%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV485^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:39:34 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 105 ( 5 ~; 3 |; 5 &; 92 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 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(f1,axiom,
! [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 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_BOOL_') ).
thf(f3,conjecture,
'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o,
file('/export/starexec/sandbox/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/CARD' @ X0 @ X1 )
= X2 ) )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f6,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(fool_elimination,[],[f5]) ).
thf(f7,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(f8,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,[],[f7]) ).
thf(f9,plain,
~ ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,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,[],[f8]) ).
thf(f14,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f20,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,[],[f18]) ).
thf(f113,plain,
( ( $true = $false )
| ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true ) ),
inference(constrained_superposition,[],[f20,f13]) ).
thf(f114,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f118,plain,
$false,
inference(forward_subsumption_resolution,[],[f114,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV485^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:56:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25 % (3704608)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (3704618)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4014578415:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (3704618) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3704608-3704618"...
% 0.07/0.25 % (3704618)...printing done.
% 0.07/0.25 % (3704620)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1403096038:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (3704618)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (3704618)------------------------------
% 0.07/0.25 % (3704618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (3704618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (3704618)CaDiCaL version: 2.1.3
% 0.07/0.25 % (3704618)Termination reason: Refutation
% 0.07/0.25 % (3704618)Time elapsed: 0.003 s
% 0.07/0.25 % (3704618)Peak memory usage: 12 MB
% 0.07/0.25 % (3704618)Instructions burned: 4 (million)
% 0.07/0.25 % (3704608)Success in time 0.035 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------