%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU639^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 2.88s 0.74s
% Output : Refutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 32
% Syntax : Number of formulae : 327 ( 100 unt; 0 typ; 23 def)
% Number of atoms : 2628 ( 510 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 3918 ( 435 ~; 586 |; 25 &;2316 @)
% ( 23 <=>; 317 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 51 usr; 36 con; 0-4 aty)
% ( 195 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 501 ( 0 sgn 218 !; 2 ?; 501 :)
% 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,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_13,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
sK3: $i > $o ).
thf(func_def_30,type,
sK4: $i > $i > $i ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f3,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(f5,axiom,
( uniqinunit
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(f6,axiom,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(f7,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f8,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f9,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(f10,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,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(f14,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,[],[f13]) ).
thf(f15,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X0 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f18,plain,
( $true
= ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f22,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f24,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f26,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
inference(rectify,[],[f7]) ).
thf(f28,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f30,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f32,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,[],[f14]) ).
thf(f33,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f34,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f35,plain,
( $true
= ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f36,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f37,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f40,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f37,f31]) ).
thf(f41,plain,
( ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( ( setadjoin @ Y6 @ emptyset )
= Y5 )
& ( in @ Y6 @ Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f35,f40]) ).
thf(f42,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f43,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f44,plain,
( $true
= ( ~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f45,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f47,plain,
( ( dsetconstrI = $false )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f49,plain,
( ( dsetconstrER = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f43]) ).
thf(f50,plain,
( $false
= ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f52,plain,
( ( setext = $false )
| ( $true
= ( !! @ $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(iff_proxy_clausification,[],[f32]) ).
thf(f54,plain,
( ( dsetconstrEL = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f56,plain,
( ( eqinunit = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f36]) ).
thf(f58,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true )
| ( uniqinunit = $false ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f60,definition,
( spl0_1
<=> ( dsetconstrI = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f62,plain,
( ( dsetconstrI = $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f64,definition,
( spl0_2
<=> ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f66,plain,
( ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f47,f64,f60]) ).
thf(f69,definition,
( spl0_3
<=> ( dsetconstrI = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f71,plain,
( ( dsetconstrI = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f78,definition,
( spl0_5
<=> ( dsetconstrER = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f80,plain,
( ( dsetconstrER = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f82,definition,
( spl0_6
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f84,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f85,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f49,f82,f78]) ).
thf(f87,definition,
( spl0_7
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f89,plain,
( ( dsetconstrER = $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f95,plain,
( ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f96,plain,
dsetconstrI = $true,
inference(imp_proxy_clausification,[],[f50]) ).
thf(f98,definition,
( spl0_9
<=> ( setext = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f100,plain,
( ( setext = $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f102,definition,
( spl0_10
<=> ( $true
= ( !! @ $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 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f104,plain,
( ( $true
= ( !! @ $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 ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f105,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f52,f102,f98]) ).
thf(f107,definition,
( spl0_11
<=> ( setext = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f109,plain,
( ( setext = $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f116,definition,
( spl0_13
<=> ( dsetconstrEL = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f118,plain,
( ( dsetconstrEL = $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f125,definition,
( spl0_15
<=> ( dsetconstrEL = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f127,plain,
( ( dsetconstrEL = $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f129,definition,
( spl0_16
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f131,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f132,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f129,f125]) ).
thf(f134,definition,
( spl0_17
<=> ( eqinunit = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f136,plain,
( ( eqinunit = $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f134]) ).
thf(f138,definition,
( spl0_18
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
thf(f140,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f141,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f56,f138,f134]) ).
thf(f143,definition,
( spl0_19
<=> ( eqinunit = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
thf(f145,plain,
( ( eqinunit = $true )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f156,definition,
( spl0_22
<=> ( uniqinunit = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f158,plain,
( ( uniqinunit = $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f156]) ).
thf(f161,definition,
( spl0_23
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
thf(f163,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f165,definition,
( spl0_24
<=> ( uniqinunit = $false ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
thf(f167,plain,
( ( uniqinunit = $false )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f168,plain,
( spl0_23
| spl0_24 ),
inference(avatar_split_clause,[],[f58,f165,f161]) ).
thf(f169,plain,
( $false
= ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f170,plain,
dsetconstrEL = $true,
inference(imp_proxy_clausification,[],[f95]) ).
thf(f171,plain,
spl0_3,
inference(avatar_split_clause,[],[f96,f69]) ).
thf(f172,plain,
spl0_13,
inference(avatar_split_clause,[],[f170,f116]) ).
thf(f173,plain,
( $false
= ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f174,plain,
dsetconstrER = $true,
inference(imp_proxy_clausification,[],[f169]) ).
thf(f175,plain,
( $false
= ( uniqinunit
=> ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f176,plain,
setext = $true,
inference(imp_proxy_clausification,[],[f173]) ).
thf(f177,plain,
spl0_7,
inference(avatar_split_clause,[],[f174,f87]) ).
thf(f178,plain,
( $false
= ( eqinunit
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f179,plain,
uniqinunit = $true,
inference(imp_proxy_clausification,[],[f175]) ).
thf(f180,plain,
spl0_11,
inference(avatar_split_clause,[],[f176,f107]) ).
thf(f181,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f182,plain,
eqinunit = $true,
inference(imp_proxy_clausification,[],[f178]) ).
thf(f183,plain,
spl0_22,
inference(avatar_split_clause,[],[f179,f156]) ).
thf(f184,plain,
spl0_19,
inference(avatar_split_clause,[],[f182,f143]) ).
