%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:20:16 AM UTC 2026
% Result : Theorem 0.28s 0.45s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of formulae : 217 ( 80 unt; 0 typ; 11 def)
% Number of atoms : 1583 ( 301 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 2234 ( 181 ~; 309 |; 15 &;1460 @)
% ( 12 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 703 ( 703 >; 0 *; 0 +; 0 <<)
% Number of symbols : 147 ( 143 usr; 19 con; 0-4 aty)
% ( 138 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 585 ( 0 sgn 75 !; 0 ?; 585 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
rel: $i > $i > $o ).
thf(func_def_20,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_21,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_23,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_24,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_25,type,
god: mu > $i > $o ).
thf(func_def_26,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_27,type,
necessary_existence: mu > $i > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vIFF: $o > $o > $o ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
sF0: $o ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
sK1: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > $i ).
thf(func_def_47,type,
sK2: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > mu ).
thf(func_def_49,type,
sK4: mu ).
thf(func_def_50,type,
sK5: mu > $i > $o ).
thf(func_def_51,type,
sK6: mu > $i > $o ).
thf(func_def_53,type,
sK8: mu ).
thf(func_def_54,type,
sK9: mu ).
thf(func_def_55,type,
sK10: $i > mu > mu > $i > $o ).
thf(func_def_56,type,
sK11: mu > $i > mu > $i > $o ).
thf(func_def_57,type,
sK12: mu > $i > mu > $i > $o ).
thf(func_def_59,type,
sK14: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_60,type,
sK15: ( mu > $i > $o ) > $i > mu ).
thf(func_def_61,type,
sK16: ( mu > $i > $o ) > $i ).
thf(func_def_62,type,
sK17: ( mu > $i > $o ) > $i > mu ).
thf(func_def_63,type,
sK18: ( mu > $i > $o ) > mu ).
thf(func_def_64,type,
sK19: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_65,type,
sK20: ( mu > $i > $o ) > $i > mu ).
thf(func_def_66,type,
sK21: ( mu > $i > $o ) > $i ).
thf(func_def_67,type,
sK22: ( mu > $i > $o ) > mu ).
thf(func_def_68,type,
sK23: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_69,type,
sK24: ( mu > $i > $o ) > $i > mu ).
thf(func_def_70,type,
sK25: ( mu > $i > $o ) > $i ).
thf(func_def_71,type,
sK26: ( mu > $i > $o ) > $i > mu ).
thf(func_def_72,type,
sK27: ( mu > $i > $o ) > mu ).
thf(func_def_73,type,
sK28: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_74,type,
sK29: ( mu > $i > $o ) > $i > mu ).
thf(func_def_75,type,
sK30: ( mu > $i > $o ) > $i > mu ).
thf(func_def_76,type,
sK31: ( mu > $i > $o ) > $i ).
thf(func_def_77,type,
sK32: ( mu > $i > $o ) > mu ).
thf(func_def_78,type,
sK33: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_79,type,
sK34: ( mu > $i > $o ) > $i > mu ).
thf(func_def_80,type,
sK35: ( mu > $i > $o ) > $i ).
thf(func_def_81,type,
sK36: ( mu > $i > $o ) > $i > mu ).
thf(func_def_82,type,
sK37: ( mu > $i > $o ) > mu ).
thf(func_def_83,type,
sK38: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_84,type,
sK39: $i > ( mu > $i > $o ) > mu ).
thf(func_def_85,type,
sK40: ( mu > $i > $o ) > $i ).
thf(func_def_86,type,
sK41: $i > ( mu > $i > $o ) > mu ).
thf(func_def_87,type,
sK42: ( mu > $i > $o ) > mu ).
thf(func_def_88,type,
sK43: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_89,type,
sK44: ( mu > $i > $o ) > $i > mu ).
thf(func_def_90,type,
sK45: ( mu > $i > $o ) > $i ).
thf(func_def_91,type,
sK46: ( mu > $i > $o ) > $i > mu ).
thf(func_def_92,type,
sK47: ( mu > $i > $o ) > mu ).
thf(func_def_93,type,
sK48: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_94,type,
sK49: ( mu > $i > $o ) > $i > mu ).
thf(func_def_95,type,
sK50: ( mu > $i > $o ) > $i ).
