%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:14:40 AM UTC 2026
% Result : Theorem 0.33s 0.47s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 32
% Syntax : Number of formulae : 231 ( 50 unt; 0 typ; 25 def)
% Number of atoms : 1719 ( 371 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2330 ( 377 ~; 449 |; 14 &;1350 @)
% ( 24 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 330 ( 330 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 80 usr; 32 con; 0-4 aty)
% ( 109 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 596 ( 0 sgn 194 !; 14 ?; 596 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
db2:
!>[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,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vNOT: $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,
sK1: $i > $i > $o ).
thf(func_def_52,type,
sF5: $o ).
thf(func_def_53,type,
sF6: $o ).
thf(func_def_54,type,
sF7: $o ).
thf(func_def_55,type,
sF8: $o ).
thf(func_def_56,type,
sF9: $i > $i > $o ).
thf(func_def_57,type,
sF10: $i > $i > $o ).
thf(func_def_59,type,
sK12: $i > $o ).
thf(func_def_62,type,
sK15: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
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,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( X0 @ X3 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( X0 @ X3 @ X5 )
& ( X1 @ X3 @ X4 ) )
=> ( X0 @ X4 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f35,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f36,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f37,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f46,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f47,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ X2 ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( X0 @ X5 @ X4 )
& ( X1 @ X5 @ X3 ) )
=> ( X0 @ X3 @ X4 ) ) ),
inference(rectify,[],[f33]) ).
thf(f49,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( X0 @ X5 @ X4 )
= $true )
& ( ( X1 @ X5 @ X3 )
= $true ) )
=> ( ( X0 @ X3 @ X4 )
= $true ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f69,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f74,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f81,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f82,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<=> ! [X3: $i,X4: $i,X2: $i] :
( ( ( ( X0 @ X4 @ X3 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) )
=> ( ( X0 @ X2 @ X3 )
= $true ) ) ),
inference(rectify,[],[f49]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
<~> ! [X3: $i,X4: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X0 @ X4 @ X3 )
!= $true )
| ( ( X1 @ X4 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X0 @ X4 @ X3 )
!= $true )
| ( ( X1 @ X4 @ X2 )
!= $true ) )
<~> ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
| ? [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X3 )
!= $true )
& ( ( X0 @ X4 @ X3 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) ) )
& ( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
| ! [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X0 @ X4 @ X3 )
!= $true )
| ( ( X1 @ X4 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
thf(f91,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
| ? [X2: $i,X3: $i,X4: $i] :
( ( ( X0 @ X2 @ X3 )
!= $true )
& ( ( X0 @ X4 @ X3 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) ) )
& ( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X1 @ ( mnot @ ( mbox @ X0 @ Y0 ) ) ) ) ) ) )
| ! [X5: $i,X6: $i,X7: $i] :
( ( ( X0 @ X5 @ X6 )
= $true )
| ( ( X0 @ X7 @ X6 )
!= $true )
| ( $true
!= ( X1 @ X7 @ X5 ) ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f92,plain,
( ( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ( ( ( sK0 @ sK2 @ sK3 )
!= $true )
& ( $true
= ( sK0 @ sK4 @ sK3 ) )
& ( ( sK1 @ sK4 @ sK2 )
= $true ) ) )
& ( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ! [X5: $i,X6: $i,X7: $i] :
( ( ( sK0 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X7 @ X6 ) )
| ( ( sK1 @ X7 @ X5 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f91]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f101,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f114,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f116,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ( ( sK0 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X7 @ X6 ) )
| ( ( sK1 @ X7 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f117,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ( ( sK1 @ sK4 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f118,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( sK0 @ sK4 @ sK3 ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f119,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK1 @ ( mnot @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f122,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f123,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f126,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f131,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,[],[f98,f101,f123]) ).
thf(f139,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
!= $true )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(definition_unfolding,[],[f119,f122,f126,f131,f123,f114,f114,f123,f114]) ).
