%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV141^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:37:53 AM UTC 2026
% Result : Theorem 3.50s 1.00s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 252 ( 24 unt; 0 typ; 14 def)
% Number of atoms : 2433 ( 216 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 7708 ( 346 ~; 447 |; 395 &;4813 @)
% ( 14 <=>; 613 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 626 ( 626 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 38 con; 0-4 aty)
% (1080 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1303 ( 0 sgn 132 !; 0 ?;1303 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vOR: $o > $o > $o ).
thf(func_def_11,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
sK0: a > a > $o ).
thf(func_def_19,type,
sK1: a > a > $o ).
thf(func_def_20,type,
sK2: a ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_23,type,
sK5: a > a > $o ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a > a > $o ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a > a > $o ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a ).
thf(func_def_35,type,
sK17: a > a > $o ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a > a > $o ).
thf(func_def_41,type,
sK23: a > a > $o ).
thf(func_def_42,type,
sK24: a > a > $o ).
thf(func_def_43,type,
sK25: a > a > $o ).
thf(func_def_44,type,
sK26: a ).
thf(func_def_45,type,
sK27: a ).
thf(func_def_46,type,
sK28: a ).
thf(func_def_47,type,
sK29: a ).
thf(func_def_48,type,
sK30: a ).
thf(func_def_49,type,
sK31: a ).
thf(f1,conjecture,
! [X1: a > a > $o,X0: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X9: a,X7: a,X10: a] :
( ( ( X8 @ X10 @ X7 )
& ( X8 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X7: a,X9: a,X10: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X0: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X9: a,X7: a,X10: a] :
( ( ( X8 @ X10 @ X7 )
& ( X8 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X7: a,X9: a,X10: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X1 @ X6 @ X5 )
| ( X0 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X5 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X10: a,X11: a] :
! [X12: a > a > $o] :
( ( ! [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
& ( X12 @ X14 @ X13 ) )
=> ( X12 @ X15 @ X13 ) )
& ! [X16: a,X17: a] :
( ( ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a] :
( ( X1 @ X20 @ X19 )
=> ( X18 @ X20 @ X19 ) )
& ! [X21: a,X22: a,X23: a] :
( ( ( X18 @ X23 @ X22 )
& ( X18 @ X21 @ X23 ) )
=> ( X18 @ X21 @ X22 ) ) )
=> ( X18 @ X16 @ X17 ) )
| ! [X24: a > a > $o] :
( ( ! [X25: a,X26: a,X27: a] :
( ( ( X24 @ X26 @ X27 )
& ( X24 @ X27 @ X25 ) )
=> ( X24 @ X26 @ X25 ) )
& ! [X28: a,X29: a] :
( ( X0 @ X29 @ X28 )
=> ( X24 @ X29 @ X28 ) ) )
=> ( X24 @ X16 @ X17 ) ) )
=> ( X12 @ X16 @ X17 ) ) )
=> ( X12 @ X10 @ X11 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( sK0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( sK0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( $false
= ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK1 @ Y3 @ Y4 )
| ( sK0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK1 @ Y3 @ Y4 )
| ( sK0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK2 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK1 @ Y3 @ Y4 )
| ( sK0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f15]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK1 @ Y2 @ Y3 )
| ( sK0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK1 @ Y2 @ Y3 )
| ( sK0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f17]) ).
thf(f19,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f23,definition,
( spl4_1
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f27,definition,
( spl4_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f29,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f20,f27,f23]) ).
thf(f32,definition,
( spl4_3
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f33,plain,
( ( $false
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| spl4_3 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f34,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,definition,
( spl4_4
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f21,f36,f32]) ).
thf(f40,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK5 ) )
| ~ spl4_3 ),
inference(sigma_proxy_clausification,[],[f34]) ).
thf(f41,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
=> ( sK5 @ sK2 @ sK3 ) ) )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl4_3 ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f44,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true )
| ~ spl4_2 ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f45,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) ) )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f51,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[],[f45,f42]) ).
thf(f52,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(boolean_simplification,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_3 ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f54,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl4_3 ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f55,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl4_3 ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f56,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK1 @ X1 @ Y0 )
| ( sK0 @ X1 @ Y0 ) )
=> ( sK5 @ X1 @ Y0 ) ) )
= $true )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK1 @ X1 @ Y0 )
| ( sK0 @ X1 @ Y0 ) )
=> ( sK5 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl4_3 ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK1 @ X1 @ X2 )
| ( sK0 @ X1 @ X2 ) )
=> ( sK5 @ X1 @ X2 ) )
= $true )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f63,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl4_3 ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f64,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ X1 @ Y1 )
& ( sK5 @ Y0 @ X1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f71,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ X1 @ Y1 )
& ( sK5 @ Y0 @ X1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl4_3 ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f72,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
& ( sK5 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ Y0 ) ) )
= $true )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f85,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
& ( sK5 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ Y0 ) )
@ X3 )
= $true )
| ~ spl4_3 ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f115,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(not_proxy_clausification,[],[f52]) ).
thf(f125,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
| ~ spl4_2
| ~ spl4_3 ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f127,definition,
( spl4_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f129,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f131,definition,
( spl4_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f133,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f134,plain,
( spl4_5
| spl4_6
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f125,f32,f27,f131,f127]) ).
thf(f135,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f25,f34]) ).
thf(f136,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f137,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f136]) ).
thf(f147,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK5 @ Y1 @ Y0 ) ) )
@ sK6 ) )
| ~ spl4_5 ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f148,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) )
=> ( sK5 @ Y0 @ sK6 ) ) ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) )
=> ( sK5 @ Y0 @ sK6 ) )
@ sK7 ) )
| ~ spl4_5 ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f159,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
=> ( sK5 @ sK7 @ sK6 ) ) )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f162,plain,
( ( $false
= ( sK5 @ sK7 @ sK6 ) )
| ~ spl4_5 ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f163,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
= $true )
| ~ spl4_5 ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f179,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
= $true )
| ~ spl4_5 ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f181,definition,
( spl4_7
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f183,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
= $true )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f185,definition,
( spl4_8
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f187,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f188,plain,
( spl4_7
| spl4_8
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f179,f127,f185,f181]) ).
thf(f196,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ X1 ) )
| ~ spl4_7 ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f197,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 @ sK6 ) ) )
| ~ spl4_7 ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f208,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[],[f197,f162]) ).
thf(f209,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(boolean_simplification,[],[f208]) ).
thf(f230,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f243,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f245,definition,
( spl4_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f247,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl4_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
thf(f251,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f261,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ X1 )
= $true )
| ~ spl4_8 ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f262,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK7 @ sK6 ) ) )
| ~ spl4_8 ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f268,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f262,f162]) ).
thf(f271,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl4_5
| ~ spl4_8 ),
inference(boolean_simplification,[],[f268]) ).
thf(f275,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) )
& $true ) )
= $true )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_demodulation,[],[f271,f54]) ).
thf(f276,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(boolean_simplification,[],[f275]) ).
thf(f279,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f282,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ sK9 ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(sigma_proxy_clausification,[],[f279]) ).
