%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI004^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:20:20 AM UTC 2026
% Result : Theorem 0.98s 0.42s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 25
% Syntax : Number of formulae : 247 ( 86 unt; 0 typ; 11 def)
% Number of atoms : 1690 ( 327 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 2249 ( 240 ~; 314 |; 12 &;1449 @)
% ( 13 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 601 ( 601 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 19 con; 0-4 aty)
% ( 117 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 526 ( 10 sgn 110 !; 0 ?; 526 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_30,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vIFF: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK1: mu ).
thf(func_def_45,type,
sK2: mu > $i > $o ).
thf(func_def_46,type,
sK3: mu > $i > $o ).
thf(func_def_48,type,
sK5: mu ).
thf(func_def_49,type,
sK6: mu ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f6,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_ind) ).
thf(f12,axiom,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axA1) ).
thf(f24,axiom,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD1) ).
thf(f25,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] : ( mimplies @ ( positive @ X0 ) @ ( mbox @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA4) ).
thf(f26,axiom,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mand @ ( X0 @ X1 )
@ ( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD2) ).
thf(f27,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT2) ).
thf(f28,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f32,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f33,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f37,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f39,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f42,plain,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f43,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f46,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f47,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f49,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f58,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f59,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f63,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f67,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f69,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] : ( mimplies @ ( positive @ X0 ) @ ( mbox @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f71,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f72,plain,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mand @ ( X0 @ X1 )
@ ( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f73,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mand @ ( Y0 @ Y1 )
@ ( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f75,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f76,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(flattening,[],[f75]) ).
thf(f80,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f82,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f83,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f85,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f87,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f88,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f93,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f95,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f99,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f100,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f101,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f102,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mand @ ( Y0 @ Y1 )
@ ( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f103,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f106,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f95,f93]) ).
thf(f108,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,[],[f100,f88,f83]) ).
thf(f109,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( Y0 @ Y1 )
@ ( ^ [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 > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y4 @ Y6 ) ) )
@ rel
@ ( ^ [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,[],[f102,f82,f88,f83,f106,f87,f83]) ).
thf(f110,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,[],[f99,f97,f88,f85,f80,f80]) ).
thf(f111,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 @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ rel
@ ( positive @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f101,f97,f88,f83,f106]) ).
thf(f112,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( ^ [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 )
@ ( ^ [Y1: mu > $i > $o,Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( Y1 @ Y2 )
@ ( ^ [Y3: ( mu > $i > $o ) > $i > $o,Y4: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: mu > $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
=> ( Y5 @ Y6 ) )
@ ( Y3 @ Y2 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ rel
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y1 @ Y4 )
@ ( Y3 @ Y4 ) ) ) ) ) ) )
@ ^ [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 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f97,f87,f83,f108,f109,f108]) ).
thf(f113,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ 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 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( positive @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ 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 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( positive @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f120,plain,
! [X1: mu > $i > $o] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X1: mu > $i > $o] :
( $true
= ( ( positive @ X1 @ sK0 )
=> ( X1 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK0 ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f118]) ).
thf(f124,plain,
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) )
| ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( $false
= ( ( sK2 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f127]) ).
thf(f132,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f134,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f134]) ).
thf(f137,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) )
@ sK5 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f139,plain,
( ( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) ) )
=> ( sK2 @ sK5 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( $false
= ( sK2 @ sK5 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) )
@ X1 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ( positive @ X1 @ sK4 )
=> ( X1 @ sK5 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f146,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) )
@ sK6 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f150,plain,
( ( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) ) )
=> ( sK2 @ sK6 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( sK2 @ sK6 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) )
@ X1 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ( positive @ X1 @ sK4 )
=> ( X1 @ sK6 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ Y0 @ Y2 )
| ( positive @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ Y0 @ Y2 )
| ( positive @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( positive @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ X1 @ Y1 )
| ( positive @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( ~ ( rel @ X1 @ X3 )
| ( positive @ X2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( positive @ X2 @ X3 ) )
| ( $true
= ( ~ ( rel @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( positive @ X2 @ X3 ) )
| ( $false
= ( rel @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,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,[],[f110]) ).
thf(f167,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,[],[f166]) ).
thf(f168,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,[],[f167]) ).
thf(f169,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,[],[f168]) ).
thf(f170,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $false
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $true
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f171]) ).
