%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU464^1 : 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 : 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 08:29:44 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 164 ( 22 ~; 13 |; 24 &; 97 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 4 con; 0-4 aty)
% Number of variables : 37 ( 0 ^; 25 !; 12 ?; 37 :)
% 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,
vNOT: $o > $o ).
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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(func_def_45,type,
sK1: $i > $i > $o ).
thf(f30,conjecture,
! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive4) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f84,plain,
~ ! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( ! [X4: $i > $i > $o] :
( ( ( trans @ X4 )
& ( subrel @ X0 @ X4 ) )
=> ( X4 @ X1 @ X2 ) )
& ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
inference(rectify,[],[f31]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o,X3: $i > $i > $o,X1: $i,X2: $i] :
( ( ( ( trans @ X3 )
= $true )
& ! [X4: $i > $i > $o] :
( ( ( ( trans @ X4 )
= $true )
& ( ( subrel @ X0 @ X4 )
= $true ) )
=> ( $true
= ( X4 @ X1 @ X2 ) ) )
& ( ( subrel @ X0 @ X3 )
= $true ) )
=> ( ( X3 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f84]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X3: $i > $i > $o,X1: $i,X2: $i] :
( ( ( X3 @ X1 @ X2 )
!= $true )
& ( ( trans @ X3 )
= $true )
& ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ X1 @ X2 ) )
| ( ( trans @ X4 )
!= $true )
| ( ( subrel @ X0 @ X4 )
!= $true ) )
& ( ( subrel @ X0 @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f85]) ).
thf(f89,plain,
? [X3: $i > $i > $o,X0: $i > $i > $o,X2: $i,X1: $i] :
( ( ( trans @ X3 )
= $true )
& ( ( subrel @ X0 @ X3 )
= $true )
& ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ X1 @ X2 ) )
| ( ( subrel @ X0 @ X4 )
!= $true )
| ( ( trans @ X4 )
!= $true ) )
& ( ( X3 @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( trans @ X0 )
= $true )
& ( ( subrel @ X1 @ X0 )
= $true )
& ! [X4: $i > $i > $o] :
( ( ( X4 @ X3 @ X2 )
= $true )
| ( ( subrel @ X1 @ X4 )
!= $true )
| ( ( trans @ X4 )
!= $true ) )
& ( ( X0 @ X3 @ X2 )
!= $true ) ),
inference(rectify,[],[f89]) ).
thf(f91,plain,
( ( ( trans @ sK0 )
= $true )
& ( ( subrel @ sK1 @ sK0 )
= $true )
& ! [X4: $i > $i > $o] :
( ( ( X4 @ sK3 @ sK2 )
= $true )
| ( $true
!= ( subrel @ sK1 @ X4 ) )
| ( ( trans @ X4 )
!= $true ) )
& ( $true
!= ( sK0 @ sK3 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f90]) ).
thf(f107,plain,
( $true
!= ( sK0 @ sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f108,plain,
! [X4: $i > $i > $o] :
( ( $true
!= ( subrel @ sK1 @ X4 ) )
| ( ( trans @ X4 )
!= $true )
| ( ( X4 @ sK3 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f109,plain,
( ( subrel @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f110,plain,
( ( trans @ sK0 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f129,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 @ sK2 ) )
| ( ( trans @ sK0 )
!= $true ) ),
inference(superposition,[],[f108,f109]) ).
thf(f130,plain,
( ( $true
= ( sK0 @ sK3 @ sK2 ) )
| ( ( trans @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
( ( trans @ sK0 )
!= $true ),
inference(forward_subsumption_resolution,[],[f130,f107]) ).
thf(f132,plain,
$false,
inference(forward_subsumption_resolution,[],[f131,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU464^1 : 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 : n002.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 13:44:38 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.28 % (1303433)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1303442)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2190313375:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1303442) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1303433-1303442"...
% 0.20/0.28 % (1303444)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (1303444)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
% 0.20/0.28 % (1303442)...printing done.
% 0.20/0.28 % (1303442)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1303442)------------------------------
% 0.20/0.28 % (1303442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1303442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1303442)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1303442)Termination reason: Refutation
% 0.20/0.28 % (1303442)Time elapsed: 0.003 s
% 0.20/0.28 % (1303442)Peak memory usage: 12 MB
% 0.20/0.28 % (1303442)Instructions burned: 10 (million)
% 0.20/0.28 % (1303433)Success in time 0.028 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------