%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI003^1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:20:16 AM UTC 2026
% Result : Theorem 2.27s 0.61s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 124 ( 115 unt; 0 typ; 0 def)
% Number of atoms : 621 ( 122 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1285 ( 76 ~; 26 |; 33 &; 952 @)
% ( 2 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 440 ( 440 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 50 usr; 5 con; 0-4 aty)
% ( 106 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 426 ( 356 ^; 66 !; 4 ?; 426 :)
% 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_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
rel: $i > $i > $o ).
thf(func_def_20,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_21,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_23,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_24,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_25,type,
god: mu > $i > $o ).
thf(func_def_26,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_27,type,
necessary_existence: mu > $i > $o ).
thf(func_def_28,type,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIFF: $o > $o > $o ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
sK1: $i > $i ).
thf(func_def_47,type,
sK2: mu > mu > $i > $o ).
thf(func_def_48,type,
sK3: $i > $i ).
thf(func_def_49,type,
sK4: $i > $i ).
thf(func_def_50,type,
sK5: $i > $i ).
thf(func_def_51,type,
sK6: $i > mu ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.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/LCL016^0.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/LCL016^0.ax',mexists_ind) ).
thf(f17,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox_generic ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f18,axiom,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',axA1) ).
thf(f24,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/Axioms/PHI001^0.ax',axA2) ).
thf(f25,axiom,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',defD1) ).
thf(f26,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',axA3) ).
thf(f31,conjecture,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corC) ).
thf(f32,negated_conjecture,
~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
thf(f37,plain,
~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f38,plain,
( $true
= ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f40,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f11]) ).
thf(f44,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f46,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f6]) ).
thf(f47,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f49,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f9]) ).
thf(f51,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox_generic ),
inference(rectify,[],[f17]) ).
thf(f55,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f57,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_indset ),
inference(rectify,[],[f12]) ).
thf(f59,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(fool_elimination,[],[f19]) ).
thf(f66,plain,
mvalid @ ( positive @ god ),
inference(rectify,[],[f26]) ).
thf(f67,plain,
( ( mvalid @ ( positive @ god ) )
= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f73,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(fool_elimination,[],[f20]) ).
thf(f74,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,[],[f24]) ).
thf(f75,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,[],[f74]) ).
thf(f78,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f4]) ).
thf(f79,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f7]) ).
thf(f81,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
inference(rectify,[],[f25]) ).
thf(f85,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f92,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f93,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f94,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f97,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f98,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f101,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f102,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f106,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f107,plain,
( ( mvalid @ ( positive @ god ) )
= $true ),
inference(cnf_transformation,[],[f67]) ).
thf(f108,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f40]) ).
thf(f109,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,[],[f75]) ).
thf(f112,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f115,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f117,plain,
( $true
= ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f123,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f101,f98]) ).
thf(f124,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f102,f97]) ).
thf(f125,plain,
( god
= ( ^ [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 ) )
@ ( positive @ Y1 )
@ ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f92,f94,f91]) ).
thf(f129,plain,
( ( ^ [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 ) )
@ ( positive @ Y1 )
@ ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f107,f95,f125]) ).
thf(f130,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,[],[f108,f95,f94,f115,f120,f120]) ).
thf(f131,plain,
( ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f109,f95,f94,f94,f91,f112,f123,f106,f91]) ).
thf(f133,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [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 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f117,f95,f124,f93,f125]) ).
thf(f134,plain,
( $true
= ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f135,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f137,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f138,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,[],[f130]) ).
thf(f140,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f135]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
& ( rel @ Y0 @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f144,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ sK0 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f145,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
& ( rel @ sK0 @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( ( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) ) )
& ( rel @ sK0 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f148,plain,
! [X1: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f149,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 )
= ( ~ ( positive @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f150,plain,
! [X1: $i] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
= ( ~ ( positive @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,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,[],[f150]) ).
thf(f152,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ~ ( positive @ X2 @ X1 ) )
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ),
inference(iff_proxy_clausification,[],[f152]) ).
thf(f176,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f177,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f182,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ X1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( positive @ Y0 @ X1 ) )
=> ( positive @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f183,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ( positive @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f188,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( ^ [Y2: mu,Y3: $i] :
~ ( X0 @ Y2 @ Y3 )
@ Y1
@ Y0 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ~ ( positive @ X0 @ X1 ) ) ),
inference(superposition,[],[f185,f153]) ).
thf(f191,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ~ ( X0 @ Y1 @ Y0 ) ) ) ) )
& ( positive @ X2 @ X1 ) )
=> ~ ( positive @ X0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f198,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ) )
& ( positive @ X1 @ X0 ) )
=> ~ $true )
= $true ),
inference(superposition,[],[f191,f148]) ).
