) ) ) ) ) ) ) ) ) ) ) )
& ( ZP
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ F ) ) ) ) ) ) ) ) ) ) ) )
& ( ZR
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ F ) ) ) ) ) ) ) ) ) ) ) )
& ( ZS
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ G ) ) ) ) ) ) ) ) ) ) ) )
& ( ZU
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ G ) ) ) ) ) ) ) ) ) ) ) )
& ( ZT
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ H ) ) ) ) ) ) ) ) ) ) ) )
& ( ZV
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ H ) ) ) ) ) ) ) ) ) ) ) )
& ( ZW
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ I ) ) ) ) ) ) ) ) ) ) ) )
& ( ZY
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ I ) ) ) ) ) ) ) ) ) ) ) )
& ( ZX
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ J ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ J ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZA
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ K ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZC
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ K ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZB
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ L ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZD
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ L ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZE
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ M ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZG
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ M ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZF
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ N ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZH
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ N ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZI
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ O ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZK
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ O ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZJ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ P ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZL
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ P ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZM
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Q ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZO
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Q ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZN
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ R ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZP
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ R ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZQ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ S ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZS
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ S ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZR
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ T ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZT
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ T ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZU
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ U ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZW
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ U ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZV
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ V ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZX
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ V ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZY
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ W ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZA
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ W ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ X ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZB
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZC
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Y ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZE
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZD
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Z ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZF
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Z ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZG
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZA ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZI
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZA ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZH
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZB ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZJ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZB ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZK
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZC ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZM
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZC ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZL
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZD ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZN
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZD ) ) ) ) ) ) ) ) ) ) ) )
& ( C
= ( sum @ ( sum @ ( pred @ A ) @ ( succ @ B ) ) @ ( sum @ ( pred @ B ) @ ( succ @ A ) ) ) )
& ( D
= ( sum @ ( pred @ ZI ) @ ( sum @ ( succ @ ZG ) @ ( sum @ ( pred @ ZJ ) @ ( succ @ ZH ) ) ) ) )
& ( E
= ( sum @ ( sum @ ( pred @ C ) @ ( succ @ D ) ) @ ( sum @ ( pred @ D ) @ ( succ @ C ) ) ) )
& ( F
= ( sum @ ( pred @ ZM ) @ ( sum @ ( succ @ ZK ) @ ( sum @ ( pred @ ZN ) @ ( succ @ ZL ) ) ) ) )
& ( G
= ( sum @ ( sum @ ( pred @ E ) @ ( succ @ F ) ) @ ( sum @ ( pred @ F ) @ ( succ @ E ) ) ) )
& ( H
= ( sum @ ( pred @ ZQ ) @ ( sum @ ( succ @ ZO ) @ ( sum @ ( pred @ ZR ) @ ( succ @ ZP ) ) ) ) )
& ( I
= ( sum @ ( sum @ ( pred @ G ) @ ( succ @ H ) ) @ ( sum @ ( pred @ H ) @ ( succ @ G ) ) ) )
& ( J
= ( sum @ ( pred @ ZU ) @ ( sum @ ( succ @ ZS ) @ ( sum @ ( pred @ ZV ) @ ( succ @ ZT ) ) ) ) )
& ( K
= ( sum @ ( sum @ ( pred @ I ) @ ( succ @ J ) ) @ ( sum @ ( pred @ J ) @ ( succ @ I ) ) ) )
& ( L
= ( sum @ ( pred @ ZY ) @ ( sum @ ( succ @ ZW ) @ ( sum @ ( pred @ ZZ ) @ ( succ @ ZX ) ) ) ) )
& ( M
= ( sum @ ( sum @ ( pred @ K ) @ ( succ @ L ) ) @ ( sum @ ( pred @ L ) @ ( succ @ K ) ) ) )
& ( N
= ( sum @ ( pred @ ZZC ) @ ( sum @ ( succ @ ZZA ) @ ( sum @ ( pred @ ZZD ) @ ( succ @ ZZB ) ) ) ) )