thf(func_def_96,type,
sK51: ( mu > $i > $o ) > $i > mu ).
thf(func_def_97,type,
sK52: ( mu > $i > $o ) > mu ).
thf(func_def_98,type,
sK53: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_99,type,
sK54: ( mu > $i > $o ) > $i > mu ).
thf(func_def_100,type,
sK55: ( mu > $i > $o ) > $i ).
thf(func_def_101,type,
sK56: ( mu > $i > $o ) > $i > mu ).
thf(func_def_102,type,
sK57: ( mu > $i > $o ) > mu ).
thf(func_def_103,type,
sK58: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_104,type,
sK59: $i > ( mu > $i > $o ) > mu ).
thf(func_def_105,type,
sK60: ( mu > $i > $o ) > $i ).
thf(func_def_106,type,
sK61: $i > ( mu > $i > $o ) > mu ).
thf(func_def_107,type,
sK62: ( mu > $i > $o ) > mu ).
thf(func_def_108,type,
sK63: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_109,type,
sK64: $i > ( mu > $i > $o ) > mu ).
thf(func_def_110,type,
sK65: ( mu > $i > $o ) > $i ).
thf(func_def_111,type,
sK66: $i > ( mu > $i > $o ) > mu ).
thf(func_def_112,type,
sK67: ( mu > $i > $o ) > mu ).
thf(func_def_113,type,
sK68: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_114,type,
sK69: $i > ( mu > $i > $o ) > mu ).
thf(func_def_115,type,
sK70: ( mu > $i > $o ) > $i ).
thf(func_def_116,type,
sK71: ( mu > $i > $o ) > mu ).
thf(func_def_117,type,
sK72: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_118,type,
sK73: ( mu > $i > $o ) > $i > mu ).
thf(func_def_119,type,
sK74: ( mu > $i > $o ) > $i ).
thf(func_def_120,type,
sK75: ( mu > $i > $o ) > $i > mu ).
thf(func_def_121,type,
sK76: ( mu > $i > $o ) > mu ).
thf(func_def_122,type,
sK77: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_123,type,
sK78: ( mu > $i > $o ) > $i > mu ).
thf(func_def_124,type,
sK79: ( mu > $i > $o ) > $i ).
thf(func_def_125,type,
sK80: ( mu > $i > $o ) > mu ).
thf(func_def_126,type,
sK81: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_127,type,
sK82: ( mu > $i > $o ) > $i > mu ).
thf(func_def_128,type,
sK83: ( mu > $i > $o ) > $i > mu ).
thf(func_def_129,type,
sK84: ( mu > $i > $o ) > $i ).
thf(func_def_130,type,
sK85: ( mu > $i > $o ) > mu ).
thf(func_def_131,type,
sK86: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_132,type,
sK87: ( mu > $i > $o ) > $i > mu ).
thf(func_def_133,type,
sK88: ( mu > $i > $o ) > $i ).
thf(func_def_134,type,
sK89: ( mu > $i > $o ) > $i > mu ).
thf(func_def_135,type,
sK90: ( mu > $i > $o ) > 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] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/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,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox_generic ),
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/Axioms/PHI001^0.ax',axA1) ).
thf(f25,axiom,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
file('/export/starexec/sandbox2/benchmark/Axioms/PHI001^0.ax',defD1) ).
thf(f27,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] : ( mimplies @ ( positive @ X0 ) @ ( mbox @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PHI001^0.ax',axA4) ).
thf(f28,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/Axioms/PHI001^0.ax',defD2) ).
thf(f31,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT2) ).
thf(f32,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
thf(f33,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox_generic ),
inference(rectify,[],[f17]) ).
thf(f34,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f36,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f38,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f44,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f45,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f50,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] : ( mimplies @ ( positive @ X0 ) @ ( mbox @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f51,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f9]) ).
thf(f53,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f7]) ).
thf(f55,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f57,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) )
= god ),
inference(rectify,[],[f25]) ).
thf(f59,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f63,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,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,[],[f28]) ).
thf(f65,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,[],[f64]) ).
thf(f80,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f11]) ).
thf(f81,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f82,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f83,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f88,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(flattening,[],[f36]) ).
