%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA053^2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:20:25 AM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 115 ( 49 unt; 0 typ; 8 def)
% Number of atoms : 656 ( 125 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 905 ( 47 ~; 85 |; 29 &; 636 @)
% ( 7 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 42 usr; 15 con; 0-4 aty)
% ( 31 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 239 ( 0 sgn 48 !; 2 ?; 239 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
sF0: $o ).
thf(func_def_30,type,
sK1: mworld > $i ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
sK2: mworld > $i > $i ).
thf(func_def_33,type,
sK3: mworld ).
thf(func_def_35,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK6: mworld > $i > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f18,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f20,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f25,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f26,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f31,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f32,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f31]) ).
thf(f33,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f34,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
inference(rectify,[],[f10]) ).
thf(f36,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f46,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f20]) ).
thf(f48,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f49,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f50,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f51,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(f53,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f55,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f58,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f60,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f65,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,[],[f51,f48,f56,f53,f55,f60,f50]) ).
thf(f66,plain,
( ( ^ [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 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f58,f48,f56,f53,f55,f56,f60,f50]) ).
thf(f68,definition,
( sF0
= ( ^ [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 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f69,plain,
sF0 != $true,
inference(definition_folding,[],[f65,f68]) ).
thf(f76,plain,
( ( ( ^ [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 ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f68]) ).
thf(f88,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f89,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) )
@ sK3 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( sF0 = $true )
| ( $false
= ( ( mrel @ mactual @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( ( sF0 = $true )
| ( ( mrel @ mactual @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f93,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( bomb @ sK4 @ sK3 )
& ( h @ Y0 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( ( bomb @ sK4 @ sK3 )
& ( h @ Y0 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: $i] :
( ( $false
= ( ( ( bomb @ sK4 @ sK3 )
& ( h @ X1 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( $false
= ( defused @ sK4 @ sK3 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ( bomb @ sK4 @ sK3 )
& ( h @ X1 @ sK3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f99,plain,
! [X1: $i] :
( ( $true
= ( h @ X1 @ sK3 ) )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( sF0 = $true )
| ( $true
= ( bomb @ sK4 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f114,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(f115,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,[],[f114]) ).
thf(f116,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,[],[f115]) ).
thf(f117,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $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,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) )
@ ( sK6 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK6 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK6 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) )
@ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X1 @ X3 )
=> ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK6 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK6 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( defused @ X2 @ X3 ) )
| ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK6 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( h @ ( sK6 @ X1 @ X2 ) @ X3 )
= $false )
| ( $true
= ( defused @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( bomb @ X2 @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f136,definition,
( spl7_3
<=> ( ( mrel @ mactual @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f138,plain,
( ( ( mrel @ mactual @ sK3 )
= $true )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f140,definition,
( spl7_4
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f143,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f92,f140,f136]) ).
thf(f145,definition,
( spl7_5
<=> ( $true
= ( bomb @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f147,plain,
( ( $true
= ( bomb @ sK4 @ sK3 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f148,plain,
( spl7_4
| spl7_5 ),
inference(avatar_split_clause,[],[f100,f145,f140]) ).
thf(f150,definition,
( spl7_6
<=> ! [X1: $i] :
( $true
= ( h @ X1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f151,plain,
( ! [X1: $i] :
( $true
= ( h @ X1 @ sK3 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f152,plain,
( spl7_6
| spl7_4 ),
inference(avatar_split_clause,[],[f99,f140,f150]) ).
thf(f154,definition,
( spl7_7
<=> ( $false
= ( defused @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f156,plain,
( ( $false
= ( defused @ sK4 @ sK3 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f157,plain,
( spl7_7
| spl7_4 ),
inference(avatar_split_clause,[],[f97,f140,f154]) ).
thf(f158,plain,
~ spl7_4,
inference(avatar_split_clause,[],[f69,f140]) ).
thf(f172,plain,
( ! [X0: mworld,X1: $i] :
( ( ( defused @ X1 @ sK3 )
= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( bomb @ X1 @ sK3 )
= $false )
| ( $true = $false )
| ( ( mrel @ X0 @ sK3 )
= $false ) )
| ~ spl7_6 ),
inference(constrained_superposition,[],[f126,f151]) ).
thf(f176,plain,
( ! [X0: mworld,X1: $i] :
( ( ( bomb @ X1 @ sK3 )
= $false )
| ( ( defused @ X1 @ sK3 )
= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK3 )
= $false ) )
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f179,definition,
( spl7_8
<=> ! [X0: mworld] :
( ( ( mrel @ X0 @ sK3 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f180,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK3 )
= $false ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f182,definition,
( spl7_9
<=> ! [X1: $i] :
( ( ( defused @ X1 @ sK3 )
= $true )
| ( ( bomb @ X1 @ sK3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f183,plain,
( ! [X1: $i] :
( ( ( defused @ X1 @ sK3 )
= $true )
| ( ( bomb @ X1 @ sK3 )
= $false ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f185,plain,
( spl7_8
| spl7_9
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f176,f150,f182,f179]) ).
