%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL718^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:14:33 AM UTC 2026
% Result : Theorem 0.36s 0.48s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of formulae : 187 ( 60 unt; 0 typ; 16 def)
% Number of atoms : 1555 ( 345 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2340 ( 296 ~; 416 |; 36 &;1434 @)
% ( 14 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 291 ( 291 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 69 usr; 23 con; 0-4 aty)
% ( 111 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 581 ( 0 sgn 211 !; 3 ?; 581 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_51,type,
sK4: $i > $o ).
thf(func_def_54,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_55,type,
sK8: $i > ( $i > $o ) > $i ).
thf(func_def_59,type,
sK12: $i > $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f27,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ? [X4: $i] :
( ( X0 @ X2 @ X4 )
& ( X0 @ X3 @ X4 ) ) ) )
= mweakly_directed ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mweakly_directed) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( mweakly_directed @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( mweakly_directed @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f43,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mdia @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) ) ) )
=> ( mweakly_directed @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f44,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) ) )
=> ( ( mweakly_directed @ X0 )
= $true ) ),
inference(fool_elimination,[],[f43]) ).
thf(f48,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f49,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f55,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f56,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f63,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f64,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f71,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f77,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f78,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f83,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ? [X4: $i] :
( ( X0 @ X2 @ X4 )
& ( X0 @ X1 @ X4 ) ) ) )
= mweakly_directed ),
inference(rectify,[],[f27]) ).
thf(f84,plain,
( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ Y0 ) ) ) ) ) )
& ( ( mweakly_directed @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f44]) ).
thf(f88,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
= $true )
& ( $true
!= ( mweakly_directed @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f93,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f99,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f101,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f107,plain,
( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f111,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f112,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f118,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f120,plain,
( $true
!= ( mweakly_directed @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f121,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mdia @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ ( mdia @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f125,plain,
( mimplies
= ( ^ [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,[],[f99,f111,f100]) ).
thf(f132,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f93,f100,f118,f100]) ).
thf(f133,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f121,f112,f101,f125,f132,f118,f118,f132]) ).
thf(f134,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
@ sK0 )
!= $true ),
inference(definition_unfolding,[],[f120,f107]) ).
thf(f135,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f135]) ).
thf(f137,plain,
$true = sF1,
inference(definition_folding,[],[f133,f136]) ).
thf(f138,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f139,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
@ sK0 )
= sF2 ),
inference(reorient_equations,[],[f138]) ).
thf(f140,plain,
sF2 != $true,
inference(definition_folding,[],[f134,f139]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
| ( sF1 = $false ) ),
inference(iff_proxy_clausification,[],[f136]) ).
thf(f173,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f174,plain,
! [X1: $i] :
( ( sF1 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( sK0 @ Y2 @ Y3 ) ) )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( sF1 = $false )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( sK0 @ Y1 @ Y2 ) ) )
| ~ ( sK0 @ X1 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X1: $i] :
( ( sF1 = $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( sF1 = $false ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i > $o,X1: $i] :
( ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( sF1 = $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 )
| ~ ( sK0 @ Y0 @ Y1 ) ) )
| ~ ( sK0 @ X1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X3 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( ~ ( sK0 @ X1 @ X3 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) ) ) )
| ( sF1 = $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) )
| ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) )
| ( sF1 = $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) )
= $false )
| ( $true
= ( ~ ( sK0 @ X1 @ X4 ) ) )
| ( sF1 = $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( sK0 @ X4 @ Y0 ) )
@ ( sK8 @ X4 @ X2 ) )
= $false )
| ( sF1 = $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 )
| ~ ( sK0 @ X3 @ Y0 ) )
@ ( sK7 @ X3 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
| ~ ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( sF1 = $false )
| ( ( ~ ( X2 @ ( sK7 @ X3 @ X2 ) )
| ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( X2 @ ( sK7 @ X3 @ X2 ) )
| ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( ( ~ ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( X2 @ ( sK7 @ X3 @ X2 ) )
| ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( sF1 = $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( sF1 = $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $false
= ( ~ ( X2 @ ( sK7 @ X3 @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( sF1 = $false ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
| ( sF1 = $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f199,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( sF1 = $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ~ ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) ) )
= $false )
| ( ( ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f200,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( $false
= ( ~ ( X2 @ ( sK7 @ X3 @ X2 ) ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( ~ ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f201,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( ~ ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( sF1 = $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( sF1 = $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( ~ ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f204,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( sF1 = $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
@ sK0 )
= $false )
| ( sF2 = $true ) ),
inference(iff_proxy_clausification,[],[f139]) ).
