%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV430^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:39:57 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 167 ( 60 unt; 0 typ; 10 def)
% Number of atoms : 1387 ( 262 equ; 0 cnn)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 2008 ( 177 ~; 302 |; 0 &;1306 @)
% ( 9 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 349 ( 349 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 17 con; 0-4 aty)
% ( 100 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 605 ( 0 sgn 110 !; 0 ?; 605 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
rel: $i > $i > $o ).
thf(func_def_21,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
icl_true: $i > $o ).
thf(func_def_27,type,
icl_false: $i > $o ).
thf(func_def_28,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_29,type,
iclval: ( $i > $o ) > $o ).
thf(func_def_30,type,
icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_31,type,
a: $i > $o ).
thf(func_def_32,type,
b: $i > $o ).
thf(func_def_33,type,
c: $i > $o ).
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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
sF0: $o ).
thf(func_def_48,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_53,type,
sK6: $i > $i ).
thf(func_def_54,type,
sK7: $i > $i ).
thf(func_def_55,type,
sK8: $i > $i ).
thf(func_def_56,type,
sK9: $i > $i ).
thf(func_def_57,type,
sK10: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f17,axiom,
( icl_princ
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( icl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f24,axiom,
( ( ^ [X0: $i > $o] : ( mvalid @ X0 ) )
= iclval ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f26,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',trans_axiom) ).
thf(f27,axiom,
( icl_impl_princ
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^2.ax',icl_impl_princ) ).
thf(f28,conjecture,
iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans) ).
thf(f29,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f30,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f31,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f35,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f42,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f43,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f44,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f48,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f49,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f55,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f56,plain,
~ ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f57,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f59,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f61,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f70,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) )
!= $true ),
inference(flattening,[],[f57]) ).
thf(f73,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f74,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f78,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f81,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f83,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f85,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f86,plain,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f91,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f94,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f97,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f98,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f101,plain,
( mimpl
= ( ^ [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,[],[f83,f73,f85]) ).
thf(f106,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f98,f91,f101]) ).
thf(f110,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f78,f81]) ).
thf(f111,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f97,f91,f101]) ).
thf(f112,plain,
! [X0: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 ) ) ) ) ),
inference(definition_unfolding,[],[f74,f81,f101,f91,f91,f91]) ).
thf(f114,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) ) ),
inference(definition_unfolding,[],[f86,f110,f106,f111,f94,f94,f106,f111,f94,f94,f111,f94,f94]) ).
thf(f115,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f116,plain,
( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f115]) ).
thf(f117,plain,
$true != sF0,
inference(definition_folding,[],[f114,f116]) ).
thf(f128,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [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 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f116]) ).
thf(f129,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( c @ Y3 )
| ~ ( a @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( c @ Y3 )
| ~ ( b @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ~ ( a @ Y2 ) ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( c @ Y3 )
| ~ ( a @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( c @ Y3 )
| ~ ( b @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ~ ( a @ Y2 ) ) ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( c @ Y2 )
| ~ ( a @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( c @ Y2 )
| ~ ( b @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( c @ Y2 )
| ~ ( a @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( c @ Y2 )
| ~ ( b @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) )
@ sK3 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( $true = sF0 )
| ( $false
= ( ( rel @ sK2 @ sK3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( b @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( b @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f136,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f134]) ).
thf(f137,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( b @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f134]) ).
