%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO049^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:46:23 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 19
% Syntax : Number of formulae : 206 ( 59 unt; 0 typ; 9 def)
% Number of atoms : 1994 ( 317 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 2820 ( 649 ~; 598 |; 0 &;1427 @)
% ( 9 <=>; 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 : 214 ( 214 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 16 con; 0-4 aty)
% ( 137 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 418 ( 0 sgn 56 !; 1 ?; 418 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK2: $i > $o ).
thf(func_def_50,type,
sK3: $i > $o ).
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] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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 @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f38,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f39,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f41,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f48,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f49,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f51,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f62,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f63,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f67,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f75,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f76,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f77,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,plain,
~ ! [X0: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] :
( mforall_prop
@ ^ [X2: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ X1 @ X2 ) ) @ ( mor @ ( mdia @ X0 @ X1 ) @ ( mdia @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f79,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ X0 @ Y0 ) @ ( mdia @ X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mdia @ X0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ X0 @ Y0 ) @ ( mdia @ X0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f79]) ).
thf(f88,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mdia @ sK0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f99,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mequiv @ ( mdia @ sK0 @ ( mor @ Y0 @ Y1 ) ) @ ( mor @ ( mdia @ sK0 @ Y0 ) @ ( mdia @ sK0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f100,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f102,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f103,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f112,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f114,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f116,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f117,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
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,[],[f116,f117,f119,f117,f117]) ).
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,[],[f112,f119,f117]) ).
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,[],[f102,f123,f124,f124]) ).
thf(f131,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f100,f117,f103,f117]) ).
thf(f132,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $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 > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) )
@ Y2
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ sK0
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f99,f97,f114,f114,f126,f131,f119,f119,f131,f131]) ).
thf(f133,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) )
| ~ ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( sK0 @ sK1 @ Y2 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( sK2 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( sK2 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( sK2 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK2 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( sK2 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK4 ) )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( ~ ( sK2 @ sK4 )
| ~ ( sK0 @ sK1 @ sK4 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK4 ) ) )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( sK2 @ sK4 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( sK2 @ sK4 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( ( ~ ( sK2 @ sK4 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK2 @ sK4 )
= $true )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( sK2 @ sK4 )
= $true )
| ( ( ~ ( sK3 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
= $true )
| ( ( ~ ( sK3 @ sK6 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ( sK3 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( ~ ( sK3 @ sK6 ) )
= $false )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ( sK3 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK2 @ sK4 )
= $true )
| ( ( sK3 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
= $true )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f169,plain,
( ( ( sK3 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( sK3 @ sK5 )
= $true )
| ( ( sK2 @ sK4 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( sK2 @ sK4 ) )
= $false )
| ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f172,plain,
( ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK0 @ sK1 @ sK5 )
= $true )
| ( ( ~ ( sK2 @ sK4 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( ~ ( sK3 @ sK6 ) )
= $false )
| ( ( sK0 @ sK1 @ sK5 )
= $true )
| ( ( ~ ( sK2 @ sK4 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( ( ~ ( sK2 @ sK4 ) )
= $false )
| ( ( sK3 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( sK3 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK5 )
= $true )
| ( ( ~ ( sK2 @ sK4 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f177,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( sK2 @ sK4 )
= $true )
| ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( sK3 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f179,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( sK3 @ sK6 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
| ~ ( sK0 @ sK1 @ sK5 ) )
= $false )
| ( ( sK3 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) )
| ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( sK3 @ sK6 )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ( sK3 @ sK6 )
= $true )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
= $true )
| ( ( sK3 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( ( sK3 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK3 @ sK5 )
= $true ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( ( sK3 @ sK6 )
= $true )
| ( ( sK0 @ sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f187,plain,
( ( $false
= ( ~ ( sK0 @ sK1 @ sK5 ) ) )
| ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f188,plain,
( ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f189,plain,
( ( ( ~ ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( ( sK2 @ sK5 )
| ( sK3 @ sK5 ) )
= $true )
| ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( sK3 @ sK5 )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( ~ ( sK0 @ sK1 @ sK6 ) )
= $false )
| ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f193,plain,
( ( ( sK0 @ sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK1 @ sK4 )
= $true )
| ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f258,plain,
( ( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f259,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f284,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f285,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f286,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK2 @ X2 )
| ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( ~ ( sK2 @ X2 ) )
= $true )
| ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( ~ ( sK2 @ X2 ) )
= $true )
| ( ( sK0 @ sK1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK2 @ X2 ) )
= $true )
| ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) )
= $true )
| ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) )
= $true )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X2 )
= $false )
| ( ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
= $false )
| ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f292]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( sK2 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( sK2 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f293]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f298,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( sK2 @ Y0 )
| ( sK3 @ Y0 ) )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( sK3 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( ~ ( sK3 @ X2 )
| ~ ( sK0 @ sK1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( sK2 @ X1 )
| ( sK3 @ X1 ) ) )
= $true )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( ~ ( sK3 @ X2 )
| ~ ( sK0 @ sK1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( ~ ( sK3 @ X2 )
| ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( sK3 @ X2 )
| ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK2 @ X1 )
| ( sK3 @ X1 ) )
= $false )
| ( ( ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( ~ ( sK3 @ X2 ) )
= $true )
| ( ( sK0 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( ~ ( sK3 @ X2 ) )
= $true )
| ( ( ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f309,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $false )
| ( ( ~ ( sK0 @ sK1 @ X2 ) )
= $true )
| ( ( sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f310,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK1 @ X2 )
= $false )
| ( ( sK3 @ X2 )
= $false )
| ( ( sK3 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f312,definition,
( spl12_1
<=> ( ( sK3 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f314,plain,
( ( ( sK3 @ sK5 )
= $true )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f316,definition,
( spl12_2
<=> ( ( sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f318,plain,
( ( ( sK2 @ sK4 )
= $true )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f320,definition,
( spl12_3
<=> ( ( sK3 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f322,plain,
( ( ( sK3 @ sK6 )
= $true )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f324,definition,
( spl12_4
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f326,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f167,f324,f320,f316,f312]) ).
