%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU625^2 : 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 : n005.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 08:30:23 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of formulae : 276 ( 96 unt; 0 typ; 37 def)
% Number of atoms : 1592 ( 356 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 1684 ( 217 ~; 312 |; 28 &; 909 @)
% ( 26 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 65 ( 61 usr; 50 con; 0-4 aty)
% ( 96 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 274 ( 0 sgn 153 !; 12 ?; 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,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
subsetI2: $o ).
thf(func_def_6,type,
subsetE: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
binunionLsub: $o ).
thf(func_def_9,type,
binunionRsub: $o ).
thf(func_def_10,type,
upairset2E: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
sF4: $o ).
thf(func_def_26,type,
sF5: $o ).
thf(func_def_27,type,
sF6: $o ).
thf(func_def_28,type,
sF7: $o ).
thf(func_def_32,type,
sF11: $o ).
thf(func_def_33,type,
sF12: $o ).
thf(func_def_34,type,
sF13: $o ).
thf(func_def_35,type,
sF14: $o ).
thf(func_def_38,type,
sK17: $i > $i > $i ).
thf(f1,axiom,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(f2,axiom,
( subsetE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(f4,axiom,
( binunionRsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(f5,axiom,
( upairset2E
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(f6,conjecture,
( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(f7,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( binunionRsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
( binunionRsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f13,plain,
~ ( ( subsetI2 = $true )
=> ( ( subsetE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( upairset2E = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X0 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
( binunionLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( upairset2E
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X0 = X2 )
| ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( upairset2E = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f21,plain,
( ( binunionLsub = $true )
& ( upairset2E = $true )
& ( binunionRsub = $true )
& ( subsetE = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( subsetI2 = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( binunionLsub = $true )
& ( upairset2E = $true )
& ( binunionRsub = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
& ( subsetI2 = $true ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( binunionLsub = $true )
& ( upairset2E = $true )
& ( binunionRsub = $true )
& ( subsetE = $true )
& ( ( in @ sK0 @ sK1 )
= $true )
& ( ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK3 @ sK2 )
= $true )
& ( subsetI2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f22]) ).
thf(f24,plain,
( binunionRsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
subsetI2 = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f28,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f29,plain,
( ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f30,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f31,plain,
subsetE = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
binunionRsub = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
upairset2E = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f34,plain,
binunionLsub = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f35,plain,
( binunionLsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f36,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f39,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f32]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f25,f27]) ).
thf(f41,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f26,f33]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f35,f34]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f36,f31]) ).
thf(f44,definition,
( sF4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f45,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) )
= sF4 ),
inference(reorient_equations,[],[f44]) ).
thf(f46,plain,
$true = sF4,
inference(definition_folding,[],[f39,f45]) ).
thf(f47,definition,
( sF5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f48,plain,
$true = sF5,
inference(definition_folding,[],[f40,f47]) ).
thf(f49,definition,
( sF6
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
= sF6 ),
inference(reorient_equations,[],[f49]) ).
thf(f51,plain,
$true = sF6,
inference(definition_folding,[],[f41,f50]) ).
thf(f52,definition,
( sF7
= ( in @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f53,plain,
( ( in @ sK0 @ sK1 )
= sF7 ),
inference(reorient_equations,[],[f52]) ).
thf(f54,plain,
sF7 = $true,
inference(definition_folding,[],[f30,f53]) ).
thf(f55,definition,
( sF8
= ( setadjoin @ sK3 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f56,plain,
( ( setadjoin @ sK3 @ emptyset )
= sF8 ),
inference(reorient_equations,[],[f55]) ).
thf(f57,definition,
( sF9
= ( setadjoin @ sK0 @ sF8 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f58,plain,
( ( setadjoin @ sK0 @ sF8 )
= sF9 ),
inference(reorient_equations,[],[f57]) ).
thf(f59,definition,
( sF10
= ( binunion @ sK1 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f60,plain,
( ( binunion @ sK1 @ sK2 )
= sF10 ),
inference(reorient_equations,[],[f59]) ).
thf(f61,definition,
( sF11
= ( subset @ sF9 @ sF10 ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f62,plain,
( ( subset @ sF9 @ sF10 )
= sF11 ),
inference(reorient_equations,[],[f61]) ).