thf(f90,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f91,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f92,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f95,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f97,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f98,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f101,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f104,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f106,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,[],[f65]) ).
thf(f108,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f109,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f111,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f113,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f116,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f122,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f109,f92]) ).
thf(f124,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,[],[f91,f104,f97]) ).
thf(f125,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ 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,[],[f106,f116,f104,f97,f122,f108,f97]) ).
thf(f128,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,[],[f95,f113,f104,f97,f122]) ).
thf(f129,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] :
( ( Y2 @ Y3 )
= ( Y1 @ 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,[],[f98,f113,f104,f101,f90,f90]) ).
thf(f131,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] :
( ( Y4 @ Y5 )
& ( Y3 @ 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,[],[f111,f113,f108,f97,f124,f125,f124]) ).
thf(f133,definition,
( sF0
= ( ^ [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] :
( ( Y4 @ Y5 )
& ( Y3 @ 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 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f134,plain,
( ( ^ [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] :
( ( Y4 @ Y5 )
& ( Y3 @ 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 ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f133]) ).
thf(f135,plain,
$true != sF0,
inference(definition_folding,[],[f131,f134]) ).
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,[],[f128]) ).
thf(f157,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ Y0 @ Y2 )
| ( positive @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
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] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
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] :
( ( $true
= ( ~ ( rel @ X1 @ X3 ) ) )
| ( $true
= ( positive @ X2 @ X3 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( positive @ X2 @ X3 ) )
| ( ( rel @ X1 @ X3 )
= $false )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [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] :
( ( Y4 @ Y5 )
& ( Y3 @ 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(iff_proxy_clausification,[],[f134]) ).
thf(f168,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $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] :
( ( 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 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( ( ^ [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] :
( ( 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 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
@ sK3 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK3 )
=> ( Y1 @ Y0 @ sK3 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK3 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK3 )
=> ( Y1 @ Y0 @ sK3 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK3 )
=> ( Y1 @ Y0 @ sK3 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK3 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK3 )
=> ( Y1 @ Y0 @ sK3 ) ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true = sF0 )
| ( ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK3 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $true = sF0 )
| ( ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK3 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: mu > $i > $o] :
( ( $true = sF0 )
| ( ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: mu > $i > $o] :
( ( ( ( positive @ X1 @ sK3 )
=> ( X1 @ sK4 @ sK3 ) )
= $true )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X1: mu > $i > $o] :
( ( ( X1 @ sK4 @ sK3 )
= $true )
| ( $true = sF0 )
| ( $false
= ( positive @ X1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
| ( $true = sF0 )
| ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK3 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f179,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK5 ) )
| ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK3 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK3 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK3 )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true = sF0 )
| ( $false
= ( ( sK6 @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK3 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( positive @ sK5 @ sK3 )
=> ( sK5 @ sK4 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK3 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( positive @ sK5 @ sK3 )
=> ( sK5 @ sK4 @ sK3 ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ( sK6 @ sK4 @ sK3 )
= $true )
| ( $false
= ( ( positive @ sK5 @ sK3 )
=> ( sK5 @ sK4 @ sK3 ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( ( sK6 @ sK4 @ sK3 )
= $true )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true )
| ( ( sK6 @ sK4 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK3 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK7 ) )
| ( $true = sF0 )
| ( $false
= ( ( positive @ sK5 @ sK3 )
=> ( sK5 @ sK4 @ sK3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f187,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK3 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK7 ) )
