%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU593^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:32:35 AM UTC 2026
% Result : Theorem 1.49s 0.53s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 139 ( 66 unt; 0 typ; 7 def)
% Number of atoms : 1095 ( 279 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1308 ( 9 ~; 103 |; 18 &; 943 @)
% ( 0 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 17 con; 0-4 aty)
% ( 101 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 324 ( 180 ^; 140 !; 4 ?; 324 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
subsetI1: $o ).
thf(func_def_5,type,
subsetE: $o ).
thf(func_def_6,type,
setextsub: $o ).
thf(func_def_7,type,
binintersect: $i > $i > $i ).
thf(func_def_8,type,
binintersectI: $o ).
thf(func_def_9,type,
binintersectLsub: $o ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
sF2: $o ).
thf(func_def_22,type,
sF3: $o ).
thf(func_def_23,type,
sF4: $o ).
thf(func_def_24,type,
sF5: $o ).
thf(func_def_25,type,
sF6: $o ).
thf(func_def_27,type,
sF8: $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_31,type,
sK11: $i > $i > $i ).
thf(f1,axiom,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(f2,axiom,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(f4,axiom,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect) ).
thf(f5,axiom,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(f6,axiom,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(f7,conjecture,
( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(f8,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( binintersectLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y1 @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( setextsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectLsub = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectLsub = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectLsub = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( sK0
!= ( binintersect @ sK0 @ sK1 ) )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( binintersectLsub = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
thf(f26,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f28,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( binintersectI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binintersect @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f31,plain,
( binintersectLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( binintersect @ Y1 @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
subsetI1 = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
subsetE = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
setextsub = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
binintersectLsub = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
( sK0
!= ( binintersect @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f33]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f34]) ).
thf(f44,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f30,f35,f29]) ).
thf(f45,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( ^ [Y2: $i,Y3: $i] :
( dsetconstr @ Y2
@ ^ [Y4: $i] : ( in @ Y4 @ Y3 ) )
@ Y1
@ Y0 )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f31,f36,f29]) ).
thf(f46,plain,
( sK0
!= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f38,f29]) ).
thf(f47,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f47]) ).
thf(f49,plain,
$true = sF2,
inference(definition_folding,[],[f41,f48]) ).
thf(f50,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f51,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= sF3 ),
inference(reorient_equations,[],[f50]) ).
thf(f52,plain,
$true = sF3,
inference(definition_folding,[],[f42,f51]) ).
thf(f53,definition,
( sF4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f54,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= sF4 ),
inference(reorient_equations,[],[f53]) ).
thf(f55,plain,
$true = sF4,
inference(definition_folding,[],[f43,f54]) ).
thf(f56,definition,
( sF5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f57,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
= sF5 ),
inference(reorient_equations,[],[f56]) ).
thf(f58,plain,
$true = sF5,
inference(definition_folding,[],[f44,f57]) ).
thf(f59,definition,
( sF6
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( ^ [Y2: $i,Y3: $i] :
( dsetconstr @ Y2
@ ^ [Y4: $i] : ( in @ Y4 @ Y3 ) )
@ Y1
@ Y0 )
@ Y1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f60,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( ^ [Y2: $i,Y3: $i] :
( dsetconstr @ Y2
@ ^ [Y4: $i] : ( in @ Y4 @ Y3 ) )
@ Y1
@ Y0 )
@ Y1 ) ) )
= sF6 ),
inference(reorient_equations,[],[f59]) ).
thf(f61,plain,
$true = sF6,
inference(definition_folding,[],[f45,f60]) ).
thf(f62,definition,
( sF7
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f63,plain,
( ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 )
= sF7 ),
inference(reorient_equations,[],[f62]) ).
thf(f64,plain,
sK0 != sF7,
inference(definition_folding,[],[f46,f63]) ).
thf(f65,definition,
( sF8
= ( subset @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f66,plain,
( ( subset @ sK0 @ sK1 )
= sF8 ),
inference(reorient_equations,[],[f65]) ).
thf(f67,plain,
$true = sF8,
inference(definition_folding,[],[f37,f66]) ).
thf(f68,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true )
| ( $false = sF2 ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f79,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f80,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false = sF2 )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK11 @ X1 @ X2 ) ) )
| ( $false = sF2 )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK11 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK11 @ X1 @ X2 ) @ X1 ) ) )
| ( $false = sF2 )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK11 @ X1 @ X2 ) @ X1 ) )
| ( $false = sF2 )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK11 @ X1 @ X2 ) @ X2 ) )
| ( $false = sF2 )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f51]) ).
thf(f100,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f101,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( subset @ X3 @ X2 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false = sF3 )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false = sF3 )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= $true )
| ( $false = sF4 ) ),
inference(iff_proxy_clausification,[],[f54]) ).
thf(f119,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f120,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false = sF4 )
| ( $true
= ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false = sF4 )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false = sF4 )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f57]) ).
