%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PRO029^16 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:20:31 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of formulae : 194 ( 73 unt; 0 typ; 12 def)
% Number of atoms : 1160 ( 225 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 1471 ( 128 ~; 168 |; 20 &; 996 @)
% ( 12 <=>; 100 =>; 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 : 47 ( 43 usr; 19 con; 0-4 aty)
% ( 47 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 244 ( 0 sgn 63 !; 0 ?; 244 :)
% 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_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
sK0: mworld ).
thf(func_def_31,type,
sK1: mworld > mworld ).
thf(func_def_32,type,
sK2: mworld > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ '#c' @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#c_reflexive') ).
thf(f14,axiom,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_charge_u) ).
thf(f15,axiom,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(f16,axiom,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(f17,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f22,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f23,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f25,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f28,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
! [X0: mworld] : ( mrel @ '#c' @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f37,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f46,plain,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
inference(rectify,[],[f14]) ).
thf(f47,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
inference(rectify,[],[f15]) ).
thf(f49,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
inference(rectify,[],[f16]) ).
thf(f51,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f53,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f57,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f57]) ).
thf(f63,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f65,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f67,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f71,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f76,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f77,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f78,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(cnf_transformation,[],[f51]) ).
thf(f79,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f81,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(f85,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] :
( ( Y0 @ Y2 )
& ( Y1 @ 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,f63,f67,f65,f69,f69]) ).
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 ) ) )
@ '#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 ) ) ) ) ),
inference(definition_unfolding,[],[f77,f63,f69,f67,f69]) ).
thf(f87,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,[],[f78,f63,f69,f67,f69]) ).
thf(f88,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,[],[f79,f63,f67,f64,f69,f69,f64,f69]) ).
thf(f90,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] :
( ( Y0 @ Y2 )
& ( Y1 @ 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] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ called
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ paid ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f81,f63,f67,f64,f67,f65,f64,f69,f64,f67,f65,f64]) ).
thf(f91,plain,
( $true
!= ( ~ ( ( charge @ mactual )
=> ( ( called @ mactual )
& ~ ( paid @ mactual ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ( called @ Y0 )
& ~ ( paid @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ( called @ Y0 )
& ~ ( paid @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( $true
= ( ~ ( ( charge @ mactual )
=> ( ( called @ mactual )
& ~ ( paid @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( $false
= ( ( charge @ mactual )
=> ( ( called @ mactual )
& ~ ( paid @ mactual ) ) ) ),
inference(not_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $false
= ( ( called @ mactual )
& ~ ( paid @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( $true
= ( charge @ mactual ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f97,plain,
( ( $false
= ( ~ ( paid @ mactual ) ) )
| ( $false
= ( called @ mactual ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f98,plain,
( ( $true
= ( paid @ mactual ) )
| ( $false
= ( called @ mactual ) ) ),
inference(not_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ( called @ Y0 )
& ~ ( paid @ Y0 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f92]) ).
thf(f100,plain,
( $false
= ( ( mrel @ '#u' @ mactual @ sK0 )
=> ~ ( ( charge @ sK0 )
=> ( ( called @ sK0 )
& ~ ( paid @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
( $false
= ( ~ ( ( charge @ sK0 )
=> ( ( called @ sK0 )
& ~ ( paid @ sK0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( $true
= ( mrel @ '#u' @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( $true
= ( ( charge @ sK0 )
=> ( ( called @ sK0 )
& ~ ( paid @ sK0 ) ) ) ),
inference(not_proxy_clausification,[],[f101]) ).
thf(f104,plain,
( ( $false
= ( charge @ sK0 ) )
| ( $true
= ( ( called @ sK0 )
& ~ ( paid @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( ( $false
= ( charge @ sK0 ) )
| ( $true
= ( ~ ( paid @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( $false
= ( charge @ sK0 ) )
| ( $true
= ( called @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f107,plain,
( ( $false
= ( charge @ sK0 ) )
| ( $false
= ( paid @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f105]) ).
thf(f121,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,[],[f88]) ).
