%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET066^1 : 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 : n015.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 08:23:13 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 303 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 105 ( 20 ~; 49 |; 0 &; 34 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 6 !; 2 ?; 31 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(f4,axiom,
( unord_pair
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( X2 = X1 )
| ( X2 = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',unord_pair) ).
thf(f15,conjecture,
! [X1: $i,X0: $i] :
( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f20,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f39,plain,
~ ! [X1: $i,X0: $i] :
( ( unord_pair @ X0 @ X1 )
= ( unord_pair @ X1 @ X0 ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
? [X0: $i,X1: $i] :
( ( unord_pair @ X0 @ X1 )
!= ( unord_pair @ X1 @ X0 ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f41,plain,
( ( unord_pair @ sK1 @ sK0 )
!= ( unord_pair @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
thf(f46,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f49,plain,
( ( unord_pair @ sK1 @ sK0 )
!= ( unord_pair @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f60,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) )
@ sK1
@ sK0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f49,f46,f46]) ).
thf(f61,plain,
( ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 )
!= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f61]) ).
thf(f63,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( $false
= ( ( sK0 = sK2 )
| ( sK1 = sK2 ) ) )
| ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $false )
| ( ( sK1 = sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( ( sK0 = sK2 )
= $false )
| ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $false )
| ( sK2 != sK0 ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( sK0 = sK2 )
= $false )
| ( sK2 != sK0 ) ),
inference(or_proxy_clausification,[],[f68]) ).
thf(f72,plain,
( ( sK2 != sK0 )
| ( sK2 != sK0 ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f73,plain,
sK2 != sK0,
inference(duplicate_literal_removal,[],[f72]) ).
thf(f75,plain,
( ( ( sK1 = sK2 )
= $false )
| ( ( sK1 = sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f76,plain,
( ( sK1 != sK2 )
| ( sK1 != sK2 ) ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f77,plain,
sK1 != sK2,
inference(duplicate_literal_removal,[],[f76]) ).
thf(f80,plain,
( ( $true
= ( ( sK0 = sK2 )
| ( sK1 = sK2 ) ) )
| ( $true
= ( ( sK1 = sK2 )
| ( sK0 = sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f81,plain,
( ( $true
= ( sK1 = sK2 ) )
| ( $true
= ( sK0 = sK2 ) )
| ( $true
= ( ( sK1 = sK2 )
| ( sK0 = sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( $true
= ( ( sK1 = sK2 )
| ( sK0 = sK2 ) ) )
| ( sK1 = sK2 )
| ( $true
= ( sK0 = sK2 ) ) ),
inference(equality_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( $true
= ( sK0 = sK2 ) )
| ( $true
= ( sK0 = sK2 ) )
| ( $true
= ( sK1 = sK2 ) )
| ( sK1 = sK2 ) ),
inference(or_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( sK2 = sK0 )
| ( $true
= ( sK1 = sK2 ) )
| ( sK2 = sK0 )
| ( sK1 = sK2 ) ),
inference(equality_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( sK2 = sK0 )
| ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK2 = sK0 ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( sK2 = sK0 )
| ( sK1 = sK2 ) ),
inference(duplicate_literal_removal,[],[f85]) ).
thf(f88,definition,
( spl3_1
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f92,definition,
( spl3_2
<=> ( sK2 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f96,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f73,f92]) ).
thf(f97,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f77,f88]) ).
thf(f99,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[],[f86,f88,f92]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f97]) ).
cnf(s5,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f99]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6]) ).
thf(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET066^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:39:48 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.21/0.28 % (3529969)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3529975)lrs+10_16_si=on:nwc=1.5:random_seed=80291994:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (3529975) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3529969-3529975"...
% 0.21/0.28 % (3529975)...printing done.
% 0.21/0.28 % (3529975)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3529975)------------------------------
% 0.21/0.28 % (3529975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3529975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3529975)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3529975)Termination reason: Refutation
% 0.21/0.28 % (3529975)Time elapsed: 0.002 s
% 0.21/0.28 % (3529975)Peak memory usage: 12 MB
% 0.21/0.28 % (3529975)Instructions burned: 4 (million)
% 0.21/0.28 % (3529969)Success in time 0.027 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------