| ( ( sK5 @ sK4 @ sK3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK3 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK7 ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( $false
= ( ~ ( rel @ sK3 @ sK7 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ( ( positive @ sK5 @ sK3 )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $false
= ( ~ ( rel @ sK3 @ sK7 ) ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( $true
= ( rel @ sK3 @ sK7 ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f194,plain,
( ( ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) ) )
=> ( sK6 @ sK8 @ sK7 ) )
= $false )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ( ( positive @ sK5 @ sK3 )
= $true )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( ( positive @ sK5 @ sK3 )
= $true )
| ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ( ( positive @ sK5 @ sK3 )
= $true )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: mu > $i > $o] :
( ( ( ( positive @ X1 @ sK7 )
=> ( X1 @ sK8 @ sK7 ) )
= $true )
| ( ( positive @ sK5 @ sK3 )
= $true )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: mu > $i > $o] :
( ( ( X1 @ sK8 @ sK7 )
= $true )
| ( $false
= ( positive @ X1 @ sK7 ) )
| ( $true = sF0 )
| ( ( positive @ sK5 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $false
= ( ~ ( rel @ sK3 @ sK7 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) ) )
| ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f201,plain,
( ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $false
= ( ~ ( rel @ sK3 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( $true
= ( rel @ sK3 @ sK7 ) )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK7 )
=> ( Y1 @ Y0 @ sK7 ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK9 ) )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f205,plain,
( ( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) ) )
=> ( sK6 @ sK9 @ sK7 ) ) )
| ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
( ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $false
= ( sK6 @ sK9 @ sK7 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X1: mu > $i > $o] :
( ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK7 )
=> ( Y0 @ sK9 @ sK7 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ( positive @ X1 @ sK7 )
=> ( X1 @ sK9 @ sK7 ) ) )
| ( $true = sF0 )
| ( ( sK5 @ sK4 @ sK3 )
= $false ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X1: mu > $i > $o] :
( ( ( sK5 @ sK4 @ sK3 )
= $false )
| ( $true
= ( X1 @ sK9 @ sK7 ) )
| ( $true = sF0 )
| ( $false
= ( positive @ X1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f252,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ~ ( positive @ Y1 @ Y0 ) )
= ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f253,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( ~ ( positive @ Y1 @ Y0 ) )
= ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( ~ ( positive @ Y0 @ X1 ) )
= ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( ~ ( positive @ Y0 @ X1 ) )
= ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( ~ ( positive @ X2 @ X1 ) )
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( ~ ( positive @ X2 @ X1 ) )
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ),
inference(iff_proxy_clausification,[],[f256]) ).
thf(f259,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( positive @ X2 @ X1 ) ) )
| ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f257]) ).
thf(f260,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,[],[f259]) ).
thf(f265,definition,
( spl13_1
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
thf(f269,definition,
( spl13_2
<=> ! [X1: mu > $i > $o] :
( ( ( X1 @ sK4 @ sK3 )
= $true )
| ( $false
= ( positive @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
thf(f270,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK3 ) )
| ( ( X1 @ sK4 @ sK3 )
= $true ) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f177,f269,f265]) ).
thf(f273,definition,
( spl13_3
<=> ( ( sK6 @ sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
thf(f275,plain,
( ( ( sK6 @ sK4 @ sK3 )
= $true )
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f277,definition,
( spl13_4
<=> ( ( positive @ sK5 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
thf(f279,plain,
( ( ( positive @ sK5 @ sK3 )
= $true )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f280,plain,
( spl13_1
| spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f185,f277,f273,f265]) ).
thf(f282,definition,
( spl13_5
<=> ( ( sK5 @ sK4 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
thf(f284,plain,
( ( ( sK5 @ sK4 @ sK3 )
= $false )
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f285,plain,
( spl13_5
| spl13_3
| spl13_1 ),
inference(avatar_split_clause,[],[f184,f265,f273,f282]) ).
thf(f287,definition,
( spl13_6
<=> ( $true
= ( rel @ sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
thf(f289,plain,
( ( $true
= ( rel @ sK3 @ sK7 ) )
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f290,plain,
( spl13_1
| spl13_6
| spl13_4 ),
inference(avatar_split_clause,[],[f192,f277,f287,f265]) ).
thf(f292,definition,
( spl13_7
<=> ! [X1: mu > $i > $o] :
( ( ( X1 @ sK8 @ sK7 )
= $true )
| ( $false
= ( positive @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
thf(f293,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK7 ) )
| ( ( X1 @ sK8 @ sK7 )
= $true ) )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f294,plain,
( spl13_4
| spl13_1
| spl13_7 ),
inference(avatar_split_clause,[],[f199,f292,f265,f277]) ).
thf(f296,definition,
( spl13_8
<=> ( $false
= ( sK6 @ sK8 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
thf(f298,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl13_8
| spl13_1
| spl13_4 ),
inference(avatar_split_clause,[],[f195,f277,f265,f296]) ).
thf(f300,plain,
( spl13_1
| spl13_5
| spl13_6 ),
inference(avatar_split_clause,[],[f203,f287,f282,f265]) ).
