%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:15:02 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 157 ( 49 unt; 0 typ; 8 def)
% Number of atoms : 1140 ( 210 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1301 ( 104 ~; 181 |; 27 &; 810 @)
% ( 8 <=>; 91 =>; 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 : 74 ( 70 usr; 17 con; 0-4 aty)
% ( 80 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 263 ( 0 sgn 73 !; 4 ?; 263 :)
% 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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vIMP: $o > $o > $o ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vIFF: $o > $o > $o ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sK1: $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f24,axiom,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f49,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f50,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f57,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f79,plain,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f80,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f85,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f86,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f104,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(f105,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) )
=> ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f104]) ).
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 ) )
& ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f105]) ).
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 ) ) ) ) ) )
& ( $true
= ( transitive @ sK0 ) )
& ( $true
= ( reflexive @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f107]) ).
thf(f111,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f112,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f114,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f116,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f132,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f135,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f145,plain,
( $true
= ( reflexive @ sK0 ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f146,plain,
( $true
= ( transitive @ sK0 ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f147,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ sK1 ) ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f150,plain,
( mimpl
= ( ^ [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,[],[f114,f112,f111]) ).
thf(f154,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 )
@ sK1 ) ) )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f147,f120,f150,f116,f120,f150,f116,f116,f116]) ).
thf(f155,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f146,f135]) ).
thf(f156,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f145,f132]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) ) )
| ( $true
= ( sK0 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) )
@ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( sK1 @ sK2 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ sK2 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $true
= ( ( sK0 @ sK3 @ X2 )
=> ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( ( sK0 @ sK3 @ X2 )
=> ( sK1 @ X2 ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,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(sigma_proxy_clausification,[],[f177]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK2 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $false
= ( ( sK0 @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f189,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK5 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ sK4 @ sK5 )
=> ( sK1 @ sK5 ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f194,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f195,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK3 @ X1 )
=> ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f200,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 @ sK6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK6 @ sK7 )
=> ( sK1 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK6 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f208,definition,
( spl8_1
<=> ( $false
= ( sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f210,plain,
( ( $false
= ( sK1 @ sK7 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f212,definition,
( spl8_2
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f213,plain,
( ( $false
!= ( sK1 @ sK2 ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f215,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f205,f212,f208]) ).
thf(f217,definition,
( spl8_3
<=> ( $true
= ( sK0 @ sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f219,plain,
( ( $true
= ( sK0 @ sK3 @ sK6 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f220,plain,
( spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f202,f212,f217]) ).
thf(f222,definition,
( spl8_4
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f224,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f232,definition,
( spl8_7
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f233,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f234,plain,
( spl8_4
| spl8_7 ),
inference(avatar_split_clause,[],[f191,f232,f222]) ).
thf(f260,definition,
( spl8_8
<=> ( $true
= ( sK0 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f262,plain,
( ( $true
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl8_8
| spl8_7 ),
inference(avatar_split_clause,[],[f188,f232,f260]) ).
thf(f264,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK2 ) )
| ~ spl8_7 ),
inference(constrained_superposition,[],[f233,f159]) ).
thf(f267,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f271,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_7 ),
inference(forward_demodulation,[],[f267,f214]) ).
thf(f272,plain,
( $false
| ~ spl8_2
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f273,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f272]) ).
thf(f275,definition,
( spl8_9
<=> ( $true
= ( sK0 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f277,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f278,plain,
( spl8_9
| spl8_7 ),
inference(avatar_split_clause,[],[f192,f232,f275]) ).
thf(f295,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl8_9 ),
inference(constrained_superposition,[],[f277,f168]) ).
thf(f300,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f737,definition,
( spl8_17
<=> ! [X2: $i] :
( ( $false
= ( sK0 @ sK3 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
thf(f738,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ sK3 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f737]) ).
thf(f739,plain,
( spl8_17
| spl8_7 ),
inference(avatar_split_clause,[],[f183,f232,f737]) ).
thf(f832,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl8_9
| ~ spl8_17 ),
inference(constrained_superposition,[],[f300,f738]) ).
thf(f843,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl8_9
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f832]) ).
thf(f846,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(forward_demodulation,[],[f843,f262]) ).
thf(f847,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f846]) ).
thf(f848,plain,
( ( $false = $true )
| ~ spl8_4
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(forward_demodulation,[],[f847,f224]) ).
thf(f849,plain,
( $false
| ~ spl8_4
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f850,plain,
( ~ spl8_4
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(avatar_contradiction_clause,[],[f849]) ).
