%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV476^1 : 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 : n006.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 08:38:42 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 178 ( 17 ~; 10 |; 5 &; 139 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 53 ( 0 ^; 50 !; 3 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_6,type,
sK1: sK0 > $o ).
thf(func_def_7,type,
sK2: sK0 > $o ).
thf(func_def_8,type,
sK3: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_DIFF_') ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_DIFF_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
=> ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
=> ( 'const/sets/FINITE' @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
!= $true )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f15,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f16,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f40,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(constrained_superposition,[],[f15,f18]) ).
thf(f41,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f42,plain,
! [X0: sK0 > $o] :
( ( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f41,f16]) ).
thf(f43,plain,
! [X0: sK0 > $o] :
( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
$true != $true,
inference(backward_demodulation,[],[f17,f43]) ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV476^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n006.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 15:49:40 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.26 Running higher-order theorem proving
% 0.21/0.27 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
% 0.21/0.31 % (898013)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (898023)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=709752528:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (898023) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-898013-898023"...
% 0.21/0.31 % (898023)...printing done.
% 0.21/0.31 % (898023)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (898023)------------------------------
% 0.21/0.31 % (898023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (898023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (898023)CaDiCaL version: 2.1.3
% 0.21/0.31 % (898023)Termination reason: Refutation
% 0.21/0.31 % (898023)Time elapsed: 0.002 s
% 0.21/0.31 % (898023)Peak memory usage: 12 MB
% 0.21/0.31 % (898023)Instructions burned: 3 (million)
% 0.21/0.31 % (898013)Success in time 0.031 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------