%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU824^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:31:45 AM UTC 2026
% Result : Theorem 0.85s 0.39s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 9
% Syntax : Number of formulae : 159 ( 115 unt; 0 typ; 4 def)
% Number of atoms : 1863 ( 207 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 3256 ( 87 ~; 133 |; 163 &;2108 @)
% ( 4 <=>; 463 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 13 con; 0-4 aty)
% ( 277 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 398 ( 0 sgn 61 !; 2 ?; 398 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
nonempty: $i > $o ).
thf(func_def_3,type,
transitiveset: $i > $o ).
thf(func_def_4,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_6,type,
wellorderedByIn: $i > $o ).
thf(func_def_7,type,
ordinal: $i > $o ).
thf(func_def_8,type,
ordinalTransSet: $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X1 @ X2 )
& ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 )
| ( in @ X3 @ X2 ) ) ) ) ) )
= stricttotalorderedByIn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f2,axiom,
( ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) )
& ( in @ X2 @ X1 ) ) ) ) ) )
= wellorderedByIn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(f4,axiom,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) )
= ordinalTransSet ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(f5,conjecture,
( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X3: $i,X2: $i,X1: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransIn) ).
thf(f6,negated_conjecture,
~ ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X3: $i,X2: $i,X1: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X1 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X3 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( $true
= ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
& ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( in @ X5 @ X6 )
| ( X5 = X6 )
| ( in @ X6 @ X5 ) ) ) ) ) )
= stricttotalorderedByIn ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) )
& ( in @ X2 @ X1 ) ) ) ) ) )
= wellorderedByIn ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) )
= ordinalTransSet ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f18,plain,
( $true
= ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f19,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f20,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f24,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
| ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f19,f21]) ).
thf(f25,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) ) ) ) ) ) )
& ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y4 @ Y3 )
| ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 ) )
@ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f17,f24]) ).
thf(f26,plain,
( $true
= ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y2 ) )
=> ( ( nonempty @ Y3 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 ) ) ) ) ) ) ) ) )
& ( ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y5 @ Y4 )
| ( Y4 = Y5 )
| ( in @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ( ( in @ Y5 @ Y6 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y4 @ Y6 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ~ ( in @ Y4 @ Y4 ) ) ) )
@ Y2 ) )
@ Y1 )
& ( transitiveset @ Y1 ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f18,f25]) ).
thf(f27,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y2 ) )
=> ( ( nonempty @ Y3 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
& ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 ) ) ) ) ) ) ) ) )
& ( ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y5 @ Y4 )
| ( Y4 = Y5 )
| ( in @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ( ( in @ Y5 @ Y6 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y4 @ Y6 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ~ ( in @ Y4 @ Y4 ) ) ) )
@ Y2 ) )
@ Y1 )
& ( transitiveset @ Y1 ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f20,f25]) ).
thf(f28,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f30,plain,
( ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
ordinalTransSet = $true,
inference(imp_proxy_clausification,[],[f30]) ).
thf(f41,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f44,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( transitiveset @ sK0 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ sK0 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ sK0 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f51,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( transitiveset @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f52,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ sK0 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f50]) ).
thf(f53,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK1 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ sK0 )
=> ( in @ sK1 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ sK1 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ sK0 )
=> ( in @ sK1 @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ sK1 @ sK2 )
=> ( ( in @ sK2 @ Y0 )
=> ( ( in @ Y0 @ sK0 )
=> ( in @ sK1 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ sK1 @ sK2 )
=> ( ( in @ sK2 @ Y0 )
=> ( ( in @ Y0 @ sK0 )
=> ( in @ sK1 @ Y0 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f57,plain,
( ( ( in @ sK1 @ sK2 )
=> ( ( in @ sK2 @ sK3 )
=> ( ( in @ sK3 @ sK0 )
=> ( in @ sK1 @ sK3 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
( $false
= ( ( in @ sK2 @ sK3 )
=> ( ( in @ sK3 @ sK0 )
=> ( in @ sK1 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
( ( in @ sK1 @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f62,plain,
( ( ( in @ sK3 @ sK0 )
=> ( in @ sK1 @ sK3 ) )
= $false ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f63,plain,
( ( in @ sK2 @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f74,plain,
( $false
= ( in @ sK1 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f75,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f116,plain,
( $true
= ( transitiveset @ sK0 ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f117,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f126,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f137,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f138,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f139,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f140,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ~ ( in @ X1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f142,plain,
( ( $true
=> ~ ( in @ sK3 @ sK3 ) )
= $true ),
inference(constrained_superposition,[],[f140,f75]) ).