thf(f140,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
!= $true )
| ( $true
= ( sK0 @ sK4 @ sK3 ) ) ),
inference(definition_unfolding,[],[f118,f122,f126,f131,f123,f114,f114,f123,f114]) ).
thf(f141,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
!= $true )
| ( ( sK1 @ sK4 @ sK2 )
= $true ) ),
inference(definition_unfolding,[],[f117,f122,f126,f131,f123,f114,f114,f123,f114]) ).
thf(f142,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( ^ [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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
= $true )
| ( ( sK0 @ X5 @ X6 )
= $true )
| ( $true
!= ( sK0 @ X7 @ X6 ) )
| ( ( sK1 @ X7 @ X5 )
!= $true ) ),
inference(definition_unfolding,[],[f116,f122,f126,f131,f123,f114,f114,f123,f114]) ).
thf(f143,definition,
( sF5
= ( ^ [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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f144,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
= sF5 ),
inference(reorient_equations,[],[f143]) ).
thf(f145,definition,
( sF6
= ( sK0 @ sK2 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f146,plain,
( ( sK0 @ sK2 @ sK3 )
= sF6 ),
inference(reorient_equations,[],[f145]) ).
thf(f147,plain,
( ( $true != sF5 )
| ( $true != sF6 ) ),
inference(definition_folding,[],[f139,f146,f144]) ).
thf(f148,definition,
( sF7
= ( sK0 @ sK4 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f149,plain,
( ( sF7 = $true )
| ( $true != sF5 ) ),
inference(definition_folding,[],[f140,f148,f144]) ).
thf(f150,definition,
( sF8
= ( sK1 @ sK4 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f151,plain,
( ( sK1 @ sK4 @ sK2 )
= sF8 ),
inference(reorient_equations,[],[f150]) ).
thf(f152,plain,
( ( $true != sF5 )
| ( sF8 = $true ) ),
inference(definition_folding,[],[f141,f151,f144]) ).
thf(f153,definition,
! [X6: $i,X5: $i] :
( ( sF9 @ X6 @ X5 )
= ( sK0 @ X5 @ X6 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f154,plain,
! [X6: $i,X5: $i] :
( ( sK0 @ X5 @ X6 )
= ( sF9 @ X6 @ X5 ) ),
inference(reorient_equations,[],[f153]) ).
thf(f155,definition,
! [X7: $i,X5: $i] :
( ( sF10 @ X5 @ X7 )
= ( sK1 @ X7 @ X5 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f156,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( sF10 @ X5 @ X7 )
!= $true )
| ( ( sF9 @ X6 @ X7 )
!= $true )
| ( ( sF9 @ X6 @ X5 )
= $true )
| ( $true = sF5 ) ),
inference(definition_folding,[],[f142,f155,f154,f154,f144]) ).
thf(f157,plain,
( ( $false = sF8 )
| ( ( sK1 @ sK4 @ sK2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f159,plain,
! [X6: $i,X5: $i] :
( ( $false
= ( sF9 @ X6 @ X5 ) )
| ( ( sK0 @ X5 @ X6 )
= $true ) ),
inference(iff_proxy_clausification,[],[f154]) ).
thf(f160,plain,
! [X6: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X6 ) )
| ( ( sF9 @ X6 @ X5 )
= $true ) ),
inference(iff_proxy_clausification,[],[f154]) ).
thf(f162,plain,
( ( $true
= ( sK0 @ sK4 @ sK3 ) )
| ( $false = sF7 ) ),
inference(iff_proxy_clausification,[],[f148]) ).
thf(f164,plain,
( ( $false
= ( sK0 @ sK2 @ sK3 ) )
| ( $true = sF6 ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f165,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) )
= $true )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f144]) ).
thf(f166,plain,
( ( $true = sF5 )
| ( $false
= ( ^ [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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK1
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f144]) ).
