%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM801^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:18:56 AM UTC 2026
% Result : Theorem 0.23s 0.38s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 867 ( 21 ~; 4 |; 0 &; 842 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 286 ( 286 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 1 con; 0-4 aty)
% Number of variables : 324 ( 288 ^; 30 !; 6 ?; 324 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
zero: ( $i > $i ) > $i > $i ).
thf(func_def_1,type,
one: ( $i > $i ) > $i > $i ).
thf(func_def_2,type,
two: ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
three: ( $i > $i ) > $i > $i ).
thf(func_def_4,type,
four: ( $i > $i ) > $i > $i ).
thf(func_def_5,type,
five: ( $i > $i ) > $i > $i ).
thf(func_def_6,type,
six: ( $i > $i ) > $i > $i ).
thf(func_def_7,type,
seven: ( $i > $i ) > $i > $i ).
thf(func_def_8,type,
eight: ( $i > $i ) > $i > $i ).
thf(func_def_9,type,
nine: ( $i > $i ) > $i > $i ).
thf(func_def_10,type,
ten: ( $i > $i ) > $i > $i ).
thf(func_def_11,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_12,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_13,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK0: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(func_def_21,type,
sK1: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > $i ).
thf(func_def_22,type,
db4:
!>[X0: $tType] : X0 ).
thf(f5,axiom,
( four
= ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',four_ax) ).
thf(f6,axiom,
( five
= ( ^ [X0: $i > $i,X1: $i] : ( X0 @ ( X0 @ ( X0 @ ( X0 @ ( X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',five_ax) ).
thf(f13,axiom,
( ( ^ [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X0 @ X2 @ ( X1 @ X2 @ X3 ) ) )
= plus ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',plus_ax) ).
thf(f14,axiom,
( ( ^ [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X0 @ ( X1 @ X2 ) @ X3 ) )
= mult ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM006^0.ax',mult_ax) ).
thf(f15,conjecture,
? [X1: ( $i > $i ) > $i > $i,X0: ( $i > $i ) > $i > $i] :
( ( mult @ X0 @ four )
= ( plus @ five @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ? [X1: ( $i > $i ) > $i > $i,X0: ( $i > $i ) > $i > $i] :
( ( mult @ X0 @ four )
= ( plus @ five @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f21,plain,
( plus
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f22,plain,
( five
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f25,plain,
( mult
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f30,plain,
( four
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f31,plain,
~ ? [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( plus @ five @ X0 )
= ( mult @ X1 @ four ) ),
inference(rectify,[],[f16]) ).
thf(f32,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( plus @ five @ X0 )
!= ( mult @ X1 @ four ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f34,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( plus @ five @ X0 )
!= ( mult @ X1 @ four ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f35,plain,
( plus
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f39,plain,
( five
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f43,plain,
( four
= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f44,plain,
( mult
= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f48,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ ( Y1 @ Y2 ) @ Y3 )
@ X1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) )
!= ( ^ [Y0: ( $i > $i ) > $i > $i,Y1: ( $i > $i ) > $i > $i,Y2: $i > $i,Y3: $i] : ( Y0 @ Y2 @ ( Y1 @ Y2 @ Y3 ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) )
@ X0 ) ),
inference(definition_unfolding,[],[f34,f35,f39,f44,f43]) ).
thf(f49,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i > $i] :
( X1
@ ^ [Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i > $i] :
( X1
@ ^ [Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ Y1 ) ) ) ) )
@ ( sK0 @ X1 @ X0 ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
@ ( sK0 @ X1 @ X0 ) ) ),
inference(negative_extensionality,[],[f49]) ).
thf(f51,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( X1
@ ^ [Y0: $i] : ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ Y0 ) ) ) ) )
!= ( ^ [Y0: $i] : ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( X0 @ ( sK0 @ X1 @ X0 ) @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ^ [Y0: $i] : ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( X0 @ ( sK0 @ X1 @ X0 ) @ Y0 ) ) ) ) ) )
@ ( sK1 @ X1 @ X0 ) )
!= ( X1
@ ^ [Y0: $i] : ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ Y0 ) ) ) )
@ ( sK1 @ X1 @ X0 ) ) ),
inference(negative_extensionality,[],[f51]) ).
thf(f53,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( X0 @ ( sK0 @ X1 @ X0 ) @ ( sK1 @ X1 @ X0 ) ) ) ) ) ) )
!= ( X1
@ ^ [Y0: $i] : ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ ( sK0 @ X1 @ X0 @ Y0 ) ) ) )
@ ( sK1 @ X1 @ X0 ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( X0
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ) ) )
!= ( X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) )
@ X1 )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) )
@ X1 ) ) )
| ( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ),
inference(equality_resolution,[],[f53]) ).
thf(f63,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( X0
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ) ) )
!= ( X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f64,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1
@ ( X0
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ X1
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ) ) )
!= ( X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) )
@ ( X1
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i,Y4: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 ) )
@ Y1
@ Y2 ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i,Y4: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 ) )
@ Y1
@ Y2 ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i,Y4: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 ) )
@ Y1
@ Y2 ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i,Y4: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 ) )
@ Y1
@ Y2 ) )
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( X0
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i,Y3: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ),
inference(equality_resolution,[],[f64]) ).
