%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL621^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:14:28 AM UTC 2026
% Result : Theorem 0.31s 0.42s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 147 ( 52 unt; 0 typ; 8 def)
% Number of atoms : 1088 ( 226 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1558 ( 108 ~; 212 |; 55 &;1020 @)
% ( 7 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 244 ( 244 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 51 usr; 14 con; 0-4 aty)
% ( 60 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 423 ( 0 sgn 141 !; 8 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
sK0: $i > $o ).
thf(func_def_34,type,
sK1: $i > $o ).
thf(func_def_35,type,
sK2: $i > $i > $o ).
thf(func_def_36,type,
sF3: $o ).
thf(func_def_37,type,
sK4: $i > $i ).
thf(func_def_38,type,
sK5: $i > $i ).
thf(func_def_39,type,
sK6: $i > $i ).
thf(func_def_40,type,
sK7: $i > $i ).
thf(func_def_41,type,
sK8: $i > $i ).
thf(func_def_42,type,
sK9: $i > $i ).
thf(func_def_44,type,
sK11: $i > $i ).
thf(func_def_46,type,
sK13: ( $i > $i > $o ) > ( $i > $o ) > $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mand) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f9,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
! [X1: $i > $o,X0: $i > $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4) ).
thf(f17,conjecture,
! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f18,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f21,plain,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f22,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f26,plain,
! [X0: $i > $o,X1: $i > $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X1 @ X0 ) @ ( mbox @ X1 @ ( mbox @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f27,plain,
! [X0: $i > $o,X1: $i > $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X1 @ X0 ) @ ( mbox @ X1 @ ( mbox @ X1 @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f26]) ).
thf(f34,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f37,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f39,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f41,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
~ ! [X2: $i > $o,X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X0 @ ( mdia @ X0 @ X1 ) ) @ ( mbox @ X0 @ X2 ) ) @ ( mbox @ X0 @ ( mdia @ X0 @ ( mand @ X1 @ X2 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f48]) ).
thf(f50,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $i > $o] :
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mbox @ X2 @ ( mdia @ X2 @ X0 ) ) @ ( mbox @ X2 @ X1 ) ) @ ( mbox @ X2 @ ( mdia @ X2 @ ( mand @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f51,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mbox @ sK2 @ ( mdia @ sK2 @ sK0 ) ) @ ( mbox @ sK2 @ sK1 ) ) @ ( mbox @ sK2 @ ( mdia @ sK2 @ ( mand @ sK0 @ sK1 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f50]) ).
thf(f55,plain,
! [X0: $i > $o,X1: $i > $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X1 @ X0 ) @ ( mbox @ X1 @ ( mbox @ X1 @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f56,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f57,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mand @ ( mbox @ sK2 @ ( mdia @ sK2 @ sK0 ) ) @ ( mbox @ sK2 @ sK1 ) ) @ ( mbox @ sK2 @ ( mdia @ sK2 @ ( mand @ sK0 @ sK1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f58,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f61,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f64,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f71,plain,
( mimpl
= ( ^ [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,[],[f61,f66,f68]) ).
thf(f73,plain,
! [X0: $i > $o,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X1
@ X0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X1
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X1
@ X0 ) ) ) ) ),
inference(definition_unfolding,[],[f55,f59,f71,f64,f64,f64]) ).
thf(f74,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ sK0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK0
@ sK1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f57,f59,f71,f56,f64,f58,f64,f64,f58,f56]) ).
thf(f75,definition,
( sF3
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ sK0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK0
@ sK1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f76,plain,
sF3 != $true,
inference(definition_folding,[],[f74,f75]) ).
thf(f77,plain,
( ( sF3 = $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ sK0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ sK1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK0
@ sK1 ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f75]) ).
thf(f130,plain,
( ( sF3 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
& ( sK0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f131,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
& ( sK0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
& ( sK1 @ Y2 )
& ( sK0 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) ) )
= $false )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) ) )
| ( sF3 = $true ) ),
inference(or_proxy_clausification,[],[f132]) ).
thf(f134,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) )
= $false )
| ( sF3 = $true ) ),
inference(or_proxy_clausification,[],[f132]) ).
thf(f135,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) )
| ( sF3 = $true ) ),
inference(not_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( ( sF3 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( sF3 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f135]) ).
