%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU567^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:32:29 AM UTC 2026
% Result : Theorem 0.23s 0.26s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 173 ( 45 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 229 ( 19 ~; 8 |; 4 &; 151 @)
% ( 0 <=>; 31 =>; 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 : 18 ( 14 usr; 6 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 56 ( 19 ^; 35 !; 2 ?; 56 :)
% 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_2,type,
subsetI1: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(f2,conjecture,
( subsetI1
=> ! [X0: $i,X1: $i] :
( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(f3,negated_conjecture,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
=> ( X0 != X1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
=> ( X0 != X1 ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( subset @ X0 @ X1 )
!= $true ) )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
( ( sK0 = sK1 )
& ( $true
!= ( subset @ sK0 @ sK1 ) )
& ( subsetI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( subsetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
subsetI1 = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( $true
!= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f11,f12]) ).
thf(f18,plain,
( $true
!= ( subset @ sK1 @ sK1 ) ),
inference(definition_unfolding,[],[f13,f14]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f29,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ X0 ) )
| ( $true
= ( subset @ X0 @ X0 ) ) ),
inference(constrained_superposition,[],[f26,f27]) ).
thf(f30,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f29]) ).
thf(f31,plain,
! [X0: $i] :
( $true
= ( subset @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f34,plain,
$true != $true,
inference(constrained_superposition,[],[f18,f31]) ).
thf(f35,plain,
$false,
inference(trivial_inequality_removal,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU567^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:51:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.26 % (3187477)Will run a generic schedule for satisfiability detection.
% 0.23/0.26 % (3187488)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=462924448:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.26 % (3187488) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3187477-3187488"...
% 0.23/0.26 % (3187488)...printing done.
% 0.23/0.26 % (3187483)% WARNING: option uhcvi not known.
% 0.23/0.26 % (3187488)Refutation found. Thanks to Tanya!
% 0.23/0.26 % SZS status Theorem for theBenchmark
% 0.23/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.26 % (3187488)------------------------------
% 0.23/0.26 % (3187488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.26 % (3187488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.26 % (3187488)CaDiCaL version: 2.1.3
% 0.23/0.26 % (3187488)Termination reason: Refutation
% 0.23/0.26 % (3187488)Time elapsed: 0.002 s
% 0.23/0.26 % (3187488)Peak memory usage: 12 MB
% 0.23/0.26 % (3187488)Instructions burned: 3 (million)
% 0.23/0.26 % (3187477)Success in time 0.033 s
% 0.23/0.27 % Vampire exiting
%------------------------------------------------------------------------------