thf(f138,plain,
( ( ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
| ~ ( b @ Y1 ) ) ) ) ) )
@ sK4 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( $false
= ( ( rel @ sK3 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( a @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( b @ Y0 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( a @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( b @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( $true = sF0 )
| ( ( rel @ sK3 @ sK4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( $true = sF0 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( b @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f144,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( a @ Y0 ) ) )
@ sK5 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ( rel @ sK4 @ sK5 )
=> ( ( c @ sK5 )
| ~ ( a @ sK5 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ( c @ sK5 )
| ~ ( a @ sK5 ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $true = sF0 )
| ( $true
= ( rel @ sK4 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( a @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( $false
= ( c @ sK5 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f150,plain,
( ( $true
= ( a @ sK5 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( b @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK4 @ Y0 )
=> ( ( c @ Y0 )
| ~ ( b @ Y0 ) ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( rel @ sK4 @ X1 )
=> ( ( c @ X1 )
| ~ ( b @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( rel @ sK4 @ X1 ) )
| ( $true
= ( ( c @ X1 )
| ~ ( b @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( rel @ sK4 @ X1 ) )
| ( $true
= ( ~ ( b @ X1 ) ) )
| ( $true
= ( c @ X1 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $false
= ( b @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( rel @ sK4 @ X1 ) )
| ( $true
= ( c @ X1 ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK3 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( ( rel @ sK3 @ X1 )
=> ( ( b @ X1 )
| ~ ( a @ X1 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( ( b @ X1 )
| ~ ( a @ X1 ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( ~ ( a @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true = sF0 )
| ( ( a @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f236,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f237,plain,
! [X0: $i > $o,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK10 @ X1 @ X0 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ( rel @ X1 @ ( sK10 @ X1 @ X0 ) )
=> ( X0 @ ( sK10 @ X1 @ X0 ) ) )
= $false )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $false
= ( X0 @ ( sK10 @ X1 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f246,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( rel @ X1 @ ( sK10 @ X1 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( rel @ X1 @ ( sK10 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) )
| ( $true
= ( rel @ X1 @ ( sK10 @ X1 @ X0 ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK10 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( X0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK10 @ X1 @ X0 ) ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( X0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f259,definition,
( spl11_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f264,definition,
( spl11_3
<=> ( ( rel @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f266,plain,
( ( ( rel @ sK3 @ sK4 )
= $true )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( spl11_2
| spl11_3 ),
inference(avatar_split_clause,[],[f141,f264,f259]) ).
thf(f269,definition,
( spl11_4
<=> ( $true
= ( rel @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f271,plain,
( ( $true
= ( rel @ sK4 @ sK5 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,plain,
( spl11_2
| spl11_4 ),
inference(avatar_split_clause,[],[f147,f269,f259]) ).
thf(f274,definition,
( spl11_5
<=> ( $false
= ( c @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f276,plain,
( ( $false
= ( c @ sK5 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f277,plain,
( spl11_5
| spl11_2 ),
inference(avatar_split_clause,[],[f149,f259,f274]) ).
thf(f279,definition,
( spl11_6
<=> ( $true
= ( a @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f281,plain,
( ( $true
= ( a @ sK5 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f282,plain,
( spl11_6
| spl11_2 ),
inference(avatar_split_clause,[],[f150,f259,f279]) ).
thf(f284,definition,
( spl11_7
<=> ! [X1: $i] :
( ( $false
= ( b @ X1 ) )
| ( $true
= ( c @ X1 ) )
| ( $false
= ( rel @ sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f285,plain,
( ! [X1: $i] :
( ( $false
= ( rel @ sK4 @ X1 ) )
| ( $true
= ( c @ X1 ) )
| ( $false
= ( b @ X1 ) ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f286,plain,
( spl11_2
| spl11_7 ),
inference(avatar_split_clause,[],[f156,f284,f259]) ).
thf(f288,definition,
( spl11_8
<=> ! [X1: $i] :
( ( $true
= ( b @ X1 ) )
| ( ( a @ X1 )
= $false )
| ( $false
= ( rel @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f289,plain,
( ! [X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( ( a @ X1 )
= $false )
| ( $true
= ( b @ X1 ) ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f290,plain,
( spl11_8
| spl11_2 ),
inference(avatar_split_clause,[],[f162,f259,f288]) ).
thf(f331,plain,
~ spl11_2,
inference(avatar_split_clause,[],[f117,f259]) ).
thf(f368,plain,
( ( $false
= ( b @ sK5 ) )
| ( $true = $false )
| ( $true
= ( c @ sK5 ) )
| ~ spl11_4
| ~ spl11_7 ),
inference(constrained_superposition,[],[f271,f285]) ).
thf(f369,plain,
( ( $true
= ( c @ sK5 ) )
| ( $false
= ( b @ sK5 ) )
| ~ spl11_4
| ~ spl11_7 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f372,plain,
( ( $false
= ( b @ sK5 ) )
| ( $true = $false )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_7 ),
inference(forward_demodulation,[],[f369,f276]) ).
thf(f373,plain,
( ( $false
= ( b @ sK5 ) )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_7 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f442,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true = $false )
| ( $true
= ( rel @ X0 @ X4 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $false
= ( rel @ X0 @ X1 ) )
| ( $true
= ( rel @ X0 @ X2 ) )
| ( $false
= ( rel @ X0 @ X3 ) )
| ( $false
= ( rel @ X3 @ X4 ) ) ),
inference(constrained_superposition,[],[f253,f249]) ).
