%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO068^4.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:46:29 AM UTC 2026
% Result : Theorem 0.35s 0.50s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 105
% Number of leaves : 20
% Syntax : Number of formulae : 349 ( 114 unt; 0 typ; 0 def)
% Number of atoms : 3826 ( 791 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 5709 ( 203 ~; 625 |; 0 &;3934 @)
% ( 0 <=>; 528 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 273 ( 273 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 4 con; 0-4 aty)
% ( 419 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1374 ( 869 ^; 505 !; 0 ?;1374 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
p0: $i > $o ).
thf(func_def_22,type,
p1: $i > $o ).
thf(func_def_23,type,
p10: $i > $o ).
thf(func_def_24,type,
p2: $i > $o ).
thf(func_def_25,type,
p3: $i > $o ).
thf(func_def_26,type,
p4: $i > $o ).
thf(func_def_27,type,
p5: $i > $o ).
thf(func_def_28,type,
p6: $i > $o ).
thf(func_def_29,type,
p7: $i > $o ).
thf(func_def_30,type,
p8: $i > $o ).
thf(func_def_31,type,
p9: $i > $o ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i ).
thf(func_def_45,type,
sK1: $i > $i ).
thf(func_def_46,type,
sK2: $i > $i ).
thf(func_def_47,type,
sK3: $i > $i ).
thf(func_def_48,type,
sK4: $i > $i ).
thf(func_def_49,type,
sK5: $i > $i ).
thf(func_def_50,type,
sK6: $i > $i ).
thf(func_def_51,type,
sK7: $i > $i ).
thf(func_def_52,type,
sK8: $i > $i ).
thf(func_def_53,type,
sK9: $i > $i ).
thf(func_def_54,type,
sK10: $i > $i ).
thf(func_def_55,type,
sK11: $i > $i ).
thf(func_def_56,type,
sK12: $i > $i ).
thf(func_def_57,type,
sK13: $i > $i ).
thf(func_def_58,type,
sK14: $i > $i ).
thf(func_def_59,type,
sK15: $i > $i ).
thf(func_def_60,type,
sK16: $i > $i ).
thf(func_def_61,type,
sK17: $i > $i ).
thf(func_def_62,type,
sK18: $i > $i ).
thf(func_def_63,type,
sK19: $i > $i ).
thf(func_def_64,type,
sK20: $i > $i ).
thf(func_def_65,type,
sK21: $i > $i ).
thf(func_def_66,type,
sK22: $i > $i ).
thf(func_def_67,type,
sK23: $i > $i ).
thf(func_def_68,type,
sK24: $i > $i ).
thf(func_def_69,type,
sK25: $i > $i ).
thf(func_def_70,type,
sK26: $i > $i ).
thf(func_def_72,type,
sK28: $i > $i ).
thf(func_def_73,type,
sK29: $i > $i ).
thf(func_def_74,type,
sK30: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(f25,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(f26,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(f27,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(f28,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
thf(f29,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(f30,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(f31,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(f32,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(f33,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f34,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
thf(f35,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f36,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f35]) ).
thf(f40,plain,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
inference(rectify,[],[f28]) ).
thf(f41,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
inference(rectify,[],[f30]) ).
thf(f45,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
ivalid @ ( iatom @ p10 ),
inference(rectify,[],[f22]) ).
thf(f47,plain,
( ( ivalid @ ( iatom @ p10 ) )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f49,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
inference(rectify,[],[f25]) ).
thf(f51,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f53,plain,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
inference(rectify,[],[f27]) ).
thf(f54,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(rectify,[],[f34]) ).
thf(f56,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
inference(rectify,[],[f32]) ).
thf(f58,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
inference(rectify,[],[f31]) ).
thf(f62,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(fool_elimination,[],[f61]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f69,plain,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
inference(rectify,[],[f29]) ).
thf(f70,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f72,plain,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f73,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f75,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f76,plain,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
inference(rectify,[],[f26]) ).
thf(f77,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(fool_elimination,[],[f76]) ).
thf(f81,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f82,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f85,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f86,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f87,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f89,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f56]) ).
thf(f93,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f94,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f95,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f96,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f97,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f102,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f87]) ).
