%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PRO029^16 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:20:30 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 179 ( 71 unt; 0 typ; 9 def)
% Number of atoms : 1126 ( 224 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 1438 ( 111 ~; 154 |; 20 &; 997 @)
% ( 9 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 40 usr; 16 con; 0-4 aty)
% ( 46 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 247 ( 0 sgn 66 !; 0 ?; 247 :)
% 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,
'#c': mindex ).
thf(func_def_2,type,
'#u': 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,
charge: mworld > $o ).
thf(func_def_14,type,
called: mworld > $o ).
thf(func_def_15,type,
paid: mworld > $o ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vIFF: $o > $o > $o ).
thf(func_def_30,type,
sK0: mworld > mworld ).
thf(func_def_31,type,
sK1: mworld ).
thf(func_def_32,type,
sK2: 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(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
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: 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 @ '#c' @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_reflexive') ).
thf(f14,axiom,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_charge_u) ).
thf(f15,axiom,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(f16,axiom,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(f17,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(f19,conjecture,
mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',requirement_1) ).
thf(f20,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f21,plain,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
inference(rectify,[],[f15]) ).
thf(f22,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
! [X0: mworld] : ( mrel @ '#c' @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f26,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
inference(rectify,[],[f16]) ).
thf(f31,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f33,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f35,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f37,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f48,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f51,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
inference(rectify,[],[f14]) ).
thf(f53,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f58,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f37]) ).
thf(f65,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f66,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f67,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f69,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f70,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f72,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f74,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f75,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f76,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f83,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f86,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ paid
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ paid ) ) ) ) ),
inference(definition_unfolding,[],[f69,f72,f65,f67,f65]) ).
thf(f88,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ called
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ called ) ) ) )
= $true ),
inference(definition_unfolding,[],[f74,f72,f65,f67,f65]) ).
thf(f89,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 ) ) )
@ '#c'
@ called ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ called ) ) ) ) ) ),
inference(definition_unfolding,[],[f75,f72,f67,f81,f65,f65,f81,f65]) ).
thf(f90,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ charge )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ charge ) ) ) ) ),
inference(definition_unfolding,[],[f76,f72,f67,f66,f65,f65]) ).
thf(f92,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: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ called
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ paid ) ) ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ called
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ paid ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f83,f72,f67,f81,f67,f66,f81,f65,f81,f67,f66,f81]) ).
thf(f93,plain,
( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f94,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( called @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( called @ X2 ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ ( sK0 @ X1 ) )
= $false )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( ( mrel @ '#c' @ X1 @ ( sK0 @ X1 ) )
=> ( called @ ( sK0 @ X1 ) ) )
= $false )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( called @ X2 ) )
| ( ( called @ ( sK0 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( called @ X2 ) )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f108,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f109,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#c' @ mactual @ X1 )
=> ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
! [X1: mworld] :
( ( ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) )
= $true )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X1: mworld] :
( ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( ( paid @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) )
@ X2 ) )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( ( paid @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#u' @ X1 @ X2 )
=> ( paid @ X2 ) ) )
| ( ( paid @ X1 )
= $false )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ X1 @ X2 )
= $false )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( $true
= ( paid @ X2 ) )
| ( ( paid @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( $true
!= ( ~ ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f117,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f118,plain,
( $true
= ( ~ ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f119,plain,
( ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) )
= $false ),
inference(not_proxy_clausification,[],[f118]) ).
thf(f120,plain,
( ( ~ ( paid @ mactual )
& ( called @ mactual ) )
= $false ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( $true
= ( charge @ mactual ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( ( ~ ( paid @ mactual ) )
= $false )
| ( ( called @ mactual )
= $false ) ),
inference(and_proxy_clausification,[],[f120]) ).
thf(f123,plain,
( ( ( called @ mactual )
= $false )
| ( $true
= ( paid @ mactual ) ) ),
inference(not_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f125,plain,
( ( ( mrel @ '#u' @ mactual @ sK1 )
=> ~ ( ( charge @ sK1 )
=> ( ~ ( paid @ sK1 )
& ( called @ sK1 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
( $false
= ( ~ ( ( charge @ sK1 )
=> ( ~ ( paid @ sK1 )
& ( called @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
( $true
= ( mrel @ '#u' @ mactual @ sK1 ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f128,plain,
( ( ( charge @ sK1 )
=> ( ~ ( paid @ sK1 )
& ( called @ sK1 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( ( charge @ sK1 )
= $false )
| ( $true
= ( ~ ( paid @ sK1 )
& ( called @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( ( charge @ sK1 )
= $false )
| ( ( called @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( ( ~ ( paid @ sK1 ) )
= $true )
| ( ( charge @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( ( charge @ sK1 )
= $false )
| ( ( paid @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f131]) ).
thf(f146,plain,
( $true
= ( ( charge @ mactual )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f147,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) )
| ( ( charge @ mactual )
= $false ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( ( charge @ mactual )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f147]) ).
