%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU603^2 : 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 : n016.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 08:32:38 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 166 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 247 ( 18 ~; 2 |; 4 &; 187 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 7 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 81 ( 42 ^; 36 !; 3 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrER: $o ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) )
& ( dsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
thf(f14,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f22,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f17,f15]) ).
thf(f23,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f36,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 )
@ sK2 ) ) ),
inference(constrained_superposition,[],[f30,f23]) ).
thf(f37,plain,
( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 )
@ sK2 ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
( $true
= ( ~ ( in @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
( ( in @ sK2 @ sK1 )
= $false ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f44,plain,
$true = $false,
inference(constrained_superposition,[],[f18,f39]) ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU603^2 : 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 : n016.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
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:01:50 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.08/0.25 % (400036)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (400045)dis+10_1_sil=32000:sp=arity:random_seed=2338950861:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.25 % (400045) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-400036-400045"...
% 0.08/0.25 % (400045)...printing done.
% 0.08/0.25 % (400045)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (400045)------------------------------
% 0.08/0.25 % (400045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (400045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (400045)CaDiCaL version: 2.1.3
% 0.08/0.26 % (400045)Termination reason: Refutation
% 0.08/0.26 % (400045)Time elapsed: 0.002 s
% 0.08/0.26 % (400045)Peak memory usage: 12 MB
% 0.08/0.26 % (400045)Instructions burned: 4 (million)
% 0.08/0.26 % (400036)Success in time 0.015 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------