%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO048^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:46:22 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 20
% Syntax : Number of formulae : 218 ( 52 unt; 0 typ; 11 def)
% Number of atoms : 2344 ( 414 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 3183 ( 707 ~; 738 |; 0 &;1580 @)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 302 ( 302 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 18 con; 0-4 aty)
% ( 148 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 538 ( 0 sgn 53 !; 1 ?; 538 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vOR: $o > $o > $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,
sK2: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_51,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_53,type,
sK6: $i > $o ).
thf(func_def_54,type,
sK7: $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ X1 @ X2 ) ) @ ( mand @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f46,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f50,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f54,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f55,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f64,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f65,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f75,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f77,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f78,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f79,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ X0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f46]) ).
thf(f88,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ sK0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f102,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f103,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f104,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f105,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f107,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mbox @ sK0 @ ( mand @ Y0 @ Y1 ) ) @ ( mand @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f108,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f113,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f115,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f123,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f108,f103,f115,f103,f103]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f102,f115,f103]) ).
thf(f126,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f105,f123,f124,f124]) ).
thf(f132,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 ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y1 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f107,f116,f104,f104,f126,f113,f123,f123,f113,f113]) ).
thf(f133,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 ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f134,plain,
sF1 != $true,
inference(definition_folding,[],[f132,f133]) ).
thf(f135,plain,
( ( $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 ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ sK0
@ Y1 ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f133]) ).
thf(f232,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f233,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y0 @ Y3 )
| ~ ( ~ ( Y1 @ Y3 )
| ~ ( Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ sK5 @ Y2 )
| ~ ( ~ ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ~ ( ~ ( sK6 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( sK6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( sK6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ~ ( ~ ( sK6 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ~ ( ~ ( sK6 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( sK6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( sK6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK5 @ Y1 )
| ~ ( ~ ( sK6 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( sF1 = $true )
| ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
( ( sF1 = $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) )
= $true )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) )
= $true )
| ( sF1 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( sF1 = $true )
| ( ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f242]) ).
thf(f245,plain,
( ( sF1 = $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f248,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $false )
| ( sF1 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f249,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) )
| ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f251,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ X2 )
= $true )
| ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X1 )
| ( sK6 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 )
| ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X2 )
| ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( sF1 = $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( $false
= ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK6 @ X2 ) )
= $false )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( ( sK6 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( ( sK6 @ X2 )
= $true )
| ( sF1 = $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( sF1 = $true )
| ( ( sK6 @ X2 )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( ( sK6 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( sK0 @ sK5 @ X2 )
= $false )
| ( sF1 = $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK6 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f267,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f268,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $true )
| ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK5 @ X1 )
| ( sK7 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 )
| ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X2 )
| ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( ( sK7 @ X1 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( ( sK7 @ X1 )
= $true )
| ( sF1 = $true )
| ( $true
= ( ~ ( sK0 @ sK5 @ X1 ) ) )
| ( ( ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( ( ~ ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( ( sK7 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( $false
= ( ~ ( sK6 @ X2 )
| ~ ( sK7 @ X2 ) ) )
| ( ( sK7 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK7 @ X2 ) )
= $false )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK7 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK7 @ X1 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ X2 ) )
= $true )
| ( ( sK7 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( ( sK0 @ sK5 @ X2 )
= $false )
| ( sF1 = $true )
| ( ( sK7 @ X2 )
= $true )
| ( ( sK7 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f328,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f357,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f328]) ).
thf(f358,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f359,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) ) )
= $true )
| ( sF1 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false ) ),
inference(or_proxy_clausification,[],[f358]) ).
thf(f360,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f359]) ).
thf(f361,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) ) )
= $false )
| ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
( ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) )
@ sK14 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f361]) ).
thf(f363,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK7 @ Y0 ) )
@ sK15 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ~ ( ~ ( sK6 @ Y0 )
| ~ ( sK7 @ Y0 ) ) )
@ sK13 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( sK0 @ sK5 @ Y0 )
| ( sK6 @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f362]) ).
