%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:20:21 AM UTC 2026
% Result : ContradictoryAxioms 8.47s 1.60s
% Output : Refutation 9.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 139 ( 80 unt; 0 typ; 1 def)
% Number of atoms : 944 ( 183 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 2214 ( 80 ~; 90 |; 13 &;1652 @)
% ( 1 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 668 ( 668 >; 0 *; 0 +; 0 <<)
% Number of symbols : 132 ( 127 usr; 5 con; 0-4 aty)
% ( 208 !!; 35 ??; 0 @@+; 0 @@-)
% Number of variables : 811 ( 83 sgn 133 !; 2 ?; 811 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_22,type,
god: mu > $i > $o ).
thf(func_def_23,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_24,type,
necessary_existence: mu > $i > $o ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vIFF: $o > $o > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $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_45,type,
sK3: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_46,type,
sK4: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_47,type,
sK5: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_48,type,
sK6: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_49,type,
sK7: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_50,type,
sK8: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_51,type,
sK9: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_52,type,
sK10: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_53,type,
sK11: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_54,type,
sK12: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_55,type,
sK13: ( mu > $i > $o ) > mu ).
thf(func_def_56,type,
sK14: ( mu > $i > $o ) > mu ).
thf(func_def_57,type,
sK15: ( mu > $i > $o ) > mu ).
thf(func_def_58,type,
sK16: ( mu > $i > $o ) > $i ).
thf(func_def_59,type,
sK17: ( mu > $i > $o ) > $i ).
thf(func_def_60,type,
sK18: ( mu > $i > $o ) > mu ).
thf(func_def_61,type,
sK19: ( mu > $i > $o ) > $i ).
thf(func_def_62,type,
sK20: ( mu > $i > $o ) > $i ).
thf(func_def_63,type,
sK21: ( mu > $i > $o ) > mu ).
thf(func_def_64,type,
sK22: ( mu > $i > $o ) > $i ).
thf(func_def_65,type,
sK23: ( mu > $i > $o ) > $i ).
thf(func_def_66,type,
sK24: ( mu > $i > $o ) > mu ).
thf(func_def_67,type,
sK25: ( mu > $i > $o ) > $i ).
thf(func_def_68,type,
sK26: ( mu > $i > $o ) > $i ).
thf(func_def_69,type,
sK27: ( mu > $i > $o ) > mu ).
thf(func_def_70,type,
sK28: ( mu > $i > $o ) > $i ).
thf(func_def_71,type,
sK29: ( mu > $i > $o ) > $i ).
thf(func_def_72,type,
sK30: ( mu > $i > $o ) > mu ).
thf(func_def_73,type,
sK31: ( mu > $i > $o ) > $i ).
thf(func_def_74,type,
sK32: ( mu > $i > $o ) > $i ).
thf(func_def_75,type,
sK33: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_76,type,
sK34: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_77,type,
sK35: ( mu > $i > $o ) > mu ).
thf(func_def_78,type,
sK36: ( mu > $i > $o ) > $i ).
thf(func_def_79,type,
sK37: ( mu > $i > $o ) > $i ).
thf(func_def_80,type,
sK38: ( mu > $i > $o ) > ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_81,type,
sK39: $i > ( mu > $i > $o ) > mu ).
thf(func_def_82,type,
sK40: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_83,type,
sK41: $i > ( mu > $i > $o ) > mu ).
thf(func_def_84,type,
sK42: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_85,type,
sK43: ( mu > $i > $o ) > ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_86,type,
sK44: $i > ( mu > $i > $o ) > mu ).
thf(func_def_87,type,
sK45: ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).
thf(func_def_88,type,
sK46: $i > ( mu > $i > $o ) > mu ).
thf(func_def_89,type,
sK47: ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_90,type,
sK48: ( mu > $i > $o ) > mu ).
thf(func_def_91,type,
sK49: ( mu > $i > $o ) > mu ).
thf(func_def_92,type,
sK50: ( mu > $i > $o ) > mu ).
thf(func_def_93,type,
sK51: ( mu > $i > $o ) > $i ).
