%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV425^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:39:55 AM UTC 2026
% Result : Theorem 0.31s 0.41s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 136 ( 60 unt; 0 typ; 7 def)
% Number of atoms : 924 ( 184 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1259 ( 69 ~; 155 |; 0 &; 855 @)
% ( 6 <=>; 93 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 14 con; 0-4 aty)
% ( 81 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 385 ( 0 sgn 87 !; 0 ?; 385 :)
% 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,
s: $i > $o ).
thf(func_def_31,type,
a: $i > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sF0: $o ).
thf(func_def_46,type,
sK1: $i > $i ).
thf(func_def_51,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_52,type,
sK7: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) )
= icl_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_atom) ).
thf(f17,axiom,
( ( ^ [X0: $i > $o] : X0 )
= icl_princ ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) )
= icl_impl ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f23,axiom,
( icl_says
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( iclval
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f26,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',trans_axiom) ).
thf(f27,conjecture,
iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unit) ).
thf(f28,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f33,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f34,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f37,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f39,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f41,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f42,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f49,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f50,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
~ ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f54,plain,
( ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
!= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f56,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f62,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f68,plain,
( ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
!= $true ),
inference(flattening,[],[f54]) ).
thf(f69,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f71,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f74,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f75,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f78,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f79,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f83,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f84,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f86,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f87,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f89,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f94,plain,
( ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f68]) ).
thf(f98,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,[],[f75,f83,f86]) ).
thf(f100,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,[],[f74,f84]) ).
thf(f103,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,[],[f89,f84,f98]) ).
thf(f106,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,[],[f79,f84,f83]) ).
thf(f107,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f78,f87]) ).
thf(f108,plain,
! [X0: $i > $o] :
( $true
= ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 ) ) ) ) ),
inference(definition_unfolding,[],[f69,f87,f98,f84,f84,f84]) ).
thf(f110,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 > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s )
@ ( ^ [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
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ),
inference(definition_unfolding,[],[f94,f107,f103,f100,f106,f71,f100]) ).
thf(f111,definition,
( sF0
= ( ^ [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 > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s )
@ ( ^ [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
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f112,plain,
$true != sF0,
inference(definition_folding,[],[f110,f111]) ).
thf(f113,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [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 > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s )
@ ( ^ [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
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f111]) ).
thf(f136,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( a @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f137,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( a @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) ) ) )
@ sK3 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( $true = sF0 )
| ( ( ( rel @ sK2 @ sK3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( s @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( s @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f145,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) )
@ sK4 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ( rel @ sK3 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( s @ Y0 ) ) )
| ( a @ sK4 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( s @ Y0 ) ) )
| ( a @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $true = sF0 )
| ( $true
= ( rel @ sK3 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f150,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( s @ Y0 ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( s @ Y0 ) )
@ sK5 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true = sF0 )
| ( $false
= ( ( rel @ sK4 @ sK5 )
=> ( s @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( s @ sK5 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $true
= ( rel @ sK4 @ sK5 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( s @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f156,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( s @ Y0 ) )
@ X1 )
= $true )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ( rel @ sK3 @ X1 )
=> ( s @ X1 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( s @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f160,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK6 @ X1 @ X0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK6 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ( rel @ X1 @ ( sK6 @ X1 @ X0 ) )
=> ( X0 @ ( sK6 @ X1 @ X0 ) ) )
= $false )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( rel @ X1 @ ( sK6 @ X1 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( rel @ X1 @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( rel @ X1 @ ( sK6 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( rel @ X1 @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK6 @ X1 @ X0 ) ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK6 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( X0 @ ( sK6 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) )
| ( $false
= ( X0 @ ( sK6 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK6 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f199,definition,
( spl8_4
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f208,definition,
( spl8_6
<=> ( $true
= ( rel @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f210,plain,
( ( $true
= ( rel @ sK3 @ sK4 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f211,plain,
( spl8_6
| spl8_4 ),
inference(avatar_split_clause,[],[f148,f199,f208]) ).
