%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:14:28 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 159 ( 9 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 157 ( 10 ~; 3 |; 0 &; 143 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 3 con; 0-4 aty)
% Number of variables : 9 ( 0 sgn 8 !; 1 ?; 9 :)
% 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,
r: $i > $i > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vAND: $o > $o > $o ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
sK0: $i > $o ).
thf(func_def_36,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_37,type,
sK3: ( $i > $o ) > $i ).
thf(f16,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gl) ).
thf(f17,conjecture,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',loeb) ).
thf(f18,negated_conjecture,
~ ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f19,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) ),
inference(rectify,[],[f16]) ).
thf(f20,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f25,plain,
~ ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) ),
inference(rectify,[],[f18]) ).
thf(f26,plain,
~ ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f49,plain,
? [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[],[f26]) ).
thf(f50,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) @ ( mbox @ r @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f49]) ).
thf(f53,plain,
( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) @ ( mbox @ r @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f59,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) @ ( mbox @ r @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f128,definition,
( spl1_12
<=> ( $true
= ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) @ ( mbox @ r @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
thf(f130,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) @ ( mbox @ r @ sK0 ) ) ) )
| spl1_12 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f131,plain,
~ spl1_12,
inference(avatar_split_clause,[],[f53,f128]) ).
thf(f168,plain,
( ( $true != $true )
| spl1_12 ),
inference(superposition,[],[f130,f59]) ).
thf(f169,plain,
( $false
| spl1_12 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
spl1_12,
inference(avatar_contradiction_clause,[],[f169]) ).
cnf(s12,plain,
~ spl1_12,
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
spl1_12,
inference(sat_conversion,[],[f170]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s12,s17]) ).
thf(f171,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL623^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n004.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 09:28:08 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.24/0.29 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
% 0.24/0.33 % (1056005)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.33 % (1056016)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4155468605:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.33 % (1056014)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=221773100: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)
% 0.24/0.33 % (1056014) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1056005-1056014"...
% 0.24/0.33 % (1056017)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.33 % (1056017)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
% 0.24/0.33 % (1056014)...printing done.
% 0.24/0.33 % (1056014)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.33 % (1056014)------------------------------
% 0.24/0.33 % (1056014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (1056014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (1056014)CaDiCaL version: 2.1.3
% 0.24/0.34 % (1056014)Termination reason: Refutation
% 0.24/0.34 % (1056014)Time elapsed: 0.006 s
% 0.24/0.34 % (1056014)Peak memory usage: 13 MB
% 0.24/0.34 % (1056014)Instructions burned: 7 (million)
% 0.24/0.34 % (1056005)Success in time 0.033 s
% 0.24/0.34 % Vampire exiting
%------------------------------------------------------------------------------