%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU816^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:33:32 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 135 ( 53 unt; 0 typ; 5 def)
% Number of atoms : 1266 ( 228 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 1940 ( 59 ~; 147 |; 65 &;1347 @)
% ( 5 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 37 usr; 14 con; 0-4 aty)
% ( 113 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 274 ( 0 sgn 92 !; 4 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
binintTransitive: $o ).
thf(func_def_9,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_10,type,
wellorderedByIn: $i > $o ).
thf(func_def_11,type,
ordinal: $i > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK2: $i > $i ).
thf(func_def_29,type,
sK3: $i > $i ).
thf(func_def_31,type,
sK5: $i > $i ).
thf(func_def_32,type,
sK6: $i > $i ).
thf(func_def_33,type,
sK7: $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f2,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(f3,axiom,
( binintTransitive
= ( ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(f4,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f5,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f6,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(f7,conjecture,
( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalMinLem1) ).
thf(f8,negated_conjecture,
~ ( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f10,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binintTransitive
= ( ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( binintTransitive
= ( !! @ $i
@ ^ [Y0: $i] :
( ( transitiveset @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( transitiveset @ Y1 )
=> ( transitiveset @ ( binintersect @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X5 @ X6 )
& ( in @ X4 @ X5 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f21,plain,
~ ( ( binintTransitive = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( ordinal @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( binintTransitive = $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f23,plain,
( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( ordinal @ sK1 ) )
& ( $true
= ( ordinal @ sK0 ) )
& ( binintTransitive = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
thf(f24,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f25,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f26,plain,
( binintTransitive
= ( !! @ $i
@ ^ [Y0: $i] :
( ( transitiveset @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( transitiveset @ Y1 )
=> ( transitiveset @ ( binintersect @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f27,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
binintTransitive = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
( $true
= ( ordinal @ sK1 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f36,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( ^ [Y2: $i] : ( emptyset != Y2 )
@ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f28,f27,f24]) ).
thf(f37,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f29,f25,f36]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ Y1 )
=> ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ ( binintersect @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f26,f30,f25,f25,f25]) ).
thf(f39,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ ( binintersect @ sK0 @ sK1 ) ) ),
inference(definition_unfolding,[],[f33,f25]) ).
thf(f40,plain,
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ sK1 ) ),
inference(definition_unfolding,[],[f32,f37]) ).
thf(f41,plain,
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f31,f37]) ).
thf(f42,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f44,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f93,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK1 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK1 ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f95,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f93]) ).
thf(f96,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( subset @ Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK1 )
=> ( subset @ X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f144,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f145,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ Y0 @ ( binintersect @ sK0 @ sK1 ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $false
= ( ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) )
=> ( subset @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( $false
= ( subset @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $true
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ Y1 )
=> ( ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( subset @ Y3 @ Y2 ) ) )
@ ( binintersect @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) )
=> ( subset @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) )
=> ( subset @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) )
=> ( subset @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) )
=> ( subset @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK5 @ X1 ) @ X1 )
=> ( subset @ ( sK5 @ X1 ) @ X1 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) )
@ ( sK6 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) )
@ ( sK6 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK6 @ X2 ) @ X2 )
=> ( subset @ ( sK6 @ X2 ) @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( subset @ ( sK6 @ X2 ) @ X2 ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( in @ ( sK6 @ X2 ) @ X2 ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( in @ ( sK6 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( subset @ ( sK6 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) )
@ ( sK7 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( subset @ Y0 @ X2 ) )
@ ( sK7 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ Y0 @ ( binintersect @ X1 @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK7 @ X2 ) @ X2 )
=> ( subset @ ( sK7 @ X2 ) @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( subset @ ( sK7 @ X2 ) @ X2 ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( in @ ( sK7 @ X2 ) @ X2 ) )
| ( $true
= ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $true
= ( in @ ( sK7 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ ( sK5 @ X1 ) @ X1 ) )
| ( $false
= ( subset @ ( sK7 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f191,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f147,f163]) ).
thf(f192,plain,
( ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f194,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f192,f148]) ).
thf(f195,plain,
( ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f199,definition,
( spl8_1
<=> ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f201,plain,
( ( $true
= ( in @ ( sK6 @ sK1 ) @ sK1 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f203,definition,
( spl8_2
<=> ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f204,plain,
( ( $true
!= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f205,plain,
( ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f195,f203,f199]) ).
thf(f216,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f147,f164]) ).
thf(f217,plain,
( ( $true
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f230,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f171,f147]) ).
thf(f239,plain,
( ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f248,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f239,f148]) ).
thf(f249,plain,
( ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f251,definition,
( spl8_3
<=> ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f253,plain,
( ( $true
= ( in @ ( sK7 @ sK1 ) @ sK1 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f255,definition,
( spl8_4
<=> ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f257,plain,
( ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f259,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f249,f255,f251]) ).