thf(f203,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( positive @ X1 @ X0 ) )
=> ~ $true )
= $true ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f204,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( positive @ X1 @ X0 ) )
=> $false )
= $true ),
inference(boolean_simplification,[],[f203]) ).
thf(f205,plain,
! [X0: $i,X1: mu > $i > $o] :
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( positive @ X1 @ X0 ) ) ) ),
inference(boolean_simplification,[],[f204]) ).
thf(f291,plain,
! [X0: $i] :
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
& $true ) )
= $true ),
inference(superposition,[],[f205,f148]) ).
thf(f294,plain,
! [X0: $i] :
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
& $true ) )
= $true ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f295,plain,
! [X0: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f294]) ).
thf(f296,plain,
! [X0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f295]) ).
thf(f304,plain,
! [X0: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f314,plain,
! [X0: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel @ X0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ ( sK1 @ X0 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f304]) ).
thf(f315,plain,
! [X0: $i] :
( $false
= ( ~ ( rel @ X0 @ ( sK1 @ X0 ) )
| ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ X0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ X0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f326,plain,
! [X0: $i] :
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ X0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ X0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f327,plain,
! [X0: $i] :
( ( ~ ( rel @ X0 @ ( sK1 @ X0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f342,plain,
! [X0: $i] :
( $true
= ( rel @ X0 @ ( sK1 @ X0 ) ) ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f361,plain,
( $false
= ( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ sK0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ sK0 ) ) ) ) )
& $true ) ),
inference(superposition,[],[f146,f342]) ).
thf(f365,plain,
( ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ sK0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ sK0 ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f361]) ).
thf(f376,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ sK0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ sK0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f365]) ).
thf(f377,plain,
! [X1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK1 @ sK0 ) )
=> ( Y0 @ X1 @ ( sK1 @ sK0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f376]) ).
thf(f388,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK1 @ sK0 ) )
=> ( Y0 @ X1 @ ( sK1 @ sK0 ) ) )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f377]) ).
thf(f389,plain,
! [X1: mu] :
( ( ( positive @ ( sK2 @ X1 ) @ ( sK1 @ sK0 ) )
=> ( sK2 @ X1 @ X1 @ ( sK1 @ sK0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f388]) ).
thf(f1234,plain,
! [X0: $i] :
( $false
= ( ^ [Y0: mu] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK1 @ X0 ) )
=> ( Y1 @ Y0 @ ( sK1 @ X0 ) ) ) )
@ ( sK6 @ X0 ) ) ),
inference(sigma_proxy_clausification,[],[f326]) ).
thf(f1235,plain,
! [X0: $i] :
( ( ~ ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK1 @ X0 ) )
=> ( Y0 @ ( sK6 @ X0 ) @ ( sK1 @ X0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f1234]) ).
thf(f1303,plain,
! [X0: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK1 @ X0 ) )
=> ( Y0 @ ( sK6 @ X0 ) @ ( sK1 @ X0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f1235]) ).
thf(f1373,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK1 @ X0 ) )
=> ( Y0 @ ( sK6 @ X0 ) @ ( sK1 @ X0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1303]) ).
thf(f1374,plain,
! [X0: $i,X1: mu > $i > $o] :
( $true
= ( ( positive @ X1 @ ( sK1 @ X0 ) )
=> ( X1 @ ( sK6 @ X0 ) @ ( sK1 @ X0 ) ) ) ),
inference(beta-eta_normalization,[],[f1373]) ).
thf(f1449,plain,
$false = $true,
inference(superposition,[],[f1374,f389]) ).
thf(f1456,plain,
$false,
inference(trivial_inequality_removal,[],[f1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI003^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:17:40 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.21/0.35 % (3132119)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.35 % (3132124)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3796758008:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.35 % (3132130)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.35 % (3132130)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
% 0.21/0.35 % (3132126)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3163102131:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.35 % (3132125)lrs+10_16_si=on:nwc=1.5:random_seed=3153521022:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.35 % (3132129)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1773452196:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.35 % (3132128)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1659418652:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.35 % (3132127)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=1137565997: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)
% 0.21/0.35 % (3132130)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=2883558709:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.35 % (3132126)Instruction limit reached!
% 0.21/0.35 % (3132126)------------------------------
% 0.21/0.35 % (3132126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3132126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3132126)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3132126)Termination reason: Instruction limit
% 0.21/0.35 % (3132126)Termination phase: Property scanning
% 0.21/0.35 % (3132126)Time elapsed: 0.002 s
% 0.21/0.35 % (3132126)Peak memory usage: 10 MB
% 0.21/0.35 % (3132126)Instructions burned: 4 (million)
% 0.21/0.35 % (3132125)Instruction limit reached!