thf(f174,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $true
= ( positive @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f177,definition,
( spl7_1
<=> ( $true
= ( positive @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f179,plain,
( ( $true
= ( positive @ sK3 @ sK0 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f181,definition,
( spl7_2
<=> ( $true
= ( sK2 @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f183,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f184,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f130,f181,f177]) ).
thf(f186,definition,
( spl7_3
<=> ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f188,plain,
( ( $false
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f189,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f129,f181,f186]) ).
thf(f191,definition,
( spl7_4
<=> ( $true
= ( rel @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f193,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f194,plain,
( spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f137,f191,f177]) ).
thf(f196,definition,
( spl7_5
<=> ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f197,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f198,plain,
( spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f144,f196,f177]) ).
thf(f200,definition,
( spl7_6
<=> ( $false
= ( sK2 @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f202,plain,
( ( $false
= ( sK2 @ sK5 @ sK4 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,plain,
( spl7_1
| spl7_6 ),
inference(avatar_split_clause,[],[f140,f200,f177]) ).
thf(f204,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f148,f191,f186]) ).
thf(f206,definition,
( spl7_7
<=> ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f207,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f208,plain,
( spl7_3
| spl7_7 ),
inference(avatar_split_clause,[],[f155,f206,f186]) ).
thf(f210,definition,
( spl7_8
<=> ( $false
= ( sK2 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f212,plain,
( ( $false
= ( sK2 @ sK6 @ sK4 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,plain,
( spl7_3
| spl7_8 ),
inference(avatar_split_clause,[],[f151,f210,f186]) ).
thf(f214,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f122,f179]) ).
thf(f221,plain,
( ( $true
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f214]) ).
thf(f225,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3 ),
inference(forward_demodulation,[],[f221,f188]) ).
thf(f226,plain,
( $false
| ~ spl7_1
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f227,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f226]) ).
thf(f258,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ sK0 ) )
| ( $true
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f193,f165]) ).
thf(f261,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( positive @ X0 @ sK0 ) ) )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f258]) ).
thf(f292,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( positive @ X0 @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f207,f261]) ).
thf(f293,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f302,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f165,f293]) ).
thf(f309,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f374,definition,
( spl7_9
<=> ( $false
= ( rel @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f375,plain,
( ( $false
!= ( rel @ sK0 @ sK0 ) )
| spl7_9 ),
inference(avatar_component_clause,[],[f374]) ).
thf(f376,plain,
( ( $false
= ( rel @ sK0 @ sK0 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f374]) ).
thf(f445,plain,
( ! [X2: $i,X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ X2 ) )
| ( $false
= ( rel @ X2 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f165,f309]) ).
thf(f454,plain,
( ! [X2: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X2 ) )
| ( $false
= ( rel @ X2 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f445]) ).
thf(f719,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK0 ) )
| ( $false
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f261,f174]) ).
thf(f720,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK0 ) )
| ( $false
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f719]) ).
thf(f1183,plain,
! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f122,f175]) ).
thf(f1185,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK6
@ sK4 ) )
| ( $true
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_7 ),
inference(constrained_superposition,[],[f207,f175]) ).
thf(f1186,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK6
@ sK4 ) )
| ( $true
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f1185]) ).
thf(f1187,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( ~ ( X0 @ sK6 @ sK4 ) ) )
| ( $true
= ( positive @ X0 @ sK4 ) ) )
| ~ spl7_7 ),
inference(beta-eta_normalization,[],[f1186]) ).
thf(f1188,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_7 ),
inference(not_proxy_clausification,[],[f1187]) ).
thf(f1190,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f1183]) ).
thf(f1191,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( ~ ( X0 @ sK1 @ sK0 ) ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f1190]) ).
thf(f1192,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK0 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f1191]) ).
thf(f1258,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( X0 @ sK1 @ sK0 ) )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f1192,f454]) ).
thf(f1279,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f720,f1192]) ).
thf(f1284,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f1279]) ).
thf(f1285,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ~ ( X0 @ sK1 @ sK0 ) ) ) )
| ~ spl7_4 ),
inference(beta-eta_normalization,[],[f1284]) ).
thf(f1286,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_4 ),
inference(not_proxy_clausification,[],[f1285]) ).
thf(f1313,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( X0 @ sK1 @ sK0 ) )
| ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f1258]) ).