thf(f207,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
& ( sK0 @ Y1 @ Y3 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
& ( sK0 @ Y1 @ Y3 ) ) ) ) ) )
@ sK9 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK9 @ Y1 )
& ( sK0 @ sK9 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK9 @ Y1 )
& ( sK0 @ sK9 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK9 @ Y0 )
& ( sK0 @ sK9 @ sK10 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK10 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK9 @ Y0 )
& ( sK0 @ sK9 @ sK10 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK10 @ Y1 ) ) ) )
@ sK11 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( ( ( ( sK0 @ sK9 @ sK11 )
& ( sK0 @ sK9 @ sK10 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
& ( sK0 @ sK10 @ Y0 ) ) ) )
= $false )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ( sF2 = $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
& ( sK0 @ sK10 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( sF2 = $true )
| ( $true
= ( ( sK0 @ sK9 @ sK11 )
& ( sK0 @ sK9 @ sK10 ) ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( sF2 = $true )
| ( $true
= ( sK0 @ sK9 @ sK10 ) ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $true
= ( sK0 @ sK9 @ sK11 ) )
| ( sF2 = $true ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
& ( sK0 @ sK10 @ Y0 ) )
@ X1 )
= $false )
| ( sF2 = $true ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f219,plain,
! [X1: $i] :
( ( sF2 = $true )
| ( ( ( sK0 @ sK11 @ X1 )
& ( sK0 @ sK10 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( sF2 = $true )
| ( ( sK0 @ sK10 @ X1 )
= $false )
| ( ( sK0 @ sK11 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f219]) ).
thf(f235,definition,
( spl13_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
thf(f237,plain,
( ( $true = sF1 )
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f257,definition,
( spl13_6
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
thf(f259,plain,
( ( sF1 = $false )
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f261,definition,
( spl13_7
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
thf(f262,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f263,plain,
( spl13_6
| spl13_7 ),
inference(avatar_split_clause,[],[f197,f261,f257]) ).
thf(f265,definition,
( spl13_8
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
thf(f266,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( X2 @ ( sK8 @ X4 @ X2 ) )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) )
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f267,plain,
( spl13_8
| spl13_6 ),
inference(avatar_split_clause,[],[f198,f257,f265]) ).
thf(f269,definition,
( spl13_9
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true )
| ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
thf(f270,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true )
| ( $true
= ( X2 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X4 )
= $false ) )
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl13_6
| spl13_9 ),
inference(avatar_split_clause,[],[f202,f269,f257]) ).
thf(f273,definition,
( spl13_10
<=> ! [X2: $i > $o,X4: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
thf(f274,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK7 @ X3 @ X2 ) ) )
| ( ( sK0 @ X1 @ X4 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X4 @ ( sK8 @ X4 @ X2 ) )
= $true ) )
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f275,plain,
( spl13_6
| spl13_10 ),
inference(avatar_split_clause,[],[f204,f273,f257]) ).
thf(f277,definition,
( spl13_11
<=> ( $true
= ( sK0 @ sK9 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
thf(f279,plain,
( ( $true
= ( sK0 @ sK9 @ sK11 ) )
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f281,definition,
( spl13_12
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
thf(f284,plain,
( spl13_11
| spl13_12 ),
inference(avatar_split_clause,[],[f217,f281,f277]) ).
