%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV451^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:38:39 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 220 ( 55 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 291 ( 26 ~; 26 |; 6 &; 230 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 70 ( 0 sgn 68 !; 2 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
sK1: sK0 > $o ).
thf(func_def_7,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
sK3: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(f2,axiom,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X3: X0,X2: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= 'const/sets/UNIV' )
@ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNION_UNIV_1') ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= 'const/sets/UNIV' )
@ X0 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f9,plain,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) )
| ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true ) )
<=> ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
!= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f15,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
thf(f19,plain,
! [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) ) )
& ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) )
| ( ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f20,plain,
! [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) ) )
& ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) )
| ( ( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) )
!= $true ) )
& ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f24,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f28,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f23]) ).
thf(f39,plain,
( ( 'const/sets/UNIV' @ sK0 @ sK3 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK3 ) ),
inference(negative_extensionality,[],[f24]) ).
thf(f41,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK3 ) )
| ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f39]) ).
thf(f43,definition,
( spl4_1
<=> ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f45,plain,
( ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f47,definition,
( spl4_2
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f49,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f50,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f41,f47,f43]) ).
thf(f61,plain,
! [X0: $tType,X1: X0] :
( ( $false = $true )
| ( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f22,f35]) ).
thf(f62,plain,
! [X0: $tType,X1: X0] :
( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f87,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ 'const/sets/UNIV' @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f28,f22]) ).
thf(f93,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ 'const/sets/UNIV' @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f96,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $false = $true )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ 'const/sets/UNIV' @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f93,f35]) ).
thf(f100,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ 'const/sets/UNIV' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f105,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f49,f100]) ).
thf(f108,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f109,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f108]) ).
thf(f114,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f45,f62]) ).
thf(f115,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f116,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f109]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f116]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s6]) ).
thf(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV451^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:48:32 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.29 % (950530)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (950535)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=296453167:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (950535) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-950530-950535"...
% 0.21/0.29 % (950535)...printing done.
% 0.21/0.29 % (950541)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (950541)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
% 0.21/0.29 % (950535)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (950535)------------------------------
% 0.21/0.29 % (950535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (950535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (950535)CaDiCaL version: 2.1.3
% 0.21/0.29 % (950535)Termination reason: Refutation
% 0.21/0.29 % (950535)Time elapsed: 0.003 s
% 0.21/0.29 % (950535)Peak memory usage: 13 MB
% 0.21/0.29 % (950535)Instructions burned: 9 (million)
% 0.21/0.29 % (950530)Success in time 0.034 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------