%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI006^4 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:20:18 AM UTC 2026
% Result : ContradictoryAxioms 1.44s 0.50s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 13
% Syntax : Number of formulae : 106 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 768 ( 156 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 2001 ( 48 ~; 57 |; 13 &;1517 @)
% ( 0 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 635 ( 635 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 52 usr; 4 con; 0-4 aty)
% ( 203 !!; 34 ??; 0 @@+; 0 @@-)
% Number of variables : 698 ( 569 ^; 127 !; 2 ?; 698 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_22,type,
god: mu > $i > $o ).
thf(func_def_23,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_24,type,
necessary_existence: mu > $i > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vAND: $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,
vNOT: $o > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vIFF: $o > $o > $o ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
sK0: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_43,type,
sK1: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_44,type,
sK2: ( mu > $i > $o ) > ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_45,type,
sK3: $i > ( mu > $i > $o ) > mu ).
thf(func_def_46,type,
sK4: $i > ( mu > $i > $o ) > mu ).
thf(func_def_47,type,
sK5: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_48,type,
sK6: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_49,type,
sK7: ( mu > $i > $o ) > ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_50,type,
sK8: $i > ( mu > $i > $o ) > mu ).
thf(func_def_51,type,
sK9: $i > ( mu > $i > $o ) > mu ).
thf(func_def_52,type,
sK10: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_53,type,
sK11: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mnot) ).
thf(f6,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mand) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.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/LCL017^0.ax',mforall_indset) ).
thf(f14,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mexists_ind) ).
thf(f17,axiom,
( mbox
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] : ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mbox) ).
thf(f19,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL017^0.ax',mvalid) ).
thf(f21,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1a) ).
thf(f23,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA2) ).
thf(f27,axiom,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD2) ).
thf(f28,axiom,
( necessary_existence
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD3) ).
thf(f29,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5) ).
thf(f40,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f7]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f19]) ).
thf(f45,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mbox
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] : ( X0 @ X2 ) ) ),
inference(rectify,[],[f17]) ).
thf(f47,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f54,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f55,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ X0 )
@ ( mbox
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) ) )
@ ( positive @ X1 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f57,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,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) )
= mexists_ind ),
inference(rectify,[],[f14]) ).
thf(f59,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f67,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f69,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f73,plain,
mvalid @ ( positive @ necessary_existence ),
inference(rectify,[],[f29]) ).
thf(f74,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(fool_elimination,[],[f73]) ).
thf(f78,plain,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f79,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f81,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f83,plain,
( necessary_existence
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f89,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f90,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f92,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f94,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f95,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f97,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f98,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f99,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f101,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f102,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f105,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( mforall_indset
@ ^ [Y2: mu > $i > $o] :
( mimplies @ ( Y2 @ Y1 )
@ ( mbox
@ ( mforall_ind
@ ^ [Y3: mu] : ( mimplies @ ( Y0 @ Y3 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f111,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,[],[f57]) ).
thf(f113,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f119,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y2 @ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 ) )
@ ( ^ [Y3: mu > $i > $o,Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
=> ( Y5 @ Y6 ) )
@ ( Y0 @ Y3 )
@ ( Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f105,f95,f113,f99,f94,f113]) ).
thf(f120,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: mu] :
( ^ [Y4: ( mu > $i > $o ) > $i > $o,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y6: mu > $i > $o] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu > $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y4 @ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] : ( Y5 @ Y7 ) )
@ ( ^ [Y5: mu > $i > $o,Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] : ( Y5 @ Y7 @ Y6 ) )
@ ^ [Y5: mu] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
=> ( Y7 @ Y8 ) )
@ ( Y2 @ Y5 )
@ ( Y4 @ Y5 ) ) ) ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f102,f95,f113,f119,f99,f101]) ).
thf(f121,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: $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 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f89,f90,f95,f113,f92,f92]) ).
thf(f122,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 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: mu] :
( ^ [Y4: ( mu > $i > $o ) > $i > $o,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y6: mu > $i > $o] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu > $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y4 @ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] : ( Y5 @ Y7 ) )
@ ( ^ [Y5: mu > $i > $o,Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] : ( Y5 @ Y7 @ Y6 ) )
@ ^ [Y5: mu] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
=> ( Y7 @ Y8 ) )
@ ( Y2 @ Y5 )
@ ( Y4 @ Y5 ) ) ) ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f97,f90,f120]) ).
thf(f126,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( positive @ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y0 @ Y2 )
@ ( Y1 @ Y2 ) ) ) ) )
@ ( positive @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f111,f90,f95,f95,f113,f98,f99,f94,f113]) ).