thf(f138,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( sF3 = $true ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( $true
= ( ( sK2 @ sK10 @ X1 )
=> ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( sF3 = $true )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK0 @ Y1 ) ) ) )
@ X1 ) )
| ( sF3 = $true ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f142,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( $true
= ( ( sK2 @ sK10 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= $true )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
& ( sK0 @ Y0 ) )
@ ( sK11 @ X1 ) )
= $true )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( $true
= ( ( sK2 @ X1 @ ( sK11 @ X1 ) )
& ( sK0 @ ( sK11 @ X1 ) ) ) )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK11 @ X1 ) )
= $true )
| ( sF3 = $true )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( sF3 = $true )
| ( $true
= ( sK2 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ sK10 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
& ( sK1 @ Y1 )
& ( sK0 @ Y1 ) ) ) )
@ sK12 ) )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f149,plain,
( ( sF3 = $true )
| ( $false
= ( ( sK2 @ sK10 @ sK12 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK12 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
( ( sF3 = $true )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK12 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $true )
| ( sF3 = $true ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ sK12 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( $false
= ( ( sK2 @ sK12 @ X1 )
& ( sK1 @ X1 )
& ( sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( sF3 = $true )
| ( ( ( sK1 @ X1 )
& ( sK0 @ X1 ) )
= $false )
| ( ( sK2 @ sK12 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( sK2 @ sK12 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( sF3 = $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X0: $i > $o,X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f157,plain,
! [X2: $i,X0: $i > $o,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X0: $i > $o,X1: $i > $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $true
= ( ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $false
= ( ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) )
=> ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) ) )
| ( $true
= ( ( X1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $true
= ( ( X1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $false
= ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $true
= ( ( X1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $false
= ( X1 @ X2 @ X3 ) )
| ( $true
= ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( X1 @ X2 @ X3 ) )
| ( $true
= ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( ( ( X1 @ X3 @ X4 )
=> ( X0 @ X4 ) )
= $true )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( $true
= ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $true
= ( X1 @ X2 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( $true
= ( X0 @ X4 ) )
| ( $false
= ( X1 @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o] :
( ( $false
= ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
=> ( X0 @ Y0 ) )
@ X4 ) )
| ( $false
= ( X1 @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( ( ( X1 @ X3 @ X4 )
=> ( X0 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( X0 @ ( sK13 @ X1 @ X0 @ X2 ) ) )
| ( $false
= ( X1 @ X2 @ X3 ) )
| ( $false
= ( X1 @ X3 @ X4 ) )
| ( $true
= ( X0 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f227,definition,
( spl14_14
<=> ! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f228,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f230,definition,
( spl14_15
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f233,plain,
( spl14_14
| spl14_15 ),
inference(avatar_split_clause,[],[f140,f230,f227]) ).
thf(f235,definition,
( spl14_16
<=> ! [X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( $true
= ( sK2 @ X1 @ ( sK11 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f236,plain,
( ! [X1: $i] :
( ( $true
= ( sK2 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( sK2 @ sK10 @ X1 )
= $false ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f237,plain,
( spl14_15
| spl14_16 ),
inference(avatar_split_clause,[],[f147,f235,f230]) ).
thf(f239,definition,
( spl14_17
<=> ! [X1: $i] :
( ( ( sK0 @ ( sK11 @ X1 ) )
= $true )
| ( ( sK2 @ sK10 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f240,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( ( sK0 @ ( sK11 @ X1 ) )
= $true ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f241,plain,
( spl14_15
| spl14_17 ),
inference(avatar_split_clause,[],[f146,f239,f230]) ).
thf(f243,definition,
( spl14_18
<=> ( ( sK2 @ sK10 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f245,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $true )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl14_18
| spl14_15 ),
inference(avatar_split_clause,[],[f151,f230,f243]) ).
thf(f248,definition,
( spl14_19
<=> ! [X1: $i] :
( ( ( sK2 @ sK12 @ X1 )
= $false )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
thf(f249,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK12 @ X1 )
= $false )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f250,plain,
( spl14_15
| spl14_19 ),
inference(avatar_split_clause,[],[f155,f248,f230]) ).
thf(f251,plain,
~ spl14_15,
inference(avatar_split_clause,[],[f76,f230]) ).
thf(f273,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ ( sK11 @ sK12 ) ) )
| ~ spl14_17
| ~ spl14_18 ),
inference(constrained_superposition,[],[f245,f240]) ).
thf(f275,plain,
( ( $true
= ( sK0 @ ( sK11 @ sK12 ) ) )
| ~ spl14_17
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f291,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $false )
| ( $true = $false )
| ( $false
= ( sK0 @ ( sK11 @ sK12 ) ) )
| ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ~ spl14_16
| ~ spl14_19 ),
inference(constrained_superposition,[],[f249,f236]) ).
