%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU909^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:31:55 AM UTC 2026
% Result : Theorem 2.59s 0.78s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 123 ( 15 unt; 0 typ; 8 def)
% Number of atoms : 1456 ( 195 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 3184 ( 171 ~; 281 |; 251 &;1684 @)
% ( 8 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 486 ( 486 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 67 usr; 43 con; 0-4 aty)
% ( 349 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 576 ( 67 sgn 68 !; 6 ?; 576 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cA: ( a > $o ) > $o ).
thf(func_def_2,type,
vNOT: $o > $o ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK1: a > $o ).
thf(func_def_19,type,
sK2: a > $o ).
thf(func_def_20,type,
sK3: a > $o ).
thf(func_def_21,type,
sK4: a > $o ).
thf(func_def_22,type,
sK5: a > a > $o ).
thf(func_def_23,type,
sK6: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_24,type,
sK7: a > $o ).
thf(func_def_25,type,
sK8: a ).
thf(func_def_26,type,
sK9: a ).
thf(func_def_27,type,
sK10: a ).
thf(func_def_28,type,
sK11: a ).
thf(func_def_29,type,
sK12: a ).
thf(func_def_30,type,
sK13: a ).
thf(func_def_31,type,
sK14: a ).
thf(func_def_32,type,
sK15: a ).
thf(func_def_33,type,
sK16: a ).
thf(func_def_34,type,
sK17: a ).
thf(func_def_35,type,
sK18: a ).
thf(func_def_36,type,
sK19: a ).
thf(func_def_37,type,
sK20: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_38,type,
sK21: ( a > $o ) > a > $o ).
thf(func_def_39,type,
sK22: a ).
thf(func_def_40,type,
sK23: a ).
thf(func_def_41,type,
sK24: a ).
thf(func_def_42,type,
sK25: a ).
thf(func_def_43,type,
sK26: a ).
thf(func_def_44,type,
sK27: a ).
thf(func_def_45,type,
sK28: a ).
thf(func_def_46,type,
sK29: a ).
thf(func_def_47,type,
sK30: a ).
thf(func_def_48,type,
sK31: a ).
thf(func_def_49,type,
sK32: a ).
thf(func_def_50,type,
sK33: a ).
thf(func_def_51,type,
sK34: ( ( a > $o ) > $o ) > a ).
thf(func_def_52,type,
sK35: a ).
thf(func_def_53,type,
sK36: a ).
thf(func_def_54,type,
sK37: a ).
thf(func_def_55,type,
sK38: a > $o ).
thf(func_def_56,type,
sK39: a ).
thf(func_def_57,type,
sK40: a ).
thf(func_def_58,type,
sK41: a ).
thf(func_def_59,type,
sK42: ( a > $o ) > a ).
thf(func_def_60,type,
sK43: a ).
thf(func_def_61,type,
sK44: ( a > $o ) > a ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X0: a] :
( ( X1 @ X0 )
=> ? [X6: a > $o] :
( ( cA @ X6 )
& ( X6 @ X0 ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X0: a > $o] :
( ( X2 @ X0 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) )
=> ( ! [X0: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) )
& ( cA @ X0 ) )
=> ? [X8: a > $o] :
( ! [X7: a] :
( ( X8 @ X7 )
=> ( X0 @ X7 ) )
& ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X7: a > $o] :
( ( X2 @ X7 )
=> ! [X4: a] :
( ( X8 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X7 @ X5 )
| ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X8 ) )
& ! [X3: a > $o] :
( ( ! [X7: a] :
( ( X8 @ X7 )
=> ( X3 @ X7 ) )
& ( cA @ X3 ) )
=> ( ! [X7: a] :
( ( X1 @ X7 )
=> ( X3 @ X7 ) )
& ( cA @ X3 ) ) ) ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ( cA @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMTHM8_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X0: a] :
( ( X1 @ X0 )
=> ? [X6: a > $o] :
( ( cA @ X6 )
& ( X6 @ X0 ) ) )
& ! [X2: ( a > $o ) > $o] :
( ( ! [X0: a > $o] :
( ( X2 @ X0 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X0 @ X5 )
| ( X4 = X5 ) ) ) ) )
& ( X2
@ ^ [X3: a] : $false ) )
=> ( X2 @ X1 ) ) )
=> ( ! [X0: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) )
& ( cA @ X0 ) )
=> ? [X8: a > $o] :
( ! [X7: a] :
( ( X8 @ X7 )
=> ( X0 @ X7 ) )
& ! [X2: ( a > $o ) > $o] :
( ( ( X2
@ ^ [X3: a] : $false )
& ! [X7: a > $o] :
( ( X2 @ X7 )
=> ! [X4: a] :
( ( X8 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ( X7 @ X5 )
| ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X8 ) )
& ! [X3: a > $o] :
( ( ! [X7: a] :
( ( X8 @ X7 )
=> ( X3 @ X7 ) )
& ( cA @ X3 ) )
=> ( ! [X7: a] :
( ( X1 @ X7 )
=> ( X3 @ X7 ) )
& ( cA @ X3 ) ) ) ) )
& ! [X0: a > $o] :
( ( ( cA @ X0 )
& ! [X7: a] :
( ( X1 @ X7 )
=> ( X0 @ X7 ) ) )
=> ( cA @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: a > $o] :
( ( cA @ X0 )
=> ( cA @ X0 ) )
& ! [X1: a > $o] :
( ( ! [X2: a] :
( ( X1 @ X2 )
=> ? [X3: a > $o] :
( ( cA @ X3 )
& ( X3 @ X2 ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ( X5 @ X7 )
| ( X6 = X7 ) ) ) ) )
& ( X4
@ ^ [X8: a] : $false ) )
=> ( X4 @ X1 ) ) )
=> ( ! [X9: a > $o] :
( ( ! [X10: a] :
( ( X1 @ X10 )
=> ( X9 @ X10 ) )
& ( cA @ X9 ) )
=> ? [X11: a > $o] :
( ! [X12: a] :
( ( X11 @ X12 )
=> ( X9 @ X12 ) )
& ! [X13: ( a > $o ) > $o] :
( ( ( X13
@ ^ [X14: a] : $false )
& ! [X15: a > $o] :
( ( X13 @ X15 )
=> ! [X16: a] :
( ( X11 @ X16 )
=> ( X13
@ ^ [X17: a] :
( ( X15 @ X17 )
| ( X16 = X17 ) ) ) ) ) )
=> ( X13 @ X11 ) )
& ! [X18: a > $o] :
( ( ! [X19: a] :
( ( X11 @ X19 )
=> ( X18 @ X19 ) )
& ( cA @ X18 ) )
=> ( ! [X20: a] :
( ( X1 @ X20 )
=> ( X18 @ X20 ) )
& ( cA @ X18 ) ) ) ) )
& ! [X21: a > $o] :
( ( ( cA @ X21 )
& ! [X22: a] :
( ( X1 @ X22 )
=> ( X21 @ X22 ) ) )
=> ( cA @ X21 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( cA @ Y0 )
=> ( cA @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( cA @ Y0 )
=> ( cA @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) ) ) ),
inference(boolean_simplification,[],[f5]) ).
