%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU637^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:30:27 AM UTC 2026
% Result : Theorem 3.39s 1.02s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 31
% Syntax : Number of formulae : 333 ( 95 unt; 0 typ; 23 def)
% Number of atoms : 2914 ( 560 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 4248 ( 478 ~; 689 |; 43 &;2450 @)
% ( 23 <=>; 336 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 50 usr; 36 con; 0-4 aty)
% ( 195 !!; 34 ??; 0 @@+; 0 @@-)
% Number of variables : 520 ( 0 sgn 239 !; 5 ?; 520 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
dsetconstrI: $o ).
thf(func_def_6,type,
dsetconstrEL: $o ).
thf(func_def_7,type,
dsetconstrER: $o ).
thf(func_def_8,type,
setext: $o ).
thf(func_def_9,type,
uniqinunit: $o ).
thf(func_def_10,type,
eqinunit: $o ).
thf(func_def_11,type,
singleton: $i > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
sK1: $i > $o ).
thf(func_def_29,type,
sK4: $i > $i > $i ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f3,axiom,
! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f4,axiom,
( setext
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(f5,axiom,
( uniqinunit
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f6,axiom,
( eqinunit
= ( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(f7,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f8,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(f9,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( X1 @ X4 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( singleton
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( eqinunit
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f13,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) )
= dsetconstrER ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f21,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f23,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f30,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f31,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f32,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( singleton
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f33,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f36,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f32,f30]) ).
thf(f37,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f38,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f39,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f40,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f42,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true )
| ( setext = $false ) ),
inference(iff_proxy_clausification,[],[f29]) ).
thf(f44,plain,
( ( dsetconstrER = $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f46,plain,
( ( eqinunit = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true )
| ( dsetconstrEL = $false ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f50,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true )
| ( uniqinunit = $false ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f52,plain,
( ( dsetconstrI = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f53,plain,
( $false
= ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f55,definition,
( spl0_1
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f57,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f59,definition,
( spl0_2
<=> ( setext = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f61,plain,
( ( setext = $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f59,f55]) ).
thf(f64,definition,
( spl0_3
<=> ( setext = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f66,plain,
( ( setext = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f73,definition,
( spl0_5
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f75,plain,
( ( dsetconstrER = $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f82,definition,
( spl0_7
<=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f84,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl0_8
<=> ( dsetconstrER = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f88,plain,
( ( dsetconstrER = $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f89,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f44,f86,f82]) ).
thf(f91,definition,
( spl0_9
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f93,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f95,definition,
( spl0_10
<=> ( eqinunit = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f97,plain,
( ( eqinunit = $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f46,f95,f91]) ).
thf(f100,definition,
( spl0_11
<=> ( eqinunit = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f102,plain,
( ( eqinunit = $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f109,definition,
( spl0_13
<=> ( dsetconstrEL = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f111,plain,
( ( dsetconstrEL = $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f113,definition,
( spl0_14
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f115,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f116,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f113,f109]) ).
thf(f118,definition,
( spl0_15
<=> ( dsetconstrEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f120,plain,
( ( dsetconstrEL = $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f127,definition,
( spl0_17
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f129,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f131,definition,
( spl0_18
<=> ( uniqinunit = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
thf(f133,plain,
( ( uniqinunit = $false )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f134,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f50,f131,f127]) ).
thf(f140,definition,
( spl0_20
<=> ( uniqinunit = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
thf(f142,plain,
( ( uniqinunit = $true )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f149,definition,
( spl0_22
<=> ( dsetconstrI = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f151,plain,
( ( dsetconstrI = $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f154,definition,
( spl0_23
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
thf(f156,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f158,definition,
( spl0_24
<=> ( dsetconstrI = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
thf(f160,plain,
( ( dsetconstrI = $false )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f161,plain,
( spl0_23
| spl0_24 ),
inference(avatar_split_clause,[],[f52,f158,f154]) ).
thf(f162,plain,
( $false
= ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f163,plain,
dsetconstrI = $true,
inference(imp_proxy_clausification,[],[f53]) ).
thf(f164,plain,
( $false
= ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f165,plain,
dsetconstrEL = $true,
inference(imp_proxy_clausification,[],[f162]) ).
thf(f166,plain,
spl0_22,
inference(avatar_split_clause,[],[f163,f149]) ).
thf(f167,plain,
( $false
= ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f168,plain,
dsetconstrER = $true,
inference(imp_proxy_clausification,[],[f164]) ).
thf(f169,plain,
spl0_15,
inference(avatar_split_clause,[],[f165,f118]) ).
thf(f170,plain,
( $false
= ( uniqinunit
=> ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f171,plain,
setext = $true,
inference(imp_proxy_clausification,[],[f167]) ).
thf(f172,plain,
spl0_5,
inference(avatar_split_clause,[],[f168,f73]) ).
thf(f173,plain,
( $false
= ( eqinunit
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f174,plain,
uniqinunit = $true,
inference(imp_proxy_clausification,[],[f170]) ).
thf(f175,plain,
spl0_3,
inference(avatar_split_clause,[],[f171,f64]) ).
thf(f176,plain,
spl0_20,
inference(avatar_split_clause,[],[f174,f140]) ).
thf(f177,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f178,plain,
eqinunit = $true,
inference(imp_proxy_clausification,[],[f173]) ).
thf(f179,plain,
spl0_11,
inference(avatar_split_clause,[],[f178,f100]) ).
thf(f180,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( ( Y0 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
& ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f181,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( sK1 @ Y1 )
=> ( ( sK1 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ sK1 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ sK1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( sK1 @ Y1 )
=> ( ( sK1 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ sK1 ) )
& ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ Y0 @ sK1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK1 @ Y0 )
=> ( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( in @ Y0 @ sK2 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( in @ Y0 @ sK2 ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK1 @ Y0 )
=> ( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( in @ Y0 @ sK2 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f188,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( sK1 @ Y0 )
=> ( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f189,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK1 @ X1 )
=> ( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK1 @ X1 )
=> ( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK1 @ X1 )
=> ( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) ) )
@ X2 )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f190]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ sK2 )
=> ( ( sK1 @ X1 )
=> ( ( sK1 @ X2 )
=> ( X1 = X2 ) ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ sK2 ) )
| ( ( ( sK1 @ X1 )
=> ( ( sK1 @ X2 )
=> ( X1 = X2 ) ) )
= $true )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK1 @ X2 )
=> ( X1 = X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( in @ X2 @ sK2 ) )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( $false
= ( in @ X2 @ sK2 ) )
| ( ( X1 = X2 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ sK2 ) )
| ( X1 = X2 )
| ( $false
= ( sK1 @ X2 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f66,f61]) ).