thf(f167,plain,
( ( $true = sF5 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( ( $true = sF5 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true = sF5 )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK11 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK11 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ sK11 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK11 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK12 ) )
| ( $true = sF5 ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK11 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK12 @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK11 @ Y0 )
| ( sK12 @ Y0 ) ) ) ) )
| ( $true = sF5 ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( ( $true = sF5 )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK11 @ Y0 )
| ( sK12 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true = sF5 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ sK11 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK12 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true = sF5 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK1 @ sK11 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK12 @ Y1 ) ) ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( ~ ( sK1 @ sK11 @ sK13 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK12 @ Y0 ) ) ) ) )
| ( $true = sF5 ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK12 @ Y0 ) ) ) ) )
| ( $true = sF5 ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ( sK1 @ sK11 @ sK13 ) ) )
| ( $true = sF5 ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $true
= ( sK1 @ sK11 @ sK13 ) )
| ( $true = sF5 ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK12 @ Y0 ) ) ) )
| ( $true = sF5 ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK13 @ Y0 )
| ( sK12 @ Y0 ) )
@ X1 ) )
| ( $true = sF5 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ sK13 @ X1 )
| ( sK12 @ X1 ) ) )
| ( $true = sF5 ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true = sF5 )
| ( ( sK12 @ X1 )
= $true )
| ( ( ~ ( sK0 @ sK13 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK13 @ X1 ) )
| ( $true = sF5 )
| ( ( sK12 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK11 @ Y0 )
| ( sK12 @ Y0 ) ) ) )
= $true )
| ( $true = sF5 ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f185,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK11 @ Y0 )
| ( sK12 @ Y0 ) ) ) )
| ( $true = sF5 ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true = sF5 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK11 @ Y0 )
| ( sK12 @ Y0 ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ~ ( sK0 @ sK11 @ sK14 )
| ( sK12 @ sK14 ) ) )
| ( $true = sF5 ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( sK12 @ sK14 ) )
| ( $true = sF5 ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $true = sF5 )
| ( $false
= ( ~ ( sK0 @ sK11 @ sK14 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( ( sK0 @ sK11 @ sK14 )
= $true )
| ( $true = sF5 ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) )
= $true )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK1 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ X1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i > $o,X1: $i] :
( ( $false = sF5 )
| ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK1 @ X1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) ) )
= $true )
| ( $false = sF5 )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $false )
| ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF5 )
| ( ( ~ ( sK0 @ X1 @ X4 )
| ( X2 @ X4 ) )
= $true )
| ( ( ~ ( sK1 @ X1 @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF5 )
| ( ( X2 @ X4 )
= $true )
| ( ( ~ ( sK1 @ X1 @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( sK1 @ X1 @ X3 ) ) )
| ( $false = sF5 )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false = sF5 )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF5 )
| ( ( ~ ( sK0 @ X1 @ X4 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false = sF5 )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false = sF5 )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X3 @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK15 @ X3 @ X2 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK1 @ X1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ~ ( sK0 @ X3 @ ( sK15 @ X3 @ X2 ) )
| ( X2 @ ( sK15 @ X3 @ X2 ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false = sF5 )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( X2 @ ( sK15 @ X3 @ X2 ) ) )
| ( $false = sF5 ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( ~ ( sK0 @ X3 @ ( sK15 @ X3 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false = sF5 )
| ( ( X2 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f211,plain,
! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK15 @ X3 @ X2 ) ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false = sF5 )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X7: $i,X5: $i] :
( ( $false
= ( sK1 @ X7 @ X5 ) )
| ( ( sF10 @ X5 @ X7 )
= $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f215,definition,
( spl16_1
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f217,plain,
( ( sF8 = $true )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f224,definition,
( spl16_3
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f226,plain,
( ( $false = sF8 )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f228,definition,
( spl16_4
<=> ( ( sK1 @ sK4 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f230,plain,
( ( ( sK1 @ sK4 @ sK2 )
= $true )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f157,f228,f224]) ).
thf(f233,definition,
( spl16_5
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f234,plain,
( ( $true = sF5 )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,plain,
( spl16_1
| ~ spl16_5 ),
inference(avatar_split_clause,[],[f152,f233,f215]) ).