thf(f9,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) ) ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f10,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f9]) ).
thf(f14,definition,
( spl0_1
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f18,definition,
( spl0_2
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f19,plain,
( ( $false
!= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f18,f14]) ).
thf(f22,plain,
( ( $false
= ( ^ [Y0: a > $o] : $true
@ sK1 ) )
| ~ spl0_2 ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f24]) ).
thf(f28,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( Y1
@ ^ [Y2: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( cA @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( cA @ Y1 ) )
=> ( cA @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( ( cA @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y3: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 )
=> ( Y3
@ ^ [Y6: a] :
( ( Y5 = Y6 )
| ( Y4 @ Y6 ) ) ) ) ) ) )
& ( Y3
@ ^ [Y4: a] : $false ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f29,plain,
( ( $false
= ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( cA @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( cA @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f33,plain,
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true )
| ~ spl0_1 ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f36,definition,
( spl0_3
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl0_4
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f42,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f34,f14,f40,f36]) ).
thf(f46,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( cA @ Y0 ) )
=> ( cA @ Y0 ) )
@ sK3 ) )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f42]) ).
thf(f47,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( cA @ sK3 ) )
=> ( cA @ sK3 ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f49,plain,
( ( $false
= ( cA @ sK3 ) )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f51,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& $false )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[],[f47,f49]) ).
thf(f52,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& $false ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f51]) ).
thf(f53,plain,
( ( ( ~ $false ) = $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f52]) ).
thf(f54,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f53]) ).
thf(f55,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f55]) ).
thf(f60,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( ( cA @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y2
@ ^ [Y5: a] :
( ( Y4 = Y5 )
| ( Y3 @ Y5 ) ) ) ) ) ) )
& ( Y2
@ ^ [Y3: a] : $false ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
@ sK4 ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f61,plain,
( ( ( ( ( cA @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: a] : $false ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ^ [Y0: ( a > $o ) > $o] :
( ( ( Y0
@ ^ [Y1: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
=> ( Y0 @ sK2 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f63,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( ( X1
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
=> ( X1 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: a] : $false ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f65,plain,
( ( ( ( cA @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f66,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f77,plain,
( ! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( ( cA @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1
@ ^ [Y4: a] :
( ( Y3 = Y4 )
| ( Y2 @ Y4 ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: a] : $false ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f78,plain,
( ! [X1: a > $o] :
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ X1 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f80,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ X1 )
=> ( sK4 @ X1 ) ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
( ! [X1: a > $o] :
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ X1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f1078,plain,
( ! [X1: a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ X1 ) ) ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f1083,plain,
( ! [X1: a > $o] :
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( X1 @ Y2 )
=> ( Y0
@ ^ [Y3: a] :
( ( Y2 = Y3 )
| ( Y1 @ Y3 ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: a] : $false ) )
=> ( Y0 @ X1 ) )
@ ( sK20 @ X1 ) ) ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f1078]) ).
thf(f1084,plain,
( ! [X1: a > $o] :
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( sK20 @ X1
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ X1
@ ^ [Y0: a] : $false ) )
=> ( sK20 @ X1 @ X1 ) ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f1083]) ).
thf(f2275,plain,
( ! [X1: a > $o] :
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f1084]) ).
thf(f2514,plain,
( ! [X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
@ ( sK21 @ X1 ) ) ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f2275]) ).
thf(f2519,plain,
( ( ( ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
=> $false )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f63,f2275]) ).
thf(f2528,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f2519]) ).
thf(f2529,plain,
( ( ( ~ ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f2528]) ).
thf(f2532,plain,
( ! [X1: a > $o] :
( ( $false
= ( ( ( cA @ ( sK21 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK21 @ X1 @ Y0 ) ) ) )
=> ( ( cA @ ( sK21 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK21 @ X1 @ Y0 ) ) ) ) ) )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f2514]) ).
thf(f2541,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2529,f19]) ).
thf(f2551,plain,
( ( ( ~ ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false = $true )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f2541,f66]) ).
thf(f2552,plain,
( ( ( ~ ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f2551]) ).
thf(f2565,plain,
( ( $false
= ( ( sK20 @ sK2
@ ^ [Y0: a] : $false )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f2552]) ).
thf(f2575,plain,
( ( $false
= ( sK20 @ sK2
@ ^ [Y0: a] : $false ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f2565]) ).
thf(f2577,definition,
( spl0_46
<=> ( $false
= ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
thf(f2579,plain,
( ( $false
= ( sK20 @ sK2
@ ^ [Y0: a] : $false ) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f2577]) ).
thf(f2581,definition,
( spl0_47
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
thf(f2583,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f2581]) ).
thf(f2584,plain,
( spl0_46
| spl0_47
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f2575,f36,f18,f14,f2581,f2577]) ).
thf(f2681,plain,
( ! [X1: a > $o] :
( ( ( ( cA @ ( sK21 @ X1 ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK21 @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f2532]) ).
thf(f3007,plain,
( ! [X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( ( cA @ ( sK21 @ X1 ) )
= $true ) )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f2681]) ).
thf(f3119,plain,
( ! [X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) )
@ ( sK44 @ X1 ) )
= $false )
| ( ( cA @ ( sK21 @ X1 ) )
= $true )
| ( $false
= ( sK20 @ X1 @ X1 ) ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f3007]) ).