thf(f283,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ sK9 @ Y0 )
=> ( sK5 @ sK9 @ Y0 ) ) ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f293,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ sK9 @ Y0 )
=> ( sK5 @ sK9 @ Y0 ) )
@ sK10 )
= $false )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(sigma_proxy_clausification,[],[f283]) ).
thf(f294,plain,
( ( $false
= ( ( sK1 @ sK9 @ sK10 )
=> ( sK5 @ sK9 @ sK10 ) ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
( ( $false
= ( sK5 @ sK9 @ sK10 ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( ( sK1 @ sK9 @ sK10 )
= $true )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f301,plain,
( ( ( ( ( sK1 @ sK9 @ sK10 )
| ( sK0 @ sK9 @ sK10 ) )
=> $false )
= $true )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f58,f295]) ).
thf(f305,plain,
( ( $true
= ( ~ ( ( sK1 @ sK9 @ sK10 )
| ( sK0 @ sK9 @ sK10 ) ) ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(boolean_simplification,[],[f301]) ).
thf(f311,plain,
( ( ( ~ ( $true
| ( sK0 @ sK9 @ sK10 ) ) )
= $true )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_demodulation,[],[f305,f296]) ).
thf(f312,plain,
( ( $true = ( ~ $true ) )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(boolean_simplification,[],[f311]) ).
thf(f313,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(boolean_simplification,[],[f312]) ).
thf(f314,plain,
( $false
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
( ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f314]) ).
thf(f317,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK5 ) )
| spl4_1 ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f318,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
=> ( sK5 @ sK2 @ sK3 ) ) )
| spl4_1 ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f325,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| spl4_1 ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f326,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) )
| spl4_1 ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f336,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true )
| spl4_3 ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f337,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true )
| spl4_3 ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f341,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| spl4_1
| spl4_3 ),
inference(superposition,[],[f337,f325]) ).
thf(f342,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) ) ) )
| spl4_1
| spl4_3 ),
inference(boolean_simplification,[],[f341]) ).
thf(f343,plain,
( ( $true = ( ~ $true ) )
| spl4_1
| spl4_3 ),
inference(forward_demodulation,[],[f342,f326]) ).
thf(f344,plain,
( ( $false = $true )
| spl4_1
| spl4_3 ),
inference(boolean_simplification,[],[f343]) ).
thf(f345,plain,
( $false
| spl4_1
| spl4_3 ),
inference(trivial_inequality_removal,[],[f344]) ).
thf(f346,plain,
( spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f345]) ).
thf(f438,plain,
( spl4_9
| spl4_10
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f243,f181,f127,f249,f245]) ).
thf(f473,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK11 ) )
| ~ spl4_4 ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f474,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK11 @ sK2 @ sK3 ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f473]) ).
thf(f481,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y0 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y2 @ Y1 ) ) ) )
@ sK12 ) )
| ~ spl4_9 ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f482,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ sK12 )
& ( sK5 @ sK12 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
| ~ spl4_9 ),
inference(beta-eta_normalization,[],[f481]) ).
thf(f484,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ sK12 )
& ( sK5 @ sK12 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) )
@ sK13 ) )
| ~ spl4_9 ),
inference(sigma_proxy_clausification,[],[f482]) ).
thf(f485,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK12 )
& ( sK5 @ sK12 @ sK13 ) )
=> ( sK5 @ Y0 @ sK13 ) ) ) )
| ~ spl4_9 ),
inference(beta-eta_normalization,[],[f484]) ).
thf(f488,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK12 )
& ( sK5 @ sK12 @ sK13 ) )
=> ( sK5 @ Y0 @ sK13 ) )
@ sK14 ) )
| ~ spl4_9 ),
inference(sigma_proxy_clausification,[],[f485]) ).
thf(f489,plain,
( ( $false
= ( ( ( sK5 @ sK14 @ sK12 )
& ( sK5 @ sK12 @ sK13 ) )
=> ( sK5 @ sK14 @ sK13 ) ) )
| ~ spl4_9 ),
inference(beta-eta_normalization,[],[f488]) ).
thf(f490,plain,
( ( $false
= ( sK11 @ sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(imp_proxy_clausification,[],[f474]) ).
thf(f491,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl4_4 ),
inference(imp_proxy_clausification,[],[f474]) ).
thf(f493,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| spl4_3
| ~ spl4_4 ),
inference(superposition,[],[f337,f490]) ).
thf(f495,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| spl4_3
| ~ spl4_4 ),
inference(boolean_simplification,[],[f493]) ).
thf(f498,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl4_4 ),
inference(and_proxy_clausification,[],[f491]) ).
thf(f499,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl4_4 ),
inference(and_proxy_clausification,[],[f491]) ).
thf(f500,plain,
( ( $false
= ( sK5 @ sK14 @ sK13 ) )
| ~ spl4_9 ),
inference(imp_proxy_clausification,[],[f489]) ).
thf(f501,plain,
( ( ( ( sK5 @ sK14 @ sK12 )
& ( sK5 @ sK12 @ sK13 ) )
= $true )
| ~ spl4_9 ),
inference(imp_proxy_clausification,[],[f489]) ).
thf(f502,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y1 @ Y2 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl4_4 ),
inference(pi_proxy_clausification,[],[f498]) ).
thf(f503,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ X1 @ Y0 ) )
=> ( sK11 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f502]) ).
thf(f508,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ X1 @ Y0 ) )
=> ( sK11 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl4_4 ),
inference(pi_proxy_clausification,[],[f503]) ).
thf(f509,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ X2 @ Y0 )
& ( sK11 @ X1 @ X2 ) )
=> ( sK11 @ X1 @ Y0 ) ) )
= $true )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f508]) ).
thf(f510,plain,
( ( $true
= ( sK5 @ sK12 @ sK13 ) )
| ~ spl4_9 ),
inference(and_proxy_clausification,[],[f501]) ).
thf(f511,plain,
( ( ( sK5 @ sK14 @ sK12 )
= $true )
| ~ spl4_9 ),
inference(and_proxy_clausification,[],[f501]) ).
thf(f537,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
| spl4_3
| ~ spl4_4 ),
inference(not_proxy_clausification,[],[f495]) ).
thf(f547,definition,
( spl4_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f549,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f547]) ).
thf(f551,definition,
( spl4_12
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
thf(f553,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f551]) ).
thf(f581,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK5 @ X1 @ X3 )
& ( sK5 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ X3 ) )
= $true )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f593,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
& ( sK5 @ X2 @ X1 ) )
=> ( sK5 @ X2 @ Y0 ) ) )
= $true )
| ~ spl4_3 ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f842,plain,
( ! [X0: a] :
( ( ( $true
& ( sK5 @ X0 @ sK12 ) )
=> ( sK5 @ X0 @ sK13 ) )
= $true )
| ~ spl4_3
| ~ spl4_9 ),
inference(superposition,[],[f581,f510]) ).
thf(f848,plain,
( ! [X0: a] :
( $true
= ( ( sK5 @ X0 @ sK12 )
=> ( sK5 @ X0 @ sK13 ) ) )
| ~ spl4_3
| ~ spl4_9 ),
inference(boolean_simplification,[],[f842]) ).
