%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:31 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 160 ( 67 unt; 0 typ; 6 def)
% Number of atoms : 1038 ( 203 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1507 ( 305 ~; 252 |; 12 &; 827 @)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 57 usr; 13 con; 0-4 aty)
% ( 82 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 336 ( 0 sgn 54 !; 3 ?; 336 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK2: $i > $o ).
thf(func_def_54,type,
sK7: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(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,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f24,axiom,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mfunctional) ).
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] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f38,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f39,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
~ ! [X0: $i > $i > $o] :
( ( mfunctional @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mequiv @ ( mdia @ X0 @ X1 ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f48,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mfunctional @ X0 )
= $true )
=> ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f50,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f57,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f67,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f72,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f76,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f77,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,plain,
( mfunctional
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X2 = X3 ) )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f79,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f82,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f85,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f86,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( mfunctional @ X0 )
= $true )
& ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ X0 @ Y0 ) @ ( mbox @ X0 @ Y0 ) ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f48]) ).
thf(f88,plain,
( ( ( mfunctional @ sK0 )
= $true )
& ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f90,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f92,plain,
( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f93,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mequiv @ ( mdia @ sK0 @ Y0 ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f94,plain,
( ( mfunctional @ sK0 )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f96,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f97,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f101,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f105,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f110,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f111,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f124,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,[],[f101,f112,f111,f112,f112]) ).
thf(f125,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,[],[f96,f111,f112]) ).
thf(f127,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,[],[f97,f124,f125,f125]) ).
thf(f132,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f90,f112,f110,f112]) ).
thf(f133,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f94,f92]) ).
thf(f134,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y1
@ Y2 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y2
@ Y1 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) )
@ Y1
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f93,f120,f105,f127,f132,f110]) ).
thf(f135,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( ( ^ [Y0: $i > $o] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( Y0 @ Y1 )
| ~ ( sK0 @ sK1 @ Y1 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $false
= ( ~ ( sK2 @ sK3 )
| ~ ( sK0 @ sK1 @ sK3 ) ) )
| ( ( ( sK2 @ X1 )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $false
= ( ~ ( sK0 @ sK1 @ sK3 ) ) )
| ( ( ( sK2 @ X1 )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( ( sK2 @ X1 )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( sK2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( ( sK2 @ X1 )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( sK0 @ sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( ( sK2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( ( sK2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f170,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f188,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f189,plain,
( ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK6 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
| ~ ( sK0 @ sK1 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( ( ~ ( sK2 @ X1 )
| ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( $false
= ( ( sK2 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( ~ ( sK2 @ X1 ) )
= $true )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true )
| ( $false
= ( ( sK2 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ( sK2 @ sK6 )
| ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $false
= ( ~ ( sK0 @ sK1 @ sK6 ) ) )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ sK6 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK2 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ~ ( sK0 @ sK1 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f200,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ X1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ ( sK7 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 @ ( sK7 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK7 @ X1 )
= Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK7 @ X1 )
= Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK7 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK7 @ X1 )
= Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X1 @ X2 )
=> ( ( sK7 @ X1 )
= X2 ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK7 @ X1 )
= X2 )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( ( sK7 @ X1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f208]) ).
thf(f211,definition,
( spl8_1
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f213,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f215,definition,
( spl8_2
<=> ! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $false
= ( sK0 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f216,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( ( sK2 @ X1 )
= $true ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f217,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f158,f215,f211]) ).
thf(f219,definition,
( spl8_3
<=> ( ( sK0 @ sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f221,plain,
( ( ( sK0 @ sK1 @ sK3 )
= $true )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f222,plain,
( spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f161,f219,f215]) ).
thf(f234,definition,
( spl8_6
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f235,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f247,definition,
( spl8_9
<=> ( $false
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f249,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f250,plain,
( spl8_9
| spl8_6 ),
inference(avatar_split_clause,[],[f196,f234,f247]) ).
thf(f252,definition,
( spl8_10
<=> ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f254,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f255,plain,
( spl8_10
| spl8_6 ),
inference(avatar_split_clause,[],[f198,f234,f252]) ).
thf(f256,plain,
( ( ( sK2 @ ( sK7 @ sK1 ) )
= $true )
| ( $false = $true )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f216,f205]) ).
thf(f258,plain,
( ( ( sK2 @ ( sK7 @ sK1 ) )
= $true )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f260,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK7 @ sK1 ) ) )
| ~ spl8_6 ),
inference(constrained_superposition,[],[f235,f205]) ).
thf(f261,plain,
( ( $false
= ( sK2 @ ( sK7 @ sK1 ) ) )
| ( $false = $true )
| ~ spl8_6 ),
inference(constrained_superposition,[],[f205,f235]) ).
thf(f263,plain,
( ( $false
= ( sK2 @ ( sK7 @ sK1 ) ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f267,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_6 ),
inference(forward_demodulation,[],[f263,f258]) ).
thf(f268,plain,
( $false
| ~ spl8_2
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f269,plain,
( ~ spl8_2
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[],[f268]) ).
