%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV436^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:39:59 AM UTC 2026
% Result : Theorem 0.32s 0.42s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 203 ( 93 unt; 0 typ; 8 def)
% Number of atoms : 1552 ( 334 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1843 ( 124 ~; 314 |; 0 &;1180 @)
% ( 7 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 13 con; 0-4 aty)
% ( 102 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 506 ( 5 sgn 177 !; 0 ?; 506 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
rel: $i > $i > $o ).
thf(func_def_21,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
icl_true: $i > $o ).
thf(func_def_27,type,
icl_false: $i > $o ).
thf(func_def_28,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_29,type,
iclval: ( $i > $o ) > $o ).
thf(func_def_30,type,
admin: $i > $o ).
thf(func_def_31,type,
bob: $i > $o ).
thf(func_def_32,type,
deletefile1: $i > $o ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
sF0: $o ).
thf(func_def_49,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK4: $i > ( $i > $o ) > $i ).
thf(f1,axiom,
( mfalse
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mfalse) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) )
= icl_atom ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_atom) ).
thf(f17,axiom,
( ( ^ [X0: $i > $o] : X0 )
= icl_princ ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( icl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f22,axiom,
icl_false = mfalse,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_false) ).
thf(f23,axiom,
( icl_says
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( ( ^ [X0: $i > $o] : ( mvalid @ X0 ) )
= iclval ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).
thf(f27,axiom,
iclval @ ( icl_says @ ( icl_impl @ ( icl_princ @ admin ) @ icl_false ) @ ( icl_atom @ deletefile1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f28,axiom,
iclval @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_says @ ( icl_impl @ ( icl_princ @ bob ) @ ( icl_princ @ admin ) ) @ ( icl_atom @ deletefile1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f29,axiom,
iclval @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_atom @ deletefile1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f30,conjecture,
iclval @ ( icl_atom @ deletefile1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex3) ).
thf(f31,negated_conjecture,
~ ( iclval @ ( icl_atom @ deletefile1 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f1]) ).
thf(f33,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f34,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f35,plain,
iclval @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_says @ ( icl_impl @ ( icl_princ @ bob ) @ ( icl_princ @ admin ) ) @ ( icl_atom @ deletefile1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f36,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_says @ ( icl_impl @ ( icl_princ @ bob ) @ ( icl_princ @ admin ) ) @ ( icl_atom @ deletefile1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f38,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
~ ( iclval @ ( icl_atom @ deletefile1 ) ),
inference(rectify,[],[f31]) ).
thf(f40,plain,
( ( iclval @ ( icl_atom @ deletefile1 ) )
!= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f46,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f50,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f53,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f56,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f68,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f69,plain,
iclval @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_atom @ deletefile1 ) ),
inference(rectify,[],[f29]) ).
thf(f70,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_atom @ deletefile1 ) ) )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f74,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
iclval @ ( icl_says @ ( icl_impl @ ( icl_princ @ admin ) @ icl_false ) @ ( icl_atom @ deletefile1 ) ),
inference(rectify,[],[f27]) ).
thf(f76,plain,
( ( iclval @ ( icl_says @ ( icl_impl @ ( icl_princ @ admin ) @ icl_false ) @ ( icl_atom @ deletefile1 ) ) )
= $true ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
( ( iclval @ ( icl_atom @ deletefile1 ) )
!= $true ),
inference(flattening,[],[f40]) ).
thf(f79,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f80,plain,
( ( iclval @ ( icl_says @ ( icl_impl @ ( icl_princ @ admin ) @ icl_false ) @ ( icl_atom @ deletefile1 ) ) )
= $true ),
inference(cnf_transformation,[],[f76]) ).
thf(f83,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f85,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ admin ) @ ( icl_says @ ( icl_impl @ ( icl_princ @ bob ) @ ( icl_princ @ admin ) ) @ ( icl_atom @ deletefile1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f86,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f87,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f88,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f93,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f94,plain,
mfalse = icl_false,
inference(cnf_transformation,[],[f22]) ).
thf(f96,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ bob ) @ ( icl_atom @ deletefile1 ) ) )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f98,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f99,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f101,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f102,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f103,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f105,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f107,plain,
( ( iclval @ ( icl_atom @ deletefile1 ) )
!= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f110,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f93,f88,f86]) ).