thf(f143,plain,
( $true
= ( ~ ( in @ sK3 @ sK3 ) ) ),
inference(boolean_simplification,[],[f142]) ).
thf(f144,plain,
( $false
= ( in @ sK3 @ sK3 ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f152,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f153,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y0 @ X1 )
| ( X1 = Y0 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f157,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y0 @ sK3 )
| ( sK3 = Y0 )
| ( in @ sK3 @ Y0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f155,f75]) ).
thf(f158,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y0 @ sK3 )
| ( sK3 = Y0 )
| ( in @ sK3 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y0 @ sK3 )
| ( sK3 = Y0 )
| ( in @ sK3 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ( in @ X1 @ sK3 )
| ( sK3 = X1 )
| ( in @ sK3 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f165,plain,
( ( ( in @ sK1 @ sK0 )
=> ( $false
| ( sK3 = sK1 )
| ( in @ sK3 @ sK1 ) ) )
= $true ),
inference(constrained_superposition,[],[f160,f74]) ).
thf(f176,plain,
( $true
= ( ( in @ sK1 @ sK0 )
=> ( ( sK3 = sK1 )
| ( in @ sK3 @ sK1 ) ) ) ),
inference(boolean_simplification,[],[f165]) ).
thf(f186,plain,
( ( ( ( sK3 = sK1 )
| ( in @ sK3 @ sK1 ) )
= $true )
| ( ( in @ sK1 @ sK0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f188,definition,
( spl4_1
<=> ( ( ( sK3 = sK1 )
| ( in @ sK3 @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f190,plain,
( ( ( ( sK3 = sK1 )
| ( in @ sK3 @ sK1 ) )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f192,definition,
( spl4_2
<=> ( ( in @ sK1 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f194,plain,
( ( ( in @ sK1 @ sK0 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f195,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f186,f192,f188]) ).
thf(f204,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f205,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ X1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f207,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ sK3 @ Y0 ) )
=> ( in @ sK3 @ Y1 ) ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f205,f75]) ).
thf(f209,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ sK3 @ Y0 ) )
=> ( in @ sK3 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f207]) ).
thf(f216,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ sK3 @ Y0 ) )
=> ( in @ sK3 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f217,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ X1 @ Y0 )
& ( in @ sK3 @ X1 ) )
=> ( in @ sK3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f230,plain,
( ( ordinalTransSet = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f231,plain,
( ( $true = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(forward_demodulation,[],[f230,f32]) ).
thf(f232,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( transitiveset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( transitiveset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f236,plain,
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& $true )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK0 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f234,f116]) ).
thf(f237,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f236]) ).
thf(f238,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK0 ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f237,f117]) ).
thf(f239,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ sK0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ sK0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ sK0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ sK0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ sK0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ sK0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f249,plain,
( $true
= ( ( in @ sK2 @ sK0 )
=> ( $true
=> ( in @ sK1 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f243,f59]) ).
thf(f250,plain,
( $true
= ( ( in @ sK3 @ sK0 )
=> ( $true
=> ( in @ sK2 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f243,f63]) ).
thf(f263,plain,
( ( ( in @ sK3 @ sK0 )
=> ( in @ sK2 @ sK0 ) )
= $true ),
inference(boolean_simplification,[],[f250]) ).
thf(f267,plain,
( ( ( in @ sK2 @ sK0 )
=> ( in @ sK1 @ sK0 ) )
= $true ),
inference(boolean_simplification,[],[f249]) ).
thf(f270,plain,
( ( $true
=> ( in @ sK2 @ sK0 ) )
= $true ),
inference(forward_demodulation,[],[f263,f75]) ).
thf(f271,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(boolean_simplification,[],[f270]) ).
thf(f272,plain,
( ( ( ( in @ sK2 @ sK0 )
=> $false )
= $true )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f267,f194]) ).
thf(f273,plain,
( ( $true
= ( ~ ( in @ sK2 @ sK0 ) ) )
| ~ spl4_2 ),
inference(boolean_simplification,[],[f272]) ).
thf(f274,plain,
( ( $true = ( ~ $true ) )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f273,f271]) ).
thf(f275,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(boolean_simplification,[],[f274]) ).