thf(f185,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f186,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ sK1 @ Y0 )
=> ( ( Y1 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( sK1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ sK1 @ Y0 )
=> ( ( Y1 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( sK1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ sK1 @ sK2 )
=> ( ( Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 @ Y1 )
=> ( sK1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ sK2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( in @ sK1 @ sK2 )
=> ( ( Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( Y0 @ Y1 )
=> ( sK1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ sK2 @ Y0 ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( $false
= ( ( in @ sK1 @ sK2 )
=> ( ( sK3 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( sK1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( $false
= ( ( sK3 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( sK1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( sK1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( $true
= ( sK3 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f191]) ).
thf(f195,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( sK1 = Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f212,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f89,f80]) ).
thf(f213,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f212]) ).
thf(f214,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( sK3 @ Y0 )
=> ( sK1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f216,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( sK3 @ X1 )
=> ( sK1 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $true
= ( ( sK3 @ X1 )
=> ( sK1 = X1 ) ) )
| ( $false
= ( in @ X1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( $true
= ( sK1 = X1 ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK2 ) )
| ( sK1 = X1 )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f218]) ).
thf(f224,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ Y0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f227,plain,
! [X1: $i] :
( $false
= ( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
& ( in @ X1 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f228,plain,
! [X1: $i] :
( ( $false
= ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( in @ X1 @ ( dsetconstr @ sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( dsetconstr @ sK2 @ sK3 ) )
| ( ( in @ X1 @ ( dsetconstr @ sK2 @ sK3 ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f228]) ).
thf(f232,plain,
( ( $true = $false )
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f109,f100]) ).
thf(f233,plain,
( $false
| ~ spl0_9
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f234,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f233]) ).
thf(f237,plain,
( ( $true = $false )
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f127,f118]) ).
thf(f243,plain,
( $false
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f244,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f243]) ).
thf(f248,plain,
( ( $true = $false )
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f145,f136]) ).
thf(f249,plain,
( $false
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f250,plain,
( ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f249]) ).
thf(f253,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 )
= $true )
| ~ spl0_18 ),
inference(pi_proxy_clausification,[],[f140]) ).
thf(f254,plain,
( ! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) )
| ~ spl0_18 ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) )
| ~ spl0_18 ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ~ spl0_18 ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
( ! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $false )
| ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ~ spl0_18 ),
inference(imp_proxy_clausification,[],[f256]) ).
thf(f258,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 != X2 ) )
| ~ spl0_18 ),
inference(equality_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) )
| ~ spl0_23 ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f260,plain,
( ! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) ) ) )
| ~ spl0_23 ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) )
| ~ spl0_23 ),
inference(pi_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X2 = X1 ) ) )
| ~ spl0_23 ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ~ spl0_23 ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( X1 = X2 ) )
| ~ spl0_23 ),
inference(equality_proxy_clausification,[],[f263]) ).
thf(f269,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f270,plain,
( ! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) )
| ~ spl0_6 ),
inference(beta-eta_normalization,[],[f269]) ).
thf(f271,plain,
( ! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) )
| ~ spl0_6 ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f272,plain,
( ! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) )
| ~ spl0_6 ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) )
| ~ spl0_6 ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) )
| ~ spl0_6 ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( X2 @ X1 )
= $true ) )
| ~ spl0_6 ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f278,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_16 ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f279,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_16 ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ X1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_16 ),
inference(pi_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( in @ X1 @ X2 ) ) ) )
| ~ spl0_16 ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( in @ X1 @ X2 ) )
@ X3 ) )
| ~ spl0_16 ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( in @ X1 @ X2 ) ) )
| ~ spl0_16 ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
( ! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
= $false )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ~ spl0_16 ),
inference(imp_proxy_clausification,[],[f283]) ).
thf(f287,plain,
( ! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f288,plain,
( ! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
( ! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f288]) ).
thf(f290,plain,
( ! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f289]) ).
thf(f291,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f292,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f293,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false ) )
| ~ spl0_2 ),
inference(imp_proxy_clausification,[],[f292]) ).
thf(f294,plain,
( ! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
= $true )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( X1 @ X3 )
= $false ) )
| ~ spl0_2 ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f303,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_10 ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f304,plain,
( ! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,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_10 ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( X2 = X1 ) ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f307]) ).
thf(f309,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( X1 = X2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false ) )
| ~ spl0_10 ),
inference(equality_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK4 @ X1 @ X2 ) ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(sigma_proxy_clausification,[],[f309]) ).
thf(f312,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $false
= ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f310]) ).
thf(f314,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( X1 = X2 )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f315,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f316,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X2 @ X1 ) ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(sigma_proxy_clausification,[],[f314]) ).
thf(f318,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
=> ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) )
= $false ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f320,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) )
| ( X1 = X2 )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f321,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X2 @ X1 ) @ X1 ) )
| ( $false
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f322,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( $true = $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( $false
= ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ X1 ) ) )
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f320,f258]) ).
thf(f328,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( $false
= ( in @ ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ X1 ) )
| ( ( setadjoin @ X0 @ emptyset )
= X1 ) )
| ~ spl0_10
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f322]) ).
thf(f333,plain,
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X2 @ X1 ) ) )
| ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) ) )
| ~ spl0_10 ),
inference(sigma_proxy_clausification,[],[f315]) ).
thf(f336,plain,
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) )
| ( ( ( in @ ( sK4 @ X2 @ X1 ) @ X1 )
=> ( in @ ( sK4 @ X2 @ X1 ) @ X2 ) )
= $false ) )
| ~ spl0_10 ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f338,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X2 @ X1 ) @ X1 ) )
| ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) )
| ~ spl0_10 ),
inference(imp_proxy_clausification,[],[f336]) ).
thf(f339,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
| ( $false
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ ( setadjoin @ X1 @ emptyset ) ) )
| ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( $true = $false ) )
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f321,f264]) ).
thf(f340,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X0 )
| ( $false
= ( in @ ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ X0 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) )
| ( $true = $false ) )
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f321,f284]) ).