thf(f211,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f212,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f211]) ).
thf(f213,plain,
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( in @ Y0 @ sK2 ) )
@ sK3 )
= $true ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f214,plain,
( ( ( sK1 @ sK3 )
& ( in @ sK3 @ sK2 ) )
= $true ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( sK1 @ sK3 )
= $true ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f222,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK2 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f225,plain,
! [X1: $i] :
( $false
= ( ( in @ X1 @ ( dsetconstr @ sK2 @ sK1 ) )
& ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f226,plain,
! [X1: $i] :
( ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) )
= $false )
| ( $false
= ( in @ X1 @ ( dsetconstr @ sK2 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK2 @ sK1 ) )
| ( $false
= ( in @ X1 @ ( dsetconstr @ sK2 @ sK1 ) ) ) ),
inference(equality_proxy_clausification,[],[f226]) ).
thf(f229,plain,
! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK3 = X0 )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $false = $true ) ),
inference(superposition,[],[f215,f209]) ).
thf(f231,plain,
! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( sK3 = X0 ) ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f233,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( $false = $true )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) ) ),
inference(forward_demodulation,[],[f231,f216]) ).
thf(f234,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( sK3 = X0 )
| ( $false
= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f241,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f120,f111]) ).
thf(f242,plain,
( $false
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f243,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f242]) ).
thf(f246,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 )
= $true )
| ~ spl0_9 ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f247,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true )
| ~ spl0_9 ),
inference(beta-eta_normalization,[],[f246]) ).
thf(f248,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= $true )
| ~ spl0_9 ),
inference(pi_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ~ spl0_9 ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= $true ) )
| ~ spl0_9 ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
= $true )
| ( X1 != X2 ) )
| ~ spl0_9 ),
inference(equality_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_17 ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f253,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true )
| ~ spl0_17 ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true )
| ~ spl0_17 ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X2 = X1 ) )
= $true )
| ~ spl0_17 ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f256,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( ( X2 = X1 )
= $true ) )
| ~ spl0_17 ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f257,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( X1 = X2 ) )
| ~ spl0_17 ),
inference(equality_proxy_clausification,[],[f256]) ).
thf(f262,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f263,plain,
( ! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
( ! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( X1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_7 ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ X2 ) ) )
= $true )
| ~ spl0_7 ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_7 ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
=> ( X1 @ X2 ) )
= $true )
| ~ spl0_7 ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( X1 @ X2 )
= $true ) )
| ~ spl0_7 ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f271,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_14 ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f272,plain,
( ! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) )
| ~ spl0_14 ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
( ! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_14 ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
( ! [X2: $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_14 ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_14 ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) )
= $true )
| ~ spl0_14 ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $true ) )
| ~ spl0_14 ),
inference(imp_proxy_clausification,[],[f276]) ).
thf(f280,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_23 ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f281,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ~ spl0_23 ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 )
= $true )
| ~ spl0_23 ),
inference(pi_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) )
= $true )
| ~ spl0_23 ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
= $true ) )
| ~ spl0_23 ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( $false
= ( X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false ) )
| ~ spl0_23 ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f296,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f297,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f298,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
( ! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( ( X2 = X1 )
= $true ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( X1 = X2 ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK4 @ X1 @ X2 ) ) )
| ( X1 = X2 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f306,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( X1 = X2 ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f307,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( X1 = X2 )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( X1 = X2 )
| ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $true ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f306]) ).
thf(f309,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X2 @ X1 ) )
= $false ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f311,plain,
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
=> ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f313,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f314,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
= $true ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f315,plain,
( ! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X2 @ X1 ) )
= $false )
| ( X1 = X2 )
| ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $true ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f318,plain,
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
=> ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) ) )
| ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $true ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f320,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
= $true )
| ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $true )
| ( X1 = X2 ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f324,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( $false
= ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ X1 ) ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f251,f313]) ).
thf(f327,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( $false
= ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ X1 ) ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f335,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) )
= $true )
| ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f251,f314]) ).
thf(f339,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) )
= $true )
| ( ( setadjoin @ X0 @ emptyset )
= X1 ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f343,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( $true
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ X0 ) )
| ( ( setadjoin @ X1 @ emptyset )
= X0 )
| ( $false = $true ) )
| ~ spl0_1
| ~ spl0_17 ),
inference(superposition,[],[f320,f257]) ).
thf(f356,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ X0 ) )
| ( ( setadjoin @ X1 @ emptyset )
= X0 )
| ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) )
| ~ spl0_1
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f399,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) @ X1 )
= $true )
| ( $false = $true )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f277,f356]) ).
thf(f400,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( X2 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f268,f356]) ).
thf(f404,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) @ X1 )
= $true )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f399]) ).
thf(f409,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( X2 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f688,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $false = $true )
| ( ( dsetconstr @ sK2 @ X1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f404,f234]) ).
thf(f689,plain,
( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ sK2 ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= X2 )
| ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) ) )
| ( $false
= ( sK1 @ X2 ) )
| ( ( dsetconstr @ sK2 @ X1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( $false = $true ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f404,f209]) ).
thf(f697,plain,
( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) ) )
| ( ( dsetconstr @ sK2 @ X1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X2 @ sK2 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= X2 )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f689]) ).
thf(f701,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= sK3 )
| ( ( dsetconstr @ sK2 @ X1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f717,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X1 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $false = $true )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f697,f409]) ).
thf(f721,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $false = $true )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X1 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f717]) ).
thf(f722,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X1 )
| ( $false
= ( in @ X1 @ sK2 ) )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f964,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f409,f701]) ).
thf(f967,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f964]) ).
thf(f968,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f967]) ).