thf(f112,plain,
( icl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 ) ) ),
inference(definition_unfolding,[],[f103,f79]) ).
thf(f115,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f87,f79,f110]) ).
thf(f117,plain,
( icl_false
= ( ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f94,f102]) ).
thf(f118,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f98,f79,f88]) ).
thf(f119,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f101,f105]) ).
thf(f120,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ admin )
@ ^ [Y0: $i] : $false )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ) ),
inference(definition_unfolding,[],[f80,f119,f118,f115,f99,f117,f112]) ).
thf(f121,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ X0 ) )
= $true ),
inference(definition_unfolding,[],[f83,f105,f110,f79]) ).
thf(f122,plain,
( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ admin )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ bob )
@ ( ^ [Y0: $i > $o] : Y0
@ admin ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f85,f119,f118,f99,f118,f115,f99,f99,f112]) ).
thf(f123,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ bob )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ) ),
inference(definition_unfolding,[],[f96,f119,f118,f99,f112]) ).
thf(f125,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ),
inference(definition_unfolding,[],[f107,f119,f112]) ).
thf(f126,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f127,plain,
$true != sF0,
inference(definition_folding,[],[f125,f126]) ).
thf(f128,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( $false
| ~ ( admin @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f129,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( $false
| ~ ( admin @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( $false
| ~ ( admin @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( $false
| ~ ( admin @ Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( $false
| ~ ( admin @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( $false
| ~ ( admin @ Y0 ) ) ) ) ) )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( $false
| ~ ( admin @ Y0 ) ) ) )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( $false
| ~ ( admin @ Y0 ) ) ) )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( $false
| ~ ( admin @ Y0 ) ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) )
@ X3 ) )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) )
| ( ( ( rel @ X2 @ X4 )
=> ( $false
| ~ ( admin @ X4 ) ) )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( ( rel @ X2 @ X4 )
=> ( $false
| ~ ( admin @ X4 ) ) )
= $true )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( deletefile1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( deletefile1 @ X3 ) )
| ( ( rel @ X2 @ X4 )
= $false )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( ( $false
| ~ ( admin @ X4 ) )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( admin @ X4 ) )
= $true )
| ( $true
= ( deletefile1 @ X3 ) )
| ( ( rel @ X2 @ X4 )
= $false )
| ( $true = $false )
| ( ( rel @ X1 @ X2 )
= $false )
| ( $false
= ( rel @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( deletefile1 @ X3 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( ( admin @ X4 )
= $false )
| ( $true = $false )
| ( ( rel @ X2 @ X4 )
= $false )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( deletefile1 @ X3 ) )
| ( ( rel @ X1 @ X2 )
= $false )
| ( ( admin @ X4 )
= $false )
| ( ( rel @ X2 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f143,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ deletefile1 ) ) ) ),
inference(iff_proxy_clausification,[],[f126]) ).