& ( O
= ( sum @ ( sum @ ( pred @ M ) @ ( succ @ N ) ) @ ( sum @ ( pred @ N ) @ ( succ @ M ) ) ) )
& ( P
= ( sum @ ( pred @ ZZG ) @ ( sum @ ( succ @ ZZE ) @ ( sum @ ( pred @ ZZH ) @ ( succ @ ZZF ) ) ) ) )
& ( Q
= ( sum @ ( sum @ ( pred @ O ) @ ( succ @ P ) ) @ ( sum @ ( pred @ P ) @ ( succ @ O ) ) ) )
& ( R
= ( sum @ ( pred @ ZZK ) @ ( sum @ ( succ @ ZZI ) @ ( sum @ ( pred @ ZZL ) @ ( succ @ ZZJ ) ) ) ) )
& ( S
= ( sum @ ( sum @ ( pred @ Q ) @ ( succ @ R ) ) @ ( sum @ ( pred @ R ) @ ( succ @ Q ) ) ) )
& ( T
= ( sum @ ( pred @ ZZO ) @ ( sum @ ( succ @ ZZM ) @ ( sum @ ( pred @ ZZP ) @ ( succ @ ZZN ) ) ) ) )
& ( U
= ( sum @ ( sum @ ( pred @ S ) @ ( succ @ T ) ) @ ( sum @ ( pred @ T ) @ ( succ @ S ) ) ) )
& ( V
= ( sum @ ( pred @ ZZS ) @ ( sum @ ( succ @ ZZQ ) @ ( sum @ ( pred @ ZZT ) @ ( succ @ ZZR ) ) ) ) )
& ( W
= ( sum @ ( sum @ ( pred @ U ) @ ( succ @ V ) ) @ ( sum @ ( pred @ V ) @ ( succ @ U ) ) ) )
& ( X
= ( sum @ ( pred @ ZZW ) @ ( sum @ ( succ @ ZZU ) @ ( sum @ ( pred @ ZZX ) @ ( succ @ ZZV ) ) ) ) )
& ( Y
= ( sum @ ( sum @ ( pred @ W ) @ ( succ @ X ) ) @ ( sum @ ( pred @ X ) @ ( succ @ W ) ) ) )
& ( Z
= ( sum @ ( pred @ ZZZA ) @ ( sum @ ( succ @ ZZY ) @ ( sum @ ( pred @ ZZZB ) @ ( succ @ ZZZ ) ) ) ) )
& ( ZA
= ( sum @ ( sum @ ( pred @ Y ) @ ( succ @ Z ) ) @ ( sum @ ( pred @ Z ) @ ( succ @ Y ) ) ) )
& ( ZB
= ( sum @ ( pred @ ZZZE ) @ ( sum @ ( succ @ ZZZC ) @ ( sum @ ( pred @ ZZZF ) @ ( succ @ ZZZD ) ) ) ) )
& ( ZC
= ( sum @ ( sum @ ( pred @ ZA ) @ ( succ @ ZB ) ) @ ( sum @ ( pred @ ZB ) @ ( succ @ ZA ) ) ) )
& ( ZD
= ( sum @ ( pred @ ZZZI ) @ ( sum @ ( succ @ ZZZG ) @ ( sum @ ( pred @ ZZZJ ) @ ( succ @ ZZZH ) ) ) ) )
& ( ZE
= ( sum @ ( sum @ ( pred @ ZC ) @ ( succ @ ZD ) ) @ ( sum @ ( pred @ ZD ) @ ( succ @ ZC ) ) ) )
& ( ZF
= ( sum @ ( pred @ ZZZM ) @ ( sum @ ( succ @ ZZZK ) @ ( sum @ ( pred @ ZZZN ) @ ( succ @ ZZZL ) ) ) ) )
& ( ( Y != Z )
| ( ZA != ZB )
| ( ZC != ZD )
| ( ZE != ZF ) )
& ( n0 != n1 )
& ( n0 != n2 )
& ( n0 != n3 )
& ( n0 != n4 )
& ( n0 != n5 )
& ( n0 != n6 )
& ( n0 != n7 )
& ( n0 != n8 )
& ( n0 != n9 )
& ( n0 != n10 )
& ( n1 != n2 )
& ( n1 != n3 )
& ( n1 != n4 )
& ( n1 != n5 )
& ( n1 != n6 )
& ( n1 != n7 )
& ( n1 != n8 )
& ( n1 != n9 )
& ( n1 != n10 )
& ( n2 != n3 )
& ( n2 != n4 )
& ( n2 != n5 )
& ( n2 != n6 )
& ( n2 != n7 )
& ( n2 != n8 )
& ( n2 != n9 )
& ( n2 != n10 )
& ( n3 != n4 )
& ( n3 != n5 )
& ( n3 != n6 )
& ( n3 != n7 )
& ( n3 != n8 )
& ( n3 != n9 )
& ( n3 != n10 )
& ( n4 != n5 )
& ( n4 != n6 )
& ( n4 != n7 )
& ( n4 != n8 )
& ( n4 != n9 )
& ( n4 != n10 )
& ( n5 != n6 )
& ( n5 != n7 )
& ( n5 != n8 )
& ( n5 != n9 )
& ( n5 != n10 )
& ( n6 != n7 )
& ( n6 != n8 )
& ( n6 != n9 )
& ( n6 != n10 )
& ( n7 != n8 )
& ( n7 != n9 )
& ( n7 != n10 )
& ( n8 != n9 )
& ( n8 != n10 )
& ( n9 != n10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',try_satisfy_this) ).
thf(2,plain,
? [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i,ZA: $i,ZB: $i,ZC: $i,ZD: $i,ZE: $i,ZF: $i,ZG: $i,ZH: $i,ZI: $i,ZJ: $i,ZK: $i,ZL: $i,ZM: $i,ZN: $i,ZO: $i,ZP: $i,ZQ: $i,ZR: $i,ZS: $i,ZT: $i,ZU: $i,ZV: $i,ZW: $i,ZX: $i,ZY: $i,ZZ: $i,ZZA: $i,ZZB: $i,ZZC: $i,ZZD: $i,ZZE: $i,ZZF: $i,ZZG: $i,ZZH: $i,ZZI: $i,ZZJ: $i,ZZK: $i,ZZL: $i,ZZM: $i,ZZN: $i,ZZO: $i,ZZP: $i,ZZQ: $i,ZZR: $i,ZZS: $i,ZZT: $i,ZZU: $i,ZZV: $i,ZZW: $i,ZZX: $i,ZZY: $i,ZZZ: $i,ZZZA: $i,ZZZB: $i,ZZZC: $i,ZZZD: $i,ZZZE: $i,ZZZF: $i,ZZZG: $i,ZZZH: $i,ZZZI: $i,ZZZJ: $i,ZZZK: $i,ZZZL: $i,ZZZM: $i,ZZZN: $i] :