thf(f238,definition,
( spl16_6
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f241,plain,
( ~ spl16_5
| ~ spl16_6 ),
inference(avatar_split_clause,[],[f147,f238,f233]) ).
thf(f243,definition,
( spl16_7
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( ( sF10 @ X5 @ X7 )
!= $true )
| ( ( sF9 @ X6 @ X5 )
= $true )
| ( ( sF9 @ X6 @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f244,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( ( sF9 @ X6 @ X5 )
= $true )
| ( ( sF9 @ X6 @ X7 )
!= $true )
| ( ( sF10 @ X5 @ X7 )
!= $true ) )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f245,plain,
( spl16_7
| spl16_5 ),
inference(avatar_split_clause,[],[f156,f233,f243]) ).
thf(f247,definition,
( spl16_8
<=> ( $true
= ( sK0 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f249,plain,
( ( $true
= ( sK0 @ sK4 @ sK3 ) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f251,definition,
( spl16_9
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f253,plain,
( ( $false = sF7 )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl16_8
| spl16_9 ),
inference(avatar_split_clause,[],[f162,f251,f247]) ).
thf(f256,definition,
( spl16_10
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f258,plain,
( ( sF7 = $true )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f265,definition,
( spl16_12
<=> ( $false
= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f267,plain,
( ( $false
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl16_6
| spl16_12 ),
inference(avatar_split_clause,[],[f164,f265,f238]) ).
thf(f278,plain,
( ~ spl16_5
| spl16_10 ),
inference(avatar_split_clause,[],[f149,f256,f233]) ).
thf(f280,definition,
( spl16_15
<=> ( $true
= ( sK1 @ sK11 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f282,plain,
( ( $true
= ( sK1 @ sK11 @ sK13 ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f283,plain,
( spl16_5
| spl16_15 ),
inference(avatar_split_clause,[],[f178,f280,f233]) ).
thf(f285,definition,
( spl16_16
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK13 @ X1 ) )
| ( ( sK12 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f286,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK13 @ X1 ) )
| ( ( sK12 @ X1 )
= $true ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f287,plain,
( spl16_16
| spl16_5 ),
inference(avatar_split_clause,[],[f183,f233,f285]) ).
thf(f289,definition,
( spl16_17
<=> ( ( sK0 @ sK11 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f291,plain,
( ( ( sK0 @ sK11 @ sK14 )
= $true )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f292,plain,
( spl16_5
| spl16_17 ),
inference(avatar_split_clause,[],[f190,f289,f233]) ).
thf(f294,definition,
( spl16_18
<=> ( $false
= ( sK12 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_18])],[avatar_definition]) ).
thf(f296,plain,
( ( $false
= ( sK12 @ sK14 ) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f297,plain,
( spl16_18
| spl16_5 ),
inference(avatar_split_clause,[],[f188,f233,f294]) ).
thf(f299,definition,
( spl16_19
<=> ! [X4: $i,X3: $i,X2: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK15 @ X3 @ X2 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK1 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
thf(f300,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK15 @ X3 @ X2 ) ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f302,definition,
( spl16_20
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl16_20])],[avatar_definition]) ).
thf(f304,plain,
( ( $false = sF5 )
| ~ spl16_20 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl16_19
| spl16_20 ),
inference(avatar_split_clause,[],[f211,f302,f299]) ).
thf(f307,definition,
( spl16_21
<=> ! [X2: $i > $o,X4: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( X2 @ ( sK15 @ X3 @ X2 ) ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( ( X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition]) ).
thf(f308,plain,
( ! [X2: $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK15 @ X3 @ X2 ) ) )
| ( $false
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f309,plain,
( spl16_21
| spl16_20 ),
inference(avatar_split_clause,[],[f209,f302,f307]) ).
thf(f332,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false = $true )
| ( ( sF10 @ X1 @ X2 )
!= $true )
| ( $true
!= ( sF9 @ X0 @ X2 ) ) )
| ~ spl16_7 ),
inference(constrained_superposition,[],[f244,f159]) ).
