%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:23:12 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 52 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 52 ( 7 ~; 0 |; 0 &; 44 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 4 con; 0-4 aty)
% Number of variables : 11 ( 0 sgn 0 !; 0 ?; 11 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_19,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_20,type,
inductive: $i > mworld > $o ).
thf(func_def_21,type,
disjoint: $i > $i > mworld > $o ).
thf(func_def_22,type,
function: $i > mworld > $o ).
thf(func_def_23,type,
member: $i > $i > mworld > $o ).
thf(func_def_24,type,
subclass: $i > $i > mworld > $o ).
thf(func_def_25,type,
singleton: $i > $i ).
thf(func_def_26,type,
image: $i > $i > $i ).
thf(func_def_27,type,
inverse: $i > $i ).
thf(func_def_28,type,
rotate: $i > $i ).
thf(func_def_29,type,
unordered_pair: $i > $i > $i ).
thf(func_def_30,type,
successor: $i > $i ).
thf(func_def_31,type,
apply: $i > $i > $i ).
thf(func_def_32,type,
power_class: $i > $i ).
thf(func_def_33,type,
range_of: $i > $i ).
thf(func_def_34,type,
union: $i > $i > $i ).
thf(func_def_35,type,
restrict: $i > $i > $i > $i ).
thf(func_def_36,type,
second: $i > $i ).
thf(func_def_37,type,
ordered_pair: $i > $i > $i ).
thf(func_def_38,type,
domain_of: $i > $i ).
thf(func_def_39,type,
sum_class: $i > $i ).
thf(func_def_40,type,
compose: $i > $i > $i ).
thf(func_def_41,type,
intersection: $i > $i > $i ).
thf(func_def_42,type,
cross_product: $i > $i > $i ).
thf(func_def_43,type,
complement: $i > $i ).
thf(func_def_44,type,
flip: $i > $i ).
thf(func_def_45,type,
first: $i > $i ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vAND: $o > $o > $o ).
thf(func_def_58,type,
vIFF: $o > $o > $o ).
thf(func_def_59,type,
vOR: $o > $o > $o ).
thf(func_def_60,type,
sK0: mworld > $i ).
thf(f13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(f96,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_0) ).
thf(f97,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
thf(f146,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(rectify,[],[f97]) ).
thf(f147,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
!= $true ),
inference(fool_elimination,[],[f146]) ).
thf(f281,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(rectify,[],[f13]) ).
thf(f282,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f281]) ).
thf(f289,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
!= $true ),
inference(flattening,[],[f147]) ).
thf(f352,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f289]) ).
thf(f357,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f282]) ).
thf(f530,definition,
( spl1_29
<=> ( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition]) ).
thf(f533,plain,
~ spl1_29,
inference(avatar_split_clause,[],[f352,f530]) ).
thf(f709,plain,
spl1_29,
inference(avatar_split_clause,[],[f357,f530]) ).
cnf(s29,plain,
~ spl1_29,
inference(sat_conversion,[],[f533]) ).
cnf(s65,plain,
spl1_29,
inference(sat_conversion,[],[f709]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s29,s65]) ).
thf(f855,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:34:41 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 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
% 0.21/0.27 % (3361073)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (3361081)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=747237433: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)
% 0.21/0.27 % (3361078)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1140308466:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (3361079)lrs+10_16_si=on:nwc=1.5:random_seed=1850072553:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (3361080)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=811571528:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (3361082)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2236114240:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (3361080)Instruction limit reached!
% 0.21/0.28 % (3361080)------------------------------
% 0.21/0.28 % (3361080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3361080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3361080)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3361080)Termination reason: Instruction limit
% 0.21/0.28 % (3361080)Termination phase: shuffling
% 0.21/0.28 % (3361080)Time elapsed: 0.002 s
% 0.21/0.28 % (3361080)Peak memory usage: 10 MB
% 0.21/0.28 % (3361080)Instructions burned: 5 (million)
% 0.21/0.28 % (3361081) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3361073-3361081"...
% 0.21/0.28 % (3361081)...printing done.
% 0.21/0.28 % (3361081)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3361081)------------------------------
% 0.21/0.28 % (3361081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3361081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3361081)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3361081)Termination reason: Refutation
% 0.21/0.28 % (3361081)Time elapsed: 0.012 s
% 0.21/0.28 % (3361081)Peak memory usage: 13 MB
% 0.21/0.28 % (3361081)Instructions burned: 51 (million)
% 0.21/0.28 % (3361073)Success in time 0.047 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------