thf(f122,plain,
( ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#c' @ mactual @ X1 )
=> ( called @ X1 ) ) )
| ( $true
= ( ( mrel @ '#u' @ mactual @ X2 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X2 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ '#u' @ mactual @ X2 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X2 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( called @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X2 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X2 @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X2 @ Y0 )
=> ( called @ Y0 ) )
@ ( sK2 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $false
= ( ( mrel @ '#c' @ X2 @ ( sK2 @ X2 ) )
=> ( called @ ( sK2 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $false
= ( called @ ( sK2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( called @ X1 ) )
| ( $true
= ( mrel @ '#c' @ X2 @ ( sK2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f134,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f135,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,[],[f134]) ).
thf(f136,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#c' @ mactual @ X1 )
=> ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $true
= ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( paid @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( paid @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $false
= ( paid @ X1 ) )
| ( $true
= ( ( mrel @ '#u' @ X1 @ X2 )
=> ( paid @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( ( mrel @ '#u' @ X1 @ X2 )
= $false )
| ( $false
= ( paid @ X1 ) )
| ( $true
= ( paid @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f143,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,[],[f142]) ).
thf(f144,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ X1 ) )
| ( $true
= ( ( mrel @ '#c' @ X1 @ X2 )
=> ( called @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ X2 )
= $false )
| ( $false
= ( called @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( called @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $true
= ( ( charge @ mactual )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f151,plain,
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X1: mworld] :
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: mworld] :
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( charge @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X1: mworld] :
( ( $false
= ( charge @ mactual ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( charge @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f163,definition,
( spl3_1
<=> ( $false
= ( called @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f165,plain,
( ( $false
= ( called @ mactual ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f163]) ).
thf(f167,definition,
( spl3_2
<=> ( $true
= ( paid @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f169,plain,
( ( $true
= ( paid @ mactual ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f170,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f98,f167,f163]) ).
thf(f172,definition,
( spl3_3
<=> ( $true
= ( called @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f174,plain,
( ( $true
= ( called @ sK0 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f176,definition,
( spl3_4
<=> ( $false
= ( charge @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f178,plain,
( ( $false
= ( charge @ sK0 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f176]) ).
thf(f179,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f106,f176,f172]) ).
thf(f181,definition,
( spl3_5
<=> ( $false
= ( paid @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f183,plain,
( ( $false
= ( paid @ sK0 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f184,plain,
( spl3_5
| spl3_4 ),
inference(avatar_split_clause,[],[f107,f176,f181]) ).
thf(f189,definition,
( spl3_7
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( paid @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
thf(f190,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( paid @ X1 ) ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f197,definition,
( spl3_9
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $true
= ( mrel @ '#c' @ X2 @ ( sK2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
thf(f198,plain,
( ! [X2: mworld] :
( ( $true
= ( mrel @ '#c' @ X2 @ ( sK2 @ X2 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X2 ) ) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f200,definition,
( spl3_10
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $true
= ( called @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
thf(f201,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( $true
= ( called @ X1 ) ) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f202,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f133,f200,f197]) ).
thf(f204,definition,
( spl3_11
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $false
= ( called @ ( sK2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
thf(f205,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X2 ) )
| ( $false
= ( called @ ( sK2 @ X2 ) ) ) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f206,plain,
( spl3_11
| spl3_10 ),
inference(avatar_split_clause,[],[f132,f200,f204]) ).
thf(f208,definition,
( spl3_12
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( charge @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
thf(f209,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( charge @ X1 ) ) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f211,definition,
( spl3_13
<=> ( $false
= ( charge @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
thf(f213,plain,
( ( $false
= ( charge @ mactual ) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f214,plain,
( spl3_12
| spl3_13 ),
inference(avatar_split_clause,[],[f156,f211,f208]) ).
thf(f224,definition,
( spl3_16
<=> ( $false
= ( paid @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
thf(f226,plain,
( ( $false
= ( paid @ mactual ) )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f236,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ '#u' @ mactual @ X0 ) )
| ( $false
= ( paid @ mactual ) )
| ( $true
= ( paid @ X0 ) ) ),
inference(constrained_superposition,[],[f141,f71]) ).
