%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET624^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:23:24 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 135 ( 19 unt; 0 typ; 9 def)
% Number of atoms : 1021 ( 200 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 891 ( 105 ~; 249 |; 61 &; 441 @)
% ( 13 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 15 con; 0-4 aty)
% ( 0 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 128 ( 0 sgn 38 !; 14 ?; 128 :)
% 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,
vNOT: $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= union ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f13,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= meets ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',meets) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( meets @ X0 @ X1 )
| ( meets @ X0 @ X2 ) )
<=> ( meets @ X0 @ ( union @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( meets @ X0 @ X1 )
| ( meets @ X0 @ X2 ) )
<=> ( meets @ X0 @ ( union @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f22,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( meets @ X0 @ X1 )
| ( meets @ X0 @ X2 ) )
<=> ( meets @ X0 @ ( union @ X1 @ X2 ) ) ),
inference(rectify,[],[f16]) ).
thf(f23,plain,
~ ! [X1: $i > $o,X0: $i > $o,X2: $i > $o] :
( ( ( ( meets @ X0 @ X2 )
= $true )
| ( ( meets @ X0 @ X1 )
= $true ) )
<=> ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= union ),
inference(rectify,[],[f6]) ).
thf(f25,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= meets ),
inference(rectify,[],[f13]) ).
thf(f38,plain,
( meets
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f41,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( ( ( meets @ X0 @ X2 )
= $true )
| ( ( meets @ X0 @ X1 )
= $true ) )
<~> ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f42,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
!= $true )
| ( ( ( meets @ X0 @ X2 )
!= $true )
& ( ( meets @ X0 @ X1 )
!= $true ) ) )
& ( ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
= $true )
| ( ( meets @ X0 @ X2 )
= $true )
| ( ( meets @ X0 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[],[f41]) ).
thf(f43,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
!= $true )
| ( ( ( meets @ X0 @ X2 )
!= $true )
& ( ( meets @ X0 @ X1 )
!= $true ) ) )
& ( ( ( meets @ X0 @ ( union @ X1 @ X2 ) )
= $true )
| ( ( meets @ X0 @ X2 )
= $true )
| ( ( meets @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f42]) ).
thf(f44,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( $true
!= ( meets @ X2 @ ( union @ X0 @ X1 ) ) )
| ( ( $true
!= ( meets @ X2 @ X1 ) )
& ( ( meets @ X2 @ X0 )
!= $true ) ) )
& ( ( $true
= ( meets @ X2 @ ( union @ X0 @ X1 ) ) )
| ( $true
= ( meets @ X2 @ X1 ) )
| ( ( meets @ X2 @ X0 )
= $true ) ) ),
inference(rectify,[],[f43]) ).
thf(f45,plain,
( ( ( $true
!= ( meets @ sK2 @ ( union @ sK0 @ sK1 ) ) )
| ( ( ( meets @ sK2 @ sK1 )
!= $true )
& ( $true
!= ( meets @ sK2 @ sK0 ) ) ) )
& ( ( $true
= ( meets @ sK2 @ ( union @ sK0 @ sK1 ) ) )
| ( ( meets @ sK2 @ sK1 )
= $true )
| ( $true
= ( meets @ sK2 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f44]) ).
thf(f49,plain,
( ( $true
= ( meets @ sK2 @ ( union @ sK0 @ sK1 ) ) )
| ( ( meets @ sK2 @ sK1 )
= $true )
| ( $true
= ( meets @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f50,plain,
( ( $true
!= ( meets @ sK2 @ ( union @ sK0 @ sK1 ) ) )
| ( $true
!= ( meets @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f51,plain,
( ( $true
!= ( meets @ sK2 @ ( union @ sK0 @ sK1 ) ) )
| ( ( meets @ sK2 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f54,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f58,plain,
( meets
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f66,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK1 ) ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ sK1 ) ) ),
inference(definition_unfolding,[],[f51,f58,f54,f58]) ).
thf(f67,plain,
( ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK1 ) ) ) ),
inference(definition_unfolding,[],[f50,f58,f54,f58]) ).
thf(f68,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK1 ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
@ sK2
@ sK1 ) ) ),
inference(definition_unfolding,[],[f49,f58,f54,f58,f58]) ).
thf(f69,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK4 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK4 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( ( ( sK2 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( ( sK2 @ sK4 )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( ( ( sK2 @ sK4 )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
= $true )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK2 @ sK4 )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK2 @ sK4 )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK4 )
& ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f78]) ).
thf(f81,plain,
( ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f82,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f83,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f81]) ).