thf(f151,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f152,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
@ sK1 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( deletefile1 @ Y0 ) )
@ sK2 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ( rel @ sK1 @ sK2 )
=> ( deletefile1 @ sK2 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( $true = sF0 )
| ( ( deletefile1 @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( rel @ sK1 @ sK2 )
= $true )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( deletefile1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( admin @ Y3 )
| ~ ( bob @ Y3 ) ) ) ) ) ) )
| ( admin @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( deletefile1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( admin @ Y3 )
| ~ ( bob @ Y3 ) ) ) ) ) ) )
| ( admin @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( admin @ Y2 )
| ~ ( bob @ Y2 ) ) ) ) ) ) )
| ( admin @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( admin @ Y2 )
| ~ ( bob @ Y2 ) ) ) ) ) ) )
| ( admin @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( admin @ Y1 )
| ~ ( bob @ Y1 ) ) ) ) ) ) )
| ( admin @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( admin @ Y1 )
| ~ ( bob @ Y1 ) ) ) ) ) ) )
| ( admin @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( admin @ Y1 )
| ~ ( bob @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( admin @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( admin @ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( admin @ Y1 )
| ~ ( bob @ Y1 ) ) ) ) ) )
@ X3 )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( admin @ X2 )
= $true )
| ( ( ( rel @ X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( ( admin @ Y0 )
| ~ ( bob @ Y0 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( admin @ X2 )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( ( admin @ Y0 )
| ~ ( bob @ Y0 ) ) ) ) ) )
| ( $false
= ( rel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( admin @ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( ( admin @ Y0 )
| ~ ( bob @ Y0 ) ) ) )
= $true )
| ( ( rel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
= $true )
| ( $false
= ( rel @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( ( admin @ Y0 )
| ~ ( bob @ Y0 ) ) )
@ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
= $true )
| ( ( admin @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( admin @ X2 )
= $true )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( ( rel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( ( admin @ Y0 )
| ~ ( bob @ Y0 ) ) )
@ X4 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X3 @ Y0 )
=> ( deletefile1 @ Y0 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( ( rel @ X1 @ X2 )
= $false )
| ( $true
= ( ( rel @ X3 @ X4 )
=> ( ( admin @ X4 )
| ~ ( bob @ X4 ) ) ) )
| ( ( admin @ X2 )
= $true )
| ( ( ( rel @ X3 @ X5 )
=> ( deletefile1 @ X5 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( admin @ X2 )
= $true )
| ( ( rel @ X3 @ X4 )
= $false )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( ( admin @ X4 )
| ~ ( bob @ X4 ) ) )
| ( ( ( rel @ X3 @ X5 )
=> ( deletefile1 @ X5 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel @ X3 @ X4 )
= $false )
| ( ( ( rel @ X3 @ X5 )
=> ( deletefile1 @ X5 ) )
= $true )
| ( ( admin @ X2 )
= $true )
| ( ( admin @ X4 )
= $true )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( ( rel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( bob @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( deletefile1 @ X5 )
= $true )
| ( ( admin @ X4 )
= $true )
| ( ( rel @ X3 @ X5 )
= $false )
| ( ( rel @ X3 @ X4 )
= $false )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( ~ ( bob @ X4 ) ) )
| ( ( admin @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( ( admin @ X4 )
= $true )
| ( ( rel @ X3 @ X5 )
= $false )
| ( ( rel @ X1 @ X2 )
= $false )
| ( ( admin @ X2 )
= $true )
| ( $false
= ( bob @ X4 ) )
| ( ( rel @ X3 @ X4 )
= $false )
| ( ( deletefile1 @ X5 )
= $true ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( bob @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f177,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( deletefile1 @ Y2 ) ) )
| ( bob @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( bob @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( deletefile1 @ Y1 ) ) )
| ( bob @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( bob @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) )
| ( bob @ X2 ) ) )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ X1 @ X2 )
= $false )
| ( ( bob @ X2 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( deletefile1 @ Y0 ) )
@ X3 ) )
| ( ( bob @ X2 )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( bob @ X2 )
= $true )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( deletefile1 @ X3 ) )
| ( ( bob @ X2 )
= $true )
| ( ( rel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f187,plain,
! [X0: $i > $o,X1: $i] :
( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( X0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X0: $i > $o,X1: $i] :
( ( ( ( rel @ X1 @ ( sK3 @ X1 @ X0 ) )
=> ( X0 @ ( sK3 @ X1 @ X0 ) ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK3 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f220,definition,
( spl5_3
<=> ( ( rel @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f222,plain,
( ( ( rel @ sK1 @ sK2 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f224,definition,
( spl5_4
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f227,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f157,f224,f220]) ).
thf(f229,definition,
( spl5_5
<=> ( ( deletefile1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f231,plain,
( ( ( deletefile1 @ sK2 )
= $false )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f232,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f156,f229,f224]) ).
thf(f233,plain,
~ spl5_4,
inference(avatar_split_clause,[],[f127,f224]) ).
thf(f249,plain,
! [X0: $i] :
( ( $true
= ( rel @ X0 @ X0 ) )
| ( $true
= ( rel @ X0 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f193,f194]) ).
thf(f250,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel @ X0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f249]) ).