thf(f103,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f106,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f107,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f108,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f109,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f111,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f112,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f114,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f62]) ).
thf(f118,plain,
( ( ivalid @ ( iatom @ p10 ) )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f119,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f120,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f121,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f51]) ).
thf(f122,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f124,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f128,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f119,f111,f97]) ).
thf(f133,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f93,f128,f106,f106]) ).
thf(f137,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
inference(definition_unfolding,[],[f96,f122,f95]) ).
thf(f138,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ) ) ),
inference(definition_unfolding,[],[f102,f122,f133,f95,f133,f95,f95]) ).
thf(f139,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f103,f122,f133,f95,f133,f95,f95]) ).
thf(f140,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 ) ) ) ) ),
inference(definition_unfolding,[],[f107,f122,f133,f95,f133,f95,f95]) ).
thf(f141,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f108,f122,f133,f95,f133,f95,f95]) ).
thf(f142,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f109,f122,f133,f95,f133,f95,f95]) ).
thf(f143,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f112,f122,f133,f95,f133,f95,f95]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f114,f122,f133,f95,f133,f95,f95]) ).
thf(f145,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 ) ) ),
inference(definition_unfolding,[],[f118,f122,f95]) ).
thf(f146,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f120,f122,f133,f95,f133,f95,f95]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f122,f133,f95,f133,f95,f95]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f124,f122,f133,f95,f133,f95,f95]) ).
thf(f149,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f150,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p1 @ ( sK0 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
= $true )
| ( $false
= ( p1 @ ( sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK2 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK2 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( p1 @ ( sK2 @ X2 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( ( p1 @ ( sK2 @ X2 ) )
= $false )
| ( $false
= ( p1 @ ( sK0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p0 @ X3 ) )
| ( $false
= ( p1 @ ( sK0 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p1 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f178,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f179,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( p8 @ ( sK3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( p8 @ ( sK3 @ X1 ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK5 @ X2 ) )
= $false )
| ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK5 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( p8 @ ( sK5 @ X2 ) ) ) )
| ( ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( $false
= ( p8 @ ( sK5 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p7 @ X3 ) )
| ( $false
= ( p8 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK5 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f207,plain,
( $true
= ( !! @ $i @ p10 ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f208,plain,
! [X1: $i] :
( ( p10 @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f210,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( p7 @ ( sK6 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK8 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK8 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) )
= $true )
| ( $false
= ( ( irel @ X2 @ ( sK8 @ X2 ) )
=> ( p7 @ ( sK8 @ X2 ) ) ) )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p7 @ ( sK6 @ X1 ) )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK8 @ X2 ) )
=> ( p7 @ ( sK8 @ X2 ) ) ) )
| ( $true
= ( p6 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p7 @ ( sK8 @ X2 ) ) )
| ( $true
= ( p6 @ X3 ) )
| ( ( p7 @ ( sK6 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f238,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f239,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK9 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) )
= $true )
| ( ( ( irel @ X1 @ ( sK9 @ X1 ) )
=> ( p6 @ ( sK9 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK9 @ X1 ) )
=> ( p6 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $true )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p6 @ ( sK9 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK11 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK11 @ X2 ) )
=> ( p6 @ ( sK11 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK11 @ X2 ) ) )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p6 @ ( sK9 @ X1 ) ) )
| ( $true
= ( p5 @ X3 ) )
| ( $false
= ( p6 @ ( sK11 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f263]) ).
thf(f267,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f268,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK12 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK12 @ X1 ) )
=> ( p5 @ ( sK12 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK12 @ X1 ) )
=> ( p5 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK12 @ X1 ) )
=> ( p5 @ ( sK12 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK12 @ X1 ) )
=> ( p5 @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f288,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK14 @ X2 ) )
= $false )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK14 @ X2 ) )
=> ( p5 @ ( sK14 @ X2 ) ) ) )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK14 @ X2 ) )
=> ( p5 @ ( sK14 @ X2 ) ) ) )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p5 @ ( sK14 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p5 @ ( sK12 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f290]) ).
thf(f293,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f294,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f294]) ).