thf(f334,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $true
!= ( sF9 @ X0 @ X2 ) )
| ( ( sF10 @ X1 @ X2 )
!= $true ) )
| ~ spl16_7 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f353,plain,
( ( $false = $true )
| ( $true
= ( sF9 @ sK14 @ sK11 ) )
| ~ spl16_17 ),
inference(constrained_superposition,[],[f291,f160]) ).
thf(f356,plain,
( ( $true
= ( sF9 @ sK14 @ sK11 ) )
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f392,plain,
( ( $false = $true )
| ( ( sF10 @ sK13 @ sK11 )
= $true )
| ~ spl16_15 ),
inference(constrained_superposition,[],[f282,f212]) ).
thf(f393,plain,
( ( ( sF10 @ sK13 @ sK11 )
= $true )
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f392]) ).
thf(f483,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_3 ),
inference(forward_demodulation,[],[f217,f226]) ).
thf(f484,plain,
( $false
| ~ spl16_1
| ~ spl16_3 ),
inference(trivial_inequality_removal,[],[f483]) ).
thf(f485,plain,
( ~ spl16_1
| ~ spl16_3 ),
inference(avatar_contradiction_clause,[],[f484]) ).
thf(f486,plain,
( ( $false = $true )
| ~ spl16_5
| ~ spl16_20 ),
inference(forward_demodulation,[],[f234,f304]) ).
thf(f487,plain,
( $false
| ~ spl16_5
| ~ spl16_20 ),
inference(trivial_inequality_removal,[],[f486]) ).
thf(f488,plain,
( ~ spl16_5
| ~ spl16_20 ),
inference(avatar_contradiction_clause,[],[f487]) ).
thf(f521,plain,
( ( $false = $true )
| ~ spl16_9
| ~ spl16_10 ),
inference(forward_demodulation,[],[f253,f258]) ).
thf(f522,plain,
( $false
| ~ spl16_9
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f523,plain,
( ~ spl16_9
| ~ spl16_10 ),
inference(avatar_contradiction_clause,[],[f522]) ).
thf(f575,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( sF10 @ sK13 @ X1 )
!= $true )
| ( ( sK12 @ X0 )
= $true )
| ( $true
!= ( sF9 @ X0 @ X1 ) ) )
| ~ spl16_7
| ~ spl16_16 ),
inference(constrained_superposition,[],[f334,f286]) ).
thf(f576,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( sF9 @ X0 @ X1 ) )
| ( ( sK12 @ X0 )
= $true )
| ( ( sF10 @ sK13 @ X1 )
!= $true ) )
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f575]) ).
thf(f582,plain,
( ( $true != $true )
| ( ( sK12 @ sK14 )
= $true )
| ( ( sF10 @ sK13 @ sK11 )
!= $true )
| ~ spl16_7
| ~ spl16_16
| ~ spl16_17 ),
inference(constrained_superposition,[],[f576,f356]) ).
thf(f586,plain,
( ( ( sK12 @ sK14 )
= $true )
| ( ( sF10 @ sK13 @ sK11 )
!= $true )
| ~ spl16_7
| ~ spl16_16
| ~ spl16_17 ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f587,plain,
( ( ( sK12 @ sK14 )
= $true )
| ~ spl16_7
| ~ spl16_15
| ~ spl16_16
| ~ spl16_17 ),
inference(forward_subsumption_resolution,[],[f586,f393]) ).
thf(f588,plain,
( ( $false = $true )
| ~ spl16_7
| ~ spl16_15
| ~ spl16_16
| ~ spl16_17
| ~ spl16_18 ),
inference(forward_demodulation,[],[f587,f296]) ).
thf(f589,plain,
( $false
| ~ spl16_7
| ~ spl16_15
| ~ spl16_16
| ~ spl16_17
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f588]) ).
thf(f590,plain,
( ~ spl16_7
| ~ spl16_15
| ~ spl16_16
| ~ spl16_17
| ~ spl16_18 ),
inference(avatar_contradiction_clause,[],[f589]) ).
