%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:20:20 AM UTC 2026
% Result : Theorem 0.91s 0.48s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 22
% Syntax : Number of formulae : 211 ( 83 unt; 0 typ; 8 def)
% Number of atoms : 1422 ( 269 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1994 ( 188 ~; 236 |; 12 &;1327 @)
% ( 10 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 571 ( 571 >; 0 *; 0 +; 0 <<)
% Number of symbols : 164 ( 160 usr; 16 con; 0-4 aty)
% ( 117 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 487 ( 6 sgn 85 !; 0 ?; 487 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_31,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vIFF: $o > $o > $o ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sK1: mu ).
thf(func_def_46,type,
sK2: mu > $i > $o ).
thf(func_def_47,type,
sK3: mu > $i > $o ).
thf(func_def_49,type,
sK5: mu ).
thf(func_def_50,type,
sK6: mu ).
thf(func_def_51,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK7: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > $i ).
thf(func_def_53,type,
sK8: ( mu > $i > $o ) > $i > ( mu > $i > $o ) > mu ).
thf(func_def_55,type,
sK10: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_56,type,
sK11: ( mu > $i > $o ) > $i > mu ).
thf(func_def_57,type,
sK12: ( mu > $i > $o ) > $i ).
thf(func_def_58,type,
sK13: ( mu > $i > $o ) > $i > mu ).
thf(func_def_59,type,
sK14: ( mu > $i > $o ) > mu ).
thf(func_def_60,type,
sK15: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_61,type,
sK16: ( mu > $i > $o ) > $i > mu ).
thf(func_def_62,type,
sK17: ( mu > $i > $o ) > $i ).
thf(func_def_63,type,
sK18: ( mu > $i > $o ) > $i > mu ).
thf(func_def_64,type,
sK19: ( mu > $i > $o ) > mu ).
thf(func_def_65,type,
sK20: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_66,type,
sK21: ( mu > $i > $o ) > $i > mu ).
thf(func_def_67,type,
sK22: ( mu > $i > $o ) > $i ).
thf(func_def_68,type,
sK23: ( mu > $i > $o ) > $i > mu ).
thf(func_def_69,type,
sK24: ( mu > $i > $o ) > mu ).
thf(func_def_70,type,
sK25: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_71,type,
sK26: ( mu > $i > $o ) > $i > mu ).
thf(func_def_72,type,
sK27: ( mu > $i > $o ) > $i ).
thf(func_def_73,type,
sK28: ( mu > $i > $o ) > $i > mu ).
thf(func_def_74,type,
sK29: ( mu > $i > $o ) > mu ).
thf(func_def_75,type,
sK30: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_76,type,
sK31: ( mu > $i > $o ) > $i > mu ).
thf(func_def_77,type,
sK32: ( mu > $i > $o ) > $i ).
thf(func_def_78,type,
sK33: ( mu > $i > $o ) > $i > mu ).
thf(func_def_79,type,
sK34: ( mu > $i > $o ) > mu ).
thf(func_def_80,type,
sK35: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_81,type,
sK36: ( mu > $i > $o ) > $i > mu ).
thf(func_def_82,type,
sK37: ( mu > $i > $o ) > $i ).
thf(func_def_83,type,
sK38: ( mu > $i > $o ) > $i > mu ).
thf(func_def_84,type,
sK39: ( mu > $i > $o ) > mu ).
thf(func_def_85,type,
sK40: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_86,type,
sK41: ( mu > $i > $o ) > $i > mu ).
thf(func_def_87,type,
sK42: ( mu > $i > $o ) > $i ).
thf(func_def_88,type,
sK43: ( mu > $i > $o ) > $i > mu ).
thf(func_def_89,type,
sK44: ( mu > $i > $o ) > mu ).
thf(func_def_90,type,
sK45: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_91,type,
sK46: ( mu > $i > $o ) > $i > mu ).
thf(func_def_92,type,
sK47: ( mu > $i > $o ) > $i ).
thf(func_def_93,type,
sK48: ( mu > $i > $o ) > $i > mu ).
