%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU562^2 : 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 : n019.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 08:30:05 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 148 ( 14 ~; 5 |; 6 &; 99 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 7 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 37 ( 15 ^; 18 !; 4 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
subsetI1: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK2: $i > $i > $i ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(f3,conjecture,
( subsetI1
=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(f4,negated_conjecture,
~ ( subsetI1
=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f7,plain,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) )
& ( subsetI1 = $true ) ),
inference(rectify,[],[f11]) ).
thf(f17,plain,
( ! [X2: $i] :
( ( ( in @ X2 @ sK3 )
!= $true )
| ( $true
= ( in @ X2 @ sK4 ) ) )
& ( ( subset @ sK3 @ sK4 )
!= $true )
& ( subsetI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f16]) ).
thf(f18,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f24,plain,
( ( subset @ sK3 @ sK4 )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK3 )
!= $true )
| ( $true
= ( in @ X2 @ sK4 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f32,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ sK3
@ sK4 ) ),
inference(definition_unfolding,[],[f24,f18]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ sK4 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f44,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ Y0 @ sK4 ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( $false
= ( ( in @ sK5 @ sK3 )
=> ( in @ sK5 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $false
= ( in @ sK5 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( $true != $true )
| ( ( in @ sK5 @ sK4 )
= $true ) ),
inference(constrained_superposition,[],[f25,f47]) ).
thf(f49,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
$false = $true,
inference(forward_demodulation,[],[f49,f46]) ).
thf(f51,plain,
$false,
inference(trivial_inequality_removal,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU562^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % 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 13:50:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.28 % (799539)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (799548)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=62704674:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (799548) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-799539-799548"...
% 0.22/0.28 % (799548)...printing done.
% 0.22/0.28 % (799548)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (799548)------------------------------
% 0.22/0.28 % (799548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (799548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (799548)CaDiCaL version: 2.1.3
% 0.22/0.28 % (799548)Termination reason: Refutation
% 0.22/0.28 % (799548)Time elapsed: 0.002 s
% 0.22/0.28 % (799548)Peak memory usage: 12 MB
% 0.22/0.28 % (799548)Instructions burned: 3 (million)
% 0.22/0.28 % (799539)Success in time 0.027 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------