%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:28 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 497 ( 89 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 651 ( 18 ~; 24 |; 16 &; 485 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 7 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 176 ( 136 ^; 39 !; 1 ?; 176 :)
% 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_41,type,
r: $i > $i > $o ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
vIMP: $o > $o > $o ).
thf(func_def_56,type,
vNOT: $o > $o ).
thf(func_def_57,type,
vIFF: $o > $o > $o ).
thf(func_def_58,type,
sK0: $i > $o ).
thf(func_def_63,type,
sK5: ( $i > $o ) > $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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,axiom,
( ( upwards_well_founded @ r )
& ( transitive @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwf_trans) ).
thf(f38,conjecture,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4) ).
thf(f39,negated_conjecture,
~ ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f50,plain,
~ ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f51,plain,
~ ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f53,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f69,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f70,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f75,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f76,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f89,plain,
( ( upwards_well_founded @ r )
& ( transitive @ r ) ),
inference(rectify,[],[f37]) ).
thf(f90,plain,
( ( ( transitive @ r )
= $true )
& ( ( upwards_well_founded @ r )
= $true ) ),
inference(fool_elimination,[],[f89]) ).
thf(f95,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f96,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f101,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f109,plain,
? [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f51]) ).
thf(f110,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ sK0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f109]) ).
thf(f117,plain,
( ( transitive @ r )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f125,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f126,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f131,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f132,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f139,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ sK0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f142,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f144,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f152,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,[],[f125,f144,f131]) ).
thf(f156,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ r ) ),
inference(definition_unfolding,[],[f117,f132]) ).
thf(f158,plain,
( ( ^ [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 ) ) )
@ r
@ sK0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ sK0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f139,f142,f152,f126,f126,f126,f126]) ).
thf(f159,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( r @ Y1 @ Y2 )
& ( r @ Y0 @ Y1 ) )
=> ( r @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( r @ Y1 @ Y2 )
& ( r @ Y0 @ Y1 ) )
=> ( r @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( r @ Y0 @ Y1 )
& ( r @ X1 @ Y0 ) )
=> ( r @ X1 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( r @ Y0 @ Y1 )
& ( r @ X1 @ Y0 ) )
=> ( r @ X1 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( r @ X2 @ Y0 )
& ( r @ X1 @ X2 ) )
=> ( r @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( r @ X2 @ Y0 )
& ( r @ X1 @ X2 ) )
=> ( r @ X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( r @ X2 @ X3 )
& ( r @ X1 @ X2 ) )
=> ( r @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( r @ X1 @ X3 )
= $true )
| ( $false
= ( ( r @ X2 @ X3 )
& ( r @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( r @ X1 @ X2 ) )
| ( ( r @ X1 @ X3 )
= $true )
| ( $false
= ( r @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( r @ Y2 @ Y3 )
=> ( sK0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f169,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( r @ Y2 @ Y3 )
=> ( sK0 @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( $true
= ( ( r @ sK1 @ X1 )
=> ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( r @ sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f178,plain,
( $false
= ( ( r @ sK1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( $true
= ( r @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( $false
= ( ( r @ sK2 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( r @ sK2 @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( $false
= ( ( r @ sK3 @ sK4 )
=> ( sK0 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
( $false
= ( sK0 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( r @ sK3 @ sK4 )
= $true ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f217,plain,
! [X0: $i] :
( ( $false
= ( r @ X0 @ sK2 ) )
| ( $true
= ( r @ X0 @ sK3 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f184,f167]) ).
thf(f219,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ sK3 ) )
| ( $false
= ( r @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f221,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ sK4 ) )
| ( $false = $true )
| ( $false
= ( r @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f188,f167]) ).
thf(f223,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ sK4 ) )
| ( $false
= ( r @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f264,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $false
= ( r @ sK1 @ sK3 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f176,f223]) ).
thf(f267,plain,
( ( $false
= ( r @ sK1 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f273,plain,
( ( $false = $true )
| ( $false
= ( r @ sK1 @ sK3 ) ) ),
inference(forward_demodulation,[],[f267,f187]) ).
thf(f274,plain,
( $false
= ( r @ sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f280,plain,
( ( $false
= ( r @ sK1 @ sK2 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f219,f274]) ).
thf(f281,plain,
( $false
= ( r @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f289,plain,
$false = $true,
inference(constrained_superposition,[],[f180,f281]) ).
thf(f293,plain,
$false,
inference(trivial_inequality_removal,[],[f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 09:33:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (2624172)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (2624188)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2097731528:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (2624190)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (2624190)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.28 % (2624184)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3641938394:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (2624185)lrs+10_16_si=on:nwc=1.5:random_seed=3476788304:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (2624186)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=271776504:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (2624187)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2854328299:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.28 % (2624188)Instruction limit reached!
% 0.20/0.28 % (2624188)------------------------------
% 0.20/0.28 % (2624188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2624188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2624188)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2624188)Termination reason: Instruction limit
% 0.20/0.28 % (2624188)Termination phase: Saturation
% 0.20/0.28 % (2624188)Time elapsed: 0.008 s
% 0.20/0.28 % (2624188)Peak memory usage: 12 MB
% 0.20/0.28 % (2624188)Instructions burned: 26 (million)
% 0.20/0.28 % (2624189)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=393191131:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (2624190)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3834440442:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (2624186)Instruction limit reached!
% 0.20/0.28 % (2624186)------------------------------
% 0.20/0.28 % (2624186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2624186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2624186)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2624186)Termination reason: Instruction limit
% 0.20/0.28 % (2624186)Termination phase: Property scanning
% 0.20/0.28 % (2624186)Time elapsed: 0.002 s
% 0.20/0.28 % (2624186)Peak memory usage: 10 MB
% 0.20/0.28 % (2624186)Instructions burned: 3 (million)
% 0.20/0.28 % (2624185) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2624172-2624185"...
% 0.20/0.28 % (2624185)...printing done.
% 0.20/0.28 % (2624184) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2624172-2624184"...
% 0.20/0.28 % (2624185)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2624185)------------------------------
% 0.20/0.28 % (2624185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2624185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2624185)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2624185)Termination reason: Refutation
% 0.20/0.28 % (2624185)Time elapsed: 0.011 s
% 0.20/0.28 % (2624185)Peak memory usage: 12 MB
% 0.20/0.28 % (2624185)Instructions burned: 21 (million)
% 0.20/0.28 % (2624172)Success in time 0.044 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------