thf(f302,definition,
( spl13_9
<=> ! [X1: mu > $i > $o] :
( ( $true
= ( X1 @ sK9 @ sK7 ) )
| ( $false
= ( positive @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
thf(f303,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK7 ) )
| ( $true
= ( X1 @ sK9 @ sK7 ) ) )
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f304,plain,
( spl13_5
| spl13_1
| spl13_9 ),
inference(avatar_split_clause,[],[f210,f302,f265,f282]) ).
thf(f306,definition,
( spl13_10
<=> ( $false
= ( sK6 @ sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
thf(f308,plain,
( ( $false
= ( sK6 @ sK9 @ sK7 ) )
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f306]) ).
thf(f309,plain,
( spl13_1
| spl13_5
| spl13_10 ),
inference(avatar_split_clause,[],[f206,f306,f282,f265]) ).
thf(f338,plain,
~ spl13_1,
inference(avatar_split_clause,[],[f135,f265]) ).
thf(f355,plain,
( ( $false = $true )
| ( ( sK5 @ sK4 @ sK3 )
= $true )
| ~ spl13_2
| ~ spl13_4 ),
inference(constrained_superposition,[],[f279,f270]) ).
thf(f358,plain,
( ( ( sK5 @ sK4 @ sK3 )
= $true )
| ~ spl13_2
| ~ spl13_4 ),
inference(trivial_inequality_removal,[],[f355]) ).
thf(f362,plain,
( ( $false = $true )
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5 ),
inference(forward_demodulation,[],[f358,f284]) ).
thf(f363,plain,
( $false
| ~ spl13_2
| ~ spl13_4
| ~ spl13_5 ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f364,plain,
( ~ spl13_2
| ~ spl13_4
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f363]) ).
thf(f374,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( rel @ X1 @ sK7 ) )
| ( ( X0 @ sK9 @ sK7 )
= $true )
| ( $false
= ( positive @ X0 @ X1 ) ) )
| ~ spl13_9 ),
inference(constrained_superposition,[],[f303,f165]) ).
thf(f378,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( rel @ X1 @ sK7 ) )
| ( ( X0 @ sK9 @ sK7 )
= $true ) )
| ~ spl13_9 ),
inference(trivial_inequality_removal,[],[f374]) ).
thf(f506,plain,
( ! [X0: mu > $i > $o] :
( ( $false = $true )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK4
@ sK3 ) )
| ( $true
= ( positive @ X0 @ sK3 ) ) )
| ~ spl13_2 ),
inference(constrained_superposition,[],[f270,f260]) ).
thf(f514,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK4
@ sK3 ) )
| ( $true
= ( positive @ X0 @ sK3 ) ) )
| ~ spl13_2 ),
inference(trivial_inequality_removal,[],[f506]) ).
thf(f515,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK3 ) )
| ( $true
= ( ~ ( X0 @ sK4 @ sK3 ) ) ) )
| ~ spl13_2 ),
inference(beta-eta_normalization,[],[f514]) ).
thf(f516,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK3 ) )
| ( ( X0 @ sK4 @ sK3 )
= $false ) )
| ~ spl13_2 ),
inference(not_proxy_clausification,[],[f515]) ).
thf(f1035,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( rel @ sK3 @ sK7 ) )
| ( ( X0 @ sK9 @ sK7 )
= $true )
| ( $false = $true )
| ( ( X0 @ sK4 @ sK3 )
= $false ) )
| ~ spl13_2
| ~ spl13_9 ),
inference(constrained_superposition,[],[f378,f516]) ).
thf(f1042,plain,
( ! [X0: mu > $i > $o] :
( ( ( X0 @ sK9 @ sK7 )
= $true )
| ( ( X0 @ sK4 @ sK3 )
= $false )
| ( $false
= ( rel @ sK3 @ sK7 ) ) )
| ~ spl13_2
| ~ spl13_9 ),
inference(trivial_inequality_removal,[],[f1035]) ).
thf(f1047,plain,
( ! [X0: mu > $i > $o] :
( ( ( X0 @ sK9 @ sK7 )
= $true )
| ( ( X0 @ sK4 @ sK3 )
= $false )
| ( $false = $true ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_9 ),
inference(forward_demodulation,[],[f1042,f289]) ).