thf(f296,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK15 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK15 @ X1 ) )
=> ( p9 @ ( sK15 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK15 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f301]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK17 @ X2 ) ) )
| ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK17 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK17 @ X2 ) )
=> ( p9 @ ( sK17 @ X2 ) ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK17 @ X2 ) ) )
| ( $false
= ( p9 @ ( sK15 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p9 @ ( sK15 @ X1 ) ) )
| ( $false
= ( p9 @ ( sK17 @ X2 ) ) )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f323,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f324,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK18 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK18 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK18 @ X1 ) )
=> ( p10 @ ( sK18 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f330]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK18 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK18 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK20 @ X2 ) ) )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) )
= $true )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK20 @ X2 ) )
=> ( p10 @ ( sK20 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p9 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK20 @ X2 ) )
=> ( p10 @ ( sK20 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK20 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p9 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f349]) ).
thf(f352,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f353,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK21 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK21 @ X1 ) )
=> ( p4 @ ( sK21 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK21 @ X1 ) )
=> ( p4 @ ( sK21 @ X1 ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f360]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f361]) ).
thf(f373,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( p4 @ ( sK21 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK23 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK23 @ X2 ) )
=> ( p4 @ ( sK23 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f377,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) )
| ( ( p4 @ ( sK23 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f380,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p4 @ ( sK23 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p4 @ ( sK21 @ X1 ) ) )
| ( $true
= ( p3 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f377]) ).
thf(f381,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f382,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f382]) ).
thf(f384,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK24 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f386]) ).
thf(f388,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
= $true )
| ( ( ( irel @ X1 @ ( sK24 @ X1 ) )
=> ( p3 @ ( sK24 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f387]) ).
thf(f389,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK24 @ X1 ) )
=> ( p3 @ ( sK24 @ X1 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f389]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
= $true )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f390]) ).
thf(f402,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 )
= $true )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f401]) ).
thf(f403,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK26 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK26 @ X2 ) )
=> ( p3 @ ( sK26 @ X2 ) ) ) )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f404]) ).
thf(f406,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p3 @ ( sK26 @ X2 ) )
= $false )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f405]) ).
thf(f409,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p3 @ ( sK24 @ X1 ) )
= $false )
| ( ( p3 @ ( sK26 @ X2 ) )
= $false )
| ( $true
= ( p2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f406]) ).
thf(f410,plain,
( $true
!= ( !! @ $i @ p0 ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f411,plain,
( $false
= ( p0 @ sK27 ) ),
inference(sigma_proxy_clausification,[],[f410]) ).
thf(f412,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f413,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f413]) ).
thf(f415,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK28 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f417]) ).
thf(f419,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK28 @ X1 ) )
=> ( p2 @ ( sK28 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f418]) ).
thf(f420,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f419]) ).
thf(f432,plain,
! [X2: $i,X1: $i] :
( ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f420]) ).
thf(f433,plain,
! [X2: $i,X1: $i] :
( ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f432]) ).
thf(f434,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f433]) ).
thf(f435,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
= $false )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f434]) ).
thf(f436,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK30 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f437,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p2 @ ( sK30 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f436]) ).
thf(f438,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p2 @ ( sK30 @ X2 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( ( p1 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p2 @ ( sK28 @ X1 ) )
= $false )
| ( $false
= ( p2 @ ( sK30 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f438]) ).
thf(f445,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p9 @ X3 ) )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f350,f208]) ).
thf(f446,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p9 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p10 @ ( sK18 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f445]) ).
thf(f447,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false = $true )
| ( $true
= ( p9 @ X3 ) ) ),
inference(forward_demodulation,[],[f446,f208]) ).
thf(f448,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p9 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f449,plain,
! [X0: $i] :
( ( ( p9 @ X0 )
= $true )
| ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f448]) ).
thf(f451,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p9 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f453,plain,
! [X0: $i] :
( ( ( p9 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f451,f94]) ).
thf(f454,plain,
! [X0: $i] :
( ( p9 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f458,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK17 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p8 @ X3 ) ) ),
inference(backward_demodulation,[],[f322,f454]) ).
thf(f461,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p8 @ X3 ) )
| ( $false
= ( p9 @ ( sK17 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f458]) ).
thf(f463,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p8 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f461,f454]) ).