thf(f892,plain,
( ( ( $true
=> ( sK5 @ sK14 @ sK13 ) )
= $true )
| ~ spl4_3
| ~ spl4_9 ),
inference(superposition,[],[f848,f511]) ).
thf(f895,plain,
( ( $true
= ( sK5 @ sK14 @ sK13 ) )
| ~ spl4_3
| ~ spl4_9 ),
inference(boolean_simplification,[],[f892]) ).
thf(f900,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_9 ),
inference(forward_demodulation,[],[f895,f500]) ).
thf(f901,plain,
( $false
| ~ spl4_3
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f900]) ).
thf(f902,plain,
( ~ spl4_3
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f901]) ).
thf(f916,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ sK15 ) )
| ~ spl4_10 ),
inference(sigma_proxy_clausification,[],[f251]) ).
thf(f917,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK15 @ Y0 )
=> ( sK5 @ sK15 @ Y0 ) ) ) )
| ~ spl4_10 ),
inference(beta-eta_normalization,[],[f916]) ).
thf(f928,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ sK15 @ Y0 )
=> ( sK5 @ sK15 @ Y0 ) )
@ sK16 ) )
| ~ spl4_10 ),
inference(sigma_proxy_clausification,[],[f917]) ).
thf(f929,plain,
( ( $false
= ( ( sK0 @ sK15 @ sK16 )
=> ( sK5 @ sK15 @ sK16 ) ) )
| ~ spl4_10 ),
inference(beta-eta_normalization,[],[f928]) ).
thf(f932,plain,
( ( $false
= ( sK5 @ sK15 @ sK16 ) )
| ~ spl4_10 ),
inference(imp_proxy_clausification,[],[f929]) ).
thf(f933,plain,
( ( ( sK0 @ sK15 @ sK16 )
= $true )
| ~ spl4_10 ),
inference(imp_proxy_clausification,[],[f929]) ).
thf(f940,plain,
( ( ( ( ( sK1 @ sK15 @ sK16 )
| ( sK0 @ sK15 @ sK16 ) )
=> $false )
= $true )
| ~ spl4_3
| ~ spl4_10 ),
inference(superposition,[],[f58,f932]) ).
thf(f947,plain,
( ( ( ~ ( ( sK1 @ sK15 @ sK16 )
| ( sK0 @ sK15 @ sK16 ) ) )
= $true )
| ~ spl4_3
| ~ spl4_10 ),
inference(boolean_simplification,[],[f940]) ).
thf(f950,plain,
( ( ( ~ ( ( sK1 @ sK15 @ sK16 )
| $true ) )
= $true )
| ~ spl4_3
| ~ spl4_10 ),
inference(forward_demodulation,[],[f947,f933]) ).
thf(f951,plain,
( ( $true = ( ~ $true ) )
| ~ spl4_3
| ~ spl4_10 ),
inference(boolean_simplification,[],[f950]) ).
thf(f952,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_10 ),
inference(boolean_simplification,[],[f951]) ).
thf(f953,plain,
( $false
| ~ spl4_3
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f952]) ).
thf(f954,plain,
( ~ spl4_3
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[],[f953]) ).
thf(f969,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y0 @ Y1 ) )
=> ( sK5 @ Y0 @ Y2 ) ) ) )
@ sK18 ) )
| ~ spl4_6 ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f970,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
& ( sK5 @ sK18 @ Y0 ) )
=> ( sK5 @ sK18 @ Y1 ) ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f969]) ).
thf(f973,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
& ( sK5 @ sK18 @ Y0 ) )
=> ( sK5 @ sK18 @ Y1 ) ) )
@ sK19 ) )
| ~ spl4_6 ),
inference(sigma_proxy_clausification,[],[f970]) ).
thf(f974,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK19 @ Y0 )
& ( sK5 @ sK18 @ sK19 ) )
=> ( sK5 @ sK18 @ Y0 ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f973]) ).
thf(f975,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f974,f593]) ).
thf(f976,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f975]) ).
thf(f977,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f976]) ).
thf(f1103,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK20 ) )
| ~ spl4_11 ),
inference(sigma_proxy_clausification,[],[f549]) ).
thf(f1104,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK1 @ sK20 @ Y0 )
| ( sK0 @ sK20 @ Y0 ) )
=> ( sK11 @ sK20 @ Y0 ) ) ) )
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1103]) ).
thf(f1105,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK1 @ sK20 @ Y0 )
| ( sK0 @ sK20 @ Y0 ) )
=> ( sK11 @ sK20 @ Y0 ) )
@ sK21 ) )
| ~ spl4_11 ),
inference(sigma_proxy_clausification,[],[f1104]) ).
thf(f1106,plain,
( ( $false
= ( ( ( sK1 @ sK20 @ sK21 )
| ( sK0 @ sK20 @ sK21 ) )
=> ( sK11 @ sK20 @ sK21 ) ) )
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1105]) ).
thf(f1107,plain,
( ( $false
= ( sK11 @ sK20 @ sK21 ) )
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1106]) ).
thf(f1108,plain,
( ( ( ( sK1 @ sK20 @ sK21 )
| ( sK0 @ sK20 @ sK21 ) )
= $true )
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1106]) ).
thf(f1123,plain,
( ( ( sK1 @ sK20 @ sK21 )
= $true )
| ( ( sK0 @ sK20 @ sK21 )
= $true )
| ~ spl4_11 ),
inference(or_proxy_clausification,[],[f1108]) ).
thf(f1127,definition,
( spl4_13
<=> ( ( sK1 @ sK20 @ sK21 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
thf(f1129,plain,
( ( ( sK1 @ sK20 @ sK21 )
= $true )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f1127]) ).
thf(f1131,definition,
( spl4_14
<=> ( ( sK0 @ sK20 @ sK21 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
thf(f1133,plain,
( ( ( sK0 @ sK20 @ sK21 )
= $true )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f1131]) ).
thf(f1134,plain,
( spl4_13
| spl4_14
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f1123,f547,f1131,f1127]) ).
thf(f1135,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK0 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
| spl4_3
| ~ spl4_4 ),
inference(and_proxy_clausification,[],[f537]) ).
thf(f1174,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl4_4 ),
inference(pi_proxy_clausification,[],[f499]) ).
thf(f1175,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK11 @ Y0 @ X1 ) ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f1174]) ).
thf(f1178,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK11 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl4_4 ),
inference(pi_proxy_clausification,[],[f1175]) ).
thf(f1179,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f1178]) ).
thf(f1186,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) ) )
=> $false )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(superposition,[],[f1179,f1107]) ).
thf(f1188,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(boolean_simplification,[],[f1186]) ).
thf(f1232,plain,
( ( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(not_proxy_clausification,[],[f1188]) ).
thf(f1235,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(or_proxy_clausification,[],[f1232]) ).
thf(f1236,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(or_proxy_clausification,[],[f1232]) ).
thf(f1280,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) )
@ sK24 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(sigma_proxy_clausification,[],[f1235]) ).