thf(f1048,plain,
( ! [X0: mu > $i > $o] :
( ( ( X0 @ sK9 @ sK7 )
= $true )
| ( ( X0 @ sK4 @ sK3 )
= $false ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_9 ),
inference(trivial_inequality_removal,[],[f1047]) ).
thf(f1051,plain,
( ( $false = $true )
| ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(constrained_superposition,[],[f1048,f308]) ).
thf(f1054,plain,
( ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(trivial_inequality_removal,[],[f1051]) ).
thf(f1058,plain,
( ( $false = $true )
| ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(forward_demodulation,[],[f1054,f275]) ).
thf(f1059,plain,
( $false
| ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(trivial_inequality_removal,[],[f1058]) ).
thf(f1060,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(avatar_contradiction_clause,[],[f1059]) ).
thf(f1106,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ sK7 ) )
| ( $false = $true )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $true
= ( X0 @ sK8 @ sK7 ) ) )
| ~ spl13_7 ),
inference(constrained_superposition,[],[f165,f293]) ).
thf(f1140,plain,
( ! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( $false
= ( rel @ X1 @ sK7 ) ) )
| ~ spl13_7 ),
inference(trivial_inequality_removal,[],[f1106]) ).
thf(f1202,plain,
( ! [X0: mu > $i > $o] :
( ( $false = $true )
| ( ( X0 @ sK4 @ sK3 )
= $false )
| ( $false
= ( rel @ sK3 @ sK7 ) )
| ( $true
= ( X0 @ sK8 @ sK7 ) ) )
| ~ spl13_2
| ~ spl13_7 ),
inference(constrained_superposition,[],[f1140,f516]) ).
thf(f1212,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( ( X0 @ sK4 @ sK3 )
= $false )
| ( $false
= ( rel @ sK3 @ sK7 ) ) )
| ~ spl13_2
| ~ spl13_7 ),
inference(trivial_inequality_removal,[],[f1202]) ).
thf(f1287,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( ( X0 @ sK4 @ sK3 )
= $false )
| ( $false = $true ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_7 ),
inference(forward_demodulation,[],[f1212,f289]) ).
thf(f1288,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK8 @ sK7 ) )
| ( ( X0 @ sK4 @ sK3 )
= $false ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_7 ),
inference(trivial_inequality_removal,[],[f1287]) ).
thf(f1324,plain,
( ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ( $false = $true )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(constrained_superposition,[],[f298,f1288]) ).
thf(f1326,plain,
( ( $false
= ( sK6 @ sK4 @ sK3 ) )
| ~ spl13_2
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(trivial_inequality_removal,[],[f1324]) ).
thf(f1330,plain,
( ( $false = $true )
| ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(forward_demodulation,[],[f1326,f275]) ).
thf(f1331,plain,
( $false
| ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1332,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(avatar_contradiction_clause,[],[f1331]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f271]) ).
cnf(s2,plain,
( spl13_1
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f280]) ).
cnf(s3,plain,
( spl13_1
| spl13_3
| spl13_5 ),
inference(sat_conversion,[],[f285]) ).
cnf(s4,plain,
( spl13_1
| spl13_4
| spl13_6 ),
inference(sat_conversion,[],[f290]) ).
cnf(s5,plain,
( spl13_1
| spl13_4
| spl13_7 ),
inference(sat_conversion,[],[f294]) ).
cnf(s6,plain,
( spl13_1
| spl13_4
| spl13_8 ),
inference(sat_conversion,[],[f299]) ).
cnf(s7,plain,
( spl13_1
| spl13_5
| spl13_6 ),
inference(sat_conversion,[],[f300]) ).
cnf(s8,plain,
( spl13_1
| spl13_5
| spl13_9 ),
inference(sat_conversion,[],[f304]) ).
cnf(s9,plain,
( spl13_1
| spl13_5
| spl13_10 ),
inference(sat_conversion,[],[f309]) ).
cnf(s16,plain,
~ spl13_1,
inference(sat_conversion,[],[f338]) ).
cnf(s18,plain,
( ~ spl13_2
| ~ spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f364]) ).