thf(f1321,definition,
( spl7_13
<=> ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
thf(f1322,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f1321]) ).
thf(f1324,definition,
( spl7_14
<=> ! [X1: $i] :
( ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
thf(f1325,plain,
( ! [X1: $i] :
( ( $false
= ( rel @ sK0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK0 ) ) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f1324]) ).
thf(f1333,plain,
( spl7_14
| spl7_13
| ~ spl7_4
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f1313,f206,f191,f1321,f1324]) ).
thf(f1424,plain,
( ! [X0: mu > $i > mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK6
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(constrained_superposition,[],[f212,f1322]) ).
thf(f1439,plain,
( ! [X0: mu > $i > mu] :
( ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK6
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f1424]) ).
thf(f1440,plain,
( ! [X0: mu > $i > mu] :
( ( sK6
!= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( sK2 @ ( X0 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(beta-eta_normalization,[],[f1439]) ).
thf(f2262,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f175,f1286]) ).
thf(f2269,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( X0 @ sK6 @ sK4 ) )
| ( $true
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f1188,f1286]) ).
thf(f2278,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( X0 @ sK6 @ sK4 ) )
| ( $true
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f2269]) ).
thf(f2289,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f2262]) ).
thf(f2290,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ~ ( X0 @ sK1 @ sK0 ) ) ) )
| ~ spl7_4 ),
inference(beta-eta_normalization,[],[f2289]) ).
thf(f2291,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_4 ),
inference(not_proxy_clausification,[],[f2290]) ).
thf(f2504,plain,
( ( $false
= ( sK2
@ ( ^ [Y0: mu,Y1: $i] : Y0
@ sK1
@ sK0 )
@ sK0 ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(equality_resolution,[],[f1440]) ).
thf(f2507,plain,
( ( $false
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(beta-eta_normalization,[],[f2504]) ).
thf(f2521,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(constrained_superposition,[],[f2507,f183]) ).
thf(f2538,plain,
( $false
| ~ spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f2521]) ).
thf(f2539,plain,
( ~ spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f2538]) ).
thf(f3029,plain,
( ! [X0: mu > $i > $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
( rel @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK0
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f193,f2278]) ).
thf(f3079,plain,
( ! [X0: mu > $i > $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
( rel @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK0
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f3029]) ).
thf(f3080,plain,
( ! [X0: mu > $i > $i] :
( ( sK0
!= ( X0 @ sK6 @ sK4 ) )
| ( $true
= ( rel @ ( X0 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(beta-eta_normalization,[],[f3079]) ).
thf(f3666,plain,
( ( $true
= ( rel
@ ( ^ [Y0: mu,Y1: $i] : sK0
@ sK1
@ sK0 )
@ sK0 ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(equality_resolution,[],[f3080]) ).
thf(f3667,plain,
( ( $true
= ( rel @ sK0 @ sK0 ) )
| ~ spl7_4
| ~ spl7_7 ),
inference(beta-eta_normalization,[],[f3666]) ).
thf(f3668,plain,
( ( $true = $false )
| ~ spl7_4
| ~ spl7_7
| ~ spl7_9 ),
inference(forward_demodulation,[],[f3667,f376]) ).
thf(f3669,plain,
( $false
| ~ spl7_4
| ~ spl7_7
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f3668]) ).
thf(f3670,plain,
( ~ spl7_4
| ~ spl7_7
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f3669]) ).
thf(f3681,plain,
( ( $false != $false )
| ( $false
= ( rel @ sK0 @ sK0 ) )
| spl7_9
| ~ spl7_14 ),
inference(constrained_superposition,[],[f375,f1325]) ).
thf(f3724,plain,
( ( $false
= ( rel @ sK0 @ sK0 ) )
| spl7_9
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f3681]) ).
thf(f3727,plain,
( $false
| spl7_9
| ~ spl7_14 ),
inference(forward_subsumption_resolution,[],[f3724,f375]) ).
thf(f3728,plain,
( spl7_9
| ~ spl7_14 ),
inference(avatar_contradiction_clause,[],[f3727]) ).
thf(f3854,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( X0 @ sK1 @ sK0 ) )
| ( $true
= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_5 ),
inference(constrained_superposition,[],[f2291,f197]) ).
thf(f3861,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK5 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f3854]) ).