% 0.21/0.35 % (3132125)------------------------------
% 0.21/0.35 % (3132125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3132125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3132125)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3132125)Termination reason: Instruction limit
% 0.21/0.35 % (3132125)Termination phase: Saturation
% 0.21/0.35 % (3132125)Time elapsed: 0.009 s
% 0.21/0.35 % (3132125)Peak memory usage: 12 MB
% 0.21/0.35 % (3132125)Instructions burned: 19 (million)
% 0.21/0.35 % (3132124)Instruction limit reached!
% 0.21/0.35 % (3132124)------------------------------
% 0.21/0.35 % (3132124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3132124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3132124)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3132124)Termination reason: Instruction limit
% 0.21/0.35 % (3132124)Termination phase: Saturation
% 0.21/0.35 % (3132124)Time elapsed: 0.020 s
% 0.21/0.35 % (3132124)Peak memory usage: 12 MB
% 0.21/0.35 % (3132124)Instructions burned: 90 (million)
% 0.21/0.35 % (3132128)Instruction limit reached!
% 0.21/0.35 % (3132128)------------------------------
% 0.21/0.35 % (3132128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (3132128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (3132128)CaDiCaL version: 2.1.3
% 0.21/0.35 % (3132128)Termination reason: Instruction limit
% 0.21/0.35 % (3132128)Termination phase: Saturation
% 0.21/0.35 % (3132128)Time elapsed: 0.014 s
% 0.21/0.35 % (3132128)Peak memory usage: 11 MB
% 0.21/0.35 % (3132128)Instructions burned: 25 (million)
% 0.21/0.35 % (3132139)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=429397991:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (3132141)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.81/0.37 % (3132139)Instruction limit reached!
% 0.81/0.37 % (3132139)------------------------------
% 0.81/0.37 % (3132139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.37 % (3132139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.37 % (3132139)CaDiCaL version: 2.1.3
% 0.81/0.37 % (3132139)Termination reason: Instruction limit
% 0.81/0.37 % (3132139)Termination phase: Property scanning
% 0.81/0.37 % (3132139)Time elapsed: 0.001 s
% 0.81/0.37 % (3132139)Peak memory usage: 10 MB
% 0.81/0.37 % (3132139)Instructions burned: 2 (million)
% 0.81/0.37 % (3132141)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4177386441:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.81/0.37 % (3132141)Instruction limit reached!
% 0.81/0.37 % (3132141)------------------------------
% 0.81/0.37 % (3132141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.37 % (3132141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.37 % (3132141)CaDiCaL version: 2.1.3
% 0.81/0.37 % (3132141)Termination reason: Instruction limit
% 0.81/0.37 % (3132141)Termination phase: Saturation
% 0.81/0.37 % (3132141)Time elapsed: 0.002 s
% 0.81/0.37 % (3132141)Peak memory usage: 11 MB
% 0.81/0.37 % (3132141)Instructions burned: 9 (million)
% 0.81/0.37 % (3132140)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3378140510:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.81/0.37 % (3132140)Instruction limit reached!
% 0.81/0.37 % (3132140)------------------------------
% 0.81/0.37 % (3132140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.37 % (3132140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.37 % (3132140)CaDiCaL version: 2.1.3
% 0.81/0.37 % (3132140)Termination reason: Instruction limit
% 0.81/0.37 % (3132140)Termination phase: Property scanning
% 0.81/0.37 % (3132140)Time elapsed: 0.003 s
% 0.81/0.37 % (3132140)Peak memory usage: 10 MB
% 0.81/0.37 % (3132140)Instructions burned: 6 (million)
% 0.81/0.37 % (3132142)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1811474012:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.81/0.37 % (3132146)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=2868542720:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.81/0.37 % (3132144)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
% 0.81/0.37 % (3132144)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.81/0.37 % (3132129)Instruction limit reached!
% 0.81/0.37 % (3132129)------------------------------
% 0.81/0.37 % (3132129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.37 % (3132129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.37 % (3132129)CaDiCaL version: 2.1.3
% 0.81/0.37 % (3132129)Termination reason: Instruction limit
% 0.81/0.37 % (3132129)Termination phase: Saturation
% 0.81/0.37 % (3132129)Time elapsed: 0.038 s
% 0.81/0.37 % (3132129)Peak memory usage: 12 MB
% 0.81/0.37 % (3132129)Instructions burned: 76 (million)
% 0.81/0.37 % (3132142)Instruction limit reached!
