%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ149^13 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:37 AM UTC 2026
% Result : Theorem 1.71s 1.36s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 121 ( 48 unt; 0 typ; 6 def)
% Number of atoms : 765 ( 169 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1071 ( 101 ~; 114 |; 38 &; 727 @)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 23 con; 0-3 aty)
% ( 20 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 206 ( 151 ^; 53 !; 2 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mindex: $tType ).
thf(type_def_6,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mindex: $tType ).
thf(func_def_2,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_3,type,
'#pour_b': mindex ).
thf(func_def_4,type,
'#make_c': mindex ).
thf(func_def_5,type,
'#pour_a': mindex ).
thf(func_def_6,type,
mactual: mworld ).
thf(func_def_7,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_9,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
acid: mworld > $o ).
thf(func_def_32,type,
sK1: mworld ).
thf(func_def_33,type,
sK2: mworld ).
thf(func_def_34,type,
sK3: mworld ).
thf(func_def_35,type,
sK4: mworld ).
thf(func_def_36,type,
sK5: mworld ).
thf(func_def_37,type,
sK6: mworld ).
thf(func_def_38,type,
sK7: mworld ).
thf(func_def_39,type,
sK8: mworld ).
thf(func_def_40,type,
sK9: mworld ).
thf(f272,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f212,f217,f222,f229,f243,f257,f271]) ).
thf(f271,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f270]) ).
thf(f270,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f211,f265]) ).
thf(f265,plain,
( ( ( acid @ sK2 )
= $false )
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f263]) ).
thf(f263,plain,
( ( $true = $false )
| ( ( acid @ sK2 )
= $false )
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f216,f261]) ).
thf(f261,plain,
( ! [X0: mworld] :
( ( ( mrel @ '#pour_b' @ sK1 @ X0 )
= $false )
| ( ( acid @ X0 )
= $false ) )
| ~ spl0_14
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f259]) ).
thf(f259,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( ( mrel @ '#pour_b' @ sK1 @ X0 )
= $false )
| ( ( acid @ X0 )
= $false ) )
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f221,f228]) ).
thf(f228,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#pour_b' @ X2 @ X3 )
= $false )
| ( $false
= ( acid @ X3 ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f227]) ).
thf(f227,definition,
( spl0_16
<=> ! [X2: mworld,X3: mworld] :
( ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( $false
= ( acid @ X3 ) )
| ( ( mrel @ '#pour_b' @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f221,plain,
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK1 ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f219]) ).
thf(f219,definition,
( spl0_14
<=> ( $true
= ( mrel @ '#pour_a' @ mactual @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f216,plain,
( ( $true
= ( mrel @ '#pour_b' @ sK1 @ sK2 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f214]) ).
thf(f214,definition,
( spl0_13
<=> ( $true
= ( mrel @ '#pour_b' @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f211,plain,
( ( $true
= ( acid @ sK2 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f209]) ).
thf(f209,definition,
( spl0_12
<=> ( $true
= ( acid @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f257,plain,
( ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f256]) ).
thf(f256,plain,
( $false
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f252]) ).
thf(f252,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f249,f251]) ).
thf(f251,plain,
( ( ( acid @ sK1 )
= $true )
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( acid @ sK1 )
= $true )
| ( $true = $false )
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f225,f221]) ).
thf(f225,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( acid @ X1 )
= $true ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f224]) ).
thf(f224,definition,
( spl0_15
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( acid @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f249,plain,
( ( ( acid @ sK1 )
= $false )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( $true = $false )
| ( ( acid @ sK1 )
= $false )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f86,f221]) ).
thf(f86,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( acid @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: mworld] :
( ( ( ~ ( acid @ X1 ) )
= $true )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#pour_a' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) ) ),
inference(definition_unfolding,[status(thm)],[f61,f51,f59,f57]) ).
thf(f57,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) )
= mnot ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mnot_def) ).
thf(f59,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) )
= mbox ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mbox_def) ).
thf(f51,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mlocal_def) ).
thf(f61,plain,
( ( mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,plain,
mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',pour_a_acid) ).
thf(f243,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[status(thm)],[f242]) ).