thf(f286,definition,
( spl13_13
<=> ( $true
= ( sK0 @ sK9 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
thf(f288,plain,
( ( $true
= ( sK0 @ sK9 @ sK10 ) )
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f289,plain,
( spl13_13
| spl13_12 ),
inference(avatar_split_clause,[],[f216,f281,f286]) ).
thf(f291,definition,
( spl13_14
<=> ! [X1: $i] :
( ( ( sK0 @ sK10 @ X1 )
= $false )
| ( ( sK0 @ sK11 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
thf(f292,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK11 @ X1 )
= $false )
| ( ( sK0 @ sK10 @ X1 )
= $false ) )
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f293,plain,
( spl13_14
| spl13_12 ),
inference(avatar_split_clause,[],[f220,f281,f291]) ).
thf(f306,plain,
spl13_1,
inference(avatar_split_clause,[],[f137,f235]) ).
thf(f307,plain,
~ spl13_12,
inference(avatar_split_clause,[],[f140,f281]) ).
thf(f317,plain,
( ( $true = $false )
| ~ spl13_1
| ~ spl13_6 ),
inference(forward_demodulation,[],[f259,f237]) ).
thf(f318,plain,
( $false
| ~ spl13_1
| ~ spl13_6 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f319,plain,
( ~ spl13_1
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f318]) ).
thf(f329,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK0 @ sK10 @ ( sK7 @ sK11 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ sK11 )
= $false )
| ( ( X0 @ ( sK8 @ X1 @ X0 ) )
= $false ) )
| ~ spl13_8
| ~ spl13_14 ),
inference(constrained_superposition,[],[f266,f292]) ).
thf(f332,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK0 @ sK10 @ ( sK7 @ sK11 @ X0 ) )
= $false )
| ( ( X0 @ ( sK8 @ X1 @ X0 ) )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ sK11 )
= $false ) )
| ~ spl13_8
| ~ spl13_14 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f341,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK10 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) ) )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ sK10 @ ( sK8 @ X2 @ ( sK0 @ sK10 ) ) )
= $false )
| ( ( sK0 @ X3 @ sK11 )
= $false )
| ( $true = $false )
| ( ( sK0 @ X1 @ X0 )
= $false ) )
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14 ),
inference(constrained_superposition,[],[f262,f332]) ).
thf(f344,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X3 @ sK11 )
= $false )
| ( $false
= ( sK0 @ sK10 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) ) )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ sK10 @ ( sK8 @ X2 @ ( sK0 @ sK10 ) ) )
= $false )
| ( ( sK0 @ X3 @ X2 )
= $false ) )
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f348,definition,
( spl13_18
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK10 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) ) )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X1 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
thf(f349,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK10 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) ) )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X1 @ X0 )
= $false ) )
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f351,plain,
( spl13_18
| spl13_18
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f344,f291,f265,f261,f348,f348]) ).
thf(f360,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK10 ) )
| ( $true
= ( sK0 @ sK10 @ ( sK7 @ X1 @ ( sK0 @ sK10 ) ) ) )
| ( ( sK0 @ X0 @ sK11 )
= $false )
| ( ( sK0 @ X0 @ sK10 )
= $false )
| ( $true = $false )
| ( ( sK0 @ X2 @ X1 )
= $false ) )
| ~ spl13_9
| ~ spl13_18 ),
inference(constrained_superposition,[],[f349,f270]) ).
thf(f364,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X0 @ sK10 )
= $false )
| ( $false
= ( sK0 @ X2 @ sK10 ) )
| ( $true
= ( sK0 @ sK10 @ ( sK7 @ X1 @ ( sK0 @ sK10 ) ) ) )
| ( ( sK0 @ X0 @ sK11 )
= $false ) )
| ~ spl13_9
| ~ spl13_18 ),
inference(trivial_inequality_removal,[],[f360]) ).
