%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:38:37 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 304 ( 91 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 557 ( 13 ~; 30 |; 52 &; 390 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 45 usr; 4 con; 0-4 aty)
% ( 28 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 113 ^; 34 !; 14 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
is_function: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_16,type,
injection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_17,type,
surjection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_18,type,
bijection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_19,type,
equinumerous: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_20,type,
embedding: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK0: $i > $o ).
thf(func_def_37,type,
sK1: $i > $o ).
thf(func_def_38,type,
sK2: $i > $o ).
thf(func_def_39,type,
sK3: $i > $o ).
thf(func_def_40,type,
sK4: ( $i > $i ) > $i ).
thf(func_def_41,type,
sK5: ( $i > $i ) > $i ).
thf(func_def_42,type,
sK6: $i > $i ).
thf(func_def_45,type,
sK9: $i > $i ).
thf(func_def_46,type,
sK10: $i > $i ).
thf(func_def_49,type,
sK13: $i > $i ).
thf(func_def_50,type,
sK14: $i > $i ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',union) ).
thf(f15,axiom,
( ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 @ ( X1 @ X3 ) ) ) )
= is_function ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_function) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
( ( is_function @ X0 @ X1 @ X2 )
=> ! [X4: $i,X3: $i] :
( ( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
& ( X0 @ X4 )
& ( X0 @ X3 ) )
=> ( X3 = X4 ) ) ) )
= injection ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection) ).
thf(f20,axiom,
( embedding
= ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i > $i] : ( injection @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',embedding) ).
thf(f21,conjecture,
! [X3: $i > $o,X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( equinumerous @ X2 @ X3 )
& ( equinumerous @ X0 @ X1 )
& ( ( intersection @ X1 @ X3 )
= emptyset ) )
=> ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f22,negated_conjecture,
~ ! [X3: $i > $o,X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( equinumerous @ X2 @ X3 )
& ( equinumerous @ X0 @ X1 )
& ( ( intersection @ X1 @ X3 )
= emptyset ) )
=> ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
thf(f33,plain,
( ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
( ( is_function @ X0 @ X1 @ X2 )
=> ! [X3: $i,X4: $i] :
( ( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
& ( X0 @ X3 )
& ( X0 @ X4 ) )
=> ( X3 = X4 ) ) ) )
= injection ),
inference(rectify,[],[f16]) ).
thf(f34,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( is_function @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y3 )
& ( Y0 @ Y4 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f36,plain,
( embedding
= ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i > $i] : ( injection @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f20]) ).
thf(f37,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( injection @ Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f46,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( equinumerous @ X3 @ X0 )
& ( equinumerous @ X1 @ X2 )
& ( emptyset
= ( intersection @ X2 @ X0 ) ) )
=> ( embedding @ ( union @ X1 @ X3 ) @ ( union @ X2 @ X0 ) ) ),
inference(rectify,[],[f22]) ).
thf(f47,plain,
~ ! [X2: $i > $o,X3: $i > $o,X1: $i > $o,X0: $i > $o] :
( ( ( $true
= ( equinumerous @ X3 @ X0 ) )
& ( ( equinumerous @ X1 @ X2 )
= $true )
& ( emptyset
= ( intersection @ X2 @ X0 ) ) )
=> ( $true
= ( embedding @ ( union @ X1 @ X3 ) @ ( union @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f49,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 @ ( X1 @ X3 ) ) ) )
= is_function ),
inference(rectify,[],[f15]) ).
thf(f58,plain,
( is_function
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
=> ( Y2 @ ( Y1 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
? [X2: $i > $o,X3: $i > $o,X1: $i > $o,X0: $i > $o] :
( ( $true
!= ( embedding @ ( union @ X1 @ X3 ) @ ( union @ X2 @ X0 ) ) )
& ( $true
= ( equinumerous @ X3 @ X0 ) )
& ( ( equinumerous @ X1 @ X2 )
= $true )
& ( emptyset
= ( intersection @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f47]) ).
thf(f60,plain,
? [X2: $i > $o,X3: $i > $o,X1: $i > $o,X0: $i > $o] :
( ( $true
= ( equinumerous @ X3 @ X0 ) )
& ( $true
!= ( embedding @ ( union @ X1 @ X3 ) @ ( union @ X2 @ X0 ) ) )
& ( emptyset
= ( intersection @ X2 @ X0 ) )
& ( ( equinumerous @ X1 @ X2 )
= $true ) ),
inference(flattening,[],[f59]) ).