thf(f1281,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK24 @ Y2 @ Y0 )
& ( sK24 @ Y0 @ Y1 ) )
=> ( sK24 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK24 @ Y0 @ Y1 ) ) ) ) )
=> ( sK24 @ sK20 @ sK21 ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1280]) ).
thf(f1291,plain,
( ( $false
= ( sK24 @ sK20 @ sK21 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1281]) ).
thf(f1292,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK24 @ Y2 @ Y0 )
& ( sK24 @ Y0 @ Y1 ) )
=> ( sK24 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK24 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1281]) ).
thf(f1297,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK20 @ sK21 ) )
@ sK25 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(sigma_proxy_clausification,[],[f1236]) ).
thf(f1298,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK25 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK25 @ Y0 @ Y2 )
& ( sK25 @ Y1 @ Y0 ) )
=> ( sK25 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK25 @ sK20 @ sK21 ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1297]) ).
thf(f1301,plain,
( ( $false
= ( sK25 @ sK20 @ sK21 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1298]) ).
thf(f1302,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK25 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK25 @ Y0 @ Y2 )
& ( sK25 @ Y1 @ Y0 ) )
=> ( sK25 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(imp_proxy_clausification,[],[f1298]) ).
thf(f1395,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK24 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(and_proxy_clausification,[],[f1292]) ).
thf(f1401,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK25 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(and_proxy_clausification,[],[f1302]) ).
thf(f1434,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK24 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(pi_proxy_clausification,[],[f1395]) ).
thf(f1435,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ X1 @ Y0 )
=> ( sK24 @ X1 @ Y0 ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1434]) ).
thf(f1438,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK0 @ X1 @ Y0 )
=> ( sK24 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(pi_proxy_clausification,[],[f1435]) ).
thf(f1439,plain,
( ! [X2: a,X1: a] :
( ( ( sK0 @ X1 @ X2 )
=> ( sK24 @ X1 @ X2 ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1438]) ).
thf(f1545,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK25 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(pi_proxy_clausification,[],[f1401]) ).
thf(f1546,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ X1 @ Y0 )
=> ( sK25 @ X1 @ Y0 ) ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1545]) ).
thf(f1555,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK1 @ X1 @ Y0 )
=> ( sK25 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(pi_proxy_clausification,[],[f1546]) ).
thf(f1556,plain,
( ! [X2: a,X1: a] :
( ( ( sK1 @ X1 @ X2 )
=> ( sK25 @ X1 @ X2 ) )
= $true )
| ~ spl4_4
| ~ spl4_11 ),
inference(beta-eta_normalization,[],[f1555]) ).
thf(f1571,plain,
( ( $true
= ( $true
=> ( sK25 @ sK20 @ sK21 ) ) )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(superposition,[],[f1556,f1129]) ).
thf(f1575,plain,
( ( ( sK25 @ sK20 @ sK21 )
= $true )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(boolean_simplification,[],[f1571]) ).
thf(f1582,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(forward_demodulation,[],[f1575,f1301]) ).
thf(f1583,plain,
( $false
| ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(trivial_inequality_removal,[],[f1582]) ).
thf(f1584,plain,
( ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(avatar_contradiction_clause,[],[f1583]) ).
thf(f1587,plain,
( ( ( $true
=> ( sK24 @ sK20 @ sK21 ) )
= $true )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(superposition,[],[f1439,f1133]) ).
thf(f1593,plain,
( ( ( sK24 @ sK20 @ sK21 )
= $true )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(boolean_simplification,[],[f1587]) ).
thf(f1596,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(forward_demodulation,[],[f1593,f1291]) ).
thf(f1597,plain,
( $false
| ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(trivial_inequality_removal,[],[f1596]) ).
thf(f1598,plain,
( ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(avatar_contradiction_clause,[],[f1597]) ).
thf(f1599,plain,
( spl4_11
| spl4_12
| spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f1135,f36,f32,f551,f547]) ).
thf(f1672,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) )
@ sK30 ) )
| ~ spl4_12 ),
inference(sigma_proxy_clausification,[],[f553]) ).
thf(f1673,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ sK30 @ Y1 )
& ( sK11 @ Y0 @ sK30 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl4_12 ),
inference(beta-eta_normalization,[],[f1672]) ).
thf(f1684,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ sK30 @ Y1 )
& ( sK11 @ Y0 @ sK30 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK31 )
= $false )
| ~ spl4_12 ),
inference(sigma_proxy_clausification,[],[f1673]) ).
thf(f1685,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ sK30 @ Y0 )
& ( sK11 @ sK31 @ sK30 ) )
=> ( sK11 @ sK31 @ Y0 ) ) ) )
| ~ spl4_12 ),
inference(beta-eta_normalization,[],[f1684]) ).
thf(f1686,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_12 ),
inference(forward_demodulation,[],[f1685,f509]) ).
thf(f1687,plain,
( $false
| ~ spl4_4
| ~ spl4_12 ),
inference(trivial_inequality_removal,[],[f1686]) ).
thf(f1688,plain,
( ~ spl4_4
| ~ spl4_12 ),
inference(avatar_contradiction_clause,[],[f1687]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s4,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
( ~ spl4_5
| spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f188]) ).
cnf(s7,plain,
( ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(sat_conversion,[],[f315]) ).
cnf(s8,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f346]) ).
cnf(s9,plain,
( ~ spl4_5
| ~ spl4_7
| spl4_9
| spl4_10 ),
inference(sat_conversion,[],[f438]) ).
cnf(s13,plain,
( ~ spl4_3
| ~ spl4_9 ),
inference(sat_conversion,[],[f902]) ).
cnf(s14,plain,
( ~ spl4_3
| ~ spl4_10 ),
inference(sat_conversion,[],[f954]) ).
cnf(s15,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f977]) ).
cnf(s17,plain,
( ~ spl4_11
| spl4_13
| spl4_14 ),
inference(sat_conversion,[],[f1134]) ).
cnf(s21,plain,
( ~ spl4_4
| ~ spl4_11
| ~ spl4_13 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s22,plain,
( ~ spl4_4
| ~ spl4_11
| ~ spl4_14 ),
inference(sat_conversion,[],[f1598]) ).
cnf(s23,plain,
( spl4_3
| ~ spl4_4
| spl4_11
| spl4_12 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s24,plain,
( ~ spl4_4
| ~ spl4_12 ),
inference(sat_conversion,[],[f1688]) ).
cnf(s25,plain,
spl4_1,
inference(rat,[],[s5,s7,s9,s3,s13,s14,s15,s1,s8]) ).
cnf(s26,plain,
~ spl4_3,
inference(rat,[],[s4,s25]) ).
cnf(s27,plain,
spl4_4,
inference(rat,[],[s2,s26]) ).
cnf(s28,plain,
~ spl4_12,
inference(rat,[],[s24,s27]) ).
cnf(s29,plain,
spl4_11,
inference(rat,[],[s23,s28,s26,s27]) ).
cnf(s31,plain,
~ spl4_14,
inference(rat,[],[s22,s27,s29]) ).
cnf(s32,plain,
~ spl4_13,
inference(rat,[],[s21,s27,s29]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s17,s31,s32,s29]) ).
thf(f1689,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV141^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n016.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 15:20:50 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/0.50 % (474989)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.21/0.50 % (474994)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2229016091:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.21/0.50 % (475000)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.21/0.50 % (475000)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.21/0.50 % (474999)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2700127937:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.21/0.50 % (474995)lrs+10_16_si=on:nwc=1.5:random_seed=2547018213:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.21/0.50 % (474996)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2549912613:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.21/0.50 % (474997)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3315562725:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.21/0.50 % (474998)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1278630261:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.21/0.50 % (475000)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2431562364:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.21/0.50 % (474996)Instruction limit reached!