thf(f364,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK15 )
| ( sK7 @ sK15 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
( ( ( sK7 @ sK15 )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f366,plain,
( ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK15 ) )
= $false )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f367,plain,
( ( ( sK6 @ sK14 )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK15 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f366]) ).
thf(f368,plain,
( ( ( ~ ( sK0 @ sK5 @ sK15 ) )
= $false )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f366]) ).
thf(f369,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f368]) ).
thf(f370,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false )
| ( ( ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(or_proxy_clausification,[],[f369]) ).
thf(f371,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK13 ) )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(or_proxy_clausification,[],[f369]) ).
thf(f372,plain,
( ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 ) )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f373,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( sK0 @ sK5 @ sK13 )
= $true )
| ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f372]) ).
thf(f374,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f370]) ).
thf(f375,plain,
( ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(not_proxy_clausification,[],[f374]) ).
thf(f376,plain,
( ( ( ~ ( sK6 @ sK13 ) )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(or_proxy_clausification,[],[f375]) ).
thf(f377,plain,
( ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( sF1 = $true )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( $false
= ( sK6 @ sK13 ) )
| ( ( sK0 @ sK5 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( ( sK7 @ sK13 )
= $false )
| ( $false
= ( sK6 @ sK13 ) )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f379,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 )
| ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(not_proxy_clausification,[],[f367]) ).
thf(f380,plain,
( ( ( sK6 @ sK14 )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f379]) ).
thf(f381,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 ) )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f379]) ).
thf(f382,plain,
( ( sF1 = $true )
| ( ( sK6 @ sK14 )
= $false )
| ( ( sK0 @ sK5 @ sK13 )
= $true )
| ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
inference(not_proxy_clausification,[],[f381]) ).
thf(f383,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) )
= $true )
| ( sF1 = $true )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(not_proxy_clausification,[],[f380]) ).
thf(f384,plain,
( ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK6 @ sK13 ) )
= $true )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f383]) ).
thf(f385,plain,
( ( ( sK6 @ sK14 )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( sF1 = $true )
| ( ( ~ ( sK6 @ sK13 ) )
= $true )
| ( ( sK7 @ sK13 )
= $false ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f386,plain,
( ( ( sK7 @ sK13 )
= $false )
| ( ( sK0 @ sK5 @ sK15 )
= $true )
| ( $false
= ( sK6 @ sK13 ) )
| ( sF1 = $true )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(not_proxy_clausification,[],[f385]) ).
thf(f387,plain,
( ( ( ~ ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( sK7 @ sK15 )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f365]) ).
thf(f388,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK13 ) )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( sK7 @ sK15 )
= $false ) ),
inference(or_proxy_clausification,[],[f365]) ).
thf(f389,plain,
( ( ( sK0 @ sK5 @ sK13 )
= $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( sK7 @ sK15 )
= $false )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f388]) ).
thf(f390,plain,
( ( ( sK7 @ sK15 )
= $false )
| ( ( sK0 @ sK5 @ sK13 )
= $true )
| ( sF1 = $true )
| ( ( sK6 @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f389]) ).
thf(f391,plain,
( ( sF1 = $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false )
| ( ( sK7 @ sK15 )
= $false )
| ( ( sK0 @ sK5 @ sK13 )
= $true ) ),
inference(or_proxy_clausification,[],[f389]) ).
thf(f392,plain,
( ( sF1 = $true )
| ( ( sK7 @ sK15 )
= $false )
| ( ( sK0 @ sK5 @ sK13 )
= $true )
| ( ( sK0 @ sK5 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f391]) ).
thf(f393,plain,
( ( ( ~ ( sK6 @ sK13 )
| ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK7 @ sK15 )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f387]) ).
thf(f394,plain,
( ( ( ~ ( sK6 @ sK13 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK7 @ sK15 )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f393]) ).
thf(f395,plain,
( ( ( ~ ( sK0 @ sK5 @ sK14 )
| ( sK6 @ sK14 ) )
= $false )
| ( ( sK7 @ sK15 )
= $false )
| ( $false
= ( sK6 @ sK13 ) )
| ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f394]) ).