% 0.81/0.37 % (3132142)------------------------------
% 0.81/0.37 % (3132142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.37 % (3132142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.37 % (3132142)CaDiCaL version: 2.1.3
% 0.81/0.37 % (3132142)Termination reason: Instruction limit
% 0.81/0.37 % (3132142)Termination phase: Saturation
% 0.81/0.37 % (3132142)Time elapsed: 0.006 s
% 0.81/0.37 % (3132142)Peak memory usage: 11 MB
% 0.81/0.37 % (3132142)Instructions burned: 13 (million)
% 0.81/0.37 % (3132144)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=178003630:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.81/0.37 % (3132148)lrs+10_1_si=on:cs=on:random_seed=2122275535:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.81/0.37 % (3132151)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.81/0.40 % (3132148)Instruction limit reached!
% 0.81/0.40 % (3132148)------------------------------
% 0.81/0.40 % (3132148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132148)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132148)Termination reason: Instruction limit
% 0.81/0.40 % (3132148)Termination phase: Saturation
% 0.81/0.40 % (3132148)Time elapsed: 0.004 s
% 0.81/0.40 % (3132148)Peak memory usage: 11 MB
% 0.81/0.40 % (3132148)Instructions burned: 8 (million)
% 0.81/0.40 % (3132151)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=27358633:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.81/0.40 % (3132144)Instruction limit reached!
% 0.81/0.40 % (3132144)------------------------------
% 0.81/0.40 % (3132144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132144)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132144)Termination reason: Instruction limit
% 0.81/0.40 % (3132144)Termination phase: Saturation
% 0.81/0.40 % (3132153)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2427746962:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.81/0.40 % (3132144)Time elapsed: 0.019 s
% 0.81/0.40 % (3132144)Peak memory usage: 12 MB
% 0.81/0.40 % (3132144)Instructions burned: 36 (million)
% 0.81/0.40 % (3132146)Instruction limit reached!
% 0.81/0.40 % (3132146)------------------------------
% 0.81/0.40 % (3132146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132146)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132146)Termination reason: Instruction limit
% 0.81/0.40 % (3132146)Termination phase: Saturation
% 0.81/0.40 % (3132146)Time elapsed: 0.024 s
% 0.81/0.40 % (3132146)Peak memory usage: 13 MB
% 0.81/0.40 % (3132146)Instructions burned: 91 (million)
% 0.81/0.40 % (3132151)Instruction limit reached!
% 0.81/0.40 % (3132151)------------------------------
% 0.81/0.40 % (3132151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132151)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132151)Termination reason: Instruction limit
% 0.81/0.40 % (3132151)Termination phase: Property scanning
% 0.81/0.40 % (3132151)Time elapsed: 0.003 s
% 0.81/0.40 % (3132151)Peak memory usage: 10 MB
% 0.81/0.40 % (3132151)Instructions burned: 6 (million)
% 0.81/0.40 % (3132130)Instruction limit reached!
% 0.81/0.40 % (3132130)------------------------------
% 0.81/0.40 % (3132130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132130)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132130)Termination reason: Instruction limit
% 0.81/0.40 % (3132130)Termination phase: Saturation
% 0.81/0.40 % (3132130)Time elapsed: 0.059 s
% 0.81/0.40 % (3132130)Peak memory usage: 12 MB
% 0.81/0.40 % (3132130)Instructions burned: 159 (million)
% 0.81/0.40 % (3132153)Refutation not found, incomplete strategy
% 0.81/0.40 % (3132153)------------------------------
% 0.81/0.40 % (3132153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.40 % (3132153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.40 % (3132153)CaDiCaL version: 2.1.3
% 0.81/0.40 % (3132153)Termination reason: Refutation not found, incomplete strategy
% 0.81/0.40 % (3132153)Time elapsed: 0.005 s
% 0.81/0.40 % (3132153)Peak memory usage: 12 MB
% 0.81/0.40 % (3132153)Instructions burned: 9 (million)
% 0.81/0.40 % (3132153)------------------------------
% 0.81/0.40 % (3132153)------------------------------
% 0.81/0.40 % (3132159)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=935104227:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.81/0.40 % (3132155)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=120315401:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.81/0.44 % (3132159)Instruction limit reached!