thf(f61,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( equinumerous @ X1 @ X3 )
= $true )
& ( $true
!= ( embedding @ ( union @ X2 @ X1 ) @ ( union @ X0 @ X3 ) ) )
& ( emptyset
= ( intersection @ X0 @ X3 ) )
& ( $true
= ( equinumerous @ X2 @ X0 ) ) ),
inference(rectify,[],[f60]) ).
thf(f62,plain,
( ( ( equinumerous @ sK1 @ sK3 )
= $true )
& ( $true
!= ( embedding @ ( union @ sK2 @ sK1 ) @ ( union @ sK0 @ sK3 ) ) )
& ( emptyset
= ( intersection @ sK0 @ sK3 ) )
& ( $true
= ( equinumerous @ sK2 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f61]) ).
thf(f66,plain,
( $true
!= ( embedding @ ( union @ sK2 @ sK1 ) @ ( union @ sK0 @ sK3 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f72,plain,
( is_function
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
=> ( Y2 @ ( Y1 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f78,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( is_function @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y3 )
& ( Y0 @ Y4 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f82,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f83,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( injection @ Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f91,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 )
=> ( Y5 @ ( Y4 @ Y6 ) ) ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y3 )
& ( Y0 @ Y4 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f78,f72]) ).
thf(f95,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( ( ^ [Y6: $i > $o,Y7: $i > $i,Y8: $i > $o] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 )
=> ( Y8 @ ( Y7 @ Y9 ) ) ) )
@ Y3
@ Y4
@ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y3 @ Y6 )
& ( Y3 @ Y7 )
& ( ( Y4 @ Y7 )
= ( Y4 @ Y6 ) ) )
=> ( Y7 = Y6 ) ) ) ) )
@ Y0
@ Y2
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f83,f91]) ).
thf(f97,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( ( ^ [Y6: $i > $o,Y7: $i > $i,Y8: $i > $o] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 )
=> ( Y8 @ ( Y7 @ Y9 ) ) ) )
@ Y3
@ Y4
@ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y3 @ Y6 )
& ( Y3 @ Y7 )
& ( ( Y4 @ Y7 )
= ( Y4 @ Y6 ) ) )
=> ( Y7 = Y6 ) ) ) ) )
@ Y0
@ Y2
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK2
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK3 ) ) ),
inference(definition_unfolding,[],[f66,f95,f82,f82]) ).
thf(f100,plain,
( $true
!= ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
=> ( ( sK0 @ ( Y0 @ Y1 ) )
| ( sK3 @ ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y2 )
| ( sK1 @ Y2 ) )
& ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f101,plain,
! [X1: $i > $i] :
( $false
= ( ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
=> ( ( sK0 @ ( Y0 @ Y1 ) )
| ( sK3 @ ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y2 )
| ( sK1 @ Y2 ) )
& ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) ) )
=> ( Y2 = Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X1: $i > $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
=> ( ( sK0 @ ( X1 @ Y0 ) )
| ( sK3 @ ( X1 @ Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X1: $i > $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f112,plain,
! [X1: $i > $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ ( sK4 @ X1 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f113,plain,
! [X1: $i > $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK2 @ ( sK4 @ X1 ) )
| ( sK1 @ ( sK4 @ X1 ) ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( X1 @ Y0 )
= ( X1 @ ( sK4 @ X1 ) ) ) )
=> ( Y0
= ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X1: $i > $i] :
( $false
= ( ^ [Y0: $i] :
( ( ( ( sK2 @ ( sK4 @ X1 ) )
| ( sK1 @ ( sK4 @ X1 ) ) )
& ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( X1 @ Y0 )
= ( X1 @ ( sK4 @ X1 ) ) ) )
=> ( Y0
= ( sK4 @ X1 ) ) )
@ ( sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: $i > $i] :
( $false
= ( ( ( ( sK2 @ ( sK4 @ X1 ) )
| ( sK1 @ ( sK4 @ X1 ) ) )
& ( ( sK2 @ ( sK5 @ X1 ) )
| ( sK1 @ ( sK5 @ X1 ) ) )
& ( ( X1 @ ( sK5 @ X1 ) )
= ( X1 @ ( sK4 @ X1 ) ) ) )
=> ( ( sK5 @ X1 )
= ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X1: $i > $i] :
( ( ( sK5 @ X1 )
= ( sK4 @ X1 ) )
= $false ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: $i > $i] :
( $true
= ( ( ( sK2 @ ( sK4 @ X1 ) )
| ( sK1 @ ( sK4 @ X1 ) ) )
& ( ( sK2 @ ( sK5 @ X1 ) )
| ( sK1 @ ( sK5 @ X1 ) ) )
& ( ( X1 @ ( sK5 @ X1 ) )
= ( X1 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
! [X1: $i > $i] :
( $true
= ( ( X1 @ ( sK5 @ X1 ) )
= ( X1 @ ( sK4 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f124,plain,
! [X1: $i > $i] :
( ( X1 @ ( sK4 @ X1 ) )
= ( X1 @ ( sK5 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f118]) ).
