%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET670^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:23:47 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 256 ( 47 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 306 ( 18 ~; 12 |; 31 &; 207 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 7 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 0 sgn 30 !; 4 ?; 92 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $o ).
thf(func_def_53,type,
sK1: $i > $i > $o ).
thf(func_def_54,type,
sK2: $i > $o ).
thf(func_def_55,type,
sK3: $i > $o ).
thf(f19,axiom,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X3: $i,X4: $i] :
( ( X0 @ X3 @ X4 )
=> ( ( X2 @ X4 )
& ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',is_rel_on) ).
thf(f20,axiom,
( restrict_rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',restrict_rel_domain) ).
thf(f36,conjecture,
! [X0: $i > $o,X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ( is_rel_on @ X1 @ X2 @ X3 )
=> ( is_rel_on @ ( restrict_rel_domain @ X1 @ X0 ) @ X0 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ( is_rel_on @ X1 @ X2 @ X3 )
=> ( is_rel_on @ ( restrict_rel_domain @ X1 @ X0 ) @ X0 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f67,plain,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X3: $i,X4: $i] :
( ( X0 @ X3 @ X4 )
=> ( ( X2 @ X4 )
& ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f68,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y1 @ Y4 )
& ( Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
( restrict_rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f70,plain,
( restrict_rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f99,plain,
~ ! [X0: $i > $o,X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ( is_rel_on @ X1 @ X2 @ X3 )
=> ( is_rel_on @ ( restrict_rel_domain @ X1 @ X0 ) @ X0 @ X3 ) ),
inference(rectify,[],[f37]) ).
thf(f100,plain,
~ ! [X0: $i > $o,X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( is_rel_on @ X1 @ X2 @ X3 )
= $true )
=> ( ( is_rel_on @ ( restrict_rel_domain @ X1 @ X0 ) @ X0 @ X3 )
= $true ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
? [X0: $i > $o,X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( is_rel_on @ ( restrict_rel_domain @ X1 @ X0 ) @ X0 @ X3 )
!= $true )
& ( ( is_rel_on @ X1 @ X2 @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f100]) ).
thf(f102,plain,
( ( $true
!= ( is_rel_on @ ( restrict_rel_domain @ sK1 @ sK0 ) @ sK0 @ sK3 ) )
& ( $true
= ( is_rel_on @ sK1 @ sK2 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f101]) ).
thf(f121,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y1 @ Y4 )
& ( Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f122,plain,
( restrict_rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f138,plain,
( $true
= ( is_rel_on @ sK1 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f139,plain,
( $true
!= ( is_rel_on @ ( restrict_rel_domain @ sK1 @ sK0 ) @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f145,plain,
( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y1 @ Y4 )
& ( Y2 @ Y3 ) ) ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
@ sK1
@ sK0 )
@ sK0
@ sK3 ) ),
inference(definition_unfolding,[],[f139,f121,f122]) ).
thf(f146,plain,
( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y1 @ Y4 )
& ( Y2 @ Y3 ) ) ) ) )
@ sK1
@ sK2
@ sK3 ) ),
inference(definition_unfolding,[],[f138,f121]) ).
thf(f147,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
& ( sK3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
& ( sK3 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( ( sK2 @ Y0 )
& ( sK3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( ( sK2 @ Y0 )
& ( sK3 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK1 @ X2 @ X1 )
=> ( ( sK2 @ X2 )
& ( sK3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $true
= ( ( sK2 @ X2 )
& ( sK3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X2 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
& ( sK1 @ Y1 @ Y0 ) )
=> ( ( sK0 @ Y1 )
& ( sK3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
& ( sK1 @ Y1 @ Y0 ) )
=> ( ( sK0 @ Y1 )
& ( sK3 @ Y0 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 @ sK4 ) )
=> ( ( sK0 @ Y0 )
& ( sK3 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 @ sK4 ) )
=> ( ( sK0 @ Y0 )
& ( sK3 @ sK4 ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 @ sK4 ) )
=> ( ( sK0 @ sK5 )
& ( sK3 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( $false
= ( ( sK0 @ sK5 )
& ( sK3 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $true
= ( ( sK0 @ sK5 )
& ( sK1 @ sK5 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( $true
= ( sK1 @ sK5 @ sK4 ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $true
= ( sK0 @ sK5 ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( $false
= ( sK3 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f160]) ).
thf(f166,definition,
( spl6_1
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f168,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f170,definition,
( spl6_2
<=> ( $false
= ( sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f172,plain,
( ( $false
= ( sK3 @ sK4 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f173,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f164,f170,f166]) ).
thf(f188,plain,
( ( $false = $true )
| ( $true
= ( sK3 @ sK4 ) ) ),
inference(constrained_superposition,[],[f162,f153]) ).
thf(f193,plain,
( $true
= ( sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f198,plain,
( ( $false = $true )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f193,f172]) ).
thf(f199,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f198]) ).
thf(f200,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f199]) ).
thf(f202,plain,
( ( $false = $true )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f168,f163]) ).
thf(f206,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f207,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f206]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f173]) ).
cnf(s3,plain,
~ spl6_2,
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
~ spl6_1,
inference(sat_conversion,[],[f207]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f209,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET670^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:38:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.26 % (3372283)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (3372289)% WARNING: option uhcvi not known.
% 0.07/0.26 % (3372289)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1491518094:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (3372289)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % (3372289)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.26 % (3372289) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3372283-3372289"...
% 0.07/0.26 % (3372289)...printing done.
% 0.07/0.26 % (3372289)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (3372289)------------------------------
% 0.20/0.26 % (3372289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (3372289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (3372289)CaDiCaL version: 2.1.3
% 0.20/0.26 % (3372289)Termination reason: Refutation
% 0.20/0.26 % (3372289)Time elapsed: 0.004 s
% 0.20/0.26 % (3372289)Peak memory usage: 13 MB
% 0.20/0.26 % (3372289)Instructions burned: 12 (million)
% 0.20/0.26 % (3372283)Success in time 0.039 s
% 0.20/0.26 % Vampire exiting
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