thf(f127,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( positive @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( positive @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( ( positive @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( positive @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X1: $i] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( positive @ Y0 @ X1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( positive @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ( positive @ Y0 @ X1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( positive @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( positive @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( positive @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
=> ( positive @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X3 @ X1 ) )
| ( ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X3 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) )
@ ( sK0 @ X3 @ X2 ) )
= $false )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK0 @ X3 @ X2 ) )
=> ( X3 @ Y0 @ ( sK0 @ X3 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK0 @ X3 @ X2 ) )
=> ( X3 @ Y0 @ ( sK0 @ X3 @ X2 ) ) )
@ ( sK1 @ X3 @ X2 ) )
= $false )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ( X2 @ ( sK1 @ X3 @ X2 ) @ ( sK0 @ X3 @ X2 ) )
=> ( X3 @ ( sK1 @ X3 @ X2 ) @ ( sK0 @ X3 @ X2 ) ) ) )
| ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( positive @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( X3 @ ( sK1 @ X3 @ X2 ) @ ( sK0 @ X3 @ X2 ) ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f149,plain,
( ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f158,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,[],[f121]) ).
thf(f159,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,[],[f158]) ).
thf(f160,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,[],[f159]) ).
thf(f161,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
=> ~ ( positive @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
=> ~ ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $true
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,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,[],[f163]) ).
thf(f187,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 ) ) )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(superposition,[],[f164,f140]) ).
thf(f190,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f191,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( ~ ( X2
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 ) ) ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( ( X2
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X0 ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f283,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y0
@ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y0
@ Y1 )
@ X0 ) )
= $true ) ),
inference(superposition,[],[f192,f150]) ).
thf(f312,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y0
@ Y1 )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y0
@ Y1 )
@ X0 ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f313,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1
@ ( sK1
@ ^ [Y2: mu,Y3: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y2: mu,Y3: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f312]) ).
thf(f314,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1
@ ( sK1
@ ^ [Y2: mu,Y3: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y2: mu,Y3: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( Y5 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ?? @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $true
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK1
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK1
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( ( ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK1
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ( sK7 @ X0 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( ( ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK1
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y1: mu,Y2: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( Y4 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ?? @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ( sK7 @ X0 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( ( sK7 @ X0 @ X2
@ ( sK1
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 )
@ ( sK0
@ ^ [Y0: mu,Y1: $i] :
~ ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ X0 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( sK7 @ X0 @ X2 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( ?? @ mu
@ ^ [Y0: mu] : ( X2 @ Y0 @ X3 ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f320,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( ( ?? @ mu
@ ^ [Y0: mu] : ( X2 @ Y0 @ X3 ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( sK7 @ X0 @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f324,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( sK7 @ X0 @ X2 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( ( ^ [Y0: mu] : ( X2 @ Y0 @ X3 )
@ ( sK9 @ X3 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f320]) ).
thf(f325,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( sK7 @ X0 @ X2 @ Y1 @ Y0 ) ) )
@ ( sK10 @ X0 @ X2 ) ) )
| ( ( ^ [Y0: mu] : ( X2 @ Y0 @ X3 )
@ ( sK9 @ X3 @ X2 ) )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK9 @ X3 @ X2 ) @ X3 ) )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK10 @ X0 @ X2 ) )
=> ( sK7 @ X0 @ X2 @ Y0 @ ( sK10 @ X0 @ X2 ) ) ) )
= $false )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f325]) ).
thf(f327,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK10 @ X0 @ X2 ) )
=> ( sK7 @ X0 @ X2 @ Y0 @ ( sK10 @ X0 @ X2 ) ) )
@ ( sK11 @ X0 @ X2 ) ) )
| ( $true
= ( X2 @ ( sK9 @ X3 @ X2 ) @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $false
= ( ( X2 @ ( sK11 @ X0 @ X2 ) @ ( sK10 @ X0 @ X2 ) )
=> ( sK7 @ X0 @ X2 @ ( sK11 @ X0 @ X2 ) @ ( sK10 @ X0 @ X2 ) ) ) )
| ( $true
= ( X2 @ ( sK9 @ X3 @ X2 ) @ X3 ) )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f327]) ).
