%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL600^1 : 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 : n015.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 08:15:01 AM UTC 2026
% Result : Theorem 20.49s 3.23s
% Output : Refutation 20.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 19
% Syntax : Number of formulae : 194 ( 29 unt; 0 typ; 12 def)
% Number of atoms : 1748 ( 340 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 2200 ( 169 ~; 350 |; 53 &;1365 @)
% ( 16 <=>; 135 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 22 con; 0-4 aty)
% ( 111 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 471 ( 0 sgn 226 !; 5 ?; 471 :)
% 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(func_def_59,type,
sK2: ( $i > $o ) > $i > $i ).
thf(func_def_68,type,
sK11: ( $i > $o ) > ( $i > $i ) > $i ).
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(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] :
( ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ( transitive @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ( transitive @ X0 ) ),
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(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] :
( ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ( transitive @ X0 ) ),
inference(rectify,[],[f38]) ).
thf(f105,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
<=> ( ( transitive @ X0 )
= $true ) ),
inference(fool_elimination,[],[f104]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
<~> ( ( transitive @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f105]) ).
thf(f107,plain,
? [X0: $i > $i > $o] :
( ( ( ( transitive @ X0 )
!= $true )
| ? [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true ) )
& ( ( ( transitive @ X0 )
= $true )
| ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ) ),
inference(nnf_transformation,[],[f106]) ).
thf(f108,plain,
? [X0: $i > $i > $o] :
( ( ( ( transitive @ X0 )
!= $true )
| ? [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true ) )
& ( ( ( transitive @ X0 )
= $true )
| ! [X2: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f107]) ).
thf(f109,plain,
( ( ( $true
!= ( transitive @ sK0 ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) ) )
& ( ( $true
= ( transitive @ sK0 ) )
| ! [X2: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f108]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f113,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f115,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f117,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f121,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f136,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(f146,plain,
! [X2: $i > $o] :
( ( $true
= ( transitive @ sK0 ) )
| ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f147,plain,
( ( $true
!= ( transitive @ sK0 ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
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,[],[f115,f113,f112]) ).
thf(f154,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 ) )
| ( $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,f136,f121,f150,f117,f117,f117]) ).
thf(f155,plain,
! [X2: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $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
@ X2 )
@ ( ^ [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
@ X2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f146,f136,f121,f150,f117,f117,f117]) ).
thf(f156,plain,
! [X2: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) )
@ X5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) )
@ X5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X6 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X3 ) )
=> ( sK0 @ Y1 @ X3 ) ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) )
@ ( sK2 @ X2 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) ) ) )
| ( $true
= ( ( sK0 @ X4 @ X6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
=> ( X2 @ ( sK2 @ X2 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $true
= ( ( sK0 @ X4 @ X6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
=> ( X2 @ ( sK2 @ X2 @ X4 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
=> ( X2 @ ( sK2 @ X2 @ X4 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f170,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X7 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ X7 @ X3 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X7 @ X5 )
& ( sK0 @ X5 @ X3 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) )
| ( $true
= ( sK0 @ X7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) )
| ( $true
= ( sK0 @ X7 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $true
= ( sK0 @ X7 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) )
| ( $true
= ( X2 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ Y0 @ X3 ) )
@ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f176,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X7 @ X5 )
& ( sK0 @ X5 @ X3 ) )
=> ( sK0 @ X7 @ X3 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X7 @ X5 )
& ( sK0 @ X5 @ X3 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) )
| ( $true
= ( sK0 @ X7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X8 )
=> ( X2 @ X8 ) ) )
| ( $true
= ( sK0 @ X7 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $true
= ( sK0 @ X7 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) )
| ( $true
= ( X2 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ 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(f181,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $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,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $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 ) ) ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK4 @ X1 )
=> ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK6 ) )
| ( $true
= ( ( sK0 @ sK4 @ X1 )
=> ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ sK6 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK6 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK6 @ sK5 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f198,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( ( sK0 @ sK4 @ sK7 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK8 ) )
| ( $false
= ( ( sK0 @ sK4 @ sK7 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK8 ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f208,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK7 @ sK9 )
=> ( sK1 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK9 )
=> ( sK1 @ sK9 ) ) ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK7 @ sK9 )
=> ( sK1 @ sK9 ) ) ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f211,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK9 )
=> ( sK1 @ sK9 ) ) ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK9 )
=> ( sK1 @ sK9 ) ) ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK1 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK7 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $false
= ( sK1 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f216,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f217,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK1 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f218,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f220,definition,
( spl10_1
<=> ! [X4: $i,X8: $i,X6: $i,X2: $i > $o] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( X2 @ X8 ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f221,plain,
( ! [X2: $i > $o,X8: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( X2 @ X8 ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $true
= ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) ) ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f223,definition,
( spl10_2
<=> ! [X5: $i,X7: $i,X3: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) )
| ( $true
= ( sK0 @ X7 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f224,plain,
( ! [X3: $i,X7: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $false
= ( sK0 @ X7 @ X5 ) )
| ( $true
= ( sK0 @ X7 @ X3 ) ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f225,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f174,f223,f220]) ).
