%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO068^4.005 : 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 : n002.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 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 15
% Syntax : Number of formulae : 199 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 1996 ( 417 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 2946 ( 104 ~; 315 |; 0 &;2042 @)
% ( 0 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 4 con; 0-4 aty)
% ( 215 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 699 ( 474 ^; 225 !; 0 ?; 699 :)
% 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,
p2: $i > $o ).
thf(func_def_24,type,
p3: $i > $o ).
thf(func_def_25,type,
p4: $i > $o ).
thf(func_def_26,type,
p5: $i > $o ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
sK0: $i > $i ).
thf(func_def_40,type,
sK1: $i > $i ).
thf(func_def_41,type,
sK2: $i > $i ).
thf(func_def_42,type,
sK3: $i > $i ).
thf(func_def_43,type,
sK4: $i > $i ).
thf(func_def_44,type,
sK5: $i > $i ).
thf(func_def_45,type,
sK6: $i > $i ).
thf(func_def_46,type,
sK7: $i > $i ).
thf(func_def_47,type,
sK8: $i > $i ).
thf(func_def_48,type,
sK9: $i > $i ).
thf(func_def_49,type,
sK10: $i > $i ).
thf(func_def_50,type,
sK11: $i > $i ).
thf(func_def_51,type,
sK12: $i > $i ).
thf(func_def_52,type,
sK13: $i > $i ).
thf(func_def_53,type,
sK14: $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,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
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,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f14,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= iimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p5 ),
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,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f29,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f30,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f31,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f32,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f33,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f38,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f45,plain,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
inference(rectify,[],[f26]) ).
thf(f46,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
inference(rectify,[],[f27]) ).
thf(f48,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f52,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f53,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f55,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f57,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f58,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
inference(rectify,[],[f25]) ).
thf(f60,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f65,plain,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(rectify,[],[f29]) ).
thf(f66,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f67,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f68,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
ivalid @ ( iatom @ p5 ),
inference(rectify,[],[f22]) ).
thf(f72,plain,
( ( ivalid @ ( iatom @ p5 ) )
= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f74,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f66]) ).
thf(f79,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f83,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f84,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f86,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f88,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f92,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f48]) ).
thf(f93,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f95,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f97,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f99,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f100,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f101,plain,
( ( ivalid @ ( iatom @ p5 ) )
= $true ),
inference(cnf_transformation,[],[f72]) ).
thf(f104,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f105,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f108,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f93,f96,f83]) ).
thf(f113,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ 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,[],[f100,f108,f86,f86]) ).
thf(f117,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f84,f79,f113,f105,f113,f105,f105]) ).
thf(f118,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f88,f79,f113,f105,f113,f105,f105]) ).
thf(f119,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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,[],[f92,f79,f113,f105,f113,f105,f105]) ).
thf(f120,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) )
!= $true ),
inference(definition_unfolding,[],[f95,f79,f105]) ).
thf(f121,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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,[],[f97,f79,f113,f105,f113,f105,f105]) ).
thf(f122,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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,[],[f99,f79,f113,f105,f113,f105,f105]) ).
thf(f123,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 ) )
= $true ),
inference(definition_unfolding,[],[f101,f79,f105]) ).
thf(f124,plain,
( $true
= ( !! @ $i @ p5 ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X1: $i] :
( $true
= ( p5 @ X1 ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f127,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK0 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f130]) ).
thf(f132,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 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p3 @ ( sK0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p3 @ ( sK0 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p3 @ ( sK0 @ X1 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p3 @ ( sK0 @ X1 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p3 @ ( sK0 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p3 @ ( sK0 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f137]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK2 @ X2 ) )
= $false )
| ( $false
= ( p3 @ ( sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( p3 @ ( sK2 @ X2 ) ) ) )
| ( $false
= ( p3 @ ( sK0 @ X1 ) ) )
| ( ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) )
= $true )
| ( $false
= ( p3 @ ( sK0 @ X1 ) ) )
| ( ( p3 @ ( sK2 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p3 @ ( sK2 @ X2 ) )
= $false )
| ( $false
= ( p3 @ ( sK0 @ X1 ) ) )
| ( ( p2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f152,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f153,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( p2 @ ( sK3 @ X1 ) ) ) )
| ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK5 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK5 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
= $true )
| ( $false
= ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( p2 @ ( sK5 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( p2 @ ( sK5 @ X2 ) ) ) )
| ( ( p1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK3 @ X1 ) ) )
| ( ( p1 @ X3 )
= $true )
| ( $false
= ( p2 @ ( sK5 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f182,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK6 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( p1 @ ( sK6 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( p1 @ ( sK6 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( p1 @ ( sK6 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( p1 @ ( sK6 @ X1 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f191]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK8 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK8 @ X2 ) )
=> ( p1 @ ( sK8 @ X2 ) ) ) )
| ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( p1 @ ( sK8 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK8 @ X2 ) ) )
| ( $false
= ( p1 @ ( sK6 @ X1 ) ) )
| ( ( p0 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f207,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f208,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK9 @ X1 ) )
=> ( p4 @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f215]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 )
= $true )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK11 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) )
= $true )
| ( ( ( irel @ X2 @ ( sK11 @ X2 ) )
=> ( p4 @ ( sK11 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK11 @ X2 ) )
=> ( p4 @ ( sK11 @ X2 ) ) )
= $false )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( p3 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ ( sK11 @ X2 ) )
= $false )
| ( ( p3 @ X3 )
= $true )
| ( ( p4 @ ( sK9 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f237,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[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 )
=> ( p4 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK12 @ X1 ) ) ) ),
inference(sigma_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 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK12 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK12 @ X1 ) )
=> ( p5 @ ( sK12 @ X1 ) ) ) )
| ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $true )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK14 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK14 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK14 @ X2 ) )
=> ( p5 @ ( sK14 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) )
= $true )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p5 @ ( sK14 @ X2 ) ) )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p5 @ ( sK14 @ X2 ) ) )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f266,plain,
( ( !! @ $i @ p0 )
!= $true ),
inference(beta-eta_normalization,[],[f120]) ).