thf(f138,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0
@ ( ^ [Y3: $i,Y4: $i] :
( dsetconstr @ Y3
@ ^ [Y5: $i] : ( in @ Y5 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f139,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X2 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X2 ) ) ) ) )
@ X3 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false = sF5 )
| ( $true
= ( ( in @ X1 @ X2 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false = sF5 )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( ^ [Y2: $i,Y3: $i] :
( dsetconstr @ Y2
@ ^ [Y4: $i] : ( in @ Y4 @ Y3 ) )
@ Y1
@ Y0 )
@ Y1 ) ) ) )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f60]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( ^ [Y2: $i,Y3: $i] :
( dsetconstr @ Y2
@ ^ [Y4: $i] : ( in @ Y4 @ Y3 ) )
@ Y1
@ Y0 )
@ Y1 ) )
@ X1 ) )
| ( $false = sF6 ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( subset
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) )
@ Y0 ) ) )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( subset
@ ( dsetconstr @ Y0
@ ^ [Y1: $i] : ( in @ Y1 @ X1 ) )
@ Y0 )
@ X2 ) )
| ( $false = sF6 ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X2 ) )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( sF7
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f157,plain,
( ( $true
= ( subset @ sK0 @ sK1 ) )
| ( $false = sF8 ) ),
inference(iff_proxy_clausification,[],[f66]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK11 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(forward_demodulation,[],[f87,f49]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK11 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK11 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(forward_demodulation,[],[f86,f49]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK11 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( subset @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(forward_demodulation,[],[f107,f52]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(forward_demodulation,[],[f125,f55]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) ) ),
inference(forward_demodulation,[],[f145,f58]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ Y0 @ X2 ) ) ) )
| ( $false
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( subset
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X2 ) ) ),
inference(forward_demodulation,[],[f155,f61]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( $true
= ( subset
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) )
@ X2 ) ),
inference(trivial_inequality_removal,[],[f169]) ).
thf(f171,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f157,f67]) ).
thf(f172,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f201,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f172,f164]) ).
thf(f207,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f219,plain,
( $true
= ( subset @ sF7 @ sK0 ) ),
inference(constrained_superposition,[],[f170,f156]) ).
thf(f237,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK0 @ sF7 ) )
| ( sK0 = sF7 ) ),
inference(constrained_superposition,[],[f166,f219]) ).
thf(f238,plain,
( ( $false
= ( subset @ sK0 @ sF7 ) )
| ( sK0 = sF7 ) ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f244,plain,
( $false
= ( subset @ sK0 @ sF7 ) ),
inference(forward_subsumption_resolution,[],[f238,f64]) ).
thf(f248,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f168,f156]) ).
thf(f293,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ sF7 ) )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) ) ),
inference(constrained_superposition,[],[f162,f248]) ).
thf(f296,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK1 ) )
| ( $true
= ( subset @ X0 @ sF7 ) )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f2477,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) )
| ( $true
= ( subset @ X0 @ sF7 ) )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) ) ),
inference(constrained_superposition,[],[f207,f296]) ).
thf(f2507,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) )
| ( $true
= ( subset @ X0 @ sF7 ) ) ),
inference(duplicate_literal_removal,[],[f2477]) ).
thf(f2508,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK11 @ sF7 @ X0 ) @ sK0 ) )
| ( $true
= ( subset @ X0 @ sF7 ) ) ),
inference(trivial_inequality_removal,[],[f2507]) ).
thf(f2633,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK0 @ sF7 ) )
| ( $true
= ( subset @ sK0 @ sF7 ) ) ),
inference(constrained_superposition,[],[f160,f2508]) ).
thf(f2678,plain,
( ( $true = $false )
| ( $true
= ( subset @ sK0 @ sF7 ) ) ),
inference(duplicate_literal_removal,[],[f2633]) ).
thf(f2679,plain,
( $true
= ( subset @ sK0 @ sF7 ) ),
inference(trivial_inequality_removal,[],[f2678]) ).
thf(f2713,plain,
$true = $false,
inference(forward_demodulation,[],[f2679,f244]) ).
thf(f2714,plain,
$false,
inference(trivial_inequality_removal,[],[f2713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU593^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:56:41 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/0.53 % (3193773)Will run a generic schedule for satisfiability detection.
% 1.49/0.53 % (3193782)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3817677233:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.49/0.53 % (3193782)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193779)% WARNING: option uhcvi not known.
% 1.49/0.53 % (3193778)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1899765560_2999 on theBenchmark for (2999ds/0Mi)
% 1.49/0.53 % (3193779)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3387609939:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.49/0.53 % (3193780)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3381638254:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.49/0.53 % (3193781)dis+10_1_sil=32000:sp=arity:random_seed=763947248:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.49/0.53 % (3193783)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1633248655:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193784)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2815753967:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.49/0.53 % (3193779)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193779)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.49/0.53 % (3193792)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=562506366:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193782)Instruction limit reached!
