%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:31:46 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 29 unt; 0 typ; 3 def)
% Number of atoms : 321 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 238 ( 46 ~; 44 |; 0 &; 119 @)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 24 ( 20 usr; 8 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 100 ( 27 sgn 14 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
seteq: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_2,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_4,type,
emptyset: $i > $o ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIFF: $o > $o > $o ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK0: $i > $o ).
thf(f1,axiom,
( ( ^ [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
! [X2: $i > $o] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= seteq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',seteq) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subseteq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subseteq) ).
thf(f3,axiom,
( powerset
= ( ^ [X0: $i > $o,X1: $i > $o] : ( subseteq @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',poserset) ).
thf(f4,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).
thf(f5,conjecture,
( seteq @ ( powerset @ emptyset )
@ ^ [X0: $i > $o] : ( X0 = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f6,negated_conjecture,
~ ( seteq @ ( powerset @ emptyset )
@ ^ [X0: $i > $o] : ( X0 = emptyset ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f4]) ).
thf(f8,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f9,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
! [X2: $i > $o] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= seteq ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( seteq
= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( seteq @ ( powerset @ emptyset )
@ ^ [X0: $i > $o] : ( X0 = emptyset ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
( $true
!= ( seteq @ ( powerset @ emptyset )
@ ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subseteq ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( $true
!= ( seteq @ ( powerset @ emptyset )
@ ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(flattening,[],[f12]) ).
thf(f16,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( $true
!= ( seteq @ ( powerset @ emptyset )
@ ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f20,plain,
( seteq
= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 ) ) ),
inference(definition_unfolding,[],[f16,f17]) ).
thf(f24,plain,
( $true
!= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 )
@ ^ [Y0: $i] : $false )
@ ^ [Y0: $i > $o] :
( ( ^ [Y1: $i] : $false )
= Y0 ) ) ),
inference(definition_unfolding,[],[f18,f20,f23,f19,f19]) ).
thf(f25,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> $false ) )
= ( ( ^ [Y1: $i] : $false )
= Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> $false ) )
= ( ( ^ [Y1: $i] : $false )
= Y0 ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> $false ) )
= ( ( ^ [Y0: $i] : $false )
= sK0 ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) )
= ( ( ^ [Y0: $i] : $false )
= sK0 ) )
= $false ),
inference(boolean_simplification,[],[f27]) ).
thf(f29,plain,
( ( ( ^ [Y0: $i] : $false )
= sK0 )
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= sK0 ) ) ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) )
| ( ( ( ^ [Y0: $i] : $false )
= sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( ( ( ^ [Y0: $i] : $false )
= sK0 )
= $false )
| ( ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ sK1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( $false
= ( ~ ( sK0 @ sK1 ) ) )
| ( ( ^ [Y0: $i] : $false )
!= sK0 ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ X1 ) )
| ( $true
= ( ( ^ [Y0: $i] : $false )
= sK0 ) ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f37,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( $true
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ X1 ) ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( $true
= ( ~ ( sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( ( sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f41,definition,
( spl2_1
<=> ( ( ^ [Y0: $i] : $false )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f42,plain,
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| spl2_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f45,definition,
( spl2_2
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f47,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f35,f45,f41]) ).
thf(f50,definition,
( spl2_3
<=> ! [X1: $i] :
( ( sK0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f51,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f52,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f39,f50,f41]) ).
thf(f53,plain,
( ( ( sK0 @ sK3 )
!= ( ^ [Y0: $i] : $false
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f43]) ).
thf(f54,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f53]) ).
thf(f57,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true = $false )
| spl2_1 ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f58,plain,
( ( $true
= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( ( $true = $false )
| spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[],[f58,f51]) ).
thf(f60,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f60]) ).
thf(f62,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f47,f51]) ).
thf(f63,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f65,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( sK0 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[],[f42]) ).
thf(f66,plain,
( ! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] : $false
@ X1 )
= $true ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f65]) ).
thf(f69,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f70,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
= $false )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
( spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f70,f41,f50]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
spl2_1,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl2_2,
inference(rat,[],[s1,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s4,s7,s8]) ).
thf(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.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 14:38:08 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.08/0.26 % (1380397)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (1380407)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2398266312:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (1380407) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1380397-1380407"...
% 0.08/0.26 % (1380407)...printing done.
% 0.08/0.26 % (1380407)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (1380407)------------------------------
% 0.08/0.26 % (1380407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (1380407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (1380407)CaDiCaL version: 2.1.3
% 0.08/0.26 % (1380407)Termination reason: Refutation
% 0.08/0.26 % (1380407)Time elapsed: 0.002 s
% 0.08/0.26 % (1380407)Peak memory usage: 13 MB
% 0.08/0.26 % (1380407)Instructions burned: 4 (million)
% 0.08/0.26 % (1380397)Success in time 0.017 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------