thf(func_def_94,type,
sK49: ( mu > $i > $o ) > mu ).
thf(func_def_95,type,
sK50: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_96,type,
sK51: ( mu > $i > $o ) > $i > mu ).
thf(func_def_97,type,
sK52: ( mu > $i > $o ) > $i ).
thf(func_def_98,type,
sK53: ( mu > $i > $o ) > $i > mu ).
thf(func_def_99,type,
sK54: ( mu > $i > $o ) > mu ).
thf(func_def_100,type,
sK55: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_101,type,
sK56: ( mu > $i > $o ) > $i > mu ).
thf(func_def_102,type,
sK57: ( mu > $i > $o ) > $i ).
thf(func_def_103,type,
sK58: ( mu > $i > $o ) > $i > mu ).
thf(func_def_104,type,
sK59: ( mu > $i > $o ) > mu ).
thf(func_def_105,type,
sK60: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_106,type,
sK61: ( mu > $i > $o ) > $i > mu ).
thf(func_def_107,type,
sK62: ( mu > $i > $o ) > $i ).
thf(func_def_108,type,
sK63: ( mu > $i > $o ) > $i > mu ).
thf(func_def_109,type,
sK64: ( mu > $i > $o ) > mu ).
thf(func_def_110,type,
sK65: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_111,type,
sK66: ( mu > $i > $o ) > $i > mu ).
thf(func_def_112,type,
sK67: ( mu > $i > $o ) > $i ).
thf(func_def_113,type,
sK68: ( mu > $i > $o ) > $i > mu ).
thf(func_def_114,type,
sK69: ( mu > $i > $o ) > mu ).
thf(func_def_115,type,
sK70: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_116,type,
sK71: $i > ( mu > $i > $o ) > mu ).
thf(func_def_117,type,
sK72: ( mu > $i > $o ) > $i ).
thf(func_def_118,type,
sK73: $i > ( mu > $i > $o ) > mu ).
thf(func_def_119,type,
sK74: ( mu > $i > $o ) > mu ).
thf(func_def_120,type,
sK75: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_121,type,
sK76: $i > ( mu > $i > $o ) > mu ).
thf(func_def_122,type,
sK77: ( mu > $i > $o ) > $i ).
thf(func_def_123,type,
sK78: $i > ( mu > $i > $o ) > mu ).
thf(func_def_124,type,
sK79: ( mu > $i > $o ) > mu ).
thf(func_def_125,type,
sK80: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_126,type,
sK81: ( mu > $i > $o ) > $i > mu ).
thf(func_def_127,type,
sK82: ( mu > $i > $o ) > $i ).
thf(func_def_128,type,
sK83: ( mu > $i > $o ) > $i > mu ).
thf(func_def_129,type,
sK84: ( mu > $i > $o ) > mu ).
thf(func_def_130,type,
sK85: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_131,type,
sK86: ( mu > $i > $o ) > $i > mu ).
thf(func_def_132,type,
sK87: ( mu > $i > $o ) > $i ).
thf(func_def_133,type,
sK88: ( mu > $i > $o ) > $i > mu ).
thf(func_def_134,type,
sK89: ( mu > $i > $o ) > mu ).
thf(func_def_135,type,
sK90: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_136,type,
sK91: ( mu > $i > $o ) > $i > mu ).
thf(func_def_137,type,
sK92: ( mu > $i > $o ) > $i ).
thf(func_def_138,type,
sK93: ( mu > $i > $o ) > $i > mu ).
thf(func_def_139,type,
sK94: ( mu > $i > $o ) > mu ).
thf(func_def_140,type,
sK95: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_141,type,
sK96: ( mu > $i > $o ) > $i > mu ).
thf(func_def_142,type,
sK97: ( mu > $i > $o ) > $i ).
thf(func_def_143,type,
sK98: ( mu > $i > $o ) > $i > mu ).
thf(func_def_144,type,
sK99: ( mu > $i > $o ) > mu ).
thf(func_def_145,type,
sK100: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_146,type,
sK101: ( mu > $i > $o ) > $i > mu ).
