%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:20:18 AM UTC 2026
% Result : ContradictoryAxioms 0.83s 0.38s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 15
% Syntax : Number of formulae : 128 ( 92 unt; 0 typ; 2 def)
% Number of atoms : 780 ( 126 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1822 ( 51 ~; 28 |; 14 &;1321 @)
% ( 2 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 545 ( 545 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 57 usr; 11 con; 0-4 aty)
% ( 229 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 614 ( 54 sgn 54 !; 2 ?; 614 :)
% 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,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_22,type,
god: mu > $i > $o ).
thf(func_def_23,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_24,type,
necessary_existence: mu > $i > $o ).
thf(func_def_25,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
vIFF: $o > $o > $o ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
sK1: mu ).
thf(func_def_44,type,
sK2: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_45,type,
sK3: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_46,type,
sK4: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_47,type,
sK5: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_48,type,
sK6: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_49,type,
sK7: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_50,type,
sK8: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_51,type,
sK9: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_52,type,
sK10: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_53,type,
sK11: ( mu > $i > $o ) > $i > mu ).
thf(func_def_55,type,
sK13: mu ).
thf(func_def_57,type,
sK15: mu ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mnot) ).
thf(f6,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mand) ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mforall_ind) ).
thf(f12,axiom,
( ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_indset ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mforall_indset) ).
thf(f14,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mexists_ind) ).
thf(f17,axiom,
( mbox
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] : ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mbox) ).
thf(f19,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mvalid) ).
thf(f21,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1a) ).
thf(f23,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA2) ).
thf(f24,axiom,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD2) ).
thf(f25,axiom,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) )
= necessary_existence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD3) ).
thf(f26,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA5) ).
thf(f29,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f30,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) )
= necessary_existence ),
inference(rectify,[],[f25]) ).
thf(f32,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f36,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Y0 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f38,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_indset ),
inference(rectify,[],[f12]) ).
thf(f45,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f48,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f19]) ).
thf(f49,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f51,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( mbox
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] : ( X0 @ X2 ) ) ),
inference(rectify,[],[f17]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f55,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f67,plain,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f68,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f73,plain,
mvalid @ ( positive @ necessary_existence ),
inference(rectify,[],[f26]) ).
thf(f74,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f76,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f79,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f80,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f83,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f87,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f96,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f99,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f101,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Y0 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f102,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f104,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f105,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f108,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y2 @ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 ) )
@ ( ^ [Y3: mu > $i > $o,Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
=> ( Y5 @ Y6 ) )
@ ( Y0 @ Y3 )
@ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f105,f83,f98,f87,f99,f98]) ).
thf(f109,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: mu] :
( ^ [Y4: ( mu > $i > $o ) > $i > $o,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y6: mu > $i > $o] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu > $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y4 @ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] : ( Y5 @ Y7 ) )
@ ( ^ [Y5: mu > $i > $o,Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] : ( Y5 @ Y7 @ Y6 ) )
@ ^ [Y5: mu] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
=> ( Y7 @ Y8 ) )
@ ( Y2 @ Y5 )
@ ( Y4 @ Y5 ) ) ) ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f80,f83,f98,f108,f87,f79]) ).
thf(f111,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( positive
@ ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: mu] :
( ^ [Y4: ( mu > $i > $o ) > $i > $o,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y6: mu > $i > $o] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu > $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y4 @ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] : ( Y5 @ Y7 ) )
@ ( ^ [Y5: mu > $i > $o,Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] : ( Y5 @ Y7 @ Y6 ) )
@ ^ [Y5: mu] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
=> ( Y7 @ Y8 ) )
@ ( Y2 @ Y5 )
@ ( Y4 @ Y5 ) ) ) ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f96,f95,f109]) ).
thf(f112,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( positive @ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y0 @ Y2 )
@ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f101,f95,f83,f83,f98,f104,f87,f99,f98]) ).
thf(f113,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( positive
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( positive @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f102,f95,f83,f98,f100,f100]) ).
thf(f115,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 )
=> ~ ( positive @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f116,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f118,plain,
( $true
= ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f119,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 )
=> ~ ( positive @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f120,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
=> ~ ( positive @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
=> ~ ( positive @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
=> ~ ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f129,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f130,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f136,plain,
! [X1: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f137,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y1
@ Y0 )
=> ( X0 @ Y1 @ Y0 ) ) ) )
& $true )
=> ( positive @ X0 @ X1 ) )
= $true ),
inference(constrained_superposition,[],[f134,f136]) ).
