%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU602^2 : 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 : n015.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 08:30:16 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 215 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 251 ( 30 ~; 17 |; 12 &; 179 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 86 ( 29 ^; 45 !; 12 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrEL: $o ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vNOT: $o > $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_14,type,
sK3: $i > $o ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(f3,conjecture,
( dsetconstrEL
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X1 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
=> ( ( in @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( ( in @ X2 @ X1 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( dsetconstrEL = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ),
inference(rectify,[],[f11]) ).
thf(f14,plain,
( ( dsetconstrEL = $true )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK0 @ ( setminus @ sK2 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK5 @ sK4 ) )
& ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f16]) ).
thf(f18,plain,
( $true
= ( in @ sK0 @ ( setminus @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( in @ sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f24,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
( $true
= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK2
@ sK1 ) ) ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f28,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true != $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(definition_unfolding,[],[f24,f20]) ).
thf(f31,plain,
( $true
= ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f32,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f33,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
( ( ( in @ sK0 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f33,f31]) ).
thf(f35,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU602^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n015.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 14:00:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.19/0.28 % (3564502)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (3564509)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=202325405:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (3564509)Refutation not found, incomplete strategy
% 0.19/0.28 % (3564509)------------------------------
% 0.19/0.28 % (3564509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3564509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3564509)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3564509)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (3564509)Time elapsed: 0.001 s
% 0.19/0.28 % (3564509)Peak memory usage: 12 MB
% 0.19/0.28 % (3564509)Instructions burned: 1 (million)
% 0.19/0.28 % (3564509)------------------------------
% 0.19/0.28 % (3564509)------------------------------
% 0.19/0.28 % (3564513)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (3564513)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
% 0.19/0.28 % (3564507)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3390132861:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (3564511)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2333347576:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (3564508)lrs+10_16_si=on:nwc=1.5:random_seed=3752106000:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (3564510)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=4176712727: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)
% 0.19/0.28 % (3564512)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1342048208:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (3564513)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=230187550:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (3564507) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564507"...
% 0.19/0.28 % (3564508) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564508"...
% 0.19/0.28 % (3564511) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564511"...
% 0.19/0.28 % (3564512) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564512"...
% 0.19/0.28 % (3564510) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564510"...
% 0.19/0.28 % (3564507)...printing done.
% 0.19/0.28 % (3564515)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3390901296:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (3564508)...printing done.
% 0.19/0.28 % (3564511)...printing done.
% 0.19/0.28 % (3564512)...printing done.
% 0.19/0.28 % (3564513) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564502-3564513"...
% 0.19/0.28 % (3564507)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 % (3564507)------------------------------
% 0.19/0.28 % (3564507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3564507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3564507)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3564507)Termination reason: Refutation
% 0.19/0.28 % (3564507)Time elapsed: 0.003 s
% 0.19/0.28 % (3564507)Peak memory usage: 12 MB
% 0.19/0.28 % (3564507)Instructions burned: 3 (million)
% 0.19/0.28 % (3564502)Success in time 0.037 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------