thf(f396,plain,
( ( sF1 = $true )
| ( $false
= ( sK6 @ sK13 ) )
| ( ( sK6 @ sK14 )
= $false )
| ( ( sK7 @ sK15 )
= $false )
| ( ( ~ ( sK7 @ sK13 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f395]) ).
thf(f397,plain,
( ( $false
= ( sK6 @ sK13 ) )
| ( sF1 = $true )
| ( ( sK7 @ sK15 )
= $false )
| ( ( ~ ( sK0 @ sK5 @ sK14 ) )
= $false )
| ( ( ~ ( sK7 @ sK13 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f395]) ).
thf(f398,plain,
( ( ( ~ ( sK7 @ sK13 ) )
= $true )
| ( ( sK7 @ sK15 )
= $false )
| ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( $false
= ( sK6 @ sK13 ) )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f397]) ).
thf(f399,plain,
( ( ( sK0 @ sK5 @ sK14 )
= $true )
| ( sF1 = $true )
| ( $false
= ( sK6 @ sK13 ) )
| ( ( sK7 @ sK15 )
= $false )
| ( ( sK7 @ sK13 )
= $false ) ),
inference(not_proxy_clausification,[],[f398]) ).
thf(f400,plain,
( ( sF1 = $true )
| ( ( sK7 @ sK15 )
= $false )
| ( $false
= ( sK6 @ sK13 ) )
| ( ( sK6 @ sK14 )
= $false )
| ( ( sK7 @ sK13 )
= $false ) ),
inference(not_proxy_clausification,[],[f396]) ).
thf(f454,definition,
( spl16_14
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f458,definition,
( spl16_15
<=> ! [X2: $i] :
( ( ( sK0 @ sK5 @ X2 )
= $false )
| ( ( sK6 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f459,plain,
( ! [X2: $i] :
( ( ( sK0 @ sK5 @ X2 )
= $false )
| ( ( sK6 @ X2 )
= $true ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f460,plain,
( spl16_14
| spl16_15
| spl16_15 ),
inference(avatar_split_clause,[],[f263,f458,f458,f454]) ).
thf(f462,definition,
( spl16_16
<=> ! [X2: $i] :
( ( ( sK0 @ sK5 @ X2 )
= $false )
| ( ( sK7 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f463,plain,
( ! [X2: $i] :
( ( ( sK0 @ sK5 @ X2 )
= $false )
| ( ( sK7 @ X2 )
= $true ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f462]) ).
thf(f466,plain,
( spl16_14
| spl16_16
| spl16_16 ),
inference(avatar_split_clause,[],[f281,f462,f462,f454]) ).
thf(f524,definition,
( spl16_28
<=> ( ( sK0 @ sK5 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_28])],[avatar_definition]) ).
thf(f526,plain,
( ( ( sK0 @ sK5 @ sK15 )
= $true )
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f524]) ).
thf(f528,definition,
( spl16_29
<=> ( ( sK0 @ sK5 @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_29])],[avatar_definition]) ).
thf(f530,plain,
( ( ( sK0 @ sK5 @ sK13 )
= $true )
| ~ spl16_29 ),
inference(avatar_component_clause,[],[f528]) ).
thf(f532,definition,
( spl16_30
<=> ( ( sK0 @ sK5 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_30])],[avatar_definition]) ).
thf(f534,plain,
( ( ( sK0 @ sK5 @ sK14 )
= $true )
| ~ spl16_30 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f535,plain,
( spl16_14
| spl16_28
| spl16_29
| spl16_30 ),
inference(avatar_split_clause,[],[f373,f532,f528,f524,f454]) ).
thf(f537,definition,
( spl16_31
<=> ( $false
= ( sK6 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_31])],[avatar_definition]) ).
thf(f539,plain,
( ( $false
= ( sK6 @ sK13 ) )
| ~ spl16_31 ),
inference(avatar_component_clause,[],[f537]) ).
thf(f541,definition,
( spl16_32
<=> ( ( sK7 @ sK13 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_32])],[avatar_definition]) ).
thf(f543,plain,
( ( ( sK7 @ sK13 )
= $false )
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f541]) ).
