%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV467^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:38:41 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 4
% Syntax : Number of formulae : 90 ( 29 unt; 0 typ; 2 def)
% Number of atoms : 710 ( 204 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1104 ( 9 ~; 80 |; 26 &; 868 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 11 con; 0-4 aty)
% ( 38 !!; 48 ??; 0 @@+; 0 @@-)
% Number of variables : 362 ( 249 ^; 95 !; 18 ?; 362 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK3: sK0 > sK1 > $o ).
thf(func_def_17,type,
sK4: sK0 > sK1 > sK2 ).
thf(func_def_18,type,
sK5: sK2 > $o ).
thf(func_def_19,type,
sF6: $o ).
thf(func_def_20,type,
sF7: $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
sK8: sK0 ).
thf(func_def_23,type,
sK9: sK2 ).
thf(func_def_24,type,
sK10: sK1 ).
thf(func_def_25,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sK11: sK0 ).
thf(func_def_27,type,
sK12: sK1 ).
thf(f1,axiom,
! [X0: $tType,X1: ( $o > X0 > $o ) > $o,X2: X0] :
( ( X1
@ ^ [X3: $o,X4: X0] :
( X3
& ( X2 = X4 ) ) )
= ( 'const/sets/IN' @ X0 @ X2
@ ( 'const/sets/GSPEC' @ X0
@ ^ [X3: X0] : ( X1 @ ( 'const/sets/SETSPEC' @ X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_ELIM_THM_0') ).
thf(f2,conjecture,
! [X1: $tType,X0: $tType,X2: $tType,X4: X1 > X2 > $o,X5: X1 > X2 > X0,X3: X0 > $o,X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6
@ ( 'const/sets/GSPEC' @ X0
@ ^ [X7: X0] :
? [X9: X2,X8: X1] : ( 'const/sets/SETSPEC' @ X0 @ X7 @ ( X4 @ X8 @ X9 ) @ ( X5 @ X8 @ X9 ) ) ) )
=> ( X3 @ X6 ) )
= ( ! [X7: X2,X6: X1] :
( ( X4 @ X6 @ X7 )
=> ( X3 @ ( X5 @ X6 @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_GSPEC_1') ).
thf(f3,negated_conjecture,
~ ! [X1: $tType,X0: $tType,X2: $tType,X4: X1 > X2 > $o,X5: X1 > X2 > X0,X3: X0 > $o,X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6
@ ( 'const/sets/GSPEC' @ X0
@ ^ [X7: X0] :
? [X9: X2,X8: X1] : ( 'const/sets/SETSPEC' @ X0 @ X7 @ ( X4 @ X8 @ X9 ) @ ( X5 @ X8 @ X9 ) ) ) )
=> ( X3 @ X6 ) )
= ( ! [X7: X2,X6: X1] :
( ( X4 @ X6 @ X7 )
=> ( X3 @ ( X5 @ X6 @ X7 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $tType,X1: ( $o > X0 > $o ) > $o,X2: X0] :
( ( X1
@ ^ [X3: $o,X4: X0] :
( X3
& ( X2 = X4 ) ) )
= ( 'const/sets/IN' @ X0 @ X2
@ ( 'const/sets/GSPEC' @ X0
@ ^ [X5: X0] : ( X1 @ ( 'const/sets/SETSPEC' @ X0 @ X5 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $tType] :
( ( !! @ X0
@ ^ [Y0: X0] :
( !! @ ( ( $o > X0 > $o ) > $o )
@ ^ [Y1: ( $o > X0 > $o ) > $o] :
( ( Y1
@ ^ [Y2: $o,Y3: X0] :
( ( Y0 = Y3 )
& Y2 ) )
= ( 'const/sets/IN' @ X0 @ Y0
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y2: X0] : ( Y1 @ ( 'const/sets/SETSPEC' @ X0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X2 > $o,X4: X0 > X2 > X1,X5: X1 > $o,X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6
@ ( 'const/sets/GSPEC' @ X1
@ ^ [X7: X1] :
? [X8: X2,X9: X0] : ( 'const/sets/SETSPEC' @ X1 @ X7 @ ( X3 @ X9 @ X8 ) @ ( X4 @ X9 @ X8 ) ) ) )