thf(f330,plain,
! [X2: mu > $i > $o,X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK11 @ X0 @ X2 ) @ ( sK10 @ X0 @ X2 ) ) )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $true
= ( X2 @ ( sK9 @ X3 @ X2 ) @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f359,plain,
! [X3: $i,X0: mu > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK11 @ X0
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK10 @ X0
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK9 @ X3
@ ^ [Y0: mu,Y1: $i] : $false )
@ X3 ) )
| ( $false
= ( positive @ X0 @ X1 ) ) ),
inference(primitive_instantiation,[],[f330]) ).
thf(f363,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false = $true )
| ( $false = $true ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f364,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f363]) ).
thf(f365,plain,
! [X0: mu > $i > $o,X1: $i] :
( $false
= ( positive @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f382,plain,
$false = $true,
inference(superposition,[],[f150,f365]) ).
thf(f385,plain,
$false,
inference(trivial_inequality_removal,[],[f382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI006^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.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 13:15:08 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.35 % (308580)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (308591)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (308591)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
% 0.20/0.35 % (308591)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=826939007:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (308591)Refutation not found, incomplete strategy
% 0.20/0.35 % (308591)------------------------------
% 0.20/0.35 % (308591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (308591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (308591)CaDiCaL version: 2.1.3
% 0.20/0.35 % (308591)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.35 % (308591)Time elapsed: 0.004 s
% 0.20/0.35 % (308591)Peak memory usage: 12 MB
% 0.20/0.35 % (308591)Instructions burned: 14 (million)
% 0.20/0.35 % (308591)------------------------------
% 0.20/0.35 % (308591)------------------------------
% 0.20/0.35 % (308587)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1809976385:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (308585)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3817485870:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (308586)lrs+10_16_si=on:nwc=1.5:random_seed=2793214943:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (308590)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=771875358:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (308589)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=874419348:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (308588)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=3761193285: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)
% 0.20/0.35 % (308587)Instruction limit reached!
% 0.20/0.35 % (308587)------------------------------
% 0.20/0.35 % (308587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (308587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (308587)CaDiCaL version: 2.1.3
% 0.20/0.35 % (308587)Termination reason: Instruction limit
% 0.20/0.35 % (308587)Termination phase: Function definition elimination
% 0.20/0.35 % (308587)Time elapsed: 0.002 s
% 0.20/0.35 % (308587)Peak memory usage: 10 MB
% 0.20/0.35 % (308587)Instructions burned: 4 (million)
% 0.20/0.35 % (308593)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1887004822:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (308586)Instruction limit reached!
% 0.20/0.35 % (308586)------------------------------
% 0.20/0.35 % (308586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (308586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (308586)CaDiCaL version: 2.1.3
% 0.20/0.35 % (308586)Termination reason: Instruction limit
% 0.20/0.35 % (308586)Termination phase: Saturation
% 0.20/0.35 % (308586)Time elapsed: 0.009 s
% 0.20/0.35 % (308586)Peak memory usage: 12 MB
% 0.20/0.35 % (308586)Instructions burned: 18 (million)
% 0.20/0.35 % (308593)Instruction limit reached!
% 0.20/0.35 % (308593)------------------------------
% 0.20/0.35 % (308593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (308593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (308593)CaDiCaL version: 2.1.3
% 0.20/0.35 % (308593)Termination reason: Instruction limit
% 0.20/0.35 % (308593)Termination phase: Property scanning
% 0.20/0.35 % (308593)Time elapsed: 0.001 s
% 0.20/0.35 % (308593)Peak memory usage: 10 MB
% 0.20/0.35 % (308593)Instructions burned: 4 (million)
% 0.20/0.35 % (308589)Instruction limit reached!
% 0.20/0.35 % (308589)------------------------------
% 0.74/0.37 % (308589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (308589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (308589)CaDiCaL version: 2.1.3
% 0.74/0.37 % (308589)Termination reason: Instruction limit
% 0.74/0.37 % (308589)Termination phase: Saturation
% 0.74/0.37 % (308589)Time elapsed: 0.014 s
% 0.74/0.37 % (308589)Peak memory usage: 11 MB
% 0.74/0.37 % (308589)Instructions burned: 24 (million)
% 0.74/0.37 % (308602)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.37 % (308602)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1374239120:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.37 % (308600)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=870506256:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.37 % (308602)Instruction limit reached!
% 0.74/0.37 % (308602)------------------------------
% 0.74/0.37 % (308602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (308602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (308602)CaDiCaL version: 2.1.3
% 0.74/0.37 % (308602)Termination reason: Instruction limit
% 0.74/0.37 % (308602)Termination phase: Saturation
% 0.74/0.37 % (308602)Time elapsed: 0.002 s
% 0.74/0.37 % (308602)Peak memory usage: 11 MB
% 0.74/0.37 % (308602)Instructions burned: 9 (million)
% 0.74/0.37 % (308600)Instruction limit reached!