thf(f367,definition,
( spl13_21
<=> ! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ sK10 )
= $false )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( $true
= ( sK0 @ sK10 @ ( sK7 @ X0 @ ( sK0 @ sK10 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
thf(f368,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK10 @ ( sK7 @ X0 @ ( sK0 @ sK10 ) ) ) )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X1 @ sK10 )
= $false ) )
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f370,definition,
( spl13_22
<=> ! [X2: $i] :
( ( ( sK0 @ X2 @ sK11 )
= $false )
| ( $false
= ( sK0 @ X2 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
thf(f371,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ X2 @ sK10 ) )
| ( ( sK0 @ X2 @ sK11 )
= $false ) )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f370]) ).
thf(f373,plain,
( spl13_21
| spl13_22
| ~ spl13_9
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f364,f348,f269,f370,f367]) ).
thf(f390,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK0 @ sK10 @ ( sK7 @ sK11 @ X0 ) )
= $false )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X2 @ ( sK8 @ X2 @ X0 ) )
= $true )
| ( $true = $false )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl13_10
| ~ spl13_14 ),
inference(constrained_superposition,[],[f274,f292]) ).
thf(f393,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK0 @ sK10 @ ( sK7 @ sK11 @ X0 ) )
= $false )
| ( ( sK0 @ X2 @ ( sK8 @ X2 @ X0 ) )
= $true )
| ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl13_10
| ~ spl13_14 ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f398,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ sK11 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X0 @ sK10 )
= $false )
| ( $true = $false )
| ( ( sK0 @ X2 @ sK11 )
= $false )
| ( ( sK0 @ X1 @ ( sK8 @ X1 @ ( sK0 @ sK10 ) ) )
= $true ) )
| ~ spl13_10
| ~ spl13_14
| ~ spl13_21 ),
inference(constrained_superposition,[],[f368,f393]) ).
thf(f406,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ sK11 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ ( sK8 @ X1 @ ( sK0 @ sK10 ) ) )
= $true )
| ( ( sK0 @ X0 @ sK10 )
= $false )
| ( ( sK0 @ X2 @ sK11 )
= $false ) )
| ~ spl13_10
| ~ spl13_14
| ~ spl13_21 ),
inference(trivial_inequality_removal,[],[f398]) ).
thf(f408,definition,
( spl13_24
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X0 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl13_24])],[avatar_definition]) ).
thf(f409,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ ( sK8 @ X0 @ ( sK0 @ sK10 ) ) )
= $true )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( $false
= ( sK0 @ X1 @ sK11 ) ) )
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f408]) ).
thf(f411,plain,
( spl13_24
| spl13_22
| ~ spl13_10
| ~ spl13_14
| ~ spl13_21 ),
inference(avatar_split_clause,[],[f406,f367,f291,f273,f370,f408]) ).
thf(f414,plain,
( ( $true = $false )
| ( ( sK0 @ sK9 @ sK11 )
= $false )
| ~ spl13_13
| ~ spl13_22 ),
inference(constrained_superposition,[],[f288,f371]) ).
thf(f417,plain,
( ( ( sK0 @ sK9 @ sK11 )
= $false )
| ~ spl13_13
| ~ spl13_22 ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f421,plain,
( ( $true = $false )
| ~ spl13_11
| ~ spl13_13
| ~ spl13_22 ),
inference(forward_demodulation,[],[f417,f279]) ).
thf(f422,plain,
( $false
| ~ spl13_11
| ~ spl13_13
| ~ spl13_22 ),
inference(trivial_inequality_removal,[],[f421]) ).
thf(f423,plain,
( ~ spl13_11
| ~ spl13_13
| ~ spl13_22 ),
inference(avatar_contradiction_clause,[],[f422]) ).
thf(f424,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ sK11 ) )
| ( ( sK0 @ X0 @ sK10 )
= $false )
| ( ( sK0 @ X1 @ sK10 )
= $false )
| ( ( sK0 @ X0 @ sK11 )
= $false )
| ( $true = $false ) )
| ~ spl13_18
| ~ spl13_24 ),
inference(constrained_superposition,[],[f409,f349]) ).
