%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU581^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:30:10 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 280 ( 33 ~; 24 |; 15 &; 194 @)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 84 ( 20 ^; 52 !; 12 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
powersetE1: $o ).
thf(func_def_6,type,
sepInPowerset: $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: $i > $o ).
thf(func_def_16,type,
sK5: $i > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(f2,axiom,
! [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) )
= sepInPowerset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(f3,conjecture,
( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(f4,negated_conjecture,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) )
= sepInPowerset ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ( sepInPowerset = $true )
<=> ! [X1: $i > $o,X0: $i] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( powersetE1 = $true )
=> ( ( sepInPowerset = $true )
=> ! [X0: $i,X1: $i > $o] :
( $true
= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( powersetE1 = $true )
& ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( sepInPowerset = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( powersetE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f14,plain,
( ( ( sepInPowerset = $true )
| ? [X1: $i > $o,X0: $i] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
!= $true ) )
& ( ! [X1: $i > $o,X0: $i] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
= $true )
| ( sepInPowerset != $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f15,plain,
( ( ( sepInPowerset = $true )
| ? [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
!= $true ) )
& ( ! [X2: $i > $o,X3: $i] :
( ( in
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( powerset @ X3 ) )
= $true )
| ( sepInPowerset != $true ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ( sepInPowerset = $true )
| ( ( in
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
@ ( powerset @ sK1 ) )
!= $true ) )
& ( ! [X2: $i > $o,X3: $i] :
( ( in
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( powerset @ X3 ) )
= $true )
| ( sepInPowerset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
thf(f17,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X3 @ X2 ) ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ( powersetE1 = $true )
| ( ( $true
= ( in @ sK3 @ ( powerset @ sK2 ) ) )
& ( $true
!= ( subset @ sK3 @ sK2 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X3 @ X2 ) ) )
| ( powersetE1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f18]) ).
thf(f20,plain,
( ( powersetE1 = $true )
& ( $true
!= ( subset
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) )
@ sK4 ) )
& ( sepInPowerset = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f12]) ).
thf(f21,plain,
! [X2: $i > $o,X3: $i] :
( ( ( in
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( powerset @ X3 ) )
= $true )
| ( sepInPowerset != $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X3 @ X2 ) )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
sepInPowerset = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( $true
!= ( subset
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) )
@ sK4 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
! [X2: $i > $o,X3: $i] :
( ( ( in
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( powerset @ X3 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f21,f26]) ).
thf(f35,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( $true
= ( subset @ X3 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f36,plain,
! [X2: $i > $o,X3: $i] :
( ( in
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( powerset @ X3 ) )
= $true ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f37,plain,
! [X2: $i > $o,X3: $i] :
( ( in @ ( dsetconstr @ X3 @ X2 ) @ ( powerset @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
( $true
!= ( subset @ ( dsetconstr @ sK4 @ sK5 ) @ sK4 ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f39,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f40,plain,
! [X0: $i,X1: $i > $o] :
( ( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f39,f37]) ).
thf(f41,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f42,plain,
$true != $true,
inference(constrained_superposition,[],[f38,f41]) ).
thf(f43,plain,
$false,
inference(trivial_inequality_removal,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU581^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n016.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:57:05 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.30 % (392977)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (392988)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (392988)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
% 0.22/0.30 % (392983)lrs+10_16_si=on:nwc=1.5:random_seed=3851491666:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (392984)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3363073912:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (392982)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=917617913:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (392985)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=3313131018: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)
% 0.22/0.30 % (392987)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3892418587:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (392988)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=2520266074:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (392986)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3991987809:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (392984)Refutation not found, incomplete strategy
% 0.22/0.30 % (392984)------------------------------
% 0.22/0.30 % (392984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (392984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (392984)CaDiCaL version: 2.1.3
% 0.22/0.30 % (392984)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (392984)Time elapsed: 0.002 s
% 0.22/0.30 % (392984)Peak memory usage: 12 MB
% 0.22/0.30 % (392984)Instructions burned: 1 (million)
% 0.22/0.30 % (392982) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392982"...
% 0.22/0.30 % (392987) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392987"...
% 0.22/0.30 % (392983) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392983"...
% 0.22/0.30 % (392985) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392985"...
% 0.22/0.30 % (392984)------------------------------
% 0.22/0.30 % (392984)------------------------------
% 0.22/0.30 % (392986) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392986"...
% 0.22/0.30 % (392982)...printing done.
% 0.22/0.30 % (392983)...printing done.
% 0.22/0.30 % (392987)...printing done.
% 0.22/0.30 % (392988) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-392977-392988"...
% 0.22/0.30 % (392985)...printing done.
% 0.22/0.30 % (392986)...printing done.
% 0.22/0.30 % (392982)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (392982)------------------------------
% 0.22/0.30 % (392982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (392982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (392982)CaDiCaL version: 2.1.3
% 0.22/0.30 % (392982)Termination reason: Refutation
% 0.22/0.30 % (392982)Time elapsed: 0.003 s
% 0.22/0.30 % (392982)Peak memory usage: 12 MB
% 0.22/0.30 % (392982)Instructions burned: 3 (million)
% 0.22/0.30 % (392977)Success in time 0.047 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------