% 0.74/0.37 % (308600)------------------------------
% 0.74/0.37 % (308600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (308600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (308600)CaDiCaL version: 2.1.3
% 0.74/0.37 % (308600)Termination reason: Instruction limit
% 0.74/0.37 % (308600)Termination phase: Saturation
% 0.74/0.37 % (308600)Time elapsed: 0.003 s
% 0.74/0.37 % (308600)Peak memory usage: 10 MB
% 0.74/0.37 % (308600)Instructions burned: 6 (million)
% 0.74/0.37 % (308603)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=951737117:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.37 % (308604)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
% 0.74/0.37 % (308604)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.37 % (308604)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1910289189:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.37 % (308607)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=830489795:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.37 % (308603)Instruction limit reached!
% 0.74/0.37 % (308603)------------------------------
% 0.74/0.37 % (308603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (308603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (308603)CaDiCaL version: 2.1.3
% 0.74/0.37 % (308603)Termination reason: Instruction limit
% 0.74/0.37 % (308603)Termination phase: Saturation
% 0.74/0.37 % (308603)Time elapsed: 0.006 s
% 0.74/0.37 % (308603)Peak memory usage: 12 MB
% 0.74/0.37 % (308603)Instructions burned: 13 (million)
% 0.74/0.37 % (308590)Instruction limit reached!
% 0.74/0.37 % (308590)------------------------------
% 0.74/0.37 % (308590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (308590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (308590)CaDiCaL version: 2.1.3
% 0.74/0.37 % (308590)Termination reason: Instruction limit
% 0.74/0.37 % (308590)Termination phase: Saturation
% 0.74/0.37 % (308590)Time elapsed: 0.038 s
% 0.74/0.37 % (308590)Peak memory usage: 12 MB
% 0.74/0.37 % (308590)Instructions burned: 75 (million)
% 0.74/0.37 % (308608)lrs+10_1_si=on:cs=on:random_seed=3793620062:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.37 % (308585)Instruction limit reached!
% 0.74/0.39 % (308585)------------------------------
% 0.74/0.39 % (308585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308585)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308585)Termination reason: Instruction limit
% 0.74/0.39 % (308585)Termination phase: Saturation
% 0.74/0.39 % (308585)Time elapsed: 0.043 s
% 0.74/0.39 % (308585)Peak memory usage: 12 MB
% 0.74/0.39 % (308585)Instructions burned: 89 (million)
% 0.74/0.39 % (308608)Instruction limit reached!
% 0.74/0.39 % (308608)------------------------------
% 0.74/0.39 % (308608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308608)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308608)Termination reason: Instruction limit
% 0.74/0.39 % (308608)Termination phase: Saturation
% 0.74/0.39 % (308608)Time elapsed: 0.008 s
% 0.74/0.39 % (308608)Peak memory usage: 11 MB
% 0.74/0.39 % (308608)Instructions burned: 14 (million)
% 0.74/0.39 % (308604)Instruction limit reached!
% 0.74/0.39 % (308604)------------------------------
% 0.74/0.39 % (308604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308604)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308604)Termination reason: Instruction limit
% 0.74/0.39 % (308604)Termination phase: Saturation
% 0.74/0.39 % (308604)Time elapsed: 0.017 s
% 0.74/0.39 % (308604)Peak memory usage: 12 MB
% 0.74/0.39 % (308604)Instructions burned: 34 (million)
% 0.74/0.39 % (308612)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.39 % (308612)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=4056348241:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.39 % (308613)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3857040438:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.39 % (308607)Instruction limit reached!
% 0.74/0.39 % (308607)------------------------------
% 0.74/0.39 % (308607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308607)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308607)Termination reason: Instruction limit
% 0.74/0.39 % (308607)Termination phase: Saturation
% 0.74/0.39 % (308607)Time elapsed: 0.024 s
% 0.74/0.39 % (308607)Peak memory usage: 12 MB
% 0.74/0.39 % (308607)Instructions burned: 89 (million)
% 0.74/0.39 % (308612)Instruction limit reached!