=> ( X5 @ X6 ) )
= ( ! [X10: X2,X11: X0] :
( ( X3 @ X11 @ X10 )
=> ( X5 @ ( X4 @ X11 @ X10 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $tType,X0: $tType,X2: $tType,X5: X1 > $o,X3: X0 > X2 > $o,X4: X0 > X2 > X1] :
( ( !! @ X1
@ ^ [Y0: X1] :
( ( 'const/sets/IN' @ X1 @ Y0
@ ( 'const/sets/GSPEC' @ X1
@ ^ [Y1: X1] :
( ?? @ X0
@ ^ [Y2: X0] :
( ?? @ X2
@ ^ [Y3: X2] : ( 'const/sets/SETSPEC' @ X1 @ Y1 @ ( X3 @ Y2 @ Y3 ) @ ( X4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( X5 @ Y0 ) ) )
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X2
@ ^ [Y1: X2] :
( ( X3 @ Y0 @ Y1 )
=> ( X5 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $tType] :
( ( !! @ X0
@ ^ [Y0: X0] :
( !! @ ( ( $o > X0 > $o ) > $o )
@ ^ [Y1: ( $o > X0 > $o ) > $o] :
( ( Y1
@ ^ [Y2: $o,Y3: X0] :
( ( Y0 = Y3 )
& Y2 ) )
= ( 'const/sets/IN' @ X0 @ Y0
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y2: X0] : ( Y1 @ ( 'const/sets/SETSPEC' @ X0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(closure,[],[f5]) ).
thf(f9,plain,
? [X0: $tType,X2: $tType,X1: $tType,X3: X0 > X2 > $o,X4: X0 > X2 > X1,X5: X1 > $o] :
( ( !! @ X1
@ ^ [Y0: X1] :
( ( 'const/sets/IN' @ X1 @ Y0
@ ( 'const/sets/GSPEC' @ X1
@ ^ [Y1: X1] :
( ?? @ X0
@ ^ [Y2: X0] :
( ?? @ X2
@ ^ [Y3: X2] : ( 'const/sets/SETSPEC' @ X1 @ Y1 @ ( X3 @ Y2 @ Y3 ) @ ( X4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( X5 @ Y0 ) ) )
!= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X2
@ ^ [Y1: X2] :
( ( X3 @ Y0 @ Y1 )
=> ( X5 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f10,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X1 > $o,X4: X0 > X1 > X2,X5: X2 > $o] :
( ( !! @ X2
@ ^ [Y0: X2] :
( ( 'const/sets/IN' @ X2 @ Y0
@ ( 'const/sets/GSPEC' @ X2
@ ^ [Y1: X2] :
( ?? @ X0
@ ^ [Y2: X0] :
( ?? @ X1
@ ^ [Y3: X1] : ( 'const/sets/SETSPEC' @ X2 @ Y1 @ ( X3 @ Y2 @ Y3 ) @ ( X4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( X5 @ Y0 ) ) )
!= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X1
@ ^ [Y1: X1] :
( ( X3 @ Y0 @ Y1 )
=> ( X5 @ ( X4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) )
!= ( !! @ sK2
@ ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f10]) ).
thf(f12,plain,
( ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) )
!= ( !! @ sK2
@ ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
! [X0: $tType] :
( ( !! @ X0
@ ^ [Y0: X0] :
( !! @ ( ( $o > X0 > $o ) > $o )
@ ^ [Y1: ( $o > X0 > $o ) > $o] :
( ( Y1
@ ^ [Y2: $o,Y3: X0] :
( ( Y0 = Y3 )
& Y2 ) )
= ( 'const/sets/IN' @ X0 @ Y0
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y2: X0] : ( Y1 @ ( 'const/sets/SETSPEC' @ X0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( sF6
= ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f17,plain,
( ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) )
= sF6 ),
inference(reorient_equations,[],[f16]) ).
thf(f18,definition,
( sF7
= ( !! @ sK2
@ ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f19,plain,
sF7 != sF6,
inference(definition_folding,[],[f12,f18,f17]) ).