thf(f3135,plain,
( ! [X1: a > $o] :
( ( ( ( X1 @ ( sK44 @ X1 ) )
=> ( sK4 @ ( sK44 @ X1 ) ) )
= $false )
| ( $false
= ( sK20 @ X1 @ X1 ) )
| ( ( cA @ ( sK21 @ X1 ) )
= $true ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f3119]) ).
thf(f3164,plain,
( ( ( sK20 @ sK2 @ sK2 )
= $false )
| ( $false = $true )
| ( ( cA @ ( sK21 @ sK2 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[],[f3135,f80]) ).
thf(f3169,plain,
( ( ( cA @ ( sK21 @ sK2 ) )
= $true )
| ( ( sK20 @ sK2 @ sK2 )
= $false )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f3164]) ).
thf(f3177,definition,
( spl0_54
<=> ( ( sK20 @ sK2 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
thf(f3178,plain,
( ( ( sK20 @ sK2 @ sK2 )
!= $false )
| spl0_54 ),
inference(avatar_component_clause,[],[f3177]) ).
thf(f3179,plain,
( ( ( sK20 @ sK2 @ sK2 )
= $false )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3177]) ).
thf(f3181,definition,
( spl0_55
<=> ( ( cA @ ( sK21 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_55])],[avatar_definition]) ).
thf(f3183,plain,
( ( ( cA @ ( sK21 @ sK2 ) )
= $true )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f3181]) ).
thf(f3186,plain,
( spl0_55
| spl0_54
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f3169,f36,f3177,f3181]) ).
thf(f3201,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) )
=> $false ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_54 ),
inference(superposition,[],[f1084,f3179]) ).
thf(f3203,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) )
= $false )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( cA @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3201]) ).
thf(f3204,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] : $true ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) )
= $false )
| ~ spl0_3
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3203]) ).
thf(f3205,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) )
= $false )
| spl0_2
| ~ spl0_3
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f3204,f19]) ).
thf(f3206,plain,
( ( $false = $true )
| ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) )
= $false )
| spl0_2
| ~ spl0_3
| ~ spl0_54 ),
inference(forward_demodulation,[],[f3205,f66]) ).
thf(f3207,plain,
( ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) )
= $false )
| spl0_2
| ~ spl0_3
| ~ spl0_54 ),
inference(trivial_inequality_removal,[],[f3206]) ).
thf(f3208,plain,
( ( $false
= ( ~ ( $false
& ( sK20 @ sK2
@ ^ [Y0: a] : $false ) ) ) )
| spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(forward_demodulation,[],[f3207,f2583]) ).
thf(f3209,plain,
( ( ( ~ $false ) = $false )
| spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3208]) ).
thf(f3210,plain,
( ( $false = $true )
| spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3209]) ).
thf(f3211,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(trivial_inequality_removal,[],[f3210]) ).
thf(f3212,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f3211]) ).
thf(f3213,plain,
( ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK20 @ sK2 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK20 @ sK2
@ ^ [Y2: a] :
( ( Y1 = Y2 )
| ( Y0 @ Y2 ) ) ) ) ) ) )
& $false ) )
= $false )
| spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(forward_demodulation,[],[f3207,f2579]) ).
thf(f3214,plain,
( ( ( ~ $false ) = $false )
| spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3213]) ).
thf(f3215,plain,
( ( $false = $true )
| spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(boolean_simplification,[],[f3214]) ).
thf(f3216,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(trivial_inequality_removal,[],[f3215]) ).
thf(f3217,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f3216]) ).
thf(f3273,plain,
( ( ( sK20 @ sK2 @ sK2 )
= $false )
| ( $false
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK21 @ sK2 @ Y0 ) ) ) )
=> ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK21 @ sK2 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_55 ),
inference(superposition,[],[f2532,f3183]) ).
thf(f3275,plain,
( ( ( sK20 @ sK2 @ sK2 )
= $false )
| ( $false = $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_55 ),
inference(boolean_simplification,[],[f3273]) ).
thf(f3276,plain,
( ( ( sK20 @ sK2 @ sK2 )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f3275]) ).
thf(f3284,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(forward_subsumption_resolution,[],[f3276,f3178]) ).
thf(f3379,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) )
@ sK22 ) )
| ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(sigma_proxy_clausification,[],[f3284]) ).
thf(f3380,plain,
( ( ( ( sK2 @ sK22 )
=> ( sK4 @ sK22 ) )
= $false )
| ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(beta-eta_normalization,[],[f3379]) ).
thf(f3381,plain,
( ( $false = $true )
| ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(forward_demodulation,[],[f3380,f80]) ).
thf(f3382,plain,
( $false
| ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f3381]) ).
thf(f3383,plain,
( ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f3382]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
~ spl0_4,
inference(sat_conversion,[],[f56]) ).
cnf(s84,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_46
| spl0_47 ),
inference(sat_conversion,[],[f2584]) ).
cnf(s91,plain,
( ~ spl0_3
| spl0_54
| spl0_55 ),
inference(sat_conversion,[],[f3186]) ).
cnf(s94,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_47
| ~ spl0_54 ),
inference(sat_conversion,[],[f3212]) ).
cnf(s95,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_46
| ~ spl0_54 ),
inference(sat_conversion,[],[f3217]) ).
cnf(s105,plain,
( ~ spl0_3
| spl0_54
| ~ spl0_55 ),
inference(sat_conversion,[],[f3383]) ).
cnf(s107,plain,
( ~ spl0_1
| spl0_3 ),
inference(rat,[],[s3,s4]) ).
cnf(s108,plain,
spl0_1,
inference(rat,[],[s1,s2]) ).
cnf(s109,plain,
spl0_3,
inference(rat,[],[s107,s108]) ).
cnf(s116,plain,
spl0_54,
inference(rat,[],[s91,s105,s109]) ).
cnf(s117,plain,
~ spl0_46,
inference(rat,[],[s95,s109,s2,s116]) ).
cnf(s118,plain,
~ spl0_47,
inference(rat,[],[s94,s109,s2,s116]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s84,s109,s108,s2,s118,s117]) ).
thf(f3384,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU909^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:40:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (427271)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.38 % (427276)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3986132640:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.38 % (427279)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=1872234721: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)
% 0.21/0.38 % (427277)lrs+10_16_si=on:nwc=1.5:random_seed=2011981561:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (427278)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2880289939:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (427278)Instruction limit reached!
