%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL619^1 : 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 : n017.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 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 17
% Syntax : Number of formulae : 150 ( 46 unt; 0 typ; 10 def)
% Number of atoms : 1131 ( 252 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1528 ( 126 ~; 259 |; 0 &; 978 @)
% ( 9 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 237 ( 237 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 49 usr; 16 con; 0-4 aty)
% ( 71 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 422 ( 0 sgn 165 !; 6 ?; 422 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vIMP: $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 > $o ) > ( $i > $i > $o ) > $i > $i ).
thf(func_def_38,type,
sK5: $i > $i ).
thf(func_def_39,type,
sK6: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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(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(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
! [X0: $i > $i > $o,X1: $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,X2: $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ ( mimpl @ X1 @ X2 ) ) @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f18,negated_conjecture,
~ ! [X0: $i > $i > $o,X2: $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ ( mimpl @ X1 @ X2 ) ) @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f22,plain,
! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f23,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f27,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ ( mimpl @ X2 @ X1 ) ) @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f31,plain,
~ ! [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ X0 @ ( mimpl @ X2 @ X1 ) ) @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f33,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f38,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f44,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f45,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f49,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ X0 @ ( mimpl @ X2 @ X1 ) ) @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f50,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $i > $o] :
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ X2 @ ( mimpl @ X1 @ X0 ) ) @ ( mimpl @ ( mbox @ X2 @ X1 ) @ ( mbox @ X2 @ ( mbox @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f51,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK2 @ ( mimpl @ sK1 @ sK0 ) ) @ ( mimpl @ ( mbox @ sK2 @ sK1 ) @ ( mbox @ sK2 @ ( mbox @ sK2 @ sK0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f50]) ).
thf(f52,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f53,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f58,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f60,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK2 @ ( mimpl @ sK1 @ sK0 ) ) @ ( mimpl @ ( mbox @ sK2 @ sK1 ) @ ( mbox @ sK2 @ ( mbox @ sK2 @ sK0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f61,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f67,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
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,[],[f67,f58,f52]) ).
thf(f73,plain,
! [X0: $i > $i > $o,X1: $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 ) ) )
@ X0
@ X1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ X0
@ X1 ) ) ) ) ),
inference(definition_unfolding,[],[f53,f61,f71,f56,f56,f56]) ).
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 > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [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 )
@ sK1
@ sK0 ) )
@ ( ^ [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 ) ) )
@ 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
@ sK0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f60,f61,f71,f56,f71,f71,f56,f56,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 > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK2
@ ( ^ [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 )
@ sK1
@ sK0 ) )
@ ( ^ [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 ) ) )
@ 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
@ sK0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f76,plain,
$true != sF3,
inference(definition_folding,[],[f74,f75]) ).
thf(f77,plain,
! [X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f78,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK4 @ X1 @ X0 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( X0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
=> ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
= $false )
| ( $true
= ( ( X0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( ( X0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
= $true )
| ( $true
= ( ( X0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
= $true )
| ( ( X0 @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
= $true )
| ( ( X0 @ X2 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
= $true )
| ( ( ( X0 @ X3 @ X4 )
=> ( X1 @ X4 ) )
= $true )
| ( ( X0 @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ ( sK4 @ X1 @ X0 @ X2 ) )
= $true )
| ( ( X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ X3 @ X4 )
= $false )
| ( ( X1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( X0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( ( X0 @ X2 @ X3 )
= $false )
| ( ( ( X0 @ X3 @ X4 )
=> ( X1 @ X4 ) )
= $true )
| ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $o,X4: $i] :
( ( $false
= ( X1 @ ( sK4 @ X1 @ X0 @ X2 ) ) )
| ( ( X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ X2 @ X3 )
= $false )
| ( ( X1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [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 ) ) )
@ sK2
@ ( ^ [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 )
@ sK1
@ sK0 ) )
@ ( ^ [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 ) ) )
@ 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
@ sK0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f75]) ).
