%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET657^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:23:27 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 35 unt; 0 typ; 2 def)
% Number of atoms : 196 ( 42 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 273 ( 10 ~; 28 |; 0 &; 200 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 54 usr; 7 con; 0-4 aty)
% ( 6 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 136 ( 20 sgn 6 !; 5 ?; 136 :)
% 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,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_17,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_18,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_20,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_22,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_29,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_30,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_31,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_32,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_33,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vIFF: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK0: $i > $i > $o ).
thf(func_def_53,type,
sF1: $o ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= union ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subset ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f28,axiom,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_codomain) ).
thf(f29,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= rel_domain ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(f33,axiom,
( rel_field
= ( ^ [X0: $i > $i > $o,X1: $i] :
( ( rel_domain @ X0 @ X1 )
| ( rel_codomain @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_field) ).
thf(f36,conjecture,
! [X0: $i > $i > $o] :
( subset @ ( rel_field @ X0 )
@ ( union
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( subset @ ( rel_field @ X0 )
@ ( union
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $true ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( rel_field
= ( ^ [X0: $i > $i > $o,X1: $i] :
( ( rel_domain @ X0 @ X1 )
| ( rel_codomain @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f41,plain,
( rel_field
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( rel_codomain @ Y0 @ Y1 )
| ( rel_domain @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o] :
( subset @ ( rel_field @ X0 )
@ ( union
@ ^ [X1: $i] : $true
@ ^ [X2: $i] : $true ) ),
inference(rectify,[],[f37]) ).
thf(f46,plain,
~ ! [X0: $i > $i > $o] :
( ( subset @ ( rel_field @ X0 )
@ ( union
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f52,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subset ),
inference(rectify,[],[f12]) ).
thf(f53,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= union ),
inference(rectify,[],[f6]) ).
thf(f81,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f95,plain,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f96,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f99,plain,
( ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= rel_domain ),
inference(rectify,[],[f29]) ).
thf(f100,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
? [X0: $i > $i > $o] :
( ( subset @ ( rel_field @ X0 )
@ ( union
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(ennf_transformation,[],[f46]) ).
thf(f102,plain,
( ( subset @ ( rel_field @ sK0 )
@ ( union
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f101]) ).
thf(f103,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f108,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f109,plain,
( rel_field
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( rel_codomain @ Y0 @ Y1 )
| ( rel_domain @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f114,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f120,plain,
( ( subset @ ( rel_field @ sK0 )
@ ( union
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f124,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f143,plain,
( rel_field
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f109,f108,f114]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ sK0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(definition_unfolding,[],[f120,f103,f143,f124]) ).
thf(f145,definition,
( sF1
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ sK0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f146,plain,
sF1 != $true,
inference(definition_folding,[],[f144,f145]) ).
thf(f147,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ Y0
@ Y1 )
| ( ^ [Y2: $i > $i > $o,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ sK0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f161,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
| ( ?? @ $i @ ( sK0 @ Y0 ) ) )
=> ( $true
| $true ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f162,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ( ( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
| ( ?? @ $i @ ( sK0 @ Y0 ) ) )
=> ( $true
| $true ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( sF1 = $true )
| ( ( ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK2 ) )
| ( ?? @ $i @ ( sK0 @ sK2 ) ) )
=> ( $true
| $true ) )
= $false ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( sF1 = $true )
| ( ( $true
| $true )
= $false ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f171,plain,
( ( $true = $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f172,plain,
sF1 = $true,
inference(trivial_inequality_removal,[],[f171]) ).
thf(f179,definition,
( spl5_2
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f187,plain,
spl5_2,
inference(avatar_split_clause,[],[f172,f179]) ).
thf(f188,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f146,f179]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f187]) ).
cnf(s4,plain,
~ spl5_2,
inference(sat_conversion,[],[f188]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
thf(f189,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET657^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.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 13:39:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.28 % (2126364)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2126375)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (2126375)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
% 0.21/0.28 % (2126375)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=374981500:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (2126375) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2126364-2126375"...
% 0.21/0.28 % (2126375)...printing done.
% 0.21/0.28 % (2126375)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2126375)------------------------------
% 0.21/0.28 % (2126375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2126375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2126375)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2126375)Termination reason: Refutation
% 0.21/0.28 % (2126375)Time elapsed: 0.003 s
% 0.21/0.28 % (2126375)Peak memory usage: 12 MB
% 0.21/0.28 % (2126375)Instructions burned: 10 (million)
% 0.21/0.28 % (2126364)Success in time 0.02 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------