%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV485^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:38:43 AM UTC 2026
% Result : Theorem 0.25s 0.38s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 17 unt; 0 typ; 3 def)
% Number of atoms : 118 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 136 ( 13 ~; 9 |; 5 &; 107 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/HAS_SIZE':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/BIT0': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
sF0: $o ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).
thf(f2,axiom,
'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_BOOL_') ).
thf(f3,conjecture,
'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_BOOL_') ).
thf(f4,negated_conjecture,
~ ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( 'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(flattening,[],[f8]) ).
thf(f12,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( ( 'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,definition,
( sF0
= ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f18,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= sF0 ),
inference(reorient_equations,[],[f17]) ).
thf(f19,plain,
sF0 != $true,
inference(definition_folding,[],[f12,f18]) ).
thf(f21,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f22,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f28,plain,
( ( sF0 = $true )
| ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $false ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f30,definition,
( spl1_1
<=> ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f32,plain,
( ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f34,definition,
( spl1_2
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f37,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f28,f34,f30]) ).
thf(f47,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f19,f34]) ).
thf(f69,plain,
( ( $false = $true )
| ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true ) ),
inference(constrained_superposition,[],[f22,f14]) ).
thf(f71,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f77,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f71,f32]) ).
thf(f78,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f78]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
~ spl1_1,
inference(sat_conversion,[],[f79]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f80,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV485^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n017.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 15:48:52 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.25/0.33 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
% 0.25/0.38 % (495858)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.38 % (495869)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.38 % (495869)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
% 0.25/0.38 % (495869)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=1681756092:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.38 % (495869) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-495858-495869"...
% 0.25/0.38 % (495869)...printing done.
% 0.25/0.38 % (495869)Refutation found. Thanks to Tanya!
% 0.25/0.38 % SZS status Theorem for theBenchmark
% 0.25/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.38 % (495869)------------------------------
% 0.25/0.38 % (495869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (495869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (495869)CaDiCaL version: 2.1.3
% 0.25/0.38 % (495869)Termination reason: Refutation
% 0.25/0.38 % (495869)Time elapsed: 0.003 s
% 0.25/0.38 % (495869)Peak memory usage: 13 MB
% 0.25/0.38 % (495869)Instructions burned: 3 (million)
% 0.25/0.38 % (495858)Success in time 0.027 s
% 0.25/0.38 % Vampire exiting
%------------------------------------------------------------------------------