% 1.21/0.50 % (474996)------------------------------
% 1.21/0.50 % (474996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.50 % (474996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.50 % (474996)CaDiCaL version: 2.1.3
% 1.21/0.50 % (474996)Termination reason: Instruction limit
% 1.21/0.50 % (474996)Termination phase: Saturation
% 1.21/0.50 % (474996)Time elapsed: 0.004 s
% 1.21/0.50 % (474996)Peak memory usage: 11 MB
% 1.21/0.50 % (474996)Instructions burned: 3 (million)
% 1.21/0.50 % (474995)Instruction limit reached!
% 1.21/0.50 % (474995)------------------------------
% 1.21/0.50 % (474995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.50 % (474995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.50 % (474995)CaDiCaL version: 2.1.3
% 1.21/0.50 % (474995)Termination reason: Instruction limit
% 1.21/0.50 % (474995)Termination phase: Saturation
% 1.21/0.50 % (474995)Time elapsed: 0.016 s
% 1.21/0.50 % (474995)Peak memory usage: 12 MB
% 1.21/0.50 % (474995)Instructions burned: 18 (million)
% 1.21/0.50 % (474998)Instruction limit reached!
% 1.21/0.50 % (474998)------------------------------
% 1.21/0.50 % (474998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.50 % (474998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.50 % (474998)CaDiCaL version: 2.1.3
% 1.21/0.50 % (474998)Termination reason: Instruction limit
% 1.21/0.50 % (474998)Termination phase: Saturation
% 1.21/0.50 % (474998)Time elapsed: 0.021 s
% 1.21/0.50 % (474998)Peak memory usage: 11 MB
% 1.21/0.50 % (474998)Instructions burned: 24 (million)
% 1.21/0.50 % (474994)Instruction limit reached!
% 1.21/0.50 % (474994)------------------------------
% 1.21/0.50 % (474994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.50 % (474994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.50 % (474994)CaDiCaL version: 2.1.3
% 1.21/0.50 % (474994)Termination reason: Instruction limit
% 1.21/0.50 % (474994)Termination phase: Saturation
% 1.21/0.50 % (474994)Time elapsed: 0.037 s
% 1.21/0.50 % (474994)Peak memory usage: 13 MB
% 1.21/0.50 % (474994)Instructions burned: 88 (million)
% 1.21/0.50 % (475008)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=266766389:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.21/0.50 % (475008)Instruction limit reached!
% 1.21/0.50 % (475008)------------------------------
% 1.21/0.50 % (475008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.50 % (475008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.55 % (475008)CaDiCaL version: 2.1.3
% 1.21/0.55 % (475008)Termination reason: Instruction limit
% 1.21/0.55 % (475008)Termination phase: Preprocessing 3
% 1.21/0.55 % (475008)Time elapsed: 0.002 s
% 1.21/0.55 % (475008)Peak memory usage: 10 MB
% 1.21/0.55 % (475008)Instructions burned: 2 (million)
% 1.21/0.55 % (475011)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1103675410:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.21/0.55 % (475009)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1370818142:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.21/0.55 % (475011)Instruction limit reached!
% 1.21/0.55 % (475011)------------------------------
% 1.21/0.55 % (475011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.55 % (475011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.55 % (475011)CaDiCaL version: 2.1.3
% 1.21/0.55 % (475011)Termination reason: Instruction limit
% 1.21/0.55 % (475011)Termination phase: Saturation
% 1.21/0.55 % (475011)Time elapsed: 0.006 s
% 1.21/0.55 % (475011)Peak memory usage: 12 MB
% 1.21/0.55 % (475011)Instructions burned: 14 (million)
% 1.21/0.55 % (475010)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.21/0.55 % (475009)Instruction limit reached!
% 1.21/0.55 % (475009)------------------------------
% 1.21/0.55 % (475009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.55 % (475009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.55 % (475009)CaDiCaL version: 2.1.3
% 1.21/0.55 % (475009)Termination reason: Instruction limit
% 1.21/0.55 % (475009)Termination phase: Saturation
% 1.21/0.55 % (475009)Time elapsed: 0.005 s
% 1.21/0.55 % (475009)Peak memory usage: 12 MB
% 1.21/0.55 % (475009)Instructions burned: 5 (million)
% 1.21/0.55 % (475010)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=898928629:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.21/0.55 % (474999)Instruction limit reached!
% 1.21/0.55 % (474999)------------------------------
% 1.21/0.55 % (474999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.55 % (474999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.55 % (474999)CaDiCaL version: 2.1.3
% 1.21/0.55 % (474999)Termination reason: Instruction limit
% 1.21/0.55 % (474999)Termination phase: Saturation
% 1.21/0.55 % (474999)Time elapsed: 0.060 s
% 1.21/0.55 % (474999)Peak memory usage: 12 MB
% 1.21/0.55 % (474999)Instructions burned: 76 (million)
% 1.21/0.55 % (475010)Instruction limit reached!
% 1.21/0.55 % (475010)------------------------------
% 1.21/0.55 % (475010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.21/0.55 % (475010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/0.55 % (475010)CaDiCaL version: 2.1.3
% 1.21/0.55 % (475010)Termination reason: Instruction limit
% 1.21/0.55 % (475010)Termination phase: Saturation
% 1.21/0.55 % (475010)Time elapsed: 0.006 s
% 1.21/0.55 % (475010)Peak memory usage: 12 MB
% 1.21/0.55 % (475010)Instructions burned: 7 (million)
% 1.21/0.55 % (475013)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.21/0.55 % (475013)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.21/0.55 % (475016)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1483177642:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.21/0.55 % (475013)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1231266292:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.21/0.55 % (475019)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.21/0.55 % (475017)lrs+10_1_si=on:cs=on:random_seed=3630979403:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 2.07/0.61 % (475019)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3046674848:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 2.07/0.61 % (475020)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1353996139:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 2.07/0.61 % (475013)Instruction limit reached!
% 2.07/0.61 % (475013)------------------------------
% 2.07/0.61 % (475013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475019)Instruction limit reached!
% 2.07/0.61 % (475019)------------------------------
% 2.07/0.61 % (475019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475013)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475013)Termination reason: Instruction limit
% 2.07/0.61 % (475013)Termination phase: Saturation
% 2.07/0.61 % (475019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475013)Time elapsed: 0.024 s
% 2.07/0.61 % (475013)Peak memory usage: 12 MB
% 2.07/0.61 % (475019)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475019)Termination reason: Instruction limit
% 2.07/0.61 % (475019)Termination phase: Property scanning
% 2.07/0.61 % (475013)Instructions burned: 30 (million)
% 2.07/0.61 % (475019)Time elapsed: 0.002 s
% 2.07/0.61 % (475019)Peak memory usage: 10 MB
% 2.07/0.61 % (475019)Instructions burned: 2 (million)
% 2.07/0.61 % (475017)Instruction limit reached!