thf(f20,plain,
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f21,plain,
( ( $false
= ( !! @ sK0
@ ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) ) ) )
| ( $true = sF6 ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f22,plain,
! [X0: $tType,X1: X0] :
( ( ^ [Y0: X0] :
( !! @ ( ( $o > X0 > $o ) > $o )
@ ^ [Y1: ( $o > X0 > $o ) > $o] :
( ( Y1
@ ^ [Y2: $o,Y3: X0] :
( ( Y0 = Y3 )
& Y2 ) )
= ( 'const/sets/IN' @ X0 @ Y0
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y2: X0] : ( Y1 @ ( 'const/sets/SETSPEC' @ X0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f13]) ).
thf(f23,plain,
! [X0: $tType,X1: X0] :
( ( !! @ ( ( $o > X0 > $o ) > $o )
@ ^ [Y0: ( $o > X0 > $o ) > $o] :
( ( Y0
@ ^ [Y1: $o,Y2: X0] :
( ( X1 = Y2 )
& Y1 ) )
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y1: X0] : ( Y0 @ ( 'const/sets/SETSPEC' @ X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( sF7 = $true )
| ( $true = sF6 ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f25,plain,
( ( sF7 = $false )
| ( $false = sF6 ) ),
inference(xor_proxy_clausification,[],[f19]) ).
thf(f26,plain,
( ( $false
= ( !! @ sK2
@ ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) ) ) )
| ( sF7 = $true ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f27,plain,
( ( ( !! @ sK2
@ ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) ) )
= $true )
| ( sF7 = $false ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f28,plain,
( ( $true = sF6 )
| ( $false
= ( ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f29,plain,
( ( $true = sF6 )
| ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK5 @ ( sK4 @ sK8 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: sK0] :
( ( $false = sF6 )
| ( ( ^ [Y0: sK0] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK5 @ ( sK4 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f31,plain,
! [X1: sK0] :
( ( $false = sF6 )
| ( $true
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( sK3 @ X1 @ Y0 )
=> ( sK5 @ ( sK4 @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X0: $tType,X2: ( $o > X0 > $o ) > $o,X1: X0] :
( ( ^ [Y0: ( $o > X0 > $o ) > $o] :
( ( Y0
@ ^ [Y1: $o,Y2: X0] :
( ( X1 = Y2 )
& Y1 ) )
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y1: X0] : ( Y0 @ ( 'const/sets/SETSPEC' @ X0 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f33,plain,
! [X0: $tType,X2: ( $o > X0 > $o ) > $o,X1: X0] :
( ( ( X2
@ ^ [Y0: $o,Y1: X0] :
( ( X1 = Y1 )
& Y0 ) )
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y0: X0] : ( X2 @ ( 'const/sets/SETSPEC' @ X0 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: sK2] :
( ( sF7 = $false )
| ( ( ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f35,plain,
! [X1: sK2] :
( ( ( ( 'const/sets/IN' @ sK2 @ X1
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK5 @ X1 ) )
= $true )
| ( sF7 = $false ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
( ( ( ^ [Y0: sK2] :
( ( 'const/sets/IN' @ sK2 @ Y0
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y1: sK2] :
( ?? @ sK0
@ ^ [Y2: sK0] :
( ?? @ sK1
@ ^ [Y3: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y1 @ ( sK3 @ Y2 @ Y3 ) @ ( sK4 @ Y2 @ Y3 ) ) ) ) ) )
=> ( sK5 @ Y0 ) )
@ sK9 )
= $false )
| ( sF7 = $true ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f37,plain,
( ( ( ( 'const/sets/IN' @ sK2 @ sK9
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK5 @ sK9 ) )
= $false )
| ( sF7 = $true ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
( ( $true = sF6 )
| ( ( ^ [Y0: sK1] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK5 @ ( sK4 @ sK8 @ Y0 ) ) )
@ sK10 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f29]) ).