thf(f245,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X0 ) )
| ( $false
= ( paid @ mactual ) )
| ( $true
= ( paid @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f248,plain,
( spl3_16
| spl3_7 ),
inference(avatar_split_clause,[],[f245,f189,f224]) ).
thf(f267,plain,
( ( $true = $false )
| ~ spl3_13 ),
inference(constrained_superposition,[],[f213,f96]) ).
thf(f271,plain,
( $false
| ~ spl3_13 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f272,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[],[f271]) ).
thf(f284,plain,
( ( $true = $false )
| ( $true
= ( paid @ sK0 ) )
| ~ spl3_7 ),
inference(constrained_superposition,[],[f190,f102]) ).
thf(f287,plain,
( ( $true
= ( paid @ sK0 ) )
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f290,plain,
( ( $true = $false )
| ( $true
= ( called @ mactual ) )
| ~ spl3_10 ),
inference(constrained_superposition,[],[f201,f71]) ).
thf(f294,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl3_10 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f298,plain,
( ( $true = $false )
| ( $true
= ( charge @ sK0 ) )
| ~ spl3_12 ),
inference(constrained_superposition,[],[f209,f102]) ).
thf(f304,plain,
( ( $true
= ( charge @ sK0 ) )
| ~ spl3_12 ),
inference(trivial_inequality_removal,[],[f298]) ).
thf(f310,plain,
( ( $true = $false )
| ~ spl3_4
| ~ spl3_12 ),
inference(forward_demodulation,[],[f304,f178]) ).
thf(f311,plain,
( $false
| ~ spl3_4
| ~ spl3_12 ),
inference(trivial_inequality_removal,[],[f310]) ).
thf(f312,plain,
( ~ spl3_4
| ~ spl3_12 ),
inference(avatar_contradiction_clause,[],[f311]) ).
thf(f431,plain,
( ( $true = $false )
| ~ spl3_5
| ~ spl3_7 ),
inference(constrained_superposition,[],[f183,f287]) ).
thf(f435,plain,
( $false
| ~ spl3_5
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f436,plain,
( ~ spl3_5
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f435]) ).
thf(f439,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_16 ),
inference(constrained_superposition,[],[f226,f169]) ).
thf(f443,plain,
( $false
| ~ spl3_2
| ~ spl3_16 ),
inference(trivial_inequality_removal,[],[f439]) ).
thf(f444,plain,
( ~ spl3_2
| ~ spl3_16 ),
inference(avatar_contradiction_clause,[],[f443]) ).
thf(f503,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_10 ),
inference(forward_demodulation,[],[f294,f165]) ).
thf(f504,plain,
( $false
| ~ spl3_1
| ~ spl3_10 ),
inference(trivial_inequality_removal,[],[f503]) ).
thf(f505,plain,
( ~ spl3_1
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f504]) ).
thf(f516,plain,
( ( $true = $false )
| ( $false
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_11 ),
inference(constrained_superposition,[],[f102,f205]) ).
thf(f517,plain,
( ( $false
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_11 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f546,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( called @ X0 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X0 ) )
| ( $true
= ( called @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X0 ) ) )
| ~ spl3_9 ),
inference(constrained_superposition,[],[f149,f198]) ).
thf(f547,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( called @ X0 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X0 ) )
| ( $true
= ( called @ ( sK2 @ X0 ) ) ) )
| ~ spl3_9 ),
inference(duplicate_literal_removal,[],[f546]) ).
thf(f548,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X0 ) )
| ( $false
= ( called @ X0 ) )
| ( $true
= ( called @ ( sK2 @ X0 ) ) ) )
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f547]) ).
thf(f713,plain,
( ( $true = $false )
| ( $false
= ( called @ sK0 ) )
| ( $true
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_9 ),
inference(constrained_superposition,[],[f548,f102]) ).
thf(f727,plain,
( ( $false
= ( called @ sK0 ) )
| ( $true
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f735,plain,
( ( $true = $false )
| ( $true
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_3
| ~ spl3_9 ),
inference(forward_demodulation,[],[f727,f174]) ).
