%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU505^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:29:50 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 338 ( 109 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 352 ( 22 ~; 31 |; 12 &; 240 @)
% ( 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 : 80 ( 20 ^; 54 !; 6 ?; 80 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[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,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
<=> ( in @ X2 @ X1 ) )
=> ( X0 = X1 ) )
= setextAx ),
file('/export/starexec/sandbox/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/sandbox/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,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
<=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) )
= setextAx ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( 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 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $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 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $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 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
= $true ) ) )
& ( setextAx = $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( sK0 != sK1 )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
| ( ( in @ X3 @ sK1 )
= $true ) )
& ( 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 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
setextAx = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
| ( ( in @ X3 @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( in @ X2 @ sK0 )
= $true ) ),
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 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f13]) ).
thf(f20,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
= ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
= ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) ) ) )
| ( ( X2 = X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( ( X2 = X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
!= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
= $true )
| ( 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(f31,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( sK2 @ X0 @ sK0 ) @ sK1 )
= $true )
| ( $true
= ( in @ ( sK2 @ X0 @ sK0 ) @ X0 ) )
| ( sK0 = X0 ) ),
inference(constrained_superposition,[],[f14,f29]) ).
thf(f37,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ X0 @ sK0 ) @ X0 ) )
| ( ( in @ ( sK2 @ X0 @ sK0 ) @ sK1 )
= $true )
| ( sK0 = X0 ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f58,plain,
( ( ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 )
= $true )
| ( $true != $true )
| ( sK0 = sK1 ) ),
inference(equality_factoring,[],[f37]) ).
thf(f60,plain,
( ( ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 )
= $true )
| ( sK0 = sK1 ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f67,plain,
( ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 )
= $true ),
inference(forward_subsumption_resolution,[],[f60,f16]) ).
thf(f69,plain,
( ( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f15,f67]) ).
thf(f70,plain,
( $true
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK0 ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f73,plain,
( ( $false = $true )
| ( $false
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 ) )
| ( sK0 = sK1 ) ),
inference(constrained_superposition,[],[f30,f70]) ).
thf(f74,plain,
( ( sK0 = sK1 )
| ( $false
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f77,plain,
( $false
= ( in @ ( sK2 @ sK1 @ sK0 ) @ sK1 ) ),
inference(forward_subsumption_resolution,[],[f74,f16]) ).
thf(f79,plain,
$false = $true,
inference(constrained_superposition,[],[f77,f67]) ).
thf(f86,plain,
$false,
inference(trivial_inequality_removal,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU505^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % 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 13:49:38 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.30 % (1310089)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1310095)lrs+10_16_si=on:nwc=1.5:random_seed=1350205252:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1310096)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2511637085:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1310098)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=738270606:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (1310097)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1255189834:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (1310094)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=167480626:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1310096)Refutation not found, incomplete strategy
% 0.22/0.30 % (1310096)------------------------------
% 0.22/0.30 % (1310096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1310096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1310096)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1310096)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (1310096)Time elapsed: 0.002 s
% 0.22/0.30 % (1310096)Peak memory usage: 12 MB
% 0.22/0.30 % (1310096)Instructions burned: 1 (million)
% 0.22/0.30 % (1310096)------------------------------
% 0.22/0.30 % (1310096)------------------------------
% 0.22/0.30 % (1310095) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1310089-1310095"...
% 0.22/0.30 % (1310097) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1310089-1310097"...
% 0.22/0.30 % (1310098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1310089-1310098"...
% 0.22/0.30 % (1310095)...printing done.
% 0.22/0.30 % (1310097)...printing done.
% 0.22/0.30 % (1310098)...printing done.
% 0.22/0.30 % (1310095)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (1310095)------------------------------
% 0.22/0.30 % (1310095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1310095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1310095)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1310095)Termination reason: Refutation
% 0.22/0.30 % (1310095)Time elapsed: 0.005 s
% 0.22/0.30 % (1310095)Peak memory usage: 12 MB
% 0.22/0.30 % (1310095)Instructions burned: 8 (million)
% 0.22/0.30 % (1310089)Success in time 0.04 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------