thf(f213,definition,
( spl8_7
<=> ( $true
= ( rel @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f215,plain,
( ( $true
= ( rel @ sK4 @ sK5 ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl8_4
| spl8_7 ),
inference(avatar_split_clause,[],[f154,f213,f199]) ).
thf(f218,definition,
( spl8_8
<=> ( $false
= ( s @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f220,plain,
( ( $false
= ( s @ sK5 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl8_4
| spl8_8 ),
inference(avatar_split_clause,[],[f153,f218,f199]) ).
thf(f228,definition,
( spl8_10
<=> ! [X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f229,plain,
( ! [X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( s @ X1 ) ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f230,plain,
( spl8_10
| spl8_4 ),
inference(avatar_split_clause,[],[f158,f199,f228]) ).
thf(f231,plain,
~ spl8_4,
inference(avatar_split_clause,[],[f112,f199]) ).
thf(f284,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ sK3 @ X2 ) )
| ( $true
= ( s @ ( sK6 @ sK3 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true )
| ( $false
= ( rel @ X2 @ X1 ) )
| ( $true = $false ) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f172,f229]) ).
thf(f293,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( s @ ( sK6 @ sK3 @ X0 ) ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ X2 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f297,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel @ sK3 @ X0 ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $true
= ( s @ X1 ) )
| ( $true = $false )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( s @ X3 ) )
| ( $false
= ( rel @ X0 @ X1 ) ) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f176,f293]) ).
thf(f301,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( s @ X3 ) )
| ( $true
= ( s @ X1 ) )
| ( $false
= ( rel @ X0 @ X1 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ sK3 @ X0 ) ) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f311,definition,
( spl8_13
<=> ! [X2: $i,X3: $i] :
( ( $true
= ( s @ X3 ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
thf(f312,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( s @ X3 ) ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f314,plain,
( spl8_13
| spl8_13
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f301,f228,f311,f311]) ).
thf(f323,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $true = $false )
| ( $true
= ( s @ X0 ) ) )
| ~ spl8_6
| ~ spl8_13 ),
inference(constrained_superposition,[],[f312,f210]) ).
thf(f332,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $true
= ( s @ X0 ) ) )
| ~ spl8_6
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f348,plain,
( ( $true
= ( s @ sK5 ) )
| ( $true = $false )
| ~ spl8_6
| ~ spl8_7
| ~ spl8_13 ),
inference(constrained_superposition,[],[f215,f332]) ).
thf(f354,plain,
( ( $true
= ( s @ sK5 ) )
| ~ spl8_6
| ~ spl8_7
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f361,plain,
( ( $true = $false )
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_13 ),
inference(forward_demodulation,[],[f354,f220]) ).
thf(f362,plain,
( $false
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f363,plain,
( ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f362]) ).
cnf(s4,plain,
( spl8_4
| spl8_6 ),
inference(sat_conversion,[],[f211]) ).
cnf(s5,plain,
( spl8_4
| spl8_7 ),
inference(sat_conversion,[],[f216]) ).
cnf(s6,plain,
( spl8_4
| spl8_8 ),
inference(sat_conversion,[],[f221]) ).
cnf(s8,plain,
( spl8_4
| spl8_10 ),
inference(sat_conversion,[],[f230]) ).
cnf(s9,plain,
~ spl8_4,
inference(sat_conversion,[],[f231]) ).
cnf(s14,plain,
( spl8_13
| ~ spl8_10
| spl8_13 ),
inference(sat_conversion,[],[f314]) ).
cnf(s15,plain,
( ~ spl8_10
| spl8_13 ),
inference(rat,[],[s14]) ).
cnf(s19,plain,
( ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| ~ spl8_13 ),
inference(sat_conversion,[],[f363]) ).
cnf(s21,plain,
spl8_10,
inference(rat,[],[s8,s9]) ).
cnf(s22,plain,
spl8_13,
inference(rat,[],[s15,s21]) ).
cnf(s24,plain,
spl8_8,
inference(rat,[],[s6,s9]) ).
cnf(s25,plain,
spl8_7,
inference(rat,[],[s5,s9]) ).
cnf(s26,plain,
~ spl8_6,
inference(rat,[],[s19,s22,s24,s25]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s4,s26,s9]) ).
thf(f364,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV425^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n011.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 16:02:01 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.41 % (262663)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.41 % (262669)lrs+10_16_si=on:nwc=1.5:random_seed=3774647851:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.41 % (262674)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.41 % (262674)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
% 0.31/0.41 % (262669)Instruction limit reached!
