%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU453^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:29:42 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 72 ( 9 ~; 8 |; 0 &; 51 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 4 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 32 ( 25 ^; 6 !; 1 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f6,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] : ( refl @ ( rc @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure_is_reflexive) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] : ( refl @ ( rc @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o] : ( refl @ ( rc @ X0 ) ),
inference(rectify,[],[f31]) ).
thf(f46,plain,
~ ! [X0: $i > $i > $o] :
( ( refl @ ( rc @ X0 ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f48,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f50,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
inference(rectify,[],[f6]) ).
thf(f51,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( refl @ ( rc @ X0 ) )
!= $true ),
inference(ennf_transformation,[],[f46]) ).
thf(f89,plain,
( ( refl @ ( rc @ sK0 ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f109,plain,
( ( refl @ ( rc @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f111,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f119,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f137,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f109,f111,f119]) ).
thf(f138,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( ( ^ [Y0: $i] :
( ( Y0 = Y0 )
| ( sK0 @ Y0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( ( sK1 = sK1 )
| ( sK0 @ sK1 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f142,plain,
( $false
= ( sK1 = sK1 ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f143,plain,
sK1 != sK1,
inference(equality_proxy_clausification,[],[f142]) ).
thf(f144,plain,
$false,
inference(trivial_inequality_removal,[],[f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU453^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n002.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 13:44:07 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.26/0.29 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
% 0.26/0.33 % (1302302)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.33 % (1302312)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2480958567:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.33 % (1302307)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=853440718:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.33 % (1302312) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1302302-1302312"...
% 0.26/0.33 % (1302312)...printing done.
% 0.26/0.33 % (1302312)Refutation found. Thanks to Tanya!
% 0.26/0.33 % SZS status Theorem for theBenchmark
% 0.26/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.33 % (1302312)------------------------------
% 0.26/0.33 % (1302312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1302312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1302312)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1302312)Termination reason: Refutation
% 0.26/0.33 % (1302312)Time elapsed: 0.006 s
% 0.26/0.33 % (1302312)Peak memory usage: 12 MB
% 0.26/0.33 % (1302312)Instructions burned: 11 (million)
% 0.26/0.33 % (1302302)Success in time 0.031 s
% 0.26/0.33 % Vampire exiting
%------------------------------------------------------------------------------