thf(f616,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X0 ) )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( $true
= ( sK0 @ X0 @ X4 ) )
| ( $false
= ( sK1 @ X3 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false = $true ) )
| ~ spl16_19
| ~ spl16_21 ),
inference(constrained_superposition,[],[f308,f300]) ).
thf(f622,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X0 @ X4 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X1 @ X0 ) )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( $false
= ( sK1 @ X3 @ X0 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) ) )
| ~ spl16_19
| ~ spl16_21 ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f714,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK1 @ X2 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) )
| ~ spl16_12
| ~ spl16_19
| ~ spl16_21 ),
inference(constrained_superposition,[],[f622,f267]) ).
thf(f735,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ sK2 ) )
| ( $false
= ( sK1 @ X2 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 @ X1 ) ) )
| ~ spl16_12
| ~ spl16_19
| ~ spl16_21 ),
inference(trivial_inequality_removal,[],[f714]) ).
thf(f745,definition,
( spl16_33
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_33])],[avatar_definition]) ).
thf(f746,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK1 @ X0 @ sK2 ) ) )
| ~ spl16_33 ),
inference(avatar_component_clause,[],[f745]) ).
thf(f748,definition,
( spl16_34
<=> ! [X2: $i] :
( ( $false
= ( sK0 @ X2 @ sK3 ) )
| ( $false
= ( sK1 @ X2 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_34])],[avatar_definition]) ).
thf(f749,plain,
( ! [X2: $i] :
( ( $false
= ( sK1 @ X2 @ sK2 ) )
| ( $false
= ( sK0 @ X2 @ sK3 ) ) )
| ~ spl16_34 ),
inference(avatar_component_clause,[],[f748]) ).
thf(f759,plain,
( spl16_33
| spl16_34
| ~ spl16_12
| ~ spl16_19
| ~ spl16_21 ),
inference(avatar_split_clause,[],[f735,f307,f299,f265,f748,f745]) ).
thf(f761,plain,
( ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ( $false = $true )
| ~ spl16_4
| ~ spl16_34 ),
inference(constrained_superposition,[],[f749,f230]) ).
thf(f768,plain,
( ( $false
= ( sK0 @ sK4 @ sK3 ) )
| ~ spl16_4
| ~ spl16_34 ),
inference(trivial_inequality_removal,[],[f761]) ).
thf(f775,plain,
( ( $false = $true )
| ~ spl16_4
| ~ spl16_8
| ~ spl16_34 ),
inference(forward_demodulation,[],[f768,f249]) ).
thf(f776,plain,
( $false
| ~ spl16_4
| ~ spl16_8
| ~ spl16_34 ),
inference(trivial_inequality_removal,[],[f775]) ).
thf(f777,plain,
( ~ spl16_4
| ~ spl16_8
| ~ spl16_34 ),
inference(avatar_contradiction_clause,[],[f776]) ).
thf(f786,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl16_12
| ~ spl16_33 ),
inference(constrained_superposition,[],[f267,f746]) ).
thf(f790,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl16_12
| ~ spl16_33 ),
inference(trivial_inequality_removal,[],[f786]) ).
thf(f805,plain,
( spl16_34
| ~ spl16_12
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f790,f745,f265,f748]) ).
cnf(s2,plain,
( spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( spl16_1
| ~ spl16_5 ),
inference(sat_conversion,[],[f236]) ).
cnf(s4,plain,
( ~ spl16_5
| ~ spl16_6 ),
inference(sat_conversion,[],[f241]) ).
cnf(s5,plain,
( spl16_5
| spl16_7 ),
inference(sat_conversion,[],[f245]) ).
cnf(s6,plain,
( spl16_8
| spl16_9 ),
inference(sat_conversion,[],[f254]) ).
cnf(s8,plain,
( spl16_6
| spl16_12 ),
inference(sat_conversion,[],[f268]) ).
cnf(s10,plain,
( ~ spl16_5
| spl16_10 ),
inference(sat_conversion,[],[f278]) ).