thf(f736,plain,
( ( $true
= ( called @ ( sK2 @ sK0 ) ) )
| ~ spl3_3
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f735]) ).
thf(f743,plain,
( ( $true = $false )
| ~ spl3_3
| ~ spl3_9
| ~ spl3_11 ),
inference(forward_demodulation,[],[f736,f517]) ).
thf(f744,plain,
( $false
| ~ spl3_3
| ~ spl3_9
| ~ spl3_11 ),
inference(trivial_inequality_removal,[],[f743]) ).
thf(f745,plain,
( ~ spl3_3
| ~ spl3_9
| ~ spl3_11 ),
inference(avatar_contradiction_clause,[],[f744]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f170]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f179]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f184]) ).
cnf(s6,plain,
( spl3_9
| spl3_10 ),
inference(sat_conversion,[],[f202]) ).
cnf(s7,plain,
( spl3_10
| spl3_11 ),
inference(sat_conversion,[],[f206]) ).
cnf(s8,plain,
( spl3_12
| spl3_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s12,plain,
( spl3_7
| spl3_16 ),
inference(sat_conversion,[],[f248]) ).
cnf(s14,plain,
~ spl3_13,
inference(sat_conversion,[],[f272]) ).
cnf(s16,plain,
( ~ spl3_4
| ~ spl3_12 ),
inference(sat_conversion,[],[f312]) ).
cnf(s18,plain,
( ~ spl3_5
| ~ spl3_7 ),
inference(sat_conversion,[],[f436]) ).
cnf(s20,plain,
( ~ spl3_2
| ~ spl3_16 ),
inference(sat_conversion,[],[f444]) ).
cnf(s26,plain,
( ~ spl3_1
| ~ spl3_10 ),
inference(sat_conversion,[],[f505]) ).
cnf(s40,plain,
( ~ spl3_3
| ~ spl3_9
| ~ spl3_11 ),
inference(sat_conversion,[],[f745]) ).
cnf(s50,plain,
spl3_12,
inference(rat,[],[s8,s14]) ).
cnf(s51,plain,
~ spl3_4,
inference(rat,[],[s16,s50]) ).
cnf(s52,plain,
spl3_5,
inference(rat,[],[s3,s51]) ).
cnf(s53,plain,
~ spl3_7,
inference(rat,[],[s18,s52]) ).
cnf(s54,plain,
spl3_16,
inference(rat,[],[s12,s53]) ).
cnf(s57,plain,
~ spl3_2,
inference(rat,[],[s20,s54]) ).
cnf(s59,plain,
spl3_3,
inference(rat,[],[s2,s51]) ).
cnf(s60,plain,
spl3_1,
inference(rat,[],[s1,s57]) ).
cnf(s61,plain,
~ spl3_10,
inference(rat,[],[s26,s60]) ).
cnf(s63,plain,
spl3_11,
inference(rat,[],[s7,s61]) ).
cnf(s64,plain,
spl3_9,
inference(rat,[],[s6,s61]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s40,s59,s63,s64]) ).
thf(f748,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO029^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:23:14 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (2485489)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (2485495)% WARNING: option uhcvi not known.
% 0.19/0.27 % (2485495)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=813545138:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (2485495)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (2485495)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (2485497)dis+10_1_sil=32000:sp=arity:random_seed=1105591123:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (2485494)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1479433197_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (2485499)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=461007549:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (2485496)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2918083445:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (2485498)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3485265708:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (2485500)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2294108807:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (2485498)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (2485495) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2485489-2485495"...
% 0.19/0.27 % (2485495)...printing done.
% 0.19/0.27 % (2485495)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2485495)------------------------------
% 0.19/0.27 % (2485495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2485495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2485495)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2485495)Termination reason: Refutation
% 0.19/0.27 % (2485495)Time elapsed: 0.018 s
% 0.19/0.27 % (2485495)Peak memory usage: 13 MB
% 0.19/0.27 % (2485495)Instructions burned: 56 (million)
% 0.19/0.27 % (2485489)Success in time 0.049 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------