% 0.74/0.39 % (308612)------------------------------
% 0.74/0.39 % (308612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308612)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308612)Termination reason: Instruction limit
% 0.74/0.39 % (308612)Termination phase: Property scanning
% 0.74/0.39 % (308612)Time elapsed: 0.002 s
% 0.74/0.39 % (308612)Peak memory usage: 10 MB
% 0.74/0.39 % (308612)Instructions burned: 5 (million)
% 0.74/0.39 % (308613)Refutation not found, incomplete strategy
% 0.74/0.39 % (308613)------------------------------
% 0.74/0.39 % (308613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (308613)CaDiCaL version: 2.1.3
% 0.74/0.39 % (308613)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.39 % (308613)Time elapsed: 0.002 s
% 0.74/0.39 % (308613)Peak memory usage: 11 MB
% 0.74/0.39 % (308613)Instructions burned: 3 (million)
% 0.74/0.39 % (308613)------------------------------
% 0.74/0.39 % (308613)------------------------------
% 0.74/0.39 % (308615)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2810724028:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.39 % (308615)Refutation not found, incomplete strategy
% 0.74/0.39 % (308615)------------------------------
% 0.74/0.39 % (308615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (308615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308615)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308615)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.42 % (308615)Time elapsed: 0.002 s
% 0.74/0.42 % (308615)Peak memory usage: 11 MB
% 0.74/0.42 % (308615)Instructions burned: 4 (million)
% 0.74/0.42 % (308615)------------------------------
% 0.74/0.42 % (308615)------------------------------
% 0.74/0.42 % (308620)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3751003686:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.74/0.42 % (308620)Refutation not found, incomplete strategy
% 0.74/0.42 % (308620)------------------------------
% 0.74/0.42 % (308620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.42 % (308620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308620)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308620)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.42 % (308620)Time elapsed: 0.001 s
% 0.74/0.42 % (308620)Peak memory usage: 12 MB
% 0.74/0.42 % (308620)Instructions burned: 4 (million)
% 0.74/0.42 % (308620)------------------------------
% 0.74/0.42 % (308620)------------------------------
% 0.74/0.42 % (308617)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=652436763:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.74/0.42 % (308616)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2049878808:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.74/0.42 % (308616)Refutation not found, incomplete strategy
% 0.74/0.42 % (308616)------------------------------
% 0.74/0.42 % (308616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.42 % (308616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308616)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308616)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.42 % (308616)Time elapsed: 0.002 s
% 0.74/0.42 % (308616)Peak memory usage: 11 MB
% 0.74/0.42 % (308616)Instructions burned: 4 (million)
% 0.74/0.42 % (308616)------------------------------
% 0.74/0.42 % (308616)------------------------------
% 0.74/0.42 % (308621)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2155109632:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.42 % (308617)Instruction limit reached!
% 0.74/0.42 % (308617)------------------------------
% 0.74/0.42 % (308617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.42 % (308617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308617)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308617)Termination reason: Instruction limit
% 0.74/0.42 % (308617)Termination phase: Saturation
% 0.74/0.42 % (308617)Time elapsed: 0.007 s
% 0.74/0.42 % (308617)Peak memory usage: 12 MB
% 0.74/0.42 % (308617)Instructions burned: 14 (million)
% 0.74/0.42 % (308622)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2616244445:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.74/0.42 % (308626)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1096455764:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.74/0.42 % (308622)Instruction limit reached!
% 0.74/0.42 % (308622)------------------------------
% 0.74/0.42 % (308622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.42 % (308622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308622)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308622)Termination reason: Instruction limit
% 0.74/0.42 % (308622)Time elapsed: 0.002 s
% 0.74/0.42 % (308622)Peak memory usage: 11 MB
% 0.74/0.42 % (308622)Instructions burned: 3 (million)
% 0.74/0.42 % (308621)Instruction limit reached!
% 0.74/0.42 % (308621)------------------------------
% 0.74/0.42 % (308621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.42 % (308621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.42 % (308621)CaDiCaL version: 2.1.3
% 0.74/0.42 % (308621)Termination reason: Instruction limit
% 0.74/0.42 % (308621)Termination phase: Saturation
% 0.74/0.42 % (308621)Time elapsed: 0.007 s
% 0.74/0.42 % (308621)Peak memory usage: 12 MB
% 0.74/0.42 % (308621)Instructions burned: 14 (million)
% 0.74/0.42 % (308624)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1116599121:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.74/0.45 % (308626)Instruction limit reached!