thf(f3943,plain,
( ! [X0: mu > $i > mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK5
!= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(constrained_superposition,[],[f202,f3861]) ).
thf(f3956,plain,
( ! [X0: mu > $i > mu] :
( ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK5
!= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f3943]) ).
thf(f3957,plain,
( ! [X0: mu > $i > mu] :
( ( sK5
!= ( X0 @ sK5 @ sK4 ) )
| ( $false
= ( sK2 @ ( X0 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(beta-eta_normalization,[],[f3956]) ).
thf(f4871,plain,
( ( $false
= ( sK2
@ ( ^ [Y0: mu,Y1: $i] : Y0
@ sK1
@ sK0 )
@ sK0 ) )
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(equality_resolution,[],[f3957]) ).
thf(f4874,plain,
( ( $false
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(beta-eta_normalization,[],[f4871]) ).
thf(f4888,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(constrained_superposition,[],[f4874,f183]) ).
thf(f4905,plain,
( $false
| ~ spl7_2
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f4888]) ).
thf(f4906,plain,
( ~ spl7_2
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f4905]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f189]) ).
cnf(s3,plain,
( spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f194]) ).
cnf(s4,plain,
( spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f198]) ).
cnf(s5,plain,
( spl7_1
| spl7_6 ),
inference(sat_conversion,[],[f203]) ).
cnf(s6,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f204]) ).
cnf(s7,plain,
( spl7_3
| spl7_7 ),
inference(sat_conversion,[],[f208]) ).
cnf(s8,plain,
( spl7_3
| spl7_8 ),
inference(sat_conversion,[],[f213]) ).
cnf(s10,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(sat_conversion,[],[f227]) ).
cnf(s19,plain,
( ~ spl7_4
| ~ spl7_7
| spl7_13
| spl7_14 ),
inference(sat_conversion,[],[f1333]) ).
cnf(s22,plain,
( ~ spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(sat_conversion,[],[f2539]) ).
cnf(s33,plain,
( ~ spl7_4
| ~ spl7_7
| ~ spl7_9 ),
inference(sat_conversion,[],[f3670]) ).
cnf(s39,plain,
( spl7_9
| ~ spl7_14 ),
inference(sat_conversion,[],[f3728]) ).
cnf(s62,plain,
( ~ spl7_2
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f4906]) ).
cnf(s63,plain,
spl7_1,
inference(rat,[],[s62,s1,s3,s4,s5]) ).
cnf(s64,plain,
~ spl7_3,
inference(rat,[],[s10,s63]) ).
cnf(s65,plain,
spl7_8,
inference(rat,[],[s8,s64]) ).
cnf(s66,plain,
spl7_7,
inference(rat,[],[s7,s64]) ).
cnf(s67,plain,
spl7_4,
inference(rat,[],[s6,s64]) ).
cnf(s68,plain,
spl7_2,
inference(rat,[],[s2,s64]) ).
cnf(s69,plain,
~ spl7_9,
inference(rat,[],[s33,s66,s67]) ).
cnf(s70,plain,
~ spl7_13,
inference(rat,[],[s22,s65,s68]) ).
cnf(s71,plain,
~ spl7_14,
inference(rat,[],[s39,s69]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s19,s67,s66,s71,s70]) ).
thf(f4907,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:19:41 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.98/0.42 % (51595)Will run a generic schedule for satisfiability detection.
% 0.98/0.42 % (51600)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1443104222_2999 on theBenchmark for (2999ds/0Mi)
% 0.98/0.42 % Exception at run slice level
% 0.98/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.98/0.42 % (51601)% WARNING: option uhcvi not known.
% 0.98/0.42 % (51601)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3600348580:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.98/0.42 % (51602)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=156520754:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.98/0.42 % (51603)dis+10_1_sil=32000:sp=arity:random_seed=2288232266:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.98/0.42 % (51604)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1618092413:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.98/0.42 % (51606)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1489328960:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.98/0.42 % (51605)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1804407575:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.42 % (51601)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.98/0.42 % (51604)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.98/0.42 % (51601)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.98/0.42 % (51608)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=230482782:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.98/0.42 % Exception at run slice level
% 0.98/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.98/0.42 % (51616)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1839802086:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.42 % (51603)Instruction limit reached!