thf(f431,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ sK10 )
= $false )
| ( ( sK0 @ X1 @ sK10 )
= $false )
| ( ( sK0 @ X0 @ sK11 )
= $false )
| ( $false
= ( sK0 @ X1 @ sK11 ) ) )
| ~ spl13_18
| ~ spl13_24 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f443,plain,
( spl13_22
| spl13_22
| ~ spl13_18
| ~ spl13_24 ),
inference(avatar_split_clause,[],[f431,f408,f348,f370,f370]) ).
cnf(s5,plain,
( spl13_6
| spl13_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
( spl13_6
| spl13_8 ),
inference(sat_conversion,[],[f267]) ).
cnf(s7,plain,
( spl13_6
| spl13_9 ),
inference(sat_conversion,[],[f271]) ).
cnf(s8,plain,
( spl13_6
| spl13_10 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f284]) ).
cnf(s10,plain,
( spl13_12
| spl13_13 ),
inference(sat_conversion,[],[f289]) ).
cnf(s11,plain,
( spl13_12
| spl13_14 ),
inference(sat_conversion,[],[f293]) ).
cnf(s14,plain,
spl13_1,
inference(sat_conversion,[],[f306]) ).
cnf(s15,plain,
~ spl13_12,
inference(sat_conversion,[],[f307]) ).
cnf(s16,plain,
( ~ spl13_1
| ~ spl13_6 ),
inference(sat_conversion,[],[f319]) ).
cnf(s19,plain,
( spl13_18
| ~ spl13_8
| ~ spl13_14
| ~ spl13_7
| spl13_18 ),
inference(sat_conversion,[],[f351]) ).
cnf(s20,plain,
( ~ spl13_7
| ~ spl13_8
| ~ spl13_14
| spl13_18 ),
inference(rat,[],[s19]) ).
cnf(s23,plain,
( ~ spl13_9
| ~ spl13_18
| spl13_21
| spl13_22 ),
inference(sat_conversion,[],[f373]) ).
cnf(s26,plain,
( ~ spl13_10
| ~ spl13_14
| ~ spl13_21
| spl13_22
| spl13_24 ),
inference(sat_conversion,[],[f411]) ).
cnf(s28,plain,
( ~ spl13_11
| ~ spl13_13
| ~ spl13_22 ),
inference(sat_conversion,[],[f423]) ).
cnf(s32,plain,
( spl13_22
| ~ spl13_18
| spl13_22
| ~ spl13_24 ),
inference(sat_conversion,[],[f443]) ).
cnf(s33,plain,
( ~ spl13_18
| spl13_22
| ~ spl13_24 ),
inference(rat,[],[s32]) ).
cnf(s35,plain,
~ spl13_6,
inference(rat,[],[s16,s14]) ).
cnf(s36,plain,
spl13_14,
inference(rat,[],[s11,s15]) ).
cnf(s37,plain,
spl13_13,
inference(rat,[],[s10,s15]) ).
cnf(s38,plain,
spl13_11,
inference(rat,[],[s9,s15]) ).
cnf(s39,plain,
~ spl13_22,
inference(rat,[],[s28,s37,s38]) ).
cnf(s40,plain,
spl13_10,
inference(rat,[],[s8,s35]) ).
cnf(s41,plain,
spl13_9,
inference(rat,[],[s7,s35]) ).
cnf(s42,plain,
spl13_8,
inference(rat,[],[s6,s35]) ).
cnf(s43,plain,
spl13_7,
inference(rat,[],[s5,s35]) ).
cnf(s44,plain,
spl13_18,
inference(rat,[],[s20,s42,s36,s43]) ).
cnf(s45,plain,
~ spl13_24,
inference(rat,[],[s33,s39,s44]) ).
cnf(s46,plain,
spl13_21,
inference(rat,[],[s23,s39,s41,s44]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s26,s40,s39,s36,s45,s46]) ).
thf(f445,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL718^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n007.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 09:51:56 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.34 Running higher-order theorem proving
% 0.29/0.37 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
% 0.36/0.48 % (3149603)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.48 % (3149612)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3000112432:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.36/0.48 % (3149614)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.36/0.48 % (3149614)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
% 0.36/0.48 % (3149610)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=352799847:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.36/0.48 % (3149609)lrs+10_16_si=on:nwc=1.5:random_seed=2357001947:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.36/0.48 % (3149608)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=569647526:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.36/0.48 % (3149613)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=385190766:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.36/0.48 % (3149612)Instruction limit reached!