thf(f274,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f172,f147]) ).
thf(f293,plain,
( ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f310,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f293,f148]) ).
thf(f311,plain,
( ( $false
= ( subset @ ( sK5 @ sK0 ) @ sK0 ) )
| ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f310]) ).
thf(f313,definition,
( spl8_5
<=> ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f315,plain,
( ( $false
= ( subset @ ( sK7 @ sK1 ) @ sK1 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f317,plain,
( spl8_5
| spl8_4 ),
inference(avatar_split_clause,[],[f311,f255,f313]) ).
thf(f320,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ~ spl8_4 ),
inference(constrained_superposition,[],[f47,f257]) ).
thf(f321,plain,
( ( $false
= ( in @ ( sK5 @ sK0 ) @ sK0 ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f334,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4 ),
inference(constrained_superposition,[],[f321,f205]) ).
thf(f340,plain,
( $false
| ~ spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f341,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f340]) ).
thf(f346,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK7 @ sK1 ) @ sK1 ) )
| ~ spl8_5 ),
inference(constrained_superposition,[],[f98,f315]) ).
thf(f347,plain,
( ( $false
= ( in @ ( sK7 @ sK1 ) @ sK1 ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f352,plain,
( ( $true = $false )
| ~ spl8_3
| ~ spl8_5 ),
inference(constrained_superposition,[],[f253,f347]) ).
thf(f353,plain,
( $false
| ~ spl8_3
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f354,plain,
( ~ spl8_3
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f353]) ).
thf(f359,plain,
( ( $false
= ( subset @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sK4 @ ( binintersect @ sK0 @ sK1 ) ) )
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f217,f204]) ).
thf(f361,plain,
( ( $true = $false )
| ( $false
= ( subset @ ( sK6 @ sK1 ) @ sK1 ) )
| spl8_2 ),
inference(forward_demodulation,[],[f359,f148]) ).
thf(f362,plain,
( ( $false
= ( subset @ ( sK6 @ sK1 ) @ sK1 ) )
| spl8_2 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f375,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK6 @ sK1 ) @ sK1 ) )
| spl8_2 ),
inference(constrained_superposition,[],[f98,f362]) ).
thf(f376,plain,
( ( $false
= ( in @ ( sK6 @ sK1 ) @ sK1 ) )
| spl8_2 ),
inference(trivial_inequality_removal,[],[f375]) ).
thf(f382,plain,
( ( $true = $false )
| ~ spl8_1
| spl8_2 ),
inference(constrained_superposition,[],[f376,f201]) ).
thf(f388,plain,
( $false
| ~ spl8_1
| spl8_2 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f389,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_contradiction_clause,[],[f388]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f206]) ).
cnf(s4,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f259]) ).
cnf(s6,plain,
( spl8_4
| spl8_5 ),
inference(sat_conversion,[],[f317]) ).
cnf(s8,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(sat_conversion,[],[f341]) ).
cnf(s9,plain,
( ~ spl8_3
| ~ spl8_5 ),
inference(sat_conversion,[],[f354]) ).
cnf(s12,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f389]) ).
cnf(s13,plain,
spl8_4,
inference(rat,[],[s9,s4,s6]) ).
cnf(s14,plain,
~ spl8_2,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
~ spl8_1,
inference(rat,[],[s12,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s14,s15]) ).
thf(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU816^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:33:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % (187991)Will run a generic schedule for satisfiability detection.
% 0.08/0.16 % (187997)% WARNING: option uhcvi not known.
% 0.08/0.16 % (187997)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=428542842:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.16 % (187999)dis+10_1_sil=32000:sp=arity:random_seed=695422997:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.16 % (187996)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2702139343_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.16 % (187998)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1034242580:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.16 % (188000)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3001131100:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.16 % (188001)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3341148718:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.16 % (188002)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3249891203:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.16 % (188000)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % (187997)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.16 % Exception at run slice level% (187997)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.16
% 0.08/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.16 % (188000) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187991-188000"...
% 0.08/0.16 % (187999) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-187991-187999"...
% 0.08/0.16 % (188010)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=204612531:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.16 % Exception at run slice level
% 0.08/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.16 % (188000)...printing done.
% 0.08/0.16 % (188000)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.16 % (188000)------------------------------
% 0.08/0.16 % (188000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (188000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (188000)CaDiCaL version: 2.1.3
% 0.08/0.16 % (188000)Termination reason: Refutation
% 0.08/0.16 % (188000)Time elapsed: 0.013 s
% 0.08/0.16 % (188000)Peak memory usage: 12 MB
% 0.08/0.16 % (188000)Instructions burned: 47 (million)
% 0.08/0.16 % (187991)Success in time 0.04 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------