thf(f464,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p8 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f477,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p8 @ X0 )
= $true )
| ( $false != $false ) ),
inference(equality_factoring,[],[f464]) ).
thf(f478,plain,
! [X0: $i] :
( ( ( p8 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f482,plain,
! [X0: $i] :
( ( ( p8 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f478,f94]) ).
thf(f483,plain,
! [X0: $i] :
( ( p8 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f487,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p7 @ X3 ) )
| ( $false = $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK5 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(backward_demodulation,[],[f206,f483]) ).
thf(f491,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p7 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK5 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f492,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $true
= ( p7 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f491,f483]) ).
thf(f493,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p7 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f492]) ).
thf(f497,plain,
! [X0: $i] :
( ( $false != $false )
| ( $true
= ( p7 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f493]) ).
thf(f498,plain,
! [X0: $i] :
( ( $true
= ( p7 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f497]) ).
thf(f502,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p7 @ X0 ) ) ),
inference(forward_demodulation,[],[f498,f94]) ).
thf(f503,plain,
! [X0: $i] :
( $true
= ( p7 @ X0 ) ),
inference(trivial_inequality_removal,[],[f502]) ).
thf(f507,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p7 @ ( sK8 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p6 @ X3 ) )
| ( $false = $true ) ),
inference(backward_demodulation,[],[f236,f503]) ).
thf(f509,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p6 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p7 @ ( sK8 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f507]) ).
thf(f512,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p6 @ X3 ) )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f509,f503]) ).
thf(f513,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p6 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f517,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p6 @ X0 )
= $true ) ),
inference(equality_factoring,[],[f513]) ).
thf(f519,plain,
! [X0: $i] :
( ( ( p6 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f522,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( p6 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f519,f94]) ).
thf(f523,plain,
! [X0: $i] :
( ( p6 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f527,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p5 @ X3 ) )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK11 @ X2 ) ) ) ),
inference(backward_demodulation,[],[f266,f523]) ).
thf(f529,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p5 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p6 @ ( sK11 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f532,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p5 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f529,f523]) ).
thf(f533,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p5 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f537,plain,
! [X0: $i] :
( ( $true
= ( p5 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f533]) ).
thf(f540,plain,
! [X0: $i] :
( ( $true
= ( p5 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f542,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p5 @ X0 ) ) ),
inference(forward_demodulation,[],[f540,f94]) ).
thf(f543,plain,
! [X0: $i] :
( $true
= ( p5 @ X0 ) ),
inference(trivial_inequality_removal,[],[f542]) ).
thf(f547,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p5 @ ( sK14 @ X2 ) )
= $false )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(backward_demodulation,[],[f291,f543]) ).
thf(f549,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p5 @ ( sK14 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f547]) ).
thf(f552,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f549,f543]) ).
thf(f553,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f552]) ).
thf(f556,plain,
! [X0: $i] :
( ( $true
= ( p4 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f553]) ).
thf(f558,plain,
! [X0: $i] :
( ( $true
= ( p4 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f556]) ).
thf(f562,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p4 @ X0 ) ) ),
inference(forward_demodulation,[],[f558,f94]) ).
thf(f563,plain,
! [X0: $i] :
( $true
= ( p4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f567,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p4 @ ( sK23 @ X2 ) )
= $false )
| ( $false = $true )
| ( $true
= ( p3 @ X3 ) ) ),
inference(backward_demodulation,[],[f380,f563]) ).
thf(f569,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p3 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ ( sK23 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f567]) ).
thf(f572,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( p3 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f569,f563]) ).
thf(f573,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p3 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f572]) ).
thf(f576,plain,
! [X0: $i] :
( ( $false != $false )
| ( $true
= ( p3 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f573]) ).
thf(f580,plain,
! [X0: $i] :
( ( $true
= ( p3 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f582,plain,
! [X0: $i] :
( ( $true
= ( p3 @ X0 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f580,f94]) ).
thf(f583,plain,
! [X0: $i] :
( $true
= ( p3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f587,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p3 @ ( sK26 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p2 @ X3 ) )
| ( $false = $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(backward_demodulation,[],[f409,f583]) ).
