%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU829^1 : 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 : 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 08:31:46 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 25 unt; 0 typ; 3 def)
% Number of atoms : 282 ( 76 equ; 2 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 213 ( 50 ~; 46 |; 0 &; 94 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 9 con; 0-4 aty)
% ( 13 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 27 sgn 11 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(f1,axiom,
( subseteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subseteq) ).
thf(f2,axiom,
( powerset
= ( ^ [X0: $i > $o,X1: $i > $o] : ( subseteq @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',poserset) ).
thf(f3,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).
thf(f4,conjecture,
( ( ^ [X0: $i > $o] : ( X0 = emptyset ) )
= ( powerset @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f5,negated_conjecture,
( ( ^ [X0: $i > $o] : ( X0 = emptyset ) )
!= ( powerset @ emptyset ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f8,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f9,plain,
( subseteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(flattening,[],[f6]) ).
thf(f12,plain,
( ( powerset @ emptyset )
!= ( ^ [Y0: $i > $o] : ( emptyset = Y0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
( powerset
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( subseteq @ Y1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( subseteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,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,[],[f13,f15]) ).
thf(f19,plain,
( ( ^ [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,[],[f12,f18,f14,f14]) ).
thf(f20,plain,
( ( (=)
@ ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> $false ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( (=)
@ ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f22,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 )
!= ( ( ^ [Y0: $i] : $false )
= sK0 ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( ( ^ [Y0: $i] : $false )
= sK0 ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) )
| ( $false
= ( ( ^ [Y0: $i] : $false )
= sK0 ) ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) )
| ( ( ^ [Y0: $i] : $false )
!= sK0 ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| ( ( ~ ( sK0 @ sK1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( ( ^ [Y0: $i] : $false )
!= sK0 ) ),
inference(not_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f31,plain,
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 )
@ X1 ) )
| ( ( ^ [Y0: $i] : $false )
= sK0 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 ) ) )
| ( ( ^ [Y0: $i] : $false )
= sK0 ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f36,definition,
( spl2_1
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl2_2
<=> ( ( ^ [Y0: $i] : $false )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f41,plain,
( ( ( ^ [Y0: $i] : $false )
= sK0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f42,plain,
( ( ( ^ [Y0: $i] : $false )
!= sK0 )
| spl2_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f29,f40,f36]) ).
thf(f45,definition,
( spl2_3
<=> ! [X1: $i] :
( $false
= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f46,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ X1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f47,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f34,f45,f40]) ).
thf(f48,plain,
( ( ( ^ [Y0: $i] : $false
@ sK3 )
!= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f42]) ).
thf(f49,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( ( ^ [Y0: $i] : $false
@ sK3 )
= $true )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f48]) ).
thf(f52,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f53,plain,
( ( $true
= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ( $true = $false )
| spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f53,f46]) ).
thf(f55,plain,
( $false
| spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f55]) ).
thf(f57,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[],[f38,f46]) ).
thf(f58,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f58]) ).
thf(f60,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : $false
@ X1 )
= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[],[f41]) ).
thf(f61,plain,
( ! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f60]) ).
thf(f64,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true = $false ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f65,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f65,f40,f45]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f59]) ).
cnf(s5,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
spl2_2,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl2_1,
inference(rat,[],[s1,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s4,s7,s8]) ).
thf(f67,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU829^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n018.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:37:42 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.10/0.27 % (170485)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.27 % (170497)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=684002593:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.27 % (170497) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-170485-170497"...
% 0.10/0.27 % (170497)...printing done.
% 0.10/0.27 % (170497)Refutation found. Thanks to Tanya!
% 0.10/0.27 % SZS status Theorem for theBenchmark
% 0.10/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.27 % (170497)------------------------------
% 0.10/0.27 % (170497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.27 % (170497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.27 % (170497)CaDiCaL version: 2.1.3
% 0.10/0.27 % (170497)Termination reason: Refutation
% 0.10/0.27 % (170497)Time elapsed: 0.002 s
% 0.10/0.27 % (170497)Peak memory usage: 13 MB
% 0.10/0.27 % (170497)Instructions burned: 3 (million)
% 0.10/0.27 % (170485)Success in time 0.025 s
% 0.10/0.27 % Vampire exiting
%------------------------------------------------------------------------------