%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 08:39:31 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 221 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 296 ( 34 ~; 42 |; 0 &; 217 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 62 ( 0 sgn 59 !; 3 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
vOR: $o > $o > $o ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
sK1: sK0 ).
thf(func_def_9,type,
sK2: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f2,axiom,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INSERT_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_SING_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( X1 = X2 ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= ( ( X1 = X2 )
| ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= ( X1 = X2 ) ),
inference(fool_elimination,[],[f4]) ).
thf(f10,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[],[f6]) ).
thf(f11,plain,
? [X0: $tType,X1: X0,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
!= ( X1 = X2 ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f12,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
!= ( sK1 = sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= ( ( X1 = X2 )
| ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
!= ( sK1 = sK2 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ( $true
= ( sK1 = sK2 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f19,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $false )
| ( ( sK1 = sK2 )
= $false ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f20,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $false )
| ( sK1 != sK2 ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ( sK1 = sK2 ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f22,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( ( X1 = X2 )
| ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f23,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $false )
| ( $true
= ( ( X1 = X2 )
| ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f24,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( $true
= ( X1 = X2 ) ) ),
inference(or_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f27,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( X1 = X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f28,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f30,definition,
( spl3_1
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f31,plain,
( ( sK1 = sK2 )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f34,definition,
( spl3_2
<=> ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f36,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f20,f34,f30]) ).
thf(f39,definition,
( spl3_3
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f21,f39,f30]) ).
thf(f58,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ( sK1 = sK2 )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f41,f25]) ).
thf(f60,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ( sK1 = sK2 )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f63,plain,
( ( sK1 = sK2 )
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f60,f13]) ).
thf(f69,plain,
( spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f63,f39,f30]) ).
thf(f71,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f36,f31]) ).
thf(f72,plain,
( ( $true = $false )
| ( sK1 != sK1 )
| ~ spl3_1
| ~ spl3_2 ),
inference(constrained_superposition,[],[f71,f28]) ).
thf(f78,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f79,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f78]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f69]) ).
cnf(s8,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f79]) ).
cnf(s9,plain,
spl3_1,
inference(rat,[],[s2,s5]) ).
cnf(s10,plain,
~ spl3_2,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
thf(f80,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:47:33 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26 % (3028395)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3028400)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3107679082_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % Exception at run slice level
% 0.09/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.26 % (3028401)% WARNING: option uhcvi not known.
% 0.09/0.26 % (3028401)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2142135639:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (3028402)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=986568730:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (3028403)dis+10_1_sil=32000:sp=arity:random_seed=413783939:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (3028404)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1955524514:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % (3028401)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % (3028405)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1400392196:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.26 % (3028406)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=722063465:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (3028401)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.26 % (3028404)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % (3028408)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=660378133:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.26 % Exception at run slice level
% 0.09/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.26 % (3028404) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3028395-3028404"...
% 0.09/0.26 % (3028403) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3028395-3028403"...
% 0.09/0.26 % (3028405) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3028395-3028405"...
% 0.09/0.26 % (3028401) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3028395-3028401"...
% 0.09/0.26 % (3028406) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3028395-3028406"...
% 0.09/0.26 % (3028403)...printing done.
% 0.09/0.26 % (3028404)...printing done.
% 0.09/0.26 % (3028405)...printing done.
% 0.09/0.26 % (3028401)...printing done.
% 0.09/0.26 % (3028406)...printing done.
% 0.09/0.26 % (3028403)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (3028403)------------------------------
% 0.18/0.26 % (3028403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (3028403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (3028403)CaDiCaL version: 2.1.3
% 0.18/0.26 % (3028403)Termination reason: Refutation
% 0.18/0.26 % (3028403)Time elapsed: 0.004 s
% 0.18/0.26 % (3028403)Peak memory usage: 12 MB
% 0.18/0.26 % (3028403)Instructions burned: 5 (million)
% 0.18/0.26 % (3028395)Success in time 0.044 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------