%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU513^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:32:15 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 16 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 97 ( 6 ~; 0 |; 1 &; 78 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 5 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 20 ( 10 ^; 10 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,conjecture,
( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(f3,negated_conjecture,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f10,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f9,f10]) ).
thf(f15,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
$true != $true,
inference(constrained_superposition,[],[f11,f18]) ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU513^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:53:21 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24 % (1270586)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (1270598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1182149692:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.07/0.24 % (1270598) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1270586-1270598"...
% 0.07/0.24 % (1270598)...printing done.
% 0.07/0.24 % (1270598)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.24 % (1270598)------------------------------
% 0.07/0.24 % (1270598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (1270598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (1270598)CaDiCaL version: 2.1.3
% 0.07/0.24 % (1270598)Termination reason: Refutation
% 0.07/0.24 % (1270598)Time elapsed: 0.001 s
% 0.07/0.24 % (1270598)Peak memory usage: 12 MB
% 0.07/0.24 % (1270598)Instructions burned: 1 (million)
% 0.07/0.24 % (1270586)Success in time 0.017 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------