thf(f329,definition,
( spl12_5
<=> ( ( sK0 @ sK1 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f331,plain,
( ( ( sK0 @ sK1 @ sK6 )
= $true )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f332,plain,
( spl12_2
| spl12_5
| spl12_4
| spl12_1 ),
inference(avatar_split_clause,[],[f170,f312,f324,f329,f316]) ).
thf(f334,definition,
( spl12_6
<=> ( ( sK0 @ sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f336,plain,
( ( ( sK0 @ sK1 @ sK5 )
= $true )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f337,plain,
( spl12_6
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f175,f320,f316,f334]) ).
thf(f338,plain,
( spl12_6
| spl12_5
| spl12_2 ),
inference(avatar_split_clause,[],[f177,f316,f329,f334]) ).
thf(f340,definition,
( spl12_7
<=> ( ( sK0 @ sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f342,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $true )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f340]) ).
thf(f343,plain,
( spl12_3
| spl12_7
| spl12_4
| spl12_1 ),
inference(avatar_split_clause,[],[f185,f312,f324,f340,f320]) ).
thf(f344,plain,
( spl12_3
| spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f186,f340,f334,f320]) ).
thf(f345,plain,
( spl12_1
| spl12_4
| spl12_5
| spl12_7 ),
inference(avatar_split_clause,[],[f191,f340,f329,f324,f312]) ).
thf(f346,plain,
( spl12_7
| spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f193,f334,f329,f340]) ).
thf(f352,definition,
( spl12_9
<=> ! [X1: $i] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f353,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f379,definition,
( spl12_15
<=> ! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f380,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f409,plain,
( spl12_9
| spl12_9 ),
inference(avatar_split_clause,[],[f296,f352,f352]) ).
thf(f412,plain,
( spl12_15
| spl12_15 ),
inference(avatar_split_clause,[],[f310,f379,f379]) ).
thf(f418,plain,
( ( ( sK3 @ sK6 )
= $false )
| ( $false = $true )
| ~ spl12_5
| ~ spl12_15 ),
inference(constrained_superposition,[],[f331,f380]) ).
thf(f420,plain,
( ( ( sK3 @ sK6 )
= $false )
| ~ spl12_5
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f424,plain,
( ( $false = $true )
| ~ spl12_3
| ~ spl12_5
| ~ spl12_15 ),
inference(forward_demodulation,[],[f420,f322]) ).
thf(f425,plain,
( $false
| ~ spl12_3
| ~ spl12_5
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f426,plain,
( ~ spl12_3
| ~ spl12_5
| ~ spl12_15 ),
inference(avatar_contradiction_clause,[],[f425]) ).
thf(f428,plain,
( ( $false = $true )
| ( ( sK3 @ sK5 )
= $false )
| ~ spl12_6
| ~ spl12_15 ),
inference(constrained_superposition,[],[f336,f380]) ).
thf(f429,plain,
( ( ( sK2 @ sK5 )
= $false )
| ( $false = $true )
| ~ spl12_6
| ~ spl12_9 ),
inference(constrained_superposition,[],[f336,f353]) ).
thf(f432,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl12_6
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f435,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl12_6
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f439,plain,
( ( $false = $true )
| ~ spl12_1
| ~ spl12_6
| ~ spl12_15 ),
inference(forward_demodulation,[],[f435,f314]) ).
thf(f440,plain,
( $false
| ~ spl12_1
| ~ spl12_6
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f439]) ).
thf(f441,plain,
( ~ spl12_1
| ~ spl12_6
| ~ spl12_15 ),
inference(avatar_contradiction_clause,[],[f440]) ).
thf(f442,plain,
( ( $false = $true )
| ~ spl12_4
| ~ spl12_6
| ~ spl12_9 ),
inference(forward_demodulation,[],[f326,f432]) ).
thf(f443,plain,
( $false
| ~ spl12_4
| ~ spl12_6
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f444,plain,
( ~ spl12_4
| ~ spl12_6
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f443]) ).