thf(func_def_147,type,
sK102: ( mu > $i > $o ) > $i ).
thf(func_def_148,type,
sK103: ( mu > $i > $o ) > $i > mu ).
thf(func_def_149,type,
sK104: ( mu > $i > $o ) > mu ).
thf(func_def_150,type,
sK105: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_151,type,
sK106: ( mu > $i > $o ) > $i > mu ).
thf(func_def_152,type,
sK107: ( mu > $i > $o ) > $i ).
thf(func_def_153,type,
sK108: ( mu > $i > $o ) > $i > mu ).
thf(func_def_154,type,
sK109: ( mu > $i > $o ) > mu ).
thf(f4,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mnot) ).
thf(f6,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mand) ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f9,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mequiv) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI001^0.ax',axA1) ).
thf(f25,axiom,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/PHI001^0.ax',defD2) ).
thf(f31,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
file('/export/starexec/sandbox/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(f36,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f40,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f41,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f46,plain,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f47,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f50,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f51,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f53,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f62,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f63,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f67,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f70,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) )
@ ( mnot @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f71,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f74,plain,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f75,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f78,plain,
( mvalid
@ ( mforall_indset
@ ^ [X0: mu > $i > $o] : ( mimplies @ ( positive @ X0 ) @ ( mbox @ ( positive @ X0 ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f79,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,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(f81,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,[],[f80]) ).
thf(f86,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f87,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(flattening,[],[f87]) ).
thf(f92,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f94,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f95,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f97,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f99,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f100,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f105,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f107,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f111,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) )
@ ( mnot @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f113,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f115,plain,
( $true
= ( mvalid
@ ( mforall_indset
@ ^ [Y0: mu > $i > $o] : ( mimplies @ ( positive @ Y0 ) @ ( mbox @ ( positive @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f116,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,[],[f81]) ).
thf(f119,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
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,[],[f107,f105]) ).
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,[],[f113,f100,f95]) ).
thf(f125,plain,
( essence
= ( ^ [Y0: mu > $i > $o,Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( Y0 @ Y1 )
@ ( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( Y2 @ Y1 )
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y4 @ Y6 ) ) )
@ rel
@ ( ^ [Y3: mu > $i > $o,Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
=> ( Y5 @ Y6 ) )
@ ( Y0 @ Y3 )
@ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f116,f94,f100,f95,f122,f99,f95]) ).
thf(f127,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,[],[f111,f109,f100,f97,f92,f92]) ).
thf(f130,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( positive @ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ rel
@ ( positive @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f115,f109,f100,f95,f122]) ).
thf(f132,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 )
@ ( ^ [Y1: mu > $i > $o,Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( Y1 @ Y2 )
@ ( ^ [Y3: ( mu > $i > $o ) > $i > $o,Y4: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: mu > $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
=> ( Y5 @ Y6 ) )
@ ( Y3 @ Y2 )
@ ( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y5 @ Y7 ) ) )
@ rel
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( Y1 @ Y4 )
@ ( Y3 @ Y4 ) ) ) ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f119,f109,f99,f95,f124,f125,f124]) ).
thf(f133,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( positive @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y0 @ Y3 )
| ( !! @ mu
@ ^ [Y4: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y5: mu > $i > $o] :
( ( positive @ Y5 @ Y3 )
=> ( Y5 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK0 )
=> ( Y1 @ Y0 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( Y1 @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ sK0 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y2 )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
=> ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) )
& ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f140,plain,
! [X1: mu > $i > $o] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X1: mu > $i > $o] :
( $true
= ( ( positive @ X1 @ sK0 )
=> ( X1 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK0 ) )
| ( $true
= ( X1 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f144,plain,
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) )
| ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( Y0 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ sK0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK0 )
=> ( Y0 @ sK1 @ sK0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ( sK2 @ sK1 @ sK0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( ( positive @ sK3 @ sK0 )
=> ( sK3 @ sK1 @ sK0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
@ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) )
@ sK5 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f159,plain,
( ( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) ) )
=> ( sK2 @ sK5 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( sK2 @ sK5 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK5 @ sK4 ) )
@ X1 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ( positive @ X1 @ sK4 )
=> ( X1 @ sK5 @ sK4 ) ) )
| ( $true
= ( positive @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( positive @ sK3 @ sK0 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f166,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ~ ( rel @ sK0 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK4 )
=> ( Y1 @ Y0 @ sK4 ) ) )
=> ( sK2 @ Y0 @ sK4 ) )
@ sK6 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f170,plain,
( ( $false
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) ) )
=> ( sK2 @ sK6 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( sK2 @ sK6 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f173,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK4 )
=> ( Y0 @ sK6 @ sK4 ) )
@ X1 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: mu > $i > $o] :
( ( $true
= ( ( positive @ X1 @ sK4 )
=> ( X1 @ sK6 @ sK4 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $false
= ( sK3 @ sK1 @ sK0 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f178,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,[],[f130]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel @ Y0 @ Y2 )
| ( positive @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,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,[],[f179]) ).
