%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO899^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:48:36 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 44 unt; 0 typ; 2 def)
% Number of atoms : 337 ( 64 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 397 ( 19 ~; 22 |; 15 &; 283 @)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 8 con; 0-4 aty)
% ( 13 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 94 ( 0 sgn 17 !; 2 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
sK0: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f16,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f19,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f23,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f24,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f28,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f30,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(flattening,[],[f28]) ).
thf(f32,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f34,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f37,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f40,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f44,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f32,f34,f36,f35,f36,f40,f36,f40,f35]) ).
thf(f45,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK0 )
= $true ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( ( mrel @ mactual @ sK0 )
& ( ( p @ sK0 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
( $true
= ( ( p @ sK0 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( mrel @ mactual @ sK0 )
= $true ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( $false
= ( p @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( p @ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK0 @ X1 )
=> ( q @ X1 ) )
= $true )
| ( $false
= ( p @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
= $false )
| ( $false
= ( p @ sK0 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f57,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f58,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f62,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( q @ X1 ) ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f65,definition,
( spl1_1
<=> ! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f66,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,definition,
( spl1_2
<=> ( $false
= ( p @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f69,plain,
( ( $false
= ( p @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f70,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f55,f68,f65]) ).
thf(f72,plain,
( ( ( p @ sK0 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f60,f51]) ).
thf(f78,plain,
( ( p @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f82,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f78,f69]) ).
thf(f83,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f84,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f83]) ).
thf(f86,plain,
( ( $false
= ( q @ sK0 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f63,f51]) ).
thf(f90,plain,
( $false
= ( q @ sK0 ) ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f94,plain,
( ( ( q @ sK0 )
= $true )
| ( $false = $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f37,f66]) ).
thf(f96,plain,
( ( ( q @ sK0 )
= $true )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f100,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f96,f90]) ).
thf(f101,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f101]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
~ spl1_1,
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f103,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO899^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n011.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:26:31 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.23/0.29 % (394436)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (394446)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2066082558:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (394446) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-394436-394446"...
% 0.23/0.29 % (394446)...printing done.
% 0.23/0.29 % (394447)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (394447)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
% 0.23/0.29 % (394446)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (394446)------------------------------
% 0.23/0.29 % (394446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (394446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (394446)CaDiCaL version: 2.1.3
% 0.23/0.29 % (394446)Termination reason: Refutation
% 0.23/0.29 % (394446)Time elapsed: 0.003 s
% 0.23/0.29 % (394446)Peak memory usage: 13 MB
% 0.23/0.29 % (394446)Instructions burned: 8 (million)
% 0.23/0.29 % (394436)Success in time 0.04 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------