%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA116^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:05 AM UTC 2026
% Result : Theorem 0.92s 0.43s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 606 ( 488 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 5588 ( 532 ~; 473 |; 0 &;4579 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 9 con; 0-4 aty)
% Number of variables : 737 ( 30 sgn 188 !; 4 ?; 737 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_1,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_2,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_3,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_4,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_6,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_7,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_8,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_9,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_10,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_11,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_16,type,
sK1: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_17,type,
sK2: 'type/nums/num' ).
thf(func_def_18,type,
sK3: 'type/nums/num' ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK5: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_24,type,
sK6: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/realax/real' ) > 'type/nums/num' ).
thf(func_def_25,type,
sK7: ( 'type/nums/num' > 'type/realax/real' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_26,type,
sK8: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_27,type,
sK9: ( 'type/nums/num' > 'type/realax/real' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_28,type,
sK10: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_29,type,
sK11: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_30,type,
sK12: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_31,type,
sK13: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_32,type,
sK14: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_33,type,
sK15: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_34,type,
sK16: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_35,type,
sK17: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_36,type,
sK18: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_37,type,
sK19: ( 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK20: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_43,type,
sK21: ( 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_44,type,
sK22: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_45,type,
sK23: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/realax/real' ) > 'type/nums/num' ).
thf(func_def_46,type,
sK24: ( 'type/nums/num' > 'type/nums/num' ) > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_47,type,
sK25: ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_48,type,
sK26: 'type/nums/num' ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ X0 @ X1 ) @ X1 )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/ADD_SUB_') ).
thf(f2,axiom,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ X4 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X4 ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ X4 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_PARTIAL_SUC_') ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ X4 ) @ ( 'const/realax/real_sub' @ ( X1 @ X4 ) @ ( X1 @ ( 'const/arith/-' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X3 ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ X4 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_PARTIAL_PRE_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ X4 ) @ ( 'const/realax/real_sub' @ ( X1 @ X4 ) @ ( X1 @ ( 'const/arith/-' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X3 ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ X4 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ X4 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X4 ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X5: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ ( 'const/arith/+' @ X5 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ X5 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ X5 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ Y0 ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ X4 ) @ ( 'const/realax/real_sub' @ ( X1 @ X4 ) @ ( X1 @ ( 'const/arith/-' @ X4 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X3 ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X5: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ X5 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ X5 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ X5 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ Y0 ) @ ( X1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X3 ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ Y0 ) @ ( X1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ X3 ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ ( 'const/arith/-' @ X2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK2 @ sK3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sK1 @ sK3 ) ) @ ( 'const/realax/real_mul' @ ( sK0 @ sK2 ) @ ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sK0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/arith/+' @ X0 @ X1 ) @ X1 )
= X0 ),
inference(cnf_transformation,[],[f1]) ).
thf(f12,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ Y0 ) ) ) )
= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ X2 @ X3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( X0 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ ( 'const/arith/+' @ X3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) @ ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/class/COND' @ 'type/realax/real' @ ( 'const/arith/<=' @ sK2 @ sK3 )
@ ( 'const/realax/real_sub' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_mul' @ ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sK1 @ sK3 ) ) @ ( 'const/realax/real_mul' @ ( sK0 @ sK2 ) @ ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( sK0 @ Y0 ) ) ) ) )
@ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f39,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num',X4: 'type/nums/num' > 'type/realax/real',X5: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X2 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X3 @ Y0 ) ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X4 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X5 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X5 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X4 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( X2 != X4 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X5 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X3 @ X0 )
!= ( X5 @ X0 ) )
| ( ( X2 @ X0 )
!= ( X4 @ X0 ) )
| ( ( X3 @ ( 'const/arith/+' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X5 @ ( 'const/arith/+' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X2 @ ( 'const/arith/+' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X4 @ ( 'const/arith/+' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(constrained_superposition,[],[f12,f12]) ).
thf(f40,plain,
! [X0: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] :
( 'const/realax/real_mul'
@ ( ^ [Y1: 'type/nums/num'] :
( sK0
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 ) )
@ Y0 )
@ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f43,plain,
! [X0: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f172,definition,
( spl4_4
<=> ! [X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= X1 )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0 @ ( X1 @ sK2 ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f173,plain,
( ! [X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= X1 )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0 @ ( X1 @ sK2 ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) ) ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f175,definition,
( spl4_5
<=> ! [X2: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f176,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f252,plain,
( ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : Y0 ) )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0
@ ( ^ [Y0: 'type/nums/num'] : Y0
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0
@ ( ^ [Y0: 'type/nums/num'] : Y0
@ sK2 ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) ) ) )
| ~ spl4_4 ),
inference(equality_resolution,[],[f173]) ).