% 0.81/0.44 % (3132159)------------------------------
% 0.81/0.44 % (3132159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132159)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132159)Termination reason: Instruction limit
% 0.81/0.44 % (3132159)Termination phase: Saturation
% 0.81/0.44 % (3132159)Time elapsed: 0.004 s
% 0.81/0.44 % (3132159)Peak memory usage: 12 MB
% 0.81/0.44 % (3132159)Instructions burned: 15 (million)
% 0.81/0.44 % (3132155)Refutation not found, incomplete strategy
% 0.81/0.44 % (3132155)------------------------------
% 0.81/0.44 % (3132155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132155)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132155)Termination reason: Refutation not found, incomplete strategy
% 0.81/0.44 % (3132155)Time elapsed: 0.003 s
% 0.81/0.44 % (3132155)Peak memory usage: 12 MB
% 0.81/0.44 % (3132155)Instructions burned: 5 (million)
% 0.81/0.44 % (3132155)------------------------------
% 0.81/0.44 % (3132155)------------------------------
% 0.81/0.44 % (3132158)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3551726513:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.81/0.44 % (3132160)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2118132651:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.81/0.44 % (3132161)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1765162560:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.81/0.44 % (3132162)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=12997520:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.81/0.44 % (3132165)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=136437468:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.81/0.44 % (3132162)Instruction limit reached!
% 0.81/0.44 % (3132162)------------------------------
% 0.81/0.44 % (3132162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132162)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132162)Termination reason: Instruction limit
% 0.81/0.44 % (3132162)Termination phase: Preprocessing 2
% 0.81/0.44 % (3132162)Time elapsed: 0.002 s
% 0.81/0.44 % (3132162)Peak memory usage: 10 MB
% 0.81/0.44 % (3132162)Instructions burned: 4 (million)
% 0.81/0.44 % (3132161)Instruction limit reached!
% 0.81/0.44 % (3132161)------------------------------
% 0.81/0.44 % (3132161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132161)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132161)Termination reason: Instruction limit
% 0.81/0.44 % (3132161)Termination phase: Saturation
% 0.81/0.44 % (3132161)Time elapsed: 0.007 s
% 0.81/0.44 % (3132161)Peak memory usage: 12 MB
% 0.81/0.44 % (3132161)Instructions burned: 14 (million)
% 0.81/0.44 % (3132165)Instruction limit reached!
% 0.81/0.44 % (3132165)------------------------------
% 0.81/0.44 % (3132165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132165)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132165)Termination reason: Instruction limit
% 0.81/0.44 % (3132165)Termination phase: Saturation
% 0.81/0.44 % (3132165)Time elapsed: 0.007 s
% 0.81/0.44 % (3132165)Peak memory usage: 12 MB
% 0.81/0.44 % (3132165)Instructions burned: 27 (million)
% 0.81/0.44 % (3132158)Instruction limit reached!
% 0.81/0.44 % (3132158)------------------------------
% 0.81/0.44 % (3132158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.44 % (3132158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.44 % (3132158)CaDiCaL version: 2.1.3
% 0.81/0.44 % (3132158)Termination reason: Instruction limit
% 0.81/0.44 % (3132158)Termination phase: Saturation
% 0.81/0.44 % (3132158)Time elapsed: 0.015 s
% 0.81/0.44 % (3132158)Peak memory usage: 12 MB
% 0.81/0.44 % (3132158)Instructions burned: 25 (million)
% 1.54/0.49 % (3132166)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3493641336:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.54/0.49 % (3132174)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.54/0.49 % (3132174)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=4223091131:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.54/0.49 % (3132173)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.54/0.49 % (3132173)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.54/0.49 % (3132174)Instruction limit reached!
% 1.54/0.49 % (3132174)------------------------------
% 1.54/0.49 % (3132174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.49 % (3132174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.49 % (3132174)CaDiCaL version: 2.1.3
% 1.54/0.49 % (3132174)Termination reason: Instruction limit
% 1.54/0.49 % (3132174)Termination phase: Saturation
% 1.54/0.49 % (3132174)Time elapsed: 0.002 s
% 1.54/0.49 % (3132174)Peak memory usage: 11 MB
% 1.54/0.49 % (3132174)Instructions burned: 8 (million)
% 1.54/0.49 % (3132172)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1762922136:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.54/0.49 % (3132173)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2968703978:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.54/0.49 % (3132166)Instruction limit reached!
% 1.54/0.49 % (3132166)------------------------------
% 1.54/0.49 % (3132166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.49 % (3132166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.49 % (3132166)CaDiCaL version: 2.1.3
% 1.54/0.49 % (3132166)Termination reason: Instruction limit
% 1.54/0.49 % (3132166)Termination phase: Saturation
% 1.54/0.49 % (3132166)Time elapsed: 0.012 s
% 1.54/0.49 % (3132166)Peak memory usage: 12 MB
% 1.54/0.49 % (3132166)Instructions burned: 24 (million)
% 1.54/0.49 % (3132175)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4095761127:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.54/0.49 % (3132173)Instruction limit reached!