% 2.07/0.61 % (475017)------------------------------
% 2.07/0.61 % (475017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475017)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475017)Termination reason: Instruction limit
% 2.07/0.61 % (475017)Termination phase: Saturation
% 2.07/0.61 % (475017)Time elapsed: 0.009 s
% 2.07/0.61 % (475017)Peak memory usage: 12 MB
% 2.07/0.61 % (475017)Instructions burned: 8 (million)
% 2.07/0.61 % (475016)Instruction limit reached!
% 2.07/0.61 % (475016)------------------------------
% 2.07/0.61 % (475016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475016)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475016)Termination reason: Instruction limit
% 2.07/0.61 % (475016)Termination phase: Saturation
% 2.07/0.61 % (475016)Time elapsed: 0.039 s
% 2.07/0.61 % (475016)Peak memory usage: 13 MB
% 2.07/0.61 % (475016)Instructions burned: 86 (million)
% 2.07/0.61 % (475029)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2166403240:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.07/0.61 % (475000)Instruction limit reached!
% 2.07/0.61 % (475000)------------------------------
% 2.07/0.61 % (475000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475000)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475000)Termination reason: Instruction limit
% 2.07/0.61 % (475000)Termination phase: Saturation
% 2.07/0.61 % (475000)Time elapsed: 0.123 s
% 2.07/0.61 % (475000)Peak memory usage: 13 MB
% 2.07/0.61 % (475000)Instructions burned: 158 (million)
% 2.07/0.61 % (475027)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=511794975:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.07/0.61 % (475020)Instruction limit reached!
% 2.07/0.61 % (475020)------------------------------
% 2.07/0.61 % (475020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.61 % (475020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.61 % (475020)CaDiCaL version: 2.1.3
% 2.07/0.61 % (475020)Termination reason: Instruction limit
% 2.07/0.61 % (475020)Termination phase: Saturation
% 2.07/0.61 % (475020)Time elapsed: 0.033 s
% 2.07/0.61 % (475020)Peak memory usage: 12 MB
% 2.07/0.61 % (475020)Instructions burned: 39 (million)
% 2.07/0.61 % (475026)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3662210124:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.07/0.61 % (475028)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=126812252:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.41/0.68 % (475032)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2049771061:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.41/0.68 % (475028)Instruction limit reached!
% 2.41/0.68 % (475028)------------------------------
% 2.41/0.68 % (475028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.68 % (475028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.68 % (475028)CaDiCaL version: 2.1.3
% 2.41/0.68 % (475028)Termination reason: Instruction limit
% 2.41/0.68 % (475028)Termination phase: Saturation
% 2.41/0.68 % (475028)Time elapsed: 0.012 s
% 2.41/0.68 % (475028)Peak memory usage: 12 MB
% 2.41/0.68 % (475028)Instructions burned: 15 (million)
% 2.41/0.68 % (475027)Instruction limit reached!
% 2.41/0.68 % (475027)------------------------------
% 2.41/0.68 % (475027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.68 % (475027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.68 % (475027)CaDiCaL version: 2.1.3
% 2.41/0.68 % (475027)Termination reason: Instruction limit
% 2.41/0.68 % (475027)Termination phase: Saturation
% 2.41/0.68 % (475027)Time elapsed: 0.021 s
% 2.41/0.68 % (475027)Peak memory usage: 12 MB
% 2.41/0.68 % (475027)Instructions burned: 25 (million)
% 2.41/0.68 % (475032)Instruction limit reached!
% 2.41/0.68 % (475032)------------------------------
% 2.41/0.68 % (475032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.68 % (475032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.68 % (475032)CaDiCaL version: 2.1.3
% 2.41/0.68 % (475032)Termination reason: Instruction limit
% 2.41/0.68 % (475032)Termination phase: Saturation
% 2.41/0.68 % (475032)Time elapsed: 0.009 s
% 2.41/0.68 % (475032)Peak memory usage: 12 MB
% 2.41/0.68 % (475032)Instructions burned: 16 (million)
% 2.41/0.68 % (475034)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1920306229:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.41/0.68 % (475034)Instruction limit reached!
% 2.41/0.68 % (475034)------------------------------
% 2.41/0.68 % (475034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.68 % (475034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.68 % (475034)CaDiCaL version: 2.1.3
% 2.41/0.68 % (475034)Termination reason: Instruction limit
% 2.41/0.68 % (475034)Termination phase: Preprocessing 3
% 2.41/0.68 % (475034)Time elapsed: 0.002 s
% 2.41/0.68 % (475034)Peak memory usage: 10 MB
% 2.41/0.68 % (475034)Instructions burned: 2 (million)
% 2.41/0.68 % (475038)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2409575918:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.41/0.68 % (475037)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1391168049:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.41/0.68 % (475041)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.41/0.68 % (475041)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.41/0.68 % (475039)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1537653409:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.41/0.68 % (475038)Instruction limit reached!
% 2.41/0.68 % (475038)------------------------------
% 2.41/0.68 % (475038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.68 % (475038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.68 % (475038)CaDiCaL version: 2.1.3
% 2.41/0.68 % (475038)Termination reason: Instruction limit
% 2.41/0.68 % (475038)Termination phase: Saturation
% 2.41/0.68 % (475038)Time elapsed: 0.011 s
% 2.41/0.68 % (475038)Peak memory usage: 11 MB
% 2.41/0.68 % (475038)Instructions burned: 23 (million)
% 2.41/0.68 % (475041)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=25346567:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.49/0.79 % (475037)Instruction limit reached!
% 2.49/0.79 % (475037)------------------------------
% 2.49/0.79 % (475037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475037)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475037)Termination reason: Instruction limit
% 2.49/0.79 % (475037)Termination phase: Saturation
% 2.49/0.79 % (475037)Time elapsed: 0.022 s
% 2.49/0.79 % (475037)Peak memory usage: 12 MB
% 2.49/0.79 % (475037)Instructions burned: 26 (million)
% 2.49/0.79 % (475047)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.49/0.79 % (475047)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2536272192:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.49/0.79 % (475041)Instruction limit reached!
% 2.49/0.79 % (475041)------------------------------
% 2.49/0.79 % (475041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475041)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475041)Termination reason: Instruction limit
% 2.49/0.79 % (475041)Termination phase: Saturation
% 2.49/0.79 % (475041)Time elapsed: 0.021 s
% 2.49/0.79 % (475041)Peak memory usage: 12 MB
% 2.49/0.79 % (475041)Instructions burned: 14 (million)
% 2.49/0.79 % (475047)Instruction limit reached!