thf(f255,plain,
( ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0
@ ( ^ [Y0: 'type/nums/num'] : Y0
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0
@ ( ^ [Y0: 'type/nums/num'] : Y0
@ sK2 ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) ) ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f256,plain,
( ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0 @ sK2 ) )
| ( sK0 != sK0 )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f258,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f257]) ).
thf(f260,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( sK6 @ X3 @ X2 ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
@ ( sK6 @ X3 @ X2 ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(negative_extensionality,[],[f176]) ).
thf(f263,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real'] :
( ( ( X2 @ ( 'const/arith/+' @ ( sK6 @ X3 @ X2 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ ( sK6 @ X3 @ X2 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f273,plain,
( ! [X2: 'type/nums/num' > 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X4: 'type/nums/num' > 'type/realax/real'] :
( ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X2 @ Y0 ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ X0 ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X2 @ Y0 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X2 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X4 @ sK2 ) )
| ( ( X1 @ sK2 )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X2 @ Y0 ) )
@ sK2 ) ) )
| ( ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X2 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X4 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X4 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X1 != X4 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X4 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) )
@ X1 )
!= X0 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X2
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f263,f11]) ).
thf(f278,plain,
( ! [X2: 'type/nums/num' > 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X4: 'type/nums/num' > 'type/realax/real'] :
( ( ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X4 @ sK2 ) )
| ( ( X1 @ sK2 )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X2 @ sK2 ) ) ) )
| ( ( sK1 @ X0 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X4 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X4 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) )
@ X1 )
!= X0 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( X1 != X4 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X4 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X2
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( X2 @ Y0 ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f456,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num',X4: 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y2 ) )
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X2 @ sK2 ) )
| ( ( X0 @ sK2 )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ) )
| ( ( sK1 @ X3 )
!= ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y2 ) )
@ Y1 ) )
@ Y0 ) )
@ X0 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y2 ) )
@ Y1 ) )
@ Y0 ) )
@ X0 )
!= X3 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X4 )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y1 ) )
@ Y0 ) )
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X1 @ Y2 ) )
@ Y1 ) )
@ Y0 ) )
@ X0 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X4 )
| ( 'const/nums/_0'
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f278,f11]) ).
thf(f459,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num',X4: 'type/nums/num'] :
( ( ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ Y0 ) ) ) )
@ X0 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
!= X4 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X2 @ sK2 ) )
| ( ( X0 @ sK2 )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ sK2 ) ) ) ) ) )
| ( ( sK1 @ X3 )
!= ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ Y0 ) ) ) )
@ X0 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X1 @ Y0 ) ) ) )
@ X0 )
!= X3 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X4 )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( 'const/nums/_0'
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f456]) ).
thf(f518,plain,
( ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ X2 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X1 @ sK2 ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ sK2 ) ) ) ) ) )
| ( ( sK1 @ X3 )
!= ( X2
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ X2 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ X2 )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X1 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(equality_resolution,[],[f459]) ).
thf(f523,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( X1 @ sK2 )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ sK2 ) ) ) ) ) )
| ( ( sK1 @ X2 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) )
@ X1 )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( 'const/nums/_0'
!= ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(equality_resolution,[],[f518]) ).
thf(f524,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X1 @ sK2 ) )
| ( ( sK1 @ X2 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( 'const/nums/_0' != 'const/nums/_0' )
| ( X0 != X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f523]) ).
thf(f525,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X1 @ sK2 ) )
| ( ( sK1 @ X2 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
!= X2 )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X0 != X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f524]) ).
thf(f529,definition,
( spl4_6
<=> ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( X0 != X1 )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X1 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
!= X2 )
| ( ( sK1 @ X2 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f530,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( sK1 @ X2 )
!= ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X1 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ X1 )
!= X2 )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( X0 != X1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f529]) ).
thf(f532,definition,
( spl4_7
<=> ( ( ^ [Y0: 'type/nums/num'] : Y0 )
= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f534,plain,
( ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| spl4_7 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f535,plain,
( spl4_6
| ~ spl4_7
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f525,f175,f532,f529]) ).