thf(f140,plain,
! [X0: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y0
@ Y1 )
@ X0 )
=> ~ $true ) ),
inference(constrained_superposition,[],[f122,f136]) ).
thf(f143,plain,
! [X0: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 )
=> ~ $true ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f144,plain,
! [X0: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 )
=> $false ) ),
inference(boolean_simplification,[],[f143]) ).
thf(f145,plain,
! [X0: $i] :
( $true
= ( ~ ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 ) ) ),
inference(boolean_simplification,[],[f144]) ).
thf(f146,plain,
! [X0: mu > $i > $o,X1: $i] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( X0 @ Y1 @ Y0 ) ) ) )
& $true )
=> ( positive @ X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f147,plain,
! [X0: mu > $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( X0 @ Y1 @ Y0 ) ) ) )
=> ( positive @ X0 @ X1 ) ) ),
inference(boolean_simplification,[],[f146]) ).
thf(f151,plain,
! [X0: $i] :
( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f177,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( ^ [Y2: mu,Y3: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y1
@ Y0 ) ) ) )
=> $false ) ),
inference(constrained_superposition,[],[f147,f151]) ).
thf(f180,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) )
=> $false ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f181,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f180]) ).
thf(f182,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f181]) ).
thf(f183,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
( $false
= ( ^ [Y0: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ?? @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ~ ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: mu > $i > $o] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: mu > $i > $o] :
( $true
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f512,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ( sK10 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f513,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( ( sK10 @ X1 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ( sK10 @ X1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f512]) ).
thf(f515,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) )
| ( $true
= ( sK10 @ X1 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f513]) ).
thf(f516,plain,
! [X2: $i,X1: mu > $i > $o] :
( ( $true
= ( sK10 @ X1 @ sK1 @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f515]) ).
thf(f517,plain,
! [X2: $i,X1: mu > $i > $o] :
( ( $true
= ( sK10 @ X1 @ sK1 @ sK0 ) )
| ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f516]) ).
thf(f518,plain,
! [X2: $i,X1: mu > $i > $o] :
( ( $true
= ( sK10 @ X1 @ sK1 @ sK0 ) )
| ( $true
= ( ^ [Y0: mu] : ( X1 @ Y0 @ X2 )
@ ( sK11 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f517]) ).
thf(f520,plain,
! [X2: $i,X1: mu > $i > $o] :
( ( ( X1 @ ( sK11 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( sK10 @ X1 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f518]) ).
thf(f523,plain,
! [X2: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK11
@ ^ [Y0: mu,Y1: $i] : $false
@ X2 )
@ X2 ) )
| ( $true
= ( sK10
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1
@ sK0 ) ) ),
inference(primitive_instantiation,[],[f520]) ).
thf(f527,plain,
( ( $true
= ( sK10
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1
@ sK0 ) )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f523]) ).
thf(f528,plain,
( $true
= ( sK10
@ ^ [Y0: mu,Y1: $i] : $false
@ sK1
@ sK0 ) ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f529,plain,
( ( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( ^ [Y2: mu,Y3: $i] : $false
@ Y1
@ Y0 )
=> ( sK10
@ ^ [Y2: mu,Y3: $i] : $false
@ Y1
@ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] :
( ^ [Y2: mu,Y3: $i] : $false
@ Y1
@ Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f513,f528]) ).
thf(f530,plain,
( ( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( $false
=> ( sK10
@ ^ [Y2: mu,Y3: $i] : $false
@ Y1
@ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false ) ) ) ),
inference(beta-eta_normalization,[],[f529]) ).
thf(f531,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( $false
=> ( sK10
@ ^ [Y2: mu,Y3: $i] : $false
@ Y1
@ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f530]) ).
thf(f532,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] : $true ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false ) ) ) ),
inference(boolean_simplification,[],[f531]) ).
thf(f534,definition,
( spl12_1
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] : $true ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f536,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] : $true ) ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f538,definition,
( spl12_2
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f540,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f538]) ).
thf(f541,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f532,f538,f534]) ).