thf(f276,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f277,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f276]) ).
thf(f278,plain,
( ( $true
=> ( in @ sK1 @ sK0 ) )
= $true ),
inference(forward_demodulation,[],[f267,f271]) ).
thf(f279,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(boolean_simplification,[],[f278]) ).
thf(f284,plain,
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK2 @ Y0 )
& ( in @ sK3 @ sK2 ) )
=> ( in @ sK3 @ Y0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f217,f271]) ).
thf(f293,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK2 @ Y0 )
& ( in @ sK3 @ sK2 ) )
=> ( in @ sK3 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f284]) ).
thf(f302,plain,
( ( $true
=> ~ ( in @ sK1 @ sK1 ) )
= $true ),
inference(constrained_superposition,[],[f140,f279]) ).
thf(f306,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK1 @ Y0 )
& ( in @ sK3 @ sK1 ) )
=> ( in @ sK3 @ Y0 ) ) ) ) )
= $true ),
inference(constrained_superposition,[],[f217,f279]) ).
thf(f311,plain,
( $true
= ( ~ ( in @ sK1 @ sK1 ) ) ),
inference(boolean_simplification,[],[f302]) ).
thf(f312,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK1 @ Y0 )
& ( in @ sK3 @ sK1 ) )
=> ( in @ sK3 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f306]) ).
thf(f337,plain,
( $false
= ( in @ sK1 @ sK1 ) ),
inference(not_proxy_clausification,[],[f311]) ).
thf(f389,plain,
( ( ( sK3 = sK1 )
= $true )
| ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl4_1 ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f393,definition,
( spl4_3
<=> ( $true
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f395,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f397,definition,
( spl4_4
<=> ( ( sK3 = sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f399,plain,
( ( ( sK3 = sK1 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f400,plain,
( spl4_3
| spl4_4
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f389,f188,f397,f393]) ).
thf(f401,plain,
( ( sK3 = sK1 )
| ~ spl4_4 ),
inference(equality_proxy_clausification,[],[f399]) ).
thf(f414,plain,
( ( ( in @ sK2 @ sK1 )
= $true )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f63,f401]) ).
thf(f492,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK2 @ Y0 )
& ( in @ sK3 @ sK2 ) )
=> ( in @ sK3 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f293]) ).
thf(f493,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ( ( in @ sK2 @ X1 )
& ( in @ sK3 @ sK2 ) )
=> ( in @ sK3 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f492]) ).
thf(f494,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ( ( in @ sK2 @ X1 )
& ( in @ sK1 @ sK2 ) )
=> ( in @ sK1 @ X1 ) ) ) )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f493,f401]) ).
thf(f495,plain,
( ! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ( ( in @ sK2 @ X1 )
& $true )
=> ( in @ sK1 @ X1 ) ) )
= $true )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f494,f59]) ).
thf(f496,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ( in @ sK2 @ X1 )
=> ( in @ sK1 @ X1 ) ) ) )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f495]) ).
thf(f499,plain,
( ( ( ( in @ sK1 @ sK0 )
=> ( ( in @ sK2 @ sK1 )
=> $false ) )
= $true )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f496,f337]) ).
thf(f522,plain,
( ( ( ( in @ sK1 @ sK0 )
=> ~ ( in @ sK2 @ sK1 ) )
= $true )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f499]) ).
thf(f538,plain,
( ( $true
= ( $true
=> ~ ( in @ sK2 @ sK1 ) ) )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f522,f279]) ).
thf(f539,plain,
( ( ( ~ ( in @ sK2 @ sK1 ) )
= $true )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f538]) ).
thf(f553,plain,
( ( $true = ( ~ $true ) )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f539,f414]) ).
thf(f554,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(boolean_simplification,[],[f553]) ).
thf(f555,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f556,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f555]) ).
thf(f575,plain,
( $true
= ( ( in @ sK3 @ sK0 )
=> ( ( ( in @ sK2 @ sK3 )
& ( in @ sK3 @ sK2 ) )
=> $false ) ) ),
inference(constrained_superposition,[],[f493,f144]) ).
thf(f582,plain,
( ( ( in @ sK3 @ sK0 )
=> ~ ( ( in @ sK2 @ sK3 )
& ( in @ sK3 @ sK2 ) ) )
= $true ),
inference(boolean_simplification,[],[f575]) ).