% 0.21/0.38 % (427278)------------------------------
% 0.21/0.38 % (427278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (427278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (427278)CaDiCaL version: 2.1.3
% 0.21/0.38 % (427278)Termination reason: Instruction limit
% 0.21/0.38 % (427278)Termination phase: Saturation
% 0.21/0.38 % (427278)Time elapsed: 0.002 s
% 0.21/0.38 % (427278)Peak memory usage: 11 MB
% 0.21/0.38 % (427278)Instructions burned: 3 (million)
% 0.21/0.38 % (427277)Instruction limit reached!
% 0.21/0.38 % (427277)------------------------------
% 0.21/0.38 % (427277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (427277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (427277)CaDiCaL version: 2.1.3
% 0.21/0.38 % (427277)Termination reason: Instruction limit
% 0.21/0.38 % (427277)Termination phase: Saturation
% 0.21/0.38 % (427277)Time elapsed: 0.011 s
% 0.21/0.38 % (427277)Peak memory usage: 12 MB
% 0.21/0.38 % (427277)Instructions burned: 18 (million)
% 0.21/0.38 % (427282)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.38 % (427282)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
% 0.21/0.38 % (427281)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1479532536:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.38 % (427280)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1721021942:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.38 % (427282)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=526849841:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.38 % (427287)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2225470345:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (427276)Instruction limit reached!
% 0.21/0.38 % (427276)------------------------------
% 0.21/0.38 % (427276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (427276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (427276)CaDiCaL version: 2.1.3
% 0.21/0.38 % (427276)Termination reason: Instruction limit
% 0.21/0.38 % (427276)Termination phase: Saturation
% 0.21/0.38 % (427276)Time elapsed: 0.030 s
% 0.21/0.38 % (427276)Peak memory usage: 13 MB
% 0.21/0.38 % (427276)Instructions burned: 89 (million)
% 0.21/0.38 % (427287)Instruction limit reached!
% 0.21/0.38 % (427287)------------------------------
% 0.21/0.38 % (427287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (427287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (427287)CaDiCaL version: 2.1.3
% 0.21/0.38 % (427287)Termination reason: Instruction limit
% 0.21/0.38 % (427287)Termination phase: Saturation
% 0.21/0.38 % (427287)Time elapsed: 0.002 s
% 0.21/0.38 % (427287)Peak memory usage: 11 MB
% 0.21/0.38 % (427287)Instructions burned: 3 (million)
% 0.21/0.38 % (427288)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2179253013:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.38 % (427293)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.42 % (427293)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4209422338:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.85/0.42 % (427288)Instruction limit reached!
% 0.85/0.42 % (427288)------------------------------
% 0.85/0.42 % (427288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.42 % (427288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.42 % (427288)CaDiCaL version: 2.1.3
% 0.85/0.42 % (427288)Termination reason: Instruction limit
% 0.85/0.42 % (427288)Termination phase: Saturation
% 0.85/0.42 % (427288)Time elapsed: 0.003 s
% 0.85/0.42 % (427288)Peak memory usage: 11 MB
% 0.85/0.42 % (427288)Instructions burned: 5 (million)
% 0.85/0.42 % (427293)Instruction limit reached!
% 0.85/0.42 % (427293)------------------------------
% 0.85/0.42 % (427293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.42 % (427293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.42 % (427293)CaDiCaL version: 2.1.3
% 0.85/0.42 % (427293)Termination reason: Instruction limit
% 0.85/0.42 % (427293)Termination phase: Saturation
% 0.85/0.42 % (427293)Time elapsed: 0.002 s
% 0.85/0.42 % (427293)Peak memory usage: 12 MB
% 0.85/0.42 % (427293)Instructions burned: 7 (million)
% 0.85/0.42 % (427294)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1908314625:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.85/0.42 % (427298)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=3182665839:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.85/0.42 % (427280)Instruction limit reached!
% 0.85/0.42 % (427280)------------------------------
% 0.85/0.42 % (427280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.42 % (427280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.42 % (427297)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
% 0.85/0.42 % (427280)CaDiCaL version: 2.1.3
% 0.85/0.42 % (427280)Termination reason: Instruction limit
% 0.85/0.42 % (427280)Termination phase: Saturation
% 0.85/0.42 % (427280)Time elapsed: 0.031 s
% 0.85/0.42 % (427280)Peak memory usage: 12 MB
% 0.85/0.42 % (427280)Instructions burned: 25 (million)
% 0.85/0.42 % (427297)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.42 % (427294)Instruction limit reached!
% 0.85/0.42 % (427294)------------------------------
% 0.85/0.42 % (427294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.42 % (427294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.42 % (427294)CaDiCaL version: 2.1.3
% 0.85/0.42 % (427294)Termination reason: Instruction limit
% 0.85/0.42 % (427294)Termination phase: Saturation
% 0.85/0.42 % (427294)Time elapsed: 0.007 s
% 0.85/0.42 % (427294)Peak memory usage: 12 MB
% 0.85/0.42 % (427294)Instructions burned: 12 (million)
% 0.85/0.42 % (427297)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3862761622:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.85/0.42 % (427297)Instruction limit reached!
% 0.85/0.42 % (427297)------------------------------
% 0.85/0.42 % (427297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.42 % (427297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.42 % (427297)CaDiCaL version: 2.1.3
% 0.85/0.42 % (427297)Termination reason: Instruction limit
% 0.85/0.42 % (427297)Termination phase: Saturation
% 0.85/0.42 % (427297)Time elapsed: 0.013 s
% 0.85/0.42 % (427297)Peak memory usage: 11 MB
% 0.85/0.42 % (427297)Instructions burned: 28 (million)
% 0.85/0.42 % (427301)lrs+10_1_si=on:cs=on:random_seed=1755516408:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.85/0.42 % (427298)Instruction limit reached!
% 0.85/0.42 % (427298)------------------------------
% 0.85/0.42 % (427298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427298)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427298)Termination reason: Instruction limit
% 0.85/0.46 % (427298)Termination phase: Saturation
% 0.85/0.46 % (427298)Time elapsed: 0.024 s
% 0.85/0.46 % (427298)Peak memory usage: 12 MB
% 0.85/0.46 % (427298)Instructions burned: 87 (million)
% 0.85/0.46 % (427301)Instruction limit reached!