thf(func_def_94,type,
sK52: ( mu > $i > $o ) > $i ).
thf(func_def_95,type,
sK53: ( mu > $i > $o ) > mu ).
thf(func_def_96,type,
sK54: ( mu > $i > $o ) > mu ).
thf(func_def_97,type,
sK55: ( mu > $i > $o ) > mu ).
thf(func_def_98,type,
sK56: ( mu > $i > $o ) > $i ).
thf(func_def_99,type,
sK57: ( mu > $i > $o ) > $i ).
thf(func_def_100,type,
sK58: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_101,type,
sK59: ( mu > $i > $o ) > $i > mu ).
thf(func_def_102,type,
sK60: ( mu > $i > $o ) > $i ).
thf(func_def_103,type,
sK61: ( mu > $i > $o ) > $i > mu ).
thf(func_def_104,type,
sK62: ( mu > $i > $o ) > mu ).
thf(func_def_105,type,
sK63: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_106,type,
sK64: ( mu > $i > $o ) > $i > mu ).
thf(func_def_107,type,
sK65: ( mu > $i > $o ) > $i ).
thf(func_def_108,type,
sK66: ( mu > $i > $o ) > $i > mu ).
thf(func_def_109,type,
sK67: ( mu > $i > $o ) > mu ).
thf(func_def_110,type,
sK68: ( mu > $i > $o ) > mu ).
thf(func_def_111,type,
sK69: ( mu > $i > $o ) > mu ).
thf(func_def_112,type,
sK70: ( mu > $i > $o ) > mu ).
thf(func_def_113,type,
sK71: ( mu > $i > $o ) > mu ).
thf(func_def_114,type,
sK72: ( mu > $i > $o ) > $i ).
thf(func_def_115,type,
sK73: ( mu > $i > $o ) > $i ).
thf(func_def_116,type,
sK74: ( mu > $i > $o ) > $i ).
thf(func_def_117,type,
sK75: ( mu > $i > $o ) > $i ).
thf(func_def_118,type,
sK76: ( mu > $i > $o ) > $i ).
thf(func_def_119,type,
sK77: ( mu > $i > $o ) > $i ).
thf(func_def_120,type,
sK78: ( mu > $i > $o ) > mu ).
thf(func_def_121,type,
sK79: ( mu > $i > $o ) > $i ).
thf(func_def_122,type,
sK80: ( mu > $i > $o ) > $i ).
thf(func_def_123,type,
sK81: ( mu > $i > $o ) > mu ).
thf(func_def_124,type,
sK82: ( mu > $i > $o ) > $i ).
thf(func_def_125,type,
sK83: ( mu > $i > $o ) > $i ).
thf(func_def_126,type,
sK84: ( mu > $i > $o ) > mu ).
thf(func_def_127,type,
sK85: ( mu > $i > $o ) > $i ).
thf(func_def_128,type,
sK86: ( mu > $i > $o ) > $i ).
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,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
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,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
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,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
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(f22,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( mnot @ ( positive @ X0 ) )
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1b) ).
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(f24,axiom,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD2) ).
thf(f25,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(f26,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5) ).
thf(f32,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f33,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f37,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f39,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f46,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f47,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f49,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f52,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f53,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f58,plain,
( mbox
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] : ( X0 @ X2 ) ) ),
inference(rectify,[],[f17]) ).
thf(f59,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f19]) ).
thf(f63,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f67,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mimplies @ ( mnot @ ( positive @ X0 ) )
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f69,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( mnot @ ( positive @ Y0 ) )
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,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(f71,plain,
( $true
= ( 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 ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f72,plain,
( essence
= ( ^ [X0: mu > $i > $o,X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( X2 @ X1 )
@ ( mbox
@ ( mforall_ind
@ ^ [X3: mu] : ( mimplies @ ( X0 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f73,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,[],[f72]) ).
thf(f74,plain,
( necessary_existence
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f75,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,[],[f74]) ).
thf(f76,plain,
mvalid @ ( positive @ necessary_existence ),
inference(rectify,[],[f26]) ).