thf(f544,plain,
( spl16_31
| spl16_14
| spl16_30
| spl16_32
| spl16_28 ),
inference(avatar_split_clause,[],[f378,f524,f541,f532,f454,f537]) ).
thf(f546,definition,
( spl16_33
<=> ( ( sK6 @ sK14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_33])],[avatar_definition]) ).
thf(f548,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl16_33 ),
inference(avatar_component_clause,[],[f546]) ).
thf(f549,plain,
( spl16_29
| spl16_14
| spl16_33
| spl16_28 ),
inference(avatar_split_clause,[],[f382,f524,f546,f454,f528]) ).
thf(f550,plain,
( spl16_33
| spl16_32
| spl16_14
| spl16_28
| spl16_31 ),
inference(avatar_split_clause,[],[f386,f537,f524,f454,f541,f546]) ).
thf(f552,definition,
( spl16_34
<=> ( ( sK7 @ sK15 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_34])],[avatar_definition]) ).
thf(f554,plain,
( ( ( sK7 @ sK15 )
= $false )
| ~ spl16_34 ),
inference(avatar_component_clause,[],[f552]) ).
thf(f555,plain,
( spl16_30
| spl16_34
| spl16_14
| spl16_29 ),
inference(avatar_split_clause,[],[f392,f528,f454,f552,f532]) ).
thf(f556,plain,
( spl16_33
| spl16_14
| spl16_29
| spl16_34 ),
inference(avatar_split_clause,[],[f390,f552,f528,f454,f546]) ).
thf(f557,plain,
( spl16_30
| spl16_14
| spl16_34
| spl16_32
| spl16_31 ),
inference(avatar_split_clause,[],[f399,f537,f541,f552,f454,f532]) ).
thf(f558,plain,
( spl16_32
| spl16_31
| spl16_34
| spl16_33
| spl16_14 ),
inference(avatar_split_clause,[],[f400,f454,f546,f552,f537,f541]) ).
thf(f559,plain,
~ spl16_14,
inference(avatar_split_clause,[],[f134,f454]) ).
thf(f574,plain,
( ( $true
= ( sK6 @ sK13 ) )
| ( $false = $true )
| ~ spl16_15
| ~ spl16_29 ),
inference(constrained_superposition,[],[f530,f459]) ).
thf(f576,plain,
( ( $true
= ( sK6 @ sK13 ) )
| ~ spl16_15
| ~ spl16_29 ),
inference(trivial_inequality_removal,[],[f574]) ).
thf(f581,plain,
( ( $false = $true )
| ~ spl16_15
| ~ spl16_29
| ~ spl16_31 ),
inference(forward_demodulation,[],[f576,f539]) ).
thf(f582,plain,
( $false
| ~ spl16_15
| ~ spl16_29
| ~ spl16_31 ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f583,plain,
( ~ spl16_15
| ~ spl16_29
| ~ spl16_31 ),
inference(avatar_contradiction_clause,[],[f582]) ).
thf(f590,plain,
( ( ( sK7 @ sK13 )
= $true )
| ( $false = $true )
| ~ spl16_16
| ~ spl16_29 ),
inference(constrained_superposition,[],[f530,f463]) ).
thf(f593,plain,
( ( ( sK7 @ sK13 )
= $true )
| ~ spl16_16
| ~ spl16_29 ),
inference(trivial_inequality_removal,[],[f590]) ).
thf(f597,plain,
( ( $false = $true )
| ~ spl16_16
| ~ spl16_29
| ~ spl16_32 ),
inference(forward_demodulation,[],[f593,f543]) ).
thf(f598,plain,
( $false
| ~ spl16_16
| ~ spl16_29
| ~ spl16_32 ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f599,plain,
( ~ spl16_16
| ~ spl16_29
| ~ spl16_32 ),
inference(avatar_contradiction_clause,[],[f598]) ).
thf(f604,plain,
( ( ( sK7 @ sK15 )
= $true )
| ( $false = $true )
| ~ spl16_16
| ~ spl16_28 ),
inference(constrained_superposition,[],[f526,f463]) ).
