%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU559^2 : 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 : n007.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 08:30:04 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 131 ( 12 ~; 4 |; 2 &; 93 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 6 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 15 ^; 17 !; 2 ?; 34 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(f2,conjecture,
! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK0 ) )
| ( $true
= ( in @ X2 @ sK1 ) ) )
& ( $true
!= ( subset @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( $true
!= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK0 ) )
| ( $true
= ( in @ X2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f10,f12]) ).
thf(f16,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( in @ sK2 @ sK0 )
=> ( in @ sK2 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( in @ sK2 @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f11,f20]) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
$true = $false,
inference(forward_demodulation,[],[f22,f19]) ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU559^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:48:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.28 % (3392214)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3392225)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2249500551:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3392225) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3392214-3392225"...
% 0.20/0.28 % (3392225)...printing done.
% 0.20/0.28 % (3392225)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3392225)------------------------------
% 0.20/0.28 % (3392225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3392225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3392225)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3392225)Termination reason: Refutation
% 0.20/0.28 % (3392225)Time elapsed: 0.001 s
% 0.20/0.28 % (3392225)Peak memory usage: 12 MB
% 0.20/0.28 % (3392225)Instructions burned: 2 (million)
% 0.20/0.28 % (3392214)Success in time 0.033 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------