thf(f77,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(fool_elimination,[],[f76]) ).
thf(f82,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f84,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f85,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f89,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f90,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f92,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f95,plain,
( mbox
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f99,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f100,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mimplies @ ( mnot @ ( positive @ Y0 ) )
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f101,plain,
( $true
= ( 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 ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f102,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,[],[f73]) ).
thf(f103,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,[],[f75]) ).
thf(f104,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f107,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,[],[f102,f90,f85,f95,f89,f85]) ).
thf(f108,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,[],[f103,f90,f85,f107,f95,f92]) ).
thf(f109,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( positive
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( positive @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f99,f97,f90,f85,f82,f82]) ).
thf(f110,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( positive @ Y0 ) )
@ ( positive
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f100,f97,f90,f85,f82,f82]) ).
thf(f111,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: ( 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,[],[f101,f97,f90,f90,f85,f84,f95,f89,f85]) ).
thf(f112,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( positive
@ ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: mu] :
( ^ [Y4: ( mu > $i > $o ) > $i > $o,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y6: mu > $i > $o] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu > $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y4 @ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] : ( Y5 @ Y7 ) )
@ ( ^ [Y5: mu > $i > $o,Y6: $i] :
( !! @ mu
@ ^ [Y7: mu] : ( Y5 @ Y7 @ Y6 ) )
@ ^ [Y5: mu] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
=> ( Y7 @ Y8 ) )
@ ( Y2 @ Y5 )
@ ( Y4 @ Y5 ) ) ) ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 ) )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f104,f97,f108]) ).
thf(f113,plain,
( $true
= ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( Y3 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,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,[],[f113]) ).
thf(f115,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f116,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i] :
( $true
= ( !! @ ( 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 ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,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,[],[f117]) ).
thf(f119,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,[],[f118]) ).
thf(f120,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,[],[f119]) ).
thf(f121,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( $true
= ( ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) )
=> ( positive @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f122,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ( positive @ X2 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( positive @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,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,[],[f122]) ).
thf(f124,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X2 @ Y1 @ Y0 )
=> ( X3 @ Y1 @ Y0 ) ) )
@ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK0 @ X3 @ X2 ) )
=> ( X3 @ Y0 @ ( sK0 @ X3 @ X2 ) ) ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: mu] :
( ( X2 @ Y0 @ ( sK0 @ X3 @ X2 ) )
=> ( X3 @ Y0 @ ( sK0 @ X3 @ X2 ) ) )
@ ( sK1 @ X3 @ X2 ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f125]) ).
thf(f127,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 ) ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f129,plain,
! [X2: mu > $i > $o,X3: mu > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) @ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f130,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ~ ( positive @ Y1 @ Y0 )
=> ( positive
@ ^ [Y2: mu,Y3: $i] :
~ ( Y1 @ Y2 @ Y3 )
@ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f131,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,[],[f130]) ).
thf(f132,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,[],[f131]) ).
thf(f133,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,[],[f132]) ).
thf(f134,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ~ ( positive @ X2 @ X1 )
=> ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( ~ ( positive @ X2 @ X1 ) ) )
| ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f136,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,[],[f135]) ).
thf(f137,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,[],[f109]) ).
thf(f138,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,[],[f137]) ).
thf(f139,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,[],[f138]) ).
thf(f140,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] :
~ ( Y0 @ Y1 @ Y2 )
@ X1 )
=> ~ ( positive @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
=> ~ ( positive @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,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,[],[f141]) ).
thf(f143,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,[],[f142]) ).
thf(f227,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $true
= ( positive @ X0 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) )
| ( X0 != X2 ) ),
inference(constrained_superposition,[],[f136,f143]) ).
thf(f228,plain,
! [X2: mu > $i > $o,X0: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X0 @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) )
| ( X0 != X2 ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f9130,plain,
! [X3: mu > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK1 @ X3
@ ^ [Y0: mu,Y1: $i] : $false )
@ ( sK0 @ X3
@ ^ [Y0: mu,Y1: $i] : $false ) ) )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
inference(primitive_instantiation,[],[f129]) ).
thf(f9848,plain,
! [X3: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f9130]) ).