% 1.54/0.49 % (3132173)------------------------------
% 1.54/0.49 % (3132173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.49 % (3132173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.49 % (3132173)CaDiCaL version: 2.1.3
% 1.54/0.49 % (3132173)Termination reason: Instruction limit
% 1.54/0.49 % (3132173)Termination phase: Saturation
% 1.54/0.49 % (3132173)Time elapsed: 0.007 s
% 1.54/0.49 % (3132173)Peak memory usage: 12 MB
% 1.54/0.49 % (3132173)Instructions burned: 14 (million)
% 1.54/0.49 % (3132179)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4178127401:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.54/0.49 % (3132179)Instruction limit reached!
% 1.54/0.49 % (3132179)------------------------------
% 1.54/0.49 % (3132179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.49 % (3132179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.49 % (3132179)CaDiCaL version: 2.1.3
% 1.54/0.49 % (3132179)Termination reason: Instruction limit
% 1.54/0.49 % (3132179)Termination phase: Saturation
% 1.54/0.49 % (3132179)Time elapsed: 0.002 s
% 1.54/0.49 % (3132179)Peak memory usage: 11 MB
% 1.54/0.49 % (3132179)Instructions burned: 8 (million)
% 1.54/0.49 % (3132181)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=164970922:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.54/0.49 % (3132185)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1868488638:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.54/0.54 % (3132175)Instruction limit reached!
% 1.54/0.54 % (3132175)------------------------------
% 1.54/0.54 % (3132175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132175)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132175)Termination reason: Instruction limit
% 1.54/0.54 % (3132175)Termination phase: Saturation
% 1.54/0.54 % (3132175)Time elapsed: 0.016 s
% 1.54/0.54 % (3132175)Peak memory usage: 12 MB
% 1.54/0.54 % (3132175)Instructions burned: 31 (million)
% 1.54/0.54 % (3132183)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4274147056:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.54/0.54 % (3132181)Instruction limit reached!
% 1.54/0.54 % (3132181)------------------------------
% 1.54/0.54 % (3132181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132181)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132181)Termination reason: Instruction limit
% 1.54/0.54 % (3132181)Termination phase: Saturation
% 1.54/0.54 % (3132181)Time elapsed: 0.010 s
% 1.54/0.54 % (3132181)Peak memory usage: 11 MB
% 1.54/0.54 % (3132181)Instructions burned: 23 (million)
% 1.54/0.54 % (3132172)Instruction limit reached!
% 1.54/0.54 % (3132172)------------------------------
% 1.54/0.54 % (3132172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132172)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132172)Termination reason: Instruction limit
% 1.54/0.54 % (3132172)Termination phase: Saturation
% 1.54/0.54 % (3132172)Time elapsed: 0.034 s
% 1.54/0.54 % (3132172)Peak memory usage: 12 MB
% 1.54/0.54 % (3132172)Instructions burned: 61 (million)
% 1.54/0.54 % (3132183)Instruction limit reached!
% 1.54/0.54 % (3132183)------------------------------
% 1.54/0.54 % (3132183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132183)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132183)Termination reason: Instruction limit
% 1.54/0.54 % (3132183)Termination phase: Saturation
% 1.54/0.54 % (3132183)Time elapsed: 0.012 s
% 1.54/0.54 % (3132183)Peak memory usage: 12 MB
% 1.54/0.54 % (3132183)Instructions burned: 21 (million)
% 1.54/0.54 % (3132188)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3400623652:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.54/0.54 % (3132190)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=607891044:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.54/0.54 % (3132191)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2119284621:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.54/0.54 % (3132192)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.54/0.54 % (3132190)Refutation not found, incomplete strategy
% 1.54/0.54 % (3132190)------------------------------
% 1.54/0.54 % (3132190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132190)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132190)Termination reason: Refutation not found, incomplete strategy
% 1.54/0.54 % (3132190)Time elapsed: 0.006 s
% 1.54/0.54 % (3132190)Peak memory usage: 12 MB
% 1.54/0.54 % (3132190)Instructions burned: 10 (million)
% 1.54/0.54 % (3132190)------------------------------
% 1.54/0.54 % (3132190)------------------------------
% 1.54/0.54 % (3132192)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2172733946:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.54/0.54 % (3132192)Instruction limit reached!
% 1.54/0.54 % (3132192)------------------------------
% 1.54/0.54 % (3132192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.54 % (3132192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.54 % (3132192)CaDiCaL version: 2.1.3
% 1.54/0.54 % (3132192)Termination reason: Instruction limit
% 2.27/0.61 % (3132192)Termination phase: Saturation
% 2.27/0.61 % (3132192)Time elapsed: 0.003 s
% 2.27/0.61 % (3132192)Peak memory usage: 11 MB
% 2.27/0.61 % (3132192)Instructions burned: 7 (million)
% 2.27/0.61 % (3132191)Instruction limit reached!