thf(f541,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) )
@ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X2 )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] : ( sK1 @ ( X1 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X0 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f530]) ).
thf(f542,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X1 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X2 )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X0 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f541]) ).
thf(f552,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( sK1
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] : ( sK1 @ ( X0 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X1 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X2 )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) )
@ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) ) ) )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f542]) ).
thf(f553,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= X2 )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X1 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X0 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) ) ) )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f552]) ).
thf(f555,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) ) )
!= ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X1 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X0 @ Y0 ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X0 @ sK2 ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f553]) ).
thf(f556,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] :
( sK1
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X1 @ Y1 ) )
@ Y0 ) ) )
!= X0 )
| ( ( sK1 @ sK3 )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X1 @ Y1 ) )
@ Y0 ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ sK2 ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X1 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X0 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f555,f11]) ).
thf(f561,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X0 )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X0 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f556]) ).
thf(f562,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X0 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f561]) ).
thf(f591,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X1 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ sK2 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 )
@ ( X1 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/arith/-'
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 )
@ ( X1 @ Y1 ) )
@ Y0 ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f562]) ).
thf(f594,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f591]) ).
thf(f607,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ ( sK25 @ X1 ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
@ ( sK25 @ X1 ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(negative_extensionality,[],[f594]) ).
thf(f608,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ ( sK25 @ X1 ) )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ ( sK25 @ X1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ ( sK25 @ X1 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f607]) ).
thf(f611,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1
@ ( sK25
@ ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) ) ) )
!= ( sK1
@ ( sK25
@ ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1
@ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0
@ ( 'const/arith/+'
@ ( sK25
@ ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f608,f11]) ).
thf(f612,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1
@ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0
@ ( 'const/arith/+'
@ ( sK25
@ ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f613,plain,
( ! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ sK2 ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X1 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
!= X2 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0
@ ( 'const/arith/+'
@ ( sK25
@ ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X1
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X1 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f612]) ).
thf(f618,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ sK3 ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ sK2 ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X1 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+'
@ ( sK25
@ ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f613,f11]) ).
thf(f619,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ sK2 ) ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X1 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+'
@ ( sK25
@ ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f620,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X1 )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( 'const/nums/_0' != 'const/nums/_0' )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f619]) ).
thf(f621,plain,
( ! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X2 ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f620]) ).
thf(f631,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ ( 'const/arith/-' @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( X0 @ sK2 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) ) )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( X0 @ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X1 ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f621]) ).
thf(f634,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ sK3 )
!= ( sK1 @ sK3 ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X1 )
| ( 'const/nums/_0'
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f631,f11]) ).
thf(f635,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y1: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y1 ) )
@ Y0 ) )
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( ^ [Y1: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( ^ [Y2: 'type/nums/num'] : ( 'const/nums/BIT1' @ ( X0 @ Y2 ) )
@ Y1 ) )
@ Y0 ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X1 )
| ( 'const/nums/_0'
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f634]) ).
thf(f636,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) ) )
| ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ sK2 ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f635]) ).
thf(f648,plain,
( ! [X0: 'type/nums/num' > 'type/nums/num'] :
( ( ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) )
!= ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( X0
@ ( 'const/arith/+'
@ ( sK6
@ ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) )
@ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ ( X0 @ sK2 ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f636]) ).
thf(f711,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X2 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] :
( sK0
@ ( ^ [Y2: 'type/nums/num'] : Y2
@ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) ) )
!= X0 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X1 @ sK2 )
!= ( X3 @ sK2 ) )
| ( ( X0 @ sK2 )
!= ( ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) )
@ sK2 ) )
| ( ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( X2 != X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f43,f39]) ).
thf(f718,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( sK0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( sK1 @ Y0 ) @ ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK2 @ sK3 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ ( 'const/realax/real_sub' @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( X1 @ Y0 ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X2 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK0 != X0 )
| ( ( sK0 @ sK2 )
!= ( X0 @ sK2 ) )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X1 @ sK2 )
!= ( X3 @ sK2 ) )
| ( X2 != X3 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f711]) ).
thf(f763,plain,
( ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( sK1
@ ( 'const/arith/-' @ Y0
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y1: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1
@ ( 'const/arith/-' @ sK2
@ ( 'const/nums/NUMERAL'
@ ( 'const/nums/BIT1'
@ ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ sK2 ) ) ) ) ) )
| ( 'const/nums/_0'
!= ( ^ [Y0: 'type/nums/num'] : 'const/nums/_0'
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ~ spl4_6 ),
inference(equality_resolution,[],[f648]) ).
