%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET924^1 : 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 : 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 08:23:29 AM UTC 2026
% Result : Theorem 0.25s 0.38s
% Output : Refutation 0.25s
% 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 : 96 ( 6 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 162 ( 7 ~; 0 |; 0 &; 154 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 33 ( 30 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_14,type,
in: $i > $i > mworld > $o ).
thf(func_def_15,type,
empty: $i > mworld > $o ).
thf(func_def_16,type,
singleton: $i > $i ).
thf(func_def_17,type,
set_difference: $i > $i > $i ).
thf(func_def_18,type,
vIMP: $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vIFF: $o > $o > $o ).
thf(f23,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(f24,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f25,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f44,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f45,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f63,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f64,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f73,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f64]) ).
thf(f83,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f87,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f166,definition,
( spl0_14
<=> ( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f169,plain,
spl0_14,
inference(avatar_split_clause,[],[f87,f166]) ).
thf(f190,plain,
~ spl0_14,
inference(avatar_split_clause,[],[f83,f166]) ).
cnf(s14,plain,
spl0_14,
inference(sat_conversion,[],[f169]) ).
cnf(s19,plain,
~ spl0_14,
inference(sat_conversion,[],[f190]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s14,s19]) ).
thf(f216,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n008.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:41:54 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.38 % (3170856)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.38 % (3170862)lrs+10_16_si=on:nwc=1.5:random_seed=3771953524:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.38 % (3170862)Instruction limit reached!
% 0.25/0.38 % (3170862)------------------------------
% 0.25/0.38 % (3170862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3170862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3170862)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3170862)Termination reason: Instruction limit
% 0.25/0.38 % (3170862)Termination phase: Saturation
% 0.25/0.38 % (3170862)Time elapsed: 0.009 s
% 0.25/0.38 % (3170862)Peak memory usage: 12 MB
% 0.25/0.38 % (3170862)Instructions burned: 18 (million)
% 0.25/0.38 % (3170861)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=651408372:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.38 % (3170863)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2525740518:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.38 % (3170864)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=3985628709: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)
% 0.25/0.38 % (3170865)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1684758604:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.38 % (3170866)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2900099392:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.38 % (3170863)Instruction limit reached!
% 0.25/0.38 % (3170863)------------------------------
% 0.25/0.38 % (3170863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3170863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3170863)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3170863)Termination reason: Instruction limit
% 0.25/0.38 % (3170863)Termination phase: Property scanning
% 0.25/0.38 % (3170863)Time elapsed: 0.002 s
% 0.25/0.38 % (3170863)Peak memory usage: 10 MB
% 0.25/0.38 % (3170863)Instructions burned: 3 (million)
% 0.25/0.38 % (3170864) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3170856-3170864"...
% 0.25/0.38 % (3170867)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.38 % (3170867)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
% 0.25/0.38 % (3170869)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3500437409:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.25/0.38 % (3170864)...printing done.
% 0.25/0.38 % (3170869)Instruction limit reached!
% 0.25/0.38 % (3170869)------------------------------
% 0.25/0.38 % (3170869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3170869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3170869)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3170869)Termination reason: Instruction limit
% 0.25/0.38 % (3170869)Termination phase: shuffling
% 0.25/0.38 % (3170869)Time elapsed: 0.001 s
% 0.25/0.38 % (3170869)Peak memory usage: 9 MB
% 0.25/0.38 % (3170869)Instructions burned: 2 (million)
% 0.25/0.38 % (3170864)Refutation found. Thanks to Tanya!
% 0.25/0.38 % SZS status Theorem for theBenchmark
% 0.25/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.38 % (3170864)------------------------------
% 0.25/0.38 % (3170864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3170864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3170864)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3170864)Termination reason: Refutation
% 0.25/0.38 % (3170864)Time elapsed: 0.010 s
% 0.25/0.38 % (3170864)Peak memory usage: 12 MB
% 0.25/0.38 % (3170864)Instructions burned: 10 (million)
% 0.25/0.38 % (3170856)Success in time 0.059 s
% 0.25/0.38 % Vampire exiting
%------------------------------------------------------------------------------