thf(f39,plain,
( ( $true = sF6 )
| ( $false
= ( ( sK3 @ sK8 @ sK10 )
=> ( sK5 @ ( sK4 @ sK8 @ sK10 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: sK1,X1: sK0] :
( ( $false = sF6 )
| ( ( ^ [Y0: sK1] :
( ( sK3 @ X1 @ Y0 )
=> ( sK5 @ ( sK4 @ X1 @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f41,plain,
! [X2: sK1,X1: sK0] :
( ( ( ( sK3 @ X1 @ X2 )
=> ( sK5 @ ( sK4 @ X1 @ X2 ) ) )
= $true )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X0: $tType,X2: ( $o > X0 > $o ) > $o,X1: X0] :
( ( X2
@ ^ [Y0: $o,Y1: X0] :
( ( X1 = Y1 )
& Y0 ) )
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y0: X0] : ( X2 @ ( 'const/sets/SETSPEC' @ X0 @ Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f43,plain,
! [X1: sK2] :
( ( sF7 = $false )
| ( ( 'const/sets/IN' @ sK2 @ X1
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( ( sK5 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f44,plain,
( ( $false
= ( sK5 @ sK9 ) )
| ( sF7 = $true ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f45,plain,
( ( ( 'const/sets/IN' @ sK2 @ sK9
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ( sF7 = $true ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f46,plain,
( ( ( sK5 @ ( sK4 @ sK8 @ sK10 ) )
= $false )
| ( $true = sF6 ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f47,plain,
( ( ( sK3 @ sK8 @ sK10 )
= $true )
| ( $true = sF6 ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f48,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( sK5 @ ( sK4 @ X1 @ X2 ) ) )
| ( $false
= ( sK3 @ X1 @ X2 ) )
| ( $false = sF6 ) ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f49,plain,
! [X0: $tType,X2: ( $o > X0 > $o ) > $o,X1: X0] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y0: X0] : ( X2 @ ( 'const/sets/SETSPEC' @ X0 @ Y0 ) ) ) ) )
| ( ( X2
@ ^ [Y0: $o,Y1: X0] :
( ( X1 = Y1 )
& Y0 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f50,plain,
! [X0: $tType,X2: ( $o > X0 > $o ) > $o,X1: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1
@ ( 'const/sets/GSPEC' @ X0
@ ^ [Y0: X0] : ( X2 @ ( 'const/sets/SETSPEC' @ X0 @ Y0 ) ) ) ) )
| ( $false
= ( X2
@ ^ [Y0: $o,Y1: X0] :
( ( X1 = Y1 )
& Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f80,plain,
( ( $false = $true )
| ( sF7 = $true )
| ( $true
= ( ^ [Y0: $o > sK2 > $o] :
( ?? @ sK0
@ ( ^ [Y1: $o > sK2 > $o,Y2: sK0] :
( ?? @ sK1
@ ( ^ [Y3: $o > sK2 > $o,Y4: sK0,Y5: sK1] :
( Y3
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK3
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 )
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK4
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ^ [Y0: $o,Y1: sK2] :
( ( sK9 = Y1 )
& Y0 ) ) ) ),
inference(constrained_superposition,[],[f45,f49]) ).
thf(f82,plain,
( ( $true
= ( ^ [Y0: $o > sK2 > $o] :
( ?? @ sK0
@ ( ^ [Y1: $o > sK2 > $o,Y2: sK0] :
( ?? @ sK1
@ ( ^ [Y3: $o > sK2 > $o,Y4: sK0,Y5: sK1] :
( Y3
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK3
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 )
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK4
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ^ [Y0: $o,Y1: sK2] :
( ( sK9 = Y1 )
& Y0 ) ) )
| ( sF7 = $true ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f83,plain,
( ( sF7 = $true )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ?? @ sK1
@ ^ [Y1: sK1] :
( ( sK9
= ( sK4 @ Y0 @ Y1 ) )
& ( sK3 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f86,plain,
( ( ( ^ [Y0: sK0] :
( ?? @ sK1
@ ^ [Y1: sK1] :
( ( sK9
= ( sK4 @ Y0 @ Y1 ) )
& ( sK3 @ Y0 @ Y1 ) ) )
@ sK11 )
= $true )
| ( sF7 = $true ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f87,plain,
( ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( sK9
= ( sK4 @ sK11 @ Y0 ) )
& ( sK3 @ sK11 @ Y0 ) ) )
= $true )
| ( sF7 = $true ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f90,plain,
( ( ( ^ [Y0: sK1] :
( ( sK9
= ( sK4 @ sK11 @ Y0 ) )
& ( sK3 @ sK11 @ Y0 ) )
@ sK12 )
= $true )
| ( sF7 = $true ) ),
inference(sigma_proxy_clausification,[],[f87]) ).