thf(f542,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : $false )
@ X1 ) )
| ~ spl12_2 ),
inference(pi_proxy_clausification,[],[f540]) ).
thf(f543,plain,
( ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : $false ) )
| ~ spl12_2 ),
inference(beta-eta_normalization,[],[f542]) ).
thf(f544,plain,
( ( $true
= ( ^ [Y0: mu] : $false
@ sK13 ) )
| ~ spl12_2 ),
inference(sigma_proxy_clausification,[],[f543]) ).
thf(f545,plain,
( ( $true = $false )
| ~ spl12_2 ),
inference(beta-eta_normalization,[],[f544]) ).
thf(f546,plain,
( $false
| ~ spl12_2 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f547,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f546]) ).
thf(f548,plain,
( ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] : $true )
@ sK14 )
= $false )
| ~ spl12_1 ),
inference(sigma_proxy_clausification,[],[f536]) ).
thf(f549,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] : $true )
= $false )
| ~ spl12_1 ),
inference(beta-eta_normalization,[],[f548]) ).
thf(f550,plain,
( ( ( ^ [Y0: mu] : $true
@ sK15 )
= $false )
| ~ spl12_1 ),
inference(sigma_proxy_clausification,[],[f549]) ).
thf(f551,plain,
( ( $true = $false )
| ~ spl12_1 ),
inference(beta-eta_normalization,[],[f550]) ).
thf(f552,plain,
( $false
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f553,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f552]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f541]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f547]) ).
cnf(s3,plain,
~ spl12_1,
inference(sat_conversion,[],[f553]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f554,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n018.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 13:21:56 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.37 % (52951)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.37 % (52959)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=359327557:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.37 % (52962)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.37 % (52962)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.37 % (52956)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=216782239:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.37 % (52957)lrs+10_16_si=on:nwc=1.5:random_seed=3463976187:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (52960)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2163449043:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.37 % (52958)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3665700320:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.37 % (52961)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1830633075:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.37 % (52962)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=3193706047:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.37 % (52958)Instruction limit reached!
% 0.21/0.37 % (52958)------------------------------
% 0.21/0.37 % (52958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (52958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (52958)CaDiCaL version: 2.1.3
% 0.21/0.37 % (52958)Termination reason: Instruction limit
% 0.21/0.37 % (52958)Termination phase: Property scanning
% 0.21/0.37 % (52958)Time elapsed: 0.002 s
% 0.21/0.37 % (52958)Peak memory usage: 10 MB
% 0.21/0.37 % (52958)Instructions burned: 5 (million)
% 0.21/0.37 % (52962)Refutation not found, incomplete strategy
% 0.21/0.37 % (52962)------------------------------
% 0.21/0.37 % (52962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (52962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (52962)CaDiCaL version: 2.1.3
% 0.21/0.37 % (52962)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37 % (52962)Time elapsed: 0.006 s
% 0.21/0.37 % (52962)Peak memory usage: 12 MB
% 0.21/0.37 % (52962)Instructions burned: 11 (million)
% 0.21/0.37 % (52962)------------------------------
% 0.21/0.37 % (52962)------------------------------
% 0.21/0.37 % (52957)Instruction limit reached!
% 0.21/0.37 % (52957)------------------------------
% 0.21/0.37 % (52957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (52957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (52957)CaDiCaL version: 2.1.3
% 0.21/0.37 % (52957)Termination reason: Instruction limit
% 0.21/0.37 % (52957)Termination phase: Saturation
% 0.21/0.37 % (52957)Time elapsed: 0.010 s
% 0.21/0.37 % (52957)Peak memory usage: 12 MB
% 0.21/0.37 % (52957)Instructions burned: 20 (million)
% 0.21/0.37 % (52960)Instruction limit reached!
% 0.21/0.37 % (52960)------------------------------
% 0.21/0.37 % (52960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (52960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (52960)CaDiCaL version: 2.1.3
% 0.21/0.37 % (52960)Termination reason: Instruction limit
% 0.21/0.37 % (52960)Termination phase: Saturation
% 0.21/0.37 % (52960)Time elapsed: 0.014 s
% 0.21/0.37 % (52960)Peak memory usage: 11 MB
% 0.21/0.37 % (52960)Instructions burned: 25 (million)
% 0.21/0.37 % (52970)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=37326297:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (52970)Instruction limit reached!