% 1.49/0.53 % (3193782)------------------------------
% 1.49/0.53 % (3193782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193782)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193782)Termination reason: Instruction limit
% 1.49/0.53 % (3193782)Termination phase: Saturation
% 1.49/0.53 % (3193782)Time elapsed: 0.030 s
% 1.49/0.53 % (3193782)Peak memory usage: 12 MB
% 1.49/0.53 % (3193782)Instructions burned: 117 (million)
% 1.49/0.53 % (3193795)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3266322957:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.49/0.53 % (3193795)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193795)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.49/0.53 % (3193794)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2251268251:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.49/0.53 % (3193781)Instruction limit reached!
% 1.49/0.53 % (3193781)------------------------------
% 1.49/0.53 % (3193781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193781)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193781)Termination reason: Instruction limit
% 1.49/0.53 % (3193781)Termination phase: Saturation
% 1.49/0.53 % (3193781)Time elapsed: 0.050 s
% 1.49/0.53 % (3193781)Peak memory usage: 12 MB
% 1.49/0.53 % (3193781)Instructions burned: 109 (million)
% 1.49/0.53 % (3193783)Instruction limit reached!
% 1.49/0.53 % (3193783)------------------------------
% 1.49/0.53 % (3193783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193783)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193783)Termination reason: Instruction limit
% 1.49/0.53 % (3193783)Termination phase: Saturation
% 1.49/0.53 % (3193783)Time elapsed: 0.063 s
% 1.49/0.53 % (3193783)Peak memory usage: 12 MB
% 1.49/0.53 % (3193783)Instructions burned: 132 (million)
% 1.49/0.53 % (3193798)ott-21_1_sil=16000:fs=off:random_seed=3599934710:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.49/0.53 % (3193784)Instruction limit reached!
% 1.49/0.53 % (3193784)------------------------------
% 1.49/0.53 % (3193784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193784)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193784)Termination reason: Instruction limit
% 1.49/0.53 % (3193784)Termination phase: Saturation
% 1.49/0.53 % (3193784)Time elapsed: 0.078 s
% 1.49/0.53 % (3193784)Peak memory usage: 12 MB
% 1.49/0.53 % (3193784)Instructions burned: 160 (million)
% 1.49/0.53 % (3193799)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2559629853:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.49/0.53 % (3193801)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2796370506:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193794)Instruction limit reached!
% 1.49/0.53 % (3193794)------------------------------
% 1.49/0.53 % (3193794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193794)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193794)Termination reason: Instruction limit
% 1.49/0.53 % (3193794)Termination phase: Saturation
% 1.49/0.53 % (3193794)Time elapsed: 0.063 s
% 1.49/0.53 % (3193794)Peak memory usage: 12 MB
% 1.49/0.53 % (3193794)Instructions burned: 132 (million)
% 1.49/0.53 % (3193804)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=70380935:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.49/0.53 % (3193805)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=795181430:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193808)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1944457066:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.49/0.53 % (3193808)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193798)Instruction limit reached!
% 1.49/0.53 % (3193798)------------------------------
% 1.49/0.53 % (3193798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193798)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193798)Termination reason: Instruction limit
% 1.49/0.53 % (3193798)Termination phase: Saturation
% 1.49/0.53 % (3193798)Time elapsed: 0.081 s
% 1.49/0.53 % (3193798)Peak memory usage: 12 MB
% 1.49/0.53 % (3193798)Instructions burned: 182 (million)
% 1.49/0.53 % (3193810)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4046599143:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.49/0.53 % (3193810)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193795)Instruction limit reached!
% 1.49/0.53 % (3193795)------------------------------
% 1.49/0.53 % (3193795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193795)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193795)Termination reason: Instruction limit
% 1.49/0.53 % (3193795)Termination phase: Saturation
% 1.49/0.53 % (3193795)Time elapsed: 0.156 s
% 1.49/0.53 % (3193795)Peak memory usage: 13 MB
% 1.49/0.53 % (3193795)Instructions burned: 689 (million)
% 1.49/0.53 % (3193812)fmb+10_1_sil=64000:random_seed=561548669:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 1.49/0.53 % (3193812)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193814)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1046130498:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193816)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2975578184:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 1.49/0.53 % Exception at run slice level
% 1.49/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.49/0.53 % (3193818)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1454599538:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 1.49/0.53 % (3193818)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.49/0.53 % (3193804) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3193773-3193804"...
% 1.49/0.53 % (3193804)...printing done.
% 1.49/0.53 % (3193804)Refutation found. Thanks to Tanya!
% 1.49/0.53 % SZS status Theorem for theBenchmark
% 1.49/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.53 % (3193804)------------------------------
% 1.49/0.53 % (3193804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.49/0.53 % (3193804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.49/0.53 % (3193804)CaDiCaL version: 2.1.3
% 1.49/0.53 % (3193804)Termination reason: Refutation
% 1.49/0.53 % (3193804)Time elapsed: 0.121 s
% 1.49/0.53 % (3193804)Peak memory usage: 13 MB
% 1.49/0.53 % (3193804)Instructions burned: 256 (million)
% 1.49/0.53 % (3193773)Success in time 0.282 s
% 1.49/0.53 % Vampire exiting
%------------------------------------------------------------------------------