thf(f595,plain,
( ( $true
=> ~ ( ( in @ sK2 @ sK3 )
& ( in @ sK3 @ sK2 ) ) )
= $true ),
inference(forward_demodulation,[],[f582,f75]) ).
thf(f596,plain,
( ( ~ ( ( in @ sK2 @ sK3 )
& ( in @ sK3 @ sK2 ) ) )
= $true ),
inference(boolean_simplification,[],[f595]) ).
thf(f608,plain,
( $true
= ( ~ ( $true
& ( in @ sK3 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f596,f63]) ).
thf(f609,plain,
( ( ~ ( in @ sK3 @ sK2 ) )
= $true ),
inference(boolean_simplification,[],[f608]) ).
thf(f614,plain,
( ( in @ sK3 @ sK2 )
= $false ),
inference(not_proxy_clausification,[],[f609]) ).
thf(f685,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( ( ( in @ sK1 @ Y0 )
& ( in @ sK3 @ sK1 ) )
=> ( in @ sK3 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f312]) ).
thf(f686,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( ( ( in @ sK1 @ X1 )
& ( in @ sK3 @ sK1 ) )
=> ( in @ sK3 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ( ( in @ sK1 @ X1 )
& $true )
=> ( in @ sK3 @ X1 ) ) ) )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f686,f395]) ).
thf(f688,plain,
( ! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( ( in @ sK1 @ X1 )
=> ( in @ sK3 @ X1 ) ) ) )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f687]) ).
thf(f699,plain,
( ( $true
= ( $true
=> ( ( in @ sK1 @ sK2 )
=> ( in @ sK3 @ sK2 ) ) ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f688,f271]) ).
thf(f715,plain,
( ( ( ( in @ sK1 @ sK2 )
=> ( in @ sK3 @ sK2 ) )
= $true )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f699]) ).
thf(f728,plain,
( ( $true
= ( $true
=> ( in @ sK3 @ sK2 ) ) )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f715,f59]) ).
thf(f729,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ~ spl4_3 ),
inference(boolean_simplification,[],[f728]) ).
thf(f739,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f729,f614]) ).
thf(f740,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f739]) ).
thf(f741,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f740]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f195]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f277]) ).
cnf(s3,plain,
( ~ spl4_1
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f400]) ).
cnf(s9,plain,
~ spl4_4,
inference(sat_conversion,[],[f556]) ).
cnf(s12,plain,
~ spl4_3,
inference(sat_conversion,[],[f741]) ).
cnf(s13,plain,
~ spl4_1,
inference(rat,[],[s3,s9,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s2,s13]) ).
thf(f742,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU824^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n004.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:35:07 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.36 % (1373064)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (1373073)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3373153381:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (1373073)Instruction limit reached!
% 0.22/0.36 % (1373073)------------------------------
% 0.22/0.36 % (1373073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1373073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1373073)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1373073)Termination reason: Instruction limit
% 0.22/0.36 % (1373073)Termination phase: Saturation
% 0.22/0.36 % (1373073)Time elapsed: 0.007 s
% 0.22/0.36 % (1373073)Peak memory usage: 12 MB
% 0.22/0.36 % (1373073)Instructions burned: 26 (million)
% 0.22/0.36 % (1373071)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1715234935:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (1373070)lrs+10_16_si=on:nwc=1.5:random_seed=338498522:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (1373069)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1169818652:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (1373071)Instruction limit reached!
% 0.22/0.36 % (1373071)------------------------------
% 0.22/0.36 % (1373071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1373071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1373071)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1373071)Termination reason: Instruction limit
% 0.22/0.36 % (1373071)Termination phase: Property scanning
% 0.22/0.36 % (1373071)Time elapsed: 0.002 s
% 0.22/0.36 % (1373071)Peak memory usage: 10 MB
% 0.22/0.36 % (1373071)Instructions burned: 3 (million)
% 0.22/0.36 % (1373072)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=1236355582: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)
% 0.22/0.36 % (1373070)Instruction limit reached!
% 0.22/0.36 % (1373070)------------------------------
% 0.22/0.36 % (1373070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1373070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1373070)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1373070)Termination reason: Instruction limit
% 0.22/0.36 % (1373070)Termination phase: Saturation
% 0.22/0.36 % (1373070)Time elapsed: 0.008 s
% 0.22/0.36 % (1373070)Peak memory usage: 11 MB
% 0.22/0.36 % (1373070)Instructions burned: 18 (million)
% 0.22/0.36 % (1373075)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (1373075)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
% 0.22/0.36 % (1373083)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1373075)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=2358512868:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (1373083)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2846360799:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (1373081)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2859937289:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (1373074)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2354450773:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (1373083)Instruction limit reached!