% 0.85/0.46 % (427301)------------------------------
% 0.85/0.46 % (427301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427301)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427301)Termination reason: Instruction limit
% 0.85/0.46 % (427301)Termination phase: Saturation
% 0.85/0.46 % (427301)Time elapsed: 0.005 s
% 0.85/0.46 % (427301)Peak memory usage: 12 MB
% 0.85/0.46 % (427301)Instructions burned: 9 (million)
% 0.85/0.46 % (427306)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4112536769:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.85/0.46 % (427303)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.85/0.46 % (427306)Refutation not found, incomplete strategy
% 0.85/0.46 % (427306)------------------------------
% 0.85/0.46 % (427306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427306)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427306)Termination reason: Refutation not found, incomplete strategy
% 0.85/0.46 % (427306)Time elapsed: 0.001 s
% 0.85/0.46 % (427306)Peak memory usage: 12 MB
% 0.85/0.46 % (427306)Instructions burned: 5 (million)
% 0.85/0.46 % (427306)------------------------------
% 0.85/0.46 % (427306)------------------------------
% 0.85/0.46 % (427304)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3198955376:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.85/0.46 % (427281)Instruction limit reached!
% 0.85/0.46 % (427281)------------------------------
% 0.85/0.46 % (427281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427281)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427281)Termination reason: Instruction limit
% 0.85/0.46 % (427281)Termination phase: Saturation
% 0.85/0.46 % (427281)Time elapsed: 0.071 s
% 0.85/0.46 % (427281)Peak memory usage: 13 MB
% 0.85/0.46 % (427281)Instructions burned: 75 (million)
% 0.85/0.46 % (427303)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=2863035752:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.85/0.46 % (427307)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3070554321:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.85/0.46 % (427309)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=345346403:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.85/0.46 % (427303)Instruction limit reached!
% 0.85/0.46 % (427303)------------------------------
% 0.85/0.46 % (427303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427303)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427303)Termination reason: Instruction limit
% 0.85/0.46 % (427303)Termination phase: Saturation
% 0.85/0.46 % (427303)Time elapsed: 0.006 s
% 0.85/0.46 % (427303)Peak memory usage: 11 MB
% 0.85/0.46 % (427303)Instructions burned: 3 (million)
% 0.85/0.46 % (427309)Instruction limit reached!
% 0.85/0.46 % (427309)------------------------------
% 0.85/0.46 % (427309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.46 % (427309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.46 % (427309)CaDiCaL version: 2.1.3
% 0.85/0.46 % (427309)Termination reason: Instruction limit
% 0.85/0.46 % (427309)Termination phase: Saturation
% 0.85/0.46 % (427309)Time elapsed: 0.005 s
% 0.85/0.46 % (427309)Peak memory usage: 12 MB
% 0.85/0.46 % (427309)Instructions burned: 16 (million)
% 1.61/0.53 % (427316)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2173506613: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)
% 1.61/0.53 % (427307)Instruction limit reached!
% 1.61/0.53 % (427307)------------------------------
% 1.61/0.53 % (427307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.53 % (427307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.53 % (427307)CaDiCaL version: 2.1.3
% 1.61/0.53 % (427307)Termination reason: Instruction limit
% 1.61/0.53 % (427307)Termination phase: Saturation
% 1.61/0.53 % (427307)Time elapsed: 0.015 s
% 1.61/0.53 % (427307)Peak memory usage: 12 MB
% 1.61/0.53 % (427307)Instructions burned: 27 (million)
% 1.61/0.53 % (427316)Instruction limit reached!
% 1.61/0.53 % (427316)------------------------------
% 1.61/0.53 % (427316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.53 % (427316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.53 % (427316)CaDiCaL version: 2.1.3
% 1.61/0.53 % (427316)Termination reason: Instruction limit
% 1.61/0.53 % (427316)Termination phase: Twee Goal Transformation
% 1.61/0.53 % (427316)Time elapsed: 0.001 s
% 1.61/0.53 % (427316)Peak memory usage: 10 MB
% 1.61/0.53 % (427316)Instructions burned: 3 (million)
% 1.61/0.53 % (427304)Instruction limit reached!
% 1.61/0.53 % (427304)------------------------------
% 1.61/0.53 % (427304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.53 % (427304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.53 % (427304)CaDiCaL version: 2.1.3
% 1.61/0.53 % (427304)Termination reason: Instruction limit
% 1.61/0.53 % (427304)Termination phase: Saturation
% 1.61/0.53 % (427304)Time elapsed: 0.031 s
% 1.61/0.53 % (427304)Peak memory usage: 12 MB
% 1.61/0.53 % (427304)Instructions burned: 38 (million)
% 1.61/0.53 % (427319)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1883557187:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.61/0.53 % (427311)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2778502442:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.61/0.53 % (427315)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3847234301:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.61/0.53 % (427319)Instruction limit reached!
% 1.61/0.53 % (427319)------------------------------
% 1.61/0.53 % (427319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.53 % (427319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.53 % (427319)CaDiCaL version: 2.1.3
% 1.61/0.53 % (427319)Termination reason: Instruction limit
% 1.61/0.53 % (427319)Termination phase: Saturation
% 1.61/0.53 % (427319)Time elapsed: 0.007 s
% 1.61/0.53 % (427319)Peak memory usage: 11 MB
% 1.61/0.53 % (427319)Instructions burned: 27 (million)
% 1.61/0.53 % (427318)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3695102712:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.61/0.53 % (427324)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
% 1.61/0.54 % (427324)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.61/0.54 % (427315)Instruction limit reached!
% 1.61/0.54 % (427315)------------------------------
% 1.61/0.54 % (427315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.54 % (427315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.54 % (427315)CaDiCaL version: 2.1.3
% 1.61/0.54 % (427315)Termination reason: Instruction limit
% 1.61/0.54 % (427315)Termination phase: Saturation
% 1.61/0.54 % (427315)Time elapsed: 0.009 s
% 1.61/0.54 % (427315)Peak memory usage: 12 MB
% 1.61/0.54 % (427315)Instructions burned: 16 (million)
% 1.61/0.54 % (427324)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=3639444993:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.61/0.54 % (427321)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3618480384:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.61/0.60 % (427318)Instruction limit reached!