thf(f63,plain,
$true != sF11,
inference(definition_folding,[],[f29,f62,f60,f58,f56]) ).
thf(f64,definition,
( sF12
= ( in @ sK3 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
thf(f65,plain,
sF12 = $true,
inference(definition_folding,[],[f28,f64]) ).
thf(f66,definition,
( sF13
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
thf(f67,plain,
sF13 = $true,
inference(definition_folding,[],[f42,f66]) ).
thf(f68,definition,
( sF14
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
thf(f69,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) )
= sF14 ),
inference(reorient_equations,[],[f68]) ).
thf(f70,plain,
sF14 = $true,
inference(definition_folding,[],[f43,f69]) ).
thf(f72,plain,
( ( sF13 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f66]) ).
thf(f73,plain,
! [X1: $i] :
( ( sF13 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y1 @ ( binunion @ Y1 @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X1: $i] :
( ( sF13 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( binunion @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( subset @ Y0 @ ( binunion @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( sF13 = $false ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( sF13 = $false )
| ( ( subset @ X2 @ ( binunion @ X2 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f81,plain,
( ( sF7 = $false )
| ( ( in @ sK0 @ sK1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f53]) ).
thf(f84,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) )
| ( sF5 = $false ) ),
inference(iff_proxy_clausification,[],[f47]) ).
thf(f85,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( sF5 = $false ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) )
= $true )
| ( sF5 = $false ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( sF5 = $false )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) )
| ( sF5 = $false ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( sF5 = $false )
| ( $true
= ( subset @ X2 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK17 @ X1 @ X2 ) )
= $false )
| ( $true
= ( subset @ X2 @ X1 ) )
| ( sF5 = $false ) ),
inference(sigma_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK17 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
= $false )
| ( sF5 = $false )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
| ( sF5 = $false )
| ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( ( sF5 = $false )
| ( ( in @ ( sK17 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f104,plain,
( ( ( in @ sK3 @ sK2 )
= $true )
| ( sF12 = $false ) ),
inference(iff_proxy_clausification,[],[f64]) ).
thf(f106,plain,
( ( ( subset @ sF9 @ sF10 )
= $false )
| ( $true = sF11 ) ),
inference(iff_proxy_clausification,[],[f62]) ).
thf(f107,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) )
| ( sF6 = $false ) ),
inference(iff_proxy_clausification,[],[f50]) ).
thf(f121,plain,
! [X1: $i] :
( ( sF6 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y2 = Y0 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f122,plain,
! [X1: $i] :
( ( sF6 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y1 = X1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y1 = X1 ) ) ) )
@ X2 ) )
| ( sF6 = $false ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( Y0 = X1 ) ) ) )
= $true )
| ( sF6 = $false ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( Y0 = X1 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X3 = X2 )
| ( X3 = X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false )
| ( $true
= ( ( X3 = X2 )
| ( X3 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( $true
= ( X3 = X1 ) )
| ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false )
| ( ( X3 = X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false )
| ( X1 = X3 )
| ( ( X3 = X2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X1 = X3 )
| ( sF6 = $false )
| ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false )
| ( X2 = X3 ) ),
inference(equality_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( sF14 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f69]) ).
thf(f143,plain,
! [X1: $i] :
( ( sF14 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y1 @ Y2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f144,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) ) )
= $true )
| ( sF14 = $false ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( sF14 = $false ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( ( sF14 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X2 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( subset @ X2 @ Y0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) )
@ X3 ) )
| ( sF14 = $false ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF14 = $false )
| ( $true
= ( ( subset @ X2 @ X3 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( sF14 = $false )
| ( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( ( in @ X1 @ X2 )
= $false )
| ( sF14 = $false )
| ( ( in @ X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) ) )
= $true )
| ( sF4 = $false ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ Y0 @ ( binunion @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f158,plain,
! [X1: $i] :
( ( sF4 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ X1 @ ( binunion @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( subset @ X1 @ ( binunion @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( sF4 = $false )
| ( $true
= ( subset @ X1 @ ( binunion @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f162,definition,
( spl28_1
<=> ( sF13 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition]) ).
thf(f164,plain,
( ( sF13 = $false )
| ~ spl28_1 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f166,definition,
( spl28_2
<=> ! [X2: $i,X1: $i] :
( ( subset @ X2 @ ( binunion @ X2 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl28_2])],[avatar_definition]) ).