thf(f449,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( rel @ X0 @ X4 ) )
| ( $false
= ( rel @ X0 @ X3 ) )
| ( $false
= ( rel @ X3 @ X4 ) )
| ( $false
= ( rel @ X0 @ X1 ) )
| ( $true
= ( rel @ X0 @ X2 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f482,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( rel @ sK3 @ X3 ) )
| ( $true = $false )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $false
= ( a @ X0 ) ) )
| ~ spl11_8 ),
inference(constrained_superposition,[],[f289,f449]) ).
thf(f498,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( rel @ sK3 @ X2 ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ X1 @ X0 ) ) )
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f509,definition,
( spl11_31
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( rel @ X2 @ X3 ) )
| ( $true
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( rel @ sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_31])],[avatar_definition]) ).
thf(f510,plain,
( ! [X2: $i,X3: $i] :
( ( $true
= ( rel @ sK3 @ X3 ) )
| ( $false
= ( rel @ X2 @ X3 ) )
| ( $false
= ( rel @ sK3 @ X2 ) ) )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f509]) ).
thf(f512,definition,
( spl11_32
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( a @ X0 ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $true
= ( b @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_32])],[avatar_definition]) ).
thf(f513,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $false
= ( rel @ X1 @ X0 ) ) )
| ~ spl11_32 ),
inference(avatar_component_clause,[],[f512]) ).
thf(f515,plain,
( spl11_31
| spl11_32
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f498,f288,f512,f509]) ).
thf(f518,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK3 @ X1 ) )
| ( $true = $false )
| ( $false
= ( rel @ X1 @ X0 ) )
| ( $false
= ( a @ X0 ) ) )
| ~ spl11_8
| ~ spl11_31 ),
inference(constrained_superposition,[],[f510,f289]) ).
thf(f528,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel @ X1 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $false
= ( rel @ sK3 @ X1 ) ) )
| ~ spl11_8
| ~ spl11_31 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f532,plain,
( spl11_32
| ~ spl11_8
| ~ spl11_31 ),
inference(avatar_split_clause,[],[f528,f509,f288,f512]) ).
thf(f558,plain,
( ! [X0: $i] :
( ( $true
= ( b @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel @ sK4 @ X0 ) )
| ( $false
= ( a @ X0 ) ) )
| ~ spl11_3
| ~ spl11_32 ),
inference(constrained_superposition,[],[f266,f513]) ).
thf(f565,plain,
( ! [X0: $i] :
( ( $false
= ( rel @ sK4 @ X0 ) )
| ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl11_3
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f581,plain,
( ( $true = $false )
| ( $true
= ( b @ sK5 ) )
| ( $false
= ( a @ sK5 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_32 ),
inference(constrained_superposition,[],[f565,f271]) ).
thf(f595,plain,
( ( $false
= ( a @ sK5 ) )
| ( $true
= ( b @ sK5 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f605,plain,
( ( $true = $false )
| ( $true
= ( b @ sK5 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_6
| ~ spl11_32 ),
inference(forward_demodulation,[],[f595,f281]) ).
thf(f606,plain,
( ( $true
= ( b @ sK5 ) )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_6
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f605]) ).
thf(f611,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_7
| ~ spl11_32 ),
inference(forward_demodulation,[],[f606,f373]) ).
thf(f612,plain,
( $false
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_7
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f613,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_7
| ~ spl11_32 ),
inference(avatar_contradiction_clause,[],[f612]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f267]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f272]) ).
cnf(s4,plain,
( spl11_2
| spl11_5 ),
inference(sat_conversion,[],[f277]) ).
cnf(s5,plain,
( spl11_2
| spl11_6 ),
inference(sat_conversion,[],[f282]) ).
cnf(s6,plain,
( spl11_2
| spl11_7 ),
inference(sat_conversion,[],[f286]) ).
cnf(s7,plain,
( spl11_2
| spl11_8 ),
inference(sat_conversion,[],[f290]) ).
cnf(s17,plain,
~ spl11_2,
inference(sat_conversion,[],[f331]) ).
cnf(s32,plain,
( ~ spl11_8
| spl11_31
| spl11_32 ),
inference(sat_conversion,[],[f515]) ).
cnf(s33,plain,
( ~ spl11_8
| ~ spl11_31
| spl11_32 ),
inference(sat_conversion,[],[f532]) ).
cnf(s42,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_7
| ~ spl11_32 ),
inference(sat_conversion,[],[f613]) ).
cnf(s43,plain,
spl11_8,
inference(rat,[],[s7,s17]) ).