thf(f227,definition,
( spl10_3
<=> ! [X4: $i,X8: $i,X6: $i,X2: $i > $o] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( X2 @ X8 ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f228,plain,
( ! [X2: $i > $o,X8: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( X2 @ X8 ) )
| ( $false
= ( sK0 @ X6 @ X8 ) )
| ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f229,plain,
( spl10_3
| spl10_2 ),
inference(avatar_split_clause,[],[f179,f223,f227]) ).
thf(f231,definition,
( spl10_4
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f232,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f234,definition,
( spl10_5
<=> ( $true
= ( sK0 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f236,plain,
( ( $true
= ( sK0 @ sK6 @ sK5 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f237,plain,
( spl10_4
| spl10_5 ),
inference(avatar_split_clause,[],[f196,f234,f231]) ).
thf(f239,definition,
( spl10_6
<=> ( $true
= ( sK0 @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f241,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f242,plain,
( spl10_4
| spl10_6 ),
inference(avatar_split_clause,[],[f195,f239,f231]) ).
thf(f244,definition,
( spl10_7
<=> ( $false
= ( sK0 @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f246,plain,
( ( $false
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f247,plain,
( spl10_4
| spl10_7 ),
inference(avatar_split_clause,[],[f193,f244,f231]) ).
thf(f249,definition,
( spl10_8
<=> ( $true
= ( sK0 @ sK4 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f251,plain,
( ( $true
= ( sK0 @ sK4 @ sK7 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f253,definition,
( spl10_9
<=> ( $true
= ( sK0 @ sK8 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f255,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl10_8
| spl10_9 ),
inference(avatar_split_clause,[],[f206,f253,f249]) ).
thf(f257,plain,
( spl10_8
| spl10_6 ),
inference(avatar_split_clause,[],[f205,f239,f249]) ).
thf(f259,definition,
( spl10_10
<=> ( $false
= ( sK0 @ sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f261,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,plain,
( spl10_8
| spl10_10 ),
inference(avatar_split_clause,[],[f203,f259,f249]) ).
thf(f264,definition,
( spl10_11
<=> ( $true
= ( sK0 @ sK7 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f266,plain,
( ( $true
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( spl10_11
| spl10_9 ),
inference(avatar_split_clause,[],[f214,f253,f264]) ).
thf(f269,definition,
( spl10_12
<=> ( $false
= ( sK1 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f271,plain,
( ( $false
= ( sK1 @ sK9 ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,plain,
( spl10_12
| spl10_9 ),
inference(avatar_split_clause,[],[f213,f253,f269]) ).
thf(f273,plain,
( spl10_11
| spl10_6 ),
inference(avatar_split_clause,[],[f216,f239,f264]) ).
thf(f274,plain,
( spl10_12
| spl10_6 ),
inference(avatar_split_clause,[],[f215,f239,f269]) ).
thf(f275,plain,
( spl10_11
| spl10_10 ),
inference(avatar_split_clause,[],[f218,f259,f264]) ).
thf(f276,plain,
( spl10_12
| spl10_10 ),
inference(avatar_split_clause,[],[f217,f259,f269]) ).
thf(f292,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $true
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl10_2
| ~ spl10_6 ),
inference(constrained_superposition,[],[f241,f224]) ).
thf(f297,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $true
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl10_2
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f400,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl10_2
| ~ spl10_4 ),
inference(constrained_superposition,[],[f224,f232]) ).
thf(f403,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl10_2
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f587,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl10_2
| ~ spl10_6
| ~ spl10_9 ),
inference(constrained_superposition,[],[f297,f255]) ).
