%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU589^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:30:12 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 96 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 388 ( 43 ~; 33 |; 21 &; 270 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 106 ( 38 ^; 53 !; 15 ?; 106 :)
% 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,
dsetconstrI: $o ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_18,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( $true
= ( X2 @ X0 ) )
=> ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
<=> ( dsetconstrI = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( dsetconstrI = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( $true
!= ( X2 @ X0 ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ! [X0: $i,X2: $i > $o,X1: $i] :
( ( $true
!= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( ! [X0: $i,X2: $i > $o,X1: $i] :
( ( $true
!= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X0: $i,X2: $i > $o,X1: $i] :
( ( $true
= ( X2 @ X0 ) )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X3 ) )
& ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
& ( ( in @ X3 @ X5 )
= $true ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( ( sK1 @ sK0 )
= $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
!= $true )
& ( ( in @ sK0 @ sK2 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true ) )
& ( dsetconstrI = $true ) ),
inference(rectify,[],[f12]) ).
thf(f19,plain,
( ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK5 @ sK4 )
= $true )
& ( $true
!= ( in @ sK5 @ ( binintersect @ sK4 @ sK3 ) ) )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f18]) ).
thf(f23,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f25,plain,
( $true
!= ( in @ sK5 @ ( binintersect @ sK4 @ sK3 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(definition_unfolding,[],[f23,f24]) ).
thf(f35,plain,
( ( in @ sK5
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK4
@ sK3 ) )
!= $true ),
inference(definition_unfolding,[],[f25,f28]) ).
thf(f36,plain,
( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ Y0 @ sK3 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( in @ X0 @ ( dsetconstr @ X2 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X0: $i > $o] :
( ( ( X0 @ sK5 )
!= $true )
| ( $true != $true )
| ( ( in @ sK5 @ ( dsetconstr @ sK4 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f38,f26]) ).
thf(f42,plain,
! [X0: $i > $o] :
( ( ( X0 @ sK5 )
!= $true )
| ( ( in @ sK5 @ ( dsetconstr @ sK4 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f67,plain,
! [X0: $i > $i] :
( ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( in @ ( X0 @ Y0 )
@ ( ^ [Y1: $i] : sK3
@ Y0 ) ) ) )
= $true )
| ( sK5
!= ( X0 @ sK5 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f42,f27]) ).
thf(f75,plain,
! [X0: $i > $i] :
( ( sK5
!= ( X0 @ sK5 ) )
| ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( in @ ( X0 @ Y0 )
@ ( ^ [Y1: $i] : sK3
@ Y0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f76,plain,
! [X0: $i > $i] :
( ( sK5
!= ( X0 @ sK5 ) )
| ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ ( X0 @ Y0 ) @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f196,plain,
( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( in
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ sK3 ) ) )
= $true ),
inference(equality_resolution,[],[f76]) ).
thf(f199,plain,
( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( in @ Y0 @ sK3 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f200,plain,
$false,
inference(forward_subsumption_resolution,[],[f199,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU589^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:54:05 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
% 0.08/0.23 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
% 0.18/0.27 % (1092546)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.27 % (1092556)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3306560600:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.27 % (1092557)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.27 % (1092557)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
% 0.18/0.27 % (1092556) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1092546-1092556"...
% 0.18/0.27 % (1092555)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2965862491:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.27 % (1092551)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3588770471:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.27 % (1092553)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2417758542:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.27 % (1092552)lrs+10_16_si=on:nwc=1.5:random_seed=1844159040:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.27 % (1092556)...printing done.
% 0.18/0.27 % (1092557)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=2922530919:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.27 % (1092554)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=2485423467: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)
% 0.18/0.27 % (1092556)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (1092556)------------------------------
% 0.18/0.27 % (1092556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (1092556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (1092556)CaDiCaL version: 2.1.3
% 0.18/0.27 % (1092556)Termination reason: Refutation
% 0.18/0.27 % (1092556)Time elapsed: 0.007 s
% 0.18/0.27 % (1092556)Peak memory usage: 12 MB
% 0.18/0.27 % (1092556)Instructions burned: 18 (million)
% 0.18/0.27 % (1092546)Success in time 0.035 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------