thf(f9849,plain,
! [X3: mu > $i > $o,X1: $i] :
( ( $true
= ( positive @ X3 @ X1 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
inference(trivial_inequality_removal,[],[f9848]) ).
thf(f9853,definition,
( spl2_31
<=> ! [X1: $i] :
( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_31])],[avatar_definition]) ).
thf(f9854,plain,
( ! [X1: $i] :
( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) )
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f9853]) ).
thf(f9921,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
inference(constrained_superposition,[],[f143,f9849]) ).
thf(f10112,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X0 @ X1 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X1 ) ) ),
inference(trivial_inequality_removal,[],[f9921]) ).
thf(f10217,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X1 @ X0 ) )
| ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X1 ) )
| ~ spl2_31 ),
inference(constrained_superposition,[],[f228,f9854]) ).
thf(f10306,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : $false )
!= X1 )
| ( $false
= ( positive @ X1 @ X0 ) ) )
| ~ spl2_31 ),
inference(trivial_inequality_removal,[],[f10217]) ).
thf(f10349,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : $false
@ ( sK48 @ X1 ) )
!= ( X1 @ ( sK48 @ X1 ) ) )
| ( $false
= ( positive @ X1 @ X0 ) ) )
| ~ spl2_31 ),
inference(negative_extensionality,[],[f10306]) ).
thf(f10351,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( ( ^ [Y0: $i] : $false )
!= ( X1 @ ( sK48 @ X1 ) ) )
| ( $false
= ( positive @ X1 @ X0 ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10349]) ).
thf(f10362,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( ( ^ [Y0: $i] : $false
@ ( sK51 @ X1 ) )
!= ( X1 @ ( sK48 @ X1 ) @ ( sK51 @ X1 ) ) )
| ( $false
= ( positive @ X1 @ X0 ) ) )
| ~ spl2_31 ),
inference(negative_extensionality,[],[f10351]) ).
thf(f10364,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: $i] : $false
@ ( sK51 @ X1 ) ) )
| ( $false
= ( positive @ X1 @ X0 ) )
| ( $true
= ( X1 @ ( sK48 @ X1 ) @ ( sK51 @ X1 ) ) ) )
| ~ spl2_31 ),
inference(xor_proxy_clausification,[],[f10362]) ).
thf(f10367,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X1 @ X0 ) )
| ( $true
= ( X1 @ ( sK48 @ X1 ) @ ( sK51 @ X1 ) ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10364]) ).
thf(f10368,plain,
( ! [X0: $i,X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ X0 ) )
| ( $true
= ( X1 @ ( sK48 @ X1 ) @ ( sK51 @ X1 ) ) ) )
| ~ spl2_31 ),
inference(trivial_inequality_removal,[],[f10367]) ).
thf(f10521,plain,
( ( $true = $false )
| ( $true
= ( ^ [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 ) ) ) ) )
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) ) )
| ~ spl2_31 ),
inference(constrained_superposition,[],[f114,f10368]) ).
thf(f10759,plain,
( ( $true
= ( ^ [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 ) ) ) ) )
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) ) )
| ~ spl2_31 ),
inference(trivial_inequality_removal,[],[f10521]) ).
thf(f10760,plain,
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10759]) ).
thf(f10761,plain,
( ! [X1: mu > $i > $o] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl2_31 ),
inference(pi_proxy_clausification,[],[f10760]) ).
thf(f10762,plain,
( ! [X1: mu > $i > $o] :
( $true
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10761]) ).
thf(f10763,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl2_31 ),
inference(imp_proxy_clausification,[],[f10762]) ).
thf(f10764,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ( sK58 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl2_31 ),
inference(sigma_proxy_clausification,[],[f10763]) ).
thf(f10765,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( X1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ( sK58 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) )
@ X2 ) ) )
| ~ spl2_31 ),
inference(pi_proxy_clausification,[],[f10764]) ).
thf(f10766,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ( sK58 @ X1
@ ( sK48
@ ^ [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 ) ) ) ) ) )
@ ( sK51
@ ^ [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 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ( sK58 @ X1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10765]) ).