% 2.49/0.79 % (475047)------------------------------
% 2.49/0.79 % (475047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475047)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475047)Termination reason: Instruction limit
% 2.49/0.79 % (475047)Termination phase: Saturation
% 2.49/0.79 % (475047)Time elapsed: 0.005 s
% 2.49/0.79 % (475047)Peak memory usage: 12 MB
% 2.49/0.79 % (475047)Instructions burned: 8 (million)
% 2.49/0.79 % (475039)Instruction limit reached!
% 2.49/0.79 % (475039)------------------------------
% 2.49/0.79 % (475039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475039)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475039)Termination reason: Instruction limit
% 2.49/0.79 % (475039)Termination phase: Saturation
% 2.49/0.79 % (475039)Time elapsed: 0.048 s
% 2.49/0.79 % (475039)Peak memory usage: 12 MB
% 2.49/0.79 % (475039)Instructions burned: 60 (million)
% 2.49/0.79 % (475048)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3886281747:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.49/0.79 % (475052)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1051415466:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.49/0.79 % (475051)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1720841937:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.49/0.79 % (475048)Refutation not found, incomplete strategy
% 2.49/0.79 % (475048)------------------------------
% 2.49/0.79 % (475048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475048)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475048)Termination reason: Refutation not found, incomplete strategy
% 2.49/0.79 % (475048)Time elapsed: 0.012 s
% 2.49/0.79 % (475048)Peak memory usage: 12 MB
% 2.49/0.79 % (475048)Instructions burned: 12 (million)
% 2.49/0.79 % (475052)Refutation not found, incomplete strategy
% 2.49/0.79 % (475052)------------------------------
% 2.49/0.79 % (475052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.49/0.79 % (475052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.79 % (475052)CaDiCaL version: 2.1.3
% 2.49/0.79 % (475052)Termination reason: Refutation not found, incomplete strategy
% 2.49/0.79 % (475052)Time elapsed: 0.010 s
% 2.49/0.79 % (475052)Peak memory usage: 12 MB
% 2.49/0.79 % (475052)Instructions burned: 11 (million)
% 2.49/0.79 % (475048)------------------------------
% 2.49/0.79 % (475048)------------------------------
% 3.50/0.91 % (475052)------------------------------
% 3.50/0.91 % (475052)------------------------------
% 3.50/0.91 % (475053)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3485865934:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 3.50/0.91 % (475051)Instruction limit reached!
% 3.50/0.91 % (475051)------------------------------
% 3.50/0.91 % (475051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.91 % (475051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.91 % (475051)CaDiCaL version: 2.1.3
% 3.50/0.91 % (475051)Termination reason: Instruction limit
% 3.50/0.91 % (475051)Termination phase: Saturation
% 3.50/0.91 % (475051)Time elapsed: 0.007 s
% 3.50/0.91 % (475051)Peak memory usage: 12 MB
% 3.50/0.91 % (475051)Instructions burned: 7 (million)
% 3.50/0.91 % (475029)Instruction limit reached!
% 3.50/0.91 % (475029)------------------------------
% 3.50/0.91 % (475029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.91 % (475029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.91 % (475029)CaDiCaL version: 2.1.3
% 3.50/0.91 % (475029)Termination reason: Instruction limit
% 3.50/0.91 % (475029)Termination phase: Saturation
% 3.50/0.91 % (475029)Time elapsed: 0.134 s
% 3.50/0.91 % (475029)Peak memory usage: 14 MB
% 3.50/0.91 % (475029)Instructions burned: 327 (million)
% 3.50/0.91 % (475053)Instruction limit reached!
% 3.50/0.91 % (475053)------------------------------
% 3.50/0.91 % (475053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.91 % (475053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.91 % (475053)CaDiCaL version: 2.1.3
% 3.50/0.91 % (475053)Termination reason: Instruction limit
% 3.50/0.91 % (475053)Termination phase: Saturation
% 3.50/0.91 % (475053)Time elapsed: 0.011 s
% 3.50/0.91 % (475053)Peak memory usage: 12 MB
% 3.50/0.91 % (475053)Instructions burned: 20 (million)
% 3.50/0.91 % (475061)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2364184978:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 3.50/0.91 % (475062)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.50/0.91 % (475062)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1149617763:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.50/0.91 % (475059)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3554729286:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 3.50/0.91 % (475060)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3663150672:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 3.50/0.91 % (475058)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1738271629:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 3.50/0.91 % (475062)Instruction limit reached!
% 3.50/0.91 % (475062)------------------------------
% 3.50/0.91 % (475062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.91 % (475062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.91 % (475062)CaDiCaL version: 2.1.3
% 3.50/0.91 % (475062)Termination reason: Instruction limit
% 3.50/0.91 % (475062)Termination phase: Saturation
% 3.50/0.91 % (475062)Time elapsed: 0.004 s
% 3.50/0.91 % (475062)Peak memory usage: 12 MB
% 3.50/0.91 % (475062)Instructions burned: 7 (million)
% 3.50/0.91 % (475061)Instruction limit reached!
% 3.50/0.91 % (475061)------------------------------
% 3.50/0.91 % (475061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/0.91 % (475061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/0.91 % (475061)CaDiCaL version: 2.1.3
% 3.50/0.91 % (475061)Termination reason: Instruction limit
% 3.50/0.91 % (475061)Termination phase: Saturation
% 3.50/0.91 % (475061)Time elapsed: 0.018 s
% 3.50/0.91 % (475061)Peak memory usage: 12 MB
% 3.50/0.91 % (475061)Instructions burned: 43 (million)
% 3.50/0.91 % (475069)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1388044089:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.50/0.91 % (475026)Instruction limit reached!
% 3.50/1.00 % (475026)------------------------------
% 3.50/1.00 % (475026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475026)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475026)Termination reason: Instruction limit
% 3.50/1.00 % (475026)Termination phase: Saturation
% 3.50/1.00 % (475026)Time elapsed: 0.191 s
% 3.50/1.00 % (475026)Peak memory usage: 14 MB
% 3.50/1.00 % (475026)Instructions burned: 250 (million)
% 3.50/1.00 % (475068)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3365030542:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.50/1.00 % (475071)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.50/1.00 % (475071)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3948328018:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.50/1.00 % (475071)Instruction limit reached!
% 3.50/1.00 % (475071)------------------------------
% 3.50/1.00 % (475071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475071)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475071)Termination reason: Instruction limit
% 3.50/1.00 % (475071)Termination phase: Saturation
% 3.50/1.00 % (475071)Time elapsed: 0.006 s
% 3.50/1.00 % (475071)Peak memory usage: 11 MB
% 3.50/1.00 % (475071)Instructions burned: 6 (million)
% 3.50/1.00 % (475074)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4105788776:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.50/1.00 % (475074)Refutation not found, incomplete strategy
% 3.50/1.00 % (475074)------------------------------
% 3.50/1.00 % (475074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475074)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475074)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.00 % (475074)Time elapsed: 0.004 s
% 3.50/1.00 % (475074)Peak memory usage: 12 MB
% 3.50/1.00 % (475074)Instructions burned: 8 (million)
% 3.50/1.00 % (475074)------------------------------
% 3.50/1.00 % (475074)------------------------------
% 3.50/1.00 % (475069)Instruction limit reached!