thf(f914,plain,
( ( $true
= ( sK0 @ sK6 @ sK7 ) )
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f206,f213]) ).
thf(f916,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| spl8_2 ),
inference(constrained_superposition,[],[f168,f914]) ).
thf(f917,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| spl8_2 ),
inference(trivial_inequality_removal,[],[f916]) ).
thf(f1039,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ sK6 ) )
| ( $true
= ( sK1 @ sK7 ) )
| spl8_2
| ~ spl8_17 ),
inference(constrained_superposition,[],[f917,f738]) ).
thf(f1052,plain,
( ( $false
= ( sK0 @ sK3 @ sK6 ) )
| ( $true
= ( sK1 @ sK7 ) )
| spl8_2
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f1039]) ).
thf(f1058,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK7 ) )
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(forward_demodulation,[],[f1052,f219]) ).
thf(f1059,plain,
( ( $true
= ( sK1 @ sK7 ) )
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f1058]) ).
thf(f1062,plain,
( ( $false = $true )
| ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(forward_demodulation,[],[f1059,f210]) ).
thf(f1063,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1064,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(avatar_contradiction_clause,[],[f1063]) ).
thf(f1065,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) )
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f198,f213]) ).
thf(f1122,plain,
( spl8_17
| spl8_2 ),
inference(avatar_split_clause,[],[f1065,f212,f737]) ).
cnf(s16,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f215]) ).
cnf(s20,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f220]) ).
cnf(s24,plain,
( spl8_4
| spl8_7 ),
inference(sat_conversion,[],[f234]) ).
cnf(s40,plain,
( spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f263]) ).
cnf(s44,plain,
( ~ spl8_2
| ~ spl8_7 ),
inference(sat_conversion,[],[f273]) ).
cnf(s48,plain,
( spl8_7
| spl8_9 ),
inference(sat_conversion,[],[f278]) ).
cnf(s158,plain,
( spl8_7
| spl8_17 ),
inference(sat_conversion,[],[f739]) ).
cnf(s205,plain,
( ~ spl8_4
| ~ spl8_8
| ~ spl8_9
| ~ spl8_17 ),
inference(sat_conversion,[],[f850]) ).
cnf(s283,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_17 ),
inference(sat_conversion,[],[f1064]) ).
cnf(s313,plain,
( spl8_2
| spl8_17 ),
inference(sat_conversion,[],[f1122]) ).
cnf(s314,plain,
spl8_7,
inference(rat,[],[s205,s24,s40,s48,s158]) ).
cnf(s315,plain,
~ spl8_2,
inference(rat,[],[s44,s314]) ).
cnf(s316,plain,
spl8_17,
inference(rat,[],[s313,s315]) ).
cnf(s317,plain,
spl8_3,
inference(rat,[],[s20,s315]) ).
cnf(s318,plain,
spl8_1,
inference(rat,[],[s16,s315]) ).
cnf(s319,plain,
$false,
inference(rat,[],[s283,s316,s315,s318,s317]) ).
thf(f1123,plain,
$false,
inference(avatar_sat_refutation,[],[s319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 09:17:48 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.32 % (508681)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (508687)% WARNING: option uhcvi not known.
% 0.22/0.32 % (508689)dis+10_1_sil=32000:sp=arity:random_seed=320813308:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (508687)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2536481626:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (508688)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1288683427:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (508687)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (508687)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.32 % (508692)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2651975083:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.32 % (508686)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1128732716_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % Exception at run slice level
% 0.22/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.32 % (508690)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1560575974:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (508690)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (508691)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2836156173:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (508692) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-508681-508692"...
% 0.22/0.32 % (508688) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-508681-508688"...
% 0.22/0.32 % (508688)...printing done.
% 0.22/0.32 % (508692)...printing done.
% 0.22/0.32 % (508699)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3964295788:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.32 % (508688)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
% 0.22/0.32 % (508688)------------------------------
% 0.22/0.32 % (508688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (508688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (508688)CaDiCaL version: 2.1.3
% 0.22/0.32 % (508688)Termination reason: Refutation
% 0.22/0.32 % (508688)Time elapsed: 0.034 s
% 0.22/0.32 % (508688)Peak memory usage: 13 MB
% 0.22/0.32 % (508688)Instructions burned: 63 (million)
% 0.22/0.32 % (508681)Success in time 0.075 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------