thf(f167,plain,
( ! [X2: $i,X1: $i] :
( ( subset @ X2 @ ( binunion @ X2 @ X1 ) )
= $true )
| ~ spl28_2 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f168,plain,
( spl28_1
| spl28_2 ),
inference(avatar_split_clause,[],[f76,f166,f162]) ).
thf(f170,definition,
( spl28_3
<=> ( sF13 = $true ) ),
introduced(definition,[new_symbols(definition,[spl28_3])],[avatar_definition]) ).
thf(f172,plain,
( ( sF13 = $true )
| ~ spl28_3 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f183,definition,
( spl28_6
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(definition,[spl28_6])],[avatar_definition]) ).
thf(f185,plain,
( ( sF7 = $true )
| ~ spl28_6 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f188,definition,
( spl28_7
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_7])],[avatar_definition]) ).
thf(f190,plain,
( ( sF7 = $false )
| ~ spl28_7 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f192,definition,
( spl28_8
<=> ( ( in @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl28_8])],[avatar_definition]) ).
thf(f194,plain,
( ( ( in @ sK0 @ sK1 )
= $true )
| ~ spl28_8 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f195,plain,
( spl28_7
| spl28_8 ),
inference(avatar_split_clause,[],[f81,f192,f188]) ).
thf(f196,plain,
spl28_6,
inference(avatar_split_clause,[],[f54,f183]) ).
thf(f198,definition,
( spl28_9
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_9])],[avatar_definition]) ).
thf(f200,plain,
( ( sF5 = $false )
| ~ spl28_9 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f202,definition,
( spl28_10
<=> ! [X2: $i,X1: $i] :
( ( ( in @ ( sK17 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( subset @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl28_10])],[avatar_definition]) ).
thf(f203,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ ( sK17 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( subset @ X2 @ X1 ) ) )
| ~ spl28_10 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f204,plain,
( spl28_9
| spl28_10 ),
inference(avatar_split_clause,[],[f93,f202,f198]) ).
thf(f206,definition,
( spl28_11
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
| ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl28_11])],[avatar_definition]) ).
thf(f207,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X1 ) ) )
| ~ spl28_11 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f208,plain,
( spl28_9
| spl28_11 ),
inference(avatar_split_clause,[],[f92,f206,f198]) ).
thf(f213,definition,
( spl28_13
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl28_13])],[avatar_definition]) ).
thf(f215,plain,
( ( $true = sF5 )
| ~ spl28_13 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f223,definition,
( spl28_15
<=> ( sF12 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_15])],[avatar_definition]) ).
thf(f225,plain,
( ( sF12 = $false )
| ~ spl28_15 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f227,definition,
( spl28_16
<=> ( ( in @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl28_16])],[avatar_definition]) ).
thf(f229,plain,
( ( ( in @ sK3 @ sK2 )
= $true )
| ~ spl28_16 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f230,plain,
( spl28_15
| spl28_16 ),
inference(avatar_split_clause,[],[f104,f227,f223]) ).
thf(f232,definition,
( spl28_17
<=> ( sF12 = $true ) ),
introduced(definition,[new_symbols(definition,[spl28_17])],[avatar_definition]) ).
thf(f234,plain,
( ( sF12 = $true )
| ~ spl28_17 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f240,plain,
spl28_17,
inference(avatar_split_clause,[],[f65,f232]) ).
thf(f242,definition,
( spl28_19
<=> ( $true = sF11 ) ),
introduced(definition,[new_symbols(definition,[spl28_19])],[avatar_definition]) ).
thf(f246,definition,
( spl28_20
<=> ( ( subset @ sF9 @ sF10 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl28_20])],[avatar_definition]) ).
thf(f248,plain,
( ( ( subset @ sF9 @ sF10 )
= $false )
| ~ spl28_20 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f249,plain,
( spl28_19
| spl28_20 ),
inference(avatar_split_clause,[],[f106,f246,f242]) ).
thf(f259,plain,
spl28_3,
inference(avatar_split_clause,[],[f67,f170]) ).
thf(f265,definition,
( spl28_24
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl28_24])],[avatar_definition]) ).