thf(f1054,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( dsetconstr @ sK2 @ sK1 ) )
= $true ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f314,f968]) ).
thf(f1062,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( dsetconstr @ sK2 @ sK1 ) )
= $true ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f1054]) ).
thf(f1065,plain,
( ! [X0: $i] :
( ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( dsetconstr @ sK2 @ sK1 ) )
= $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1062,f227]) ).
thf(f1269,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) )
= $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false = $true ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f1065,f268]) ).
thf(f1270,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false = $true )
| ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ sK2 )
= $true ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f277,f1065]) ).
thf(f1272,plain,
( ! [X0: $i] :
( ( ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ sK2 )
= $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1270]) ).
thf(f1273,plain,
( ! [X0: $i] :
( ( ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) )
= $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1269]) ).
thf(f1394,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f234,f1272]) ).
thf(f1397,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f1394]) ).
thf(f1398,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1397]) ).
thf(f1409,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false = $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f1273,f1398]) ).
thf(f1419,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false = $true )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f1409]) ).
thf(f1420,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= sK3 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1419]) ).
thf(f1495,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) )
= $true )
| ( sK3 != X0 )
| ( ( dsetconstr @ sK2 @ sK1 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f339,f1420]) ).
thf(f1508,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) )
= $true )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1495,f227]) ).
thf(f1519,definition,
( spl0_25
<=> ( ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
thf(f1520,plain,
( ( ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) )
!= $true )
| spl0_25 ),
inference(avatar_component_clause,[],[f1519]) ).
thf(f1521,plain,
( ( ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1519]) ).
thf(f1537,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f75,f88]) ).
thf(f1541,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f1537]) ).
thf(f1542,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1541]) ).
thf(f1633,plain,
( ( $false = $true )
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[],[f133,f142]) ).
thf(f1639,plain,
( $false
| ~ spl0_18
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1633]) ).
thf(f1640,plain,
( ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1639]) ).
thf(f1915,plain,
( ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17 ),
inference(equality_resolution,[],[f1508]) ).
thf(f1917,plain,
( ( $false = $true )
| ( $true
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1915,f1521]) ).
thf(f1918,plain,
( ( $true
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1917]) ).
thf(f1927,plain,
( ! [X0: $i] :
( ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X0 )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $true ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(superposition,[],[f1918,f722]) ).
thf(f1929,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) )
= sK3 )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(superposition,[],[f257,f1918]) ).
thf(f1930,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) )
= sK3 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1929]) ).
thf(f1933,definition,
( spl0_29
<=> ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
thf(f1934,plain,
( ( ( setadjoin @ sK3 @ emptyset )
!= ( dsetconstr @ sK2 @ sK1 ) )
| spl0_29 ),
inference(avatar_component_clause,[],[f1933]) ).
thf(f1935,plain,
( ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1933]) ).
thf(f1937,definition,
( spl0_30
<=> ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X0 )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
thf(f1938,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X0 )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1937]) ).
thf(f1940,definition,
( spl0_31
<=> ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
thf(f1942,plain,
( ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $true )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1940]) ).
thf(f1979,plain,
( ( $false = $true )
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f102,f97]) ).
thf(f1982,plain,
( $false
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1979]) ).
thf(f1983,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1982]) ).
thf(f2004,definition,
( spl0_33
<=> ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
thf(f2006,plain,
( ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f2004]) ).
thf(f2038,plain,
( ( $false = $true )
| ~ spl0_22
| ~ spl0_24 ),
inference(superposition,[],[f160,f151]) ).
thf(f2044,plain,
( $false
| ~ spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f2038]) ).
thf(f2045,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f2044]) ).
thf(f2230,plain,
( ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $true )
| ~ spl0_25
| ~ spl0_29 ),
inference(superposition,[],[f1521,f1935]) ).
thf(f2273,plain,
( spl0_31
| ~ spl0_25
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f2230,f1933,f1519,f1940]) ).
thf(f2311,plain,
( ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( in @ ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( setadjoin @ sK3 @ emptyset ) )
= $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(superposition,[],[f313,f1930]) ).
thf(f2315,plain,
( ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( ( in @ ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( setadjoin @ sK3 @ emptyset ) )
= $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f2311,f227]) ).
thf(f2328,plain,
( ( ( in @ ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( setadjoin @ sK3 @ emptyset ) )
= $false )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(forward_demodulation,[],[f2315,f1521]) ).
thf(f2329,plain,
( ( ( in @ ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) ) @ ( setadjoin @ sK3 @ emptyset ) )
= $false )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f2328]) ).
thf(f2345,plain,
( ( $true != $true )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl0_23
| spl0_25 ),
inference(superposition,[],[f1520,f287]) ).
thf(f2354,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl0_23
| spl0_25 ),
inference(trivial_inequality_removal,[],[f2345]) ).
thf(f2361,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl0_23
| spl0_25 ),
inference(forward_demodulation,[],[f2354,f216]) ).
thf(f2362,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl0_23
| spl0_25 ),
inference(trivial_inequality_removal,[],[f2361]) ).
thf(f2365,plain,
( ( $false = $true )
| ~ spl0_23
| spl0_25 ),
inference(superposition,[],[f215,f2362]) ).
thf(f2369,plain,
( $false
| ~ spl0_23
| spl0_25 ),
inference(trivial_inequality_removal,[],[f2365]) ).
thf(f2370,plain,
( ~ spl0_23
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f2369]) ).
thf(f2386,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $true )
| ( ( sK4 @ ( setadjoin @ sK3 @ emptyset ) @ ( dsetconstr @ sK2 @ sK1 ) )
= X0 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29 ),
inference(forward_subsumption_resolution,[],[f1927,f1934]) ).
thf(f2390,plain,
( spl0_31
| spl0_30
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29 ),
inference(avatar_split_clause,[],[f2386,f1933,f1519,f127,f113,f91,f82,f55,f1937,f1940]) ).
thf(f2401,plain,
( ( $false = $true )
| ~ spl0_25
| ~ spl0_33 ),
inference(superposition,[],[f2006,f1521]) ).
thf(f2410,plain,
( $false
| ~ spl0_25
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f2401]) ).