thf(f345,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( dsetconstr @ X1 @ X2 )
= X0 )
| ( $true
= ( X2 @ ( sK4 @ X0 @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ( $false
= ( in @ ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ X0 ) @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f275,f321]) ).
thf(f348,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ X0 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( ( dsetconstr @ X1 @ X2 )
= X0 )
| ( $true
= ( X2 @ ( sK4 @ X0 @ ( dsetconstr @ X1 @ X2 ) ) ) ) )
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f345]) ).
thf(f349,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ ( setadjoin @ X1 @ emptyset ) ) )
| ( ( setadjoin @ X1 @ emptyset )
= X0 )
| ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) )
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f339]) ).
thf(f353,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ X0 ) @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $true
= ( in @ ( sK4 @ X0 @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) )
| ( ( dsetconstr @ X1 @ X2 )
= X0 ) )
| ~ spl0_10
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f362,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( $true
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ X0 ) )
| ( ( setadjoin @ X1 @ emptyset )
= X0 ) )
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f264,f338]) ).
thf(f371,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ X1 @ emptyset ) @ X0 ) @ X0 ) )
| ( ( setadjoin @ X1 @ emptyset )
= X0 )
| ( ( sK4 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) )
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f401,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) )
| ( $true = $false )
| ( $true
= ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) ) )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f371,f284]) ).
thf(f402,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) )
| ( $true
= ( X2 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $true = $false ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f371,f275]) ).
thf(f408,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( X2 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) ) )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f402]) ).
thf(f412,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X0 @ emptyset ) )
| ( ( sK4 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f446,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( $true = $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_23 ),
inference(superposition,[],[f349,f258]) ).
thf(f449,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= X0 )
| ( ( setadjoin @ X0 @ emptyset )
= X1 )
| ( ( sK4 @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f718,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ X1 ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) )
= $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= sK1 ) )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f219,f412]) ).
thf(f723,plain,
( ! [X0: $i,X1: $i > $o] :
( ( ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) ) )
= $false )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ X1 ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ X1 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ X1 ) )
= sK1 ) )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f718]) ).
thf(f739,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $true = $false )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f723,f408]) ).
thf(f743,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $true = $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f739]) ).
thf(f744,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f743]) ).
thf(f748,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $true
= ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f353,f744]) ).
thf(f749,plain,
( ! [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f348,f744]) ).
thf(f756,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f748]) ).
thf(f761,plain,
( ! [X0: $i] :
( ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f749]) ).
thf(f763,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f756,f229]) ).
thf(f765,plain,
( ! [X0: $i] :
( ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f761,f229]) ).
thf(f790,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f763,f219]) ).
thf(f792,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( $true = $false )
| ( ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f790]) ).
thf(f793,plain,
( ! [X0: $i] :
( ( ( sK3 @ ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f792]) ).
thf(f860,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f793,f765]) ).
thf(f867,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f860]) ).
thf(f868,plain,
( ! [X0: $i] :
( ( ( sK4 @ ( setadjoin @ X0 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f867]) ).
thf(f889,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( setadjoin @ X0 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( sK1 != X0 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23 ),
inference(superposition,[],[f449,f868]) ).
thf(f896,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( in @ X0 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f889,f229]) ).
thf(f904,definition,
( spl0_25
<=> ( $true
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
thf(f905,plain,
( ( $true
!= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| spl0_25 ),
inference(avatar_component_clause,[],[f904]) ).
thf(f906,plain,
( ( $true
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f904]) ).
thf(f919,plain,
( ( $true = $false )
| ~ spl0_22
| ~ spl0_24 ),
inference(superposition,[],[f167,f158]) ).
thf(f924,plain,
( $false
| ~ spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f919]) ).
thf(f925,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f924]) ).
thf(f1094,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ( sK1 != sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23 ),
inference(imitation,[],[f896]) ).
thf(f1095,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23 ),
inference(equality_resolution,[],[f896]) ).
thf(f1096,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1094]) ).
thf(f1097,plain,
( ( $true = $false )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1096,f906]) ).
thf(f1098,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1097]) ).
thf(f1099,plain,
( ( $true = $false )
| ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1095,f906]) ).
thf(f1100,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1099]) ).
thf(f1120,plain,
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( setadjoin @ sK1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(superposition,[],[f353,f1098]) ).
thf(f1121,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( setadjoin @ sK1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(superposition,[],[f348,f1098]) ).
thf(f1129,plain,
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1120,f229]) ).
thf(f1139,definition,
( spl0_31
<=> ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
thf(f1141,plain,
( ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1139]) ).
thf(f1143,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1121,f229]) ).
thf(f1145,definition,
( spl0_32
<=> ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
thf(f1147,plain,
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1145]) ).
thf(f1164,plain,
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ( $true = $false )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1129,f906]) ).
thf(f1165,plain,
( ( $true
= ( in @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) @ sK2 ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1164]) ).
thf(f1166,plain,
( ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ( $true = $false )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1143,f906]) ).
thf(f1167,plain,
( ( $true
= ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) ) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1166]) ).
thf(f1173,plain,
( spl0_32
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1165,f904,f161,f138,f129,f102,f82,f1145]) ).
thf(f1174,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1167,f904,f161,f138,f129,f102,f82,f1139]) ).
thf(f1180,definition,
( spl0_35
<=> ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
thf(f1182,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1180]) ).
thf(f1184,definition,
( spl0_36
<=> ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
thf(f1186,plain,
( ( ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) )
= sK1 )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1184]) ).
thf(f1193,plain,
( ( $true != $true )
| ( ( sK3 @ sK1 )
= $false )
| ( ( in @ sK1 @ sK2 )
= $false )
| ~ spl0_2
| spl0_25 ),
inference(superposition,[],[f905,f294]) ).
