%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET646^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:23:26 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 43 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 149 ( 8 ~; 10 |; 11 &; 100 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 7 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 74 ^; 12 !; 2 ?; 88 :)
% 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_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(f15,axiom,
( cartesian_product
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',cartesian_product) ).
thf(f16,axiom,
( pair_rel
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X0 )
| ( X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',pair_rel) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X3: $i,X2: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= sub_rel ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',sub_rel) ).
thf(f36,conjecture,
! [X0: $i,X1: $i] :
( sub_rel @ ( pair_rel @ X0 @ X1 )
@ ( cartesian_product
@ ^ [X0: $i] : $true
@ ^ [X0: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( sub_rel @ ( pair_rel @ X0 @ X1 )
@ ( cartesian_product
@ ^ [X0: $i] : $true
@ ^ [X0: $i] : $true ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f62,plain,
~ ! [X0: $i,X1: $i] :
( sub_rel @ ( pair_rel @ X0 @ X1 )
@ ( cartesian_product
@ ^ [X2: $i] : $true
@ ^ [X3: $i] : $true ) ),
inference(rectify,[],[f37]) ).
thf(f63,plain,
~ ! [X0: $i,X1: $i] :
( $true
= ( sub_rel @ ( pair_rel @ X0 @ X1 )
@ ( cartesian_product
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f68,plain,
( cartesian_product
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f69,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f72,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) )
= sub_rel ),
inference(rectify,[],[f18]) ).
thf(f73,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f86,plain,
( pair_rel
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y1 = Y3 )
| ( Y0 = Y2 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f101,plain,
? [X0: $i,X1: $i] :
( $true
!= ( sub_rel @ ( pair_rel @ X0 @ X1 )
@ ( cartesian_product
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) ) ),
inference(ennf_transformation,[],[f63]) ).
thf(f102,plain,
( ( sub_rel @ ( pair_rel @ sK0 @ sK1 )
@ ( cartesian_product
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f101]) ).
thf(f106,plain,
( pair_rel
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y1 = Y3 )
| ( Y0 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f119,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f129,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f130,plain,
( ( sub_rel @ ( pair_rel @ sK0 @ sK1 )
@ ( cartesian_product
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y1 = Y3 )
| ( Y0 = Y2 ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) )
@ ^ [Y0: $i] : $true
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(definition_unfolding,[],[f130,f129,f106,f119]) ).
thf(f145,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 = Y1 )
| ( sK0 = Y0 ) )
=> ( $true
& $true ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 = Y1 )
| ( sK0 = Y0 ) )
=> ( $true
& $true ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
| ( sK0 = sK2 ) )
=> ( $true
& $true ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK1 = Y0 )
| ( sK0 = sK2 ) )
=> ( $true
& $true ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( ( ( sK1 = sK3 )
| ( sK0 = sK2 ) )
=> ( $true
& $true ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
( ( $true
& $true )
= $false ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f155,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f156,plain,
$false = $true,
inference(duplicate_literal_removal,[],[f155]) ).
thf(f157,plain,
$false,
inference(trivial_inequality_removal,[],[f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:46:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.30 % (1260119)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (1260128)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1866974033:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (1260130)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (1260130)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
% 0.21/0.30 % (1260125)lrs+10_16_si=on:nwc=1.5:random_seed=3409834062:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (1260127)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3532109117:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.30 % (1260126)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3388251510:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (1260128)Instruction limit reached!
% 0.21/0.30 % (1260128)------------------------------
% 0.21/0.30 % (1260128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1260128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1260128)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1260128)Termination reason: Instruction limit
% 0.21/0.30 % (1260128)Termination phase: Saturation
% 0.21/0.30 % (1260128)Time elapsed: 0.008 s
% 0.21/0.30 % (1260128)Peak memory usage: 12 MB
% 0.21/0.30 % (1260128)Instructions burned: 26 (million)
% 0.21/0.30 % (1260126)Instruction limit reached!
% 0.21/0.30 % (1260126)------------------------------
% 0.21/0.30 % (1260126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1260126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1260126)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1260126)Termination reason: Instruction limit
% 0.21/0.30 % (1260126)Termination phase: Property scanning
% 0.21/0.30 % (1260126)Time elapsed: 0.002 s
% 0.21/0.30 % (1260126)Peak memory usage: 10 MB
% 0.21/0.30 % (1260126)Instructions burned: 4 (million)
% 0.21/0.30 % (1260130)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=4028293570:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (1260124)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3186762009:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (1260125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1260119-1260125"...
% 0.21/0.30 % (1260125)...printing done.
% 0.21/0.30 % (1260125)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1260125)------------------------------
% 0.21/0.30 % (1260125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1260125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1260125)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1260125)Termination reason: Refutation
% 0.21/0.30 % (1260125)Time elapsed: 0.005 s
% 0.21/0.30 % (1260125)Peak memory usage: 12 MB
% 0.21/0.30 % (1260125)Instructions burned: 9 (million)
% 0.21/0.30 % (1260119)Success in time 0.048 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------