thf(f181,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,[],[f180]) ).
thf(f182,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,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,[],[f182]) ).
thf(f184,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel @ X1 @ Y0 )
| ( positive @ X2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( ~ ( rel @ X1 @ X3 )
| ( positive @ X2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( positive @ X2 @ X3 ) )
| ( $true
= ( ~ ( rel @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: mu > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( positive @ X2 @ X1 ) )
| ( $true
= ( positive @ X2 @ X3 ) )
| ( $false
= ( rel @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f208,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,[],[f127]) ).
thf(f209,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,[],[f208]) ).
thf(f210,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,[],[f209]) ).
thf(f211,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,[],[f210]) ).
thf(f212,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $false
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X2 @ Y0 @ Y1 )
@ X1 ) )
| ( $true
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f213]) ).
thf(f216,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,[],[f215]) ).
thf(f217,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,[],[f214]) ).
thf(f219,definition,
( spl9_1
<=> ( $true
= ( positive @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f221,plain,
( ( $true
= ( positive @ sK3 @ sK0 ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f223,definition,
( spl9_2
<=> ( $true
= ( sK2 @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f225,plain,
( ( $true
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f150,f223,f219]) ).
thf(f228,definition,
( spl9_3
<=> ( $false
= ( sK3 @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f230,plain,
( ( $false
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl9_3
| spl9_2 ),
inference(avatar_split_clause,[],[f149,f223,f228]) ).
thf(f233,definition,
( spl9_4
<=> ( $true
= ( rel @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f235,plain,
( ( $true
= ( rel @ sK0 @ sK4 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f157,f233,f219]) ).
thf(f238,definition,
( spl9_5
<=> ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f239,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK5 @ sK4 ) ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f240,plain,
( spl9_1
| spl9_5 ),
inference(avatar_split_clause,[],[f164,f238,f219]) ).
thf(f242,definition,
( spl9_6
<=> ( $false
= ( sK2 @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f244,plain,
( ( $false
= ( sK2 @ sK5 @ sK4 ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f245,plain,
( spl9_1
| spl9_6 ),
inference(avatar_split_clause,[],[f160,f242,f219]) ).
thf(f246,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f168,f233,f228]) ).
thf(f248,definition,
( spl9_7
<=> ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f249,plain,
( ! [X1: mu > $i > $o] :
( ( $false
= ( positive @ X1 @ sK4 ) )
| ( $true
= ( X1 @ sK6 @ sK4 ) ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f250,plain,
( spl9_3
| spl9_7 ),
inference(avatar_split_clause,[],[f175,f248,f228]) ).
thf(f252,definition,
( spl9_8
<=> ( $false
= ( sK2 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f254,plain,
( ( $false
= ( sK2 @ sK6 @ sK4 ) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f255,plain,
( spl9_3
| spl9_8 ),
inference(avatar_split_clause,[],[f171,f252,f228]) ).
thf(f265,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl9_1 ),
inference(constrained_superposition,[],[f142,f221]) ).