thf(f91,plain,
( ( ( ( sK9
= ( sK4 @ sK11 @ sK12 ) )
& ( sK3 @ sK11 @ sK12 ) )
= $true )
| ( sF7 = $true ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f94,plain,
( ( ( sK3 @ sK11 @ sK12 )
= $true )
| ( sF7 = $true ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f95,plain,
( ( sF7 = $true )
| ( ( sK9
= ( sK4 @ sK11 @ sK12 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f98,plain,
( ( ( sK4 @ sK11 @ sK12 )
= sK9 )
| ( sF7 = $true ) ),
inference(equality_proxy_clausification,[],[f95]) ).
thf(f100,plain,
( ( ( sK3 @ sK11 @ sK12 )
= $false )
| ( $false = sF6 )
| ( ( sK5 @ sK9 )
= $true )
| ( sF7 = $true ) ),
inference(constrained_superposition,[],[f48,f98]) ).
thf(f102,plain,
( ( $false = sF6 )
| ( $false = $true )
| ( ( sK5 @ sK9 )
= $true )
| ( sF7 = $true )
| ( sF7 = $true ) ),
inference(constrained_superposition,[],[f100,f94]) ).
thf(f105,plain,
( ( sF7 = $true )
| ( $false = sF6 )
| ( ( sK5 @ sK9 )
= $true )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f102]) ).
thf(f106,plain,
( ( ( sK5 @ sK9 )
= $true )
| ( $false = sF6 )
| ( sF7 = $true ) ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f109,plain,
( ( sF7 = $true )
| ( $false = sF6 )
| ( sF7 = $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f106,f44]) ).
thf(f111,plain,
( ( $false = $true )
| ( sF7 = $true )
| ( $false = sF6 ) ),
inference(duplicate_literal_removal,[],[f109]) ).
thf(f112,plain,
( ( sF7 = $true )
| ( $false = sF6 ) ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f115,plain,
( ( $false = sF6 )
| ( $false = sF6 )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f112,f25]) ).
thf(f117,plain,
( ( $false = $true )
| ( $false = sF6 ) ),
inference(duplicate_literal_removal,[],[f115]) ).
thf(f118,plain,
$false = sF6,
inference(trivial_inequality_removal,[],[f117]) ).
thf(f121,plain,
( ( $false = $true )
| ( sF7 = $true ) ),
inference(backward_demodulation,[],[f24,f118]) ).
thf(f122,plain,
( ( ( sK5 @ ( sK4 @ sK8 @ sK10 ) )
= $false )
| ( $false = $true ) ),
inference(backward_demodulation,[],[f46,f118]) ).
thf(f123,plain,
( ( ( sK3 @ sK8 @ sK10 )
= $true )
| ( $false = $true ) ),
inference(backward_demodulation,[],[f47,f118]) ).
thf(f124,plain,
sF7 = $true,
inference(trivial_inequality_removal,[],[f121]) ).
thf(f125,plain,
( ( sK3 @ sK8 @ sK10 )
= $true ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f126,plain,
( ( sK5 @ ( sK4 @ sK8 @ sK10 ) )
= $false ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f127,plain,
! [X1: sK2] :
( ( ( sK5 @ X1 )
= $true )
| ( $false = $true )
| ( ( 'const/sets/IN' @ sK2 @ X1
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(backward_demodulation,[],[f43,f124]) ).
