%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET683^3 : 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 : n004.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 08:23:28 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 216 ( 58 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 287 ( 16 ~; 9 |; 24 &; 198 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 55 usr; 6 con; 0-4 aty)
% ( 10 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 55 ^; 40 !; 16 ?; 111 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $i > $o ).
thf(func_def_53,type,
sK1: $i > $o ).
thf(func_def_54,type,
sK2: $i > $o ).
thf(f19,axiom,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X4: $i,X3: $i] :
( ( X0 @ X3 @ X4 )
=> ( ( X1 @ X3 )
& ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',is_rel_on) ).
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(f36,conjecture,
! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( is_rel_on @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X2 @ X3 )
=> ( ( rel_codomain @ X0 @ X3 )
=> ? [X4: $i] :
( ( X1 @ X4 )
& ( rel_domain @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( is_rel_on @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X2 @ X3 )
=> ( ( rel_codomain @ X0 @ X3 )
=> ? [X4: $i] :
( ( X1 @ X4 )
& ( rel_domain @ X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f62,plain,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X3: $i,X4: $i] :
( ( X0 @ X4 @ X3 )
=> ( ( X1 @ X4 )
& ( X2 @ X3 ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f63,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
=> ( ( Y2 @ Y4 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f72,plain,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f73,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f95,plain,
( ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= rel_domain ),
inference(rectify,[],[f29]) ).
thf(f96,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( is_rel_on @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X2 @ X3 )
=> ( ( rel_codomain @ X0 @ X3 )
=> ? [X4: $i] :
( ( X1 @ X4 )
& ( rel_domain @ X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f98,plain,
~ ! [X1: $i > $o,X0: $i > $i > $o,X2: $i > $o] :
( ( ( is_rel_on @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ( ( ( rel_codomain @ X0 @ X3 )
= $true )
=> ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( rel_domain @ X0 @ X4 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f101,plain,
? [X1: $i > $o,X0: $i > $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( rel_domain @ X0 @ X4 )
!= $true ) )
& ( ( rel_codomain @ X0 @ X3 )
= $true )
& ( ( X2 @ X3 )
= $true ) )
& ( ( is_rel_on @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f98]) ).
thf(f102,plain,
? [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( ( is_rel_on @ X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( X2 @ X3 )
= $true )
& ( ( rel_codomain @ X0 @ X3 )
= $true )
& ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( rel_domain @ X0 @ X4 )
!= $true ) ) ) ),
inference(flattening,[],[f101]) ).
thf(f103,plain,
( ( ( is_rel_on @ sK0 @ sK1 @ sK2 )
= $true )
& ( ( sK2 @ sK3 )
= $true )
& ( ( rel_codomain @ sK0 @ sK3 )
= $true )
& ! [X4: $i] :
( ( ( sK1 @ X4 )
!= $true )
| ( ( rel_domain @ sK0 @ X4 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f102]) ).
thf(f115,plain,
! [X4: $i] :
( ( ( sK1 @ X4 )
!= $true )
| ( ( rel_domain @ sK0 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f116,plain,
( ( rel_codomain @ sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f118,plain,
( ( is_rel_on @ sK0 @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f125,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f127,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f136,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
=> ( ( Y2 @ Y4 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
=> ( ( Y2 @ Y4 )
& ( Y1 @ Y3 ) ) ) ) )
@ sK0
@ sK1
@ sK2 )
= $true ),
inference(definition_unfolding,[],[f118,f136]) ).
thf(f149,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ sK0
@ sK3 )
= $true ),
inference(definition_unfolding,[],[f116,f125]) ).
thf(f150,plain,
! [X4: $i] :
( ( ( sK1 @ X4 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK0
@ X4 )
!= $true ) ),
inference(definition_unfolding,[],[f115,f127]) ).
thf(f151,plain,
( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK3 ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f152,plain,
( ( ^ [Y0: $i] : ( sK0 @ Y0 @ sK3 )
@ sK4 )
= $true ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( sK0 @ sK4 @ sK3 )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X4: $i] :
( ( ( sK1 @ X4 )
!= $true )
| ( $true
!= ( ?? @ $i @ ( sK0 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f155,plain,
! [X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $false )
| ( ( sK1 @ X4 )
!= $true ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
& ( sK1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f157,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( ( sK2 @ Y1 )
& ( sK1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK2 @ Y0 )
& ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( ( sK2 @ Y0 )
& ( sK1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
=> ( ( sK2 @ X2 )
& ( sK1 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( ( sK2 @ X2 )
& ( sK1 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( sK0 @ X1 @ X2 )
= $false ),
inference(forward_subsumption_resolution,[],[f162,f155]) ).
thf(f165,plain,
$true = $false,
inference(constrained_superposition,[],[f164,f153]) ).
thf(f167,plain,
$false,
inference(trivial_inequality_removal,[],[f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET683^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.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 13:40:38 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (1299970)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1299975)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4048180725:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1299975) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1299970-1299975"...
% 0.20/0.28 % (1299975)...printing done.
% 0.20/0.28 % (1299975)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1299975)------------------------------
% 0.20/0.28 % (1299975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1299975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1299975)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1299975)Termination reason: Refutation
% 0.20/0.28 % (1299975)Time elapsed: 0.003 s
% 0.20/0.28 % (1299975)Peak memory usage: 12 MB
% 0.20/0.28 % (1299975)Instructions burned: 11 (million)
% 0.20/0.28 % (1299970)Success in time 0.041 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------