%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU618^2 : 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 : n008.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 08:30:21 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 434 ( 95 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 505 ( 66 ~; 58 |; 18 &; 340 @)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 22 ( 19 usr; 17 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 61 !; 14 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
setunionI: $o ).
thf(func_def_6,type,
secondinupair: $o ).
thf(f1,axiom,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(f2,axiom,
( secondinupair
= ( ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(f3,conjecture,
( setunionI
=> ( secondinupair
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(f4,negated_conjecture,
~ ( setunionI
=> ( secondinupair
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( setunionI
=> ( secondinupair
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( setunionI = $true )
=> ( ( secondinupair = $true )
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ! [X1: $i,X0: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
<=> ( secondinupair = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( setunionI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( $true
!= ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
& ( $true
= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ( ( $true
= ( in @ sK4 @ sK2 ) )
& ( ( in @ sK3 @ ( setunion @ sK2 ) )
!= $true )
& ( $true
= ( in @ sK3 @ sK4 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4)],[f17]) ).
thf(f19,plain,
( ( ! [X1: $i,X0: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X1: $i,X0: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ( ( in @ sK6 @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5),skolemize(X3,sK6)],[f20]) ).
thf(f22,plain,
setunionI = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
( $true
!= ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( setunionI != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
! [X0: $i,X1: $i] :
( ( secondinupair != $true )
| ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f33,definition,
( spl7_1
<=> ( $true
= ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f35,plain,
( ( $true
!= ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| spl7_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f36,plain,
~ spl7_1,
inference(avatar_split_clause,[],[f24,f33]) ).
thf(f38,definition,
( spl7_2
<=> ( setunionI = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f41,plain,
spl7_2,
inference(avatar_split_clause,[],[f22,f38]) ).
thf(f43,definition,
( spl7_3
<=> ( secondinupair = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f46,plain,
spl7_3,
inference(avatar_split_clause,[],[f23,f43]) ).
thf(f53,definition,
( spl7_5
<=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f54,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f55,plain,
( spl7_5
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f30,f43,f53]) ).
thf(f72,definition,
( spl7_9
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f73,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f74,plain,
( ~ spl7_2
| spl7_9 ),
inference(avatar_split_clause,[],[f28,f72,f38]) ).
thf(f77,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK0 @ X0 )
!= $true )
| ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true ) )
| spl7_1
| ~ spl7_9 ),
inference(superposition,[],[f35,f73]) ).
thf(f78,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( ( in @ sK0 @ X0 )
!= $true ) )
| spl7_1
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( ( $true
!= ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) )
| ( $true != $true )
| spl7_1
| ~ spl7_5
| ~ spl7_9 ),
inference(superposition,[],[f78,f54]) ).
thf(f80,plain,
( ( $true
!= ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) )
| spl7_1
| ~ spl7_5
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f81,plain,
( $false
| spl7_1
| ~ spl7_5
| ~ spl7_9 ),
inference(forward_subsumption_resolution,[],[f80,f54]) ).
thf(f82,plain,
( spl7_1
| ~ spl7_5
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s1,plain,
~ spl7_1,
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
spl7_2,
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
spl7_3,
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
( ~ spl7_3
| spl7_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s9,plain,
( ~ spl7_2
| spl7_9 ),
inference(sat_conversion,[],[f74]) ).
cnf(s10,plain,
( spl7_1
| ~ spl7_5
| ~ spl7_9 ),
inference(sat_conversion,[],[f82]) ).
cnf(s11,plain,
spl7_5,
inference(rat,[],[s5,s3]) ).
cnf(s12,plain,
spl7_9,
inference(rat,[],[s9,s2]) ).
cnf(s13,plain,
spl7_1,
inference(rat,[],[s10,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13]) ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU618^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:58:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (3198158)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3198175)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=1227833679: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)
% 0.22/0.29 % (3198173)lrs+10_16_si=on:nwc=1.5:random_seed=3563158444:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (3198172)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3379510063:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (3198174)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=178588735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (3198175) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3198158-3198175"...
% 0.22/0.29 % (3198174)Refutation not found, incomplete strategy
% 0.22/0.29 % (3198174)------------------------------
% 0.22/0.29 % (3198174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3198174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3198174)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3198174)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (3198174)Time elapsed: 0.002 s
% 0.22/0.29 % (3198174)Peak memory usage: 12 MB
% 0.22/0.29 % (3198174)Instructions burned: 2 (million)
% 0.22/0.29 % (3198175)...printing done.
% 0.22/0.29 % (3198172) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3198158-3198172"...
% 0.22/0.29 % (3198174)------------------------------
% 0.22/0.29 % (3198174)------------------------------
% 0.22/0.29 % (3198175)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3198175)------------------------------
% 0.22/0.29 % (3198175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3198175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3198175)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3198175)Termination reason: Refutation
% 0.22/0.29 % (3198175)Time elapsed: 0.005 s
% 0.22/0.29 % (3198175)Peak memory usage: 13 MB
% 0.22/0.29 % (3198175)Instructions burned: 6 (million)
% 0.22/0.29 % (3198158)Success in time 0.04 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------