thf(f267,plain,
( ( $true = sF6 )
| ~ spl28_24 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f280,definition,
( spl28_27
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( X1 = X3 )
| ( X2 = X3 )
| ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl28_27])],[avatar_definition]) ).
thf(f281,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $false )
| ( X2 = X3 )
| ( X1 = X3 ) )
| ~ spl28_27 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f283,definition,
( spl28_28
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_28])],[avatar_definition]) ).
thf(f285,plain,
( ( sF6 = $false )
| ~ spl28_28 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f286,plain,
( spl28_27
| spl28_28 ),
inference(avatar_split_clause,[],[f130,f283,f280]) ).
thf(f288,definition,
( spl28_29
<=> ( sF14 = $true ) ),
introduced(definition,[new_symbols(definition,[spl28_29])],[avatar_definition]) ).
thf(f290,plain,
( ( sF14 = $true )
| ~ spl28_29 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f307,definition,
( spl28_33
<=> ( sF14 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_33])],[avatar_definition]) ).
thf(f309,plain,
( ( sF14 = $false )
| ~ spl28_33 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f311,definition,
( spl28_34
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( ( in @ X1 @ X3 )
= $true )
| ( ( in @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl28_34])],[avatar_definition]) ).
thf(f312,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X3 ) )
| ( ( in @ X1 @ X2 )
= $false )
| ( ( in @ X1 @ X3 )
= $true ) )
| ~ spl28_34 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f313,plain,
( spl28_33
| spl28_34 ),
inference(avatar_split_clause,[],[f150,f311,f307]) ).
thf(f314,plain,
spl28_29,
inference(avatar_split_clause,[],[f70,f288]) ).
thf(f315,plain,
spl28_13,
inference(avatar_split_clause,[],[f48,f213]) ).
thf(f321,definition,
( spl28_36
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl28_36])],[avatar_definition]) ).
thf(f323,plain,
( ( $true = sF4 )
| ~ spl28_36 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f326,definition,
( spl28_37
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl28_37])],[avatar_definition]) ).
thf(f328,plain,
( ( sF4 = $false )
| ~ spl28_37 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f330,definition,
( spl28_38
<=> ! [X2: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl28_38])],[avatar_definition]) ).
thf(f331,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X2 @ X1 ) ) )
| ~ spl28_38 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f332,plain,
( spl28_37
| spl28_38 ),
inference(avatar_split_clause,[],[f160,f330,f326]) ).
thf(f333,plain,
spl28_36,
inference(avatar_split_clause,[],[f46,f321]) ).
thf(f334,plain,
spl28_24,
inference(avatar_split_clause,[],[f51,f265]) ).
thf(f335,plain,
~ spl28_19,
inference(avatar_split_clause,[],[f63,f242]) ).
thf(f336,plain,
( ( $true = $false )
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f190,f185]) ).
thf(f337,plain,
( $false
| ~ spl28_6
| ~ spl28_7 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f338,plain,
( ~ spl28_6
| ~ spl28_7 ),
inference(avatar_contradiction_clause,[],[f337]) ).
thf(f340,plain,
( ( $true = $false )
| ~ spl28_15
| ~ spl28_17 ),
inference(forward_demodulation,[],[f234,f225]) ).
thf(f341,plain,
( $false
| ~ spl28_15
| ~ spl28_17 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f342,plain,
( ~ spl28_15
| ~ spl28_17 ),
inference(avatar_contradiction_clause,[],[f341]) ).
thf(f360,plain,
( ( $true = $false )
| ~ spl28_36
| ~ spl28_37 ),
inference(forward_demodulation,[],[f328,f323]) ).
thf(f361,plain,
( $false
| ~ spl28_36
| ~ spl28_37 ),
inference(trivial_inequality_removal,[],[f360]) ).
thf(f362,plain,
( ~ spl28_36
| ~ spl28_37 ),
inference(avatar_contradiction_clause,[],[f361]) ).
thf(f366,plain,
( ( $true = $false )
| ~ spl28_9
| ~ spl28_13 ),
inference(forward_demodulation,[],[f215,f200]) ).
thf(f367,plain,
( $false
| ~ spl28_9
| ~ spl28_13 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f368,plain,
( ~ spl28_9
| ~ spl28_13 ),
inference(avatar_contradiction_clause,[],[f367]) ).