thf(f125,plain,
! [X1: $i > $i] :
( ( sK5 @ X1 )
!= ( sK4 @ X1 ) ),
inference(equality_proxy_clausification,[],[f116]) ).
thf(f370,plain,
( ( sK4
@ ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : Y0
@ ( sK4
@ ^ [Y0: $i] : Y0 ) ) ),
inference(constrained_superposition,[],[f125,f124]) ).
thf(f372,plain,
( ( sK4
@ ^ [Y0: $i] : Y0 )
!= ( sK4
@ ^ [Y0: $i] : Y0 ) ),
inference(beta-eta_normalization,[],[f370]) ).
thf(f373,plain,
$false,
inference(trivial_inequality_removal,[],[f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:47:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.20/0.28 % (1207929)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1207935)lrs+10_16_si=on:nwc=1.5:random_seed=1534669606:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (1207940)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 % (1207940)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 % (1207935)Instruction limit reached!
% 0.20/0.28 % (1207935)------------------------------
% 0.20/0.28 % (1207935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1207935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1207935)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1207935)Termination reason: Instruction limit
% 0.20/0.28 % (1207935)Termination phase: Saturation
% 0.20/0.28 % (1207935)Time elapsed: 0.005 s
% 0.20/0.28 % (1207935)Peak memory usage: 12 MB
% 0.20/0.28 % (1207935)Instructions burned: 18 (million)
% 0.20/0.28 % (1207934)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3067754546:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1207936)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=149321735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (1207939)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2744945285:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1207937)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=2365861131: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 % (1207938)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1407286142:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1207940)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=1129013448:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (1207936)Instruction limit reached!
% 0.20/0.28 % (1207936)------------------------------
% 0.20/0.28 % (1207936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1207936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1207936)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1207936)Termination reason: Instruction limit
% 0.20/0.28 % (1207936)Termination phase: Clausification
% 0.20/0.28 % (1207936)Time elapsed: 0.002 s
% 0.20/0.28 % (1207936)Peak memory usage: 10 MB
% 0.20/0.28 % (1207936)Instructions burned: 4 (million)
% 0.20/0.28 % (1207942)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=984287165:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (1207942)Instruction limit reached!
% 0.20/0.28 % (1207942)------------------------------
% 0.20/0.28 % (1207942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1207942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1207942)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1207942)Termination reason: Instruction limit
% 0.20/0.28 % (1207942)Termination phase: Property scanning
% 0.20/0.28 % (1207942)Time elapsed: 0.001 s
% 0.20/0.28 % (1207942)Peak memory usage: 10 MB
% 0.20/0.28 % (1207942)Instructions burned: 4 (million)
% 0.20/0.28 % (1207939) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1207929-1207939"...
% 0.20/0.28 % (1207938)Instruction limit reached!
% 0.20/0.28 % (1207938)------------------------------
% 0.20/0.28 % (1207938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1207938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1207938)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1207938)Termination reason: Instruction limit
% 0.20/0.28 % (1207938)Termination phase: Saturation
% 0.20/0.28 % (1207938)Time elapsed: 0.013 s
% 0.20/0.28 % (1207938)Peak memory usage: 12 MB
% 0.20/0.28 % (1207938)Instructions burned: 24 (million)
% 0.20/0.28 % (1207939)...printing done.
% 0.20/0.29 % (1207939)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1207939)------------------------------
% 0.20/0.29 % (1207939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1207939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1207939)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1207939)Termination reason: Refutation
% 0.20/0.29 % (1207939)Time elapsed: 0.015 s
% 0.20/0.29 % (1207939)Peak memory usage: 12 MB
% 0.20/0.29 % (1207939)Instructions burned: 28 (million)
% 0.20/0.29 % (1207929)Success in time 0.056 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------