% 1.61/0.60 % (427318)------------------------------
% 1.61/0.60 % (427318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.60 % (427324)Instruction limit reached!
% 1.61/0.60 % (427324)------------------------------
% 1.61/0.60 % (427324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.60 % (427318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.60 % (427324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.60 % (427318)CaDiCaL version: 2.1.3
% 1.61/0.60 % (427324)CaDiCaL version: 2.1.3
% 1.61/0.60 % (427318)Termination reason: Instruction limit
% 1.61/0.60 % (427318)Termination phase: Saturation
% 1.61/0.60 % (427324)Termination reason: Instruction limit
% 1.61/0.60 % (427324)Termination phase: Saturation
% 1.61/0.60 % (427318)Time elapsed: 0.014 s
% 1.61/0.60 % (427324)Time elapsed: 0.004 s
% 1.61/0.60 % (427318)Peak memory usage: 12 MB
% 1.61/0.60 % (427324)Peak memory usage: 12 MB
% 2.02/0.60 % (427318)Instructions burned: 27 (million)
% 2.02/0.60 % (427324)Instructions burned: 14 (million)
% 2.02/0.60 % (427327)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.02/0.60 % (427329)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=2484224250:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.02/0.60 % (427327)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=965130476:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.02/0.60 % (427282)Instruction limit reached!
% 2.02/0.60 % (427282)------------------------------
% 2.02/0.60 % (427282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.60 % (427282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.60 % (427282)CaDiCaL version: 2.1.3
% 2.02/0.60 % (427282)Termination reason: Instruction limit
% 2.02/0.60 % (427282)Termination phase: Saturation
% 2.02/0.60 % (427282)Time elapsed: 0.138 s
% 2.02/0.60 % (427282)Peak memory usage: 13 MB
% 2.02/0.60 % (427282)Instructions burned: 158 (million)
% 2.02/0.60 % (427330)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1651376279:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.02/0.60 % (427329)Instruction limit reached!
% 2.02/0.60 % (427329)------------------------------
% 2.02/0.60 % (427329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.60 % (427329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.60 % (427329)CaDiCaL version: 2.1.3
% 2.02/0.60 % (427329)Termination reason: Instruction limit
% 2.02/0.60 % (427329)Termination phase: Saturation
% 2.02/0.60 % (427329)Time elapsed: 0.008 s
% 2.02/0.60 % (427329)Peak memory usage: 12 MB
% 2.02/0.60 % (427329)Instructions burned: 34 (million)
% 2.02/0.60 % (427327)Instruction limit reached!
% 2.02/0.60 % (427327)------------------------------
% 2.02/0.60 % (427327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.60 % (427327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.60 % (427327)CaDiCaL version: 2.1.3
% 2.02/0.60 % (427327)Termination reason: Instruction limit
% 2.02/0.60 % (427327)Termination phase: Saturation
% 2.02/0.60 % (427327)Time elapsed: 0.005 s
% 2.02/0.60 % (427327)Peak memory usage: 12 MB
% 2.02/0.60 % (427327)Instructions burned: 8 (million)
% 2.02/0.60 % (427330)Instruction limit reached!
% 2.02/0.60 % (427330)------------------------------
% 2.02/0.60 % (427330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.60 % (427330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.60 % (427330)CaDiCaL version: 2.1.3
% 2.02/0.60 % (427330)Termination reason: Instruction limit
% 2.02/0.60 % (427330)Termination phase: Saturation
% 2.02/0.60 % (427330)Time elapsed: 0.004 s
% 2.02/0.60 % (427330)Peak memory usage: 12 MB
% 2.02/0.60 % (427330)Instructions burned: 7 (million)
% 2.02/0.60 % (427335)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=125030219:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.02/0.60 % (427335)Instruction limit reached!
% 2.37/0.66 % (427335)------------------------------
% 2.37/0.66 % (427335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.66 % (427335)CaDiCaL version: 2.1.3
% 2.37/0.66 % (427335)Termination reason: Instruction limit
% 2.37/0.66 % (427335)Termination phase: Saturation
% 2.37/0.66 % (427335)Time elapsed: 0.007 s
% 2.37/0.66 % (427335)Peak memory usage: 12 MB
% 2.37/0.66 % (427335)Instructions burned: 23 (million)
% 2.37/0.66 % (427336)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3649224945:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.37/0.66 % (427339)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1490204378:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.37/0.66 % (427321)Instruction limit reached!
% 2.37/0.66 % (427321)------------------------------
% 2.37/0.66 % (427321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.66 % (427321)CaDiCaL version: 2.1.3
% 2.37/0.66 % (427321)Termination reason: Instruction limit
% 2.37/0.66 % (427321)Termination phase: Saturation
% 2.37/0.66 % (427321)Time elapsed: 0.051 s
% 2.37/0.66 % (427321)Peak memory usage: 12 MB
% 2.37/0.66 % (427321)Instructions burned: 60 (million)
% 2.37/0.66 % (427333)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2369701141:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.37/0.66 % (427333)Instruction limit reached!
% 2.37/0.66 % (427333)------------------------------
% 2.37/0.66 % (427333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.66 % (427333)CaDiCaL version: 2.1.3
% 2.37/0.66 % (427333)Termination reason: Instruction limit
% 2.37/0.66 % (427333)Termination phase: Saturation
% 2.37/0.66 % (427333)Time elapsed: 0.010 s
% 2.37/0.66 % (427333)Peak memory usage: 11 MB
% 2.37/0.66 % (427333)Instructions burned: 24 (million)
% 2.37/0.66 % (427337)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2702327728:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.37/0.66 % (427344)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.37/0.66 % (427344)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3413314703:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.37/0.66 % (427342)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3048306399:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.37/0.66 % (427344)Instruction limit reached!
% 2.37/0.66 % (427344)------------------------------
% 2.37/0.66 % (427344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.66 % (427344)CaDiCaL version: 2.1.3
% 2.37/0.66 % (427344)Termination reason: Instruction limit
% 2.37/0.66 % (427344)Termination phase: Saturation
% 2.37/0.66 % (427344)Time elapsed: 0.005 s
% 2.37/0.66 % (427344)Peak memory usage: 12 MB
% 2.37/0.66 % (427344)Instructions burned: 8 (million)
% 2.37/0.66 % (427339)Instruction limit reached!