thf(f371,plain,
( ( $true = $false )
| ~ spl28_29
| ~ spl28_33 ),
inference(forward_demodulation,[],[f290,f309]) ).
thf(f372,plain,
( $false
| ~ spl28_29
| ~ spl28_33 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f373,plain,
( ~ spl28_29
| ~ spl28_33 ),
inference(avatar_contradiction_clause,[],[f372]) ).
thf(f382,plain,
( ( ( subset @ sK1 @ sF10 )
= $true )
| ~ spl28_2 ),
inference(constrained_superposition,[],[f167,f60]) ).
thf(f385,plain,
( ( ( subset @ sK2 @ sF10 )
= $true )
| ~ spl28_38 ),
inference(constrained_superposition,[],[f331,f60]) ).
thf(f401,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ sF8 ) )
= $false )
| ( sK3 = X0 )
| ( X0 = X1 ) )
| ~ spl28_27 ),
inference(constrained_superposition,[],[f281,f56]) ).
thf(f418,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF9 )
= $false )
| ( sK0 = X0 )
| ( sK3 = X0 ) )
| ~ spl28_27 ),
inference(constrained_superposition,[],[f401,f58]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( in @ X0 @ sF10 )
= $true )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl28_2
| ~ spl28_34 ),
inference(constrained_superposition,[],[f312,f382]) ).
thf(f429,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( in @ X0 @ sF10 )
= $true )
| ( ( in @ X0 @ sK2 )
= $false ) )
| ~ spl28_34
| ~ spl28_38 ),
inference(constrained_superposition,[],[f312,f385]) ).
thf(f440,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF10 )
= $true )
| ( ( in @ X0 @ sK2 )
= $false ) )
| ~ spl28_34
| ~ spl28_38 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f443,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF10 )
= $true )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl28_2
| ~ spl28_34 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f449,plain,
( ! [X0: $i] :
( ( ( sK17 @ X0 @ sF9 )
= sK0 )
| ( ( subset @ sF9 @ X0 )
= $true )
| ( $true = $false )
| ( ( sK17 @ X0 @ sF9 )
= sK3 ) )
| ~ spl28_10
| ~ spl28_27 ),
inference(constrained_superposition,[],[f203,f418]) ).
thf(f450,plain,
( ! [X0: $i] :
( ( ( subset @ sF9 @ X0 )
= $true )
| ( ( sK17 @ X0 @ sF9 )
= sK3 )
| ( ( sK17 @ X0 @ sF9 )
= sK0 ) )
| ~ spl28_10
| ~ spl28_27 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f453,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( subset @ X0 @ sF10 )
= $true )
| ( ( in @ ( sK17 @ sF10 @ X0 ) @ sK2 )
= $false ) )
| ~ spl28_11
| ~ spl28_34
| ~ spl28_38 ),
inference(constrained_superposition,[],[f440,f207]) ).
thf(f455,plain,
( ! [X0: $i] :
( ( ( in @ ( sK17 @ sF10 @ X0 ) @ sK2 )
= $false )
| ( ( subset @ X0 @ sF10 )
= $true ) )
| ~ spl28_11
| ~ spl28_34
| ~ spl28_38 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f457,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sF10 )
= $true )
| ( ( in @ ( sK17 @ sF10 @ X0 ) @ sK1 )
= $false )
| ( $true = $false ) )
| ~ spl28_2
| ~ spl28_11
| ~ spl28_34 ),
inference(constrained_superposition,[],[f443,f207]) ).
thf(f459,plain,
( ! [X0: $i] :
( ( ( in @ ( sK17 @ sF10 @ X0 ) @ sK1 )
= $false )
| ( ( subset @ X0 @ sF10 )
= $true ) )
| ~ spl28_2
| ~ spl28_11
| ~ spl28_34 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f493,plain,
( ( $true = $false )
| ( ( sK17 @ sF10 @ sF9 )
= sK3 )
| ( sK0
= ( sK17 @ sF10 @ sF9 ) )
| ~ spl28_10
| ~ spl28_20
| ~ spl28_27 ),
inference(constrained_superposition,[],[f450,f248]) ).
