%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL962^16 : 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 : n017.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 08:15:29 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 50 unt; 0 typ; 3 def)
% Number of atoms : 603 ( 134 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 803 ( 56 ~; 80 |; 0 &; 575 @)
% ( 3 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 10 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 0 sgn 45 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
mindex: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_1,type,
'#b': mindex ).
thf(func_def_2,type,
'#a': mindex ).
thf(func_def_3,type,
mactual: mworld ).
thf(func_def_4,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_6,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
p: mworld > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
vIFF: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: mworld ).
thf(func_def_29,type,
sK1: mworld > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_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: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ '#b' @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_reflexive') ).
thf(f13,axiom,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).
thf(f14,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).
thf(f15,axiom,
mlocal @ ( mnot @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).
thf(f16,conjecture,
mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f17,negated_conjecture,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f19,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f20,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f25,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f30,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f33,plain,
! [X0: mworld] : ( mrel @ '#b' @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f34,plain,
! [X0: mworld] :
( ( mrel @ '#b' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f33]) ).
thf(f41,plain,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
inference(rectify,[],[f13]) ).
thf(f42,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f44,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
mlocal @ ( mnot @ p ),
inference(rectify,[],[f15]) ).
thf(f46,plain,
( ( mlocal @ ( mnot @ p ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(rectify,[],[f17]) ).
thf(f48,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(flattening,[],[f48]) ).
thf(f54,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f55,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f60,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f62,plain,
! [X0: mworld] :
( ( mrel @ '#b' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f66,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f67,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f44]) ).
thf(f68,plain,
( ( mlocal @ ( mnot @ p ) )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f69,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f72,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f66,f54,f60,f58,f60]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f67,f54,f58,f55,f60,f60,f55,f60]) ).
thf(f74,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ),
inference(definition_unfolding,[],[f68,f54,f55]) ).
thf(f75,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ),
inference(definition_unfolding,[],[f69,f54,f60,f55]) ).
thf(f76,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $false
= ( ( mrel @ '#a' @ mactual @ sK0 )
=> ~ ( p @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( $false
= ( ~ ( p @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( $true
= ( mrel @ '#a' @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f81,plain,
( $true
= ( p @ sK0 ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f82,plain,
( $true
= ( ~ ( p @ mactual ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f83,plain,
( $false
= ( p @ mactual ) ),
inference(not_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f85,plain,
( ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#b' @ mactual @ X1 )
=> ( p @ X1 ) ) )
| ( $true
= ( ( mrel @ '#a' @ mactual @ X2 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ '#a' @ mactual @ X2 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ X2 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ( mrel @ '#b' @ X2 @ ( sK1 @ X2 ) )
=> ( p @ ( sK1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( mrel @ '#b' @ X2 @ ( sK1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f97,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f98,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#a' @ mactual @ X1 )
=> ( ( p @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X1 ) )
| ( $true
= ( ( p @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ( mrel @ '#b' @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X1 ) )
| ( ( mrel @ '#b' @ X1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f106,definition,
( spl2_1
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $true
= ( mrel @ '#b' @ X2 @ ( sK1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f107,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ '#b' @ X2 @ ( sK1 @ X2 ) ) )
| ( $false
= ( mrel @ '#a' @ mactual @ X2 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f109,definition,
( spl2_2
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f110,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#b' @ mactual @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f111,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f96,f109,f106]) ).
thf(f113,definition,
( spl2_3
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $false
= ( p @ ( sK1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f114,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ '#a' @ mactual @ X2 ) )
| ( $false
= ( p @ ( sK1 @ X2 ) ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f115,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f95,f109,f113]) ).
thf(f125,plain,
( ( $true = $false )
| ( $true
= ( p @ mactual ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f110,f62]) ).
thf(f130,plain,
( ( $true
= ( p @ mactual ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f134,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f130,f83]) ).
thf(f135,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f136,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f135]) ).
thf(f140,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK1 @ sK0 ) ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f80,f114]) ).
thf(f143,plain,
( ( $false
= ( p @ ( sK1 @ sK0 ) ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f153,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ '#b' @ sK0 @ X0 ) )
| ( $false
= ( p @ sK0 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(constrained_superposition,[],[f80,f104]) ).
thf(f156,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ '#b' @ sK0 @ X0 ) )
| ( $false
= ( p @ sK0 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f163,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ '#b' @ sK0 @ X0 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(forward_demodulation,[],[f156,f81]) ).
thf(f164,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ '#b' @ sK0 @ X0 ) )
| ( $true
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f209,plain,
( ( $true = $false )
| ( $false
= ( mrel @ '#a' @ mactual @ sK0 ) )
| ( $true
= ( p @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f107,f164]) ).
thf(f210,plain,
( ( $false
= ( mrel @ '#a' @ mactual @ sK0 ) )
| ( $true
= ( p @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f215,plain,
( ( $true = $false )
| ( $false
= ( mrel @ '#a' @ mactual @ sK0 ) )
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[],[f210,f143]) ).
thf(f216,plain,
( ( $false
= ( mrel @ '#a' @ mactual @ sK0 ) )
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f219,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_3 ),
inference(constrained_superposition,[],[f216,f80]) ).
thf(f227,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f228,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f227]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f111]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f115]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f136]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f228]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s2,s4]) ).
cnf(s8,plain,
~ spl2_1,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s4,s8]) ).
thf(f229,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL962^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 10:56:07 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.24 % (194938)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (194944)% WARNING: option uhcvi not known.
% 0.07/0.24 % (194943)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3575305055_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.24 % (194945)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2524861596:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.24 % (194946)dis+10_1_sil=32000:sp=arity:random_seed=668895969:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.24 % (194947)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2850422496:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.24 % (194948)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=422374854:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.24 % (194949)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4122855569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.24 % (194947)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (194944)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3275793118:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.24 % Exception at run slice level
% 0.07/0.24 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.24 % (194944)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.24 % (194944)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.24 % (194944) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-194938-194944"...
% 0.07/0.24 % (194949) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-194938-194949"...
% 0.07/0.24 % (194946) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-194938-194946"...
% 0.07/0.24 % (194944)...printing done.
% 0.07/0.24 % (194944)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (194944)------------------------------
% 0.07/0.25 % (194944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (194944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (194944)CaDiCaL version: 2.1.3
% 0.07/0.25 % (194944)Termination reason: Refutation
% 0.07/0.25 % (194944)Time elapsed: 0.006 s
% 0.07/0.25 % (194944)Peak memory usage: 13 MB
% 0.07/0.25 % (194944)Instructions burned: 18 (million)
% 0.07/0.25 % (194938)Success in time 0.039 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------