% 2.37/0.66 % (427339)------------------------------
% 2.37/0.66 % (427339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.66 % (427339)CaDiCaL version: 2.1.3
% 2.37/0.66 % (427339)Termination reason: Instruction limit
% 2.37/0.66 % (427339)Termination phase: Saturation
% 2.37/0.66 % (427339)Time elapsed: 0.054 s
% 2.37/0.66 % (427339)Peak memory usage: 13 MB
% 2.37/0.66 % (427339)Instructions burned: 194 (million)
% 2.37/0.66 % (427348)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2346435580:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.37/0.66 % (427342)Instruction limit reached!
% 2.37/0.66 % (427342)------------------------------
% 2.37/0.66 % (427342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.37/0.66 % (427342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427342)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427342)Termination reason: Instruction limit
% 2.59/0.74 % (427342)Termination phase: Saturation
% 2.59/0.74 % (427342)Time elapsed: 0.024 s
% 2.59/0.74 % (427342)Peak memory usage: 12 MB
% 2.59/0.74 % (427342)Instructions burned: 44 (million)
% 2.59/0.74 % (427349)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=4034158829:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.59/0.74 % (427351)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.59/0.74 % (427351)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=110343170:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.59/0.74 % (427351)Instruction limit reached!
% 2.59/0.74 % (427351)------------------------------
% 2.59/0.74 % (427351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427351)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427351)Termination reason: Instruction limit
% 2.59/0.74 % (427351)Termination phase: Saturation
% 2.59/0.74 % (427351)Time elapsed: 0.003 s
% 2.59/0.74 % (427351)Peak memory usage: 12 MB
% 2.59/0.74 % (427351)Instructions burned: 6 (million)
% 2.59/0.74 % (427354)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2779378921:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.59/0.74 % (427337)Instruction limit reached!
% 2.59/0.74 % (427337)------------------------------
% 2.59/0.74 % (427337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427337)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427337)Termination reason: Instruction limit
% 2.59/0.74 % (427337)Termination phase: Saturation
% 2.59/0.74 % (427337)Time elapsed: 0.096 s
% 2.59/0.74 % (427337)Peak memory usage: 13 MB
% 2.59/0.74 % (427337)Instructions burned: 143 (million)
% 2.59/0.74 % (427354)Instruction limit reached!
% 2.59/0.74 % (427354)------------------------------
% 2.59/0.74 % (427354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427354)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427354)Termination reason: Instruction limit
% 2.59/0.74 % (427354)Termination phase: Saturation
% 2.59/0.74 % (427354)Time elapsed: 0.012 s
% 2.59/0.74 % (427354)Peak memory usage: 12 MB
% 2.59/0.74 % (427354)Instructions burned: 24 (million)
% 2.59/0.74 % (427349)Instruction limit reached!
% 2.59/0.74 % (427349)------------------------------
% 2.59/0.74 % (427349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427349)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427349)Termination reason: Instruction limit
% 2.59/0.74 % (427349)Termination phase: Saturation
% 2.59/0.74 % (427349)Time elapsed: 0.052 s
% 2.59/0.74 % (427349)Peak memory usage: 13 MB
% 2.59/0.74 % (427349)Instructions burned: 171 (million)
% 2.59/0.74 % (427311)Instruction limit reached!
% 2.59/0.74 % (427311)------------------------------
% 2.59/0.74 % (427311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427311)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427311)Termination reason: Instruction limit
% 2.59/0.74 % (427311)Termination phase: Saturation
% 2.59/0.74 % (427311)Time elapsed: 0.190 s
% 2.59/0.74 % (427311)Peak memory usage: 14 MB
% 2.59/0.74 % (427311)Instructions burned: 328 (million)
% 2.59/0.74 % (427279)Instruction limit reached!
% 2.59/0.74 % (427279)------------------------------
% 2.59/0.74 % (427279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.74 % (427279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.74 % (427279)CaDiCaL version: 2.1.3
% 2.59/0.74 % (427279)Termination reason: Instruction limit
% 2.59/0.74 % (427279)Termination phase: Saturation
% 2.59/0.74 % (427279)Time elapsed: 0.320 s
% 2.59/0.74 % (427279)Peak memory usage: 14 MB
% 2.59/0.78 % (427279)Instructions burned: 642 (million)
% 2.59/0.78 % (427358)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=1656622227:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.59/0.78 % (427356)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3150509727:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.59/0.78 % (427357)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=745680676:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.59/0.78 % (427359)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=4201092702:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.59/0.78 % (427356)Instruction limit reached!
% 2.59/0.78 % (427356)------------------------------
% 2.59/0.78 % (427356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427356)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427356)Termination reason: Instruction limit
% 2.59/0.78 % (427356)Termination phase: Saturation
% 2.59/0.78 % (427356)Time elapsed: 0.011 s
% 2.59/0.78 % (427356)Peak memory usage: 13 MB
% 2.59/0.78 % (427356)Instructions burned: 21 (million)
% 2.59/0.78 % (427361)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3087471486:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.59/0.78 % (427361)Refutation not found, incomplete strategy
% 2.59/0.78 % (427361)------------------------------
% 2.59/0.78 % (427361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427361)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427361)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.78 % (427361)Time elapsed: 0.003 s
% 2.59/0.78 % (427361)Peak memory usage: 12 MB
% 2.59/0.78 % (427361)Instructions burned: 5 (million)
% 2.59/0.78 % (427361)------------------------------
% 2.59/0.78 % (427361)------------------------------
% 2.59/0.78 % (427365)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=4291621221:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.59/0.78 % (427367)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.59/0.78 % (427367)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3519123820:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.59/0.78 % (427359)Instruction limit reached!
% 2.59/0.78 % (427359)------------------------------
% 2.59/0.78 % (427359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427359)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427359)Termination reason: Instruction limit
% 2.59/0.78 % (427359)Termination phase: Saturation
% 2.59/0.78 % (427359)Time elapsed: 0.029 s
% 2.59/0.78 % (427359)Peak memory usage: 12 MB
% 2.59/0.78 % (427359)Instructions burned: 46 (million)
% 2.59/0.78 % (427365)Instruction limit reached!