thf(f280,plain,
( ( $false = $true )
| ( ( sK7 @ sK1 )
= sK6 )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f254,f209]) ).
thf(f283,plain,
( ( $false = $true )
| ( ( sK2 @ sK6 )
= $true )
| ~ spl8_2
| ~ spl8_10 ),
inference(constrained_superposition,[],[f216,f254]) ).
thf(f285,plain,
( ( ( sK7 @ sK1 )
= sK6 )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f287,plain,
( ( ( sK2 @ sK6 )
= $true )
| ~ spl8_2
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f293,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[],[f287,f249]) ).
thf(f294,plain,
( $false
| ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f295,plain,
( ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f294]) ).
thf(f302,plain,
( ( $false
= ( sK2 @ ( sK7 @ sK1 ) ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f308,plain,
( ( $false = $true )
| ( ( sK7 @ sK1 )
= sK3 )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f221,f209]) ).
thf(f309,plain,
( ( ( sK7 @ sK1 )
= sK3 )
| ( $false = $true )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f209,f221]) ).
thf(f310,plain,
( ( ( sK7 @ sK1 )
= sK3 )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f311,plain,
( ( ( sK7 @ sK1 )
= sK3 )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f322,plain,
( ( sK6 = sK3 )
| ~ spl8_3
| ~ spl8_10 ),
inference(forward_demodulation,[],[f311,f285]) ).
thf(f329,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl8_3
| ~ spl8_9
| ~ spl8_10 ),
inference(constrained_superposition,[],[f249,f322]) ).
thf(f330,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_3
| ~ spl8_9
| ~ spl8_10 ),
inference(forward_demodulation,[],[f329,f213]) ).
thf(f331,plain,
( $false
| ~ spl8_1
| ~ spl8_3
| ~ spl8_9
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f332,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_9
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f331]) ).
thf(f352,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl8_3
| ~ spl8_6 ),
inference(constrained_superposition,[],[f302,f310]) ).
thf(f353,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_3
| ~ spl8_6 ),
inference(forward_demodulation,[],[f352,f213]) ).
thf(f354,plain,
( $false
| ~ spl8_1
| ~ spl8_3
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f355,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[],[f354]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s2,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f222]) ).
cnf(s7,plain,
( spl8_6
| spl8_9 ),
inference(sat_conversion,[],[f250]) ).
cnf(s8,plain,
( spl8_6
| spl8_10 ),
inference(sat_conversion,[],[f255]) ).
cnf(s10,plain,
( ~ spl8_2
| ~ spl8_6 ),
inference(sat_conversion,[],[f269]) ).
cnf(s12,plain,
( ~ spl8_2
| ~ spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f295]) ).
cnf(s16,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f332]) ).
cnf(s21,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_6 ),
inference(sat_conversion,[],[f355]) ).
cnf(s22,plain,
~ spl8_2,
inference(rat,[],[s12,s7,s8,s10]) ).
cnf(s25,plain,
spl8_3,
inference(rat,[],[s2,s22]) ).
cnf(s26,plain,
spl8_1,
inference(rat,[],[s1,s22]) ).
cnf(s27,plain,
~ spl8_6,
inference(rat,[],[s21,s25,s26]) ).
cnf(s28,plain,
spl8_10,
inference(rat,[],[s8,s27]) ).
cnf(s29,plain,
spl8_9,
inference(rat,[],[s7,s27]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s16,s26,s25,s28,s29]) ).
thf(f356,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 09:44:46 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.26 % (4066932)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (4066939)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2486171476:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (4066946)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (4066946)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
% 0.20/0.26 % (4066939) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4066932-4066939"...
% 0.20/0.26 % (4066940)lrs+10_16_si=on:nwc=1.5:random_seed=4126380492:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.26 % (4066941)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3943604985:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.26 % (4066942)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=3969086631: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)
% 0.20/0.26 % (4066943)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1825651310:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.26 % (4066946)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=163919172:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.26 % (4066944)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=469612050:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.26 % (4066939)...printing done.
% 0.20/0.26 % (4066941)Instruction limit reached!
% 0.20/0.26 % (4066941)------------------------------
% 0.20/0.26 % (4066941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (4066941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (4066941)CaDiCaL version: 2.1.3
% 0.20/0.26 % (4066941)Termination reason: Instruction limit
% 0.20/0.26 % (4066941)Termination phase: Property scanning
% 0.20/0.26 % (4066941)Time elapsed: 0.002 s
% 0.20/0.26 % (4066941)Peak memory usage: 10 MB
% 0.20/0.26 % (4066941)Instructions burned: 3 (million)
% 0.20/0.26 % (4066939)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (4066939)------------------------------
% 0.20/0.26 % (4066939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (4066939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (4066939)CaDiCaL version: 2.1.3
% 0.20/0.26 % (4066939)Termination reason: Refutation
% 0.20/0.26 % (4066939)Time elapsed: 0.008 s
% 0.20/0.26 % (4066939)Peak memory usage: 13 MB
% 0.20/0.26 % (4066939)Instructions burned: 25 (million)
% 0.20/0.26 % (4066932)Success in time 0.025 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------