%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU563^2 : 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 : n017.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 08:32:28 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 166 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 132 ( 9 ~; 1 |; 6 &; 86 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 8 con; 0-4 aty)
% ( 7 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 33 ( 19 ^; 12 !; 2 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
emptysetimpfalse: $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetI2: $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_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(f2,axiom,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(f4,conjecture,
( emptysetimpfalse
=> ( subsetI2
=> ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(f5,negated_conjecture,
~ ( emptysetimpfalse
=> ( subsetI2
=> ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( emptysetimpfalse
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> $false ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
~ ( emptysetimpfalse
=> ( subsetI2
=> ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( emptysetimpfalse = $true )
=> ( ( subsetI2 = $true )
=> ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( subset @ emptyset @ sK0 ) )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
thf(f17,plain,
( emptysetimpfalse
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> $false ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
!= ( subset @ emptyset @ sK0 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> $false ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f27,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ emptyset
@ sK0 ) ),
inference(definition_unfolding,[],[f22,f18]) ).
thf(f28,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( in @ Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( in @ Y0 @ sK0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( $false
= ( ( in @ sK1 @ emptyset )
=> ( in @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f32,plain,
( $true
= ( in @ sK1 @ emptyset ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> $false )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f46,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> $false ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ emptyset ) )
| ( $false = $true ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( $false
= ( in @ X1 @ emptyset ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f60,plain,
$false = $true,
inference(forward_demodulation,[],[f32,f48]) ).
thf(f61,plain,
$false,
inference(trivial_inequality_removal,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU563^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:45:53 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.26 % (366934)Will run a generic schedule for satisfiability detection.
% 0.21/0.26 % (366943)dis+10_1_sil=32000:sp=arity:random_seed=3861800410:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.21/0.26 % (366943) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366934-366943"...
% 0.21/0.26 % (366943)...printing done.
% 0.21/0.26 % (366941)% WARNING: option uhcvi not known.
% 0.21/0.26 % (366943)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (366943)------------------------------
% 0.21/0.26 % (366943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (366943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (366943)CaDiCaL version: 2.1.3
% 0.21/0.26 % (366943)Termination reason: Refutation
% 0.21/0.26 % (366943)Time elapsed: 0.002 s
% 0.21/0.26 % (366943)Peak memory usage: 12 MB
% 0.21/0.26 % (366943)Instructions burned: 3 (million)
% 0.21/0.26 % (366934)Success in time 0.021 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------