thf(f267,plain,
( $false
= ( p0 @ sK15 ) ),
inference(sigma_proxy_clausification,[],[f266]) ).
thf(f272,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( $false = $true )
| ( ( p4 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f265,f125]) ).
thf(f273,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p4 @ X3 )
= $true )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p5 @ ( sK12 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ X3 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f273,f125]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f279,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $false = $true )
| ( ( p4 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f104,f275]) ).
thf(f282,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( ( p4 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f288,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p4 @ X0 ) ) ),
inference(constrained_superposition,[],[f282,f104]) ).
thf(f290,plain,
! [X0: $i] :
( $true
= ( p4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f288]) ).
thf(f362,plain,
! [X0: $i] :
( ( ( p3 @ ( sK0 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p2 @ X0 )
= $true )
| ( $false
= ( p3 @ ( sK2 @ X0 ) ) ) ),
inference(equality_factoring,[],[f151]) ).
thf(f365,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p3 @ ( sK0 @ X0 ) )
= $false )
| ( ( p2 @ X0 )
= $true )
| ( $false
= ( p3 @ ( sK2 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f377,plain,
! [X0: $i] :
( ( $false
= ( p3 @ ( sK2 @ X0 ) ) )
| ( ( p3 @ ( sK0 @ X0 ) )
= $false )
| ( ( p2 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f365,f104]) ).
thf(f378,plain,
! [X0: $i] :
( ( $false
= ( p3 @ ( sK2 @ X0 ) ) )
| ( ( p3 @ ( sK0 @ X0 ) )
= $false )
| ( ( p2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f420,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p1 @ X0 )
= $true )
| ( $false != $false )
| ( ( p2 @ ( sK5 @ X0 ) )
= $false )
| ( ( p2 @ ( sK3 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f179]) ).
thf(f424,plain,
! [X0: $i] :
( ( ( p2 @ ( sK5 @ X0 ) )
= $false )
| ( ( p1 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p2 @ ( sK3 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f420]) ).
thf(f435,plain,
! [X0: $i] :
( ( ( p2 @ ( sK3 @ X0 ) )
= $false )
| ( ( p1 @ X0 )
= $true )
| ( $false = $true )
| ( ( p2 @ ( sK5 @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f424,f104]) ).
thf(f436,plain,
! [X0: $i] :
( ( ( p2 @ ( sK5 @ X0 ) )
= $false )
| ( ( p2 @ ( sK3 @ X0 ) )
= $false )
| ( ( p1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f466,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( p1 @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( p0 @ X1 )
= $true )
| ( $false
= ( p1 @ ( sK8 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f206,f104]) ).
thf(f480,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( ( p0 @ X1 )
= $true )
| ( $false
= ( p1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( p1 @ ( sK8 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f466]) ).
thf(f493,plain,
! [X0: $i] :
( ( ( p0 @ X0 )
= $true )
| ( $false = $true )
| ( $false
= ( p1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( p1 @ ( sK8 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f480,f104]) ).
thf(f500,plain,
! [X0: $i] :
( ( $false
= ( p1 @ ( sK8 @ X0 ) ) )
| ( ( p0 @ X0 )
= $true )
| ( $false
= ( p1 @ ( sK6 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f533,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK11 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( $false
= ( p4 @ ( sK9 @ X0 ) ) ) ),
inference(equality_factoring,[],[f234]) ).
thf(f541,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p4 @ ( sK11 @ X0 ) ) )
| ( $false
= ( p4 @ ( sK9 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f551,plain,
! [X0: $i] :
( ( $false = $true )
| ( $false
= ( p4 @ ( sK11 @ X0 ) ) )
| ( $false
= ( p4 @ ( sK9 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(forward_demodulation,[],[f541,f104]) ).
thf(f552,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK9 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) )
| ( $false
= ( p4 @ ( sK11 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f563,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK11 @ X0 ) ) )
| ( $false = $true )
| ( $true
= ( p3 @ X0 ) ) ),
inference(forward_demodulation,[],[f552,f290]) ).