% 0.21/0.37 % (52970)------------------------------
% 0.21/0.37 % (52970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52970)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52970)Termination reason: Instruction limit
% 0.83/0.38 % (52970)Termination phase: Property scanning
% 0.83/0.38 % (52970)Time elapsed: 0.002 s
% 0.83/0.38 % (52970)Peak memory usage: 10 MB
% 0.83/0.38 % (52970)Instructions burned: 3 (million)
% 0.83/0.38 % (52972)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.38 % (52971)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1139846852:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.83/0.38 % (52972)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=821659272:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.83/0.38 % (52971)Instruction limit reached!
% 0.83/0.38 % (52971)------------------------------
% 0.83/0.38 % (52971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52971)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52971)Termination reason: Instruction limit
% 0.83/0.38 % (52971)Termination phase: Saturation
% 0.83/0.38 % (52971)Time elapsed: 0.003 s
% 0.83/0.38 % (52971)Peak memory usage: 11 MB
% 0.83/0.38 % (52971)Instructions burned: 7 (million)
% 0.83/0.38 % (52973)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2485915133:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.83/0.38 % (52972)Instruction limit reached!
% 0.83/0.38 % (52972)------------------------------
% 0.83/0.38 % (52972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52972)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52972)Termination reason: Instruction limit
% 0.83/0.38 % (52972)Termination phase: Saturation
% 0.83/0.38 % (52972)Time elapsed: 0.003 s
% 0.83/0.38 % (52972)Peak memory usage: 11 MB
% 0.83/0.38 % (52972)Instructions burned: 7 (million)
% 0.83/0.38 % (52961)Instruction limit reached!
% 0.83/0.38 % (52961)------------------------------
% 0.83/0.38 % (52961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52961)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52961)Termination reason: Instruction limit
% 0.83/0.38 % (52961)Termination phase: Saturation
% 0.83/0.38 % (52961)Time elapsed: 0.039 s
% 0.83/0.38 % (52961)Peak memory usage: 13 MB
% 0.83/0.38 % (52961)Instructions burned: 76 (million)
% 0.83/0.38 % (52973)Instruction limit reached!
% 0.83/0.38 % (52973)------------------------------
% 0.83/0.38 % (52973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52973)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52973)Termination reason: Instruction limit
% 0.83/0.38 % (52973)Termination phase: Saturation
% 0.83/0.38 % (52973)Time elapsed: 0.007 s
% 0.83/0.38 % (52973)Peak memory usage: 12 MB
% 0.83/0.38 % (52973)Instructions burned: 12 (million)
% 0.83/0.38 % (52975)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
% 0.83/0.38 % (52975)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.38 % (52956)Instruction limit reached!
% 0.83/0.38 % (52956)------------------------------
% 0.83/0.38 % (52956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52956)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52956)Termination reason: Instruction limit
% 0.83/0.38 % (52956)Termination phase: Saturation
% 0.83/0.38 % (52956)Time elapsed: 0.042 s
% 0.83/0.38 % (52956)Peak memory usage: 12 MB
% 0.83/0.38 % (52956)Instructions burned: 87 (million)
% 0.83/0.38 % (52975)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4150689912:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.83/0.38 % (52978)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=1555802702:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.83/0.38 % (52981)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.83/0.38 % (52982)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3796350347:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.83/0.38 % (52981)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=4069966800:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.38 % (52975)Instruction limit reached!
% 0.83/0.38 % (52975)------------------------------
% 0.83/0.38 % (52975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52975)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52975)Termination reason: Instruction limit
% 0.83/0.38 % (52975)Termination phase: Saturation
% 0.83/0.38 % (52975)Time elapsed: 0.015 s
% 0.83/0.38 % (52975)Peak memory usage: 12 MB
% 0.83/0.38 % (52975)Instructions burned: 29 (million)
% 0.83/0.38 % (52983)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2999825599:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.83/0.38 % (52982)Refutation not found, incomplete strategy
% 0.83/0.38 % (52982)------------------------------
% 0.83/0.38 % (52982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52982)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52982)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.38 % (52982)Time elapsed: 0.002 s
% 0.83/0.38 % (52982)Peak memory usage: 11 MB
% 0.83/0.38 % (52982)Instructions burned: 3 (million)
% 0.83/0.38 % (52981)Instruction limit reached!