thf(f84,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f85,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( ( ( sK2 @ sK3 )
& ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f86,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f89,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f90,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f88]) ).
thf(f92,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f93,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X2 )
& ( sK0 @ X2 ) ) )
| ( $false
= ( ( sK2 @ X1 )
& ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( ( sK2 @ X1 )
& ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f97]) ).
thf(f100,plain,
( ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f101,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X2 )
& ( ( sK0 @ X2 )
| ( sK1 @ X2 ) ) ) )
| ( $false
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( ( sK0 @ X2 )
| ( sK1 @ X2 ) ) )
| ( $false
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( ( sK2 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f104]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f110,definition,
( spl6_1
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f112,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f114,definition,
( spl6_2
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f116,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f118,definition,
( spl6_3
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f120,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f121,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f79,f118,f114,f110]) ).
thf(f123,definition,
( spl6_4
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f125,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f127,definition,
( spl6_5
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
( spl6_3
| spl6_2
| spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f80,f127,f123,f114,f118]) ).
thf(f132,definition,
( spl6_6
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f134,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f135,plain,
( spl6_1
| spl6_3
| spl6_6 ),
inference(avatar_split_clause,[],[f82,f132,f118,f110]) ).
thf(f136,plain,
( spl6_6
| spl6_5
| spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f83,f123,f118,f127,f132]) ).
thf(f138,definition,
( spl6_7
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f140,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f141,plain,
( spl6_2
| spl6_7
| spl6_1 ),
inference(avatar_split_clause,[],[f87,f110,f138,f114]) ).
thf(f142,plain,
( spl6_1
| spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f86,f138,f132,f110]) ).
thf(f143,plain,
( spl6_2
| spl6_5
| spl6_7
| spl6_4 ),
inference(avatar_split_clause,[],[f90,f123,f138,f127,f114]) ).
thf(f144,plain,
( spl6_7
| spl6_6
| spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f91,f127,f123,f132,f138]) ).
thf(f146,definition,
( spl6_8
<=> ! [X2: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f147,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK2 @ X2 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f148,plain,
( spl6_8
| spl6_8 ),
inference(avatar_split_clause,[],[f99,f146,f146]) ).
thf(f150,definition,
( spl6_9
<=> ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f151,plain,
( ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f154,plain,
( spl6_9
| spl6_9 ),
inference(avatar_split_clause,[],[f108,f150,f150]) ).
thf(f155,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl6_6
| ~ spl6_9 ),
inference(constrained_superposition,[],[f151,f134]) ).
thf(f158,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl6_6
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f155]) ).
thf(f162,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_demodulation,[],[f158,f116]) ).
thf(f163,plain,
( $false
| ~ spl6_2
| ~ spl6_6
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f164,plain,
( ~ spl6_2
| ~ spl6_6
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( sK2 @ sK4 ) )
| ( $false = $true )
| ~ spl6_5
| ~ spl6_9 ),
inference(constrained_superposition,[],[f129,f151]) ).
thf(f168,plain,
( ( $false
= ( sK2 @ sK4 ) )
| ~ spl6_5
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f172,plain,
( ( $false = $true )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_9 ),
inference(forward_demodulation,[],[f168,f112]) ).
thf(f173,plain,
( $false
| ~ spl6_1
| ~ spl6_5
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f174,plain,
( ~ spl6_1
| ~ spl6_5
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f173]) ).
thf(f175,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ sK4 ) )
| ~ spl6_4
| ~ spl6_8 ),
inference(constrained_superposition,[],[f125,f147]) ).
thf(f178,plain,
( ( $false
= ( sK2 @ sK4 ) )
| ~ spl6_4
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f175]) ).
thf(f182,plain,
( ( $false = $true )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_8 ),
inference(forward_demodulation,[],[f178,f112]) ).
thf(f183,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f184,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f183]) ).
thf(f188,plain,
( ( $false = $true )
| ( $false
= ( sK2 @ sK5 ) )
| ~ spl6_7
| ~ spl6_8 ),
inference(constrained_superposition,[],[f140,f147]) ).
thf(f191,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f195,plain,
( ( $false = $true )
| ~ spl6_3
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f191,f120]) ).
thf(f196,plain,
( $false
| ~ spl6_3
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ~ spl6_3
| ~ spl6_7
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s1,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f121]) ).
cnf(s2,plain,
( spl6_2
| spl6_3
| spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( spl6_1
| spl6_3
| spl6_6 ),
inference(sat_conversion,[],[f135]) ).
cnf(s4,plain,
( spl6_3
| spl6_4
| spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f136]) ).