thf(f295,plain,
( ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ( $false
= ( sK0 @ ( sK11 @ sK12 ) ) )
| ( ( sK2 @ sK10 @ sK12 )
= $false )
| ~ spl14_16
| ~ spl14_19 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f313,plain,
( ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ( ( sK2 @ sK10 @ sK12 )
= $false )
| ( $true = $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19 ),
inference(forward_demodulation,[],[f295,f275]) ).
thf(f314,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $false )
| ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f318,plain,
( ( $true = $false )
| ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19 ),
inference(forward_demodulation,[],[f314,f245]) ).
thf(f319,plain,
( ( ( sK1 @ ( sK11 @ sK12 ) )
= $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19 ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f331,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK2 @ sK10 @ X1 )
= $false )
| ( ( X0 @ X2 )
= $true )
| ( ( sK2 @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( ( sK1 @ ( sK13 @ sK2 @ X0 @ sK10 ) )
= $true ) )
| ~ spl14_14 ),
inference(constrained_superposition,[],[f228,f169]) ).
thf(f338,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK1 @ ( sK13 @ sK2 @ X0 @ sK10 ) )
= $true )
| ( ( sK2 @ X1 @ X2 )
= $false )
| ( ( X0 @ X2 )
= $true )
| ( ( sK2 @ sK10 @ X1 )
= $false ) )
| ~ spl14_14 ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f346,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X2 @ X3 )
= $false )
| ( ( sK2 @ sK10 @ X0 )
= $false )
| ( $false
= ( sK2 @ sK10 @ X2 ) )
| ( ( sK2 @ X0 @ X1 )
= $false )
| ( $true = $false ) )
| ~ spl14_14 ),
inference(constrained_superposition,[],[f338,f173]) ).
thf(f351,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK2 @ X0 @ X1 )
= $false )
| ( ( sK2 @ X2 @ X3 )
= $false )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK2 @ sK10 @ X0 )
= $false )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( sK2 @ sK10 @ X2 ) ) )
| ~ spl14_14 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f361,definition,
( spl14_25
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( sK2 @ sK10 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
thf(f362,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( sK2 @ sK10 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X2 @ X3 )
= $false ) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f361]) ).
thf(f364,plain,
( spl14_25
| spl14_25
| ~ spl14_14 ),
inference(avatar_split_clause,[],[f351,f227,f361,f361]) ).
thf(f419,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK2 @ sK12 @ X0 ) ) )
| ~ spl14_18
| ~ spl14_25 ),
inference(constrained_superposition,[],[f245,f362]) ).
thf(f426,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ sK12 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl14_18
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f439,plain,
( ( $true = $false )
| ( ( sK2 @ sK10 @ sK12 )
= $false )
| ( ( sK1 @ ( sK11 @ sK12 ) )
= $true )
| ~ spl14_16
| ~ spl14_18
| ~ spl14_25 ),
inference(constrained_superposition,[],[f426,f236]) ).
thf(f451,plain,
( ( ( sK1 @ ( sK11 @ sK12 ) )
= $true )
| ( ( sK2 @ sK10 @ sK12 )
= $false )
| ~ spl14_16
| ~ spl14_18
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f439]) ).
thf(f460,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $false )
| ( $true = $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(forward_demodulation,[],[f451,f319]) ).
thf(f461,plain,
( ( ( sK2 @ sK10 @ sK12 )
= $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f465,plain,
( ( $true = $false )
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(forward_demodulation,[],[f461,f245]) ).
thf(f466,plain,
( $false
| ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f465]) ).
thf(f467,plain,
( ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(avatar_contradiction_clause,[],[f466]) ).
cnf(s13,plain,
( spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f233]) ).
cnf(s14,plain,
( spl14_15
| spl14_16 ),
inference(sat_conversion,[],[f237]) ).
cnf(s15,plain,
( spl14_15
| spl14_17 ),
inference(sat_conversion,[],[f241]) ).
cnf(s16,plain,
( spl14_15
| spl14_18 ),
inference(sat_conversion,[],[f246]) ).
cnf(s17,plain,
( spl14_15
| spl14_19 ),
inference(sat_conversion,[],[f250]) ).
cnf(s18,plain,
~ spl14_15,
inference(sat_conversion,[],[f251]) ).
cnf(s27,plain,
( spl14_25
| ~ spl14_14
| spl14_25 ),
inference(sat_conversion,[],[f364]) ).
cnf(s28,plain,
( ~ spl14_14
| spl14_25 ),
inference(rat,[],[s27]) ).
cnf(s42,plain,
( ~ spl14_16
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_25 ),
inference(sat_conversion,[],[f467]) ).
cnf(s44,plain,
spl14_19,
inference(rat,[],[s17,s18]) ).
