%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL604^1 : 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 : n009.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 08:14:26 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 164 ( 50 unt; 0 typ; 8 def)
% Number of atoms : 1157 ( 212 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1315 ( 126 ~; 188 |; 27 &; 800 @)
% ( 8 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 16 con; 0-4 aty)
% ( 77 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 258 ( 0 sgn 70 !; 4 ?; 258 :)
% 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,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_22,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_25,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_27,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_28,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_35,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_36,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_37,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_38,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_39,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_40,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vIMP: $o > $o > $o ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
vIFF: $o > $o > $o ).
thf(func_def_56,type,
vOR: $o > $o > $o ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sK1: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
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,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f24,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
~ ! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f40,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( reflexive @ X0 )
= $true )
& ( ( transitive @ X0 )
= $true ) )
=> ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f53,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f58,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f62,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f73,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
inference(rectify,[],[f24]) ).
thf(f74,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f92,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f93,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f100,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f101,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ? [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
!= $true )
| ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true ) )
& ( ( reflexive @ X0 )
= $true )
& ( ( transitive @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f40]) ).
thf(f107,plain,
? [X0: $i > $i > $o] :
( ? [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
!= $true )
| ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true ) )
& ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ),
inference(flattening,[],[f106]) ).
thf(f108,plain,
( ( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ sK1 ) ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) ) )
& ( ( transitive @ sK0 )
= $true )
& ( $true
= ( reflexive @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f107]) ).
thf(f110,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f117,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f120,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f121,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f125,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f134,plain,
( $true
= ( reflexive @ sK0 ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f135,plain,
( ( transitive @ sK0 )
= $true ),
inference(cnf_transformation,[],[f108]) ).
thf(f136,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ sK1 ) ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f143,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f150,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,[],[f121,f117,f115]) ).
thf(f154,plain,
( ( ( ^ [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 ) ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 ) ) ) )
!= $true )
| ( $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 ) ) )
@ sK0
@ sK1 )
@ sK1 ) ) ) ),
inference(definition_unfolding,[],[f136,f125,f150,f143,f125,f150,f143,f143,f143]) ).
thf(f155,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f135,f120]) ).
thf(f156,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f134,f110]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f158,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK0 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X3 )
= $true )
| ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X3 )
= $true )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f167,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ( sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) )
| ( $false
= ( ( sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ( sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK5 )
= $false )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK4 @ sK5 )
=> ( sK1 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK2 @ X1 )
=> ( sK1 @ X1 ) )
= $true )
| ( $false
= ( ( sK0 @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ( sK0 @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK6 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( ( sK0 @ sK4 @ sK6 )
=> ( sK1 @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f196,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f197,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK3 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ sK3 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $true
= ( ( sK0 @ sK2 @ X2 )
=> ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( ( sK0 @ sK2 @ X2 )
=> ( sK1 @ X2 ) ) )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ sK3 @ X1 )
= $false )
| ( ( sK0 @ sK2 @ X2 )
= $false )
| ( $true
= ( sK1 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f209,definition,
( spl7_1
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f211,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f213,definition,
( spl7_2
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f215,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f180,f213,f209]) ).
thf(f218,definition,
( spl7_3
<=> ( $true
= ( sK0 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f220,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl7_2
| spl7_3 ),
inference(avatar_split_clause,[],[f184,f218,f213]) ).
thf(f223,definition,
( spl7_4
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f225,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl7_4
| spl7_2 ),
inference(avatar_split_clause,[],[f183,f213,f223]) ).
thf(f228,definition,
( spl7_5
<=> ! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f229,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f230,plain,
( spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f190,f228,f209]) ).
thf(f232,definition,
( spl7_6
<=> ( $true
= ( sK0 @ sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f234,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f235,plain,
( spl7_6
| spl7_5 ),
inference(avatar_split_clause,[],[f194,f228,f232]) ).
thf(f237,definition,
( spl7_7
<=> ( ( sK1 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f239,plain,
( ( ( sK1 @ sK6 )
= $false )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
( spl7_5
| spl7_7 ),
inference(avatar_split_clause,[],[f193,f237,f228]) ).
thf(f242,definition,
( spl7_8
<=> ! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f243,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK3 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f244,plain,
( spl7_2
| spl7_8 ),
inference(avatar_split_clause,[],[f200,f242,f213]) ).
thf(f245,plain,
( spl7_8
| spl7_5 ),
inference(avatar_split_clause,[],[f207,f228,f242]) ).
thf(f246,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK2 ) )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f229,f168]) ).
thf(f247,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true = $false )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f168,f229]) ).
thf(f248,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f249,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f250,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_5 ),
inference(forward_demodulation,[],[f248,f215]) ).
thf(f251,plain,
( $false
| ~ spl7_2
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f252,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f251]) ).
thf(f253,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_5 ),
inference(forward_demodulation,[],[f249,f215]) ).
thf(f254,plain,
( $false
| ~ spl7_2
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f255,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f254]) ).
thf(f272,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $true = $false )
| ( $true
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl7_6 ),
inference(constrained_superposition,[],[f165,f234]) ).
thf(f285,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f305,plain,
( ( ( sK1 @ sK6 )
= $true )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true = $false )
| ~ spl7_6
| ~ spl7_8 ),
inference(constrained_superposition,[],[f243,f285]) ).