thf(f128,plain,
! [X1: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ X1
@ ( 'const/sets/GSPEC' @ sK2
@ ^ [Y0: sK2] :
( ?? @ sK0
@ ^ [Y1: sK0] :
( ?? @ sK1
@ ^ [Y2: sK1] : ( 'const/sets/SETSPEC' @ sK2 @ Y0 @ ( sK3 @ Y1 @ Y2 ) @ ( sK4 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( ( sK5 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f134,plain,
! [X0: sK2] :
( ( $false = $true )
| ( ( sK5 @ X0 )
= $true )
| ( ( ^ [Y0: $o > sK2 > $o] :
( ?? @ sK0
@ ( ^ [Y1: $o > sK2 > $o,Y2: sK0] :
( ?? @ sK1
@ ( ^ [Y3: $o > sK2 > $o,Y4: sK0,Y5: sK1] :
( Y3
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK3
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 )
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK4
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ^ [Y0: $o,Y1: sK2] :
( ( X0 = Y1 )
& Y0 ) )
= $false ) ),
inference(constrained_superposition,[],[f128,f50]) ).
thf(f137,plain,
! [X0: sK2] :
( ( ( ^ [Y0: $o > sK2 > $o] :
( ?? @ sK0
@ ( ^ [Y1: $o > sK2 > $o,Y2: sK0] :
( ?? @ sK1
@ ( ^ [Y3: $o > sK2 > $o,Y4: sK0,Y5: sK1] :
( Y3
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK3
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 )
@ ( ^ [Y6: $o > sK2 > $o,Y7: sK0,Y8: sK1] :
( sK4
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y10
@ Y6
@ Y7
@ Y8 )
@ ( ^ [Y9: $o > sK2 > $o,Y10: sK0,Y11: sK1] : Y11
@ Y6
@ Y7
@ Y8 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) )
@ ^ [Y0: $o,Y1: sK2] :
( ( X0 = Y1 )
& Y0 ) )
= $false )
| ( ( sK5 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f138,plain,
! [X0: sK2] :
( ( ( sK5 @ X0 )
= $true )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ?? @ sK1
@ ^ [Y1: sK1] :
( ( X0
= ( sK4 @ Y0 @ Y1 ) )
& ( sK3 @ Y0 @ Y1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f141,plain,
! [X0: sK2,X1: sK0] :
( ( ( ^ [Y0: sK0] :
( ?? @ sK1
@ ^ [Y1: sK1] :
( ( X0
= ( sK4 @ Y0 @ Y1 ) )
& ( sK3 @ Y0 @ Y1 ) ) )
@ X1 )
= $false )
| ( ( sK5 @ X0 )
= $true ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f142,plain,
! [X0: sK2,X1: sK0] :
( ( ( sK5 @ X0 )
= $true )
| ( $false
= ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( X0
= ( sK4 @ X1 @ Y0 ) )
& ( sK3 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f145,plain,
! [X2: sK1,X0: sK2,X1: sK0] :
( ( $false
= ( ^ [Y0: sK1] :
( ( X0
= ( sK4 @ X1 @ Y0 ) )
& ( sK3 @ X1 @ Y0 ) )
@ X2 ) )
| ( ( sK5 @ X0 )
= $true ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f146,plain,
! [X2: sK1,X0: sK2,X1: sK0] :
( ( $false
= ( ( X0
= ( sK4 @ X1 @ X2 ) )
& ( sK3 @ X1 @ X2 ) ) )
| ( ( sK5 @ X0 )
= $true ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f149,plain,
! [X2: sK1,X0: sK2,X1: sK0] :
( ( $false
= ( sK3 @ X1 @ X2 ) )
| ( $false
= ( X0
= ( sK4 @ X1 @ X2 ) ) )
| ( ( sK5 @ X0 )
= $true ) ),
inference(and_proxy_clausification,[],[f146]) ).
thf(f151,plain,
! [X2: sK1,X0: sK2,X1: sK0] :
( ( ( sK4 @ X1 @ X2 )
!= X0 )
| ( ( sK5 @ X0 )
= $true )
| ( $false
= ( sK3 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f149]) ).
thf(f153,plain,
! [X0: sK0,X1: sK1] :
( ( ( sK5 @ ( sK4 @ X0 @ X1 ) )
= $true )
| ( $false
= ( sK3 @ X0 @ X1 ) ) ),
inference(equality_resolution,[],[f151]) ).
thf(f154,plain,
( ( ( sK3 @ sK8 @ sK10 )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f153,f126]) ).