thf(f10767,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ( sK58 @ X1 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) ) )
| ~ spl2_31 ),
inference(imp_proxy_clausification,[],[f10766]) ).
thf(f10771,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ( sK58 @ X1 @ Y1 @ Y0 ) ) )
@ ( sK60 @ X1 ) ) )
| ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) ) )
| ~ spl2_31 ),
inference(sigma_proxy_clausification,[],[f10767]) ).
thf(f10772,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( X1 @ Y1 @ Y0 )
=> ( sK58 @ X1 @ Y1 @ Y0 ) ) )
@ ( sK60 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mu] : ( X1 @ Y0 @ X2 )
@ ( sK61 @ X1 @ X2 ) ) ) )
| ~ spl2_31 ),
inference(sigma_proxy_clausification,[],[f10771]) ).
thf(f10773,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( X1 @ Y0 @ ( sK60 @ X1 ) )
=> ( sK58 @ X1 @ Y0 @ ( sK60 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ ( sK61 @ X1 @ X2 ) @ X2 ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10772]) ).
thf(f10774,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ^ [Y0: mu] :
( ( X1 @ Y0 @ ( sK60 @ X1 ) )
=> ( sK58 @ X1 @ Y0 @ ( sK60 @ X1 ) ) )
@ ( sK62 @ X1 ) ) )
| ( $true
= ( X1 @ ( sK61 @ X1 @ X2 ) @ X2 ) ) )
| ~ spl2_31 ),
inference(sigma_proxy_clausification,[],[f10773]) ).
thf(f10775,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $false
= ( ( X1 @ ( sK62 @ X1 ) @ ( sK60 @ X1 ) )
=> ( sK58 @ X1 @ ( sK62 @ X1 ) @ ( sK60 @ X1 ) ) ) )
| ( $true
= ( X1 @ ( sK61 @ X1 @ X2 ) @ X2 ) ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f10774]) ).
thf(f10777,plain,
( ! [X2: $i,X1: mu > $i > $o] :
( ( $true
= ( X1 @ ( sK62 @ X1 ) @ ( sK60 @ X1 ) ) )
| ( $true
= ( X1 @ ( sK61 @ X1 @ X2 ) @ X2 ) ) )
| ~ spl2_31 ),
inference(imp_proxy_clausification,[],[f10775]) ).
thf(f14246,plain,
( ! [X2: $i,X0: mu > $i > $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
( positive
@ ( ^ [Y2: mu,Y3: $i,Y4: mu,Y5: $i] : $false
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ ( sK61
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ( ^ [Y2: mu,Y3: $i,Y4: mu,Y5: $i] : $false
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ X2 )
@ X2 ) )
| ( ( X0
@ ( sK62
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK60
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) )
| ~ spl2_31 ),
inference(constrained_superposition,[],[f10777,f9854]) ).
thf(f15007,plain,
( ! [X2: $i,X0: mu > $i > $i,X1: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
( positive
@ ( ^ [Y2: mu,Y3: $i,Y4: mu,Y5: $i] : $false
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ ( sK61
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ( ^ [Y2: mu,Y3: $i,Y4: mu,Y5: $i] : $false
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) )
@ X2 )
@ X2 ) )
| ( ( X0
@ ( sK62
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK60
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) )
| ~ spl2_31 ),
inference(trivial_inequality_removal,[],[f14246]) ).
thf(f15008,plain,
( ! [X2: $i,X0: mu > $i > $i,X1: $i] :
( ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ ( X0
@ ( sK61
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) )
@ X2 )
@ X2 ) ) )
| ( ( X0
@ ( sK62
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK60
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) )
| ~ spl2_31 ),
inference(beta-eta_normalization,[],[f15007]) ).
thf(f15153,plain,
( ! [X0: mu > $i > $i,X1: $i] :
( ( $true = $false )
| ( ( X0
@ ( sK62
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK60
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) )
| ~ spl2_31 ),
inference(forward_demodulation,[],[f15008,f9854]) ).