thf(f274,plain,
( ( $true
= ( sK3 @ sK1 @ sK0 ) )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f278,plain,
( ( $true = $false )
| ~ spl9_1
| ~ spl9_3 ),
inference(forward_demodulation,[],[f274,f230]) ).
thf(f279,plain,
( $false
| ~ spl9_1
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f280,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f279]) ).
thf(f377,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ sK0 ) )
| ( $true
= ( positive @ X0 @ sK4 ) ) )
| ~ spl9_4 ),
inference(constrained_superposition,[],[f187,f235]) ).
thf(f378,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( positive @ X0 @ sK0 ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f480,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( positive @ X0 @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(constrained_superposition,[],[f249,f378]) ).
thf(f481,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK0 ) )
| ( $true
= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f480]) ).
thf(f1488,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK0 ) )
| ( $false
= ( positive @ X0 @ sK4 ) ) )
| ~ spl9_4 ),
inference(constrained_superposition,[],[f378,f216]) ).
thf(f1489,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK0 ) )
| ( $false
= ( positive @ X0 @ sK4 ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f1488]) ).
thf(f2706,plain,
! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f142,f217]) ).
thf(f2716,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f2706]) ).
thf(f2717,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( ~ ( X0 @ sK1 @ sK0 ) ) )
| ( $true
= ( positive @ X0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f2716]) ).
thf(f2718,plain,
! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK0 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) ),
inference(not_proxy_clausification,[],[f2717]) ).
thf(f2768,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(constrained_superposition,[],[f481,f2718]) ).
thf(f2770,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl9_4 ),
inference(constrained_superposition,[],[f1489,f2718]) ).
thf(f2779,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f2770]) ).
thf(f2780,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( ~ ( X0 @ sK1 @ sK0 ) ) ) )
| ~ spl9_4 ),
inference(beta-eta_normalization,[],[f2779]) ).
thf(f2781,plain,
( ! [X0: mu > $i > $o] :
( ( $false
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl9_4 ),
inference(not_proxy_clausification,[],[f2780]) ).
thf(f2783,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f2768]) ).
thf(f2877,plain,
( ! [X0: mu > $i > mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK6
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(constrained_superposition,[],[f254,f2783]) ).
thf(f2892,plain,
( ! [X0: mu > $i > mu] :
( ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK6
!= ( X0 @ sK6 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f2877]) ).
thf(f2893,plain,
( ! [X0: mu > $i > mu] :
( ( sK6
!= ( X0 @ sK6 @ sK4 ) )
| ( $false
= ( sK2 @ ( X0 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(beta-eta_normalization,[],[f2892]) ).
thf(f3718,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl9_4 ),
inference(constrained_superposition,[],[f217,f2781]) ).
thf(f3769,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
~ ( X0 @ Y0 @ Y1 )
@ sK1
@ sK0 ) ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f3718]) ).
thf(f3770,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $true
= ( ~ ( X0 @ sK1 @ sK0 ) ) ) )
| ~ spl9_4 ),
inference(beta-eta_normalization,[],[f3769]) ).
thf(f3771,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( positive @ X0 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl9_4 ),
inference(not_proxy_clausification,[],[f3770]) ).
thf(f4128,plain,
( ( $false
= ( sK2
@ ( ^ [Y0: mu,Y1: $i] : Y0
@ sK1
@ sK0 )
@ sK0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(equality_resolution,[],[f2893]) ).
thf(f4131,plain,
( ( $false
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(beta-eta_normalization,[],[f4128]) ).
thf(f4185,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(constrained_superposition,[],[f4131,f225]) ).
thf(f4226,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f4185]) ).
thf(f4227,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f4226]) ).
thf(f4469,plain,
( ! [X0: mu > $i > $o] :
( ( $true = $false )
| ( $false
= ( X0 @ sK1 @ sK0 ) )
| ( $true
= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_5 ),
inference(constrained_superposition,[],[f3771,f239]) ).
thf(f4476,plain,
( ! [X0: mu > $i > $o] :
( ( $true
= ( X0 @ sK5 @ sK4 ) )
| ( $false
= ( X0 @ sK1 @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f4469]) ).
