%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:15:04 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 66 unt; 0 typ; 3 def)
% Number of atoms : 544 ( 93 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 687 ( 33 ~; 36 |; 16 &; 491 @)
% ( 3 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 10 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 176 ( 0 sgn 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_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_56,type,
db4:
!>[X0: $tType] : X0 ).
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/sandbox/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/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(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/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,axiom,
( ( upwards_well_founded @ r )
& ( transitive @ r ) ),
file('/export/starexec/sandbox/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/sandbox/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(f42,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f45,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f48,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f50,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f58,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f86,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(f87,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,[],[f86]) ).
thf(f105,plain,
( ( upwards_well_founded @ r )
& ( transitive @ r ) ),
inference(rectify,[],[f37]) ).
thf(f106,plain,
( ( ( upwards_well_founded @ r )
= $true )
& ( ( transitive @ r )
= $true ) ),
inference(fool_elimination,[],[f105]) ).
thf(f107,plain,
~ ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f108,plain,
~ ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
? [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X0 ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f108]) ).
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(f113,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f114,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f116,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f118,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f122,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f137,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,[],[f87]) ).
thf(f147,plain,
( ( transitive @ r )
= $true ),
inference(cnf_transformation,[],[f106]) ).
thf(f149,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ sK0 ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ sK0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
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,[],[f116,f114,f113]) ).
thf(f157,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ r ) ),
inference(definition_unfolding,[],[f147,f137]) ).
thf(f158,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 ) ) )
@ 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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f149,f122,f152,f118,f118,f118,f118]) ).
thf(f159,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(f160,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,[],[f159]) ).
thf(f161,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,[],[f160]) ).
thf(f162,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,[],[f161]) ).
thf(f163,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( r @ sK1 @ Y0 )
=> ( sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ( r @ sK1 @ X1 )
=> ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( r @ sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,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,[],[f162]) ).
thf(f169,plain,
( $false
= ( ( r @ sK1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( $true
= ( r @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $false
= ( ( r @ sK2 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $true
= ( r @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ sK3 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $false
= ( ( r @ sK3 @ sK4 )
=> ( sK0 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
( $false
= ( sK0 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( $true
= ( r @ sK3 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( r @ Y2 @ Y1 )
& ( r @ Y1 @ Y0 ) )
=> ( r @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( r @ Y2 @ Y1 )
& ( r @ Y1 @ Y0 ) )
=> ( r @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( r @ Y1 @ Y0 )
& ( r @ Y0 @ X1 ) )
=> ( r @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( r @ Y1 @ Y0 )
& ( r @ Y0 @ X1 ) )
=> ( r @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( r @ Y0 @ X2 )
& ( r @ X2 @ X1 ) )
=> ( r @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( r @ Y0 @ X2 )
& ( r @ X2 @ X1 ) )
=> ( r @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( r @ X3 @ X2 )
& ( r @ X2 @ X1 ) )
=> ( r @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( r @ X3 @ X2 )
& ( r @ X2 @ X1 ) ) )
| ( $true
= ( r @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( r @ X2 @ X1 ) )
| ( $true
= ( r @ X3 @ X1 ) )
| ( $false
= ( r @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f187]) ).
thf(f451,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( r @ X0 @ sK3 ) )
| ( $false
= ( r @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f175,f188]) ).
thf(f453,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( r @ X0 @ sK4 ) )
| ( $false
= ( r @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f179,f188]) ).
thf(f477,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ sK4 ) )
| ( $false
= ( r @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f479,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ sK3 ) )
| ( $false
= ( r @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f591,definition,
( spl6_3
<=> ( $false
= ( r @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f593,plain,
( ( $false
= ( r @ sK1 @ sK2 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f591]) ).
thf(f630,plain,
( ( $false = $true )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f593,f171]) ).
thf(f648,plain,
( $false
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f630]) ).
thf(f649,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f648]) ).
thf(f686,plain,
( ( $false = $true )
| ( $false
= ( r @ sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f477,f167]) ).
thf(f721,plain,
( ( $false
= ( r @ sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f686]) ).
thf(f723,definition,
( spl6_6
<=> ( $false
= ( r @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f725,plain,
( ( $false
= ( r @ sK1 @ sK3 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f723]) ).
thf(f731,definition,
( spl6_8
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f733,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f731]) ).
thf(f736,plain,
( spl6_8
| spl6_6 ),
inference(avatar_split_clause,[],[f721,f723,f731]) ).
thf(f754,plain,
( ( $false = $true )
| ( $false
= ( r @ sK1 @ sK2 ) )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f479,f725]) ).
thf(f758,plain,
( ( $false
= ( r @ sK1 @ sK2 ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f754]) ).
thf(f765,plain,
( spl6_3
| ~ spl6_6 ),
inference(avatar_split_clause,[],[f758,f723,f591]) ).
thf(f766,plain,
( ( $false = $true )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f733,f178]) ).
thf(f782,plain,
( $false
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f766]) ).
thf(f783,plain,
~ spl6_8,
inference(avatar_contradiction_clause,[],[f782]) ).
cnf(s8,plain,
~ spl6_3,
inference(sat_conversion,[],[f649]) ).
cnf(s12,plain,
( spl6_6
| spl6_8 ),
inference(sat_conversion,[],[f736]) ).
cnf(s13,plain,
( spl6_3
| ~ spl6_6 ),
inference(sat_conversion,[],[f765]) ).
cnf(s16,plain,
~ spl6_8,
inference(sat_conversion,[],[f783]) ).
cnf(s17,plain,
spl6_6,
inference(rat,[],[s12,s16]) ).
cnf(s18,plain,
spl6_3,
inference(rat,[],[s13,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s8,s18]) ).
thf(f784,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 09:39:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (1013527)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (1013535)dis+10_1_sil=32000:sp=arity:random_seed=2102648018:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (1013533)% WARNING: option uhcvi not known.
% 0.19/0.28 % (1013532)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2502392515_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (1013533)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1716908109:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (1013534)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1500973168:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (1013537)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2168294915:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (1013536)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4173569918:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (1013538)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1195817271:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (1013533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (1013536)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (1013533)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (1013535)Instruction limit reached!
% 0.19/0.28 % (1013535)------------------------------
% 0.19/0.28 % (1013535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1013535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1013535)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1013535)Termination reason: Instruction limit
% 0.19/0.28 % (1013535)Termination phase: Saturation
% 0.19/0.28 % (1013535)Time elapsed: 0.028 s
% 0.19/0.28 % (1013535)Peak memory usage: 12 MB
% 0.19/0.28 % (1013535)Instructions burned: 105 (million)
% 0.19/0.28 % (1013546)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2462800394:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (1013538) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1013527-1013538"...
% 0.19/0.28 % (1013538)...printing done.
% 0.19/0.28 % (1013547)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3390838970:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (1013538)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1013538)------------------------------
% 0.19/0.29 % (1013538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1013538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1013538)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1013538)Termination reason: Refutation
% 0.19/0.29 % (1013538)Time elapsed: 0.029 s
% 0.19/0.29 % (1013538)Peak memory usage: 13 MB
% 0.19/0.29 % (1013538)Instructions burned: 52 (million)
% 0.19/0.29 % (1013527)Success in time 0.055 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------