%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU816^2 : 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 : 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 08:31:39 AM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 285 ( 80 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 225 ( 31 ~; 27 |; 22 &; 125 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 6 ^; 30 !; 6 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
binintTransitive: $o ).
thf(func_def_9,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_10,type,
wellorderedByIn: $i > $o ).
thf(func_def_11,type,
ordinal: $i > $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(f3,axiom,
( binintTransitive
= ( ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintTransitive) ).
thf(f6,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(f7,conjecture,
( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalMinLem1) ).
thf(f8,negated_conjecture,
~ ( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f13,plain,
~ ( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f14,plain,
~ ( ( binintTransitive = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f17,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f18,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f20,plain,
( binintTransitive
= ( ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( ( binintTransitive = $true )
<=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( ordinal @ X1 )
= $true ) ) )
& ( binintTransitive = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f23,plain,
( ( binintTransitive = $true )
<=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f24,plain,
( ( ( binintTransitive = $true )
| ? [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
& ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) ) ) )
& ( ! [X0: $i] :
( ( ( transitiveset @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X1 )
!= $true ) ) )
| ( binintTransitive != $true ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f25,plain,
( ( ( binintTransitive = $true )
| ? [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
& ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) ) ) )
& ( ! [X2: $i] :
( ( $true
!= ( transitiveset @ X2 ) )
| ! [X3: $i] :
( ( $true
= ( transitiveset @ ( binintersect @ X2 @ X3 ) ) )
| ( ( transitiveset @ X3 )
!= $true ) ) )
| ( binintTransitive != $true ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( ( binintTransitive = $true )
| ( ( $true
= ( transitiveset @ sK0 ) )
& ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( ( transitiveset @ sK1 )
= $true ) ) )
& ( ! [X2: $i] :
( ( $true
!= ( transitiveset @ X2 ) )
| ! [X3: $i] :
( ( $true
= ( transitiveset @ ( binintersect @ X2 @ X3 ) ) )
| ( ( transitiveset @ X3 )
!= $true ) ) )
| ( binintTransitive != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f25]) ).
thf(f27,plain,
( ( ( ordinal @ sK2 )
= $true )
& ( ( transitiveset @ ( binintersect @ sK2 @ sK3 ) )
!= $true )
& ( $true
= ( ordinal @ sK3 ) )
& ( binintTransitive = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f22]) ).
thf(f28,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( transitiveset @ ( binintersect @ X2 @ X3 ) ) )
| ( $true
!= ( transitiveset @ X2 ) )
| ( ( transitiveset @ X3 )
!= $true )
| ( binintTransitive != $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f36,plain,
binintTransitive = $true,
inference(cnf_transformation,[],[f27]) ).
thf(f37,plain,
( $true
= ( ordinal @ sK3 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
( ( transitiveset @ ( binintersect @ sK2 @ sK3 ) )
!= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
( ( ordinal @ sK2 )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f54,plain,
! [X1: $i] :
( ( ordinal @ X1 )
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f28]) ).
thf(f56,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) )
@ X1 ) )
| ( ( ordinal @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f54]) ).
thf(f57,plain,
! [X1: $i] :
( ( ( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f59,plain,
! [X1: $i] :
( ( ( ordinal @ X1 )
= $false )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f62,plain,
( ( ( transitiveset @ sK3 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f59,f37]) ).
thf(f65,plain,
( ( $false = $true )
| ( $true
= ( transitiveset @ sK2 ) ) ),
inference(superposition,[],[f39,f59]) ).
thf(f66,plain,
( ( transitiveset @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f67,plain,
( $true
= ( transitiveset @ sK2 ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f70,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( transitiveset @ ( binintersect @ X2 @ X3 ) ) )
| ( $true
!= ( transitiveset @ X2 ) )
| ( ( transitiveset @ X3 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f30,f36]) ).
thf(f71,plain,
( ( $true
!= ( transitiveset @ sK2 ) )
| ( $true != $true )
| ( ( transitiveset @ sK3 )
!= $true ) ),
inference(superposition,[],[f38,f70]) ).
thf(f72,plain,
( ( $true
!= ( transitiveset @ sK2 ) )
| ( ( transitiveset @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f73,plain,
( ( transitiveset @ sK3 )
!= $true ),
inference(forward_subsumption_resolution,[],[f72,f67]) ).
thf(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU816^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n001.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 14:39:51 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.35 % (1332694)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (1332704)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3717792749:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.35 % (1332703)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1747025395:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.35 % (1332705)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.35 % (1332705)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
% 0.25/0.35 % (1332703) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1332694-1332703"...
% 0.25/0.35 % (1332699)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=173355196:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.35 % (1332700)lrs+10_16_si=on:nwc=1.5:random_seed=2839955899:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (1332701)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1088959435:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.35 % (1332702)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=1560813234: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)
% 0.25/0.35 % (1332705)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=3250099709:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.35 % (1332703)...printing done.
% 0.25/0.35 % (1332703)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (1332703)------------------------------
% 0.25/0.35 % (1332703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (1332703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (1332703)CaDiCaL version: 2.1.3
% 0.25/0.35 % (1332703)Termination reason: Refutation
% 0.25/0.35 % (1332703)Time elapsed: 0.005 s
% 0.25/0.35 % (1332703)Peak memory usage: 12 MB
% 0.25/0.35 % (1332703)Instructions burned: 6 (million)
% 0.25/0.35 % (1332694)Success in time 0.039 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------