thf(f589,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p3 @ ( sK26 @ X2 ) )
= $false )
| ( $true
= ( p2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f587]) ).
thf(f592,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p2 @ X3 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f589,f583]) ).
thf(f593,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f596,plain,
! [X0: $i] :
( ( $false != $false )
| ( $true
= ( p2 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f593]) ).
thf(f599,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f602,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p2 @ X0 ) ) ),
inference(forward_demodulation,[],[f599,f94]) ).
thf(f603,plain,
! [X0: $i] :
( $true
= ( p2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f607,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( p1 @ X3 )
= $true )
| ( $false
= ( p2 @ ( sK30 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(backward_demodulation,[],[f439,f603]) ).
thf(f611,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p1 @ X3 )
= $true )
| ( $false
= ( p2 @ ( sK30 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f612,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p1 @ X3 )
= $true )
| ( $false = $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(forward_demodulation,[],[f611,f603]) ).
thf(f613,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p1 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f616,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( p1 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f613]) ).
thf(f618,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f622,plain,
! [X0: $i] :
( ( ( p1 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f618,f94]) ).
thf(f623,plain,
! [X0: $i] :
( ( p1 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f622]) ).
thf(f627,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = $true )
| ( ( p1 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p0 @ X3 ) ) ),
inference(backward_demodulation,[],[f177,f623]) ).
thf(f631,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p0 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p1 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f632,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false = $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p0 @ X3 ) ) ),
inference(forward_demodulation,[],[f631,f623]) ).
thf(f633,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p0 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f639,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( ( p0 @ X0 )
= $true ) ),
inference(equality_factoring,[],[f633]) ).
thf(f642,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p0 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f639]) ).
thf(f646,plain,
! [X0: $i] :
( ( ( p0 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f642,f94]) ).
thf(f647,plain,
! [X0: $i] :
( ( p0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f650,plain,
$false = $true,
inference(backward_demodulation,[],[f411,f647]) ).
thf(f651,plain,
$false,
inference(trivial_inequality_removal,[],[f650]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO068^4.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 % Computer : n010.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8046.5625MB
% 0.10/0.28 % OS : Linux 6.8.0-71-generic
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Sep 29 16:29:48 UTC 2026
% 0.27/0.28 % CPUTime :
% 0.27/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.34 Running higher-order theorem proving
% 0.27/0.36 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.50 % (3087792)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.50 % (3087797)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2396404840:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.50 % (3087803)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.50 % (3087803)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.35/0.50 % (3087799)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3434610109:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.50 % (3087798)lrs+10_16_si=on:nwc=1.5:random_seed=2411791250:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.50 % (3087801)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3450835396:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.50 % (3087800)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=234119809:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.35/0.50 % (3087802)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=220807657:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.50 % (3087803)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3641087712:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.50 % (3087799)Instruction limit reached!
% 0.35/0.50 % (3087799)------------------------------
% 0.35/0.50 % (3087799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087799)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087799)Termination reason: Instruction limit
% 0.35/0.50 % (3087799)Termination phase: Property scanning
% 0.35/0.50 % (3087799)Time elapsed: 0.003 s
% 0.35/0.50 % (3087799)Peak memory usage: 10 MB
% 0.35/0.50 % (3087799)Instructions burned: 3 (million)
% 0.35/0.50 % (3087798)Instruction limit reached!
% 0.35/0.50 % (3087798)------------------------------
% 0.35/0.50 % (3087798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087798)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087798)Termination reason: Instruction limit
% 0.35/0.50 % (3087798)Termination phase: Saturation
% 0.35/0.50 % (3087798)Time elapsed: 0.015 s
% 0.35/0.50 % (3087798)Peak memory usage: 11 MB
% 0.35/0.50 % (3087798)Instructions burned: 19 (million)
% 0.35/0.50 % (3087801)Instruction limit reached!
% 0.35/0.50 % (3087801)------------------------------
% 0.35/0.50 % (3087801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087801)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087801)Termination reason: Instruction limit
% 0.35/0.50 % (3087801)Termination phase: Saturation
% 0.35/0.50 % (3087801)Time elapsed: 0.023 s
% 0.35/0.50 % (3087801)Peak memory usage: 11 MB
% 0.35/0.50 % (3087801)Instructions burned: 25 (million)
% 0.35/0.50 % (3087797)Instruction limit reached!