thf(f1197,plain,
( ( ( in @ sK1 @ sK2 )
= $false )
| ( ( sK3 @ sK1 )
= $false )
| ~ spl0_2
| spl0_25 ),
inference(trivial_inequality_removal,[],[f1193]) ).
thf(f1199,plain,
( ( $true = $false )
| ( ( sK3 @ sK1 )
= $false )
| ~ spl0_2
| spl0_25 ),
inference(forward_demodulation,[],[f1197,f192]) ).
thf(f1200,plain,
( ( ( sK3 @ sK1 )
= $false )
| ~ spl0_2
| spl0_25 ),
inference(trivial_inequality_removal,[],[f1199]) ).
thf(f1204,plain,
( ( $true = $false )
| ~ spl0_2
| spl0_25 ),
inference(superposition,[],[f194,f1200]) ).
thf(f1208,plain,
( $false
| ~ spl0_2
| spl0_25 ),
inference(trivial_inequality_removal,[],[f1204]) ).
thf(f1209,plain,
( ~ spl0_2
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f1208]) ).
thf(f1213,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f62,f71]) ).
thf(f1218,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f1213]) ).
thf(f1219,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f1218]) ).
thf(f1306,plain,
( ( $true = $false )
| ~ spl0_25
| ~ spl0_35 ),
inference(forward_demodulation,[],[f906,f1182]) ).
thf(f1307,plain,
( $false
| ~ spl0_25
| ~ spl0_35 ),
inference(trivial_inequality_removal,[],[f1306]) ).
thf(f1308,plain,
( ~ spl0_25
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1307]) ).
thf(f1312,plain,
( spl0_36
| ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1100,f904,f161,f138,f129,f102,f82,f1184]) ).
thf(f1398,plain,
( ( $true = $false )
| ( ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ~ spl0_32 ),
inference(superposition,[],[f1147,f219]) ).
thf(f1400,plain,
( ( ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ( ( sK3 @ ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
= $false )
| ~ spl0_32 ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1402,plain,
( ( $true = $false )
| ( ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ~ spl0_31
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1400,f1141]) ).
thf(f1403,plain,
( ( ( sK4 @ ( setadjoin @ sK1 @ emptyset ) @ ( dsetconstr @ sK2 @ sK3 ) )
= sK1 )
| ~ spl0_31
| ~ spl0_32 ),
inference(trivial_inequality_removal,[],[f1402]) ).
thf(f1417,plain,
( ( ( setadjoin @ sK1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $false
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( sK1 != sK1 )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32 ),
inference(superposition,[],[f328,f1403]) ).
thf(f1421,plain,
( ( $false
= ( in @ ( sK4 @ ( dsetconstr @ sK2 @ sK3 ) @ ( setadjoin @ sK1 @ emptyset ) ) @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ( ( setadjoin @ sK1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32 ),
inference(trivial_inequality_removal,[],[f1417]) ).
thf(f1423,plain,
( ( ( setadjoin @ sK1 @ emptyset )
= ( dsetconstr @ sK2 @ sK3 ) )
| ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1421,f1186]) ).
thf(f1425,plain,
( ( $false
= ( in @ sK1 @ ( dsetconstr @ sK2 @ sK3 ) ) )
| ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f1423,f229]) ).
thf(f1428,plain,
( spl0_35
| ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f1425,f1184,f1145,f1139,f138,f102,f1180]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s5,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s8,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f132]) ).
cnf(s9,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f141]) ).
cnf(s12,plain,
( spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f168]) ).
cnf(s13,plain,
spl0_3,
inference(sat_conversion,[],[f171]) ).
cnf(s14,plain,
spl0_13,
inference(sat_conversion,[],[f172]) ).
cnf(s15,plain,
spl0_7,
inference(sat_conversion,[],[f177]) ).
cnf(s16,plain,
spl0_11,
inference(sat_conversion,[],[f180]) ).
cnf(s17,plain,
spl0_22,
inference(sat_conversion,[],[f183]) ).
cnf(s18,plain,
spl0_19,
inference(sat_conversion,[],[f184]) ).
cnf(s19,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f214]) ).
cnf(s20,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f234]) ).
cnf(s22,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f244]) ).
cnf(s23,plain,
( ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f250]) ).
cnf(s28,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f925]) ).
cnf(s37,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25
| spl0_32 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s38,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25
| spl0_31 ),
inference(sat_conversion,[],[f1174]) ).
cnf(s48,plain,
( ~ spl0_2
| spl0_25 ),
inference(sat_conversion,[],[f1209]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f1219]) ).
cnf(s52,plain,
( ~ spl0_25
| ~ spl0_35 ),
inference(sat_conversion,[],[f1308]) ).
cnf(s55,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_16
| ~ spl0_18
| ~ spl0_23
| ~ spl0_25
| spl0_36 ),
inference(sat_conversion,[],[f1312]) ).
cnf(s75,plain,
( ~ spl0_10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_32
| spl0_35
| ~ spl0_36 ),
inference(sat_conversion,[],[f1428]) ).
cnf(s77,plain,
~ spl0_17,
inference(rat,[],[s23,s18]) ).
cnf(s78,plain,
~ spl0_24,
inference(rat,[],[s28,s17]) ).
cnf(s79,plain,
~ spl0_9,
inference(rat,[],[s20,s16]) ).
cnf(s80,plain,
~ spl0_5,
inference(rat,[],[s19,s15]) ).
cnf(s81,plain,
~ spl0_15,
inference(rat,[],[s22,s14]) ).
cnf(s82,plain,
~ spl0_1,
inference(rat,[],[s50,s13]) ).
cnf(s83,plain,
spl0_23,
inference(rat,[],[s12,s78]) ).