% 2.27/0.61 % (3132191)------------------------------
% 2.27/0.61 % (3132191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132191)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132191)Termination reason: Instruction limit
% 2.27/0.61 % (3132191)Termination phase: Saturation
% 2.27/0.61 % (3132191)Time elapsed: 0.023 s
% 2.27/0.61 % (3132191)Peak memory usage: 12 MB
% 2.27/0.61 % (3132191)Instructions burned: 44 (million)
% 2.27/0.61 % (3132197)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3857552418:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 2.27/0.61 % (3132197)Refutation not found, incomplete strategy
% 2.27/0.61 % (3132197)------------------------------
% 2.27/0.61 % (3132197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132197)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132197)Termination reason: Refutation not found, incomplete strategy
% 2.27/0.61 % (3132197)Time elapsed: 0.004 s
% 2.27/0.61 % (3132197)Peak memory usage: 12 MB
% 2.27/0.61 % (3132197)Instructions burned: 5 (million)
% 2.27/0.61 % (3132198)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2321734910:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.27/0.61 % (3132197)------------------------------
% 2.27/0.61 % (3132197)------------------------------
% 2.27/0.61 % (3132198)Refutation not found, incomplete strategy
% 2.27/0.61 % (3132198)------------------------------
% 2.27/0.61 % (3132198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132198)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132198)Termination reason: Refutation not found, incomplete strategy
% 2.27/0.61 % (3132198)Time elapsed: 0.006 s
% 2.27/0.61 % (3132198)Peak memory usage: 12 MB
% 2.27/0.61 % (3132198)Instructions burned: 13 (million)
% 2.27/0.61 % (3132198)------------------------------
% 2.27/0.61 % (3132198)------------------------------
% 2.27/0.61 % (3132200)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.27/0.61 % (3132200)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2328741275:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.27/0.61 % (3132160)Instruction limit reached!
% 2.27/0.61 % (3132160)------------------------------
% 2.27/0.61 % (3132160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132160)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132160)Termination reason: Instruction limit
% 2.27/0.61 % (3132160)Termination phase: Saturation
% 2.27/0.61 % (3132160)Time elapsed: 0.122 s
% 2.27/0.61 % (3132160)Peak memory usage: 12 MB
% 2.27/0.61 % (3132160)Instructions burned: 329 (million)
% 2.27/0.61 % (3132200)Instruction limit reached!
% 2.27/0.61 % (3132200)------------------------------
% 2.27/0.61 % (3132200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132200)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132200)Termination reason: Instruction limit
% 2.27/0.61 % (3132200)Termination phase: Function definition elimination
% 2.27/0.61 % (3132200)Time elapsed: 0.003 s
% 2.27/0.61 % (3132200)Peak memory usage: 11 MB
% 2.27/0.61 % (3132200)Instructions burned: 6 (million)
% 2.27/0.61 % (3132202)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=251164041:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.27/0.61 % (3132203)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1285267761:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.27/0.61 % (3132202)Instruction limit reached!
% 2.27/0.61 % (3132202)------------------------------
% 2.27/0.61 % (3132202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132202)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132202)Termination reason: Instruction limit
% 2.27/0.61 % (3132202)Termination phase: Saturation
% 2.27/0.61 % (3132202)Time elapsed: 0.012 s
% 2.27/0.61 % (3132202)Peak memory usage: 12 MB
% 2.27/0.61 % (3132202)Instructions burned: 23 (million)
% 2.27/0.61 % (3132188)Instruction limit reached!
% 2.27/0.61 % (3132188)------------------------------
% 2.27/0.61 % (3132188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132188)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132188)Termination reason: Instruction limit
% 2.27/0.61 % (3132188)Termination phase: Saturation
% 2.27/0.61 % (3132188)Time elapsed: 0.069 s
% 2.27/0.61 % (3132188)Peak memory usage: 13 MB
% 2.27/0.61 % (3132188)Instructions burned: 145 (million)
% 2.27/0.61 % (3132203)Refutation not found, incomplete strategy
% 2.27/0.61 % (3132203)------------------------------
% 2.27/0.61 % (3132203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132203)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132203)Termination reason: Refutation not found, incomplete strategy
% 2.27/0.61 % (3132203)Time elapsed: 0.007 s
% 2.27/0.61 % (3132203)Peak memory usage: 12 MB
% 2.27/0.61 % (3132203)Instructions burned: 14 (million)
% 2.27/0.61 % (3132205)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4085884446:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.27/0.61 % (3132203)------------------------------
% 2.27/0.61 % (3132203)------------------------------
% 2.27/0.61 % (3132206)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=173080740:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.27/0.61 % (3132209)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2315576991:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.27/0.61 % (3132210)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2207704098:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.27/0.61 % (3132212)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2472738493:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2997 on theBenchmark for (2997ds/21Mi)
% 2.27/0.61 % (3132210)Refutation not found, incomplete strategy
% 2.27/0.61 % (3132210)------------------------------
% 2.27/0.61 % (3132210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132210)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132210)Termination reason: Refutation not found, incomplete strategy
% 2.27/0.61 % (3132210)Time elapsed: 0.004 s
% 2.27/0.61 % (3132210)Peak memory usage: 12 MB
% 2.27/0.61 % (3132210)Instructions burned: 7 (million)
% 2.27/0.61 % (3132210)------------------------------
% 2.27/0.61 % (3132210)------------------------------
% 2.27/0.61 % (3132212)Instruction limit reached!