thf(f251,plain,
! [X0: $i] :
( $true
= ( rel @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f261,plain,
! [X0: $i] :
( ( $true
= ( deletefile1 @ X0 ) )
| ( $false != $false )
| ( $true
= ( bob @ X0 ) )
| ( $false
= ( rel @ X0 @ X0 ) ) ),
inference(equality_factoring,[],[f185]) ).
thf(f266,plain,
! [X0: $i] :
( ( $true
= ( bob @ X0 ) )
| ( $false
= ( rel @ X0 @ X0 ) )
| ( $true
= ( deletefile1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f270,plain,
! [X0: $i] :
( ( $true
= ( bob @ X0 ) )
| ( $true
= ( deletefile1 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f266,f251]) ).
thf(f271,plain,
! [X0: $i] :
( ( $true
= ( deletefile1 @ X0 ) )
| ( $true
= ( bob @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f277,definition,
( spl5_6
<=> ! [X0: $i] :
( $false
= ( rel @ X0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f278,plain,
( ! [X0: $i] :
( $false
= ( rel @ X0 @ sK1 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f287,plain,
( ( $true = $false )
| ~ spl5_6 ),
inference(constrained_superposition,[],[f251,f278]) ).
thf(f291,plain,
( $false
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f292,plain,
~ spl5_6,
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f294,plain,
( ( $true = $false )
| ( $true
= ( bob @ sK2 ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f271,f231]) ).
thf(f297,plain,
( ( $true
= ( bob @ sK2 ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f307,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( deletefile1 @ sK2 ) )
| ( $true = $false )
| ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( admin @ X1 ) )
| ( $false
= ( rel @ X0 @ sK1 ) ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f222,f142]) ).
thf(f318,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( deletefile1 @ sK2 ) )
| ( $false
= ( rel @ X0 @ sK1 ) )
| ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( admin @ X1 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f323,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( admin @ X1 ) )
| ( $true = $false )
| ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( rel @ X0 @ sK1 ) ) )
| ~ spl5_3
| ~ spl5_5 ),
inference(forward_demodulation,[],[f318,f231]) ).
thf(f324,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel @ X0 @ sK1 ) )
| ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( admin @ X1 ) ) )
| ~ spl5_3
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f326,definition,
( spl5_8
<=> ! [X1: $i] :
( ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( admin @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f327,plain,
( ! [X1: $i] :
( ( ( rel @ sK1 @ X1 )
= $false )
| ( $false
= ( admin @ X1 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f329,plain,
( spl5_6
| spl5_8
| ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f324,f229,f220,f326,f277]) ).
thf(f334,plain,
( ( $true = $false )
| ( ( admin @ sK1 )
= $false )
| ~ spl5_8 ),
inference(constrained_superposition,[],[f251,f327]) ).
thf(f336,plain,
( ( $true = $false )
| ( ( admin @ sK2 )
= $false )
| ~ spl5_3
| ~ spl5_8 ),
inference(constrained_superposition,[],[f222,f327]) ).
thf(f338,plain,
( ( ( admin @ sK2 )
= $false )
| ~ spl5_3
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f339,plain,
( ( ( admin @ sK1 )
= $false )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f372,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( admin @ sK1 )
= $true )
| ( $true = $false )
| ( ( admin @ X0 )
= $true )
| ( $false
= ( bob @ X0 ) )
| ( $false
= ( rel @ X2 @ sK1 ) )
| ( ( rel @ sK2 @ X0 )
= $false )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( ( deletefile1 @ X1 )
= $true ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f175,f222]) ).
thf(f388,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( rel @ sK2 @ X0 )
= $false )
| ( ( admin @ sK1 )
= $true )
| ( ( deletefile1 @ X1 )
= $true )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( $false
= ( rel @ X2 @ sK1 ) )
| ( ( admin @ X0 )
= $true )
| ( $false
= ( bob @ X0 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f397,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( deletefile1 @ X1 )
= $true )
| ( ( admin @ X0 )
= $true )
| ( ( rel @ sK2 @ X0 )
= $false )
| ( $false
= ( rel @ X2 @ sK1 ) )
| ( $true = $false )
| ( $false
= ( bob @ X0 ) )
| ( ( rel @ sK2 @ X1 )
= $false ) )
| ~ spl5_3
| ~ spl5_8 ),
inference(forward_demodulation,[],[f388,f339]) ).