thf(f4609,plain,
( ! [X0: mu > $i > mu] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK5
!= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(constrained_superposition,[],[f244,f4476]) ).
thf(f4622,plain,
( ! [X0: mu > $i > mu] :
( ( $false
= ( ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X0 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ sK1
@ sK0 ) )
| ( sK5
!= ( X0 @ sK5 @ sK4 ) ) )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f4609]) ).
thf(f4623,plain,
( ! [X0: mu > $i > mu] :
( ( sK5
!= ( X0 @ sK5 @ sK4 ) )
| ( $false
= ( sK2 @ ( X0 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(beta-eta_normalization,[],[f4622]) ).
thf(f5659,plain,
( ( $false
= ( sK2
@ ( ^ [Y0: mu,Y1: $i] : Y0
@ sK1
@ sK0 )
@ sK0 ) )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(equality_resolution,[],[f4623]) ).
thf(f5662,plain,
( ( $false
= ( sK2 @ sK1 @ sK0 ) )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(beta-eta_normalization,[],[f5659]) ).
thf(f5716,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(constrained_superposition,[],[f5662,f225]) ).
thf(f5757,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f5716]) ).
thf(f5758,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(avatar_contradiction_clause,[],[f5757]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f226]) ).
cnf(s2,plain,
( spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f236]) ).
cnf(s4,plain,
( spl9_1
| spl9_5 ),
inference(sat_conversion,[],[f240]) ).
cnf(s5,plain,
( spl9_1
| spl9_6 ),
inference(sat_conversion,[],[f245]) ).
cnf(s6,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s7,plain,
( spl9_3
| spl9_7 ),
inference(sat_conversion,[],[f250]) ).
cnf(s8,plain,
( spl9_3
| spl9_8 ),
inference(sat_conversion,[],[f255]) ).
cnf(s10,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(sat_conversion,[],[f280]) ).
cnf(s74,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_8 ),
inference(sat_conversion,[],[f4227]) ).
cnf(s83,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(sat_conversion,[],[f5758]) ).
cnf(s84,plain,
spl9_1,
inference(rat,[],[s83,s1,s3,s4,s5]) ).
cnf(s85,plain,
~ spl9_3,
inference(rat,[],[s10,s84]) ).
cnf(s86,plain,
spl9_8,
inference(rat,[],[s8,s85]) ).
cnf(s87,plain,
spl9_7,
inference(rat,[],[s7,s85]) ).
cnf(s88,plain,
spl9_4,
inference(rat,[],[s6,s85]) ).
cnf(s89,plain,
spl9_2,
inference(rat,[],[s2,s85]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s74,s86,s87,s88,s89]) ).
thf(f5767,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:22:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/0.48 % (329518)Will run a generic schedule for satisfiability detection.
% 0.91/0.48 % (329529)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1892043028:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.91/0.48 % (329524)% WARNING: option uhcvi not known.
% 0.91/0.48 % (329527)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2197063051:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.91/0.48 % (329523)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1705468971_2999 on theBenchmark for (2999ds/0Mi)
% 0.91/0.48 % (329526)dis+10_1_sil=32000:sp=arity:random_seed=1777958153:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.91/0.48 % (329524)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=629297683:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.91/0.48 % (329525)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=347858512:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.91/0.48 % (329527)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.91/0.48 % (329524)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.91/0.48 % Exception at run slice level
% 0.91/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.91/0.48 % (329524)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.91/0.48 % (329528)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=296459408:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.91/0.48 % (329536)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4232836682:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.91/0.48 % Exception at run slice level
% 0.91/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.91/0.48 % (329529)Instruction limit reached!
% 0.91/0.48 % (329529)------------------------------
% 0.91/0.48 % (329529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329529)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329529)Termination reason: Instruction limit
% 0.91/0.48 % (329529)Termination phase: Saturation
% 0.91/0.48 % (329529)Time elapsed: 0.042 s
% 0.91/0.48 % (329529)Peak memory usage: 13 MB
% 0.91/0.48 % (329529)Instructions burned: 162 (million)
% 0.91/0.48 % (329540)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=20535800:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.91/0.48 % (329539)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4191896674:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.91/0.48 % (329540)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.91/0.48 % (329540)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.91/0.48 % (329526)Instruction limit reached!