thf(f156,plain,
( ( sK3 @ sK8 @ sK10 )
= $false ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f158,plain,
$false = $true,
inference(backward_demodulation,[],[f125,f156]) ).
thf(f159,plain,
$false,
inference(trivial_inequality_removal,[],[f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV467^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:49:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (1462709)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (1462718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=357543335:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (1462718)Refutation not found, incomplete strategy
% 0.21/0.31 % (1462718)------------------------------
% 0.21/0.31 % (1462718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462718)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462718)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1462718)Time elapsed: 0.002 s
% 0.21/0.31 % (1462718)Peak memory usage: 12 MB
% 0.21/0.31 % (1462718)Instructions burned: 4 (million)
% 0.21/0.31 % (1462718)------------------------------
% 0.21/0.31 % (1462718)------------------------------
% 0.21/0.31 % (1462720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (1462720)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
% 0.21/0.31 % (1462714)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1759781660:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (1462715)lrs+10_16_si=on:nwc=1.5:random_seed=519600842:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (1462716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2049508735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (1462719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3745560253:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (1462717)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=1985644906: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)
% 0.21/0.31 % (1462720)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=420148087:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (1462714)Refutation not found, incomplete strategy
% 0.21/0.31 % (1462714)------------------------------
% 0.21/0.31 % (1462714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462714)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462714)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1462714)Time elapsed: 0.003 s
% 0.21/0.31 % (1462714)Peak memory usage: 12 MB
% 0.21/0.31 % (1462714)Instructions burned: 3 (million)
% 0.21/0.31 % (1462716)Refutation not found, incomplete strategy
% 0.21/0.31 % (1462716)------------------------------
% 0.21/0.31 % (1462716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462716)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462716)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1462716)Time elapsed: 0.002 s
% 0.21/0.31 % (1462716)Peak memory usage: 12 MB
% 0.21/0.31 % (1462716)Instructions burned: 2 (million)
% 0.21/0.31 % (1462714)------------------------------
% 0.21/0.31 % (1462714)------------------------------
% 0.21/0.31 % (1462716)------------------------------
% 0.21/0.31 % (1462716)------------------------------
% 0.21/0.31 % (1462717)Refutation not found, incomplete strategy
% 0.21/0.31 % (1462717)------------------------------
% 0.21/0.31 % (1462717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462717)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462717)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1462717)Time elapsed: 0.003 s
% 0.21/0.31 % (1462717)Peak memory usage: 12 MB
% 0.21/0.31 % (1462717)Instructions burned: 4 (million)
% 0.21/0.31 % (1462717)------------------------------
% 0.21/0.31 % (1462717)------------------------------
% 0.21/0.31 % (1462720)Refutation not found, incomplete strategy
% 0.21/0.31 % (1462720)------------------------------
% 0.21/0.31 % (1462720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462720)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462720)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1462720)Time elapsed: 0.004 s
% 0.21/0.31 % (1462720)Peak memory usage: 12 MB
% 0.21/0.31 % (1462720)Instructions burned: 6 (million)
% 0.21/0.31 % (1462722)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1553289893:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (1462720)------------------------------
% 0.21/0.31 % (1462720)------------------------------
% 0.21/0.31 % (1462722)Instruction limit reached!
% 0.21/0.31 % (1462722)------------------------------
% 0.21/0.31 % (1462722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462722)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462722)Termination reason: Instruction limit
% 0.21/0.31 % (1462722)Termination phase: Saturation
% 0.21/0.31 % (1462722)Time elapsed: 0.001 s
% 0.21/0.31 % (1462722)Peak memory usage: 12 MB
% 0.21/0.31 % (1462722)Instructions burned: 2 (million)
% 0.21/0.31 % (1462715)Instruction limit reached!