thf(f600,plain,
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl10_2
| ~ spl10_6
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f587]) ).
thf(f608,plain,
( ( $false = $true )
| ~ spl10_2
| ~ spl10_6
| ~ spl10_9
| ~ spl10_10 ),
inference(forward_demodulation,[],[f600,f261]) ).
thf(f609,plain,
( $false
| ~ spl10_2
| ~ spl10_6
| ~ spl10_9
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f610,plain,
( ~ spl10_2
| ~ spl10_6
| ~ spl10_9
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f609]) ).
thf(f1089,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 @ sK7 ) )
| ( $true
= ( sK1 @ sK9 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_11 ),
inference(constrained_superposition,[],[f266,f403]) ).
thf(f1102,plain,
( ( $false
= ( sK0 @ sK4 @ sK7 ) )
| ( $true
= ( sK1 @ sK9 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f1089]) ).
thf(f1150,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 @ sK7 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(forward_demodulation,[],[f1102,f271]) ).
thf(f1151,plain,
( ( $false
= ( sK0 @ sK4 @ sK7 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f1150]) ).
thf(f1197,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl10_2
| ~ spl10_5
| ~ spl10_6 ),
inference(constrained_superposition,[],[f236,f297]) ).
thf(f1228,plain,
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl10_2
| ~ spl10_5
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f1197]) ).
thf(f1246,plain,
( ( $false = $true )
| ~ spl10_2
| ~ spl10_5
| ~ spl10_6
| ~ spl10_7 ),
inference(forward_demodulation,[],[f1228,f246]) ).
thf(f1247,plain,
( $false
| ~ spl10_2
| ~ spl10_5
| ~ spl10_6
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f1246]) ).
thf(f1248,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_6
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f1247]) ).
thf(f4536,plain,
( ( $false = $true )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_8
| ~ spl10_11
| ~ spl10_12 ),
inference(constrained_superposition,[],[f1151,f251]) ).
thf(f4554,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_8
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f4536]) ).
thf(f4555,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_8
| ~ spl10_11
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f4554]) ).
thf(f4563,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK2
@ ^ [Y0: $i] : ( Y0 != X0 )
@ X1 )
= X0 )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) )
| ~ spl10_3 ),
inference(leibniz_equality_elimination,[],[f228]) ).
thf(f6783,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X3 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(constrained_superposition,[],[f221,f4563]) ).
thf(f6826,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( X3 != X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(beta-eta_normalization,[],[f6783]) ).
thf(f6827,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( X3 = X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(not_proxy_clausification,[],[f6826]) ).
thf(f6828,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( X0 != X3 ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(equality_proxy_clausification,[],[f6827]) ).
thf(f35423,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( X1 != X1 ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(equality_factoring,[],[f6828]) ).
thf(f35424,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( X1 != X1 ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(duplicate_literal_removal,[],[f35423]) ).
thf(f35425,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) )
| ~ spl10_1
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f35424]) ).
thf(f36115,plain,
( spl10_2
| ~ spl10_1
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f35425,f227,f220,f223]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f225]) ).
cnf(s2,plain,
( spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f229]) ).
cnf(s3,plain,
( spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f237]) ).
cnf(s4,plain,
( spl10_4
| spl10_6 ),
inference(sat_conversion,[],[f242]) ).
cnf(s5,plain,
( spl10_4
| spl10_7 ),
inference(sat_conversion,[],[f247]) ).
cnf(s6,plain,
( spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( spl10_6
| spl10_8 ),
inference(sat_conversion,[],[f257]) ).
cnf(s8,plain,
( spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( spl10_9
| spl10_11 ),
inference(sat_conversion,[],[f267]) ).
cnf(s10,plain,
( spl10_9
| spl10_12 ),
inference(sat_conversion,[],[f272]) ).
cnf(s11,plain,
( spl10_6
| spl10_11 ),
inference(sat_conversion,[],[f273]) ).
cnf(s12,plain,
( spl10_6
| spl10_12 ),
inference(sat_conversion,[],[f274]) ).
cnf(s13,plain,
( spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f275]) ).
cnf(s14,plain,
( spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f276]) ).
cnf(s16,plain,
( ~ spl10_2
| ~ spl10_6
| ~ spl10_9
| ~ spl10_10 ),
inference(sat_conversion,[],[f610]) ).