thf(f608,plain,
( ( ( sK7 @ sK15 )
= $true )
| ~ spl16_16
| ~ spl16_28 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f615,plain,
( ( ( sK6 @ sK14 )
= $true )
| ( $false = $true )
| ~ spl16_15
| ~ spl16_30 ),
inference(constrained_superposition,[],[f459,f534]) ).
thf(f617,plain,
( ( ( sK6 @ sK14 )
= $true )
| ~ spl16_15
| ~ spl16_30 ),
inference(trivial_inequality_removal,[],[f615]) ).
thf(f623,plain,
( ( $false = $true )
| ~ spl16_15
| ~ spl16_30
| ~ spl16_33 ),
inference(forward_demodulation,[],[f617,f548]) ).
thf(f624,plain,
( $false
| ~ spl16_15
| ~ spl16_30
| ~ spl16_33 ),
inference(trivial_inequality_removal,[],[f623]) ).
thf(f625,plain,
( ~ spl16_15
| ~ spl16_30
| ~ spl16_33 ),
inference(avatar_contradiction_clause,[],[f624]) ).
thf(f626,plain,
( ( $false = $true )
| ~ spl16_16
| ~ spl16_28
| ~ spl16_34 ),
inference(forward_demodulation,[],[f554,f608]) ).
thf(f627,plain,
( $false
| ~ spl16_16
| ~ spl16_28
| ~ spl16_34 ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f628,plain,
( ~ spl16_16
| ~ spl16_28
| ~ spl16_34 ),
inference(avatar_contradiction_clause,[],[f627]) ).
cnf(s13,plain,
( spl16_15
| spl16_14
| spl16_15 ),
inference(sat_conversion,[],[f460]) ).
cnf(s14,plain,
( spl16_14
| spl16_15 ),
inference(rat,[],[s13]) ).
cnf(s17,plain,
( spl16_16
| spl16_14
| spl16_16 ),
inference(sat_conversion,[],[f466]) ).
cnf(s18,plain,
( spl16_14
| spl16_16 ),
inference(rat,[],[s17]) ).
cnf(s31,plain,
( spl16_14
| spl16_28
| spl16_29
| spl16_30 ),
inference(sat_conversion,[],[f535]) ).
cnf(s32,plain,
( spl16_14
| spl16_28
| spl16_30
| spl16_31
| spl16_32 ),
inference(sat_conversion,[],[f544]) ).
cnf(s33,plain,
( spl16_14
| spl16_28
| spl16_29
| spl16_33 ),
inference(sat_conversion,[],[f549]) ).
cnf(s34,plain,
( spl16_14
| spl16_28
| spl16_31
| spl16_32
| spl16_33 ),
inference(sat_conversion,[],[f550]) ).
cnf(s35,plain,
( spl16_14
| spl16_29
| spl16_30
| spl16_34 ),
inference(sat_conversion,[],[f555]) ).
cnf(s36,plain,
( spl16_14
| spl16_29
| spl16_33
| spl16_34 ),
inference(sat_conversion,[],[f556]) ).
cnf(s37,plain,
( spl16_14
| spl16_30
| spl16_31
| spl16_32
| spl16_34 ),
inference(sat_conversion,[],[f557]) ).
cnf(s38,plain,
( spl16_14
| spl16_31
| spl16_32
| spl16_33
| spl16_34 ),
inference(sat_conversion,[],[f558]) ).
cnf(s39,plain,
~ spl16_14,
inference(sat_conversion,[],[f559]) ).
cnf(s41,plain,
( ~ spl16_15
| ~ spl16_29
| ~ spl16_31 ),
inference(sat_conversion,[],[f583]) ).
cnf(s43,plain,
( ~ spl16_16
| ~ spl16_29
| ~ spl16_32 ),
inference(sat_conversion,[],[f599]) ).
cnf(s45,plain,
( ~ spl16_15
| ~ spl16_30
| ~ spl16_33 ),
inference(sat_conversion,[],[f625]) ).
cnf(s46,plain,
( ~ spl16_16
| ~ spl16_28
| ~ spl16_34 ),
inference(sat_conversion,[],[f628]) ).