thf(f153,plain,
! [X1: mworld] :
( ( ( charge @ mactual )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f154,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( charge @ X1 ) ) )
| ( ( charge @ mactual )
= $false ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( charge @ X1 ) )
| ( ( charge @ mactual )
= $false ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f157,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
=> ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: mworld] :
( ( ( called @ X1 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: mworld,X1: mworld] :
( ( ( called @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#c' @ X1 @ X2 )
=> ( called @ X2 ) ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ X2 )
= $false )
| ( ( called @ X1 )
= $false )
| ( $true
= ( called @ X2 ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f165,definition,
( spl3_1
<=> ! [X2: mworld] :
( ( $true
= ( called @ X2 ) )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f166,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f168,definition,
( spl3_2
<=> ! [X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f169,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f170,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f105,f168,f165]) ).
thf(f172,definition,
( spl3_3
<=> ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ ( sK0 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f173,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ ( sK0 @ X1 ) )
= $false ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f174,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f104,f172,f165]) ).
thf(f185,definition,
( spl3_6
<=> ( $true
= ( paid @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f187,plain,
( ( $true
= ( paid @ mactual ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f189,definition,
( spl3_7
<=> ( ( called @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
thf(f191,plain,
( ( ( called @ mactual )
= $false )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f192,plain,
( spl3_6
| spl3_7 ),
inference(avatar_split_clause,[],[f123,f189,f185]) ).
thf(f194,definition,
( spl3_8
<=> ( ( paid @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
thf(f196,plain,
( ( ( paid @ sK1 )
= $false )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f198,definition,
( spl3_9
<=> ( ( charge @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
thf(f200,plain,
( ( ( charge @ sK1 )
= $false )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f201,plain,
( spl3_8
| spl3_9 ),
inference(avatar_split_clause,[],[f132,f198,f194]) ).
thf(f203,definition,
( spl3_10
<=> ( ( called @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
thf(f205,plain,
( ( ( called @ sK1 )
= $true )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f130,f203,f198]) ).
thf(f208,definition,
( spl3_11
<=> ! [X2: mworld] :
( ( ( mrel @ '#u' @ mactual @ X2 )
= $false )
| ( $true
= ( paid @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
thf(f209,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#u' @ mactual @ X2 )
= $false )
| ( $true
= ( paid @ X2 ) ) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f220,plain,
! [X1: mworld] :
( ( $true
= ( charge @ X1 ) )
| ( $true = $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f155,f121]) ).
thf(f221,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( charge @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f226,plain,
( ( ( charge @ sK1 )
= $true )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f221,f127]) ).
thf(f229,plain,
( ( charge @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f233,plain,
( ( $true = $false )
| ~ spl3_9 ),
inference(forward_demodulation,[],[f229,f200]) ).
thf(f234,plain,
( $false
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f235,plain,
~ spl3_9,
inference(avatar_contradiction_clause,[],[f234]) ).
thf(f247,plain,
( ( $true = $false )
| ( $true
= ( paid @ sK1 ) )
| ~ spl3_11 ),
inference(constrained_superposition,[],[f127,f209]) ).
thf(f252,plain,
( ( $true
= ( paid @ sK1 ) )
| ~ spl3_11 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f262,plain,
( ( $true = $false )
| ~ spl3_8
| ~ spl3_11 ),
inference(forward_demodulation,[],[f252,f196]) ).
thf(f263,plain,
( $false
| ~ spl3_8
| ~ spl3_11 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f264,plain,
( ~ spl3_8
| ~ spl3_11 ),
inference(avatar_contradiction_clause,[],[f263]) ).
thf(f267,plain,
( ( $true = $false )
| ( ( called @ ( sK0 @ sK1 ) )
= $false )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f127,f173]) ).
thf(f269,plain,
( ( ( called @ ( sK0 @ sK1 ) )
= $false )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f314,plain,
! [X0: mworld] :
( ( ( paid @ mactual )
= $false )
| ( $true = $false )
| ( $true
= ( paid @ X0 ) )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f70,f115]) ).
thf(f315,plain,
! [X0: mworld] :
( ( ( paid @ mactual )
= $false )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false )
| ( $true
= ( paid @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f338,plain,
( ! [X0: mworld] :
( ( ( mrel @ '#u' @ mactual @ X0 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false )
| ( ( called @ ( sK0 @ X0 ) )
= $true )
| ( $true = $false )
| ( ( called @ X0 )
= $false ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f163,f169]) ).
thf(f341,plain,
( ! [X0: mworld] :
( ( ( called @ ( sK0 @ X0 ) )
= $true )
| ( $true = $false )
| ( ( called @ X0 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false ) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f338]) ).
thf(f342,plain,
( ! [X0: mworld] :
( ( ( mrel @ '#u' @ mactual @ X0 )
= $false )
| ( ( called @ X0 )
= $false )
| ( ( called @ ( sK0 @ X0 ) )
= $true ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f347,plain,
( ( $true = $false )
| ( ( called @ ( sK0 @ sK1 ) )
= $true )
| ( ( called @ sK1 )
= $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f342,f127]) ).