cnf(s29,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_6
| ~ spl10_7 ),
inference(sat_conversion,[],[f1248]) ).
cnf(s220,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_8
| ~ spl10_11
| ~ spl10_12 ),
inference(sat_conversion,[],[f4555]) ).
cnf(s297,plain,
( ~ spl10_1
| spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f36115]) ).
cnf(s313,plain,
( spl10_4
| ~ spl10_2 ),
inference(rat,[],[s29,s3,s4,s5]) ).
cnf(s314,plain,
( spl10_8
| ~ spl10_6
| ~ spl10_2 ),
inference(rat,[],[s16,s6,s8]) ).
cnf(s315,plain,
( spl10_10
| ~ spl10_8
| ~ spl10_2 ),
inference(rat,[],[s220,s13,s14,s313]) ).
cnf(s316,plain,
( ~ spl10_6
| ~ spl10_2 ),
inference(rat,[],[s220,s9,s10,s16,s315,s314,s313]) ).
cnf(s317,plain,
~ spl10_2,
inference(rat,[],[s220,s7,s11,s12,s316,s313]) ).
cnf(s318,plain,
spl10_3,
inference(rat,[],[s2,s317]) ).
cnf(s319,plain,
spl10_1,
inference(rat,[],[s1,s317]) ).
cnf(s320,plain,
$false,
inference(rat,[],[s297,s317,s319,s318]) ).
thf(f36160,plain,
$false,
inference(avatar_sat_refutation,[],[s320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.26 % Computer : n015.cluster.edu
% 0.13/0.26 % Model : x86_64 x86_64
% 0.13/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.26 % Memory : 8046.5625MB
% 0.13/0.26 % OS : Linux 6.8.0-71-generic
% 0.13/0.26 % CPULimit : 300
% 0.13/0.26 % WCLimit : 300
% 0.13/0.26 % DateTime : Tue Sep 29 09:18:03 UTC 2026
% 0.13/0.27 % CPUTime :
% 0.13/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.32 Running first-order model finding
% 0.27/0.32 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
% 6.68/1.44 % (3283137)Will run a generic schedule for satisfiability detection.
% 6.68/1.44 % (3283144)% WARNING: option uhcvi not known.
% 6.68/1.44 % (3283144)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1849219110:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.68/1.44 % (3283144)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.68/1.44 % (3283143)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=808709466_2999 on theBenchmark for (2999ds/0Mi)
% 6.68/1.44 % (3283144)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.68/1.44 % Exception at run slice level
% 6.68/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.68/1.44 % (3283146)dis+10_1_sil=32000:sp=arity:random_seed=3336709961:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.68/1.44 % (3283147)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3384181728:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.68/1.44 % (3283145)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2386934250:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.68/1.44 % (3283149)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3454578399:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.68/1.44 % (3283147)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.68/1.44 % (3283148)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1666802213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.68/1.44 % (3283153)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2062783975:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.68/1.44 % Exception at run slice level
% 6.68/1.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.68/1.44 % (3283160)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=396911369:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.68/1.44 % (3283146)Instruction limit reached!
% 6.68/1.44 % (3283146)------------------------------
% 6.68/1.44 % (3283146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.68/1.44 % (3283146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/1.44 % (3283146)CaDiCaL version: 2.1.3
% 6.68/1.44 % (3283146)Termination reason: Instruction limit
% 6.68/1.44 % (3283146)Termination phase: Saturation
% 6.68/1.44 % (3283146)Time elapsed: 0.081 s
% 6.68/1.44 % (3283146)Peak memory usage: 12 MB
% 6.68/1.44 % (3283146)Instructions burned: 104 (million)
% 6.68/1.44 % (3283147)Instruction limit reached!
% 6.68/1.44 % (3283147)------------------------------
% 6.68/1.44 % (3283147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.68/1.44 % (3283147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/1.44 % (3283147)CaDiCaL version: 2.1.3
% 6.68/1.44 % (3283147)Termination reason: Instruction limit
% 6.68/1.44 % (3283147)Termination phase: Saturation
% 6.68/1.44 % (3283147)Time elapsed: 0.093 s
% 6.68/1.44 % (3283147)Peak memory usage: 12 MB
% 6.68/1.44 % (3283147)Instructions burned: 119 (million)
% 6.68/1.44 % (3283148)Instruction limit reached!