thf(f499,plain,
( ( ( sK17 @ sF10 @ sF9 )
= sK3 )
| ( sK0
= ( sK17 @ sF10 @ sF9 ) )
| ~ spl28_10
| ~ spl28_20
| ~ spl28_27 ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f502,definition,
( spl28_39
<=> ( sK0
= ( sK17 @ sF10 @ sF9 ) ) ),
introduced(definition,[new_symbols(definition,[spl28_39])],[avatar_definition]) ).
thf(f504,plain,
( ( sK0
= ( sK17 @ sF10 @ sF9 ) )
| ~ spl28_39 ),
inference(avatar_component_clause,[],[f502]) ).
thf(f506,definition,
( spl28_40
<=> ( ( sK17 @ sF10 @ sF9 )
= sK3 ) ),
introduced(definition,[new_symbols(definition,[spl28_40])],[avatar_definition]) ).
thf(f508,plain,
( ( ( sK17 @ sF10 @ sF9 )
= sK3 )
| ~ spl28_40 ),
inference(avatar_component_clause,[],[f506]) ).
thf(f510,plain,
( spl28_39
| spl28_40
| ~ spl28_10
| ~ spl28_20
| ~ spl28_27 ),
inference(avatar_split_clause,[],[f499,f280,f246,f202,f506,f502]) ).
thf(f511,plain,
( ( $true = $false )
| ~ spl28_24
| ~ spl28_28 ),
inference(forward_demodulation,[],[f285,f267]) ).
thf(f512,plain,
( $false
| ~ spl28_24
| ~ spl28_28 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f513,plain,
( ~ spl28_24
| ~ spl28_28 ),
inference(avatar_contradiction_clause,[],[f512]) ).
thf(f515,plain,
( ( ( in @ sK0 @ sK1 )
= $false )
| ( ( subset @ sF9 @ sF10 )
= $true )
| ~ spl28_2
| ~ spl28_11
| ~ spl28_34
| ~ spl28_39 ),
inference(constrained_superposition,[],[f459,f504]) ).
thf(f521,plain,
( ( ( subset @ sF9 @ sF10 )
= $true )
| ( $true = $false )
| ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_34
| ~ spl28_39 ),
inference(forward_demodulation,[],[f515,f194]) ).
thf(f522,plain,
( ( ( subset @ sF9 @ sF10 )
= $true )
| ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_34
| ~ spl28_39 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f527,plain,
( ( $true = $false )
| ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_20
| ~ spl28_34
| ~ spl28_39 ),
inference(forward_demodulation,[],[f522,f248]) ).
thf(f528,plain,
( $false
| ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_20
| ~ spl28_34
| ~ spl28_39 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f529,plain,
( ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_20
| ~ spl28_34
| ~ spl28_39 ),
inference(avatar_contradiction_clause,[],[f528]) ).
thf(f540,plain,
( ( ( in @ sK3 @ sK2 )
= $false )
| ( ( subset @ sF9 @ sF10 )
= $true )
| ~ spl28_11
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(constrained_superposition,[],[f455,f508]) ).
thf(f547,plain,
( ( $true = $false )
| ( ( subset @ sF9 @ sF10 )
= $true )
| ~ spl28_11
| ~ spl28_16
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(forward_demodulation,[],[f540,f229]) ).
thf(f548,plain,
( ( ( subset @ sF9 @ sF10 )
= $true )
| ~ spl28_11
| ~ spl28_16
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(trivial_inequality_removal,[],[f547]) ).
thf(f551,plain,
( ( $true = $false )
| ~ spl28_11
| ~ spl28_16
| ~ spl28_20
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(forward_demodulation,[],[f548,f248]) ).
thf(f552,plain,
( $false
| ~ spl28_11
| ~ spl28_16
| ~ spl28_20
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f553,plain,
( ~ spl28_11
| ~ spl28_16
| ~ spl28_20
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(avatar_contradiction_clause,[],[f552]) ).
thf(f554,plain,
( ( $true = $false )
| ~ spl28_1
| ~ spl28_3 ),
inference(forward_demodulation,[],[f164,f172]) ).
thf(f555,plain,
( $false
| ~ spl28_1
| ~ spl28_3 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f556,plain,
( ~ spl28_1
| ~ spl28_3 ),
inference(avatar_contradiction_clause,[],[f555]) ).