thf(f144,plain,
( ( $true = sF3 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ~ ( sK1 @ Y1 )
| ( sK0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f145,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ~ ( sK1 @ Y1 )
| ( sK0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true = sF3 ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $true = sF3 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) )
| ( $true = sF3 ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( $true = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $true
= ( ( sK2 @ sK7 @ X1 )
=> ( ~ ( sK1 @ X1 )
| ( sK0 @ X1 ) ) ) )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK1 @ X1 )
| ( sK0 @ X1 ) ) )
| ( $true = sF3 )
| ( ( sK2 @ sK7 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true = sF3 )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( ~ ( sK1 @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( $true = sF3 )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK2 @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) )
| ( $true = sF3 ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f156,plain,
( ( $true = sF3 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f157,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $true = sF3 ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $true = sF3 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true = sF3 )
| ( ( ( sK2 @ sK7 @ X1 )
=> ( sK1 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true = sF3 )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) )
@ sK8 ) )
| ( $true = sF3 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f162,plain,
( ( $true = sF3 )
| ( ( ( sK2 @ sK7 @ sK8 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK0 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $true = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK0 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true = sF3 )
| ( ( sK2 @ sK7 @ sK8 )
= $true ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( ( ( sK2 @ sK8 @ sK9 )
=> ( sK0 @ sK9 ) )
= $false )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( ( sK0 @ sK9 )
= $false )
| ( $true = sF3 ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true = sF3 )
| ( $true
= ( sK2 @ sK8 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f198,definition,
( spl10_8
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f202,definition,
( spl10_9
<=> ! [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f203,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $true )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f204,plain,
( spl10_8
| spl10_9 ),
inference(avatar_split_clause,[],[f154,f202,f198]) ).
thf(f206,definition,
( spl10_10
<=> ! [X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f207,plain,
( ! [X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $true ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f208,plain,
( spl10_10
| spl10_8 ),
inference(avatar_split_clause,[],[f160,f198,f206]) ).
thf(f210,definition,
( spl10_11
<=> ( ( sK2 @ sK7 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f212,plain,
( ( ( sK2 @ sK7 @ sK8 )
= $true )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,plain,
( spl10_8
| spl10_11 ),
inference(avatar_split_clause,[],[f164,f210,f198]) ).
thf(f215,definition,
( spl10_12
<=> ( $true
= ( sK2 @ sK8 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f217,plain,
( ( $true
= ( sK2 @ sK8 @ sK9 ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f218,plain,
( spl10_12
| spl10_8 ),
inference(avatar_split_clause,[],[f168,f198,f215]) ).
thf(f220,definition,
( spl10_13
<=> ( ( sK0 @ sK9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f222,plain,
( ( ( sK0 @ sK9 )
= $false )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f223,plain,
( spl10_8
| spl10_13 ),
inference(avatar_split_clause,[],[f167,f220,f198]) ).
thf(f224,plain,
~ spl10_8,
inference(avatar_split_clause,[],[f76,f198]) ).
thf(f264,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( X0 @ X4 @ X5 ) )
| ( $true = $false )
| ( ( X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ X1 @ X5 ) )
| ( $false
= ( X0 @ X1 @ X4 ) )
| ( $true
= ( X0 @ X1 @ X3 ) ) ),
inference(constrained_superposition,[],[f90,f94]) ).
thf(f266,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( X0 @ X2 )
= $true )
| ( $true = $false )
| ( ( sK2 @ X1 @ X2 )
= $false )
| ( $true
= ( sK1 @ ( sK4 @ X0 @ sK2 @ sK7 ) ) ) )
| ~ spl10_10 ),
inference(constrained_superposition,[],[f207,f90]) ).
thf(f271,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( X0 @ X1 @ X5 ) )
| ( $false
= ( X0 @ X1 @ X4 ) )
| ( $true
= ( X0 @ X1 @ X3 ) )
| ( $false
= ( X0 @ X4 @ X5 ) )
| ( ( X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f272,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( sK1 @ ( sK4 @ X0 @ sK2 @ sK7 ) ) )
| ( ( sK2 @ X1 @ X2 )
= $false )
| ( ( X0 @ X2 )
= $true )
| ( ( sK2 @ sK7 @ X1 )
= $false ) )
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f278,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $true )
| ( ( sK2 @ sK7 @ X0 )
= $false )
| ( ( sK2 @ X2 @ X3 )
= $false )
| ( $false
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK2 @ X0 @ X1 )
= $false ) )
| ~ spl10_10 ),
inference(constrained_superposition,[],[f272,f94]) ).