cnf(s84,plain,
spl0_18,
inference(rat,[],[s9,s77]) ).
cnf(s85,plain,
spl0_16,
inference(rat,[],[s8,s81]) ).
cnf(s86,plain,
spl0_10,
inference(rat,[],[s5,s79]) ).
cnf(s87,plain,
spl0_6,
inference(rat,[],[s3,s80]) ).
cnf(s88,plain,
spl0_2,
inference(rat,[],[s1,s82]) ).
cnf(s89,plain,
spl0_25,
inference(rat,[],[s48,s88]) ).
cnf(s90,plain,
~ spl0_35,
inference(rat,[],[s52,s89]) ).
cnf(s91,plain,
spl0_36,
inference(rat,[],[s55,s87,s86,s83,s84,s85,s89]) ).
cnf(s93,plain,
spl0_31,
inference(rat,[],[s38,s87,s86,s83,s84,s85,s89]) ).
cnf(s94,plain,
spl0_32,
inference(rat,[],[s37,s87,s86,s83,s84,s85,s89]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s75,s91,s90,s86,s84,s94,s93]) ).
thf(f1430,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU639^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n001.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 14:07:06 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.09/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.98/0.46 % (1292749)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.98/0.46 % (1292762)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.98/0.46 % (1292762)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.98/0.46 % (1292762)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=127307372:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.98/0.46 % (1292757)lrs+10_16_si=on:nwc=1.5:random_seed=3486772069:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.98/0.46 % (1292758)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2183494754:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.98/0.46 % (1292756)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3347201470:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.98/0.46 % (1292760)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4048345403:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.98/0.46 % (1292759)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=362800636:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.98/0.46 % (1292761)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1485732305:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.98/0.46 % (1292758)Instruction limit reached!
% 0.98/0.46 % (1292758)------------------------------
% 0.98/0.46 % (1292758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.46 % (1292758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.46 % (1292758)CaDiCaL version: 2.1.3
% 0.98/0.46 % (1292758)Termination reason: Instruction limit
% 0.98/0.46 % (1292758)Termination phase: Saturation
% 0.98/0.46 % (1292758)Time elapsed: 0.004 s
% 0.98/0.46 % (1292758)Peak memory usage: 12 MB
% 0.98/0.46 % (1292758)Instructions burned: 4 (million)
% 0.98/0.46 % (1292757)Instruction limit reached!
% 0.98/0.46 % (1292757)------------------------------
% 0.98/0.46 % (1292757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.46 % (1292757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.46 % (1292757)CaDiCaL version: 2.1.3
% 0.98/0.46 % (1292757)Termination reason: Instruction limit
% 0.98/0.46 % (1292757)Termination phase: Saturation
% 0.98/0.46 % (1292757)Time elapsed: 0.011 s
% 0.98/0.46 % (1292757)Peak memory usage: 12 MB
% 0.98/0.46 % (1292757)Instructions burned: 18 (million)
% 0.98/0.46 % (1292773)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4285568725:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.98/0.46 % (1292760)Instruction limit reached!
% 0.98/0.46 % (1292760)------------------------------
% 0.98/0.46 % (1292760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.46 % (1292760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.46 % (1292760)CaDiCaL version: 2.1.3
% 0.98/0.46 % (1292760)Termination reason: Instruction limit
% 0.98/0.46 % (1292760)Termination phase: Saturation
% 0.98/0.46 % (1292760)Time elapsed: 0.023 s
% 0.98/0.46 % (1292760)Peak memory usage: 12 MB
% 0.98/0.46 % (1292760)Instructions burned: 24 (million)
% 0.98/0.46 % (1292773)Instruction limit reached!
% 0.98/0.46 % (1292773)------------------------------
% 0.98/0.46 % (1292773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.46 % (1292773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.46 % (1292773)CaDiCaL version: 2.1.3
% 0.98/0.46 % (1292773)Termination reason: Instruction limit
% 0.98/0.46 % (1292773)Termination phase: Saturation
% 0.98/0.46 % (1292773)Time elapsed: 0.004 s
% 0.98/0.46 % (1292773)Peak memory usage: 12 MB
% 0.98/0.46 % (1292773)Instructions burned: 6 (million)
% 0.98/0.46 % (1292772)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4114645060:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.69/0.52 % (1292772)Instruction limit reached!
% 1.69/0.52 % (1292772)------------------------------
% 1.69/0.52 % (1292772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292772)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292772)Termination reason: Instruction limit
% 1.69/0.52 % (1292772)Termination phase: Property scanning
% 1.69/0.52 % (1292772)Time elapsed: 0.005 s
% 1.69/0.52 % (1292772)Peak memory usage: 10 MB
% 1.69/0.52 % (1292772)Instructions burned: 2 (million)
% 1.69/0.52 % (1292776)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.69/0.52 % (1292777)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=350688492:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.69/0.52 % (1292776)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3490672861:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.69/0.52 % (1292762)Instruction limit reached!
% 1.69/0.52 % (1292762)------------------------------
% 1.69/0.52 % (1292762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292762)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292762)Termination reason: Instruction limit
% 1.69/0.52 % (1292762)Termination phase: Saturation
% 1.69/0.52 % (1292762)Time elapsed: 0.073 s
% 1.69/0.52 % (1292762)Peak memory usage: 12 MB
% 1.69/0.52 % (1292762)Instructions burned: 158 (million)
% 1.69/0.52 % (1292776)Instruction limit reached!