thf(f764,plain,
( ( ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( 'const/nums/_0' != 'const/nums/_0' )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f763]) ).
thf(f765,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f764]) ).
thf(f766,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f765]) ).
thf(f769,plain,
( ( ( ^ [Y0: 'type/nums/num'] : Y0
@ sK26 )
!= ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
@ sK26 ) )
| spl4_7 ),
inference(negative_extensionality,[],[f534]) ).
thf(f770,plain,
( ( sK26
!= ( 'const/arith/-' @ ( 'const/arith/+' @ sK26 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
| spl4_7 ),
inference(beta-eta_normalization,[],[f769]) ).
thf(f771,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f770,f11]) ).
thf(f772,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f771]) ).
thf(f797,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] : ( sK0 @ ( X1 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) ) ) )
| ( ( sK0 @ sK2 )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) )
@ sK2 ) )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] :
( ^ [Y1: 'type/nums/num'] : ( sK1 @ ( X3 @ Y1 ) )
@ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ Y0 ) )
@ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( ( X2 @ sK2 )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ Y0 ) )
@ sK2 ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 ) ),
inference(equality_resolution,[],[f718]) ).
thf(f798,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/nums/num'] :
( ( ( sK1 @ ( 'const/arith/-' @ sK2 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( X0 @ sK2 ) )
| ( ( sK1 @ sK3 )
!= ( X0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
| ( sK1
!= ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( sK0
!= ( ^ [Y0: 'type/nums/num'] : ( sK0 @ ( X1 @ Y0 ) ) ) )
| ( ( sK0 @ sK2 )
!= ( sK0 @ ( X1 @ sK2 ) ) )
| ( ( sK0 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK0 @ ( X1 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( sK1 @ ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) )
| ( ( X2 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= ( sK1 @ ( X3 @ ( 'const/arith/+' @ sK3 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( X2 @ sK2 )
!= ( sK1 @ ( X3 @ sK2 ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
!= ( ^ [Y0: 'type/nums/num'] : ( X2 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= X1 )
| ( ( ^ [Y0: 'type/nums/num'] : Y0 )
!= ( ^ [Y0: 'type/nums/num'] : ( X3 @ ( 'const/arith/+' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) )
| ( ( ^ [Y0: 'type/nums/num'] : ( 'const/arith/-' @ Y0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
!= X3 ) ),
inference(beta-eta_normalization,[],[f797]) ).
thf(f801,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f798,f175,f172]) ).
cnf(s4,plain,
~ spl4_4,
inference(sat_conversion,[],[f258]) ).
cnf(s5,plain,
( ~ spl4_5
| spl4_6
| ~ spl4_7 ),
inference(sat_conversion,[],[f535]) ).
cnf(s8,plain,
~ spl4_6,
inference(sat_conversion,[],[f766]) ).
cnf(s9,plain,
spl4_7,
inference(sat_conversion,[],[f772]) ).
cnf(s10,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f801]) ).
cnf(s11,plain,
~ spl4_5,
inference(rat,[],[s5,s9,s8]) ).
cnf(s12,plain,
spl4_4,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12]) ).
thf(f802,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA116^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n011.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 17:42:16 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.23 Running first-order model finding
% 0.12/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/0.43 % (420847)Will run a generic schedule for satisfiability detection.
% 0.92/0.43 % (420865)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1007731098:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.92/0.43 % (420865)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.43 % (420863)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4260077765:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.92/0.43 % (420866)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2562343558:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.92/0.43 % (420861)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=392914572_2999 on theBenchmark for (2999ds/0Mi)
% 0.92/0.43 % (420864)dis+10_1_sil=32000:sp=arity:random_seed=1101592963:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.92/0.43 % (420867)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2689425014:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.92/0.43 % (420862)% WARNING: option uhcvi not known.
% 0.92/0.43 % Exception at run slice level
% 0.92/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.43 % (420862)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3332722903:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.92/0.43 % (420862)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.43 % (420862)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.92/0.43 % (420886)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3583818094:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.92/0.43 % Exception at run slice level
% 0.92/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.43 % (420865)Instruction limit reached!
