%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET014^4 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:10 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 264 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 253 ( 24 ~; 26 |; 12 &; 161 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 32 usr; 6 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 69 ( 0 sgn 20 !; 9 ?; 69 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vIMP: $o > $o > $o ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $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,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f12,axiom,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f18,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f28,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[],[f16]) ).
thf(f29,plain,
~ ! [X2: $i > $o,X1: $i > $o,X0: $i > $o] :
( ( ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true ) )
=> ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(fool_elimination,[],[f28]) ).
thf(f41,plain,
? [X2: $i > $o,X1: $i > $o,X0: $i > $o] :
( ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f42,plain,
? [X1: $i > $o,X0: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ ( union @ X1 @ X0 ) @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ),
inference(rectify,[],[f42]) ).
thf(f44,plain,
( ( ( subset @ sK0 @ sK2 )
= $true )
& ( ( subset @ ( union @ sK1 @ sK0 ) @ sK2 )
!= $true )
& ( $true
= ( subset @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f43]) ).
thf(f45,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f46,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f55,plain,
( $true
= ( subset @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f56,plain,
( ( subset @ ( union @ sK1 @ sK0 ) @ sK2 )
!= $true ),
inference(cnf_transformation,[],[f44]) ).
thf(f57,plain,
( ( subset @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f44]) ).
thf(f65,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[],[f57,f46]) ).
thf(f66,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK1
@ sK0 )
@ sK2 )
!= $true ),
inference(definition_unfolding,[],[f56,f46,f45]) ).
thf(f67,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f55,f46]) ).
thf(f68,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f69,plain,
( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
=> ( sK2 @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) )
=> ( sK2 @ sK3 ) )
= $false ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( $true
= ( ( sK1 @ sK3 )
| ( sK0 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f75,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
=> ( sK2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f79,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f83,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f85,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f87,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f89,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f73,f87,f83]) ).
thf(f92,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true = $false )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f77,f89]) ).
thf(f94,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f98,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f94,f71]) ).
thf(f99,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f100,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f99]) ).
thf(f102,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f81,f85]) ).
thf(f105,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f109,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f105,f71]) ).
thf(f110,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f111,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f110]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f100]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f111]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f112,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:35:33 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.25 % (2856664)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (2856670)lrs+10_16_si=on:nwc=1.5:random_seed=1041775525:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.25 % (2856670) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2856664-2856670"...
% 0.08/0.25 % (2856670)...printing done.
% 0.08/0.25 % (2856670)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (2856670)------------------------------
% 0.08/0.25 % (2856670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2856670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2856670)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2856670)Termination reason: Refutation
% 0.08/0.25 % (2856670)Time elapsed: 0.003 s
% 0.08/0.25 % (2856670)Peak memory usage: 13 MB
% 0.08/0.25 % (2856670)Instructions burned: 6 (million)
% 0.08/0.25 % (2856664)Success in time 0.031 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------