cnf(s47,plain,
( spl16_31
| spl16_32
| spl16_33
| spl16_34 ),
inference(rat,[],[s38,s39]) ).
cnf(s48,plain,
( spl16_30
| spl16_31
| spl16_32
| spl16_34 ),
inference(rat,[],[s37,s39]) ).
cnf(s49,plain,
( spl16_29
| spl16_33
| spl16_34 ),
inference(rat,[],[s36,s39]) ).
cnf(s50,plain,
( spl16_29
| spl16_30
| spl16_34 ),
inference(rat,[],[s35,s39]) ).
cnf(s51,plain,
( spl16_28
| spl16_31
| spl16_32
| spl16_33 ),
inference(rat,[],[s34,s39]) ).
cnf(s52,plain,
( spl16_28
| spl16_29
| spl16_33 ),
inference(rat,[],[s33,s39]) ).
cnf(s53,plain,
( spl16_28
| spl16_30
| spl16_31
| spl16_32 ),
inference(rat,[],[s32,s39]) ).
cnf(s54,plain,
( spl16_28
| spl16_29
| spl16_30 ),
inference(rat,[],[s31,s39]) ).
cnf(s67,plain,
spl16_16,
inference(rat,[],[s18,s39]) ).
cnf(s68,plain,
spl16_15,
inference(rat,[],[s14,s39]) ).
cnf(s69,plain,
( spl16_29
| spl16_28 ),
inference(rat,[],[s45,s54,s52,s68]) ).
cnf(s70,plain,
( spl16_31
| spl16_32
| spl16_28 ),
inference(rat,[],[s45,s53,s51,s68]) ).
cnf(s71,plain,
spl16_28,
inference(rat,[],[s70,s41,s43,s69,s68,s67]) ).
cnf(s72,plain,
~ spl16_34,
inference(rat,[],[s46,s67,s71]) ).
cnf(s73,plain,
spl16_33,
inference(rat,[],[s47,s41,s43,s49,s72,s68,s67]) ).
cnf(s74,plain,
~ spl16_30,
inference(rat,[],[s45,s68,s73]) ).
cnf(s75,plain,
spl16_29,
inference(rat,[],[s50,s72,s74]) ).
cnf(s76,plain,
~ spl16_32,
inference(rat,[],[s43,s67,s75]) ).
cnf(s77,plain,
~ spl16_31,
inference(rat,[],[s41,s68,s75]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s48,s74,s72,s76,s77]) ).
thf(f629,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO048^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:24:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.31 % (2323541)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (2323552)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (2323552)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
% 0.23/0.31 % (2323552)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=759541413:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (2323548)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1246201333:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (2323549)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=3693700597: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)
% 0.23/0.31 % (2323547)lrs+10_16_si=on:nwc=1.5:random_seed=451815907:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (2323546)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3594883069:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (2323552) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2323541-2323552"...
% 0.23/0.31 % (2323548)Instruction limit reached!
% 0.23/0.31 % (2323548)------------------------------
% 0.23/0.31 % (2323548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (2323548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (2323548)CaDiCaL version: 2.1.3
% 0.23/0.31 % (2323548)Termination reason: Instruction limit
% 0.23/0.31 % (2323548)Termination phase: Saturation
% 0.23/0.31 % (2323548)Time elapsed: 0.005 s
% 0.23/0.31 % (2323548)Peak memory usage: 11 MB
% 0.23/0.31 % (2323548)Instructions burned: 10 (million)
% 0.23/0.31 % (2323552)...printing done.
% 0.23/0.31 % (2323552)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (2323552)------------------------------
% 0.23/0.31 % (2323552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (2323552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (2323552)CaDiCaL version: 2.1.3
% 0.23/0.31 % (2323552)Termination reason: Refutation
% 0.23/0.31 % (2323552)Time elapsed: 0.012 s
% 0.23/0.31 % (2323552)Peak memory usage: 13 MB
% 0.23/0.31 % (2323552)Instructions burned: 43 (million)
% 0.23/0.31 % (2323541)Success in time 0.045 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------