thf(f190,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $true = $false )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f49,f180]) ).
thf(f195,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f205,plain,
( ( $true = $false )
| ~ spl7_3
| ~ spl7_8 ),
inference(forward_demodulation,[],[f195,f138]) ).
thf(f206,plain,
( $false
| ~ spl7_3
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f207,plain,
( ~ spl7_3
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( bomb @ sK4 @ sK3 ) )
| ( $true = $false )
| ~ spl7_7
| ~ spl7_9 ),
inference(constrained_superposition,[],[f183,f156]) ).
thf(f211,plain,
( ( $false
= ( bomb @ sK4 @ sK3 ) )
| ~ spl7_7
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f208]) ).
thf(f215,plain,
( ( $true = $false )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(forward_demodulation,[],[f211,f147]) ).
thf(f216,plain,
( $false
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f217,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f216]) ).
cnf(s2,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f143]) ).
cnf(s3,plain,
( spl7_4
| spl7_5 ),
inference(sat_conversion,[],[f148]) ).
cnf(s4,plain,
( spl7_4
| spl7_6 ),
inference(sat_conversion,[],[f152]) ).
cnf(s5,plain,
( spl7_4
| spl7_7 ),
inference(sat_conversion,[],[f157]) ).
cnf(s6,plain,
~ spl7_4,
inference(sat_conversion,[],[f158]) ).
cnf(s8,plain,
( ~ spl7_6
| spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f185]) ).
cnf(s12,plain,
( ~ spl7_3
| ~ spl7_8 ),
inference(sat_conversion,[],[f207]) ).
cnf(s14,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(sat_conversion,[],[f217]) ).
cnf(s15,plain,
spl7_7,
inference(rat,[],[s5,s6]) ).
cnf(s16,plain,
spl7_6,
inference(rat,[],[s4,s6]) ).
cnf(s17,plain,
spl7_5,
inference(rat,[],[s3,s6]) ).
cnf(s18,plain,
~ spl7_9,
inference(rat,[],[s14,s15,s17]) ).
cnf(s19,plain,
spl7_8,
inference(rat,[],[s8,s16,s18]) ).
cnf(s20,plain,
~ spl7_3,
inference(rat,[],[s12,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s2,s6,s20]) ).
thf(f218,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053^2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:25:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.25/0.35 % (332799)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (332804)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2416378232:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.35 % (332805)lrs+10_16_si=on:nwc=1.5:random_seed=2932428296:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (332806)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1018814919:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.35 % (332806)Instruction limit reached!
% 0.25/0.35 % (332806)------------------------------
% 0.25/0.35 % (332806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (332806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (332806)CaDiCaL version: 2.1.3
% 0.25/0.35 % (332806)Termination reason: Instruction limit
% 0.25/0.35 % (332806)Termination phase: Saturation
% 0.25/0.35 % (332806)Time elapsed: 0.002 s
% 0.25/0.35 % (332806)Peak memory usage: 11 MB
% 0.25/0.35 % (332806)Instructions burned: 4 (million)
% 0.25/0.35 % (332808)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=596638833:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.35 % (332810)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.35 % (332810)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
% 0.25/0.35 % (332805)Instruction limit reached!
% 0.25/0.35 % (332805)------------------------------
% 0.25/0.35 % (332805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (332805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (332805)CaDiCaL version: 2.1.3
% 0.25/0.35 % (332805)Termination reason: Instruction limit
% 0.25/0.35 % (332805)Termination phase: Saturation
% 0.25/0.35 % (332805)Time elapsed: 0.015 s
% 0.25/0.35 % (332805)Peak memory usage: 12 MB
% 0.25/0.35 % (332805)Instructions burned: 19 (million)
% 0.25/0.35 % (332807)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=1066953528: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)
% 0.25/0.35 % (332809)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1033158672:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.35 % (332810)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=3965976677:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.35 % (332808)Instruction limit reached!
% 0.25/0.35 % (332808)------------------------------
% 0.25/0.35 % (332808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (332808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (332808)CaDiCaL version: 2.1.3
% 0.25/0.35 % (332808)Termination reason: Instruction limit
% 0.25/0.35 % (332808)Termination phase: Saturation
% 0.25/0.35 % (332808)Time elapsed: 0.015 s
% 0.25/0.35 % (332808)Peak memory usage: 12 MB
% 0.25/0.35 % (332808)Instructions burned: 25 (million)
% 0.25/0.35 % (332810) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-332799-332810"...
% 0.25/0.35 % (332809) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-332799-332809"...
% 0.25/0.35 % (332810)...printing done.
% 0.25/0.35 % (332810)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (332810)------------------------------
% 0.25/0.35 % (332810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (332810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (332810)CaDiCaL version: 2.1.3
% 0.25/0.35 % (332810)Termination reason: Refutation
% 0.25/0.35 % (332810)Time elapsed: 0.017 s
% 0.25/0.35 % (332810)Peak memory usage: 13 MB
% 0.25/0.35 % (332810)Instructions burned: 17 (million)
% 0.25/0.35 % (332799)Success in time 0.09 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------