% 0.31/0.41 % (262669)------------------------------
% 0.31/0.41 % (262669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262669)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262669)Termination reason: Instruction limit
% 0.31/0.41 % (262669)Termination phase: Saturation
% 0.31/0.41 % (262669)Time elapsed: 0.010 s
% 0.31/0.41 % (262669)Peak memory usage: 12 MB
% 0.31/0.41 % (262669)Instructions burned: 19 (million)
% 0.31/0.41 % (262668)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1338934889:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.41 % (262670)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1353630802:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.41 % (262672)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1689032295:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.41 % (262673)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4193428150:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.41 % (262674)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=4289460490:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.41 % (262671)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=3788081255: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)
% 0.31/0.41 % (262670)Instruction limit reached!
% 0.31/0.41 % (262670)------------------------------
% 0.31/0.41 % (262670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262670)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262670)Termination reason: Instruction limit
% 0.31/0.41 % (262670)Termination phase: Property scanning
% 0.31/0.41 % (262670)Time elapsed: 0.003 s
% 0.31/0.41 % (262670)Peak memory usage: 10 MB
% 0.31/0.41 % (262670)Instructions burned: 4 (million)
% 0.31/0.41 % (262674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-262663-262674"...
% 0.31/0.41 % (262676)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2064243044:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.31/0.41 % (262676)Instruction limit reached!
% 0.31/0.41 % (262676)------------------------------
% 0.31/0.41 % (262676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262676)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262676)Termination reason: Instruction limit
% 0.31/0.41 % (262676)Termination phase: Property scanning
% 0.31/0.41 % (262676)Time elapsed: 0.002 s
% 0.31/0.41 % (262676)Peak memory usage: 10 MB
% 0.31/0.41 % (262676)Instructions burned: 4 (million)
% 0.31/0.41 % (262683)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=514147740:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.31/0.41 % (262683)Instruction limit reached!
% 0.31/0.41 % (262683)------------------------------
% 0.31/0.41 % (262683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262683)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262683)Termination reason: Instruction limit
% 0.31/0.41 % (262683)Termination phase: Saturation
% 0.31/0.41 % (262683)Time elapsed: 0.003 s
% 0.31/0.41 % (262683)Peak memory usage: 11 MB
% 0.31/0.41 % (262683)Instructions burned: 7 (million)
% 0.31/0.41 % (262672)Instruction limit reached!
% 0.31/0.41 % (262672)------------------------------
% 0.31/0.41 % (262672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262672)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262672)Termination reason: Instruction limit
% 0.31/0.41 % (262672)Termination phase: Saturation
% 0.31/0.41 % (262672)Time elapsed: 0.025 s
% 0.31/0.41 % (262672)Peak memory usage: 11 MB
% 0.31/0.41 % (262672)Instructions burned: 25 (million)
% 0.31/0.41 % (262674)...printing done.
% 0.31/0.41 % (262674)Refutation found. Thanks to Tanya!
% 0.31/0.41 % SZS status Theorem for theBenchmark
% 0.31/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.41 % (262674)------------------------------
% 0.31/0.41 % (262674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (262674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (262674)CaDiCaL version: 2.1.3
% 0.31/0.41 % (262674)Termination reason: Refutation
% 0.31/0.41 % (262674)Time elapsed: 0.025 s
% 0.31/0.41 % (262674)Peak memory usage: 13 MB
% 0.31/0.41 % (262674)Instructions burned: 26 (million)
% 0.31/0.41 % (262663)Success in time 0.067 s
% 0.31/0.41 % Vampire exiting
%------------------------------------------------------------------------------