thf(f311,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( ( sK1 @ sK6 )
= $true )
| ~ spl7_6
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f316,plain,
( ( ( sK1 @ sK6 )
= $true )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_6
| ~ spl7_8 ),
inference(forward_demodulation,[],[f311,f211]) ).
thf(f317,plain,
( ( ( sK1 @ sK6 )
= $true )
| ~ spl7_1
| ~ spl7_6
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f321,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f317,f239]) ).
thf(f322,plain,
( $false
| ~ spl7_1
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f323,plain,
( ~ spl7_1
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f322]) ).
thf(f329,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $true
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl7_3 ),
inference(constrained_superposition,[],[f165,f220]) ).
thf(f330,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f348,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl7_3
| ~ spl7_8 ),
inference(constrained_superposition,[],[f330,f243]) ).
thf(f363,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl7_3
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f370,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(forward_demodulation,[],[f363,f225]) ).
thf(f371,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f375,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(forward_demodulation,[],[f371,f211]) ).
thf(f376,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f375]) ).
thf(f377,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f376]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f216]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f221]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f226]) ).
cnf(s4,plain,
( spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f230]) ).
cnf(s5,plain,
( spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
( spl7_5
| spl7_7 ),
inference(sat_conversion,[],[f240]) ).
cnf(s7,plain,
( spl7_2
| spl7_8 ),
inference(sat_conversion,[],[f244]) ).
cnf(s8,plain,
( spl7_5
| spl7_8 ),
inference(sat_conversion,[],[f245]) ).
cnf(s9,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s10,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(sat_conversion,[],[f255]) ).
cnf(s12,plain,
( ~ spl7_1
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f323]) ).
cnf(s14,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_8 ),
inference(sat_conversion,[],[f377]) ).
cnf(s15,plain,
spl7_1,
inference(rat,[],[s9,s1,s4]) ).
cnf(s16,plain,
spl7_5,
inference(rat,[],[s12,s5,s6,s8,s15]) ).
cnf(s17,plain,
~ spl7_2,
inference(rat,[],[s10,s16]) ).
cnf(s18,plain,
spl7_8,
inference(rat,[],[s7,s17]) ).
cnf(s19,plain,
spl7_4,
inference(rat,[],[s3,s17]) ).
cnf(s20,plain,
spl7_3,
inference(rat,[],[s2,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s14,s18,s15,s19,s20]) ).
thf(f378,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 09:17:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.29 % (3744127)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3744133)lrs+10_16_si=on:nwc=1.5:random_seed=4261031197:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3744134)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3449821769:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3744134)Instruction limit reached!
% 0.20/0.29 % (3744134)------------------------------
% 0.20/0.29 % (3744134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3744134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3744134)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3744134)Termination reason: Instruction limit
% 0.20/0.29 % (3744134)Termination phase: Property scanning
% 0.20/0.29 % (3744134)Time elapsed: 0.003 s
% 0.20/0.29 % (3744134)Peak memory usage: 10 MB
% 0.20/0.29 % (3744134)Instructions burned: 6 (million)
% 0.20/0.29 % (3744138)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3744138)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
% 0.20/0.29 % (3744133)Instruction limit reached!
% 0.20/0.29 % (3744133)------------------------------
% 0.20/0.29 % (3744133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3744133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3744133)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3744133)Termination reason: Instruction limit
% 0.20/0.29 % (3744133)Termination phase: Saturation
% 0.20/0.29 % (3744133)Time elapsed: 0.014 s
% 0.20/0.29 % (3744133)Peak memory usage: 12 MB
% 0.20/0.29 % (3744133)Instructions burned: 22 (million)
% 0.20/0.29 % (3744132)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2335263878:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3744138)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=930488623:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3744142)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=59708430:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.29 % (3744132) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3744127-3744132"...
% 0.20/0.29 % (3744138) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3744127-3744138"...
% 0.20/0.29 % (3744142)Instruction limit reached!
% 0.20/0.29 % (3744142)------------------------------
% 0.20/0.29 % (3744142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3744142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3744142)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3744142)Termination reason: Instruction limit
% 0.20/0.29 % (3744142)Termination phase: Property scanning
% 0.20/0.29 % (3744142)Time elapsed: 0.001 s
% 0.20/0.29 % (3744142)Peak memory usage: 10 MB
% 0.20/0.29 % (3744142)Instructions burned: 6 (million)
% 0.20/0.29 % (3744135)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=74511012: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)
% 0.20/0.29 % (3744137)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2740946334:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3744141)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3892623937:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (3744136)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3361614784:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3744132)...printing done.
% 0.20/0.29 % (3744138)...printing done.
% 0.20/0.29 % (3744132)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3744132)------------------------------
% 0.20/0.30 % (3744132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3744132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3744132)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3744132)Termination reason: Refutation
% 0.20/0.30 % (3744132)Time elapsed: 0.015 s
% 0.20/0.30 % (3744132)Peak memory usage: 13 MB
% 0.20/0.30 % (3744132)Instructions burned: 26 (million)
% 0.20/0.30 % (3744127)Success in time 0.056 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------