thf(f15154,plain,
( ! [X0: mu > $i > $i,X1: $i] :
( ( X0
@ ( sK62
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK60
@ ^ [Y0: mu,Y1: $i] :
( positive
@ ^ [Y2: mu,Y3: $i] : $false
@ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 )
| ~ spl2_31 ),
inference(trivial_inequality_removal,[],[f15153]) ).
thf(f15155,plain,
( $false
| ~ spl2_31 ),
inference(flex-flex_simplification,[],[f15154]) ).
thf(f15156,plain,
~ spl2_31,
inference(avatar_contradiction_clause,[],[f15155]) ).
thf(f16109,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X0 ) ) ),
inference(equality_factoring,[],[f10112]) ).
thf(f16110,plain,
! [X0: $i] :
( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : $false
@ X0 ) ),
inference(trivial_inequality_removal,[],[f16109]) ).
thf(f16314,plain,
spl2_31,
inference(avatar_split_clause,[],[f16110,f9853]) ).
cnf(s4225,plain,
~ spl2_31,
inference(sat_conversion,[],[f15156]) ).
cnf(s4460,plain,
spl2_31,
inference(sat_conversion,[],[f16314]) ).
cnf(s4461,plain,
$false,
inference(rat,[],[s4225,s4460]) ).
thf(f16315,plain,
$false,
inference(avatar_sat_refutation,[],[s4461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n005.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:19:32 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.74/0.89 % (1639025)Will run a generic schedule for satisfiability detection.
% 3.74/0.89 % (1639035)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1382940885:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.74/0.89 % (1639031)% WARNING: option uhcvi not known.
% 3.74/0.89 % (1639030)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1693800660_2999 on theBenchmark for (2999ds/0Mi)
% 3.74/0.89 % (1639033)dis+10_1_sil=32000:sp=arity:random_seed=2531177296:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.74/0.89 % (1639032)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1531586276:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.74/0.89 % (1639034)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=920408639:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.74/0.89 % (1639036)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2413343490:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.74/0.89 % (1639031)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1670359702:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.74/0.89 % (1639034)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.74/0.89 % (1639031)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.74/0.89 % Exception at run slice level
% 3.74/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.74/0.89 % (1639031)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.74/0.89 % (1639044)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1677603871:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.74/0.89 % Exception at run slice level
% 3.74/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.74/0.89 % (1639035)Instruction limit reached!
% 3.74/0.89 % (1639035)------------------------------
% 3.74/0.89 % (1639035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.74/0.89 % (1639035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/0.89 % (1639035)CaDiCaL version: 2.1.3
% 3.74/0.89 % (1639035)Termination reason: Instruction limit
% 3.74/0.89 % (1639035)Termination phase: Saturation
% 3.74/0.89 % (1639035)Time elapsed: 0.033 s
% 3.74/0.89 % (1639035)Peak memory usage: 12 MB
% 3.74/0.89 % (1639035)Instructions burned: 132 (million)
% 3.74/0.89 % (1639047)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=414152715:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.74/0.89 % (1639047)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.74/0.89 % (1639047)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.74/0.89 % (1639046)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=717923258:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.74/0.89 % (1639033)Instruction limit reached!
% 3.74/0.89 % (1639033)------------------------------
% 3.74/0.89 % (1639033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.74/0.89 % (1639033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/0.89 % (1639033)CaDiCaL version: 2.1.3
% 3.74/0.89 % (1639033)Termination reason: Instruction limit
% 3.74/0.89 % (1639033)Termination phase: Saturation
% 3.74/0.89 % (1639033)Time elapsed: 0.051 s
% 3.74/0.89 % (1639033)Peak memory usage: 12 MB
% 3.74/0.89 % (1639033)Instructions burned: 104 (million)
% 3.74/0.89 % (1639034)Instruction limit reached!
% 3.74/0.89 % (1639034)------------------------------
% 3.74/0.89 % (1639034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.74/0.89 % (1639034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/0.89 % (1639034)CaDiCaL version: 2.1.3
% 3.74/0.89 % (1639034)Termination reason: Instruction limit
% 3.74/0.89 % (1639034)Termination phase: Saturation
% 3.74/0.89 % (1639034)Time elapsed: 0.057 s
% 3.74/0.89 % (1639034)Peak memory usage: 12 MB
% 3.74/0.89 % (1639034)Instructions burned: 117 (million)
% 3.74/0.89 % (1639036)Instruction limit reached!