cnf(s5,plain,
( spl6_1
| spl6_2
| spl6_7 ),
inference(sat_conversion,[],[f141]) ).
cnf(s6,plain,
( spl6_1
| spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f142]) ).
cnf(s7,plain,
( spl6_2
| spl6_4
| spl6_5
| spl6_7 ),
inference(sat_conversion,[],[f143]) ).
cnf(s8,plain,
( spl6_4
| spl6_5
| spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f144]) ).
cnf(s9,plain,
( spl6_8
| spl6_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s10,plain,
spl6_8,
inference(rat,[],[s9]) ).
cnf(s13,plain,
( spl6_9
| spl6_9 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
spl6_9,
inference(rat,[],[s13]) ).
cnf(s16,plain,
( ~ spl6_2
| ~ spl6_6
| ~ spl6_9 ),
inference(sat_conversion,[],[f164]) ).
cnf(s18,plain,
( ~ spl6_1
| ~ spl6_5
| ~ spl6_9 ),
inference(sat_conversion,[],[f174]) ).
cnf(s20,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f184]) ).
cnf(s22,plain,
( ~ spl6_3
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f197]) ).
cnf(s23,plain,
( spl6_2
| spl6_1 ),
inference(rat,[],[s22,s1,s5,s10]) ).
cnf(s24,plain,
( spl6_6
| spl6_1 ),
inference(rat,[],[s22,s3,s6,s10]) ).
cnf(s25,plain,
spl6_1,
inference(rat,[],[s24,s16,s23,s14]) ).
cnf(s26,plain,
~ spl6_4,
inference(rat,[],[s20,s10,s25]) ).
cnf(s27,plain,
~ spl6_5,
inference(rat,[],[s18,s14,s25]) ).
cnf(s28,plain,
spl6_7,
inference(rat,[],[s16,s8,s7,s14,s26,s27]) ).
cnf(s29,plain,
~ spl6_3,
inference(rat,[],[s22,s10,s28]) ).
cnf(s30,plain,
spl6_6,
inference(rat,[],[s4,s26,s27,s29]) ).
cnf(s31,plain,
spl6_2,
inference(rat,[],[s2,s26,s27,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s16,s14,s30,s31]) ).
thf(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.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 13:41:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.20/0.30 % (81005)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (81014)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=7743550:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (81016)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (81016)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
% 0.20/0.30 % (81010)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1369468208:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (81012)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3093516328:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (81011)lrs+10_16_si=on:nwc=1.5:random_seed=1888899409:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (81013)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=238382403: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)
% 0.20/0.30 % (81014)Instruction limit reached!
% 0.20/0.30 % (81014)------------------------------
% 0.20/0.30 % (81014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (81014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (81014)CaDiCaL version: 2.1.3
% 0.20/0.30 % (81014)Termination reason: Instruction limit
% 0.20/0.30 % (81014)Termination phase: Saturation
% 0.20/0.30 % (81014)Time elapsed: 0.008 s
% 0.20/0.30 % (81014)Peak memory usage: 12 MB
% 0.20/0.30 % (81014)Instructions burned: 25 (million)
% 0.20/0.30 % (81015)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3282876290:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (81016)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=3825277597:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (81012)Instruction limit reached!
% 0.20/0.30 % (81012)------------------------------
% 0.20/0.30 % (81012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (81012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (81012)CaDiCaL version: 2.1.3
% 0.20/0.30 % (81012)Termination reason: Instruction limit
% 0.20/0.30 % (81012)Termination phase: Saturation
% 0.20/0.30 % (81012)Time elapsed: 0.002 s
% 0.20/0.30 % (81012)Peak memory usage: 12 MB
% 0.20/0.30 % (81012)Instructions burned: 4 (million)
% 0.20/0.30 % (81010) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-81005-81010"...
% 0.20/0.30 % (81011) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-81005-81011"...
% 0.20/0.30 % (81015) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-81005-81015"...
% 0.20/0.30 % (81016) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-81005-81016"...
% 0.20/0.30 % (81010)...printing done.
% 0.20/0.30 % (81011)...printing done.
% 0.20/0.30 % (81015)...printing done.
% 0.20/0.30 % (81010)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (81010)------------------------------
% 0.20/0.30 % (81010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (81010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (81010)CaDiCaL version: 2.1.3
% 0.20/0.30 % (81010)Termination reason: Refutation
% 0.20/0.30 % (81010)Time elapsed: 0.007 s
% 0.20/0.30 % (81010)Peak memory usage: 13 MB
% 0.20/0.30 % (81010)Instructions burned: 11 (million)
% 0.20/0.30 % (81005)Success in time 0.044 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------