% 6.68/1.44 % (3283148)------------------------------
% 6.68/1.44 % (3283148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.68/1.44 % (3283148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.68/1.44 % (3283148)CaDiCaL version: 2.1.3
% 6.68/1.44 % (3283148)Termination reason: Instruction limit
% 6.68/1.44 % (3283148)Termination phase: Saturation
% 6.68/1.44 % (3283148)Time elapsed: 0.110 s
% 6.68/1.44 % (3283148)Peak memory usage: 12 MB
% 6.68/1.44 % (3283148)Instructions burned: 132 (million)
% 6.68/1.44 % (3283165)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=258651835:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.68/1.44 % (3283166)ott-21_1_sil=16000:fs=off:random_seed=2729775603:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.68/1.44 % (3283165)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.68/1.44 % (3283165)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.68/1.44 % (3283149)Instruction limit reached!
% 20.49/3.23 % (3283149)------------------------------
% 20.49/3.23 % (3283149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283149)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283149)Termination reason: Instruction limit
% 20.49/3.23 % (3283149)Termination phase: Saturation
% 20.49/3.23 % (3283149)Time elapsed: 0.132 s
% 20.49/3.23 % (3283149)Peak memory usage: 12 MB
% 20.49/3.23 % (3283149)Instructions burned: 160 (million)
% 20.49/3.23 % (3283160)Instruction limit reached!
% 20.49/3.23 % (3283160)------------------------------
% 20.49/3.23 % (3283160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283160)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283160)Termination reason: Instruction limit
% 20.49/3.23 % (3283160)Termination phase: Saturation
% 20.49/3.23 % (3283160)Time elapsed: 0.102 s
% 20.49/3.23 % (3283160)Peak memory usage: 12 MB
% 20.49/3.23 % (3283160)Instructions burned: 132 (million)
% 20.49/3.23 % (3283168)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1050972750:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 20.49/3.23 % (3283174)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4277049449:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 20.49/3.23 % (3283172)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1246377090:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283178)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1051190831:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283181)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=486834108:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 20.49/3.23 % (3283166)Instruction limit reached!
% 20.49/3.23 % (3283166)------------------------------
% 20.49/3.23 % (3283166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283166)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283166)Termination reason: Instruction limit
% 20.49/3.23 % (3283166)Termination phase: Saturation
% 20.49/3.23 % (3283166)Time elapsed: 0.145 s
% 20.49/3.23 % (3283166)Peak memory usage: 12 MB
% 20.49/3.23 % (3283166)Instructions burned: 181 (million)
% 20.49/3.23 % (3283181)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.49/3.23 % (3283184)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3638936907:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 20.49/3.23 % (3283184)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.49/3.23 % (3283168)Instruction limit reached!
% 20.49/3.23 % (3283168)------------------------------
% 20.49/3.23 % (3283168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283168)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283168)Termination reason: Instruction limit
% 20.49/3.23 % (3283168)Termination phase: Saturation
% 20.49/3.23 % (3283168)Time elapsed: 0.415 s
% 20.49/3.23 % (3283168)Peak memory usage: 13 MB
% 20.49/3.23 % (3283168)Instructions burned: 477 (million)
% 20.49/3.23 % (3283189)fmb+10_1_sil=64000:random_seed=1178214626:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 20.49/3.23 % (3283189)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283192)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=620523616:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283165)Instruction limit reached!
% 20.49/3.23 % (3283165)------------------------------
% 20.49/3.23 % (3283165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283165)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283165)Termination reason: Instruction limit
% 20.49/3.23 % (3283165)Termination phase: Saturation
% 20.49/3.23 % (3283165)Time elapsed: 0.562 s
% 20.49/3.23 % (3283165)Peak memory usage: 15 MB
% 20.49/3.23 % (3283165)Instructions burned: 684 (million)
% 20.49/3.23 % (3283194)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4253768275:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283197)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2862566817:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 20.49/3.23 % (3283197)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.49/3.23 % (3283198)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1157235726:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 20.49/3.23 % (3283198)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.49/3.23 % (3283198)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 20.49/3.23 % (3283181)Instruction limit reached!