% 3.74/0.89 % (1639036)------------------------------
% 3.74/0.89 % (1639036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639036)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639036)Termination reason: Instruction limit
% 8.47/1.60 % (1639036)Termination phase: Saturation
% 8.47/1.60 % (1639036)Time elapsed: 0.061 s
% 8.47/1.60 % (1639036)Peak memory usage: 12 MB
% 8.47/1.60 % (1639036)Instructions burned: 159 (million)
% 8.47/1.60 % (1639050)ott-21_1_sil=16000:fs=off:random_seed=1870427994:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 8.47/1.60 % (1639051)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=83975941:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 8.47/1.60 % (1639052)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3139789039:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639056)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1626743740:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.47/1.60 % (1639046)Instruction limit reached!
% 8.47/1.60 % (1639046)------------------------------
% 8.47/1.60 % (1639046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639046)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639046)Termination reason: Instruction limit
% 8.47/1.60 % (1639046)Termination phase: Saturation
% 8.47/1.60 % (1639046)Time elapsed: 0.063 s
% 8.47/1.60 % (1639046)Peak memory usage: 13 MB
% 8.47/1.60 % (1639046)Instructions burned: 131 (million)
% 8.47/1.60 % (1639058)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=753845664:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639060)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=495858329:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 8.47/1.60 % (1639060)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.47/1.60 % (1639050)Instruction limit reached!
% 8.47/1.60 % (1639050)------------------------------
% 8.47/1.60 % (1639050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639050)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639050)Termination reason: Instruction limit
% 8.47/1.60 % (1639050)Termination phase: Saturation
% 8.47/1.60 % (1639050)Time elapsed: 0.084 s
% 8.47/1.60 % (1639050)Peak memory usage: 12 MB
% 8.47/1.60 % (1639050)Instructions burned: 180 (million)
% 8.47/1.60 % (1639062)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1501459257:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 8.47/1.60 % (1639062)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.47/1.60 % (1639047)Instruction limit reached!
% 8.47/1.60 % (1639047)------------------------------
% 8.47/1.60 % (1639047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639047)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639047)Termination reason: Instruction limit
% 8.47/1.60 % (1639047)Termination phase: Saturation
% 8.47/1.60 % (1639047)Time elapsed: 0.161 s
% 8.47/1.60 % (1639047)Peak memory usage: 14 MB
% 8.47/1.60 % (1639047)Instructions burned: 687 (million)
% 8.47/1.60 % (1639064)fmb+10_1_sil=64000:random_seed=661058799:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 8.47/1.60 % (1639064)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639066)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1634196078:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639068)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=46973944:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639070)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=406493339:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 8.47/1.60 % (1639070)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.47/1.60 % (1639051)Instruction limit reached!
% 8.47/1.60 % (1639051)------------------------------
% 8.47/1.60 % (1639051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639051)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639051)Termination reason: Instruction limit
% 8.47/1.60 % (1639051)Termination phase: Saturation
% 8.47/1.60 % (1639051)Time elapsed: 0.222 s
% 8.47/1.60 % (1639051)Peak memory usage: 13 MB
% 8.47/1.60 % (1639051)Instructions burned: 477 (million)
% 8.47/1.60 % (1639072)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4112562505:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 8.47/1.60 % (1639072)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.47/1.60 % (1639072)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.47/1.60 % (1639060)Instruction limit reached!
% 8.47/1.60 % (1639060)------------------------------
% 8.47/1.60 % (1639060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639060)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639060)Termination reason: Instruction limit
% 8.47/1.60 % (1639060)Termination phase: Saturation
% 8.47/1.60 % (1639060)Time elapsed: 0.229 s
% 8.47/1.60 % (1639060)Peak memory usage: 13 MB
% 8.47/1.60 % (1639060)Instructions burned: 695 (million)
% 8.47/1.60 % (1639074)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=147283322:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639076)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4218678719:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639078)ott-2_1_sil=16000:newcnf=on:random_seed=2181567230:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 8.47/1.60 % (1639078)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.47/1.60 % (1639062)Instruction limit reached!