cnf(s11,plain,
( spl16_5
| spl16_15 ),
inference(sat_conversion,[],[f283]) ).
cnf(s12,plain,
( spl16_5
| spl16_16 ),
inference(sat_conversion,[],[f287]) ).
cnf(s13,plain,
( spl16_5
| spl16_17 ),
inference(sat_conversion,[],[f292]) ).
cnf(s14,plain,
( spl16_5
| spl16_18 ),
inference(sat_conversion,[],[f297]) ).
cnf(s15,plain,
( spl16_19
| spl16_20 ),
inference(sat_conversion,[],[f305]) ).
cnf(s16,plain,
( spl16_20
| spl16_21 ),
inference(sat_conversion,[],[f309]) ).
cnf(s31,plain,
( ~ spl16_1
| ~ spl16_3 ),
inference(sat_conversion,[],[f485]) ).
cnf(s32,plain,
( ~ spl16_5
| ~ spl16_20 ),
inference(sat_conversion,[],[f488]) ).
cnf(s37,plain,
( ~ spl16_9
| ~ spl16_10 ),
inference(sat_conversion,[],[f523]) ).
cnf(s40,plain,
( ~ spl16_7
| ~ spl16_15
| ~ spl16_16
| ~ spl16_17
| ~ spl16_18 ),
inference(sat_conversion,[],[f590]) ).
cnf(s59,plain,
( ~ spl16_12
| ~ spl16_19
| ~ spl16_21
| spl16_33
| spl16_34 ),
inference(sat_conversion,[],[f759]) ).
cnf(s63,plain,
( ~ spl16_4
| ~ spl16_8
| ~ spl16_34 ),
inference(sat_conversion,[],[f777]) ).
cnf(s65,plain,
( ~ spl16_12
| ~ spl16_33
| spl16_34 ),
inference(sat_conversion,[],[f805]) ).
cnf(s68,plain,
spl16_5,
inference(rat,[],[s40,s5,s11,s12,s13,s14]) ).
cnf(s69,plain,
~ spl16_20,
inference(rat,[],[s32,s68]) ).
cnf(s70,plain,
spl16_10,
inference(rat,[],[s10,s68]) ).
cnf(s71,plain,
~ spl16_6,
inference(rat,[],[s4,s68]) ).
cnf(s72,plain,
spl16_1,
inference(rat,[],[s3,s68]) ).
cnf(s73,plain,
spl16_21,
inference(rat,[],[s16,s69]) ).
cnf(s74,plain,
spl16_19,
inference(rat,[],[s15,s69]) ).
cnf(s75,plain,
~ spl16_9,
inference(rat,[],[s37,s70]) ).
cnf(s77,plain,
spl16_12,
inference(rat,[],[s8,s71]) ).
cnf(s78,plain,
~ spl16_3,
inference(rat,[],[s31,s72]) ).
cnf(s79,plain,
spl16_8,
inference(rat,[],[s6,s75]) ).
cnf(s80,plain,
spl16_4,
inference(rat,[],[s2,s78]) ).
cnf(s83,plain,
~ spl16_34,
inference(rat,[],[s63,s79,s80]) ).
cnf(s85,plain,
~ spl16_33,
inference(rat,[],[s65,s77,s83]) ).
cnf(s86,plain,
$false,
inference(rat,[],[s59,s77,s74,s73,s83,s85]) ).
thf(f807,plain,
$false,
inference(avatar_sat_refutation,[],[s86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n020.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 10:25:35 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.34 Running higher-order theorem proving
% 0.27/0.36 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
% 0.33/0.47 % (882316)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.47 % (882325)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3277414319:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.47 % (882327)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.47 % (882327)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
% 0.33/0.47 % (882321)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=289419424:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.47 % (882322)lrs+10_16_si=on:nwc=1.5:random_seed=3587659484:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.47 % (882325)Instruction limit reached!