thf(f283,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK2 @ X0 @ X1 )
= $false )
| ( ( sK2 @ X2 @ X3 )
= $false )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $true )
| ( ( sK2 @ sK7 @ X0 )
= $false )
| ( $false
= ( sK2 @ sK7 @ X2 ) ) )
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f285,definition,
( spl10_14
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK2 @ X2 @ X3 )
= $false )
| ( ( sK1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f286,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X2 @ X3 )
= $false ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f296,plain,
( spl10_14
| spl10_14
| ~ spl10_10 ),
inference(avatar_split_clause,[],[f283,f206,f285,f285]) ).
thf(f297,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK8 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl10_11
| ~ spl10_14 ),
inference(constrained_superposition,[],[f286,f212]) ).
thf(f304,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK8 @ X0 )
= $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl10_11
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f309,plain,
( ( $true
= ( sK1 @ sK9 ) )
| ( $true = $false )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_14 ),
inference(constrained_superposition,[],[f304,f217]) ).
thf(f315,plain,
( ( $true
= ( sK1 @ sK9 ) )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f320,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK2 @ X3 @ X2 ) )
| ( $true = $false )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( $true
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK0 @ X0 )
= $true )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK2 @ sK7 @ X3 )
= $false ) )
| ~ spl10_9 ),
inference(constrained_superposition,[],[f271,f203]) ).
thf(f341,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( ( sK2 @ sK7 @ X3 )
= $false )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK0 @ X0 )
= $true )
| ( $false
= ( sK2 @ X3 @ X2 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f354,definition,
( spl10_19
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( sK2 @ X3 @ X2 ) )
| ( $true
= ( sK2 @ sK7 @ X2 ) )
| ( ( sK2 @ sK7 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
thf(f355,plain,
( ! [X2: $i,X3: $i] :
( ( $true
= ( sK2 @ sK7 @ X2 ) )
| ( $false
= ( sK2 @ X3 @ X2 ) )
| ( ( sK2 @ sK7 @ X3 )
= $false ) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f357,definition,
( spl10_20
<=> ! [X0: $i,X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK0 @ X0 )
= $true )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( $false
= ( sK1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_20])],[avatar_definition]) ).
thf(f358,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK0 @ X0 )
= $true ) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f365,plain,
( spl10_19
| spl10_20
| ~ spl10_9 ),
inference(avatar_split_clause,[],[f341,f202,f357,f354]) ).
thf(f371,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( sK2 @ sK7 @ X1 )
= $false )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $true ) )
| ~ spl10_9
| ~ spl10_19 ),
inference(constrained_superposition,[],[f203,f355]) ).
thf(f380,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK2 @ sK7 @ X1 )
= $false )
| ( ( sK2 @ X1 @ X0 )
= $false )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK0 @ X0 )
= $true ) )
| ~ spl10_9
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f385,plain,
( spl10_20
| ~ spl10_9
| ~ spl10_19 ),
inference(avatar_split_clause,[],[f380,f354,f202,f357]) ).
thf(f560,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK1 @ X0 ) )
| ( ( sK0 @ X0 )
= $true )
| ( ( sK2 @ sK8 @ X0 )
= $false ) )
| ~ spl10_11
| ~ spl10_20 ),
inference(constrained_superposition,[],[f358,f212]) ).
thf(f574,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK8 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $true )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl10_11
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f581,plain,
( ( $false
= ( sK1 @ sK9 ) )
| ( $true
= ( sK0 @ sK9 ) )
| ( $true = $false )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_20 ),
inference(constrained_superposition,[],[f574,f217]) ).
thf(f601,plain,
( ( $false
= ( sK1 @ sK9 ) )
| ( $true
= ( sK0 @ sK9 ) )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f605,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK9 ) )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_14
| ~ spl10_20 ),
inference(forward_demodulation,[],[f601,f315]) ).
thf(f606,plain,
( ( $true
= ( sK0 @ sK9 ) )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_14
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f605]) ).
thf(f610,plain,
( ( $true = $false )
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13
| ~ spl10_14
| ~ spl10_20 ),
inference(forward_demodulation,[],[f606,f222]) ).
thf(f611,plain,
( $false
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13
| ~ spl10_14
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f612,plain,
( ~ spl10_11
| ~ spl10_12
| ~ spl10_13
| ~ spl10_14
| ~ spl10_20 ),
inference(avatar_contradiction_clause,[],[f611]) ).