% 2.27/0.61 % (3132212)------------------------------
% 2.27/0.61 % (3132212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132212)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132212)Termination reason: Instruction limit
% 2.27/0.61 % (3132212)Termination phase: Saturation
% 2.27/0.61 % (3132212)Time elapsed: 0.011 s
% 2.27/0.61 % (3132212)Peak memory usage: 12 MB
% 2.27/0.61 % (3132212)Instructions burned: 21 (million)
% 2.27/0.61 % (3132217)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.27/0.61 % (3132209)Instruction limit reached!
% 2.27/0.61 % (3132209)------------------------------
% 2.27/0.61 % (3132209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132209)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132209)Termination reason: Instruction limit
% 2.27/0.61 % (3132209)Termination phase: Saturation
% 2.27/0.61 % (3132209)Time elapsed: 0.024 s
% 2.27/0.61 % (3132209)Peak memory usage: 12 MB
% 2.27/0.61 % (3132209)Instructions burned: 46 (million)
% 2.27/0.61 % (3132217)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=204083337:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/200Mi)
% 2.27/0.61 % (3132218)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=98209776:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/13Mi)
% 2.27/0.61 % (3132219)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2420296969:i=66:s2at=3:nm=2:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/66Mi)
% 2.27/0.61 % (3132218)Instruction limit reached!
% 2.27/0.61 % (3132218)------------------------------
% 2.27/0.61 % (3132218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132218)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132218)Termination reason: Instruction limit
% 2.27/0.61 % (3132218)Termination phase: Saturation
% 2.27/0.61 % (3132218)Time elapsed: 0.008 s
% 2.27/0.61 % (3132218)Peak memory usage: 12 MB
% 2.27/0.61 % (3132218)Instructions burned: 13 (million)
% 2.27/0.61 % (3132223)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3904588494:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 2.27/0.61 % (3132223)Refutation not found, incomplete strategy
% 2.27/0.61 % (3132223)------------------------------
% 2.27/0.61 % (3132223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132223)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132223)Termination reason: Refutation not found, incomplete strategy
% 2.27/0.61 % (3132223)Time elapsed: 0.006 s
% 2.27/0.61 % (3132223)Peak memory usage: 12 MB
% 2.27/0.61 % (3132223)Instructions burned: 12 (million)
% 2.27/0.61 % (3132223)------------------------------
% 2.27/0.61 % (3132223)------------------------------
% 2.27/0.61 % (3132219)Instruction limit reached!
% 2.27/0.61 % (3132219)------------------------------
% 2.27/0.61 % (3132219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132219)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132219)Termination reason: Instruction limit
% 2.27/0.61 % (3132219)Termination phase: Saturation
% 2.27/0.61 % (3132219)Time elapsed: 0.031 s
% 2.27/0.61 % (3132219)Peak memory usage: 13 MB
% 2.27/0.61 % (3132219)Instructions burned: 67 (million)
% 2.27/0.61 % (3132205) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3132119-3132205"...
% 2.27/0.61 % (3132205)...printing done.
% 2.27/0.61 % (3132205)Refutation found. Thanks to Tanya!
% 2.27/0.61 % SZS status Theorem for theBenchmark
% 2.27/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 2.27/0.61 % (3132205)------------------------------
% 2.27/0.61 % (3132205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.27/0.61 % (3132205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/0.61 % (3132205)CaDiCaL version: 2.1.3
% 2.27/0.61 % (3132205)Termination reason: Refutation
% 2.27/0.61 % (3132205)Time elapsed: 0.103 s
% 2.27/0.61 % (3132205)Peak memory usage: 14 MB
% 2.27/0.61 % (3132205)Instructions burned: 207 (million)
% 2.27/0.61 % (3132119)Success in time 0.361 s
% 2.27/0.61 % Vampire exiting
%------------------------------------------------------------------------------