% 0.91/0.48 % (329526)------------------------------
% 0.91/0.48 % (329526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329526)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329526)Termination reason: Instruction limit
% 0.91/0.48 % (329526)Termination phase: Saturation
% 0.91/0.48 % (329526)Time elapsed: 0.052 s
% 0.91/0.48 % (329526)Peak memory usage: 12 MB
% 0.91/0.48 % (329526)Instructions burned: 105 (million)
% 0.91/0.48 % (329527)Instruction limit reached!
% 0.91/0.48 % (329527)------------------------------
% 0.91/0.48 % (329527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329527)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329527)Termination reason: Instruction limit
% 0.91/0.48 % (329527)Termination phase: Saturation
% 0.91/0.48 % (329527)Time elapsed: 0.059 s
% 0.91/0.48 % (329527)Peak memory usage: 13 MB
% 0.91/0.48 % (329527)Instructions burned: 118 (million)
% 0.91/0.48 % (329543)ott-21_1_sil=16000:fs=off:random_seed=1178799565:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.91/0.48 % (329544)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3165044856:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.91/0.48 % (329539)Instruction limit reached!
% 0.91/0.48 % (329539)------------------------------
% 0.91/0.48 % (329539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329539)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329539)Termination reason: Instruction limit
% 0.91/0.48 % (329539)Termination phase: Saturation
% 0.91/0.48 % (329539)Time elapsed: 0.067 s
% 0.91/0.48 % (329539)Peak memory usage: 13 MB
% 0.91/0.48 % (329539)Instructions burned: 132 (million)
% 0.91/0.48 % (329528)Instruction limit reached!
% 0.91/0.48 % (329528)------------------------------
% 0.91/0.48 % (329528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329528)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329528)Termination reason: Instruction limit
% 0.91/0.48 % (329528)Termination phase: Saturation
% 0.91/0.48 % (329528)Time elapsed: 0.113 s
% 0.91/0.48 % (329528)Peak memory usage: 12 MB
% 0.91/0.48 % (329528)Instructions burned: 132 (million)
% 0.91/0.48 % (329547)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4173884430:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.91/0.48 % Exception at run slice level
% 0.91/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.91/0.48 % (329548)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=795138275:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.91/0.48 % (329550)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=456894066:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.91/0.48 % Exception at run slice level
% 0.91/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.91/0.48 % (329543)Instruction limit reached!
% 0.91/0.48 % (329543)------------------------------
% 0.91/0.48 % (329543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329543)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329543)Termination reason: Instruction limit
% 0.91/0.48 % (329543)Termination phase: Saturation
% 0.91/0.48 % (329543)Time elapsed: 0.101 s
% 0.91/0.48 % (329543)Peak memory usage: 12 MB
% 0.91/0.48 % (329543)Instructions burned: 180 (million)
% 0.91/0.48 % (329553)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=648871571:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 0.91/0.48 % (329553)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.91/0.48 % (329554)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2083529781:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 0.91/0.48 % (329554)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.91/0.48 % (329540) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-329518-329540"...
% 0.91/0.48 % (329540)...printing done.
% 0.91/0.48 % (329540)Refutation found. Thanks to Tanya!
% 0.91/0.48 % SZS status Theorem for theBenchmark
% 0.91/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.91/0.48 % (329540)------------------------------
% 0.91/0.48 % (329540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.48 % (329540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.48 % (329540)CaDiCaL version: 2.1.3
% 0.91/0.48 % (329540)Termination reason: Refutation
% 0.91/0.48 % (329540)Time elapsed: 0.163 s
% 0.91/0.48 % (329540)Peak memory usage: 15 MB
% 0.91/0.48 % (329540)Instructions burned: 590 (million)
% 0.91/0.48 % (329518)Success in time 0.251 s
% 0.91/0.48 % Vampire exiting
%------------------------------------------------------------------------------