% 0.83/0.38 % (52981)------------------------------
% 0.83/0.38 % (52981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52981)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52981)Termination reason: Instruction limit
% 0.83/0.38 % (52981)Termination phase: Property scanning
% 0.83/0.38 % (52981)Time elapsed: 0.002 s
% 0.83/0.38 % (52981)Peak memory usage: 10 MB
% 0.83/0.38 % (52981)Instructions burned: 4 (million)
% 0.83/0.38 % (52982)------------------------------
% 0.83/0.38 % (52982)------------------------------
% 0.83/0.38 % (52983)Refutation not found, incomplete strategy
% 0.83/0.38 % (52983)------------------------------
% 0.83/0.38 % (52983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52983)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52983)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.38 % (52983)Time elapsed: 0.002 s
% 0.83/0.38 % (52983)Peak memory usage: 11 MB
% 0.83/0.38 % (52983)Instructions burned: 3 (million)
% 0.83/0.38 % (52983)------------------------------
% 0.83/0.38 % (52983)------------------------------
% 0.83/0.38 % (52980)lrs+10_1_si=on:cs=on:random_seed=2911238209:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.83/0.38 % (52980)Instruction limit reached!
% 0.83/0.38 % (52980)------------------------------
% 0.83/0.38 % (52980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52980)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52980)Termination reason: Instruction limit
% 0.83/0.38 % (52980)Termination phase: Saturation
% 0.83/0.38 % (52980)Time elapsed: 0.008 s
% 0.83/0.38 % (52980)Peak memory usage: 11 MB
% 0.83/0.38 % (52980)Instructions burned: 11 (million)
% 0.83/0.38 % (52989)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=501591252:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.83/0.38 % (52990)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2444838509:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.38 % (52991)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2756762311:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.83/0.38 % (52989)Refutation not found, incomplete strategy
% 0.83/0.38 % (52989)------------------------------
% 0.83/0.38 % (52989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52989)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52989)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.38 % (52989)Time elapsed: 0.002 s
% 0.83/0.38 % (52989)Peak memory usage: 11 MB
% 0.83/0.38 % (52989)Instructions burned: 3 (million)
% 0.83/0.38 % (52989)------------------------------
% 0.83/0.38 % (52989)------------------------------
% 0.83/0.38 % (52991)Refutation not found, incomplete strategy
% 0.83/0.38 % (52991)------------------------------
% 0.83/0.38 % (52991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52991)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52991)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.38 % (52991)Time elapsed: 0.002 s
% 0.83/0.38 % (52991)Peak memory usage: 11 MB
% 0.83/0.38 % (52991)Instructions burned: 4 (million)
% 0.83/0.38 % (52978) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-52951-52978"...
% 0.83/0.38 % (52991)------------------------------
% 0.83/0.38 % (52991)------------------------------
% 0.83/0.38 % (52993)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=337822418:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.38 % (52990)Instruction limit reached!
% 0.83/0.38 % (52990)------------------------------
% 0.83/0.38 % (52990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52990)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52990)Termination reason: Instruction limit
% 0.83/0.38 % (52990)Termination phase: Saturation
% 0.83/0.38 % (52990)Time elapsed: 0.008 s
% 0.83/0.38 % (52990)Peak memory usage: 12 MB
% 0.83/0.38 % (52990)Instructions burned: 14 (million)
% 0.83/0.38 % (52978)...printing done.
% 0.83/0.38 % (52978)Refutation found. Thanks to Tanya!
% 0.83/0.38 % SZS status ContradictoryAxioms for theBenchmark
% 0.83/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.38 % (52978)------------------------------
% 0.83/0.38 % (52978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.38 % (52978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.38 % (52978)CaDiCaL version: 2.1.3
% 0.83/0.38 % (52978)Termination reason: Refutation
% 0.83/0.38 % (52978)Time elapsed: 0.038 s
% 0.83/0.38 % (52978)Peak memory usage: 13 MB
% 0.83/0.38 % (52978)Instructions burned: 73 (million)
% 0.83/0.38 % (52951)Success in time 0.133 s
% 0.83/0.38 % Vampire exiting
%------------------------------------------------------------------------------