% 0.36/0.48 % (3149612)------------------------------
% 0.36/0.48 % (3149612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (3149612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (3149612)CaDiCaL version: 2.1.3
% 0.36/0.48 % (3149612)Termination reason: Instruction limit
% 0.36/0.48 % (3149612)Termination phase: Saturation
% 0.36/0.48 % (3149612)Time elapsed: 0.013 s
% 0.36/0.48 % (3149612)Peak memory usage: 12 MB
% 0.36/0.48 % (3149612)Instructions burned: 25 (million)
% 0.36/0.48 % (3149611)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=4008040165: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)
% 0.36/0.48 % (3149614)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=1402563544:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.36/0.48 % (3149610)Instruction limit reached!
% 0.36/0.48 % (3149610)------------------------------
% 0.36/0.48 % (3149610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (3149610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (3149610)CaDiCaL version: 2.1.3
% 0.36/0.48 % (3149610)Termination reason: Instruction limit
% 0.36/0.48 % (3149610)Termination phase: Property scanning
% 0.36/0.48 % (3149610)Time elapsed: 0.003 s
% 0.36/0.48 % (3149610)Peak memory usage: 10 MB
% 0.36/0.48 % (3149610)Instructions burned: 3 (million)
% 0.36/0.48 % (3149609)Instruction limit reached!
% 0.36/0.48 % (3149609)------------------------------
% 0.36/0.48 % (3149609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (3149609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (3149609)CaDiCaL version: 2.1.3
% 0.36/0.48 % (3149609)Termination reason: Instruction limit
% 0.36/0.48 % (3149609)Termination phase: Saturation
% 0.36/0.48 % (3149609)Time elapsed: 0.016 s
% 0.36/0.48 % (3149609)Peak memory usage: 12 MB
% 0.36/0.48 % (3149609)Instructions burned: 18 (million)
% 0.36/0.48 % (3149622)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3676838530:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.36/0.48 % (3149622)Instruction limit reached!
% 0.36/0.48 % (3149622)------------------------------
% 0.36/0.48 % (3149622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (3149622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (3149622)CaDiCaL version: 2.1.3
% 0.36/0.48 % (3149622)Termination reason: Instruction limit
% 0.36/0.48 % (3149622)Termination phase: Property scanning
% 0.36/0.48 % (3149622)Time elapsed: 0.001 s
% 0.36/0.48 % (3149622)Peak memory usage: 10 MB
% 0.36/0.48 % (3149622)Instructions burned: 3 (million)
% 0.36/0.48 % (3149614) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3149603-3149614"...
% 0.36/0.48 % (3149623)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2994008359:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.36/0.48 % (3149614)...printing done.
% 0.36/0.48 % (3149626)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2452526895:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.36/0.48 % (3149614)Refutation found. Thanks to Tanya!
% 0.36/0.48 % SZS status Theorem for theBenchmark
% 0.36/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.49 % (3149614)------------------------------
% 0.36/0.49 % (3149614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.49 % (3149614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.49 % (3149614)CaDiCaL version: 2.1.3
% 0.36/0.49 % (3149614)Termination reason: Refutation
% 0.36/0.49 % (3149614)Time elapsed: 0.035 s
% 0.36/0.49 % (3149614)Peak memory usage: 13 MB
% 0.36/0.49 % (3149614)Instructions burned: 38 (million)
% 0.36/0.49 % (3149603)Success in time 0.1 s
% 0.36/0.49 % Vampire exiting
%------------------------------------------------------------------------------