thf(f2411,plain,
( ~ spl0_25
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f2410]) ).
thf(f2516,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( sK3 != X0 )
| ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) ) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_30 ),
inference(superposition,[],[f327,f1938]) ).
thf(f2522,plain,
( ! [X0: $i] :
( ( ( setadjoin @ sK3 @ emptyset )
= ( dsetconstr @ sK2 @ sK1 ) )
| ( $false
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f2516,f234]) ).
thf(f2525,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK1 ) @ ( setadjoin @ sK3 @ emptyset ) ) @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_9
| spl0_29
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f2522,f1934]) ).
thf(f2529,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(forward_demodulation,[],[f2525,f1930]) ).
thf(f2530,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false = $true )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(forward_demodulation,[],[f2529,f1521]) ).
thf(f2531,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f2530]) ).
thf(f2546,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(superposition,[],[f215,f2531]) ).
thf(f2584,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f2546]) ).
thf(f2590,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(superposition,[],[f2584,f216]) ).
thf(f2596,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f2590]) ).
thf(f2597,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f2596]) ).
thf(f2598,plain,
( ( ( in @ sK3 @ ( setadjoin @ sK3 @ emptyset ) )
= $false )
| ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25 ),
inference(superposition,[],[f2329,f1420]) ).
thf(f2605,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_31 ),
inference(forward_demodulation,[],[f2598,f1942]) ).
thf(f2606,plain,
( ( $false
= ( in @ sK3 @ ( dsetconstr @ sK2 @ sK1 ) ) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f2605]) ).
thf(f2607,plain,
( spl0_33
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f2606,f1940,f1519,f127,f113,f91,f82,f55,f2004]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f116]) ).
cnf(s9,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f134]) ).
cnf(s12,plain,
( spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f161]) ).
cnf(s13,plain,
spl0_22,
inference(sat_conversion,[],[f166]) ).
cnf(s14,plain,
spl0_15,
inference(sat_conversion,[],[f169]) ).
cnf(s15,plain,
spl0_5,
inference(sat_conversion,[],[f172]) ).
cnf(s16,plain,
spl0_3,
inference(sat_conversion,[],[f175]) ).
cnf(s17,plain,
spl0_20,
inference(sat_conversion,[],[f176]) ).
cnf(s18,plain,
spl0_11,
inference(sat_conversion,[],[f179]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f212]) ).
cnf(s20,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f243]) ).
cnf(s25,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f1542]) ).
cnf(s27,plain,
( ~ spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f1640]) ).
cnf(s33,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f1983]) ).
cnf(s46,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f2045]) ).
cnf(s57,plain,
( ~ spl0_25
| ~ spl0_29
| spl0_31 ),
inference(sat_conversion,[],[f2273]) ).
cnf(s71,plain,
( ~ spl0_23
| spl0_25 ),
inference(sat_conversion,[],[f2370]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| spl0_30
| spl0_31 ),
inference(sat_conversion,[],[f2390]) ).
cnf(s86,plain,
( ~ spl0_25
| ~ spl0_33 ),
inference(sat_conversion,[],[f2411]) ).
cnf(s89,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| spl0_29
| ~ spl0_30 ),
inference(sat_conversion,[],[f2597]) ).
cnf(s90,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_31
| spl0_33 ),
inference(sat_conversion,[],[f2607]) ).
cnf(s91,plain,
~ spl0_10,
inference(rat,[],[s33,s18]) ).
cnf(s92,plain,
~ spl0_18,
inference(rat,[],[s27,s17]) ).
cnf(s93,plain,
~ spl0_2,
inference(rat,[],[s19,s16]) ).
cnf(s94,plain,
~ spl0_8,
inference(rat,[],[s25,s15]) ).
cnf(s95,plain,
~ spl0_13,
inference(rat,[],[s20,s14]) ).
cnf(s96,plain,
~ spl0_24,
inference(rat,[],[s46,s13]) ).
cnf(s97,plain,
spl0_23,
inference(rat,[],[s12,s96]) ).
cnf(s98,plain,
spl0_25,
inference(rat,[],[s71,s97]) ).
cnf(s99,plain,
~ spl0_33,
inference(rat,[],[s86,s98]) ).
cnf(s100,plain,
spl0_17,
inference(rat,[],[s9,s92]) ).
cnf(s101,plain,
spl0_14,
inference(rat,[],[s7,s95]) ).
cnf(s102,plain,
spl0_9,
inference(rat,[],[s5,s91]) ).
cnf(s103,plain,
spl0_7,
inference(rat,[],[s4,s94]) ).
cnf(s104,plain,
spl0_1,
inference(rat,[],[s1,s93]) ).
cnf(s105,plain,
~ spl0_31,
inference(rat,[],[s90,s99,s103,s98,s100,s101,s102,s104]) ).
cnf(s108,plain,
~ spl0_29,
inference(rat,[],[s57,s98,s105]) ).
cnf(s109,plain,
~ spl0_30,
inference(rat,[],[s89,s104,s103,s98,s100,s101,s102,s108]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s82,s105,s104,s103,s98,s100,s101,s102,s109,s108]) ).
thf(f2608,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU637^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n019.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 14:01:18 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.33 Running higher-order theorem proving
% 0.29/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/0.57 % (815047)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.07/0.57 % (815056)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=311604210:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.07/0.57 % (815058)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.07/0.57 % (815058)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.07/0.57 % (815054)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1173398771:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.07/0.57 % (815052)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3466062296:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.07/0.57 % (815053)lrs+10_16_si=on:nwc=1.5:random_seed=3281044139:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.07/0.57 % (815056)Instruction limit reached!
% 1.07/0.57 % (815056)------------------------------
% 1.07/0.57 % (815056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (815056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (815056)CaDiCaL version: 2.1.3
% 1.07/0.57 % (815056)Termination reason: Instruction limit
% 1.07/0.57 % (815056)Termination phase: Saturation
% 1.07/0.57 % (815056)Time elapsed: 0.013 s
% 1.07/0.57 % (815056)Peak memory usage: 12 MB
% 1.07/0.57 % (815056)Instructions burned: 24 (million)
% 1.07/0.57 % (815055)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=3279527904:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.07/0.57 % (815057)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3742019911:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.07/0.57 % (815058)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=2214560684:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.07/0.57 % (815054)Instruction limit reached!