cnf(s7,plain,
( spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f204]) ).
cnf(s8,plain,
( spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f208]) ).
cnf(s9,plain,
( spl10_8
| spl10_11 ),
inference(sat_conversion,[],[f213]) ).
cnf(s10,plain,
( spl10_8
| spl10_12 ),
inference(sat_conversion,[],[f218]) ).
cnf(s11,plain,
( spl10_8
| spl10_13 ),
inference(sat_conversion,[],[f223]) ).
cnf(s12,plain,
~ spl10_8,
inference(sat_conversion,[],[f224]) ).
cnf(s16,plain,
( spl10_14
| ~ spl10_10
| spl10_14 ),
inference(sat_conversion,[],[f296]) ).
cnf(s17,plain,
( ~ spl10_10
| spl10_14 ),
inference(rat,[],[s16]) ).
cnf(s23,plain,
( ~ spl10_9
| spl10_19
| spl10_20 ),
inference(sat_conversion,[],[f365]) ).
cnf(s25,plain,
( ~ spl10_9
| ~ spl10_19
| spl10_20 ),
inference(sat_conversion,[],[f385]) ).
cnf(s45,plain,
( ~ spl10_11
| ~ spl10_12
| ~ spl10_13
| ~ spl10_14
| ~ spl10_20 ),
inference(sat_conversion,[],[f612]) ).
cnf(s46,plain,
spl10_13,
inference(rat,[],[s11,s12]) ).
cnf(s47,plain,
spl10_12,
inference(rat,[],[s10,s12]) ).
cnf(s48,plain,
spl10_11,
inference(rat,[],[s9,s12]) ).
cnf(s49,plain,
spl10_10,
inference(rat,[],[s8,s12]) ).
cnf(s50,plain,
spl10_14,
inference(rat,[],[s17,s49]) ).
cnf(s51,plain,
~ spl10_20,
inference(rat,[],[s45,s48,s47,s46,s50]) ).
cnf(s52,plain,
spl10_9,
inference(rat,[],[s7,s12]) ).
cnf(s53,plain,
~ spl10_19,
inference(rat,[],[s25,s51,s52]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s23,s51,s53,s52]) ).
thf(f613,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL619^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 09:21:22 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.22/0.34 % (102916)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (102921)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1532766477:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (102923)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=874860309:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (102922)lrs+10_16_si=on:nwc=1.5:random_seed=4113691882:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (102923)Instruction limit reached!
% 0.22/0.34 % (102923)------------------------------
% 0.22/0.34 % (102923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102923)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102923)Termination reason: Instruction limit
% 0.22/0.34 % (102923)Termination phase: Saturation
% 0.22/0.34 % (102923)Time elapsed: 0.002 s
% 0.22/0.34 % (102923)Peak memory usage: 10 MB
% 0.22/0.34 % (102923)Instructions burned: 4 (million)
% 0.22/0.34 % (102927)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (102927)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
% 0.22/0.34 % (102922)Instruction limit reached!
% 0.22/0.34 % (102922)------------------------------
% 0.22/0.34 % (102922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102922)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102922)Termination reason: Instruction limit
% 0.22/0.34 % (102922)Termination phase: Saturation
% 0.22/0.34 % (102922)Time elapsed: 0.010 s
% 0.22/0.34 % (102922)Peak memory usage: 12 MB
% 0.22/0.34 % (102922)Instructions burned: 19 (million)
% 0.22/0.34 % (102925)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1393618662:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (102927)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=3573583597:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (102921)Instruction limit reached!
% 0.22/0.34 % (102921)------------------------------
% 0.22/0.34 % (102921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102921)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102921)Termination reason: Instruction limit
% 0.22/0.34 % (102921)Termination phase: Saturation
% 0.22/0.34 % (102921)Time elapsed: 0.025 s
% 0.22/0.34 % (102921)Peak memory usage: 12 MB
% 0.22/0.34 % (102921)Instructions burned: 89 (million)
% 0.22/0.34 % (102926)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1429484647:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (102931)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=838852523:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.34 % (102924)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=1711556680: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)
% 0.22/0.34 % (102931)Instruction limit reached!