cnf(s44,plain,
spl11_7,
inference(rat,[],[s6,s17]) ).
cnf(s45,plain,
spl11_6,
inference(rat,[],[s5,s17]) ).
cnf(s46,plain,
spl11_5,
inference(rat,[],[s4,s17]) ).
cnf(s47,plain,
spl11_4,
inference(rat,[],[s3,s17]) ).
cnf(s48,plain,
spl11_3,
inference(rat,[],[s2,s17]) ).
cnf(s49,plain,
~ spl11_32,
inference(rat,[],[s42,s47,s44,s45,s46,s48]) ).
cnf(s50,plain,
~ spl11_31,
inference(rat,[],[s33,s43,s49]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s32,s43,s49,s50]) ).
thf(f614,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV430^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:02:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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
% 0.23/0.32 % (1477876)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (1477881)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=963750716:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (1477887)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (1477887)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
% 0.23/0.32 % (1477884)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=3285015104: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)
% 0.23/0.32 % (1477882)lrs+10_16_si=on:nwc=1.5:random_seed=3880880559:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (1477883)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2835625690:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (1477885)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3667957171:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (1477886)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2840462980:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (1477887)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=2167782770:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (1477883)Instruction limit reached!
% 0.23/0.32 % (1477883)------------------------------
% 0.23/0.32 % (1477883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1477883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1477883)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1477883)Termination reason: Instruction limit
% 0.23/0.32 % (1477883)Termination phase: Function definition elimination
% 0.23/0.32 % (1477883)Time elapsed: 0.002 s
% 0.23/0.32 % (1477883)Peak memory usage: 10 MB
% 0.23/0.32 % (1477883)Instructions burned: 4 (million)
% 0.23/0.32 % (1477882)Instruction limit reached!
% 0.23/0.32 % (1477882)------------------------------
% 0.23/0.32 % (1477882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1477882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1477882)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1477882)Termination reason: Instruction limit
% 0.23/0.32 % (1477882)Termination phase: Saturation
% 0.23/0.32 % (1477882)Time elapsed: 0.009 s
% 0.23/0.32 % (1477882)Peak memory usage: 12 MB
% 0.23/0.32 % (1477882)Instructions burned: 18 (million)
% 0.23/0.32 % (1477885)Instruction limit reached!
% 0.23/0.32 % (1477885)------------------------------
% 0.23/0.32 % (1477885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1477885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1477885)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1477885)Termination reason: Instruction limit
% 0.23/0.32 % (1477885)Termination phase: Saturation
% 0.23/0.32 % (1477885)Time elapsed: 0.015 s
% 0.23/0.32 % (1477885)Peak memory usage: 11 MB
% 0.23/0.32 % (1477885)Instructions burned: 26 (million)
% 0.23/0.32 % (1477881)Instruction limit reached!
% 0.23/0.32 % (1477881)------------------------------
% 0.23/0.32 % (1477881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1477881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1477881)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1477881)Termination reason: Instruction limit
% 0.23/0.32 % (1477881)Termination phase: Saturation
% 0.23/0.32 % (1477881)Time elapsed: 0.025 s
% 0.23/0.32 % (1477881)Peak memory usage: 12 MB
% 0.23/0.32 % (1477881)Instructions burned: 90 (million)
% 0.23/0.32 % (1477887) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1477876-1477887"...
% 0.23/0.32 % (1477895)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=473748747:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.32 % (1477895)Instruction limit reached!
% 0.23/0.32 % (1477895)------------------------------
% 0.23/0.32 % (1477895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1477895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1477895)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1477895)Termination reason: Instruction limit
% 0.23/0.32 % (1477895)Termination phase: Function definition elimination
% 0.23/0.32 % (1477895)Time elapsed: 0.002 s
% 0.23/0.32 % (1477895)Peak memory usage: 10 MB
% 0.23/0.32 % (1477895)Instructions burned: 4 (million)
% 0.23/0.32 % (1477887)...printing done.
% 0.23/0.32 % (1477887)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.33 % (1477887)------------------------------
% 0.23/0.33 % (1477887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (1477887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (1477887)CaDiCaL version: 2.1.3
% 0.23/0.33 % (1477887)Termination reason: Refutation
% 0.23/0.33 % (1477887)Time elapsed: 0.024 s
% 0.23/0.33 % (1477887)Peak memory usage: 13 MB
% 0.23/0.33 % (1477887)Instructions burned: 46 (million)
% 0.23/0.33 % (1477876)Success in time 0.068 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------