cnf(s1,plain,
( spl28_1
| spl28_2 ),
inference(sat_conversion,[],[f168]) ).
cnf(s4,plain,
( spl28_7
| spl28_8 ),
inference(sat_conversion,[],[f195]) ).
cnf(s5,plain,
spl28_6,
inference(sat_conversion,[],[f196]) ).
cnf(s6,plain,
( spl28_9
| spl28_10 ),
inference(sat_conversion,[],[f204]) ).
cnf(s7,plain,
( spl28_9
| spl28_11 ),
inference(sat_conversion,[],[f208]) ).
cnf(s10,plain,
( spl28_15
| spl28_16 ),
inference(sat_conversion,[],[f230]) ).
cnf(s12,plain,
spl28_17,
inference(sat_conversion,[],[f240]) ).
cnf(s13,plain,
( spl28_19
| spl28_20 ),
inference(sat_conversion,[],[f249]) ).
cnf(s15,plain,
spl28_3,
inference(sat_conversion,[],[f259]) ).
cnf(s19,plain,
( spl28_27
| spl28_28 ),
inference(sat_conversion,[],[f286]) ).
cnf(s23,plain,
( spl28_33
| spl28_34 ),
inference(sat_conversion,[],[f313]) ).
cnf(s24,plain,
spl28_29,
inference(sat_conversion,[],[f314]) ).
cnf(s25,plain,
spl28_13,
inference(sat_conversion,[],[f315]) ).
cnf(s27,plain,
( spl28_37
| spl28_38 ),
inference(sat_conversion,[],[f332]) ).
cnf(s28,plain,
spl28_36,
inference(sat_conversion,[],[f333]) ).
cnf(s29,plain,
spl28_24,
inference(sat_conversion,[],[f334]) ).
cnf(s30,plain,
~ spl28_19,
inference(sat_conversion,[],[f335]) ).
cnf(s31,plain,
( ~ spl28_6
| ~ spl28_7 ),
inference(sat_conversion,[],[f338]) ).
cnf(s32,plain,
( ~ spl28_15
| ~ spl28_17 ),
inference(sat_conversion,[],[f342]) ).
cnf(s34,plain,
( ~ spl28_36
| ~ spl28_37 ),
inference(sat_conversion,[],[f362]) ).
cnf(s35,plain,
( ~ spl28_9
| ~ spl28_13 ),
inference(sat_conversion,[],[f368]) ).
cnf(s36,plain,
( ~ spl28_29
| ~ spl28_33 ),
inference(sat_conversion,[],[f373]) ).
cnf(s43,plain,
( ~ spl28_10
| ~ spl28_20
| ~ spl28_27
| spl28_39
| spl28_40 ),
inference(sat_conversion,[],[f510]) ).
cnf(s44,plain,
( ~ spl28_24
| ~ spl28_28 ),
inference(sat_conversion,[],[f513]) ).
cnf(s45,plain,
( ~ spl28_2
| ~ spl28_8
| ~ spl28_11
| ~ spl28_20
| ~ spl28_34
| ~ spl28_39 ),
inference(sat_conversion,[],[f529]) ).
cnf(s46,plain,
( ~ spl28_11
| ~ spl28_16
| ~ spl28_20
| ~ spl28_34
| ~ spl28_38
| ~ spl28_40 ),
inference(sat_conversion,[],[f553]) ).
cnf(s47,plain,
( ~ spl28_1
| ~ spl28_3 ),
inference(sat_conversion,[],[f556]) ).
cnf(s49,plain,
~ spl28_28,
inference(rat,[],[s44,s29]) ).
cnf(s50,plain,
~ spl28_37,
inference(rat,[],[s34,s28]) ).
cnf(s51,plain,
spl28_38,
inference(rat,[],[s27,s50]) ).
cnf(s53,plain,
~ spl28_9,
inference(rat,[],[s35,s25]) ).
cnf(s54,plain,
~ spl28_33,
inference(rat,[],[s36,s24]) ).
cnf(s55,plain,
spl28_34,
inference(rat,[],[s23,s54]) ).
cnf(s56,plain,
spl28_27,
inference(rat,[],[s19,s49]) ).