% 0.22/0.36 % (1373083)------------------------------
% 0.22/0.36 % (1373083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1373083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.38 % (1373083)CaDiCaL version: 2.1.3
% 0.85/0.38 % (1373083)Termination reason: Instruction limit
% 0.85/0.38 % (1373083)Termination phase: Saturation
% 0.85/0.38 % (1373083)Time elapsed: 0.004 s
% 0.85/0.38 % (1373083)Peak memory usage: 12 MB
% 0.85/0.38 % (1373083)Instructions burned: 9 (million)
% 0.85/0.38 % (1373081)Instruction limit reached!
% 0.85/0.38 % (1373081)------------------------------
% 0.85/0.38 % (1373081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.38 % (1373081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.38 % (1373081)CaDiCaL version: 2.1.3
% 0.85/0.38 % (1373081)Termination reason: Instruction limit
% 0.85/0.38 % (1373081)Termination phase: Saturation
% 0.85/0.38 % (1373081)Time elapsed: 0.003 s
% 0.85/0.38 % (1373081)Peak memory usage: 11 MB
% 0.85/0.38 % (1373081)Instructions burned: 6 (million)
% 0.85/0.38 % (1373080)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4179589654:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.85/0.38 % (1373080)Instruction limit reached!
% 0.85/0.38 % (1373080)------------------------------
% 0.85/0.38 % (1373080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.38 % (1373080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.38 % (1373080)CaDiCaL version: 2.1.3
% 0.85/0.38 % (1373080)Termination reason: Instruction limit
% 0.85/0.38 % (1373080)Termination phase: Property scanning
% 0.85/0.38 % (1373080)Time elapsed: 0.002 s
% 0.85/0.38 % (1373080)Peak memory usage: 10 MB
% 0.85/0.38 % (1373080)Instructions burned: 2 (million)
% 0.85/0.38 % (1373088)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3862332926:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.85/0.38 % (1373069)Instruction limit reached!
% 0.85/0.38 % (1373069)------------------------------
% 0.85/0.38 % (1373069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.38 % (1373069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.38 % (1373069)CaDiCaL version: 2.1.3
% 0.85/0.38 % (1373069)Termination reason: Instruction limit
% 0.85/0.38 % (1373069)Termination phase: Saturation
% 0.85/0.38 % (1373069)Time elapsed: 0.038 s
% 0.85/0.38 % (1373069)Peak memory usage: 12 MB
% 0.85/0.38 % (1373069)Instructions burned: 88 (million)
% 0.85/0.38 % (1373088)Instruction limit reached!
% 0.85/0.38 % (1373088)------------------------------
% 0.85/0.38 % (1373088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.38 % (1373088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.38 % (1373088)CaDiCaL version: 2.1.3
% 0.85/0.38 % (1373088)Termination reason: Instruction limit
% 0.85/0.38 % (1373088)Termination phase: Saturation
% 0.85/0.38 % (1373088)Time elapsed: 0.004 s
% 0.85/0.38 % (1373088)Peak memory usage: 11 MB
% 0.85/0.38 % (1373088)Instructions burned: 15 (million)
% 0.85/0.38 % (1373094)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.85/0.38 % (1373089)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
% 0.85/0.38 % (1373089)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.85/0.39 % (1373094)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=201933008:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.85/0.39 % (1373094)Instruction limit reached!
% 0.85/0.39 % (1373094)------------------------------
% 0.85/0.39 % (1373094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373094)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373094)Termination reason: Instruction limit
% 0.85/0.39 % (1373094)Termination phase: Saturation
% 0.85/0.39 % (1373094)Time elapsed: 0.001 s
% 0.85/0.39 % (1373094)Peak memory usage: 10 MB
% 0.85/0.39 % (1373094)Instructions burned: 4 (million)
% 0.85/0.39 % (1373089)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=721210364:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.85/0.39 % (1373074)Instruction limit reached!