% 1.07/0.57 % (815054)------------------------------
% 1.07/0.57 % (815054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (815054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (815054)CaDiCaL version: 2.1.3
% 1.07/0.57 % (815054)Termination reason: Instruction limit
% 1.07/0.57 % (815054)Termination phase: Property scanning
% 1.07/0.57 % (815054)Time elapsed: 0.003 s
% 1.07/0.57 % (815054)Peak memory usage: 10 MB
% 1.07/0.57 % (815054)Instructions burned: 3 (million)
% 1.07/0.57 % (815053)Instruction limit reached!
% 1.07/0.57 % (815053)------------------------------
% 1.07/0.57 % (815053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (815053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (815053)CaDiCaL version: 2.1.3
% 1.07/0.57 % (815053)Termination reason: Instruction limit
% 1.07/0.57 % (815053)Termination phase: Saturation
% 1.07/0.57 % (815053)Time elapsed: 0.018 s
% 1.07/0.57 % (815053)Peak memory usage: 12 MB
% 1.07/0.57 % (815053)Instructions burned: 18 (million)
% 1.07/0.57 % (815066)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3414150045:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.07/0.57 % (815067)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=807821227:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.07/0.57 % (815066)Instruction limit reached!
% 1.07/0.57 % (815066)------------------------------
% 1.07/0.57 % (815066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (815066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (815066)CaDiCaL version: 2.1.3
% 1.07/0.57 % (815066)Termination reason: Instruction limit
% 1.07/0.57 % (815066)Termination phase: Property scanning
% 1.07/0.57 % (815066)Time elapsed: 0.004 s
% 1.07/0.57 % (815066)Peak memory usage: 11 MB
% 1.07/0.57 % (815066)Instructions burned: 3 (million)
% 1.07/0.57 % (815067)Instruction limit reached!
% 1.83/0.63 % (815067)------------------------------
% 1.83/0.63 % (815067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815067)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815067)Termination reason: Instruction limit
% 1.83/0.63 % (815067)Termination phase: Saturation
% 1.83/0.63 % (815067)Time elapsed: 0.006 s
% 1.83/0.63 % (815067)Peak memory usage: 11 MB
% 1.83/0.63 % (815067)Instructions burned: 5 (million)
% 1.83/0.63 % (815068)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.83/0.63 % (815068)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3650489431:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.83/0.63 % (815068)Instruction limit reached!
% 1.83/0.63 % (815068)------------------------------
% 1.83/0.63 % (815068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815068)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815068)Termination reason: Instruction limit
% 1.83/0.63 % (815068)Termination phase: Saturation
% 1.83/0.63 % (815068)Time elapsed: 0.007 s
% 1.83/0.63 % (815068)Peak memory usage: 12 MB
% 1.83/0.63 % (815068)Instructions burned: 7 (million)
% 1.83/0.63 % (815057)Instruction limit reached!
% 1.83/0.63 % (815057)------------------------------
% 1.83/0.63 % (815057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815057)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815057)Termination reason: Instruction limit
% 1.83/0.63 % (815057)Termination phase: Saturation
% 1.83/0.63 % (815057)Time elapsed: 0.070 s
% 1.83/0.63 % (815057)Peak memory usage: 13 MB
% 1.83/0.63 % (815057)Instructions burned: 75 (million)
% 1.83/0.63 % (815071)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=256716015:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.83/0.63 % (815072)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.83/0.63 % (815072)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.83/0.63 % (815058)Instruction limit reached!
% 1.83/0.63 % (815058)------------------------------
% 1.83/0.63 % (815058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815058)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815058)Termination reason: Instruction limit
% 1.83/0.63 % (815058)Termination phase: Saturation
% 1.83/0.63 % (815058)Time elapsed: 0.077 s
% 1.83/0.63 % (815058)Peak memory usage: 12 MB
% 1.83/0.63 % (815058)Instructions burned: 157 (million)
% 1.83/0.63 % (815072)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1017590939:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.83/0.63 % (815052)Instruction limit reached!
% 1.83/0.63 % (815052)------------------------------
% 1.83/0.63 % (815052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815052)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815052)Termination reason: Instruction limit
% 1.83/0.63 % (815052)Termination phase: Saturation
% 1.83/0.63 % (815052)Time elapsed: 0.081 s
% 1.83/0.63 % (815052)Peak memory usage: 13 MB
% 1.83/0.63 % (815052)Instructions burned: 87 (million)
% 1.83/0.63 % (815071)Instruction limit reached!
% 1.83/0.63 % (815071)------------------------------
% 1.83/0.63 % (815071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (815071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (815071)CaDiCaL version: 2.1.3
% 1.83/0.63 % (815071)Termination reason: Instruction limit
% 1.83/0.63 % (815071)Termination phase: Saturation
% 1.83/0.63 % (815071)Time elapsed: 0.012 s
% 1.83/0.63 % (815071)Peak memory usage: 12 MB
% 2.10/0.68 % (815071)Instructions burned: 12 (million)
% 2.10/0.68 % (815074)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=3257588547:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 2.10/0.68 % (815078)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 2.10/0.68 % (815078)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=45256567:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.10/0.68 % (815078)Instruction limit reached!
% 2.10/0.68 % (815078)------------------------------
% 2.10/0.68 % (815078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.68 % (815078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.68 % (815078)CaDiCaL version: 2.1.3
% 2.10/0.68 % (815078)Termination reason: Instruction limit
% 2.10/0.68 % (815078)Termination phase: Property scanning
% 2.10/0.68 % (815078)Time elapsed: 0.001 s
% 2.10/0.68 % (815078)Peak memory usage: 9 MB
% 2.10/0.68 % (815078)Instructions burned: 2 (million)
% 2.10/0.68 % (815072)Instruction limit reached!
