%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL953^8 : 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 : n005.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 08:14:55 AM UTC 2026
% Result : Theorem 0.36s 0.42s
% Output : Refutation 0.36s
% 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 : 162 ( 6 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 195 ( 7 ~; 0 |; 0 &; 187 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 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 : 34 ( 31 usr; 4 con; 0-4 aty)
% Number of variables : 22 ( 0 sgn 0 !; 0 ?; 22 :)
% 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_14,type,
in: $i > $i > mworld > $o ).
thf(func_def_15,type,
disjoint: $i > $i > mworld > $o ).
thf(func_def_16,type,
empty: $i > mworld > $o ).
thf(func_def_17,type,
singleton: $i > $i ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vAND: $o > $o > $o ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
sK0: mworld > $i ).
thf(f17,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ X0 @ X1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ X0 ) @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(f18,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ X0 @ X1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ X0 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f19,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ X0 @ X1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ X0 ) @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(f30,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ X0 @ X1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ X0 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f31,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f47,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ X0 @ X1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ X0 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
thf(f59,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f67,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f77,definition,
( spl1_1
<=> ( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ Y0 @ Y1 ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f80,plain,
spl1_1,
inference(avatar_split_clause,[],[f59,f77]) ).
thf(f131,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f67,f77]) ).
cnf(s1,plain,
spl1_1,
inference(sat_conversion,[],[f80]) ).
cnf(s12,plain,
~ spl1_1,
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s12]) ).
thf(f152,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL953^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n005.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 10:52:47 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running higher-order theorem proving
% 0.29/0.37 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
% 0.36/0.42 % (1513251)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.42 % (1513259)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=871352838: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)
% 0.36/0.42 % (1513259) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1513251-1513259"...
% 0.36/0.42 % (1513259)...printing done.
% 0.36/0.42 % (1513259)Refutation found. Thanks to Tanya!
% 0.36/0.42 % SZS status Theorem for theBenchmark
% 0.36/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.43 % (1513259)------------------------------
% 0.36/0.43 % (1513259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.43 % (1513259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.43 % (1513259)CaDiCaL version: 2.1.3
% 0.36/0.43 % (1513259)Termination reason: Refutation
% 0.36/0.43 % (1513259)Time elapsed: 0.004 s
% 0.36/0.43 % (1513259)Peak memory usage: 12 MB
% 0.36/0.43 % (1513259)Instructions burned: 7 (million)
% 0.36/0.43 % (1513251)Success in time 0.04 s
% 0.36/0.43 % Vampire exiting
%------------------------------------------------------------------------------