%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU586^2 : 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 : 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 08:30:12 AM UTC 2026
% Result : Theorem 0.12s 0.26s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 382 ( 114 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 379 ( 59 ~; 59 |; 31 &; 202 @)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 64 !; 14 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
binunionEcases: $o ).
thf(func_def_7,type,
sK1: $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i,X3: $o] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(f2,conjecture,
( binunionEcases
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f3,negated_conjecture,
~ ( binunionEcases
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( binunionEcases
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( binunionEcases = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i,X3: $o] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ X0 @ X2 )
=> X3 )
=> ( ( ( in @ X0 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X3: $o,X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
=> ( ( ( ( in @ X0 @ X2 )
= $true )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ! [X3: $o,X2: $i,X1: $i,X0: $i] :
( ( $true = X3 )
| ( ( $true
= ( in @ X0 @ X1 ) )
& ( $true != X3 ) )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true ) )
<=> ( binunionEcases = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i,X3: $o,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( ( $true
= ( in @ X0 @ X1 ) )
& ( $true != X3 ) ) )
<=> ( binunionEcases = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true ) )
& ( binunionEcases = $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( binunionEcases = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( ! [X0: $i,X3: $o,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( ( $true
= ( in @ X0 @ X1 ) )
& ( $true != X3 ) ) )
| ( binunionEcases != $true ) )
& ( ( binunionEcases = $true )
| ? [X0: $i,X3: $o,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
& ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X0 @ X2 )
!= $true ) )
& ( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true = X3 ) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( $true = X1 )
| ( ( $true != X1 )
& ( ( in @ X0 @ X3 )
= $true ) )
| ( ( ( in @ X0 @ X2 )
= $true )
& ( $true != X1 ) ) )
| ( binunionEcases != $true ) )
& ( ( binunionEcases = $true )
| ? [X4: $i,X5: $o,X6: $i,X7: $i] :
( ( ( in @ X4 @ ( binunion @ X7 @ X6 ) )
= $true )
& ( $true != X5 )
& ( ( $true = X5 )
| ( $true
!= ( in @ X4 @ X7 ) ) )
& ( ( ( in @ X4 @ X6 )
!= $true )
| ( $true = X5 ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( $true = X1 )
| ( ( $true != X1 )
& ( ( in @ X0 @ X3 )
= $true ) )
| ( ( ( in @ X0 @ X2 )
= $true )
& ( $true != X1 ) ) )
| ( binunionEcases != $true ) )
& ( ( binunionEcases = $true )
| ( ( $true
= ( in @ sK0 @ ( binunion @ sK3 @ sK2 ) ) )
& ( sK1 != $true )
& ( ( sK1 = $true )
| ( $true
!= ( in @ sK0 @ sK3 ) ) )
& ( ( $true
!= ( in @ sK0 @ sK2 ) )
| ( sK1 = $true ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f13]) ).
thf(f15,plain,
( ( $true
!= ( in @ sK6 @ sK4 ) )
& ( $true
= ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) ) )
& ( ( in @ sK6 @ sK5 )
!= $true )
& ( binunionEcases = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f11]) ).
thf(f21,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( $true = X1 )
| ( ( in @ X0 @ X3 )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( binunionEcases != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
binunionEcases = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
( ( in @ sK6 @ sK5 )
!= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f26,plain,
( $true
= ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( $true
!= ( in @ sK6 @ sK4 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( in @ X0 @ X3 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( $true = X1 )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(definition_unfolding,[],[f21,f24]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X3 )
= $true )
| ( $true = X1 )
| ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f44,definition,
( spl7_1
<=> ! [X2: $i,X0: $i,X3: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( ( in @ X0 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f45,plain,
( ! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X3 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X3 )
= $true ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f47,definition,
( spl7_2
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f48,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f49,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f41,f47,f44]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl7_2 ),
inference(constrained_superposition,[],[f25,f48]) ).
thf(f54,plain,
( $false
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f54]) ).
thf(f56,plain,
( ( $true != $true )
| ( $true
= ( in @ sK6 @ sK4 ) )
| ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f45,f26]) ).
thf(f57,plain,
( ( $true
= ( in @ sK6 @ sK4 ) )
| ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
( ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f57,f27]) ).
thf(f59,plain,
( $false
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f58,f25]) ).
thf(f60,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
~ spl7_2,
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
~ spl7_1,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU586^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n016.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 13:57:34 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.22 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
% 0.12/0.26 % (394730)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.26 % (394749)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1286129120:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.12/0.26 % (394749) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-394730-394749"...
% 0.12/0.26 % (394749)...printing done.
% 0.12/0.26 % (394750)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.12/0.26 % (394750)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.12/0.26 % (394749)Refutation found. Thanks to Tanya!
% 0.12/0.26 % SZS status Theorem for theBenchmark
% 0.12/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.26 % (394749)------------------------------
% 0.12/0.26 % (394749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.26 % (394749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.26 % (394749)CaDiCaL version: 2.1.3
% 0.12/0.26 % (394749)Termination reason: Refutation
% 0.12/0.26 % (394749)Time elapsed: 0.002 s
% 0.12/0.26 % (394749)Peak memory usage: 13 MB
% 0.12/0.26 % (394749)Instructions burned: 4 (million)
% 0.12/0.26 % (394730)Success in time 0.03 s
% 0.12/0.26 % Vampire exiting
%------------------------------------------------------------------------------