%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU457^1 : 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 : 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 08:29:43 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 28 unt; 0 typ; 2 def)
% Number of atoms : 183 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 208 ( 18 ~; 26 |; 0 &; 142 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 47 usr; 7 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 41 ( 0 sgn 8 !; 1 ?; 41 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f9,axiom,
( symm
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',symmetric) ).
thf(f12,axiom,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] : ( symm @ ( sc @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure_is_symmetric) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] : ( symm @ ( sc @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f63,plain,
( symm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f64,plain,
( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f68,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f77,plain,
~ ! [X0: $i > $i > $o] : ( symm @ ( sc @ X0 ) ),
inference(rectify,[],[f31]) ).
thf(f78,plain,
~ ! [X0: $i > $i > $o] :
( ( symm @ ( sc @ X0 ) )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( symm @ ( sc @ X0 ) )
!= $true ),
inference(ennf_transformation,[],[f78]) ).
thf(f89,plain,
( ( symm @ ( sc @ sK0 ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f98,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f102,plain,
( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f113,plain,
( ( symm @ ( sc @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f137,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f113,f102,f98]) ).
thf(f138,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK1 @ Y0 )
| ( sK0 @ Y0 @ sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
| ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK1 @ Y0 )
| ( sK0 @ Y0 @ sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
| ( sK0 @ sK1 @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ( ( sK0 @ sK1 @ sK2 )
| ( sK0 @ sK2 @ sK1 ) )
=> ( ( sK0 @ sK2 @ sK1 )
| ( sK0 @ sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $false
= ( ( sK0 @ sK2 @ sK1 )
| ( sK0 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $true
= ( ( sK0 @ sK1 @ sK2 )
| ( sK0 @ sK2 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( $true
= ( sK0 @ sK2 @ sK1 ) )
| ( ( sK0 @ sK1 @ sK2 )
= $true ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( sK0 @ sK1 @ sK2 )
= $false ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f147,plain,
( $false
= ( sK0 @ sK2 @ sK1 ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f149,definition,
( spl3_1
<=> ( $true
= ( sK0 @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f151,plain,
( ( $true
= ( sK0 @ sK2 @ sK1 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f153,definition,
( spl3_2
<=> ( ( sK0 @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f155,plain,
( ( ( sK0 @ sK1 @ sK2 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f156,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f145,f153,f149]) ).
thf(f157,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f155,f146]) ).
thf(f158,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f159,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f158]) ).
thf(f161,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f151,f147]) ).
thf(f162,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f162]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f156]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f159]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f163]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f164,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU457^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:46:35 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.27 % (369751)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (369763)lrs+10_16_si=on:nwc=1.5:random_seed=1141976330:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.27 % (369763) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-369751-369763"...
% 0.22/0.27 % (369763)...printing done.
% 0.22/0.27 % (369769)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (369769)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
% 0.22/0.27 % (369763)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (369763)------------------------------
% 0.22/0.27 % (369763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (369763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (369763)CaDiCaL version: 2.1.3
% 0.22/0.27 % (369763)Termination reason: Refutation
% 0.22/0.27 % (369763)Time elapsed: 0.003 s
% 0.22/0.27 % (369763)Peak memory usage: 12 MB
% 0.22/0.27 % (369763)Instructions burned: 11 (million)
% 0.22/0.27 % (369751)Success in time 0.02 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------