% 1.69/0.52 % (1292776)------------------------------
% 1.69/0.52 % (1292776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292776)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292776)Termination reason: Instruction limit
% 1.69/0.52 % (1292776)Termination phase: Saturation
% 1.69/0.52 % (1292776)Time elapsed: 0.007 s
% 1.69/0.52 % (1292776)Peak memory usage: 12 MB
% 1.69/0.52 % (1292776)Instructions burned: 7 (million)
% 1.69/0.52 % (1292780)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
% 1.69/0.52 % (1292780)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.69/0.52 % (1292777)Instruction limit reached!
% 1.69/0.52 % (1292777)------------------------------
% 1.69/0.52 % (1292777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292777)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292777)Termination reason: Instruction limit
% 1.69/0.52 % (1292777)Termination phase: Saturation
% 1.69/0.52 % (1292777)Time elapsed: 0.013 s
% 1.69/0.52 % (1292777)Peak memory usage: 12 MB
% 1.69/0.52 % (1292777)Instructions burned: 13 (million)
% 1.69/0.52 % (1292780)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=848139600:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.69/0.52 % (1292761)Instruction limit reached!
% 1.69/0.52 % (1292761)------------------------------
% 1.69/0.52 % (1292761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292761)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292761)Termination reason: Instruction limit
% 1.69/0.52 % (1292761)Termination phase: Saturation
% 1.69/0.52 % (1292761)Time elapsed: 0.069 s
% 1.69/0.52 % (1292761)Peak memory usage: 13 MB
% 1.69/0.52 % (1292761)Instructions burned: 75 (million)
% 1.69/0.52 % (1292756)Instruction limit reached!
% 1.69/0.52 % (1292756)------------------------------
% 1.69/0.52 % (1292756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1292756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1292756)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1292756)Termination reason: Instruction limit
% 1.69/0.57 % (1292756)Termination phase: Saturation
% 1.69/0.57 % (1292756)Time elapsed: 0.077 s
% 1.69/0.57 % (1292756)Peak memory usage: 13 MB
% 1.69/0.57 % (1292756)Instructions burned: 88 (million)
% 1.69/0.57 % (1292784)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=2743906639:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.69/0.57 % (1292780)Instruction limit reached!
% 1.69/0.57 % (1292780)------------------------------
% 1.69/0.57 % (1292780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.57 % (1292780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.57 % (1292780)CaDiCaL version: 2.1.3
% 1.69/0.57 % (1292780)Termination reason: Instruction limit
% 1.69/0.57 % (1292780)Termination phase: Saturation
% 1.69/0.57 % (1292780)Time elapsed: 0.016 s
% 1.69/0.57 % (1292780)Peak memory usage: 12 MB
% 1.69/0.57 % (1292780)Instructions burned: 28 (million)
% 1.69/0.57 % (1292790)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=82826533:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.69/0.57 % (1292788)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.69/0.57 % (1292788)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=546579264:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.69/0.57 % (1292788)Instruction limit reached!
% 1.69/0.57 % (1292788)------------------------------
% 1.69/0.57 % (1292788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.57 % (1292788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.57 % (1292788)CaDiCaL version: 2.1.3
% 1.69/0.57 % (1292788)Termination reason: Instruction limit
% 1.69/0.57 % (1292788)Termination phase: Property scanning
% 1.69/0.57 % (1292788)Time elapsed: 0.002 s
% 1.69/0.57 % (1292788)Peak memory usage: 10 MB
% 1.69/0.57 % (1292788)Instructions burned: 4 (million)
% 1.69/0.57 % (1292786)lrs+10_1_si=on:cs=on:random_seed=4025389043:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.69/0.57 % (1292789)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2490156050:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.69/0.57 % (1292786)Instruction limit reached!
% 1.69/0.57 % (1292786)------------------------------
% 1.69/0.57 % (1292786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.57 % (1292786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.57 % (1292786)CaDiCaL version: 2.1.3
% 1.69/0.57 % (1292786)Termination reason: Instruction limit
% 1.69/0.57 % (1292786)Termination phase: Saturation
% 1.69/0.57 % (1292786)Time elapsed: 0.007 s
% 1.69/0.57 % (1292786)Peak memory usage: 11 MB
% 1.69/0.57 % (1292786)Instructions burned: 8 (million)
% 1.69/0.57 % (1292792)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2433067143:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.69/0.57 % (1292799)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2869872260:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.69/0.57 % (1292802)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4152741855:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.69/0.57 % (1292792)Instruction limit reached!
% 1.69/0.57 % (1292792)------------------------------
% 1.69/0.57 % (1292792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.57 % (1292792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.57 % (1292792)CaDiCaL version: 2.1.3
% 1.69/0.57 % (1292792)Termination reason: Instruction limit
% 1.69/0.57 % (1292792)Termination phase: Saturation
% 1.69/0.57 % (1292792)Time elapsed: 0.025 s
% 1.69/0.57 % (1292792)Peak memory usage: 12 MB
% 1.69/0.57 % (1292792)Instructions burned: 25 (million)
% 1.69/0.57 % (1292789)Instruction limit reached!
% 1.69/0.57 % (1292789)------------------------------
% 1.69/0.57 % (1292789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.57 % (1292789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292789)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292789)Termination reason: Instruction limit
% 2.58/0.67 % (1292789)Termination phase: Saturation
% 2.58/0.67 % (1292789)Time elapsed: 0.037 s
% 2.58/0.67 % (1292789)Peak memory usage: 12 MB
% 2.58/0.67 % (1292789)Instructions burned: 39 (million)
% 2.58/0.67 % (1292799)Instruction limit reached!
% 2.58/0.67 % (1292799)------------------------------
% 2.58/0.67 % (1292799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.67 % (1292799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292799)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292799)Termination reason: Instruction limit
% 2.58/0.67 % (1292799)Termination phase: Saturation
% 2.58/0.67 % (1292799)Time elapsed: 0.015 s
% 2.58/0.67 % (1292799)Peak memory usage: 12 MB
% 2.58/0.67 % (1292799)Instructions burned: 16 (million)
% 2.58/0.67 % (1292784)Instruction limit reached!