( ( ( succ @ n0 )
= n1 )
& ( ( succ @ n1 )
= n2 )
& ( ( succ @ n2 )
= n3 )
& ( ( succ @ n3 )
= n4 )
& ( ( succ @ n4 )
= n5 )
& ( ( succ @ n5 )
= n6 )
& ( ( succ @ n6 )
= n7 )
& ( ( succ @ n7 )
= n8 )
& ( ( succ @ n8 )
= n9 )
& ( ( succ @ n9 )
= n10 )
& ( ( succ @ n10 )
= n0 )
& ( ( pred @ n0 )
= n10 )
& ( ( pred @ n1 )
= n0 )
& ( ( pred @ n2 )
= n1 )
& ( ( pred @ n3 )
= n2 )
& ( ( pred @ n4 )
= n3 )
& ( ( pred @ n5 )
= n4 )
& ( ( pred @ n6 )
= n5 )
& ( ( pred @ n7 )
= n6 )
& ( ( pred @ n8 )
= n7 )
& ( ( pred @ n9 )
= n8 )
& ( ( pred @ n10 )
= n9 )
& ( ( sum @ n0 @ n0 )
= n0 )
& ( ( sum @ n0 @ n1 )
= n1 )
& ( ( sum @ n0 @ n2 )
= n2 )
& ( ( sum @ n0 @ n3 )
= n3 )
& ( ( sum @ n0 @ n4 )
= n4 )
& ( ( sum @ n0 @ n5 )
= n5 )
& ( ( sum @ n0 @ n6 )
= n6 )
& ( ( sum @ n0 @ n7 )
= n7 )
& ( ( sum @ n0 @ n8 )
= n8 )
& ( ( sum @ n0 @ n9 )
= n9 )
& ( ( sum @ n0 @ n10 )
= n10 )
& ( ( sum @ n1 @ n0 )
= n1 )
& ( ( sum @ n1 @ n1 )
= n2 )
& ( ( sum @ n1 @ n2 )
= n3 )
& ( ( sum @ n1 @ n3 )
= n4 )
& ( ( sum @ n1 @ n4 )
= n5 )
& ( ( sum @ n1 @ n5 )
= n6 )
& ( ( sum @ n1 @ n6 )
= n7 )
& ( ( sum @ n1 @ n7 )
= n8 )
& ( ( sum @ n1 @ n8 )
= n9 )
& ( ( sum @ n1 @ n9 )
= n10 )
& ( ( sum @ n1 @ n10 )
= n0 )
& ( ( sum @ n2 @ n0 )
= n2 )
& ( ( sum @ n2 @ n1 )
= n3 )
& ( ( sum @ n2 @ n2 )
= n4 )
& ( ( sum @ n2 @ n3 )
= n5 )
& ( ( sum @ n2 @ n4 )
= n6 )
& ( ( sum @ n2 @ n5 )
= n7 )
& ( ( sum @ n2 @ n6 )
= n8 )
& ( ( sum @ n2 @ n7 )
= n9 )
& ( ( sum @ n2 @ n8 )
= n10 )
& ( ( sum @ n2 @ n9 )
= n0 )
& ( ( sum @ n2 @ n10 )
= n1 )
& ( ( sum @ n3 @ n0 )
= n3 )
& ( ( sum @ n3 @ n1 )
= n4 )
& ( ( sum @ n3 @ n2 )
= n5 )
& ( ( sum @ n3 @ n3 )
= n6 )
& ( ( sum @ n3 @ n4 )
= n7 )
& ( ( sum @ n3 @ n5 )
= n8 )
& ( ( sum @ n3 @ n6 )
= n9 )
& ( ( sum @ n3 @ n7 )
= n10 )
& ( ( sum @ n3 @ n8 )
= n0 )
& ( ( sum @ n3 @ n9 )
= n1 )
& ( ( sum @ n3 @ n10 )
= n2 )
& ( ( sum @ n4 @ n0 )
= n4 )
& ( ( sum @ n4 @ n1 )
= n5 )
& ( ( sum @ n4 @ n2 )
= n6 )
& ( ( sum @ n4 @ n3 )
= n7 )
& ( ( sum @ n4 @ n4 )
= n8 )
& ( ( sum @ n4 @ n5 )
= n9 )
& ( ( sum @ n4 @ n6 )
= n10 )
& ( ( sum @ n4 @ n7 )
= n0 )
& ( ( sum @ n4 @ n8 )
= n1 )
& ( ( sum @ n4 @ n9 )
= n2 )
& ( ( sum @ n4 @ n10 )
= n3 )
& ( ( sum @ n5 @ n0 )
= n5 )
& ( ( sum @ n5 @ n1 )
= n6 )
& ( ( sum @ n5 @ n2 )
= n7 )
& ( ( sum @ n5 @ n3 )
= n8 )
& ( ( sum @ n5 @ n4 )
= n9 )
& ( ( sum @ n5 @ n5 )
= n10 )
& ( ( sum @ n5 @ n6 )
= n0 )
& ( ( sum @ n5 @ n7 )
= n1 )
& ( ( sum @ n5 @ n8 )
= n2 )
& ( ( sum @ n5 @ n9 )
= n3 )
& ( ( sum @ n5 @ n10 )
= n4 )
& ( ( sum @ n6 @ n0 )
= n6 )
& ( ( sum @ n6 @ n1 )
= n7 )
& ( ( sum @ n6 @ n2 )
= n8 )
& ( ( sum @ n6 @ n3 )
= n9 )
& ( ( sum @ n6 @ n4 )
= n10 )
& ( ( sum @ n6 @ n5 )
= n0 )
& ( ( sum @ n6 @ n6 )
= n1 )
& ( ( sum @ n6 @ n7 )
= n2 )
& ( ( sum @ n6 @ n8 )
= n3 )
& ( ( sum @ n6 @ n9 )
= n4 )
& ( ( sum @ n6 @ n10 )
= n5 )
& ( ( sum @ n7 @ n0 )
= n7 )
& ( ( sum @ n7 @ n1 )
= n8 )
& ( ( sum @ n7 @ n2 )
= n9 )
& ( ( sum @ n7 @ n3 )
= n10 )
& ( ( sum @ n7 @ n4 )