% 0.74/0.45 % (308626)------------------------------
% 0.74/0.45 % (308626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.45 % (308626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.45 % (308626)CaDiCaL version: 2.1.3
% 0.74/0.45 % (308626)Termination reason: Instruction limit
% 0.74/0.45 % (308626)Termination phase: Saturation
% 0.74/0.45 % (308626)Time elapsed: 0.007 s
% 0.74/0.45 % (308626)Peak memory usage: 12 MB
% 0.74/0.45 % (308626)Instructions burned: 25 (million)
% 0.74/0.45 % (308632)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
% 0.74/0.45 % (308632)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.74/0.45 % (308629)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=342714276:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.74/0.45 % (308634)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.74/0.45 % (308637)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=296165292:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.74/0.45 % (308632)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=1869082260:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.45 % (308637)Instruction limit reached!
% 0.74/0.45 % (308637)------------------------------
% 0.74/0.45 % (308637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.45 % (308637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.45 % (308637)CaDiCaL version: 2.1.3
% 0.74/0.45 % (308637)Termination reason: Instruction limit
% 0.74/0.45 % (308637)Termination phase: Saturation
% 0.74/0.45 % (308637)Time elapsed: 0.002 s
% 0.74/0.45 % (308637)Peak memory usage: 11 MB
% 0.74/0.45 % (308637)Instructions burned: 8 (million)
% 0.74/0.45 % (308624)Instruction limit reached!
% 0.74/0.45 % (308624)------------------------------
% 0.74/0.45 % (308624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.45 % (308624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.45 % (308624)CaDiCaL version: 2.1.3
% 0.74/0.45 % (308624)Termination reason: Instruction limit
% 0.74/0.45 % (308624)Termination phase: Saturation
% 0.74/0.45 % (308624)Time elapsed: 0.014 s
% 0.74/0.45 % (308624)Peak memory usage: 12 MB
% 0.74/0.45 % (308624)Instructions burned: 28 (million)
% 0.74/0.45 % (308634)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=473065720:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.74/0.45 % (308635)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=1346045744:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.74/0.45 % (308634)Instruction limit reached!
% 0.74/0.45 % (308634)------------------------------
% 0.74/0.45 % (308634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.45 % (308634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.45 % (308634)CaDiCaL version: 2.1.3
% 0.74/0.45 % (308634)Termination reason: Instruction limit
% 0.74/0.45 % (308634)Termination phase: Saturation
% 0.74/0.45 % (308634)Time elapsed: 0.004 s
% 0.74/0.45 % (308634)Peak memory usage: 11 MB
% 0.74/0.45 % (308634)Instructions burned: 8 (million)
% 0.74/0.45 % (308632)Instruction limit reached!
% 0.74/0.45 % (308632)------------------------------
% 0.74/0.45 % (308632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.45 % (308632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.45 % (308632)CaDiCaL version: 2.1.3
% 0.74/0.45 % (308632)Termination reason: Instruction limit
% 0.74/0.45 % (308632)Termination phase: Saturation
% 1.44/0.49 % (308632)Time elapsed: 0.007 s
% 1.44/0.49 % (308632)Peak memory usage: 12 MB
% 1.44/0.49 % (308632)Instructions burned: 14 (million)
% 1.44/0.49 % (308641)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3362988869:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.49 % (308641)Instruction limit reached!
% 1.44/0.49 % (308641)------------------------------
% 1.44/0.49 % (308641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (308641)CaDiCaL version: 2.1.3
% 1.44/0.49 % (308641)Termination reason: Instruction limit
% 1.44/0.49 % (308641)Termination phase: Saturation
% 1.44/0.49 % (308641)Time elapsed: 0.006 s
% 1.44/0.49 % (308641)Peak memory usage: 11 MB
% 1.44/0.49 % (308641)Instructions burned: 28 (million)
% 1.44/0.49 % (308643)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2948183410:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.44/0.49 % (308635)Instruction limit reached!
% 1.44/0.49 % (308635)------------------------------
% 1.44/0.49 % (308635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (308635)CaDiCaL version: 2.1.3
% 1.44/0.49 % (308635)Termination reason: Instruction limit
% 1.44/0.49 % (308635)Termination phase: Saturation
% 1.44/0.49 % (308635)Time elapsed: 0.016 s
% 1.44/0.49 % (308635)Peak memory usage: 12 MB
% 1.44/0.49 % (308635)Instructions burned: 31 (million)
% 1.44/0.49 % (308645)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3861921726:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.44/0.49 % (308646)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4206014781:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.44/0.49 % (308648)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1403947437:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.44/0.49 % (308629)Instruction limit reached!
