%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PLA053^2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:20:26 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 511 ( 99 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 744 ( 21 ~; 41 |; 27 &; 562 @)
% ( 2 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 35 usr; 9 con; 0-4 aty)
% ( 27 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 201 ( 0 sgn 46 !; 2 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
h: $i > mworld > $o ).
thf(func_def_14,type,
bomb: $i > mworld > $o ).
thf(func_def_15,type,
defused: $i > mworld > $o ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
sK0: mworld ).
thf(func_def_32,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK2: mworld > $i > $i ).
thf(func_def_35,type,
sK4: mworld > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f11,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f15,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f20,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f24,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f28,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f33,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f35,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f37,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f42,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f43,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f45,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f45]) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f55,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f56,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f57,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f60,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f61,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f66,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f60,f47,f53,f56,f57,f53,f51,f49]) ).
thf(f67,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f61,f47,f53,f56,f57,f51,f49]) ).
thf(f68,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK0 )
& ( h @ Y1 @ sK0 ) )
=> ( defused @ Y0 @ sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK0 )
& ( h @ Y1 @ sK0 ) )
=> ( defused @ Y0 @ sK0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK0 )
& ( h @ Y1 @ sK0 ) )
=> ( defused @ Y0 @ sK0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( bomb @ sK1 @ sK0 )
& ( h @ Y0 @ sK0 ) )
=> ( defused @ sK1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ( bomb @ sK1 @ sK0 )
& ( h @ Y0 @ sK0 ) )
=> ( defused @ sK1 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X1: $i] :
( $false
= ( ( ( bomb @ sK1 @ sK0 )
& ( h @ X1 @ sK0 ) )
=> ( defused @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $false
= ( defused @ sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X1: $i] :
( $true
= ( ( bomb @ sK1 @ sK0 )
& ( h @ X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: $i] :
( $true
= ( h @ X1 @ sK0 ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( $true
= ( bomb @ sK1 @ sK0 ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f81,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( bomb @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f82,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( bomb @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) ) )
| ( $true
= ( defused @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( defused @ X2 @ X3 ) )
| ( $false
= ( bomb @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f173,plain,
! [X0: mworld,X1: $i] :
( ( $true = $false )
| ( $false
= ( mrel @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( defused @ X1 @ sK0 ) )
| ( $false
= ( bomb @ X1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f93,f79]) ).
thf(f178,plain,
! [X0: mworld,X1: $i] :
( ( $false
= ( mrel @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( defused @ X1 @ sK0 ) )
| ( $false
= ( bomb @ X1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f173]) ).
thf(f180,definition,
( spl5_4
<=> ! [X1: $i] :
( ( $true
= ( defused @ X1 @ sK0 ) )
| ( $false
= ( bomb @ X1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f181,plain,
( ! [X1: $i] :
( ( $true
= ( defused @ X1 @ sK0 ) )
| ( $false
= ( bomb @ X1 @ sK0 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f183,definition,
( spl5_5
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f184,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f186,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f178,f183,f180]) ).
thf(f233,plain,
( ( $true = $false )
| ( $false
= ( bomb @ sK1 @ sK0 ) )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f77,f181]) ).
thf(f234,plain,
( ( $false
= ( bomb @ sK1 @ sK0 ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f244,plain,
( ( $true = $false )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f234,f80]) ).
thf(f254,plain,
( $false
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f255,plain,
~ spl5_4,
inference(avatar_contradiction_clause,[],[f254]) ).
thf(f257,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f184,f72]) ).
thf(f266,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f271,plain,
( ( $true = $false )
| ~ spl5_5 ),
inference(forward_demodulation,[],[f266,f55]) ).
thf(f272,plain,
( $false
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f273,plain,
~ spl5_5,
inference(avatar_contradiction_clause,[],[f272]) ).
cnf(s6,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f186]) ).
cnf(s8,plain,
~ spl5_4,
inference(sat_conversion,[],[f255]) ).
cnf(s10,plain,
~ spl5_5,
inference(sat_conversion,[],[f273]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s10,s8]) ).
thf(f274,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053^2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n005.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:20:31 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (1641102)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1641110)dis+10_1_sil=32000:sp=arity:random_seed=3109365412:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (1641108)% WARNING: option uhcvi not known.
% 0.09/0.25 % (1641110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1641102-1641110"...
% 0.09/0.25 % (1641109)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1125977973:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (1641108)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2188835917:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (1641107)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=409694194_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (1641112)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4162313925:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (1641111)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2071619710:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (1641110)...printing done.
% 0.09/0.25 % (1641113)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=318328801:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (1641108)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (1641110)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (1641110)------------------------------
% 0.09/0.26 % (1641110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (1641110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (1641110)CaDiCaL version: 2.1.3
% 0.09/0.26 % (1641110)Termination reason: Refutation
% 0.09/0.26 % (1641110)Time elapsed: 0.008 s
% 0.09/0.26 % (1641110)Peak memory usage: 13 MB
% 0.09/0.26 % (1641110)Instructions burned: 25 (million)
% 0.09/0.26 % (1641102)Success in time 0.039 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------