% 2.10/0.68 % (815072)------------------------------
% 2.10/0.68 % (815072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.68 % (815072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.68 % (815072)CaDiCaL version: 2.1.3
% 2.10/0.68 % (815072)Termination reason: Instruction limit
% 2.10/0.68 % (815072)Termination phase: Saturation
% 2.10/0.68 % (815072)Time elapsed: 0.026 s
% 2.10/0.68 % (815072)Peak memory usage: 12 MB
% 2.10/0.68 % (815072)Instructions burned: 28 (million)
% 2.10/0.68 % (815076)lrs+10_1_si=on:cs=on:random_seed=4277033785:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.10/0.68 % (815076)Instruction limit reached!
% 2.10/0.68 % (815076)------------------------------
% 2.10/0.68 % (815076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.68 % (815076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.68 % (815076)CaDiCaL version: 2.1.3
% 2.10/0.68 % (815076)Termination reason: Instruction limit
% 2.10/0.68 % (815076)Termination phase: Saturation
% 2.10/0.68 % (815076)Time elapsed: 0.007 s
% 2.10/0.68 % (815076)Peak memory usage: 12 MB
% 2.10/0.68 % (815076)Instructions burned: 8 (million)
% 2.10/0.68 % (815079)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1804681992:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 2.10/0.68 % (815083)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=478960086:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.10/0.68 % (815080)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3930546694:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.10/0.68 % (815083)Instruction limit reached!
% 2.10/0.68 % (815083)------------------------------
% 2.10/0.68 % (815083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.68 % (815083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.68 % (815083)CaDiCaL version: 2.1.3
% 2.10/0.68 % (815083)Termination reason: Instruction limit
% 2.10/0.68 % (815083)Termination phase: Saturation
% 2.10/0.68 % (815083)Time elapsed: 0.014 s
% 2.10/0.68 % (815083)Peak memory usage: 12 MB
% 2.10/0.68 % (815083)Instructions burned: 25 (million)
% 2.10/0.68 % (815085)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2351803149:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.10/0.68 % (815087)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3573227410:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.10/0.68 % (815090)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2898475798:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.10/0.68 % (815079)Instruction limit reached!
% 2.10/0.68 % (815079)------------------------------
% 2.10/0.68 % (815079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.68 % (815079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815079)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815079)Termination reason: Instruction limit
% 2.85/0.81 % (815079)Termination phase: Saturation
% 2.85/0.81 % (815079)Time elapsed: 0.037 s
% 2.85/0.81 % (815079)Peak memory usage: 12 MB
% 2.85/0.81 % (815079)Instructions burned: 39 (million)
% 2.85/0.81 % (815085)Instruction limit reached!
% 2.85/0.81 % (815085)------------------------------
% 2.85/0.81 % (815085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.81 % (815085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815085)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815085)Termination reason: Instruction limit
% 2.85/0.81 % (815085)Termination phase: Saturation
% 2.85/0.81 % (815085)Time elapsed: 0.016 s
% 2.85/0.81 % (815085)Peak memory usage: 12 MB
% 2.85/0.81 % (815085)Instructions burned: 15 (million)
% 2.85/0.81 % (815090)Instruction limit reached!
% 2.85/0.81 % (815090)------------------------------
% 2.85/0.81 % (815090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.81 % (815090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815090)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815090)Termination reason: Instruction limit
% 2.85/0.81 % (815090)Termination phase: Saturation
% 2.85/0.81 % (815090)Time elapsed: 0.008 s
% 2.85/0.81 % (815090)Peak memory usage: 12 MB
% 2.85/0.81 % (815090)Instructions burned: 15 (million)
% 2.85/0.81 % (815074)Refutation not found, incomplete strategy
% 2.85/0.81 % (815074)------------------------------
% 2.85/0.81 % (815074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.81 % (815074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815074)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815074)Termination reason: Refutation not found, incomplete strategy
% 2.85/0.81 % (815074)Time elapsed: 0.069 s
% 2.85/0.81 % (815074)Peak memory usage: 12 MB
% 2.85/0.81 % (815074)Instructions burned: 74 (million)
% 2.85/0.81 % (815074)------------------------------
% 2.85/0.81 % (815074)------------------------------
% 2.85/0.81 % (815096)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3655297449:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.85/0.81 % (815094)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3194347129:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.85/0.81 % (815095)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=65465844:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.85/0.81 % (815094)Instruction limit reached!
% 2.85/0.81 % (815094)------------------------------
% 2.85/0.81 % (815094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.81 % (815094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815094)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815094)Termination reason: Instruction limit
% 2.85/0.81 % (815094)Termination phase: SInE selection
% 2.85/0.81 % (815094)Time elapsed: 0.002 s
% 2.85/0.81 % (815094)Peak memory usage: 10 MB
% 2.85/0.81 % (815094)Instructions burned: 2 (million)
% 2.85/0.81 % (815096)Instruction limit reached!
% 2.85/0.81 % (815096)------------------------------
% 2.85/0.81 % (815096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.81 % (815096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.81 % (815096)CaDiCaL version: 2.1.3
% 2.85/0.81 % (815096)Termination reason: Instruction limit
% 2.85/0.81 % (815096)Termination phase: Saturation
% 2.85/0.81 % (815096)Time elapsed: 0.013 s
% 2.85/0.81 % (815096)Peak memory usage: 11 MB
% 2.85/0.81 % (815096)Instructions burned: 24 (million)
% 2.85/0.81 % (815097)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3802127036:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.85/0.81 % (815102)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.85/0.81 % (815102)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=2534698613:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.85/0.81 % (815095)Instruction limit reached!
% 2.85/0.81 % (815095)------------------------------
% 2.85/0.89 % (815095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815095)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815095)Termination reason: Instruction limit
% 2.85/0.89 % (815095)Termination phase: Saturation
% 2.85/0.89 % (815095)Time elapsed: 0.027 s
% 2.85/0.89 % (815095)Peak memory usage: 12 MB
% 2.85/0.89 % (815095)Instructions burned: 26 (million)
% 2.85/0.89 % (815102)Instruction limit reached!