% 1.44/0.49 % (308629)------------------------------
% 1.44/0.49 % (308629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (308629)CaDiCaL version: 2.1.3
% 1.44/0.49 % (308629)Termination reason: Instruction limit
% 1.44/0.49 % (308629)Termination phase: Saturation
% 1.44/0.49 % (308629)Time elapsed: 0.033 s
% 1.44/0.49 % (308629)Peak memory usage: 12 MB
% 1.44/0.49 % (308629)Instructions burned: 61 (million)
% 1.44/0.49 % (308648)Refutation not found, incomplete strategy
% 1.44/0.49 % (308648)------------------------------
% 1.44/0.49 % (308648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (308648)CaDiCaL version: 2.1.3
% 1.44/0.49 % (308648)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.49 % (308648)Time elapsed: 0.001 s
% 1.44/0.49 % (308648)Peak memory usage: 11 MB
% 1.44/0.49 % (308648)Instructions burned: 4 (million)
% 1.44/0.49 % (308648)------------------------------
% 1.44/0.49 % (308648)------------------------------
% 1.44/0.49 % (308643)Instruction limit reached!
% 1.44/0.49 % (308643)------------------------------
% 1.44/0.49 % (308643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.49 % (308643)CaDiCaL version: 2.1.3
% 1.44/0.49 % (308643)Termination reason: Instruction limit
% 1.44/0.49 % (308643)Termination phase: Saturation
% 1.44/0.49 % (308643)Time elapsed: 0.012 s
% 1.44/0.49 % (308643)Peak memory usage: 12 MB
% 1.44/0.49 % (308643)Instructions burned: 20 (million)
% 1.44/0.49 % (308650)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2366351448:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.44/0.49 % (308655)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=68750780:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 1.44/0.49 % (308645)Refutation not found, incomplete strategy
% 1.44/0.49 % (308645)------------------------------
% 1.44/0.49 % (308645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.49 % (308645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308645)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308645)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.50 % (308645)Time elapsed: 0.016 s
% 1.44/0.50 % (308645)Peak memory usage: 13 MB
% 1.44/0.50 % (308645)Instructions burned: 28 (million)
% 1.44/0.50 % (308655)Refutation not found, incomplete strategy
% 1.44/0.50 % (308655)------------------------------
% 1.44/0.50 % (308655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308655)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308655)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.50 % (308655)Time elapsed: 0.001 s
% 1.44/0.50 % (308655)Peak memory usage: 11 MB
% 1.44/0.50 % (308655)Instructions burned: 3 (million)
% 1.44/0.50 % (308645)------------------------------
% 1.44/0.50 % (308645)------------------------------
% 1.44/0.50 % (308655)------------------------------
% 1.44/0.50 % (308655)------------------------------
% 1.44/0.50 % (308654)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.44/0.50 % (308654)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2893151450:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.44/0.50 % (308659)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.44/0.50 % (308656)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=3074658692:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/169Mi)
% 1.44/0.50 % (308654)Instruction limit reached!
% 1.44/0.50 % (308654)------------------------------
% 1.44/0.50 % (308654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308654)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308654)Termination reason: Instruction limit
% 1.44/0.50 % (308654)Termination phase: Saturation
% 1.44/0.50 % (308654)Time elapsed: 0.004 s
% 1.44/0.50 % (308654)Peak memory usage: 11 MB
% 1.44/0.50 % (308654)Instructions burned: 7 (million)
% 1.44/0.50 % (308659)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1716480925:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2998 on theBenchmark for (2998ds/6Mi)
% 1.44/0.50 % (308656)Refutation not found, incomplete strategy
% 1.44/0.50 % (308656)------------------------------
% 1.44/0.50 % (308656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308656)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308656)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.50 % (308656)Time elapsed: 0.002 s
% 1.44/0.50 % (308656)Peak memory usage: 11 MB
% 1.44/0.50 % (308656)Instructions burned: 4 (million)
% 1.44/0.50 % (308656)------------------------------
% 1.44/0.50 % (308656)------------------------------
% 1.44/0.50 % (308659)Instruction limit reached!
% 1.44/0.50 % (308659)------------------------------
% 1.44/0.50 % (308659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308659)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308659)Termination reason: Instruction limit
% 1.44/0.50 % (308659)Termination phase: Saturation
% 1.44/0.50 % (308659)Time elapsed: 0.003 s
% 1.44/0.50 % (308659)Peak memory usage: 12 MB
% 1.44/0.50 % (308659)Instructions burned: 12 (million)
% 1.44/0.50 % (308660)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1110360244:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2998 on theBenchmark for (2998ds/22Mi)
% 1.44/0.50 % (308650)Instruction limit reached!