% 0.98/0.42 % (51603)------------------------------
% 0.98/0.42 % (51603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51603)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51603)Termination reason: Instruction limit
% 0.98/0.42 % (51603)Termination phase: Saturation
% 0.98/0.42 % (51603)Time elapsed: 0.049 s
% 0.98/0.42 % (51603)Peak memory usage: 12 MB
% 0.98/0.42 % (51603)Instructions burned: 103 (million)
% 0.98/0.42 % (51616)Instruction limit reached!
% 0.98/0.42 % (51616)------------------------------
% 0.98/0.42 % (51616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51616)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51616)Termination reason: Instruction limit
% 0.98/0.42 % (51616)Termination phase: Saturation
% 0.98/0.42 % (51616)Time elapsed: 0.034 s
% 0.98/0.42 % (51616)Peak memory usage: 12 MB
% 0.98/0.42 % (51616)Instructions burned: 134 (million)
% 0.98/0.42 % (51604)Instruction limit reached!
% 0.98/0.42 % (51604)------------------------------
% 0.98/0.42 % (51604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51604)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51604)Termination reason: Instruction limit
% 0.98/0.42 % (51604)Termination phase: Saturation
% 0.98/0.42 % (51604)Time elapsed: 0.055 s
% 0.98/0.42 % (51604)Peak memory usage: 12 MB
% 0.98/0.42 % (51604)Instructions burned: 116 (million)
% 0.98/0.42 % (51618)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1727941322:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.98/0.42 % (51618)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.98/0.42 % (51618)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.98/0.42 % (51605)Instruction limit reached!
% 0.98/0.42 % (51605)------------------------------
% 0.98/0.42 % (51605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51605)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51605)Termination reason: Instruction limit
% 0.98/0.42 % (51605)Termination phase: Saturation
% 0.98/0.42 % (51605)Time elapsed: 0.064 s
% 0.98/0.42 % (51605)Peak memory usage: 12 MB
% 0.98/0.42 % (51605)Instructions burned: 132 (million)
% 0.98/0.42 % (51619)ott-21_1_sil=16000:fs=off:random_seed=2297400774:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.98/0.42 % (51620)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3623612392:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.98/0.42 % (51606)Instruction limit reached!
% 0.98/0.42 % (51606)------------------------------
% 0.98/0.42 % (51606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51606)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51606)Termination reason: Instruction limit
% 0.98/0.42 % (51606)Termination phase: Saturation
% 0.98/0.42 % (51606)Time elapsed: 0.077 s
% 0.98/0.42 % (51606)Peak memory usage: 12 MB
% 0.98/0.42 % (51606)Instructions burned: 160 (million)
% 0.98/0.42 % (51622)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1359895147:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.98/0.42 % Exception at run slice level
% 0.98/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.98/0.42 % (51625)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=77268396:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.98/0.42 % (51627)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3956697293:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.98/0.42 % Exception at run slice level
% 0.98/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.98/0.42 % (51630)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=483281780:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.98/0.42 % (51630)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.98/0.42 % (51619)Instruction limit reached!
% 0.98/0.42 % (51619)------------------------------
% 0.98/0.42 % (51619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51619)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51619)Termination reason: Instruction limit
% 0.98/0.42 % (51619)Termination phase: Saturation
% 0.98/0.42 % (51619)Time elapsed: 0.082 s
% 0.98/0.42 % (51619)Peak memory usage: 12 MB
% 0.98/0.42 % (51619)Instructions burned: 181 (million)
% 0.98/0.42 % (51618) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-51595-51618"...
% 0.98/0.42 % (51618)...printing done.
% 0.98/0.42 % (51618)Refutation found. Thanks to Tanya!
% 0.98/0.42 % SZS status Theorem for theBenchmark
% 0.98/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.98/0.42 % (51618)------------------------------
% 0.98/0.42 % (51618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.42 % (51618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.42 % (51618)CaDiCaL version: 2.1.3
% 0.98/0.42 % (51618)Termination reason: Refutation
% 0.98/0.42 % (51618)Time elapsed: 0.103 s
% 0.98/0.42 % (51618)Peak memory usage: 14 MB
% 0.98/0.42 % (51618)Instructions burned: 418 (million)
% 0.98/0.42 % (51595)Success in time 0.199 s
% 0.98/0.42 % Vampire exiting
%------------------------------------------------------------------------------