% 2.58/0.67 % (1292784)------------------------------
% 2.58/0.67 % (1292784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.67 % (1292784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292784)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292784)Termination reason: Instruction limit
% 2.58/0.67 % (1292784)Termination phase: Saturation
% 2.58/0.67 % (1292784)Time elapsed: 0.074 s
% 2.58/0.67 % (1292784)Peak memory usage: 13 MB
% 2.58/0.67 % (1292784)Instructions burned: 86 (million)
% 2.58/0.67 % (1292808)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3450357510:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.58/0.67 % (1292809)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3725661259:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.58/0.67 % (1292809)Instruction limit reached!
% 2.58/0.67 % (1292809)------------------------------
% 2.58/0.67 % (1292809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.67 % (1292809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292809)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292809)Termination reason: Instruction limit
% 2.58/0.67 % (1292809)Termination phase: Property scanning
% 2.58/0.67 % (1292809)Time elapsed: 0.002 s
% 2.58/0.67 % (1292809)Peak memory usage: 10 MB
% 2.58/0.67 % (1292809)Instructions burned: 2 (million)
% 2.58/0.67 % (1292808)Instruction limit reached!
% 2.58/0.67 % (1292808)------------------------------
% 2.58/0.67 % (1292808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.67 % (1292808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292808)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292808)Termination reason: Instruction limit
% 2.58/0.67 % (1292808)Termination phase: Saturation
% 2.58/0.67 % (1292811)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4117926434:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.58/0.67 % (1292808)Time elapsed: 0.009 s
% 2.58/0.67 % (1292808)Peak memory usage: 12 MB
% 2.58/0.67 % (1292808)Instructions burned: 14 (million)
% 2.58/0.67 % (1292812)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2007750517:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.58/0.67 % (1292817)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3206562473:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.58/0.67 % (1292811)Instruction limit reached!
% 2.58/0.67 % (1292811)------------------------------
% 2.58/0.67 % (1292811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.67 % (1292811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.67 % (1292811)CaDiCaL version: 2.1.3
% 2.58/0.67 % (1292811)Termination reason: Instruction limit
% 2.58/0.67 % (1292811)Termination phase: Saturation
% 2.58/0.67 % (1292811)Time elapsed: 0.025 s
% 2.58/0.67 % (1292811)Peak memory usage: 12 MB
% 2.58/0.67 % (1292811)Instructions burned: 27 (million)
% 2.58/0.67 % (1292819)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
% 2.58/0.67 % (1292819)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.88/0.74 % (1292819)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=1412692535:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.88/0.74 % (1292790)Instruction limit reached!
% 2.88/0.74 % (1292790)------------------------------
% 2.88/0.74 % (1292790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292790)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292790)Termination reason: Instruction limit
% 2.88/0.74 % (1292790)Termination phase: Saturation
% 2.88/0.74 % (1292790)Time elapsed: 0.117 s
% 2.88/0.74 % (1292790)Peak memory usage: 13 MB
% 2.88/0.74 % (1292790)Instructions burned: 251 (million)
% 2.88/0.74 % (1292812)Instruction limit reached!
% 2.88/0.74 % (1292812)------------------------------
% 2.88/0.74 % (1292812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292812)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292812)Termination reason: Instruction limit
% 2.88/0.74 % (1292812)Termination phase: Saturation
% 2.88/0.74 % (1292812)Time elapsed: 0.021 s
% 2.88/0.74 % (1292812)Peak memory usage: 11 MB
% 2.88/0.74 % (1292812)Instructions burned: 23 (million)
% 2.88/0.74 % (1292819)Instruction limit reached!
% 2.88/0.74 % (1292819)------------------------------
% 2.88/0.74 % (1292819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292819)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292819)Termination reason: Instruction limit
% 2.88/0.74 % (1292819)Termination phase: Saturation
% 2.88/0.74 % (1292819)Time elapsed: 0.014 s
% 2.88/0.74 % (1292819)Peak memory usage: 12 MB
% 2.88/0.74 % (1292819)Instructions burned: 14 (million)
% 2.88/0.74 % (1292827)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.88/0.74 % (1292830)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=253419519:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.88/0.74 % (1292827)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=2782900230:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.88/0.74 % (1292830)Instruction limit reached!
% 2.88/0.74 % (1292830)------------------------------
% 2.88/0.74 % (1292830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292830)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292830)Termination reason: Instruction limit
% 2.88/0.74 % (1292830)Termination phase: Saturation
% 2.88/0.74 % (1292830)Time elapsed: 0.004 s
% 2.88/0.74 % (1292830)Peak memory usage: 12 MB
% 2.88/0.74 % (1292830)Instructions burned: 8 (million)
% 2.88/0.74 % (1292817)Instruction limit reached!
% 2.88/0.74 % (1292817)------------------------------
% 2.88/0.74 % (1292817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292817)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292817)Termination reason: Instruction limit
% 2.88/0.74 % (1292817)Termination phase: Saturation
% 2.88/0.74 % (1292817)Time elapsed: 0.039 s
% 2.88/0.74 % (1292817)Peak memory usage: 12 MB
% 2.88/0.74 % (1292817)Instructions burned: 60 (million)
% 2.88/0.74 % (1292829)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=579877010:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.88/0.74 % (1292827)Instruction limit reached!