thf(f564,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK11 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f563]) ).
thf(f573,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( p3 @ X0 ) ) ),
inference(forward_demodulation,[],[f564,f290]) ).
thf(f574,plain,
! [X0: $i] :
( $true
= ( p3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f573]) ).
thf(f578,plain,
! [X0: $i] :
( ( ( p3 @ ( sK0 @ X0 ) )
= $false )
| ( ( p2 @ X0 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f378,f574]) ).
thf(f579,plain,
! [X0: $i] :
( ( ( p2 @ X0 )
= $true )
| ( ( p3 @ ( sK0 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f581,plain,
! [X0: $i] :
( ( ( p2 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f579,f574]) ).
thf(f582,plain,
! [X0: $i] :
( ( p2 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f586,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( p1 @ X0 )
= $true )
| ( ( p2 @ ( sK3 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f436,f582]) ).
thf(f587,plain,
! [X0: $i] :
( ( ( p2 @ ( sK3 @ X0 ) )
= $false )
| ( ( p1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f586]) ).
thf(f589,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( p1 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f587,f582]) ).
thf(f590,plain,
! [X0: $i] :
( ( p1 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f589]) ).
thf(f594,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( p0 @ X0 )
= $true )
| ( $false
= ( p1 @ ( sK6 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f500,f590]) ).
thf(f595,plain,
! [X0: $i] :
( ( $false
= ( p1 @ ( sK6 @ X0 ) ) )
| ( ( p0 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f594]) ).
thf(f597,plain,
! [X0: $i] :
( ( ( p0 @ X0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f595,f590]) ).
thf(f598,plain,
! [X0: $i] :
( ( p0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f602,plain,
$false = $true,
inference(constrained_superposition,[],[f267,f598]) ).
thf(f603,plain,
$false,
inference(trivial_inequality_removal,[],[f602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:32:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.22/0.32 % (1505148)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (1505157)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2447023931:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (1505155)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3200971329:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (1505153)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2619157251:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (1505156)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=1622906497: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)
% 0.22/0.32 % (1505155)Instruction limit reached!
% 0.22/0.32 % (1505155)------------------------------
% 0.22/0.32 % (1505155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1505155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1505155)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1505155)Termination reason: Instruction limit
% 0.22/0.32 % (1505155)Termination phase: Property scanning
% 0.22/0.32 % (1505155)Time elapsed: 0.002 s
% 0.22/0.32 % (1505155)Peak memory usage: 10 MB
% 0.22/0.32 % (1505155)Instructions burned: 5 (million)
% 0.22/0.32 % (1505154)lrs+10_16_si=on:nwc=1.5:random_seed=868357167:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (1505159)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (1505159)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
% 0.22/0.32 % (1505159)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=3873166325:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (1505157)Instruction limit reached!
% 0.22/0.32 % (1505157)------------------------------
% 0.22/0.32 % (1505157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1505157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1505157)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1505157)Termination reason: Instruction limit
% 0.22/0.32 % (1505157)Termination phase: Saturation
% 0.22/0.32 % (1505157)Time elapsed: 0.013 s
% 0.22/0.32 % (1505157)Peak memory usage: 11 MB
% 0.22/0.32 % (1505157)Instructions burned: 25 (million)
% 0.22/0.32 % (1505158)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1670186286:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (1505164)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=700011769:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (1505159) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1505148-1505159"...
% 0.22/0.32 % (1505153) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1505148-1505153"...
% 0.22/0.32 % (1505154)Instruction limit reached!
% 0.22/0.32 % (1505154)------------------------------
% 0.22/0.32 % (1505154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1505154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1505154)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1505154)Termination reason: Instruction limit
% 0.22/0.32 % (1505154)Termination phase: Saturation
% 0.22/0.32 % (1505154)Time elapsed: 0.017 s
% 0.22/0.32 % (1505154)Peak memory usage: 12 MB
% 0.22/0.32 % (1505154)Instructions burned: 19 (million)
% 0.22/0.32 % (1505164)Instruction limit reached!
% 0.22/0.32 % (1505164)------------------------------
% 0.22/0.32 % (1505164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1505164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1505164)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1505164)Termination reason: Instruction limit
% 0.22/0.32 % (1505164)Termination phase: Function definition elimination
% 0.22/0.32 % (1505164)Time elapsed: 0.002 s
% 0.22/0.32 % (1505164)Peak memory usage: 10 MB
% 0.22/0.32 % (1505164)Instructions burned: 4 (million)
% 0.22/0.32 % (1505167)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=143992399:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.32 % (1505153)...printing done.
% 0.22/0.32 % (1505153)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (1505153)------------------------------
% 0.22/0.33 % (1505153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1505153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1505153)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1505153)Termination reason: Refutation
% 0.22/0.33 % (1505153)Time elapsed: 0.029 s
% 0.22/0.33 % (1505153)Peak memory usage: 12 MB
% 0.22/0.33 % (1505153)Instructions burned: 62 (million)
% 0.22/0.33 % (1505148)Success in time 0.062 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------