% 2.85/0.89 % (815102)------------------------------
% 2.85/0.89 % (815102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815102)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815102)Termination reason: Instruction limit
% 2.85/0.89 % (815102)Termination phase: Saturation
% 2.85/0.89 % (815102)Time elapsed: 0.005 s
% 2.85/0.89 % (815102)Peak memory usage: 12 MB
% 2.85/0.89 % (815102)Instructions burned: 10 (million)
% 2.85/0.89 % (815101)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.85/0.89 % (815101)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.85/0.89 % (815101)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=2744431709:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.85/0.89 % (815105)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=1806586611:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.85/0.89 % (815101)Instruction limit reached!
% 2.85/0.89 % (815101)------------------------------
% 2.85/0.89 % (815101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815101)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815101)Termination reason: Instruction limit
% 2.85/0.89 % (815101)Termination phase: Saturation
% 2.85/0.89 % (815101)Time elapsed: 0.014 s
% 2.85/0.89 % (815101)Peak memory usage: 12 MB
% 2.85/0.89 % (815101)Instructions burned: 15 (million)
% 2.85/0.89 % (815106)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2575366371:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.85/0.89 % (815105)Instruction limit reached!
% 2.85/0.89 % (815105)------------------------------
% 2.85/0.89 % (815105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815105)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815105)Termination reason: Instruction limit
% 2.85/0.89 % (815105)Termination phase: Saturation
% 2.85/0.89 % (815105)Time elapsed: 0.017 s
% 2.85/0.89 % (815105)Peak memory usage: 12 MB
% 2.85/0.89 % (815105)Instructions burned: 32 (million)
% 2.85/0.89 % (815106)Instruction limit reached!
% 2.85/0.89 % (815106)------------------------------
% 2.85/0.89 % (815106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815106)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815106)Termination reason: Instruction limit
% 2.85/0.89 % (815106)Termination phase: Saturation
% 2.85/0.89 % (815106)Time elapsed: 0.008 s
% 2.85/0.89 % (815106)Peak memory usage: 12 MB
% 2.85/0.89 % (815106)Instructions burned: 7 (million)
% 2.85/0.89 % (815097)Instruction limit reached!
% 2.85/0.89 % (815097)------------------------------
% 2.85/0.89 % (815097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.89 % (815097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.89 % (815097)CaDiCaL version: 2.1.3
% 2.85/0.89 % (815097)Termination reason: Instruction limit
% 2.85/0.89 % (815097)Termination phase: Saturation
% 2.85/0.89 % (815097)Time elapsed: 0.061 s
% 2.85/0.89 % (815097)Peak memory usage: 12 MB
% 2.85/0.89 % (815097)Instructions burned: 60 (million)
% 2.85/0.89 % (815109)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1182432522:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 3.39/1.02 % (815111)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1613699448:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 3.39/1.02 % (815111)Instruction limit reached!
% 3.39/1.02 % (815111)------------------------------
% 3.39/1.02 % (815111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815111)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815111)Termination reason: Instruction limit
% 3.39/1.02 % (815111)Termination phase: Saturation
% 3.39/1.02 % (815111)Time elapsed: 0.012 s
% 3.39/1.02 % (815111)Peak memory usage: 12 MB
% 3.39/1.02 % (815111)Instructions burned: 21 (million)
% 3.39/1.02 % (815109)Instruction limit reached!
% 3.39/1.02 % (815109)------------------------------
% 3.39/1.02 % (815109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815109)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815109)Termination reason: Instruction limit
% 3.39/1.02 % (815109)Termination phase: Saturation
% 3.39/1.02 % (815109)Time elapsed: 0.019 s
% 3.39/1.02 % (815109)Peak memory usage: 11 MB
% 3.39/1.02 % (815109)Instructions burned: 23 (million)
% 3.39/1.02 % (815112)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2197160617:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 3.39/1.02 % (815113)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2382550380:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 3.39/1.02 % (815116)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4194196757:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 3.39/1.02 % (815118)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=396392927:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.39/1.02 % (815080)Instruction limit reached!
% 3.39/1.02 % (815080)------------------------------
% 3.39/1.02 % (815080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815080)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815080)Termination reason: Instruction limit
% 3.39/1.02 % (815080)Termination phase: Saturation
% 3.39/1.02 % (815080)Time elapsed: 0.220 s
% 3.39/1.02 % (815080)Peak memory usage: 13 MB
% 3.39/1.02 % (815080)Instructions burned: 249 (million)
% 3.39/1.02 % (815118)Instruction limit reached!
% 3.39/1.02 % (815118)------------------------------
% 3.39/1.02 % (815118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815118)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815118)Termination reason: Instruction limit
% 3.39/1.02 % (815118)Termination phase: Saturation
% 3.39/1.02 % (815118)Time elapsed: 0.035 s
% 3.39/1.02 % (815118)Peak memory usage: 12 MB
% 3.39/1.02 % (815118)Instructions burned: 42 (million)
% 3.39/1.02 % (815122)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.39/1.02 % (815122)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3016808419:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.39/1.02 % (815122)Instruction limit reached!
% 3.39/1.02 % (815122)------------------------------
% 3.39/1.02 % (815122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815122)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815122)Termination reason: Instruction limit
% 3.39/1.02 % (815122)Termination phase: Saturation
% 3.39/1.02 % (815122)Time elapsed: 0.007 s
% 3.39/1.02 % (815122)Peak memory usage: 12 MB
% 3.39/1.02 % (815122)Instructions burned: 8 (million)
% 3.39/1.02 % (815123)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=873207711:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/181Mi)
% 3.39/1.02 % (815116)Instruction limit reached!
% 3.39/1.02 % (815116)------------------------------
% 3.39/1.02 % (815116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815116)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815116)Termination reason: Instruction limit
% 3.39/1.02 % (815116)Termination phase: Saturation
% 3.39/1.02 % (815116)Time elapsed: 0.089 s
% 3.39/1.02 % (815116)Peak memory usage: 13 MB
% 3.39/1.02 % (815116)Instructions burned: 194 (million)
% 3.39/1.02 % (815127)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.39/1.02 % (815127)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1362663583:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 3.39/1.02 % (815125)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=1696164559:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2995 on theBenchmark for (2995ds/169Mi)
% 3.39/1.02 % (815127)Instruction limit reached!