= n0 )
& ( ( sum @ n7 @ n5 )
= n1 )
& ( ( sum @ n7 @ n6 )
= n2 )
& ( ( sum @ n7 @ n7 )
= n3 )
& ( ( sum @ n7 @ n8 )
= n4 )
& ( ( sum @ n7 @ n9 )
= n5 )
& ( ( sum @ n7 @ n10 )
= n6 )
& ( ( sum @ n8 @ n0 )
= n8 )
& ( ( sum @ n8 @ n1 )
= n9 )
& ( ( sum @ n8 @ n2 )
= n10 )
& ( ( sum @ n8 @ n3 )
= n0 )
& ( ( sum @ n8 @ n4 )
= n1 )
& ( ( sum @ n8 @ n5 )
= n2 )
& ( ( sum @ n8 @ n6 )
= n3 )
& ( ( sum @ n8 @ n7 )
= n4 )
& ( ( sum @ n8 @ n8 )
= n5 )
& ( ( sum @ n8 @ n9 )
= n6 )
& ( ( sum @ n8 @ n10 )
= n7 )
& ( ( sum @ n9 @ n0 )
= n9 )
& ( ( sum @ n9 @ n1 )
= n10 )
& ( ( sum @ n9 @ n2 )
= n0 )
& ( ( sum @ n9 @ n3 )
= n1 )
& ( ( sum @ n9 @ n4 )
= n2 )
& ( ( sum @ n9 @ n5 )
= n3 )
& ( ( sum @ n9 @ n6 )
= n4 )
& ( ( sum @ n9 @ n7 )
= n5 )
& ( ( sum @ n9 @ n8 )
= n6 )
& ( ( sum @ n9 @ n9 )
= n7 )
& ( ( sum @ n9 @ n10 )
= n8 )
& ( ( sum @ n10 @ n0 )
= n10 )
& ( ( sum @ n10 @ n1 )
= n0 )
& ( ( sum @ n10 @ n2 )
= n1 )
& ( ( sum @ n10 @ n3 )
= n2 )
& ( ( sum @ n10 @ n4 )
= n3 )
& ( ( sum @ n10 @ n5 )
= n4 )
& ( ( sum @ n10 @ n6 )
= n5 )
& ( ( sum @ n10 @ n7 )
= n6 )
& ( ( sum @ n10 @ n8 )
= n7 )
& ( ( sum @ n10 @ n9 )
= n8 )
& ( ( sum @ n10 @ n10 )
= n9 )
& ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 )
| ( A = n6 )
| ( A = n7 )
| ( A = n8 )
| ( A = n9 )
| ( A = n10 ) )
& ( ( B = n0 )
| ( B = n1 )
| ( B = n2 )
| ( B = n3 )
| ( B = n4 )
| ( B = n5 )
| ( B = n6 )
| ( B = n7 )
| ( B = n8 )
| ( B = n9 )
| ( B = n10 ) )
& ( ZG
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ A ) ) ) ) ) ) ) ) ) ) ) )
& ( ZI
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ) ) ) ) ) ) )
& ( ZH
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ B ) ) ) ) ) ) ) ) ) ) ) )
& ( ZJ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ B ) ) ) ) ) ) ) ) ) ) ) )
& ( ZK
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ C ) ) ) ) ) ) ) ) ) ) ) )
& ( ZM
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ C ) ) ) ) ) ) ) ) ) ) ) )
& ( ZL
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ D ) ) ) ) ) ) ) ) ) ) ) )
& ( ZN
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ D ) ) ) ) ) ) ) ) ) ) ) )
& ( ZO
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ E ) ) ) ) ) ) ) ) ) ) ) )
& ( ZQ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ E ) ) ) ) ) ) ) ) ) ) ) )
& ( ZP
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ F ) ) ) ) ) ) ) ) ) ) ) )
& ( ZR
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ F ) ) ) ) ) ) ) ) ) ) ) )
& ( ZS
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ G ) ) ) ) ) ) ) ) ) ) ) )
& ( ZU
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ G ) ) ) ) ) ) ) ) ) ) ) )
& ( ZT
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ H ) ) ) ) ) ) ) ) ) ) ) )
& ( ZV
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ H ) ) ) ) ) ) ) ) ) ) ) )
& ( ZW
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ I ) ) ) ) ) ) ) ) ) ) ) )
& ( ZY
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ I ) ) ) ) ) ) ) ) ) ) ) )
& ( ZX
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ J ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ J ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZA
