%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV450^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 0.36s 0.26s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 280 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 317 ( 38 ~; 60 |; 0 &; 215 @)
% ( 4 <=>; 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 : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 64 !; 2 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK1: sK0 > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK3: sK0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK6:
!>[X0: $tType] : ( X0 > ( X0 > sK0 > $o ) > sK0 ) ).
thf(func_def_18,type,
sK7:
!>[X0: $tType] : ( X0 > ( X0 > sK0 > $o ) > sK0 ) ).
thf(func_def_19,type,
sK8:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_20,type,
sK9:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > X0 > sK0 ) ).
thf(func_def_21,type,
sK10:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_22,type,
sK11:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( '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/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f9,plain,
? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
( sK1
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f12,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( sK1
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f36,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f11]) ).
thf(f37,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f11]) ).
thf(f38,plain,
( ( sK1 @ sK3 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f39,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f38]) ).
thf(f42,definition,
( spl4_1
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f44,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f46,definition,
( spl4_2
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f48,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f40,f46,f42]) ).
thf(f51,definition,
( spl4_3
<=> ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f55,definition,
( spl4_4
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f39,f55,f51]) ).
thf(f84,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $false
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f36,f33]) ).
thf(f85,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $false
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f112,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(constrained_superposition,[],[f37,f34]) ).
thf(f115,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f217,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f53,f85]) ).
thf(f220,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(duplicate_literal_removal,[],[f217]) ).
thf(f221,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f229,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f221,f37]) ).
thf(f238,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f245,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f238,f48]) ).
thf(f246,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f247,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f267,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f48,f57]) ).
thf(f279,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f280,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f279]) ).
thf(f804,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f44,f115]) ).
thf(f809,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f804]) ).
thf(f843,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f36,f809]) ).
thf(f856,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f843]) ).
thf(f868,plain,
( spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f856,f42,f46]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f247]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f280]) ).
cnf(s11,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f868]) ).
cnf(s13,plain,
~ spl4_2,
inference(rat,[],[s2,s4,s10]) ).
cnf(s14,plain,
~ spl4_1,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s14]) ).
thf(f869,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV450^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:48:15 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.26 % (1832611)Will run a generic schedule for satisfiability detection.
% 0.36/0.26 % (1832620)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3069860470:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.26 % (1832620)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.36/0.26 % (1832617)% WARNING: option uhcvi not known.
% 0.36/0.26 % (1832616)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4139030767_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.26 % (1832618)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1141028657:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.26 % (1832619)dis+10_1_sil=32000:sp=arity:random_seed=1884752722:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.26 % (1832621)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1425695539:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.26 % (1832622)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=836573590:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.26 % Exception at run slice level
% 0.36/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.36/0.26 % (1832617)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=632984650:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.26 % (1832617)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.36/0.26 % (1832617)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.36/0.26 % (1832620) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1832611-1832620"...
% 0.36/0.26 % (1832630)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2859784816:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.36/0.26 % (1832620)...printing done.
% 0.36/0.26 % Exception at run slice level
% 0.36/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.36/0.26 % (1832620)Refutation found. Thanks to Tanya!
% 0.36/0.26 % SZS status Theorem for theBenchmark
% 0.36/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.26 % (1832620)------------------------------
% 0.36/0.26 % (1832620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.26 % (1832620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.26 % (1832620)CaDiCaL version: 2.1.3
% 0.36/0.26 % (1832620)Termination reason: Refutation
% 0.36/0.26 % (1832620)Time elapsed: 0.029 s
% 0.36/0.26 % (1832620)Peak memory usage: 13 MB
% 0.36/0.26 % (1832620)Instructions burned: 99 (million)
% 0.36/0.26 % (1832611)Success in time 0.053 s
% 0.36/0.26 % Vampire exiting
%------------------------------------------------------------------------------