cnf(s54,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_9
| ~ spl13_10 ),
inference(sat_conversion,[],[f1060]) ).
cnf(s64,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(sat_conversion,[],[f1332]) ).
cnf(s65,plain,
( spl13_5
| spl13_10 ),
inference(rat,[],[s9,s16]) ).
cnf(s66,plain,
( spl13_5
| spl13_9 ),
inference(rat,[],[s8,s16]) ).
cnf(s67,plain,
( spl13_5
| spl13_6 ),
inference(rat,[],[s7,s16]) ).
cnf(s68,plain,
( spl13_4
| spl13_8 ),
inference(rat,[],[s6,s16]) ).
cnf(s69,plain,
( spl13_4
| spl13_7 ),
inference(rat,[],[s5,s16]) ).
cnf(s70,plain,
( spl13_4
| spl13_6 ),
inference(rat,[],[s4,s16]) ).
cnf(s71,plain,
( spl13_3
| spl13_5 ),
inference(rat,[],[s3,s16]) ).
cnf(s72,plain,
( spl13_3
| spl13_4 ),
inference(rat,[],[s2,s16]) ).
cnf(s73,plain,
spl13_2,
inference(rat,[],[s1,s16]) ).
cnf(s74,plain,
spl13_3,
inference(rat,[],[s18,s72,s71,s73]) ).
cnf(s75,plain,
spl13_4,
inference(rat,[],[s64,s70,s69,s68,s73,s74]) ).
cnf(s76,plain,
~ spl13_5,
inference(rat,[],[s18,s73,s75]) ).
cnf(s77,plain,
spl13_10,
inference(rat,[],[s65,s76]) ).
cnf(s78,plain,
spl13_9,
inference(rat,[],[s66,s76]) ).
cnf(s79,plain,
spl13_6,
inference(rat,[],[s67,s76]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s54,s77,s74,s73,s78,s79]) ).
thf(f1333,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.27 % Computer : n006.cluster.edu
% 0.23/0.27 % Model : x86_64 x86_64
% 0.23/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.27 % Memory : 8046.5625MB
% 0.23/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.27 % CPULimit : 300
% 0.23/0.27 % WCLimit : 300
% 0.23/0.27 % DateTime : Tue Sep 29 13:16:55 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 Running higher-order theorem proving
% 0.23/0.33 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
% 0.28/0.45 % (692323)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.45 % (692328)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3431165523:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.45 % (692334)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.45 % (692334)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
% 0.28/0.45 % (692329)lrs+10_16_si=on:nwc=1.5:random_seed=3014296735:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.45 % (692330)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1431452950:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.45 % (692332)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3788597486:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.45 % (692333)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3372738058:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.45 % (692331)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=2910852937: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)
% 0.28/0.45 % (692334)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=3022922034:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.45 % (692330)Instruction limit reached!
% 0.28/0.45 % (692330)------------------------------
% 0.28/0.45 % (692330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692330)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692330)Termination reason: Instruction limit
% 0.28/0.45 % (692330)Termination phase: Property scanning
% 0.28/0.45 % (692330)Time elapsed: 0.003 s
% 0.28/0.45 % (692330)Peak memory usage: 10 MB
% 0.28/0.45 % (692330)Instructions burned: 3 (million)
% 0.28/0.45 % (692329)Instruction limit reached!
% 0.28/0.45 % (692329)------------------------------
% 0.28/0.45 % (692329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692329)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692329)Termination reason: Instruction limit
% 0.28/0.45 % (692329)Termination phase: Saturation
% 0.28/0.45 % (692329)Time elapsed: 0.016 s
% 0.28/0.45 % (692329)Peak memory usage: 12 MB
% 0.28/0.45 % (692329)Instructions burned: 18 (million)
% 0.28/0.45 % (692328)Instruction limit reached!
% 0.28/0.45 % (692328)------------------------------
% 0.28/0.45 % (692328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692328)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692328)Termination reason: Instruction limit
% 0.28/0.45 % (692328)Termination phase: Saturation
% 0.28/0.45 % (692328)Time elapsed: 0.038 s
% 0.28/0.45 % (692328)Peak memory usage: 12 MB
% 0.28/0.45 % (692328)Instructions burned: 89 (million)
% 0.28/0.45 % (692332)Instruction limit reached!