% 8.47/1.60 % (1639062)------------------------------
% 8.47/1.60 % (1639062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639062)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639062)Termination reason: Instruction limit
% 8.47/1.60 % (1639062)Termination phase: Saturation
% 8.47/1.60 % (1639062)Time elapsed: 0.395 s
% 8.47/1.60 % (1639062)Peak memory usage: 14 MB
% 8.47/1.60 % (1639062)Instructions burned: 880 (million)
% 8.47/1.60 % (1639080)ott+10_1_sil=32000:tgt=ground:random_seed=3602065765:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 8.47/1.60 % (1639056)Instruction limit reached!
% 8.47/1.60 % (1639056)------------------------------
% 8.47/1.60 % (1639056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639056)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639056)Termination reason: Instruction limit
% 8.47/1.60 % (1639056)Termination phase: Saturation
% 8.47/1.60 % (1639056)Time elapsed: 0.522 s
% 8.47/1.60 % (1639056)Peak memory usage: 16 MB
% 8.47/1.60 % (1639056)Instructions burned: 1180 (million)
% 8.47/1.60 % (1639082)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4033374868:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 8.47/1.60 % Exception at run slice level
% 8.47/1.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.47/1.60 % (1639084)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1337590259:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 8.47/1.60 % (1639084)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.47/1.60 % (1639078)Instruction limit reached!
% 8.47/1.60 % (1639078)------------------------------
% 8.47/1.60 % (1639078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639078)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639078)Termination reason: Instruction limit
% 8.47/1.60 % (1639078)Termination phase: Saturation
% 8.47/1.60 % (1639078)Time elapsed: 0.383 s
% 8.47/1.60 % (1639078)Peak memory usage: 15 MB
% 8.47/1.60 % (1639078)Instructions burned: 871 (million)
% 8.47/1.60 % (1639086)dis+21_1_sil=32000:sas=cadical:random_seed=3530260897:i=3773:amm=off_2991 on theBenchmark for (2991ds/3773Mi)
% 8.47/1.60 % (1639072)Instruction limit reached!
% 8.47/1.60 % (1639072)------------------------------
% 8.47/1.60 % (1639072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.47/1.60 % (1639072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.47/1.60 % (1639072)CaDiCaL version: 2.1.3
% 8.47/1.60 % (1639072)Termination reason: Instruction limit
% 8.47/1.60 % (1639072)Termination phase: Saturation
% 8.47/1.60 % (1639072)Time elapsed: 0.741 s
% 8.47/1.60 % (1639072)Peak memory usage: 18 MB
% 8.47/1.60 % (1639072)Instructions burned: 1472 (million)
% 8.47/1.60 % (1639088)ott+11_1_sil=16000:gs=on:random_seed=220943106:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2989 on theBenchmark for (2989ds/2251Mi)
% 8.47/1.60 % (1639088)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.47/1.60 % (1639032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1639025-1639032"...
% 8.47/1.60 % (1639032)...printing done.
% 8.47/1.60 % (1639032)Refutation found. Thanks to Tanya!
% 8.47/1.60 % SZS status ContradictoryAxioms for theBenchmark
% 8.47/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 9.88/1.60 % (1639032)------------------------------
% 9.88/1.60 % (1639032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.88/1.60 % (1639032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/1.60 % (1639032)CaDiCaL version: 2.1.3
% 9.88/1.60 % (1639032)Termination reason: Refutation
% 9.88/1.60 % (1639032)Time elapsed: 1.344 s
% 9.88/1.60 % (1639032)Peak memory usage: 19 MB
% 9.88/1.60 % (1639032)Instructions burned: 3099 (million)
% 9.88/1.60 % (1639025)Success in time 1.379 s
% 9.88/1.60 % Vampire exiting
%------------------------------------------------------------------------------