%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL609^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:14:27 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 25 unt; 0 typ; 5 def)
% Number of atoms : 209 ( 50 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 217 ( 21 ~; 20 |; 2 &; 148 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 39 usr; 9 con; 0-4 aty)
% ( 19 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 0 sgn 31 !; 1 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
sK0: individuals > $i > $o ).
thf(func_def_34,type,
sF1: individuals > $o ).
thf(func_def_35,type,
sF2: $o ).
thf(func_def_36,type,
sK3: individuals > $i ).
thf(func_def_38,type,
sK5: individuals ).
thf(f10,axiom,
( mall
= ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mall) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
! [X0: individuals > $i > $o] :
( ! [X1: individuals] : ( mvalid @ ( X0 @ X1 ) )
=> ( mvalid
@ ( mall
@ ^ [X1: individuals] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ! [X0: individuals > $i > $o] :
( ! [X1: individuals] : ( mvalid @ ( X0 @ X1 ) )
=> ( mvalid
@ ( mall
@ ^ [X1: individuals] : ( X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f21,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f22,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f28,plain,
~ ! [X0: individuals > $i > $o] :
( ! [X1: individuals] : ( mvalid @ ( X0 @ X1 ) )
=> ( mvalid
@ ( mall
@ ^ [X2: individuals] : ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f29,plain,
~ ! [X0: individuals > $i > $o] :
( ! [X1: individuals] :
( ( mvalid @ ( X0 @ X1 ) )
= $true )
=> ( $true
= ( mvalid
@ ( mall
@ ^ [Y0: individuals] : ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mall
= ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f31,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f46,plain,
? [X0: individuals > $i > $o] :
( ! [X1: individuals] :
( ( mvalid @ ( X0 @ X1 ) )
= $true )
& ( $true
!= ( mvalid
@ ( mall
@ ^ [Y0: individuals] : ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f47,plain,
( ! [X1: individuals] :
( ( mvalid @ ( sK0 @ X1 ) )
= $true )
& ( ( mvalid
@ ( mall
@ ^ [Y0: individuals] : ( sK0 @ Y0 ) ) )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f46]) ).
thf(f48,plain,
( ( mvalid
@ ( mall
@ ^ [Y0: individuals] : ( sK0 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f49,plain,
! [X1: individuals] :
( ( mvalid @ ( sK0 @ X1 ) )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f55,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f56,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f69,plain,
! [X1: individuals] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( sK0 @ X1 ) )
= $true ),
inference(definition_unfolding,[],[f49,f55]) ).
thf(f70,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: individuals] : ( sK0 @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f48,f55,f56]) ).
thf(f71,definition,
! [X1: individuals] :
( ( sF1 @ X1 )
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f72,plain,
! [X1: individuals] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( sK0 @ X1 ) )
= ( sF1 @ X1 ) ),
inference(reorient_equations,[],[f71]) ).
thf(f73,plain,
! [X1: individuals] :
( ( sF1 @ X1 )
= $true ),
inference(definition_folding,[],[f69,f72]) ).
thf(f74,definition,
( sF2
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: individuals] : ( sK0 @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f75,plain,
sF2 != $true,
inference(definition_folding,[],[f70,f74]) ).
thf(f76,plain,
! [X1: individuals] :
( ( $false
= ( sF1 @ X1 ) )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( sK0 @ X1 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f72]) ).
thf(f80,plain,
! [X1: individuals] :
( ( $false
= ( sF1 @ X1 ) )
| ( ( !! @ $i @ ( sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f81,plain,
! [X2: $i,X1: individuals] :
( ( $false
= ( sF1 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: individuals] : ( sK0 @ Y0 ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f74]) ).
thf(f89,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ individuals
@ ^ [Y1: individuals] : ( sK0 @ Y1 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f90,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( !! @ individuals
@ ^ [Y1: individuals] : ( sK0 @ Y1 @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( sF2 = $true )
| ( ( !! @ individuals
@ ^ [Y0: individuals] : ( sK0 @ Y0 @ sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
( ( $false
= ( ^ [Y0: individuals] : ( sK0 @ Y0 @ sK4 )
@ sK5 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f99,definition,
( spl6_2
<=> ! [X2: individuals,X1: $i] :
( ( sK0 @ X2 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f100,plain,
( ! [X2: individuals,X1: $i] :
( ( sK0 @ X2 @ X1 )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f103,definition,
( spl6_3
<=> ( ( sK0 @ sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f105,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f107,definition,
( spl6_4
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f110,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f93,f107,f103]) ).
thf(f111,plain,
~ spl6_4,
inference(avatar_split_clause,[],[f75,f107]) ).
thf(f125,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f105,f100]) ).
thf(f126,plain,
( $false
| ~ spl6_2
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f130,plain,
! [X2: $i,X1: individuals] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f81,f73]) ).
thf(f131,plain,
! [X2: $i,X1: individuals] :
( ( sK0 @ X1 @ X2 )
= $true ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f132,plain,
spl6_2,
inference(avatar_split_clause,[],[f131,f99]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s3,plain,
~ spl6_4,
inference(sat_conversion,[],[f111]) ).
cnf(s5,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
spl6_2,
inference(sat_conversion,[],[f132]) ).
cnf(s7,plain,
~ spl6_3,
inference(rat,[],[s5,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s3,s7]) ).
thf(f133,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL609^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 09:22:10 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.08/0.26 % (2905584)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (2905595)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.26 % (2905595)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
% 0.08/0.26 % (2905595)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=3069291002:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.26 % (2905595) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2905584-2905595"...
% 0.08/0.26 % (2905595)...printing done.
% 0.08/0.26 % (2905595)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (2905595)------------------------------
% 0.08/0.26 % (2905595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2905595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2905595)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2905595)Termination reason: Refutation
% 0.08/0.26 % (2905595)Time elapsed: 0.003 s
% 0.08/0.26 % (2905595)Peak memory usage: 13 MB
% 0.08/0.26 % (2905595)Instructions burned: 6 (million)
% 0.08/0.26 % (2905584)Success in time 0.028 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------