% 20.49/3.23 % (3283181)------------------------------
% 20.49/3.23 % (3283181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283181)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283181)Termination reason: Instruction limit
% 20.49/3.23 % (3283181)Termination phase: Saturation
% 20.49/3.23 % (3283181)Time elapsed: 0.467 s
% 20.49/3.23 % (3283181)Peak memory usage: 15 MB
% 20.49/3.23 % (3283181)Instructions burned: 693 (million)
% 20.49/3.23 % (3283201)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1314689750:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283205)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1492732932:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283209)ott-2_1_sil=16000:newcnf=on:random_seed=107022931:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 20.49/3.23 % (3283209)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.49/3.23 % (3283174)Instruction limit reached!
% 20.49/3.23 % (3283174)------------------------------
% 20.49/3.23 % (3283174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283174)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283174)Termination reason: Instruction limit
% 20.49/3.23 % (3283174)Termination phase: Saturation
% 20.49/3.23 % (3283174)Time elapsed: 0.718 s
% 20.49/3.23 % (3283174)Peak memory usage: 14 MB
% 20.49/3.23 % (3283174)Instructions burned: 1179 (million)
% 20.49/3.23 % (3283213)ott+10_1_sil=32000:tgt=ground:random_seed=3254020717:i=5114:av=off_2990 on theBenchmark for (2990ds/5114Mi)
% 20.49/3.23 % (3283184)Instruction limit reached!
% 20.49/3.23 % (3283184)------------------------------
% 20.49/3.23 % (3283184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283184)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283184)Termination reason: Instruction limit
% 20.49/3.23 % (3283184)Termination phase: Saturation
% 20.49/3.23 % (3283184)Time elapsed: 0.736 s
% 20.49/3.23 % (3283184)Peak memory usage: 15 MB
% 20.49/3.23 % (3283184)Instructions burned: 879 (million)
% 20.49/3.23 % (3283223)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4290447688:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 20.49/3.23 % Exception at run slice level
% 20.49/3.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.49/3.23 % (3283225)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=197790622:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 20.49/3.23 % (3283225)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 20.49/3.23 % (3283209)Instruction limit reached!
% 20.49/3.23 % (3283209)------------------------------
% 20.49/3.23 % (3283209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283209)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283209)Termination reason: Instruction limit
% 20.49/3.23 % (3283209)Termination phase: Saturation
% 20.49/3.23 % (3283209)Time elapsed: 0.508 s
% 20.49/3.23 % (3283209)Peak memory usage: 15 MB
% 20.49/3.23 % (3283209)Instructions burned: 870 (million)
% 20.49/3.23 % (3283237)dis+21_1_sil=32000:sas=cadical:random_seed=2406054413:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 20.49/3.23 % (3283198)Instruction limit reached!
% 20.49/3.23 % (3283198)------------------------------
% 20.49/3.23 % (3283198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.23 % (3283198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.23 % (3283198)CaDiCaL version: 2.1.3
% 20.49/3.23 % (3283198)Termination reason: Instruction limit
% 20.49/3.23 % (3283198)Termination phase: Saturation
% 20.49/3.23 % (3283198)Time elapsed: 1.284 s
% 20.49/3.23 % (3283198)Peak memory usage: 18 MB
% 20.49/3.23 % (3283198)Instructions burned: 1473 (million)
% 20.49/3.23 % (3283256)ott+11_1_sil=16000:gs=on:random_seed=3410327510:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2979 on theBenchmark for (2979ds/2251Mi)
% 20.49/3.23 % (3283256)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 20.49/3.23 % (3283144) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3283137-3283144"...
% 20.49/3.23 % (3283144)...printing done.
% 20.49/3.23 % (3283144)Refutation found. Thanks to Tanya!
% 20.49/3.23 % SZS status Theorem for theBenchmark
% 20.49/3.23 % SZS output start Proof for theBenchmark
% See solution above
% 20.49/3.24 % (3283144)------------------------------
% 20.49/3.24 % (3283144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.49/3.24 % (3283144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.49/3.24 % (3283144)CaDiCaL version: 2.1.3
% 20.49/3.24 % (3283144)Termination reason: Refutation
% 20.49/3.24 % (3283144)Time elapsed: 2.873 s
% 20.49/3.24 % (3283144)Peak memory usage: 24 MB
% 20.49/3.24 % (3283144)Instructions burned: 7034 (million)
% 20.49/3.24 % (3283137)Success in time 2.905 s
% 20.49/3.24 % Vampire exiting
%------------------------------------------------------------------------------