cnf(s45,plain,
spl14_18,
inference(rat,[],[s16,s18]) ).
cnf(s46,plain,
spl14_17,
inference(rat,[],[s15,s18]) ).
cnf(s47,plain,
spl14_16,
inference(rat,[],[s14,s18]) ).
cnf(s48,plain,
~ spl14_25,
inference(rat,[],[s42,s46,s44,s45,s47]) ).
cnf(s49,plain,
~ spl14_14,
inference(rat,[],[s28,s48]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s13,s18,s49]) ).
thf(f468,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL621^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n010.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 09:27:03 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.33 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
% 0.31/0.42 % (2614861)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.42 % (2614867)lrs+10_16_si=on:nwc=1.5:random_seed=3156479174:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.42 % (2614867)Instruction limit reached!
% 0.31/0.42 % (2614867)------------------------------
% 0.31/0.42 % (2614867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614867)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614867)Termination reason: Instruction limit
% 0.31/0.42 % (2614867)Termination phase: Saturation
% 0.31/0.42 % (2614867)Time elapsed: 0.009 s
% 0.31/0.42 % (2614867)Peak memory usage: 12 MB
% 0.31/0.42 % (2614867)Instructions burned: 19 (million)
% 0.31/0.42 % (2614872)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.42 % (2614872)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
% 0.31/0.42 % (2614870)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2735117661:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.42 % (2614869)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=1267905787: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)
% 0.31/0.42 % (2614871)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=232360588:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.42 % (2614866)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2182063599:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.42 % (2614868)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2713871279:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.42 % (2614872)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=701848915:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.42 % (2614868)Instruction limit reached!
% 0.31/0.42 % (2614868)------------------------------
% 0.31/0.42 % (2614868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614868)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614868)Termination reason: Instruction limit
% 0.31/0.42 % (2614868)Termination phase: Property scanning
% 0.31/0.42 % (2614868)Time elapsed: 0.003 s
% 0.31/0.42 % (2614868)Peak memory usage: 11 MB
% 0.31/0.42 % (2614868)Instructions burned: 3 (million)
% 0.31/0.42 % (2614870)Instruction limit reached!
% 0.31/0.42 % (2614870)------------------------------
% 0.31/0.42 % (2614870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614870)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614870)Termination reason: Instruction limit
% 0.31/0.42 % (2614870)Termination phase: Saturation
% 0.31/0.42 % (2614870)Time elapsed: 0.025 s
% 0.31/0.42 % (2614870)Peak memory usage: 12 MB
% 0.31/0.42 % (2614870)Instructions burned: 24 (million)
% 0.31/0.42 % (2614872) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2614861-2614872"...
% 0.31/0.42 % (2614881)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2086676384:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.31/0.42 % (2614874)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1961664199:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.31/0.42 % (2614881)Instruction limit reached!
% 0.31/0.42 % (2614881)------------------------------
% 0.31/0.42 % (2614881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614881)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614881)Termination reason: Instruction limit
% 0.31/0.42 % (2614881)Termination phase: Saturation
% 0.31/0.42 % (2614881)Time elapsed: 0.003 s
% 0.31/0.42 % (2614881)Peak memory usage: 11 MB
% 0.31/0.42 % (2614881)Instructions burned: 6 (million)
% 0.31/0.42 % (2614874)Instruction limit reached!
% 0.31/0.42 % (2614874)------------------------------
% 0.31/0.42 % (2614874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614874)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614874)Termination reason: Instruction limit
% 0.31/0.42 % (2614874)Termination phase: Property scanning
% 0.31/0.42 % (2614874)Time elapsed: 0.003 s
% 0.31/0.42 % (2614874)Peak memory usage: 10 MB
% 0.31/0.42 % (2614874)Instructions burned: 2 (million)
% 0.31/0.42 % (2614872)...printing done.
% 0.31/0.42 % (2614872)Refutation found. Thanks to Tanya!
% 0.31/0.42 % SZS status Theorem for theBenchmark
% 0.31/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.42 % (2614872)------------------------------
% 0.31/0.42 % (2614872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.42 % (2614872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.42 % (2614872)CaDiCaL version: 2.1.3
% 0.31/0.42 % (2614872)Termination reason: Refutation
% 0.31/0.42 % (2614872)Time elapsed: 0.032 s
% 0.31/0.42 % (2614872)Peak memory usage: 13 MB
% 0.31/0.42 % (2614872)Instructions burned: 33 (million)
% 0.31/0.42 % (2614861)Success in time 0.077 s
% 0.31/0.42 % Vampire exiting
%------------------------------------------------------------------------------