% 3.50/1.00 % (475069)------------------------------
% 3.50/1.00 % (475069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475069)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475069)Termination reason: Instruction limit
% 3.50/1.00 % (475069)Termination phase: Saturation
% 3.50/1.00 % (475069)Time elapsed: 0.077 s
% 3.50/1.00 % (475069)Peak memory usage: 13 MB
% 3.50/1.00 % (475069)Instructions burned: 171 (million)
% 3.50/1.00 % (475059)Instruction limit reached!
% 3.50/1.00 % (475059)------------------------------
% 3.50/1.00 % (475059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475059)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475059)Termination reason: Instruction limit
% 3.50/1.00 % (475059)Termination phase: Saturation
% 3.50/1.00 % (475059)Time elapsed: 0.116 s
% 3.50/1.00 % (475059)Peak memory usage: 13 MB
% 3.50/1.00 % (475059)Instructions burned: 144 (million)
% 3.50/1.00 % (475077)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1715245673:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 3.50/1.00 % (475076)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1132028191:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 3.50/1.00 % (475078)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2271191395:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 3.50/1.00 % (475076)Instruction limit reached!
% 3.50/1.00 % (475076)------------------------------
% 3.50/1.00 % (475076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475076)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475076)Termination reason: Instruction limit
% 3.50/1.00 % (475076)Termination phase: Saturation
% 3.50/1.00 % (475076)Time elapsed: 0.017 s
% 3.50/1.00 % (475076)Peak memory usage: 12 MB
% 3.50/1.00 % (475076)Instructions burned: 19 (million)
% 3.50/1.00 % (475060)Instruction limit reached!
% 3.50/1.00 % (475060)------------------------------
% 3.50/1.00 % (475060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475060)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475060)Termination reason: Instruction limit
% 3.50/1.00 % (475060)Termination phase: Saturation
% 3.50/1.00 % (475060)Time elapsed: 0.151 s
% 3.50/1.00 % (475060)Peak memory usage: 13 MB
% 3.50/1.00 % (475060)Instructions burned: 194 (million)
% 3.50/1.00 % (475082)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3129371295:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 3.50/1.00 % (475068)Instruction limit reached!
% 3.50/1.00 % (475068)------------------------------
% 3.50/1.00 % (475068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475068)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475068)Termination reason: Instruction limit
% 3.50/1.00 % (475068)Termination phase: Saturation
% 3.50/1.00 % (475068)Time elapsed: 0.146 s
% 3.50/1.00 % (475068)Peak memory usage: 14 MB
% 3.50/1.00 % (475068)Instructions burned: 182 (million)
% 3.50/1.00 % (475083)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=918342434:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 3.50/1.00 % (475085)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2822537440:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 3.50/1.00 % (474997)Instruction limit reached!
% 3.50/1.00 % (474997)------------------------------
% 3.50/1.00 % (474997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (474997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (474997)CaDiCaL version: 2.1.3
% 3.50/1.00 % (474997)Termination reason: Instruction limit
% 3.50/1.00 % (474997)Termination phase: Saturation
% 3.50/1.00 % (474997)Time elapsed: 0.507 s
% 3.50/1.00 % (474997)Peak memory usage: 16 MB
% 3.50/1.00 % (474997)Instructions burned: 634 (million)
% 3.50/1.00 % (475082)Instruction limit reached!
% 3.50/1.00 % (475082)------------------------------
% 3.50/1.00 % (475082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475082)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475082)Termination reason: Instruction limit
% 3.50/1.00 % (475082)Termination phase: Saturation
% 3.50/1.00 % (475082)Time elapsed: 0.038 s
% 3.50/1.00 % (475082)Peak memory usage: 12 MB
% 3.50/1.00 % (475082)Instructions burned: 46 (million)
% 3.50/1.00 % (475085)Instruction limit reached!
% 3.50/1.00 % (475085)------------------------------
% 3.50/1.00 % (475085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475085)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475085)Termination reason: Instruction limit
% 3.50/1.00 % (475085)Termination phase: Saturation
% 3.50/1.00 % (475085)Time elapsed: 0.019 s
% 3.50/1.00 % (475085)Peak memory usage: 12 MB
% 3.50/1.00 % (475085)Instructions burned: 22 (million)
% 3.50/1.00 % (475089)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.50/1.00 % (475089)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=219277149:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/200Mi)
% 3.50/1.00 % (475090)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=933355819:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2994 on theBenchmark for (2994ds/13Mi)
% 3.50/1.00 % (475090)Instruction limit reached!
% 3.50/1.00 % (475090)------------------------------
% 3.50/1.00 % (475090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475090)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475090)Termination reason: Instruction limit
% 3.50/1.00 % (475090)Termination phase: Saturation
% 3.50/1.00 % (475090)Time elapsed: 0.012 s
% 3.50/1.00 % (475090)Peak memory usage: 12 MB
% 3.50/1.00 % (475090)Instructions burned: 13 (million)
% 3.50/1.00 % (475091)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=272397856:i=66:s2at=3:nm=2:rtra=on:rawr=on_2994 on theBenchmark for (2994ds/66Mi)
% 3.50/1.00 % (475095)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=282562161:i=51:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/51Mi)
% 3.50/1.00 % (475077) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-474989-475077"...
% 3.50/1.00 % (475091)Instruction limit reached!
% 3.50/1.00 % (475091)------------------------------
% 3.50/1.00 % (475091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475091)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475091)Termination reason: Instruction limit
% 3.50/1.00 % (475091)Termination phase: Saturation
% 3.50/1.00 % (475091)Time elapsed: 0.054 s
% 3.50/1.00 % (475091)Peak memory usage: 13 MB
% 3.50/1.00 % (475091)Instructions burned: 66 (million)
% 3.50/1.00 % (475077)...printing done.
% 3.50/1.00 % (475089)Instruction limit reached!
% 3.50/1.00 % (475089)------------------------------
% 3.50/1.00 % (475089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.00 % (475089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.00 % (475089)CaDiCaL version: 2.1.3
% 3.50/1.00 % (475089)Termination reason: Instruction limit
% 3.50/1.00 % (475089)Termination phase: Saturation
% 3.50/1.00 % (475089)Time elapsed: 0.090 s
% 3.50/1.00 % (475089)Peak memory usage: 12 MB
% 3.50/1.00 % (475089)Instructions burned: 201 (million)
% 3.50/1.00 % (475077)Refutation found. Thanks to Tanya!
% 3.50/1.00 % SZS status Theorem for theBenchmark
% 3.50/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.01 % (475077)------------------------------
% 3.50/1.01 % (475077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.50/1.01 % (475077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.01 % (475077)CaDiCaL version: 2.1.3
% 3.50/1.01 % (475077)Termination reason: Refutation
% 3.50/1.01 % (475077)Time elapsed: 0.221 s
% 3.50/1.01 % (475077)Peak memory usage: 14 MB
% 3.50/1.01 % (475077)Instructions burned: 290 (million)
% 3.50/1.01 % (474989)Success in time 0.675 s
% 3.50/1.01 % Vampire exiting
%------------------------------------------------------------------------------