cnf(s57,plain,
~ spl28_1,
inference(rat,[],[s47,s15]) ).
cnf(s58,plain,
spl28_20,
inference(rat,[],[s13,s30]) ).
cnf(s60,plain,
~ spl28_15,
inference(rat,[],[s32,s12]) ).
cnf(s61,plain,
spl28_16,
inference(rat,[],[s10,s60]) ).
cnf(s62,plain,
spl28_11,
inference(rat,[],[s7,s53]) ).
cnf(s63,plain,
~ spl28_40,
inference(rat,[],[s46,s61,s51,s55,s58,s62]) ).
cnf(s64,plain,
spl28_10,
inference(rat,[],[s6,s53]) ).
cnf(s65,plain,
spl28_39,
inference(rat,[],[s43,s63,s58,s56,s64]) ).
cnf(s66,plain,
~ spl28_7,
inference(rat,[],[s31,s5]) ).
cnf(s67,plain,
spl28_8,
inference(rat,[],[s4,s66]) ).
cnf(s68,plain,
~ spl28_2,
inference(rat,[],[s45,s65,s55,s58,s62,s67]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s1,s68,s57]) ).
thf(f557,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU625^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:58:46 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.32 % (1709803)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (1709809)lrs+10_16_si=on:nwc=1.5:random_seed=2246491695:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (1709810)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2588620102:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (1709808)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2327973321:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (1709812)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2497752768:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (1709811)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=3980474371: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)
% 0.23/0.32 % (1709810)Instruction limit reached!
% 0.23/0.32 % (1709810)------------------------------
% 0.23/0.32 % (1709810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1709810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1709810)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1709810)Termination reason: Instruction limit
% 0.23/0.32 % (1709810)Termination phase: Saturation
% 0.23/0.32 % (1709810)Time elapsed: 0.002 s
% 0.23/0.32 % (1709810)Peak memory usage: 12 MB
% 0.23/0.32 % (1709810)Instructions burned: 3 (million)
% 0.23/0.32 % (1709814)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (1709814)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
% 0.23/0.32 % (1709814)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=2142537970:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (1709809)Instruction limit reached!
% 0.23/0.32 % (1709809)------------------------------
% 0.23/0.32 % (1709809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1709809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1709809)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1709809)Termination reason: Instruction limit
% 0.23/0.32 % (1709809)Termination phase: Saturation
% 0.23/0.32 % (1709809)Time elapsed: 0.011 s
% 0.23/0.32 % (1709809)Peak memory usage: 12 MB
% 0.23/0.32 % (1709809)Instructions burned: 19 (million)
% 0.23/0.32 % (1709813)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4285747427:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (1709812)Instruction limit reached!
% 0.23/0.32 % (1709812)------------------------------
% 0.23/0.32 % (1709812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1709812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1709812)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1709812)Termination reason: Instruction limit
% 0.23/0.32 % (1709812)Termination phase: Saturation
% 0.23/0.32 % (1709812)Time elapsed: 0.014 s
% 0.23/0.32 % (1709812)Peak memory usage: 11 MB
% 0.23/0.32 % (1709812)Instructions burned: 25 (million)
% 0.23/0.32 % (1709831)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=925650197:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.32 % (1709831)Instruction limit reached!
% 0.23/0.32 % (1709831)------------------------------
% 0.23/0.32 % (1709831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1709831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1709831)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1709831)Termination reason: Instruction limit
% 0.23/0.32 % (1709831)Termination phase: Property scanning
% 0.23/0.32 % (1709831)Time elapsed: 0.001 s
% 0.23/0.32 % (1709831)Peak memory usage: 11 MB
% 0.23/0.32 % (1709831)Instructions burned: 2 (million)
% 0.23/0.32 % (1709814) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1709803-1709814"...
% 0.23/0.32 % (1709814)...printing done.
% 0.23/0.32 % (1709814)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (1709814)------------------------------
% 0.23/0.32 % (1709814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1709814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1709814)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1709814)Termination reason: Refutation
% 0.23/0.32 % (1709814)Time elapsed: 0.019 s
% 0.23/0.32 % (1709814)Peak memory usage: 13 MB
% 0.23/0.32 % (1709814)Instructions burned: 31 (million)
% 0.23/0.32 % (1709803)Success in time 0.072 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------