thf(f452,plain,
( ( $false = $true )
| ( ( sK2 @ sK4 )
= $false )
| ~ spl12_7
| ~ spl12_9 ),
inference(constrained_superposition,[],[f353,f342]) ).
thf(f455,plain,
( ( ( sK2 @ sK4 )
= $false )
| ~ spl12_7
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f460,plain,
( ( $false = $true )
| ~ spl12_2
| ~ spl12_7
| ~ spl12_9 ),
inference(forward_demodulation,[],[f455,f318]) ).
thf(f461,plain,
( $false
| ~ spl12_2
| ~ spl12_7
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f462,plain,
( ~ spl12_2
| ~ spl12_7
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f461]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f327]) ).
cnf(s2,plain,
( spl12_1
| spl12_2
| spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f332]) ).
cnf(s3,plain,
( spl12_2
| spl12_3
| spl12_6 ),
inference(sat_conversion,[],[f337]) ).
cnf(s4,plain,
( spl12_2
| spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f338]) ).
cnf(s5,plain,
( spl12_1
| spl12_3
| spl12_4
| spl12_7 ),
inference(sat_conversion,[],[f343]) ).
cnf(s6,plain,
( spl12_3
| spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f344]) ).
cnf(s7,plain,
( spl12_1
| spl12_4
| spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f345]) ).
cnf(s8,plain,
( spl12_5
| spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f346]) ).
cnf(s21,plain,
( spl12_9
| spl12_9 ),
inference(sat_conversion,[],[f409]) ).
cnf(s22,plain,
spl12_9,
inference(rat,[],[s21]) ).
cnf(s25,plain,
( spl12_15
| spl12_15 ),
inference(sat_conversion,[],[f412]) ).
cnf(s26,plain,
spl12_15,
inference(rat,[],[s25]) ).
cnf(s28,plain,
( ~ spl12_3
| ~ spl12_5
| ~ spl12_15 ),
inference(sat_conversion,[],[f426]) ).
cnf(s30,plain,
( ~ spl12_1
| ~ spl12_6
| ~ spl12_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s31,plain,
( ~ spl12_4
| ~ spl12_6
| ~ spl12_9 ),
inference(sat_conversion,[],[f444]) ).
cnf(s33,plain,
( ~ spl12_2
| ~ spl12_7
| ~ spl12_9 ),
inference(sat_conversion,[],[f462]) ).
cnf(s34,plain,
( spl12_3
| spl12_2
| spl12_1 ),
inference(rat,[],[s31,s1,s3,s22]) ).
cnf(s35,plain,
( spl12_2
| spl12_1 ),
inference(rat,[],[s31,s2,s4,s28,s34,s26,s22]) ).
cnf(s36,plain,
( spl12_3
| spl12_1 ),
inference(rat,[],[s31,s5,s6,s33,s35,s22]) ).
cnf(s37,plain,
( spl12_5
| spl12_7
| spl12_1 ),
inference(rat,[],[s31,s8,s7,s22]) ).
cnf(s38,plain,
spl12_1,
inference(rat,[],[s37,s28,s36,s33,s35,s26,s22]) ).
cnf(s39,plain,
~ spl12_6,
inference(rat,[],[s30,s26,s38]) ).
cnf(s40,plain,
spl12_3,
inference(rat,[],[s33,s6,s3,s22,s39]) ).
cnf(s41,plain,
~ spl12_5,
inference(rat,[],[s28,s26,s40]) ).
cnf(s42,plain,
spl12_2,
inference(rat,[],[s4,s39,s41]) ).
cnf(s43,plain,
spl12_7,
inference(rat,[],[s8,s39,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s33,s22,s43,s42]) ).
thf(f463,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO049^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:26:29 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (2701848)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (2701861)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=389486453:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (2701867)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (2701867)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
% 0.21/0.30 % (2701861) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2701848-2701861"...
% 0.21/0.30 % (2701862)lrs+10_16_si=on:nwc=1.5:random_seed=98825290:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (2701865)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3160974730:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (2701863)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2766147733:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (2701866)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=84334257:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (2701867)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=2157257648:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (2701864)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=1871492490: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)
% 0.21/0.30 % (2701861)...printing done.
% 0.21/0.30 % (2701863)Instruction limit reached!
% 0.21/0.30 % (2701863)------------------------------
% 0.21/0.30 % (2701863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2701863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2701863)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2701863)Termination reason: Instruction limit
% 0.21/0.30 % (2701863)Termination phase: Preprocessing 3
% 0.21/0.30 % (2701863)Time elapsed: 0.002 s
% 0.21/0.30 % (2701863)Peak memory usage: 10 MB
% 0.21/0.30 % (2701863)Instructions burned: 4 (million)
% 0.21/0.30 % (2701861)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (2701861)------------------------------
% 0.21/0.30 % (2701861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2701861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2701861)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2701861)Termination reason: Refutation
% 0.21/0.30 % (2701861)Time elapsed: 0.009 s
% 0.21/0.30 % (2701861)Peak memory usage: 13 MB
% 0.21/0.30 % (2701861)Instructions burned: 34 (million)
% 0.21/0.30 % (2701848)Success in time 0.048 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------