thf(f398,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( admin @ X0 )
= $true )
| ( $false
= ( rel @ X2 @ sK1 ) )
| ( ( rel @ sK2 @ X0 )
= $false )
| ( $false
= ( bob @ X0 ) )
| ( ( rel @ sK2 @ X1 )
= $false )
| ( ( deletefile1 @ X1 )
= $true ) )
| ~ spl5_3
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f402,definition,
( spl5_9
<=> ! [X0: $i] :
( ( ( rel @ sK2 @ X0 )
= $false )
| ( $false
= ( bob @ X0 ) )
| ( ( admin @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f403,plain,
( ! [X0: $i] :
( ( ( rel @ sK2 @ X0 )
= $false )
| ( ( admin @ X0 )
= $true )
| ( $false
= ( bob @ X0 ) ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f405,definition,
( spl5_10
<=> ! [X1: $i] :
( ( ( deletefile1 @ X1 )
= $true )
| ( ( rel @ sK2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f406,plain,
( ! [X1: $i] :
( ( ( rel @ sK2 @ X1 )
= $false )
| ( ( deletefile1 @ X1 )
= $true ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f408,plain,
( spl5_10
| spl5_9
| spl5_6
| ~ spl5_3
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f398,f326,f220,f277,f402,f405]) ).
thf(f412,plain,
( ( $true = $false )
| ( $true
= ( admin @ sK2 ) )
| ( ( bob @ sK2 )
= $false )
| ~ spl5_9 ),
inference(constrained_superposition,[],[f251,f403]) ).
thf(f416,plain,
( ( ( bob @ sK2 )
= $false )
| ( $true
= ( admin @ sK2 ) )
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f421,plain,
( ( $true = $false )
| ( $true
= ( admin @ sK2 ) )
| ~ spl5_5
| ~ spl5_9 ),
inference(forward_demodulation,[],[f416,f297]) ).
thf(f422,plain,
( ( $true
= ( admin @ sK2 ) )
| ~ spl5_5
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f421]) ).
thf(f426,plain,
( ( $true = $false )
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8
| ~ spl5_9 ),
inference(forward_demodulation,[],[f422,f338]) ).
thf(f427,plain,
( $false
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f428,plain,
( ~ spl5_3
| ~ spl5_5
| ~ spl5_8
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f427]) ).
thf(f429,plain,
( ( $true
= ( deletefile1 @ sK2 ) )
| ( $true = $false )
| ~ spl5_10 ),
inference(constrained_superposition,[],[f406,f251]) ).
thf(f438,plain,
( ( $true
= ( deletefile1 @ sK2 ) )
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f442,plain,
( ( $true = $false )
| ~ spl5_5
| ~ spl5_10 ),
inference(forward_demodulation,[],[f438,f231]) ).
thf(f443,plain,
( $false
| ~ spl5_5
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f444,plain,
( ~ spl5_5
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f443]) ).
cnf(s2,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f227]) ).
cnf(s3,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f232]) ).
cnf(s4,plain,
~ spl5_4,
inference(sat_conversion,[],[f233]) ).
cnf(s8,plain,
~ spl5_6,
inference(sat_conversion,[],[f292]) ).
cnf(s10,plain,
( ~ spl5_3
| ~ spl5_5
| spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f329]) ).
cnf(s12,plain,
( ~ spl5_3
| spl5_6
| ~ spl5_8
| spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f408]) ).
cnf(s14,plain,
( ~ spl5_3
| ~ spl5_5
| ~ spl5_8
| ~ spl5_9 ),
inference(sat_conversion,[],[f428]) ).
cnf(s16,plain,
( ~ spl5_5
| ~ spl5_10 ),
inference(sat_conversion,[],[f444]) ).
cnf(s19,plain,
spl5_5,
inference(rat,[],[s3,s4]) ).
cnf(s20,plain,
~ spl5_10,
inference(rat,[],[s16,s19]) ).
cnf(s21,plain,
spl5_3,
inference(rat,[],[s2,s4]) ).
cnf(s22,plain,
spl5_8,
inference(rat,[],[s10,s19,s8,s21]) ).
cnf(s24,plain,
spl5_9,
inference(rat,[],[s12,s20,s21,s8,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s14,s21,s19,s24,s22]) ).
thf(f445,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV436^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n001.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:09:51 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.33 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
% 0.32/0.42 % (1427889)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.42 % (1427896)lrs+10_16_si=on:nwc=1.5:random_seed=2231914750:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.42 % (1427901)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.42 % (1427901)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
% 0.32/0.42 % (1427896)Instruction limit reached!
