%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU505^2 : 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 : n026.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 08:32:13 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 38 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 330 ( 110 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 353 ( 24 ~; 34 |; 12 &; 236 @)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 6 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 82 ( 20 ^; 56 !; 6 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setextAx: $o ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
vIFF: $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_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
<=> ( in @ X2 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(f2,conjecture,
( setextAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(f3,negated_conjecture,
~ ( setextAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
<=> ( in @ X2 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setextAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setextAx = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ X3 @ X0 )
= $true ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( setextAx = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( setextAx = $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( sK0 != sK1 )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK0 ) )
| ( $true
!= ( in @ X2 @ sK1 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
| ( $true
!= ( in @ X3 @ sK0 ) ) )
& ( setextAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
setextAx = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
| ( $true
!= ( in @ X3 @ sK0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
= ( in @ X2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f13]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
= ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
= ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X2 ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
!= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(xor_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(xor_proxy_clausification,[],[f28]) ).
thf(f33,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(constrained_superposition,[],[f15,f29]) ).
thf(f36,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f71,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
!= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ ( sK2 @ sK1 @ X0 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(constrained_superposition,[],[f14,f30]) ).
thf(f77,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ ( sK2 @ sK1 @ X0 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f92,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 ) )
| ( sK0 = sK1 ) ),
inference(equality_factoring,[],[f36]) ).
thf(f93,plain,
( ( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 ) )
| ( sK0 = sK1 ) ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f99,plain,
( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 ) ),
inference(forward_subsumption_resolution,[],[f93,f16]) ).
thf(f118,plain,
( ( $true = $false )
| ( $true != $true )
| ( sK0 = sK1 ) ),
inference(constrained_superposition,[],[f77,f99]) ).
thf(f126,plain,
sK0 = sK1,
inference(trivial_inequality_removal,[],[f118]) ).
thf(f134,plain,
$false,
inference(forward_subsumption_resolution,[],[f126,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU505^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n026.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:49:43 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.24 % (616155)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (616168)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1092423506:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.24 % (616168)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.24 % (616168) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-616155-616168"...
% 0.08/0.24 % (616165)% WARNING: option uhcvi not known.
% 0.08/0.24 % (616168)...printing done.
% 0.08/0.24 % (616168)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24 % (616168)------------------------------
% 0.08/0.24 % (616168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (616168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (616168)CaDiCaL version: 2.1.3
% 0.08/0.24 % (616168)Termination reason: Refutation
% 0.08/0.24 % (616168)Time elapsed: 0.004 s
% 0.08/0.24 % (616168)Peak memory usage: 12 MB
% 0.08/0.24 % (616168)Instructions burned: 10 (million)
% 0.08/0.24 % (616155)Success in time 0.019 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------