%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU515^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:29:53 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 304 ( 99 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 316 ( 27 ~; 42 |; 16 &; 187 @)
% ( 5 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 11 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 76 ( 0 sgn 46 !; 12 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setadjoinAx: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIFF: $o > $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vOR: $o > $o > $o ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
sK3: $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
<=> ( ( X1 = X2 )
| ( in @ X1 @ X0 ) ) )
= setadjoinAx ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ Y2 ) )
= ( ( in @ Y1 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> X3 )
=> ( ( ( in @ X1 @ X0 )
=> X3 )
=> X3 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setadjoinAx = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 ) )
& ( ( X1 != X2 )
| ( $true = X3 ) ) )
& ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) )
& ( setadjoinAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
& ? [X3: $o] :
( ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 ) )
& ( $true != X3 )
& ( ( X1 != X2 )
| ( $true = X3 ) ) ) )
& ( setadjoinAx = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
& ? [X3: $o] :
( ( ( ( in @ X2 @ X0 )
!= $true )
| ( $true = X3 ) )
& ( $true != X3 )
& ( ( X1 != X2 )
| ( $true = X3 ) ) ) )
& ( setadjoinAx = $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( in @ sK2 @ ( setadjoin @ sK1 @ sK0 ) ) )
& ( ( ( in @ sK2 @ sK0 )
!= $true )
| ( sK3 = $true ) )
& ( sK3 != $true )
& ( ( sK1 != sK2 )
| ( sK3 = $true ) )
& ( setadjoinAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
thf(f12,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
( ( sK3 = $true )
| ( sK1 != sK2 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
sK3 != $true,
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( ( in @ sK2 @ sK0 )
!= $true )
| ( sK3 = $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( $true
= ( in @ sK2 @ ( setadjoin @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ Y2 ) )
= ( ( in @ Y1 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f20,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ Y2 ) )
= ( ( in @ Y1 @ Y2 )
| ( Y1 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f12]) ).
thf(f21,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ Y2 ) )
= ( ( in @ Y1 @ Y2 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ Y1 ) )
= ( ( in @ Y0 @ Y1 )
| ( Y0 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ Y1 ) )
= ( ( in @ Y0 @ Y1 )
| ( Y0 = X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ Y0 ) )
= ( ( in @ X2 @ Y0 )
| ( X2 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ Y0 ) )
= ( ( in @ X2 @ Y0 )
| ( X2 = X1 ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
= ( ( in @ X2 @ X3 )
| ( X2 = X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X3 )
| ( X2 = X1 ) )
= ( in @ X2 @ ( setadjoin @ X1 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X3 )
| ( X2 = X1 ) ) )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
= $false )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f28]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
= $false )
| ( ( in @ X2 @ X3 )
= $true )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f36,definition,
( spl4_1
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f38,plain,
( ( sK1 != sK2 )
| spl4_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl4_2
<=> ( sK3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f43,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f13,f40,f36]) ).
thf(f45,definition,
( spl4_3
<=> ( ( in @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f47,plain,
( ( ( in @ sK2 @ sK0 )
!= $true )
| spl4_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
( ~ spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f15,f40,f45]) ).
thf(f49,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f14,f40]) ).
thf(f50,plain,
( ( $true = $false )
| ( ( in @ sK2 @ sK0 )
= $true )
| ( sK1 = sK2 ) ),
inference(constrained_superposition,[],[f34,f16]) ).
thf(f57,plain,
( ( sK1 = sK2 )
| ( ( in @ sK2 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f59,plain,
( ( ( in @ sK2 @ sK0 )
= $true )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f57,f38]) ).
thf(f62,plain,
( $false
| spl4_1
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f59,f47]) ).
thf(f63,plain,
( spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f62]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f49]) ).
cnf(s5,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
~ spl4_3,
inference(rat,[],[s2,s3]) ).
cnf(s7,plain,
spl4_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s3,s7]) ).
thf(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU515^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.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 13:47:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.26 % (4017476)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (4017482)lrs+10_16_si=on:nwc=1.5:random_seed=4033212173:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.26 % (4017482) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4017476-4017482"...
% 0.21/0.26 % (4017482)...printing done.
% 0.21/0.26 % (4017482)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (4017482)------------------------------
% 0.21/0.26 % (4017482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (4017482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (4017482)CaDiCaL version: 2.1.3
% 0.21/0.26 % (4017482)Termination reason: Refutation
% 0.21/0.26 % (4017482)Time elapsed: 0.002 s
% 0.21/0.26 % (4017482)Peak memory usage: 13 MB
% 0.21/0.26 % (4017482)Instructions burned: 5 (million)
% 0.21/0.26 % (4017476)Success in time 0.031 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------