% 0.32/0.42 % (1427896)------------------------------
% 0.32/0.42 % (1427896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (1427896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (1427896)CaDiCaL version: 2.1.3
% 0.32/0.42 % (1427896)Termination reason: Instruction limit
% 0.32/0.42 % (1427896)Termination phase: Saturation
% 0.32/0.42 % (1427896)Time elapsed: 0.009 s
% 0.32/0.42 % (1427896)Peak memory usage: 12 MB
% 0.32/0.42 % (1427896)Instructions burned: 18 (million)
% 0.32/0.42 % (1427898)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=1923099486: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)
% 0.32/0.42 % (1427895)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=440114487:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.42 % (1427897)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1371893606:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.42 % (1427899)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=705807693:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.42 % (1427900)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1429095866:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.32/0.42 % (1427901)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1125451472:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.32/0.42 % (1427897)Instruction limit reached!
% 0.32/0.42 % (1427897)------------------------------
% 0.32/0.42 % (1427897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (1427897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (1427897)CaDiCaL version: 2.1.3
% 0.32/0.42 % (1427897)Termination reason: Instruction limit
% 0.32/0.42 % (1427897)Termination phase: Function definition elimination
% 0.32/0.42 % (1427897)Time elapsed: 0.003 s
% 0.32/0.42 % (1427897)Peak memory usage: 10 MB
% 0.32/0.42 % (1427897)Instructions burned: 3 (million)
% 0.32/0.42 % (1427899)Instruction limit reached!
% 0.32/0.42 % (1427899)------------------------------
% 0.32/0.42 % (1427899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (1427899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (1427899)CaDiCaL version: 2.1.3
% 0.32/0.42 % (1427899)Termination reason: Instruction limit
% 0.32/0.42 % (1427899)Termination phase: Saturation
% 0.32/0.42 % (1427899)Time elapsed: 0.023 s
% 0.32/0.42 % (1427899)Peak memory usage: 11 MB
% 0.32/0.42 % (1427899)Instructions burned: 24 (million)
% 0.32/0.42 % (1427901) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1427889-1427901"...
% 0.32/0.42 % (1427904)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1238760985:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.42 % (1427904)Instruction limit reached!
% 0.32/0.42 % (1427904)------------------------------
% 0.32/0.42 % (1427904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (1427904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (1427904)CaDiCaL version: 2.1.3
% 0.32/0.42 % (1427904)Termination reason: Instruction limit
% 0.32/0.42 % (1427904)Termination phase: Property scanning
% 0.32/0.42 % (1427904)Time elapsed: 0.006 s
% 0.32/0.42 % (1427904)Peak memory usage: 10 MB
% 0.32/0.42 % (1427904)Instructions burned: 2 (million)
% 0.32/0.42 % (1427910)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=193035575:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.32/0.42 % (1427901)...printing done.
% 0.32/0.42 % (1427901)Refutation found. Thanks to Tanya!
% 0.32/0.42 % SZS status Theorem for theBenchmark
% 0.32/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/0.42 % (1427901)------------------------------
% 0.32/0.42 % (1427901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.42 % (1427901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.42 % (1427901)CaDiCaL version: 2.1.3
% 0.32/0.42 % (1427901)Termination reason: Refutation
% 0.32/0.42 % (1427901)Time elapsed: 0.034 s
% 0.32/0.42 % (1427901)Peak memory usage: 13 MB
% 0.32/0.42 % (1427901)Instructions burned: 36 (million)
% 0.32/0.42 % (1427889)Success in time 0.075 s
% 0.32/0.42 % Vampire exiting
%------------------------------------------------------------------------------