% 3.39/1.02 % (815127)------------------------------
% 3.39/1.02 % (815127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815127)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815127)Termination reason: Instruction limit
% 3.39/1.02 % (815127)Termination phase: Saturation
% 3.39/1.02 % (815127)Time elapsed: 0.003 s
% 3.39/1.02 % (815127)Peak memory usage: 11 MB
% 3.39/1.02 % (815127)Instructions burned: 6 (million)
% 3.39/1.02 % (815113)Instruction limit reached!
% 3.39/1.02 % (815113)------------------------------
% 3.39/1.02 % (815113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815113)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815113)Termination reason: Instruction limit
% 3.39/1.02 % (815113)Termination phase: Saturation
% 3.39/1.02 % (815113)Time elapsed: 0.126 s
% 3.39/1.02 % (815113)Peak memory usage: 13 MB
% 3.39/1.02 % (815113)Instructions burned: 143 (million)
% 3.39/1.02 % (815130)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1326087629:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 3.39/1.02 % (815087)Instruction limit reached!
% 3.39/1.02 % (815087)------------------------------
% 3.39/1.02 % (815087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815087)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815087)Termination reason: Instruction limit
% 3.39/1.02 % (815087)Termination phase: Saturation
% 3.39/1.02 % (815087)Time elapsed: 0.289 s
% 3.39/1.02 % (815087)Peak memory usage: 13 MB
% 3.39/1.02 % (815087)Instructions burned: 327 (million)
% 3.39/1.02 % (815130)Instruction limit reached!
% 3.39/1.02 % (815130)------------------------------
% 3.39/1.02 % (815130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815130)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815130)Termination reason: Instruction limit
% 3.39/1.02 % (815130)Termination phase: Saturation
% 3.39/1.02 % (815130)Time elapsed: 0.012 s
% 3.39/1.02 % (815130)Peak memory usage: 12 MB
% 3.39/1.02 % (815130)Instructions burned: 24 (million)
% 3.39/1.02 % (815131)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2175841346:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 3.39/1.02 % (815134)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=3572749647:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 3.39/1.02 % (815133)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=3195270081:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 3.39/1.02 % (815131)Instruction limit reached!
% 3.39/1.02 % (815131)------------------------------
% 3.39/1.02 % (815131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815131)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815131)Termination reason: Instruction limit
% 3.39/1.02 % (815131)Termination phase: Saturation
% 3.39/1.02 % (815131)Time elapsed: 0.019 s
% 3.39/1.02 % (815131)Peak memory usage: 12 MB
% 3.39/1.02 % (815131)Instructions burned: 19 (million)
% 3.39/1.02 % (815138)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=1048142918:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2994 on theBenchmark for (2994ds/45Mi)
% 3.39/1.02 % (815138)Instruction limit reached!
% 3.39/1.02 % (815138)------------------------------
% 3.39/1.02 % (815138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815138)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815138)Termination reason: Instruction limit
% 3.39/1.02 % (815138)Termination phase: Saturation
% 3.39/1.02 % (815138)Time elapsed: 0.042 s
% 3.39/1.02 % (815138)Peak memory usage: 12 MB
% 3.39/1.02 % (815138)Instructions burned: 45 (million)
% 3.39/1.02 % (815055)Instruction limit reached!
% 3.39/1.02 % (815055)------------------------------
% 3.39/1.02 % (815055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815055)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815055)Termination reason: Instruction limit
% 3.39/1.02 % (815055)Termination phase: Saturation
% 3.39/1.02 % (815055)Time elapsed: 0.553 s
% 3.39/1.02 % (815055)Peak memory usage: 14 MB
% 3.39/1.02 % (815055)Instructions burned: 634 (million)
% 3.39/1.02 % (815123)Instruction limit reached!
% 3.39/1.02 % (815123)------------------------------
% 3.39/1.02 % (815123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815123)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815123)Termination reason: Instruction limit
% 3.39/1.02 % (815123)Termination phase: Saturation
% 3.39/1.02 % (815123)Time elapsed: 0.165 s
% 3.39/1.02 % (815123)Peak memory usage: 13 MB
% 3.39/1.02 % (815123)Instructions burned: 181 (million)
% 3.39/1.02 % (815125)Instruction limit reached!
% 3.39/1.02 % (815125)------------------------------
% 3.39/1.02 % (815125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.02 % (815125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.02 % (815125)CaDiCaL version: 2.1.3
% 3.39/1.02 % (815125)Termination reason: Instruction limit
% 3.39/1.02 % (815125)Termination phase: Saturation
% 3.39/1.02 % (815125)Time elapsed: 0.147 s
% 3.39/1.02 % (815125)Peak memory usage: 13 MB
% 3.39/1.02 % (815125)Instructions burned: 169 (million)
% 3.39/1.02 % (815140)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2676860144:i=480:rtra=on_2994 on theBenchmark for (2994ds/480Mi)
% 3.39/1.02 % (815142)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.39/1.02 % (815112) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-815047-815112"...
% 3.39/1.02 % (815141)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=120181556:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2993 on theBenchmark for (2993ds/21Mi)
% 3.39/1.02 % (815142)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3474826645:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/200Mi)
% 3.39/1.02 % (815143)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4073899093:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2993 on theBenchmark for (2993ds/13Mi)
% 3.39/1.02 % (815112)...printing done.
% 3.39/1.02 % (815112)Refutation found. Thanks to Tanya!
% 3.39/1.02 % SZS status Theorem for theBenchmark
% 3.39/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.03 % (815112)------------------------------
% 3.39/1.03 % (815112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.39/1.03 % (815112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.03 % (815112)CaDiCaL version: 2.1.3
% 3.39/1.03 % (815112)Termination reason: Refutation
% 3.39/1.03 % (815112)Time elapsed: 0.310 s
% 3.39/1.03 % (815112)Peak memory usage: 14 MB
% 3.39/1.03 % (815112)Instructions burned: 356 (million)
% 3.39/1.03 % (815047)Success in time 0.654 s
% 3.39/1.03 % Vampire exiting
%------------------------------------------------------------------------------