% 0.35/0.50 % (3087797)------------------------------
% 0.35/0.50 % (3087797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087797)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087797)Termination reason: Instruction limit
% 0.35/0.50 % (3087797)Termination phase: Saturation
% 0.35/0.50 % (3087797)Time elapsed: 0.037 s
% 0.35/0.50 % (3087797)Peak memory usage: 12 MB
% 0.35/0.50 % (3087797)Instructions burned: 89 (million)
% 0.35/0.50 % (3087811)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1116391390:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.35/0.50 % (3087811)Instruction limit reached!
% 0.35/0.50 % (3087811)------------------------------
% 0.35/0.50 % (3087811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087811)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087811)Termination reason: Instruction limit
% 0.35/0.50 % (3087811)Termination phase: Property scanning
% 0.35/0.50 % (3087811)Time elapsed: 0.002 s
% 0.35/0.50 % (3087811)Peak memory usage: 10 MB
% 0.35/0.50 % (3087811)Instructions burned: 2 (million)
% 0.35/0.50 % (3087814)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1007515961:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.35/0.50 % (3087803) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3087792-3087803"...
% 0.35/0.50 % (3087802) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3087792-3087802"...
% 0.35/0.50 % (3087813)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.35/0.50 % (3087814)Instruction limit reached!
% 0.35/0.50 % (3087814)------------------------------
% 0.35/0.50 % (3087814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087814)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087814)Termination reason: Instruction limit
% 0.35/0.50 % (3087814)Termination phase: Saturation
% 0.35/0.50 % (3087814)Time elapsed: 0.008 s
% 0.35/0.50 % (3087814)Peak memory usage: 11 MB
% 0.35/0.50 % (3087814)Instructions burned: 18 (million)
% 0.35/0.50 % (3087813)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3642196009:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.35/0.50 % (3087813)Instruction limit reached!
% 0.35/0.50 % (3087813)------------------------------
% 0.35/0.50 % (3087813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087813)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087813)Termination reason: Instruction limit
% 0.35/0.50 % (3087813)Termination phase: Property scanning
% 0.35/0.50 % (3087813)Time elapsed: 0.006 s
% 0.35/0.50 % (3087813)Peak memory usage: 10 MB
% 0.35/0.50 % (3087813)Instructions burned: 7 (million)
% 0.35/0.50 % (3087812)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3051473334:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.35/0.50 % (3087816)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.35/0.50 % (3087816)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.35/0.50 % (3087812)Instruction limit reached!
% 0.35/0.50 % (3087812)------------------------------
% 0.35/0.50 % (3087812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.50 % (3087812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.50 % (3087812)CaDiCaL version: 2.1.3
% 0.35/0.50 % (3087812)Termination reason: Instruction limit
% 0.35/0.50 % (3087812)Termination phase: Function definition elimination
% 0.35/0.50 % (3087812)Time elapsed: 0.005 s
% 0.35/0.50 % (3087812)Peak memory usage: 10 MB
% 0.35/0.50 % (3087812)Instructions burned: 5 (million)
% 0.35/0.50 % (3087816)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2826154528:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.35/0.50 % (3087818)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1819418634:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.35/0.50 % (3087803)...printing done.
% 0.35/0.50 % (3087802)...printing done.
% 0.35/0.50 % (3087802)Refutation found. Thanks to Tanya!
% 0.35/0.50 % SZS status Theorem for theBenchmark
% 0.35/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.51 % (3087802)------------------------------
% 0.35/0.51 % (3087802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.51 % (3087802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.51 % (3087802)CaDiCaL version: 2.1.3
% 0.35/0.51 % (3087802)Termination reason: Refutation
% 0.35/0.51 % (3087802)Time elapsed: 0.072 s
% 0.35/0.51 % (3087802)Peak memory usage: 12 MB
% 0.35/0.51 % (3087802)Instructions burned: 86 (million)
% 0.35/0.51 % (3087792)Success in time 0.127 s
% 0.35/0.51 % Vampire exiting
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