%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU569^2 : 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 08:32:29 AM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 34 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 205 ( 7 ~; 8 |; 2 &; 147 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 5 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 49 ( 19 ^; 29 !; 1 ?; 49 :)
% 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,
subsetI2: $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_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: $i > $i > $i ).
thf(f1,axiom,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(f2,conjecture,
( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(f3,negated_conjecture,
~ ( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( subsetI2
= ( !! @ $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,
~ ( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( subsetI2 = $true )
=> ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( subset @ sK0 @ sK0 ) )
& ( subsetI2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
subsetI2 = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
!= ( subset @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f16,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,[],[f15]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( subset @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,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,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK1 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK1 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK1 @ X1 @ X2 ) @ X1 ) ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK1 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK1 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f40,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( subset @ X0 @ X0 )
= $true )
| ( ( subset @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f23,f24]) ).
thf(f41,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( subset @ X0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f40]) ).
thf(f42,plain,
! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f47,plain,
$true != $true,
inference(constrained_superposition,[],[f12,f42]) ).
thf(f48,plain,
$false,
inference(trivial_inequality_removal,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU569^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16 % Computer : n001.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 13:56:50 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 Running first-order model finding
% 0.11/0.19 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
% 0.11/0.23 % (1281621)Will run a generic schedule for satisfiability detection.
% 0.11/0.23 % (1281630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3535938535:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.23 % (1281630)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.23 % (1281630) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1281621-1281630"...
% 0.11/0.23 % (1281630)...printing done.
% 0.11/0.23 % (1281627)% WARNING: option uhcvi not known.
% 0.11/0.23 % (1281630)Refutation found. Thanks to Tanya!
% 0.11/0.23 % SZS status Theorem for theBenchmark
% 0.11/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.23 % (1281630)------------------------------
% 0.11/0.23 % (1281630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.23 % (1281630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.23 % (1281630)CaDiCaL version: 2.1.3
% 0.11/0.23 % (1281630)Termination reason: Refutation
% 0.11/0.23 % (1281630)Time elapsed: 0.002 s
% 0.11/0.23 % (1281630)Peak memory usage: 12 MB
% 0.11/0.23 % (1281630)Instructions burned: 3 (million)
% 0.11/0.23 % (1281621)Success in time 0.026 s
% 0.11/0.23 % Vampire exiting
%------------------------------------------------------------------------------