thf(f242,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true = $false )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f237,f123]) ).
thf(f123,plain,
( ( acid @ sK5 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( mrel @ '#make_c' @ mactual @ sK5 )
& ( acid @ sK5 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
& ( acid @ Y0 ) )
@ sK5 )
= $true ),
inference(sigma_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
& ( acid @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#make_c'
@ acid ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f54,f51,f55]) ).
thf(f55,plain,
( mdia
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mdia
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( X1 @ X3 )
& ( mrel @ X0 @ X2 @ X3 ) ) )
= mdia ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
? [X5: mworld] :
( ( X0 @ X5 )
& ( mrel @ X4 @ X2 @ X5 ) ) )
= mdia ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mdia_def) ).
thf(f54,plain,
( ( mlocal @ ( mdia @ '#make_c' @ acid ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( mlocal @ ( mdia @ '#make_c' @ acid ) )
= $true ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
mlocal @ ( mdia @ '#make_c' @ acid ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mdia @ '#make_c' @ acid ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',make_c_acid) ).
thf(f237,plain,
( ( ( acid @ sK5 )
= $false )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( acid @ sK5 )
= $false )
| ( $true = $false )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f124,f192]) ).
thf(f192,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( ( acid @ X1 )
= $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f191]) ).
thf(f191,definition,
( spl0_8
<=> ! [X1: mworld] :
( ( ( acid @ X1 )
= $false )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f124,plain,
( $true
= ( mrel @ '#make_c' @ mactual @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f229,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f81,f227,f224]) ).
thf(f81,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#pour_b' @ X2 @ X3 )
= $false )
| ( ( acid @ X1 )
= $true )
| ( $false
= ( acid @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ~ ( acid @ X1 ) )
= $false )
| ( $false
= ( acid @ X3 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#pour_b' @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( ( ( mrel @ '#pour_b' @ X2 @ X3 )
& ( acid @ X3 ) )
= $false )
| ( ( ~ ( acid @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ~ ( acid @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X2 @ Y0 )
& ( acid @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: mworld,X1: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X2 @ Y0 )
& ( acid @ Y0 ) ) )
= $false )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( mrel @ '#pour_a' @ mactual @ X2 )
= $false )
| ( ( ~ ( acid @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( $false
= ( ( mrel @ '#pour_a' @ mactual @ X2 )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ X2 @ Y0 )
& ( acid @ Y0 ) ) ) ) )
| ( ( ~ ( acid @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: mworld,X1: mworld] :
( ( ( ~ ( acid @ X1 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) )
@ X2 )
= $false )
| ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#pour_a' @ mactual @ X1 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( acid @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: mworld] :
( ( ( ( mrel @ '#pour_a' @ mactual @ X1 )
& ~ ( acid @ X1 ) )
= $false )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) ) )
= $false )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $true
!= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ~ ( acid @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
& ( acid @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ '#pour_b'
@ acid ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f52,f51,f60,f55,f57,f55,f55]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mand_def) ).
thf(f52,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
~ ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',conj) ).
thf(f222,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f96,f191,f219]) ).
thf(f96,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_a' @ mactual @ sK1 ) )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( ( acid @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( ( ~ ( acid @ X1 ) )
= $true )
| ( $true
= ( mrel @ '#pour_a' @ mactual @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) )
| ( $true
= ( mrel @ '#pour_a' @ mactual @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: mworld] :
( ( $false
= ( ( mrel @ '#pour_a' @ mactual @ sK1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK1 @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_a' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#pour_b' @ Y0 @ Y1 )
=> ~ ( acid @ Y1 ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#make_c' @ mactual @ Y0 )
=> ~ ( acid @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_a'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#pour_b'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#make_c'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ acid ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f53,f51,f48,f59,f59,f57,f59,f57]) ).
thf(f48,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mimplies_def) ).
thf(f53,plain,
( ( mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',pour_ab_make_axiom_2) ).
thf(f217,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f102,f191,f214]) ).