% 0.33/0.47 % (882325)------------------------------
% 0.33/0.47 % (882325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882325)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882325)Termination reason: Instruction limit
% 0.33/0.47 % (882325)Termination phase: Saturation
% 0.33/0.47 % (882325)Time elapsed: 0.012 s
% 0.33/0.47 % (882325)Peak memory usage: 12 MB
% 0.33/0.47 % (882325)Instructions burned: 26 (million)
% 0.33/0.47 % (882324)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=636441645: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)
% 0.33/0.47 % (882323)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=838729215:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.47 % (882327)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=200057715:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.47 % (882323)Instruction limit reached!
% 0.33/0.47 % (882323)------------------------------
% 0.33/0.47 % (882323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882323)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882323)Termination reason: Instruction limit
% 0.33/0.47 % (882323)Termination phase: Property scanning
% 0.33/0.47 % (882323)Time elapsed: 0.003 s
% 0.33/0.47 % (882323)Peak memory usage: 10 MB
% 0.33/0.47 % (882323)Instructions burned: 4 (million)
% 0.33/0.47 % (882326)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2664815134:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.47 % (882322)Instruction limit reached!
% 0.33/0.47 % (882322)------------------------------
% 0.33/0.47 % (882322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882322)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882322)Termination reason: Instruction limit
% 0.33/0.47 % (882322)Termination phase: Saturation
% 0.33/0.47 % (882322)Time elapsed: 0.014 s
% 0.33/0.47 % (882322)Peak memory usage: 12 MB
% 0.33/0.47 % (882322)Instructions burned: 19 (million)
% 0.33/0.47 % (882334)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=436128783:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.47 % (882336)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3101494882:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.33/0.47 % (882337)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.33/0.47 % (882327) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-882316-882327"...
% 0.33/0.47 % (882336)Instruction limit reached!
% 0.33/0.47 % (882336)------------------------------
% 0.33/0.47 % (882336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882336)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882336)Termination reason: Instruction limit
% 0.33/0.47 % (882336)Termination phase: Property scanning
% 0.33/0.47 % (882336)Time elapsed: 0.005 s
% 0.33/0.47 % (882336)Peak memory usage: 10 MB
% 0.33/0.47 % (882336)Instructions burned: 6 (million)
% 0.33/0.47 % (882334)Instruction limit reached!
% 0.33/0.47 % (882334)------------------------------
% 0.33/0.47 % (882334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882334)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882334)Termination reason: Instruction limit
% 0.33/0.47 % (882334)Termination phase: Property scanning
% 0.33/0.47 % (882334)Time elapsed: 0.006 s
% 0.33/0.47 % (882334)Peak memory usage: 10 MB
% 0.33/0.47 % (882334)Instructions burned: 3 (million)
% 0.33/0.47 % (882337)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1093807219:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.33/0.47 % (882327)...printing done.
% 0.33/0.47 % (882337)Instruction limit reached!
% 0.33/0.47 % (882337)------------------------------
% 0.33/0.47 % (882337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (882337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (882337)CaDiCaL version: 2.1.3
% 0.33/0.47 % (882337)Termination reason: Instruction limit
% 0.33/0.47 % (882337)Termination phase: Saturation
% 0.33/0.47 % (882337)Time elapsed: 0.007 s
% 0.33/0.47 % (882337)Peak memory usage: 11 MB
% 0.33/0.47 % (882337)Instructions burned: 8 (million)
% 0.33/0.47 % (882327)Refutation found. Thanks to Tanya!
% 0.33/0.47 % SZS status Theorem for theBenchmark
% 0.33/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.48 % (882327)------------------------------
% 0.33/0.48 % (882327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.48 % (882327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.48 % (882327)CaDiCaL version: 2.1.3
% 0.33/0.48 % (882327)Termination reason: Refutation
% 0.33/0.48 % (882327)Time elapsed: 0.051 s
% 0.33/0.48 % (882327)Peak memory usage: 13 MB
% 0.33/0.48 % (882327)Instructions burned: 60 (million)
% 0.33/0.48 % (882316)Success in time 0.098 s
% 0.33/0.48 % Vampire exiting
%------------------------------------------------------------------------------