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ K ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZC
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ K ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZB
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ L ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZD
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ L ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZE
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ M ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZG
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ M ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZF
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ N ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZH
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ N ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZI
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ O ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZK
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ O ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZJ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ P ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZL
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ P ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZM
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Q ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZO
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Q ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZN
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ R ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZP
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ R ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZQ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ S ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZS
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ S ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZR
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ T ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZT
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ T ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZU
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ U ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZW
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ U ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZV
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ V ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZX
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ V ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZY
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ W ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZA
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ W ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZ
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ X ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZB
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZC
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Y ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZE
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZD
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ Z ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZF
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ Z ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZG
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZA ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZI
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZA ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZH
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZB ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZJ
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZB ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZK
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZC ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZM
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZC ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZL
= ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ( pred @ ZD ) ) ) ) ) ) ) ) ) ) ) )
& ( ZZZN
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ZD ) ) ) ) ) ) ) ) ) ) ) )
& ( C
= ( sum @ ( sum @ ( pred @ A ) @ ( succ @ B ) ) @ ( sum @ ( pred @ B ) @ ( succ @ A ) ) ) )
& ( D
= ( sum @ ( pred @ ZI ) @ ( sum @ ( succ @ ZG ) @ ( sum @ ( pred @ ZJ ) @ ( succ @ ZH ) ) ) ) )
& ( E
= ( sum @ ( sum @ ( pred @ C ) @ ( succ @ D ) ) @ ( sum @ ( pred @ D ) @ ( succ @ C ) ) ) )
& ( F
= ( sum @ ( pred @ ZM ) @ ( sum @ ( succ @ ZK ) @ ( sum @ ( pred @ ZN ) @ ( succ @ ZL ) ) ) ) )
& ( G
= ( sum @ ( sum @ ( pred @ E ) @ ( succ @ F ) ) @ ( sum @ ( pred @ F ) @ ( succ @ E ) ) ) )
& ( H
= ( sum @ ( pred @ ZQ ) @ ( sum @ ( succ @ ZO ) @ ( sum @ ( pred @ ZR ) @ ( succ @ ZP ) ) ) ) )
& ( I
= ( sum @ ( sum @ ( pred @ G ) @ ( succ @ H ) ) @ ( sum @ ( pred @ H ) @ ( succ @ G ) ) ) )
& ( J
= ( sum @ ( pred @ ZU ) @ ( sum @ ( succ @ ZS ) @ ( sum @ ( pred @ ZV ) @ ( succ @ ZT ) ) ) ) )
& ( K
= ( sum @ ( sum @ ( pred @ I ) @ ( succ @ J ) ) @ ( sum @ ( pred @ J ) @ ( succ @ I ) ) ) )
& ( L
= ( sum @ ( pred @ ZY ) @ ( sum @ ( succ @ ZW ) @ ( sum @ ( pred @ ZZ ) @ ( succ @ ZX ) ) ) ) )
& ( M
= ( sum @ ( sum @ ( pred @ K ) @ ( succ @ L ) ) @ ( sum @ ( pred @ L ) @ ( succ @ K ) ) ) )
& ( N
= ( sum @ ( pred @ ZZC ) @ ( sum @ ( succ @ ZZA ) @ ( sum @ ( pred @ ZZD ) @ ( succ @ ZZB ) ) ) ) )
& ( O
= ( sum @ ( sum @ ( pred @ M ) @ ( succ @ N ) ) @ ( sum @ ( pred @ N ) @ ( succ @ M ) ) ) )
& ( P
= ( sum @ ( pred @ ZZG ) @ ( sum @ ( succ @ ZZE ) @ ( sum @ ( pred @ ZZH ) @ ( succ @ ZZF ) ) ) ) )
& ( Q
= ( sum @ ( sum @ ( pred @ O ) @ ( succ @ P ) ) @ ( sum @ ( pred @ P ) @ ( succ @ O ) ) ) )
& ( R
= ( sum @ ( pred @ ZZK ) @ ( sum @ ( succ @ ZZI ) @ ( sum @ ( pred @ ZZL ) @ ( succ @ ZZJ ) ) ) ) )
& ( S
= ( sum @ ( sum @ ( pred @ Q ) @ ( succ @ R ) ) @ ( sum @ ( pred @ R ) @ ( succ @ Q ) ) ) )
& ( T
= ( sum @ ( pred @ ZZO ) @ ( sum @ ( succ @ ZZM ) @ ( sum @ ( pred @ ZZP ) @ ( succ @ ZZN ) ) ) ) )
& ( U
= ( sum @ ( sum @ ( pred @ S ) @ ( succ @ T ) ) @ ( sum @ ( pred @ T ) @ ( succ @ S ) ) ) )
& ( V
= ( sum @ ( pred @ ZZS ) @ ( sum @ ( succ @ ZZQ ) @ ( sum @ ( pred @ ZZT ) @ ( succ @ ZZR ) ) ) ) )
& ( W
