%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET014^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:23:31 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 254 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 242 ( 23 ~; 26 |; 10 &; 153 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 32 usr; 6 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 0 sgn 20 !; 6 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f12,axiom,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f22,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f23,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f33,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f34,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f39,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ X1 @ X2 )
& ( subset @ X0 @ X2 ) )
=> ( subset @ ( union @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X2 )
= $true ) )
=> ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f40]) ).
thf(f42,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( subset @ ( union @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
( ( $true
!= ( subset @ ( union @ sK0 @ sK1 ) @ sK2 ) )
& ( $true
= ( subset @ sK1 @ sK2 ) )
& ( $true
= ( subset @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f42]) ).
thf(f49,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f55,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f58,plain,
( $true
= ( subset @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f59,plain,
( $true
= ( subset @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f60,plain,
( $true
!= ( subset @ ( union @ sK0 @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f64,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK1 )
@ sK2 ) ),
inference(definition_unfolding,[],[f60,f55,f49]) ).
thf(f65,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f59,f55]) ).
thf(f66,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[],[f58,f55]) ).
thf(f67,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( ( sK1 @ X1 )
=> ( sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f76,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
=> ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
=> ( sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( $true
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f112,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f114,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f112]) ).
thf(f116,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f118,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f119,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f80,f116,f112]) ).
thf(f120,plain,
( ( $false = $true )
| ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f114,f70]) ).
thf(f123,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f127,plain,
( ( $false = $true )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f123,f78]) ).
thf(f128,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f129,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f131,plain,
( ( $false = $true )
| ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f118,f74]) ).
thf(f134,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f138,plain,
( ( $false = $true )
| ~ spl4_5 ),
inference(forward_demodulation,[],[f134,f78]) ).
thf(f139,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f140,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f139]) ).
cnf(s26,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f119]) ).
cnf(s30,plain,
~ spl4_4,
inference(sat_conversion,[],[f129]) ).
cnf(s36,plain,
~ spl4_5,
inference(sat_conversion,[],[f140]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s26,s36,s30]) ).
thf(f141,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:35:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.27 % (2654824)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (2654831)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1877686637:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (2654831) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2654824-2654831"...
% 0.19/0.27 % (2654830)% WARNING: option uhcvi not known.
% 0.19/0.27 % (2654831)...printing done.
% 0.19/0.27 % (2654831)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2654831)------------------------------
% 0.19/0.27 % (2654831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2654831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2654831)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2654831)Termination reason: Refutation
% 0.19/0.27 % (2654831)Time elapsed: 0.003 s
% 0.19/0.27 % (2654831)Peak memory usage: 13 MB
% 0.19/0.27 % (2654831)Instructions burned: 7 (million)
% 0.19/0.27 % (2654824)Success in time 0.037 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------