% 0.92/0.43 % (420865)------------------------------
% 0.92/0.43 % (420865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420865)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420865)Termination reason: Instruction limit
% 0.92/0.43 % (420865)Termination phase: Saturation
% 0.92/0.43 % (420865)Time elapsed: 0.031 s
% 0.92/0.43 % (420865)Peak memory usage: 12 MB
% 0.92/0.43 % (420865)Instructions burned: 120 (million)
% 0.92/0.43 % (420897)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2132459583:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.92/0.43 % (420897)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.43 % (420897)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.92/0.43 % (420895)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3776477089:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.92/0.43 % (420864)Instruction limit reached!
% 0.92/0.43 % (420864)------------------------------
% 0.92/0.43 % (420864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420864)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420864)Termination reason: Instruction limit
% 0.92/0.43 % (420864)Termination phase: Saturation
% 0.92/0.43 % (420864)Time elapsed: 0.050 s
% 0.92/0.43 % (420864)Peak memory usage: 12 MB
% 0.92/0.43 % (420864)Instructions burned: 104 (million)
% 0.92/0.43 % (420866)Instruction limit reached!
% 0.92/0.43 % (420866)------------------------------
% 0.92/0.43 % (420866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420866)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420866)Termination reason: Instruction limit
% 0.92/0.43 % (420866)Termination phase: Saturation
% 0.92/0.43 % (420866)Time elapsed: 0.064 s
% 0.92/0.43 % (420866)Peak memory usage: 12 MB
% 0.92/0.43 % (420866)Instructions burned: 133 (million)
% 0.92/0.43 % (420912)ott-21_1_sil=16000:fs=off:random_seed=3909036522:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.92/0.43 % (420867)Instruction limit reached!
% 0.92/0.43 % (420867)------------------------------
% 0.92/0.43 % (420867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420867)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420867)Termination reason: Instruction limit
% 0.92/0.43 % (420867)Termination phase: Saturation
% 0.92/0.43 % (420867)Time elapsed: 0.079 s
% 0.92/0.43 % (420867)Peak memory usage: 13 MB
% 0.92/0.43 % (420867)Instructions burned: 160 (million)
% 0.92/0.43 % (420921)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1630421180:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.92/0.43 % (420928)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=440509903:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.92/0.43 % Exception at run slice level
% 0.92/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.43 % (420895)Instruction limit reached!
% 0.92/0.43 % (420895)------------------------------
% 0.92/0.43 % (420895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420895)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420895)Termination reason: Instruction limit
% 0.92/0.43 % (420895)Termination phase: Saturation
% 0.92/0.43 % (420895)Time elapsed: 0.069 s
% 0.92/0.43 % (420895)Peak memory usage: 13 MB
% 0.92/0.43 % (420895)Instructions burned: 132 (million)
% 0.92/0.43 % (420938)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3790036486:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.92/0.43 % (420944)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=769583250:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.92/0.43 % Exception at run slice level
% 0.92/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.92/0.43 % (420897) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-420847-420897"...
% 0.92/0.43 % (420957)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2149094749:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.92/0.43 % (420912)Instruction limit reached!
% 0.92/0.43 % (420912)------------------------------
% 0.92/0.43 % (420912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.43 % (420912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.43 % (420912)CaDiCaL version: 2.1.3
% 0.92/0.43 % (420912)Termination reason: Instruction limit
% 0.92/0.43 % (420912)Termination phase: Saturation
% 0.92/0.43 % (420912)Time elapsed: 0.082 s
% 0.92/0.43 % (420912)Peak memory usage: 12 MB
% 0.92/0.43 % (420957)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.92/0.43 % (420912)Instructions burned: 180 (million)
% 0.92/0.43 % (420897)...printing done.
% 0.92/0.43 % (420897)Refutation found. Thanks to Tanya!
% 0.92/0.43 % SZS status Theorem for theBenchmark
% 0.92/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.92/0.44 % (420897)------------------------------
% 0.92/0.44 % (420897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.44 % (420897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.44 % (420897)CaDiCaL version: 2.1.3
% 0.92/0.44 % (420897)Termination reason: Refutation
% 0.92/0.44 % (420897)Time elapsed: 0.122 s
% 0.92/0.44 % (420897)Peak memory usage: 15 MB
% 0.92/0.44 % (420897)Instructions burned: 502 (million)
% 0.92/0.44 % (420847)Success in time 0.195 s
% 0.92/0.44 % Vampire exiting
%------------------------------------------------------------------------------