= ( sum @ ( sum @ ( pred @ U ) @ ( succ @ V ) ) @ ( sum @ ( pred @ V ) @ ( succ @ U ) ) ) )
& ( X
= ( sum @ ( pred @ ZZW ) @ ( sum @ ( succ @ ZZU ) @ ( sum @ ( pred @ ZZX ) @ ( succ @ ZZV ) ) ) ) )
& ( Y
= ( sum @ ( sum @ ( pred @ W ) @ ( succ @ X ) ) @ ( sum @ ( pred @ X ) @ ( succ @ W ) ) ) )
& ( Z
= ( sum @ ( pred @ ZZZA ) @ ( sum @ ( succ @ ZZY ) @ ( sum @ ( pred @ ZZZB ) @ ( succ @ ZZZ ) ) ) ) )
& ( ZA
= ( sum @ ( sum @ ( pred @ Y ) @ ( succ @ Z ) ) @ ( sum @ ( pred @ Z ) @ ( succ @ Y ) ) ) )
& ( ZB
= ( sum @ ( pred @ ZZZE ) @ ( sum @ ( succ @ ZZZC ) @ ( sum @ ( pred @ ZZZF ) @ ( succ @ ZZZD ) ) ) ) )
& ( ZC
= ( sum @ ( sum @ ( pred @ ZA ) @ ( succ @ ZB ) ) @ ( sum @ ( pred @ ZB ) @ ( succ @ ZA ) ) ) )
& ( ZD
= ( sum @ ( pred @ ZZZI ) @ ( sum @ ( succ @ ZZZG ) @ ( sum @ ( pred @ ZZZJ ) @ ( succ @ ZZZH ) ) ) ) )
& ( ZE
= ( sum @ ( sum @ ( pred @ ZC ) @ ( succ @ ZD ) ) @ ( sum @ ( pred @ ZD ) @ ( succ @ ZC ) ) ) )
& ( ZF
= ( sum @ ( pred @ ZZZM ) @ ( sum @ ( succ @ ZZZK ) @ ( sum @ ( pred @ ZZZN ) @ ( succ @ ZZZL ) ) ) ) )
& ( ( Y != Z )
| ( ZA != ZB )
| ( ZC != ZD )
| ( ZE != ZF ) )
& ( n0 != n1 )
& ( n0 != n2 )
& ( n0 != n3 )
& ( n0 != n4 )
& ( n0 != n5 )
& ( n0 != n6 )
& ( n0 != n7 )
& ( n0 != n8 )
& ( n0 != n9 )
& ( n0 != n10 )
& ( n1 != n2 )
& ( n1 != n3 )
& ( n1 != n4 )
& ( n1 != n5 )
& ( n1 != n6 )
& ( n1 != n7 )
& ( n1 != n8 )
& ( n1 != n9 )
& ( n1 != n10 )
& ( n2 != n3 )
& ( n2 != n4 )
& ( n2 != n5 )
& ( n2 != n6 )
& ( n2 != n7 )
& ( n2 != n8 )
& ( n2 != n9 )
& ( n2 != n10 )
& ( n3 != n4 )
& ( n3 != n5 )
& ( n3 != n6 )
& ( n3 != n7 )
& ( n3 != n8 )
& ( n3 != n9 )
& ( n3 != n10 )
& ( n4 != n5 )
& ( n4 != n6 )
& ( n4 != n7 )
& ( n4 != n8 )
& ( n4 != n9 )
& ( n4 != n10 )
& ( n5 != n6 )
& ( n5 != n7 )
& ( n5 != n8 )
& ( n5 != n9 )
& ( n5 != n10 )
& ( n6 != n7 )
& ( n6 != n8 )
& ( n6 != n9 )
& ( n6 != n10 )
& ( n7 != n8 )
& ( n7 != n9 )
& ( n7 != n10 )
& ( n8 != n9 )
& ( n8 != n10 )
& ( n9 != n10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(51669,plain,
$false,
inference(e,[status(thm)],[2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM378+1.010.015 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:34:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.01 % [INFO] Parsing done (154ms).
% 1.49/1.02 % [INFO] Running in sequential loop mode.
% 1.90/1.21 % [INFO] eprover registered as external prover.
% 1.90/1.21 % [INFO] cvc4 registered as external prover.
% 1.90/1.21 % [INFO] Scanning for conjecture ...
% 2.00/1.26 % [INFO] 1 axioms and no conjecture found.
% 3.31/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 3.31/2.11 % [INFO] Type checking passed.
% 3.31/2.11 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 88.01/45.72 % External prover 'e' found a proof!
% 88.01/45.72 % [INFO] Killing All external provers ...
% 88.01/45.72 % Time passed: 45183ms (effective reasoning time: 44696ms)
% 88.01/45.72 % Axioms used in derivation (1): try_satisfy_this
% 88.01/45.72 % No. of inferences in proof: 3
% 88.01/45.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 45183 ms resp. 44696 ms w/o parsing
% 88.13/45.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 88.37/45.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------