thf(f71,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( X1
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
!= ( X0
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f72,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( X1
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
!= ( X0
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f75,plain,
! [X0: ( $i > $i ) > $i > $i,X1: ( $i > $i ) > $i > $i] :
( ( X1
@ ( sK0
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
!= ( X0
@ ^ [Y0: $i] :
( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) ) )
@ ( sK0
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( X0 @ Y1 @ Y2 ) ) )
@ ^ [Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y1 @ ( Y1 @ ( X1 @ Y1 @ Y2 ) ) ) )
@ Y0 ) ) ) )
@ ( sK1
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( X0 @ Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i,Y1: $i] : ( Y0 @ ( Y0 @ ( Y0 @ ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(equality_resolution,[],[f72]) ).
thf(f78,plain,
$false,
inference(flex-flex_simplification,[],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM801^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:06:35 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.38 % (1202719)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.38 % (1202728)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2785147154:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.38 % (1202724)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4238582147:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.38 % (1202730)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.38 % (1202730)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
% 0.23/0.38 % (1202728)Instruction limit reached!
% 0.23/0.38 % (1202728)------------------------------
% 0.23/0.38 % (1202728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202728)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202728)Termination reason: Instruction limit
% 0.23/0.38 % (1202728)Termination phase: Saturation
% 0.23/0.38 % (1202728)Time elapsed: 0.012 s
% 0.23/0.38 % (1202728)Peak memory usage: 11 MB
% 0.23/0.38 % (1202728)Instructions burned: 24 (million)
% 0.23/0.38 % (1202724)Refutation not found, incomplete strategy
% 0.23/0.38 % (1202724)------------------------------
% 0.23/0.38 % (1202724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202724)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202724)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.38 % (1202724)Time elapsed: 0.008 s
% 0.23/0.38 % (1202724)Peak memory usage: 12 MB
% 0.23/0.38 % (1202724)Instructions burned: 15 (million)
% 0.23/0.38 % (1202725)lrs+10_16_si=on:nwc=1.5:random_seed=1106399969:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.38 % (1202726)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2114718670:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.38 % (1202727)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=2012455126: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)
% 0.23/0.38 % (1202729)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2611126532:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.38 % (1202724)------------------------------
% 0.23/0.38 % (1202724)------------------------------
% 0.23/0.38 % (1202730)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=3610009093:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.38 % (1202726)Instruction limit reached!
% 0.23/0.38 % (1202726)------------------------------
% 0.23/0.38 % (1202726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202726)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202726)Termination reason: Instruction limit
% 0.23/0.38 % (1202726)Termination phase: Saturation
% 0.23/0.38 % (1202726)Time elapsed: 0.005 s
% 0.23/0.38 % (1202726)Peak memory usage: 11 MB
% 0.23/0.38 % (1202726)Instructions burned: 4 (million)
% 0.23/0.38 % (1202730)Refutation not found, incomplete strategy
% 0.23/0.38 % (1202730)------------------------------
% 0.23/0.38 % (1202730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202730)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202730)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.38 % (1202730)Time elapsed: 0.014 s
% 0.23/0.38 % (1202730)Peak memory usage: 13 MB
% 0.23/0.38 % (1202730)Instructions burned: 16 (million)
% 0.23/0.38 % (1202725)Instruction limit reached!
% 0.23/0.38 % (1202725)------------------------------
% 0.23/0.38 % (1202725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202725)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202725)Termination reason: Instruction limit
% 0.23/0.38 % (1202725)Termination phase: Saturation
% 0.23/0.38 % (1202725)Time elapsed: 0.016 s
% 0.23/0.38 % (1202725)Peak memory usage: 12 MB
% 0.23/0.38 % (1202725)Instructions burned: 19 (million)
% 0.23/0.38 % (1202730)------------------------------
% 0.23/0.38 % (1202730)------------------------------
% 0.23/0.38 % (1202729) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1202719-1202729"...
% 0.23/0.38 % (1202729)...printing done.
% 0.23/0.38 % (1202729)Refutation found. Thanks to Tanya!
% 0.23/0.38 % SZS status Theorem for theBenchmark
% 0.23/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.38 % (1202729)------------------------------
% 0.23/0.38 % (1202729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.38 % (1202729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.38 % (1202729)CaDiCaL version: 2.1.3
% 0.23/0.38 % (1202729)Termination reason: Refutation
% 0.23/0.38 % (1202729)Time elapsed: 0.038 s
% 0.23/0.38 % (1202729)Peak memory usage: 13 MB
% 0.23/0.38 % (1202729)Instructions burned: 46 (million)
% 0.23/0.38 % (1202719)Success in time 0.091 s
% 0.23/0.38 % Vampire exiting
%------------------------------------------------------------------------------