% 0.22/0.34 % (102931)------------------------------
% 0.22/0.34 % (102931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102931)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102931)Termination reason: Instruction limit
% 0.22/0.34 % (102931)Termination phase: Saturation
% 0.22/0.34 % (102931)Time elapsed: 0.002 s
% 0.22/0.34 % (102931)Peak memory usage: 11 MB
% 0.22/0.34 % (102931)Instructions burned: 4 (million)
% 0.22/0.34 % (102935)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.34 % (102935)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1412980906:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.34 % (102932)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1216378638:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.34 % (102935)Instruction limit reached!
% 0.22/0.34 % (102935)------------------------------
% 0.22/0.34 % (102935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102935)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102935)Termination reason: Instruction limit
% 0.22/0.34 % (102935)Termination phase: Saturation
% 0.22/0.34 % (102935)Time elapsed: 0.002 s
% 0.22/0.34 % (102935)Peak memory usage: 12 MB
% 0.22/0.34 % (102935)Instructions burned: 9 (million)
% 0.22/0.34 % (102932)Instruction limit reached!
% 0.22/0.34 % (102932)------------------------------
% 0.22/0.34 % (102932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102932)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102932)Termination reason: Instruction limit
% 0.22/0.34 % (102932)Termination phase: Saturation
% 0.22/0.34 % (102932)Time elapsed: 0.003 s
% 0.22/0.34 % (102932)Peak memory usage: 11 MB
% 0.22/0.34 % (102932)Instructions burned: 5 (million)
% 0.22/0.34 % (102942)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
% 0.22/0.34 % (102942)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.34 % (102925)Instruction limit reached!
% 0.22/0.34 % (102925)------------------------------
% 0.22/0.34 % (102925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102925)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102925)Termination reason: Instruction limit
% 0.22/0.34 % (102925)Termination phase: Saturation
% 0.22/0.34 % (102925)Time elapsed: 0.024 s
% 0.22/0.34 % (102925)Peak memory usage: 12 MB
% 0.22/0.34 % (102925)Instructions burned: 25 (million)
% 0.22/0.34 % (102942)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=96096245:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.34 % (102939)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2512307307:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.34 % (102942)Instruction limit reached!
% 0.22/0.34 % (102942)------------------------------
% 0.22/0.34 % (102942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102942)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102942)Termination reason: Instruction limit
% 0.22/0.34 % (102942)Termination phase: Saturation
% 0.22/0.34 % (102942)Time elapsed: 0.008 s
% 0.22/0.34 % (102942)Peak memory usage: 12 MB
% 0.22/0.34 % (102942)Instructions burned: 29 (million)
% 0.22/0.34 % (102939)Instruction limit reached!
% 0.22/0.34 % (102939)------------------------------
% 0.22/0.34 % (102939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102939)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102939)Termination reason: Instruction limit
% 0.22/0.34 % (102939)Termination phase: Saturation
% 0.22/0.34 % (102939)Time elapsed: 0.007 s
% 0.22/0.34 % (102939)Peak memory usage: 12 MB
% 0.22/0.34 % (102939)Instructions burned: 12 (million)
% 0.22/0.34 % (102943)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1323547620:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.34 % (102927) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-102916-102927"...
% 0.22/0.34 % (102947)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.34 % (102947)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3336793700:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.34 % (102947)Instruction limit reached!
% 0.22/0.34 % (102947)------------------------------
% 0.22/0.34 % (102947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102947)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102947)Termination reason: Instruction limit
% 0.22/0.34 % (102947)Termination phase: Saturation
% 0.22/0.34 % (102947)Time elapsed: 0.001 s
% 0.22/0.34 % (102947)Peak memory usage: 11 MB
% 0.22/0.34 % (102947)Instructions burned: 5 (million)
% 0.22/0.34 % (102927)...printing done.
% 0.22/0.34 % (102927)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.34 % (102927)------------------------------
% 0.22/0.34 % (102927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (102927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (102927)CaDiCaL version: 2.1.3
% 0.22/0.34 % (102927)Termination reason: Refutation
% 0.22/0.34 % (102927)Time elapsed: 0.047 s
% 0.22/0.34 % (102927)Peak memory usage: 13 MB
% 0.22/0.34 % (102927)Instructions burned: 50 (million)
% 0.22/0.34 % (102916)Success in time 0.097 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------