% 2.59/0.78 % (427365)------------------------------
% 2.59/0.78 % (427365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427365)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427365)Termination reason: Instruction limit
% 2.59/0.78 % (427365)Termination phase: Saturation
% 2.59/0.78 % (427365)Time elapsed: 0.013 s
% 2.59/0.78 % (427365)Peak memory usage: 12 MB
% 2.59/0.78 % (427365)Instructions burned: 22 (million)
% 2.59/0.78 % (427348)Instruction limit reached!
% 2.59/0.78 % (427348)------------------------------
% 2.59/0.78 % (427348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427348)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427348)Termination reason: Instruction limit
% 2.59/0.78 % (427348)Termination phase: Saturation
% 2.59/0.78 % (427348)Time elapsed: 0.130 s
% 2.59/0.78 % (427348)Peak memory usage: 14 MB
% 2.59/0.78 % (427348)Instructions burned: 184 (million)
% 2.59/0.78 % (427370)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=831068029:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 2.59/0.78 % (427371)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=4273855021:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 2.59/0.78 % (427370)Instruction limit reached!
% 2.59/0.78 % (427370)------------------------------
% 2.59/0.78 % (427370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427370)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427370)Termination reason: Instruction limit
% 2.59/0.78 % (427370)Termination phase: Saturation
% 2.59/0.78 % (427370)Time elapsed: 0.008 s
% 2.59/0.78 % (427370)Peak memory usage: 12 MB
% 2.59/0.78 % (427370)Instructions burned: 14 (million)
% 2.59/0.78 % (427372)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3269206222:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 2.59/0.78 % (427375)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1118022842:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 2.59/0.78 % (427375)Instruction limit reached!
% 2.59/0.78 % (427375)------------------------------
% 2.59/0.78 % (427375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427375)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427375)Termination reason: Instruction limit
% 2.59/0.78 % (427375)Termination phase: Saturation
% 2.59/0.78 % (427375)Time elapsed: 0.014 s
% 2.59/0.78 % (427375)Peak memory usage: 12 MB
% 2.59/0.78 % (427375)Instructions burned: 31 (million)
% 2.59/0.78 % (427371)Instruction limit reached!
% 2.59/0.78 % (427371)------------------------------
% 2.59/0.78 % (427371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427371)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427371)Termination reason: Instruction limit
% 2.59/0.78 % (427371)Termination phase: Saturation
% 2.59/0.78 % (427371)Time elapsed: 0.038 s
% 2.59/0.78 % (427371)Peak memory usage: 13 MB
% 2.59/0.78 % (427371)Instructions burned: 66 (million)
% 2.59/0.78 % (427372)Instruction limit reached!
% 2.59/0.78 % (427372)------------------------------
% 2.59/0.78 % (427372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427372)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427372)Termination reason: Instruction limit
% 2.59/0.78 % (427372)Termination phase: Saturation
% 2.59/0.78 % (427372)Time elapsed: 0.029 s
% 2.59/0.78 % (427372)Peak memory usage: 12 MB
% 2.59/0.78 % (427372)Instructions burned: 51 (million)
% 2.59/0.78 % (427378)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1322641321:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 2.59/0.78 % (427379)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2910548867:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 2.59/0.78 % (427380)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3563937738:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 2.59/0.78 % (427378)Refutation not found, incomplete strategy
% 2.59/0.78 % (427378)------------------------------
% 2.59/0.78 % (427378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427378)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427378)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.78 % (427378)Time elapsed: 0.012 s
% 2.59/0.78 % (427378)Peak memory usage: 12 MB
% 2.59/0.78 % (427378)Instructions burned: 19 (million)
% 2.59/0.78 % (427367)Instruction limit reached!
% 2.59/0.78 % (427367)------------------------------
% 2.59/0.78 % (427367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427367)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427367)Termination reason: Instruction limit
% 2.59/0.78 % (427367)Termination phase: Saturation
% 2.59/0.78 % (427367)Time elapsed: 0.094 s
% 2.59/0.78 % (427367)Peak memory usage: 12 MB
% 2.59/0.78 % (427367)Instructions burned: 201 (million)
% 2.59/0.78 % (427378)------------------------------
% 2.59/0.78 % (427378)------------------------------
% 2.59/0.78 % (427379)Instruction limit reached!
% 2.59/0.78 % (427379)------------------------------
% 2.59/0.78 % (427379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427379)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427379)Termination reason: Instruction limit
% 2.59/0.78 % (427379)Termination phase: Saturation
% 2.59/0.78 % (427379)Time elapsed: 0.018 s
% 2.59/0.78 % (427379)Peak memory usage: 12 MB
% 2.59/0.78 % (427379)Instructions burned: 35 (million)
% 2.59/0.78 % (427384)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 2.59/0.78 % (427384)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1677030650:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 2.59/0.78 % (427386)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1076111888:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 2.59/0.78 % (427380)Instruction limit reached!
% 2.59/0.78 % (427380)------------------------------
% 2.59/0.78 % (427380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.78 % (427380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.78 % (427380)CaDiCaL version: 2.1.3
% 2.59/0.78 % (427380)Termination reason: Instruction limit
% 2.59/0.78 % (427380)Termination phase: Saturation
% 2.59/0.78 % (427380)Time elapsed: 0.035 s
% 2.59/0.78 % (427380)Peak memory usage: 12 MB
% 2.59/0.78 % (427380)Instructions burned: 68 (million)
% 2.59/0.78 % (427385)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3196418257:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 2.59/0.78 % (427357) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-427271-427357"...
% 2.59/0.78 % (427357)...printing done.
% 2.59/0.78 % (427357)Refutation found. Thanks to Tanya!
% 2.59/0.78 % SZS status Theorem for theBenchmark
% 2.59/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/0.79 % (427357)------------------------------
% 2.59/0.79 % (427357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.79 % (427357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.79 % (427357)CaDiCaL version: 2.1.3
% 2.59/0.79 % (427357)Termination reason: Refutation
% 2.59/0.79 % (427357)Time elapsed: 0.170 s
% 2.59/0.79 % (427357)Peak memory usage: 15 MB
% 2.59/0.79 % (427357)Instructions burned: 300 (million)
% 2.59/0.79 % (427271)Success in time 0.54 s
% 2.59/0.79 % Vampire exiting
%------------------------------------------------------------------------------