% 0.21/0.31 % (1462715)------------------------------
% 0.21/0.31 % (1462715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462715)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462715)Termination reason: Instruction limit
% 0.21/0.31 % (1462715)Termination phase: Saturation
% 0.21/0.31 % (1462715)Time elapsed: 0.012 s
% 0.21/0.31 % (1462715)Peak memory usage: 12 MB
% 0.21/0.31 % (1462715)Instructions burned: 19 (million)
% 0.21/0.31 % (1462734)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1807168080:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.31 % (1462730)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (1462733)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
% 0.21/0.31 % (1462733)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (1462729)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=398421517:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (1462730)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=23156502:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.31 % (1462732)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3263216949:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.31 % (1462733)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1506763036:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.31 % (1462729)Instruction limit reached!
% 0.21/0.31 % (1462729)------------------------------
% 0.21/0.31 % (1462729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462729)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462729)Termination reason: Instruction limit
% 0.21/0.31 % (1462729)Termination phase: Saturation
% 0.21/0.31 % (1462729)Time elapsed: 0.004 s
% 0.21/0.31 % (1462729)Peak memory usage: 12 MB
% 0.21/0.31 % (1462729)Instructions burned: 6 (million)
% 0.21/0.31 % (1462730)Instruction limit reached!
% 0.21/0.31 % (1462730)------------------------------
% 0.21/0.31 % (1462730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462730)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462730)Termination reason: Instruction limit
% 0.21/0.31 % (1462730)Termination phase: Saturation
% 0.21/0.31 % (1462730)Time elapsed: 0.005 s
% 0.21/0.31 % (1462730)Peak memory usage: 12 MB
% 0.21/0.31 % (1462730)Instructions burned: 8 (million)
% 0.21/0.31 % (1462735)lrs+10_1_si=on:cs=on:random_seed=4099943558:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.31 % (1462732)Instruction limit reached!
% 0.21/0.31 % (1462732)------------------------------
% 0.21/0.31 % (1462732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462732)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462732)Termination reason: Instruction limit
% 0.21/0.31 % (1462732)Termination phase: Saturation
% 0.21/0.31 % (1462732)Time elapsed: 0.008 s
% 0.21/0.31 % (1462732)Peak memory usage: 12 MB
% 0.21/0.31 % (1462732)Instructions burned: 13 (million)
% 0.21/0.31 % (1462735)Instruction limit reached!
% 0.21/0.31 % (1462735)------------------------------
% 0.21/0.31 % (1462735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462735)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462735)Termination reason: Instruction limit
% 0.21/0.31 % (1462735)Termination phase: Saturation
% 0.21/0.31 % (1462735)Time elapsed: 0.004 s
% 0.21/0.31 % (1462735)Peak memory usage: 11 MB
% 0.21/0.31 % (1462735)Instructions burned: 9 (million)
% 0.21/0.31 % (1462733) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1462709-1462733"...
% 0.21/0.31 % (1462741)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.31 % (1462734)Instruction limit reached!
% 0.21/0.31 % (1462734)------------------------------
% 0.21/0.31 % (1462734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462734)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462734)Termination reason: Instruction limit
% 0.21/0.31 % (1462734)Termination phase: Saturation
% 0.21/0.31 % (1462734)Time elapsed: 0.024 s
% 0.21/0.31 % (1462734)Peak memory usage: 12 MB
% 0.21/0.31 % (1462734)Instructions burned: 86 (million)
% 0.21/0.31 % (1462719)Instruction limit reached!
% 0.21/0.31 % (1462719)------------------------------
% 0.21/0.31 % (1462719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1462719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1462719)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1462719)Termination reason: Instruction limit
% 0.21/0.31 % (1462719)Termination phase: Saturation
% 0.21/0.31 % (1462719)Time elapsed: 0.043 s
% 0.21/0.31 % (1462719)Peak memory usage: 12 MB
% 0.21/0.31 % (1462719)Instructions burned: 75 (million)
% 0.21/0.31 % (1462733)...printing done.
% 0.21/0.31 % (1462733)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (1462733)------------------------------
% 0.21/0.32 % (1462733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1462733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1462733)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1462733)Termination reason: Refutation
% 0.21/0.32 % (1462733)Time elapsed: 0.017 s
% 0.21/0.32 % (1462733)Peak memory usage: 12 MB
% 0.21/0.32 % (1462733)Instructions burned: 31 (million)
% 0.21/0.32 % (1462709)Success in time 0.075 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------