thf(f102,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_b' @ sK1 @ sK2 ) )
| ( ( acid @ X1 )
= $false )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ '#pour_b' @ sK1 @ sK2 ) )
| ( ( ~ ( acid @ X1 ) )
= $true )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X1: mworld] :
( ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( ( ( mrel @ '#pour_b' @ sK1 @ sK2 )
=> ~ ( acid @ sK2 ) )
= $false )
| ( ( ~ ( acid @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) )
| ( ( ( mrel @ '#pour_b' @ sK1 @ sK2 )
=> ~ ( acid @ sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK1 @ Y0 )
=> ~ ( acid @ Y0 ) )
@ sK2 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#pour_b' @ sK1 @ Y0 )
=> ~ ( acid @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ '#make_c' @ mactual @ X1 )
=> ~ ( acid @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f212,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f104,f191,f209]) ).
thf(f104,plain,
! [X1: mworld] :
( ( $true
= ( acid @ sK2 ) )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( ( acid @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: mworld] :
( ( ( ~ ( acid @ X1 ) )
= $true )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false )
| ( $true
= ( acid @ sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: mworld] :
( ( $false
= ( ~ ( acid @ sK2 ) ) )
| ( ( ~ ( acid @ X1 ) )
= $true )
| ( ( mrel @ '#make_c' @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ149^13 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:34:31 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : PUZ149^13 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.46 % Domain : Puzzles
% 0.30/0.46 % Problem : The bungling chemist
% 0.30/0.46 % Version : [BP13] axioms.
% 0.30/0.46 % English : Assume that a chemical compound c is made by pouring the elements
% 0.30/0.46 % a and b into the same beaker. The two elements a and b are not
% 0.30/0.46 % acid. It is possible that after making the compound c it results
% 0.30/0.46 % in an acid. Then it is possible that pouring element a results
% 0.30/0.46 % not in an acid, and pouring a and b in the beaker results in an
% 0.30/0.46 % acid.
% 0.30/0.46
% 0.30/0.46 % Refs : [Bal98] Baldoni (1998), Normal Multimodal Logics: Automatic De
% 0.30/0.46 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.46 % Source : [TPTP]
% 0.30/0.46 % Names : MML006+1 [QMLTP]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.30/0.46 % Syntax : Number of formulae : 31 ( 8 unt; 16 typ; 8 def)
% 0.30/0.46 % Number of atoms : 65 ( 8 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 9 ( 4 avg)
% 0.30/0.46 % Number of connectives : 82 ( 1 ~; 1 |; 2 &; 75 @)
% 0.30/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 3 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 15 ( 14 usr; 4 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 23 ( 21 ^; 1 !; 1 ?; 23 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.46 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.30/0.46 % $modalities == $modal_system_K].
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(mworld,type,
% 0.30/0.46 mworld: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mindex,type,
% 0.30/0.46 mindex: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_type,type,
% 0.30/0.46 mrel: mindex > mworld > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf('#pour_b_type',type,
% 0.30/0.46 '#pour_b': mindex ).
% 0.30/0.46
% 0.30/0.46 thf('#make_c_type',type,
% 0.30/0.46 '#make_c': mindex ).
% 0.30/0.46
% 0.30/0.46 thf('#pour_a_type',type,
% 0.30/0.46 '#pour_a': mindex ).
