%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET651^3 : 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 : n011.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 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 223 ( 47 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 252 ( 8 ~; 4 |; 13 &; 184 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 54 usr; 6 con; 0-4 aty)
% ( 14 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 78 ^; 15 !; 3 ?; 96 :)
% 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,
a: $i > $o ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vIFF: $o > $o > $o ).
thf(func_def_53,type,
sK0: $i > $i > $o ).
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,axiom,
( cartesian_product
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',cartesian_product) ).
thf(f18,axiom,
( sub_rel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',sub_rel) ).
thf(f29,axiom,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(f36,conjecture,
! [X0: $i > $i > $o] :
( ( subset @ ( rel_domain @ X0 ) @ a )
=> ( sub_rel @ X0
@ ( cartesian_product @ a
@ ^ [X1: $i] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( subset @ ( rel_domain @ X0 ) @ a )
=> ( sub_rel @ X0
@ ( cartesian_product @ a
@ ^ [X1: $i] : $true ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f54,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f55,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f60,plain,
( cartesian_product
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f61,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y3 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f65,plain,
( sub_rel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f66,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f86,plain,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f29]) ).
thf(f87,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f99,plain,
~ ! [X0: $i > $i > $o] :
( ( subset @ ( rel_domain @ X0 ) @ a )
=> ( sub_rel @ X0
@ ( cartesian_product @ a
@ ^ [X1: $i] : $true ) ) ),
inference(rectify,[],[f37]) ).
thf(f100,plain,
~ ! [X0: $i > $i > $o] :
( ( ( subset @ ( rel_domain @ X0 ) @ a )
= $true )
=> ( $true
= ( sub_rel @ X0
@ ( cartesian_product @ a
@ ^ [Y0: $i] : $true ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
? [X0: $i > $i > $o] :
( ( $true
!= ( sub_rel @ X0
@ ( cartesian_product @ a
@ ^ [Y0: $i] : $true ) ) )
& ( ( subset @ ( rel_domain @ X0 ) @ a )
= $true ) ),
inference(ennf_transformation,[],[f100]) ).
thf(f102,plain,
( ( $true
!= ( sub_rel @ sK0
@ ( cartesian_product @ a
@ ^ [Y0: $i] : $true ) ) )
& ( $true
= ( subset @ ( rel_domain @ sK0 ) @ a ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f101]) ).
thf(f114,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f117,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y3 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f120,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f131,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f138,plain,
( $true
= ( subset @ ( rel_domain @ sK0 ) @ a ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f139,plain,
( $true
!= ( sub_rel @ sK0
@ ( cartesian_product @ a
@ ^ [Y0: $i] : $true ) ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f145,plain,
( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
@ sK0
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y3 ) )
@ a
@ ^ [Y0: $i] : $true ) ) ),
inference(definition_unfolding,[],[f139,f120,f117]) ).
thf(f146,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK0 )
@ a ) ),
inference(definition_unfolding,[],[f138,f114,f131]) ).
thf(f147,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( sK0 @ Y0 ) )
=> ( a @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i @ ( sK0 @ Y0 ) )
=> ( a @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i @ ( sK0 @ X1 ) )
=> ( a @ X1 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i @ ( sK0 @ X1 ) ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ( a @ Y1 )
& $true ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f153,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ( a @ Y1 )
& $true ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( ( a @ Y0 )
& $true ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( ( a @ Y0 )
& $true ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( $false
= ( ( sK0 @ sK2 @ sK1 )
=> ( ( a @ sK2 )
& $true ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( $false
= ( ( a @ sK2 )
& $true ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( $true
= ( sK0 @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( $false = $true )
| ( $false
= ( a @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( $false
= ( a @ sK2 ) ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f173,plain,
( ( $false = $true )
| ( $true
= ( a @ sK2 ) ) ),
inference(constrained_superposition,[],[f151,f158]) ).
thf(f174,plain,
( $true
= ( a @ sK2 ) ),
inference(trivial_inequality_removal,[],[f173]) ).
thf(f176,plain,
$false = $true,
inference(forward_demodulation,[],[f174,f160]) ).
thf(f177,plain,
$false,
inference(trivial_inequality_removal,[],[f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET651^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:40:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.19/0.28 % (108104)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (108110)% WARNING: option uhcvi not known.
% 0.19/0.28 % (108110)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3856985188:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (108110)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (108110)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (108112)dis+10_1_sil=32000:sp=arity:random_seed=2057324128:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (108110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-108104-108110"...
% 0.19/0.28 % (108109)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2743607389_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (108114)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2719098983:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (108110)...printing done.
% 0.19/0.28 % (108110)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (108110)------------------------------
% 0.19/0.28 % (108110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (108110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (108110)CaDiCaL version: 2.1.3
% 0.19/0.28 % (108110)Termination reason: Refutation
% 0.19/0.28 % (108110)Time elapsed: 0.007 s
% 0.19/0.28 % (108110)Peak memory usage: 12 MB
% 0.19/0.28 % (108110)Instructions burned: 10 (million)
% 0.19/0.28 % (108104)Success in time 0.039 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------