% 0.85/0.39 % (1373074)------------------------------
% 0.85/0.39 % (1373074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373074)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373074)Termination reason: Instruction limit
% 0.85/0.39 % (1373074)Termination phase: Saturation
% 0.85/0.39 % (1373074)Time elapsed: 0.033 s
% 0.85/0.39 % (1373074)Peak memory usage: 13 MB
% 0.85/0.39 % (1373074)Instructions burned: 75 (million)
% 0.85/0.39 % (1373093)lrs+10_1_si=on:cs=on:random_seed=1127769987:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.85/0.39 % (1373093)Instruction limit reached!
% 0.85/0.39 % (1373093)------------------------------
% 0.85/0.39 % (1373093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373093)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373093)Termination reason: Instruction limit
% 0.85/0.39 % (1373093)Termination phase: Saturation
% 0.85/0.39 % (1373093)Time elapsed: 0.004 s
% 0.85/0.39 % (1373093)Peak memory usage: 11 MB
% 0.85/0.39 % (1373093)Instructions burned: 8 (million)
% 0.85/0.39 % (1373096)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=347826693:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.85/0.39 % (1373096)Refutation not found, incomplete strategy
% 0.85/0.39 % (1373096)------------------------------
% 0.85/0.39 % (1373096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373096)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373096)Termination reason: Refutation not found, incomplete strategy
% 0.85/0.39 % (1373096)Time elapsed: 0.002 s
% 0.85/0.39 % (1373096)Peak memory usage: 12 MB
% 0.85/0.39 % (1373096)Instructions burned: 4 (million)
% 0.85/0.39 % (1373092)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=2920765564:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.85/0.39 % (1373096)------------------------------
% 0.85/0.39 % (1373096)------------------------------
% 0.85/0.39 % (1373100)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=754842922:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.85/0.39 % (1373089)Instruction limit reached!
% 0.85/0.39 % (1373089)------------------------------
% 0.85/0.39 % (1373089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373089)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373089)Termination reason: Instruction limit
% 0.85/0.39 % (1373089)Termination phase: Saturation
% 0.85/0.39 % (1373089)Time elapsed: 0.028 s
% 0.85/0.39 % (1373089)Peak memory usage: 11 MB
% 0.85/0.39 % (1373089)Instructions burned: 31 (million)
% 0.85/0.39 % (1373100)Refutation not found, incomplete strategy
% 0.85/0.39 % (1373100)------------------------------
% 0.85/0.39 % (1373100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373100)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373100)Termination reason: Refutation not found, incomplete strategy
% 0.85/0.39 % (1373100)Time elapsed: 0.003 s
% 0.85/0.39 % (1373100)Peak memory usage: 12 MB
% 0.85/0.39 % (1373100)Instructions burned: 3 (million)
% 0.85/0.39 % (1373100)------------------------------
% 0.85/0.39 % (1373100)------------------------------
% 0.85/0.39 % (1373075)Instruction limit reached!
% 0.85/0.39 % (1373075)------------------------------
% 0.85/0.39 % (1373075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373075)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373075)Termination reason: Instruction limit
% 0.85/0.39 % (1373075)Termination phase: Saturation
% 0.85/0.39 % (1373075)Time elapsed: 0.069 s
% 0.85/0.39 % (1373075)Peak memory usage: 14 MB
% 0.85/0.39 % (1373075)Instructions burned: 157 (million)
% 0.85/0.39 % (1373099)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1766141466:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.85/0.39 % (1373105)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3088377320:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.85/0.39 % (1373092) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1373064-1373092"...
% 0.85/0.39 % (1373103)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=797776519:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.85/0.39 % (1373107)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4165835536: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)
% 0.85/0.39 % (1373092)...printing done.
% 0.85/0.39 % (1373092)Refutation found. Thanks to Tanya!
% 0.85/0.39 % SZS status Theorem for theBenchmark
% 0.85/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.85/0.39 % (1373092)------------------------------
% 0.85/0.39 % (1373092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.39 % (1373092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.39 % (1373092)CaDiCaL version: 2.1.3
% 0.85/0.39 % (1373092)Termination reason: Refutation
% 0.85/0.39 % (1373092)Time elapsed: 0.043 s
% 0.85/0.39 % (1373092)Peak memory usage: 13 MB
% 0.85/0.39 % (1373092)Instructions burned: 76 (million)
% 0.85/0.39 % (1373064)Success in time 0.141 s
% 0.85/0.39 % Vampire exiting
%------------------------------------------------------------------------------