thf(f356,plain,
( ( ( called @ ( sK0 @ sK1 ) )
= $true )
| ( ( called @ sK1 )
= $false )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f363,plain,
( ( ( called @ sK1 )
= $false )
| ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f356,f269]) ).
thf(f364,plain,
( ( ( called @ sK1 )
= $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f363]) ).
thf(f372,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_10 ),
inference(forward_demodulation,[],[f364,f205]) ).
thf(f373,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_10 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f374,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f373]) ).
thf(f376,plain,
( ( $true = $false )
| ( $true
= ( called @ mactual ) )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f70,f166]) ).
thf(f378,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f382,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_7 ),
inference(forward_demodulation,[],[f378,f191]) ).
thf(f383,plain,
( $false
| ~ spl3_1
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f384,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f383]) ).
thf(f391,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( paid @ X0 ) )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false ) )
| ~ spl3_6 ),
inference(forward_demodulation,[],[f315,f187]) ).
thf(f392,plain,
( ! [X0: mworld] :
( ( $true
= ( paid @ X0 ) )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false ) )
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f401,plain,
( spl3_11
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f392,f185,f208]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f170]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f174]) ).
cnf(s4,plain,
( spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f192]) ).
cnf(s5,plain,
( spl3_8
| spl3_9 ),
inference(sat_conversion,[],[f201]) ).
cnf(s6,plain,
( spl3_9
| spl3_10 ),
inference(sat_conversion,[],[f206]) ).
cnf(s11,plain,
~ spl3_9,
inference(sat_conversion,[],[f235]) ).
cnf(s15,plain,
( ~ spl3_8
| ~ spl3_11 ),
inference(sat_conversion,[],[f264]) ).
cnf(s17,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_10 ),
inference(sat_conversion,[],[f374]) ).
cnf(s19,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(sat_conversion,[],[f384]) ).
cnf(s22,plain,
( ~ spl3_6
| spl3_11 ),
inference(sat_conversion,[],[f401]) ).
cnf(s24,plain,
spl3_10,
inference(rat,[],[s6,s11]) ).
cnf(s25,plain,
spl3_8,
inference(rat,[],[s5,s11]) ).
cnf(s26,plain,
~ spl3_11,
inference(rat,[],[s15,s25]) ).
cnf(s27,plain,
~ spl3_6,
inference(rat,[],[s22,s26]) ).
cnf(s30,plain,
spl3_7,
inference(rat,[],[s4,s27]) ).
cnf(s31,plain,
~ spl3_1,
inference(rat,[],[s19,s30]) ).
cnf(s32,plain,
spl3_3,
inference(rat,[],[s2,s31]) ).
cnf(s33,plain,
~ spl3_2,
inference(rat,[],[s17,s24,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s33,s31]) ).
thf(f402,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO029^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:24:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (3502495)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3502504)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=593522540:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (3502500)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4077616560:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3502503)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=583307413: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)
% 0.20/0.28 % (3502502)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3736722475:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (3502504)Instruction limit reached!
% 0.20/0.28 % (3502504)------------------------------
% 0.20/0.28 % (3502504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3502504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3502504)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3502504)Termination reason: Instruction limit
% 0.20/0.28 % (3502504)Termination phase: Saturation
% 0.20/0.28 % (3502504)Time elapsed: 0.008 s
% 0.20/0.28 % (3502504)Peak memory usage: 12 MB
% 0.20/0.28 % (3502504)Instructions burned: 26 (million)
% 0.20/0.28 % (3502502)Instruction limit reached!
% 0.20/0.28 % (3502502)------------------------------
% 0.20/0.28 % (3502502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3502502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3502502)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3502502)Termination reason: Instruction limit
% 0.20/0.28 % (3502502)Termination phase: Property scanning
% 0.20/0.28 % (3502502)Time elapsed: 0.002 s
% 0.20/0.28 % (3502502)Peak memory usage: 10 MB
% 0.20/0.28 % (3502502)Instructions burned: 4 (million)
% 0.20/0.28 % (3502506)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3502506)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
% 0.20/0.28 % (3502511)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4012307280:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (3502500) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3502495-3502500"...
% 0.20/0.28 % (3502511)Instruction limit reached!
% 0.20/0.28 % (3502511)------------------------------
% 0.20/0.28 % (3502511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3502511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3502511)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3502511)Termination reason: Instruction limit
% 0.20/0.28 % (3502511)Termination phase: Saturation
% 0.20/0.28 % (3502511)Time elapsed: 0.001 s
% 0.20/0.28 % (3502511)Peak memory usage: 10 MB
% 0.20/0.28 % (3502511)Instructions burned: 4 (million)
% 0.20/0.28 % (3502505)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1985054959:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3502500)...printing done.
% 0.20/0.28 % (3502500)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3502500)------------------------------
% 0.20/0.28 % (3502500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3502500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3502500)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3502500)Termination reason: Refutation
% 0.20/0.28 % (3502500)Time elapsed: 0.016 s
% 0.20/0.28 % (3502500)Peak memory usage: 13 MB
% 0.20/0.28 % (3502500)Instructions burned: 29 (million)
% 0.20/0.28 % (3502495)Success in time 0.05 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------