% 1.44/0.50 % (308650)------------------------------
% 1.44/0.50 % (308650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308650)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308650)Termination reason: Instruction limit
% 1.44/0.50 % (308650)Termination phase: Saturation
% 1.44/0.50 % (308650)Time elapsed: 0.025 s
% 1.44/0.50 % (308650)Peak memory usage: 12 MB
% 1.44/0.50 % (308650)Instructions burned: 43 (million)
% 1.44/0.50 % (308666)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=126685450:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2998 on theBenchmark for (2998ds/853Mi)
% 1.44/0.50 % (308664)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1314655869:i=19:add=on:rtra=on_2998 on theBenchmark for (2998ds/19Mi)
% 1.44/0.50 % (308660)Instruction limit reached!
% 1.44/0.50 % (308660)------------------------------
% 1.44/0.50 % (308660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308660)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308660)Termination reason: Instruction limit
% 1.44/0.50 % (308660)Termination phase: Saturation
% 1.44/0.50 % (308660)Time elapsed: 0.013 s
% 1.44/0.50 % (308660)Peak memory usage: 12 MB
% 1.44/0.50 % (308660)Instructions burned: 23 (million)
% 1.44/0.50 % (308665)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=1275751176:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/316Mi)
% 1.44/0.50 % (308664)Refutation not found, incomplete strategy
% 1.44/0.50 % (308664)------------------------------
% 1.44/0.50 % (308664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308664)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308664)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.50 % (308664)Time elapsed: 0.005 s
% 1.44/0.50 % (308664)Peak memory usage: 13 MB
% 1.44/0.50 % (308664)Instructions burned: 10 (million)
% 1.44/0.50 % (308664)------------------------------
% 1.44/0.50 % (308664)------------------------------
% 1.44/0.50 % (308669)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=1781143385: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)
% 1.44/0.50 % (308672)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1542496268:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 1.44/0.50 % (308646)Instruction limit reached!
% 1.44/0.50 % (308646)------------------------------
% 1.44/0.50 % (308646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308672)Refutation not found, incomplete strategy
% 1.44/0.50 % (308672)------------------------------
% 1.44/0.50 % (308672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308646)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308646)Termination reason: Instruction limit
% 1.44/0.50 % (308646)Termination phase: Saturation
% 1.44/0.50 % (308646)Time elapsed: 0.071 s
% 1.44/0.50 % (308672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308646)Peak memory usage: 13 MB
% 1.44/0.50 % (308646)Instructions burned: 145 (million)
% 1.44/0.50 % (308672)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308672)Termination reason: Refutation not found, incomplete strategy
% 1.44/0.50 % (308672)Time elapsed: 0.003 s
% 1.44/0.50 % (308673)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2552855941: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)
% 1.44/0.50 % (308672)Peak memory usage: 12 MB
% 1.44/0.50 % (308672)Instructions burned: 6 (million)
% 1.44/0.50 % (308672)------------------------------
% 1.44/0.50 % (308672)------------------------------
% 1.44/0.50 % (308669) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-308580-308669"...
% 1.44/0.50 % (308673)Instruction limit reached!
% 1.44/0.50 % (308673)------------------------------
% 1.44/0.50 % (308673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308673)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308673)Termination reason: Instruction limit
% 1.44/0.50 % (308673)Termination phase: Saturation
% 1.44/0.50 % (308673)Time elapsed: 0.011 s
% 1.44/0.50 % (308673)Peak memory usage: 12 MB
% 1.44/0.50 % (308673)Instructions burned: 21 (million)
% 1.44/0.50 % (308677)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 1.44/0.50 % (308669)...printing done.
% 1.44/0.50 % (308669)Refutation found. Thanks to Tanya!
% 1.44/0.50 % SZS status ContradictoryAxioms for theBenchmark
% 1.44/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.50 % (308669)------------------------------
% 1.44/0.50 % (308669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.50 % (308669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.50 % (308669)CaDiCaL version: 2.1.3
% 1.44/0.50 % (308669)Termination reason: Refutation
% 1.44/0.50 % (308669)Time elapsed: 0.025 s
% 1.44/0.50 % (308669)Peak memory usage: 13 MB
% 1.44/0.50 % (308669)Instructions burned: 47 (million)
% 1.44/0.50 % (308580)Success in time 0.258 s
% 1.44/0.50 % Vampire exiting
%------------------------------------------------------------------------------