% 0.28/0.45 % (692332)------------------------------
% 0.28/0.45 % (692332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692332)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692332)Termination reason: Instruction limit
% 0.28/0.45 % (692332)Termination phase: Saturation
% 0.28/0.45 % (692332)Time elapsed: 0.024 s
% 0.28/0.45 % (692332)Peak memory usage: 12 MB
% 0.28/0.45 % (692332)Instructions burned: 25 (million)
% 0.28/0.45 % (692342)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=511300945:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.45 % (692343)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=504125043:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.28/0.45 % (692342)Instruction limit reached!
% 0.28/0.45 % (692342)------------------------------
% 0.28/0.45 % (692342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692342)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692342)Termination reason: Instruction limit
% 0.28/0.45 % (692342)Termination phase: Property scanning
% 0.28/0.45 % (692342)Time elapsed: 0.002 s
% 0.28/0.45 % (692342)Peak memory usage: 10 MB
% 0.28/0.45 % (692342)Instructions burned: 2 (million)
% 0.28/0.45 % (692343)Instruction limit reached!
% 0.28/0.45 % (692343)------------------------------
% 0.28/0.45 % (692343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692343)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692343)Termination reason: Instruction limit
% 0.28/0.45 % (692343)Termination phase: Property scanning
% 0.28/0.45 % (692343)Time elapsed: 0.003 s
% 0.28/0.45 % (692343)Peak memory usage: 11 MB
% 0.28/0.45 % (692343)Instructions burned: 6 (million)
% 0.28/0.45 % (692344)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.45 % (692345)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2570202419:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.28/0.45 % (692344)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3531240596:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.28/0.45 % (692334) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-692323-692334"...
% 0.28/0.45 % (692349)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=2370508837:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.28/0.45 % (692348)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
% 0.28/0.45 % (692348)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.45 % (692333)Instruction limit reached!
% 0.28/0.45 % (692333)------------------------------
% 0.28/0.45 % (692333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692333)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692333)Termination reason: Instruction limit
% 0.28/0.45 % (692333)Termination phase: Saturation
% 0.28/0.45 % (692333)Time elapsed: 0.066 s
% 0.28/0.45 % (692333)Peak memory usage: 13 MB
% 0.28/0.45 % (692333)Instructions burned: 75 (million)
% 0.28/0.45 % (692344)Instruction limit reached!
% 0.28/0.45 % (692344)------------------------------
% 0.28/0.45 % (692344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692344)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692344)Termination reason: Instruction limit
% 0.28/0.45 % (692344)Termination phase: Saturation
% 0.28/0.45 % (692344)Time elapsed: 0.009 s
% 0.28/0.45 % (692344)Peak memory usage: 12 MB
% 0.28/0.45 % (692344)Instructions burned: 10 (million)
% 0.28/0.45 % (692345)Instruction limit reached!
% 0.28/0.45 % (692345)------------------------------
% 0.28/0.45 % (692345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (692345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (692345)CaDiCaL version: 2.1.3
% 0.28/0.45 % (692345)Termination reason: Instruction limit
% 0.28/0.45 % (692345)Termination phase: Saturation
% 0.28/0.45 % (692345)Time elapsed: 0.011 s
% 0.28/0.45 % (692345)Peak memory usage: 12 MB
% 0.28/0.45 % (692345)Instructions burned: 13 (million)
% 0.28/0.45 % (692348)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1362246690:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.28/0.45 % (692334)...printing done.
% 0.28/0.45 % (692334)Refutation found. Thanks to Tanya!
% 0.28/0.45 % SZS status Theorem for theBenchmark
% 0.28/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.46 % (692334)------------------------------
% 0.28/0.46 % (692334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.46 % (692334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.46 % (692334)CaDiCaL version: 2.1.3
% 0.28/0.46 % (692334)Termination reason: Refutation
% 0.28/0.46 % (692334)Time elapsed: 0.070 s
% 0.28/0.46 % (692334)Peak memory usage: 13 MB
% 0.28/0.46 % (692334)Instructions burned: 79 (million)
% 0.28/0.46 % (692323)Success in time 0.112 s
% 0.28/0.46 % Vampire exiting
%------------------------------------------------------------------------------