% 2.88/0.74 % (1292827)------------------------------
% 2.88/0.74 % (1292827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292827)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292827)Termination reason: Instruction limit
% 2.88/0.74 % (1292827)Termination phase: Saturation
% 2.88/0.74 % (1292827)Time elapsed: 0.016 s
% 2.88/0.74 % (1292827)Peak memory usage: 12 MB
% 2.88/0.74 % (1292827)Instructions burned: 8 (million)
% 2.88/0.74 % (1292835)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=943665524:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.88/0.74 % (1292836)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1650771185:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.88/0.74 % (1292831)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=766056851:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.88/0.74 % (1292835)Instruction limit reached!
% 2.88/0.74 % (1292835)------------------------------
% 2.88/0.74 % (1292835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292835)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292835)Termination reason: Instruction limit
% 2.88/0.74 % (1292835)Termination phase: Saturation
% 2.88/0.74 % (1292835)Time elapsed: 0.011 s
% 2.88/0.74 % (1292835)Peak memory usage: 12 MB
% 2.88/0.74 % (1292835)Instructions burned: 21 (million)
% 2.88/0.74 % (1292829)Instruction limit reached!
% 2.88/0.74 % (1292829)------------------------------
% 2.88/0.74 % (1292829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292829)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292829)Termination reason: Instruction limit
% 2.88/0.74 % (1292829)Termination phase: Saturation
% 2.88/0.74 % (1292829)Time elapsed: 0.029 s
% 2.88/0.74 % (1292829)Peak memory usage: 12 MB
% 2.88/0.74 % (1292829)Instructions burned: 32 (million)
% 2.88/0.74 % (1292831)Instruction limit reached!
% 2.88/0.74 % (1292831)------------------------------
% 2.88/0.74 % (1292831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292831)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292831)Termination reason: Instruction limit
% 2.88/0.74 % (1292831)Termination phase: Saturation
% 2.88/0.74 % (1292831)Time elapsed: 0.020 s
% 2.88/0.74 % (1292831)Peak memory usage: 12 MB
% 2.88/0.74 % (1292831)Instructions burned: 26 (million)
% 2.88/0.74 % (1292842)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3369981683:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.88/0.74 % (1292838)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3051958497:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.88/0.74 % (1292843)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2890096235:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.88/0.74 % (1292844)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.88/0.74 % (1292844)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3909084258:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.88/0.74 % (1292844)Instruction limit reached!
% 2.88/0.74 % (1292844)------------------------------
% 2.88/0.74 % (1292844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292844)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292844)Termination reason: Instruction limit
% 2.88/0.74 % (1292844)Termination phase: Saturation
% 2.88/0.74 % (1292844)Time elapsed: 0.007 s
% 2.88/0.74 % (1292844)Peak memory usage: 12 MB
% 2.88/0.74 % (1292844)Instructions burned: 8 (million)
% 2.88/0.74 % (1292843)Instruction limit reached!
% 2.88/0.74 % (1292843)------------------------------
% 2.88/0.74 % (1292843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292843)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292843)Termination reason: Instruction limit
% 2.88/0.74 % (1292843)Termination phase: Saturation
% 2.88/0.74 % (1292843)Time elapsed: 0.035 s
% 2.88/0.74 % (1292843)Peak memory usage: 12 MB
% 2.88/0.74 % (1292843)Instructions burned: 43 (million)
% 2.88/0.74 % (1292853)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2353560463:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.88/0.74 % (1292854)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=973534315:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.88/0.74 % (1292842)Instruction limit reached!
% 2.88/0.74 % (1292842)------------------------------
% 2.88/0.74 % (1292842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292842)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292842)Termination reason: Instruction limit
% 2.88/0.74 % (1292842)Termination phase: Saturation
% 2.88/0.74 % (1292842)Time elapsed: 0.091 s
% 2.88/0.74 % (1292842)Peak memory usage: 13 MB
% 2.88/0.74 % (1292842)Instructions burned: 193 (million)
% 2.88/0.74 % (1292836) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1292749-1292836"...
% 2.88/0.74 % (1292802)Instruction limit reached!
% 2.88/0.74 % (1292802)------------------------------
% 2.88/0.74 % (1292802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292802)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292802)Termination reason: Instruction limit
% 2.88/0.74 % (1292802)Termination phase: Saturation
% 2.88/0.74 % (1292802)Time elapsed: 0.269 s
% 2.88/0.74 % (1292802)Peak memory usage: 13 MB
% 2.88/0.74 % (1292802)Instructions burned: 327 (million)
% 2.88/0.74 % (1292858)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.88/0.74 % (1292858)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3227993996:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 2.88/0.74 % (1292858)Instruction limit reached!
% 2.88/0.74 % (1292858)------------------------------
% 2.88/0.74 % (1292858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292858)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292858)Termination reason: Instruction limit
% 2.88/0.74 % (1292858)Termination phase: Saturation
% 2.88/0.74 % (1292858)Time elapsed: 0.003 s
% 2.88/0.74 % (1292858)Peak memory usage: 11 MB
% 2.88/0.74 % (1292858)Instructions burned: 6 (million)
% 2.88/0.74 % (1292836)...printing done.
% 2.88/0.74 % (1292836)Refutation found. Thanks to Tanya!
% 2.88/0.74 % SZS status Theorem for theBenchmark
% 2.88/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.88/0.74 % (1292836)------------------------------
% 2.88/0.74 % (1292836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.88/0.74 % (1292836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/0.74 % (1292836)CaDiCaL version: 2.1.3
% 2.88/0.74 % (1292836)Termination reason: Refutation
% 2.88/0.74 % (1292836)Time elapsed: 0.152 s
% 2.88/0.74 % (1292836)Peak memory usage: 13 MB
% 2.88/0.74 % (1292836)Instructions burned: 184 (million)
% 2.88/0.74 % (1292749)Success in time 0.45 s
% 2.88/0.74 % Vampire exiting
%------------------------------------------------------------------------------