% 0.30/0.46
% 0.30/0.46 thf(mactual_type,type,
% 0.30/0.46 mactual: mworld ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_type,type,
% 0.30/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_def,definition,
% 0.30/0.46 ( mlocal
% 0.30/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_type,type,
% 0.30/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mand_type,type,
% 0.30/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mor_type,type,
% 0.30/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_type,type,
% 0.30/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_type,type,
% 0.30/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_def,definition,
% 0.30/0.46 ( mnot
% 0.30/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.46 ~ ( A @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mand_def,definition,
% 0.30/0.46 ( mand
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 & ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mor_def,definition,
% 0.30/0.46 ( mor
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 | ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_def,definition,
% 0.30/0.46 ( mimplies
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 => ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_def,definition,
% 0.30/0.46 ( mequiv
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 <=> ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_type,type,
% 0.30/0.46 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_def,definition,
% 0.30/0.46 ( mbox
% 0.30/0.46 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ! [V: mworld] :
% 0.30/0.46 ( ( mrel @ R @ W @ V )
% 0.30/0.46 => ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_type,type,
% 0.30/0.46 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_def,definition,
% 0.30/0.46 ( mdia
% 0.30/0.46 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ? [V: mworld] :
% 0.30/0.46 ( ( mrel @ R @ W @ V )
% 0.30/0.46 & ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(acid_decl,type,
% 0.30/0.46 acid: mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(pour_ab_make_axiom_1,axiom,
% 0.30/0.46 mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ acid ) ) @ ( mbox @ '#make_c' @ acid ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(pour_ab_make_axiom_2,axiom,
% 0.30/0.46 mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(pour_ba_make_axiom_1,axiom,
% 0.30/0.46 mlocal @ ( mimplies @ ( mbox @ '#pour_b' @ ( mbox @ '#pour_a' @ acid ) ) @ ( mbox @ '#make_c' @ acid ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(pour_ba_make_axiom_2,axiom,
% 0.30/0.46 mlocal @ ( mimplies @ ( mbox @ '#pour_b' @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(pour_a_acid,axiom,
% 0.30/0.46 mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(make_c_acid,axiom,
% 0.30/0.46 mlocal @ ( mdia @ '#make_c' @ acid ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj,conjecture,
% 0.30/0.46 mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.71/1.32 ---- Embedded in THF ---
% 1.71/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.32 %%% Generated on Tue Feb 24 11:34:32 EST 2026
% 1.71/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.32 %%% Logic specification used:
% 1.71/1.32 %%% thf(spec, logic, $$dhol).
% 1.71/1.32
% 1.71/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2DTF18616.p
% See solution above
% 1.71/1.32 ------------------------
% 1.71/1.33 ---- Cleaned THF ---
% 1.71/1.33 thf(mworld,type,
% 1.71/1.33 mworld: $tType ).
% 1.71/1.33
% 1.71/1.33 thf(mindex,type,
% 1.71/1.33 mindex: $tType ).
% 1.71/1.33
% 1.71/1.33 thf(mrel_type,type,
% 1.71/1.33 mrel: mindex > mworld > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf('#pour_b_type',type,
% 1.71/1.33 '#pour_b': mindex ).
% 1.71/1.33
% 1.71/1.33 thf('#make_c_type',type,
% 1.71/1.33 '#make_c': mindex ).
% 1.71/1.33
% 1.71/1.33 thf('#pour_a_type',type,
% 1.71/1.33 '#pour_a': mindex ).
% 1.71/1.33
% 1.71/1.33 thf(mactual_type,type,
% 1.71/1.33 mactual: mworld ).
% 1.71/1.33
% 1.71/1.33 thf(mlocal_type,type,
% 1.71/1.33 mlocal: ( mworld > $o ) > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mlocal_def,definition,
% 1.71/1.33 ( mlocal
% 1.71/1.33 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mnot_type,type,
% 1.71/1.33 mnot: ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mand_type,type,
% 1.71/1.33 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mor_type,type,
% 1.71/1.33 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mimplies_type,type,
% 1.71/1.33 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mequiv_type,type,
% 1.71/1.33 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mnot_def,definition,
% 1.71/1.33 ( mnot
% 1.71/1.33 = ( ^ [A: mworld > $o,W: mworld] :
% 1.71/1.33 ~ ( A @ W ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mand_def,definition,
% 1.71/1.33 ( mand
% 1.71/1.33 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.33 ( ( A @ W )
% 1.71/1.33 & ( B @ W ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mor_def,definition,
% 1.71/1.33 ( mor
% 1.71/1.33 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.33 ( ( A @ W )
% 1.71/1.33 | ( B @ W ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mimplies_def,definition,
% 1.71/1.33 ( mimplies
% 1.71/1.33 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.33 ( ( A @ W )
% 1.71/1.33 => ( B @ W ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mequiv_def,definition,
% 1.71/1.33 ( mequiv
% 1.71/1.33 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.33 ( ( A @ W )
% 1.71/1.33 <=> ( B @ W ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mbox_type,type,
% 1.71/1.33 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mbox_def,definition,
% 1.71/1.33 ( mbox
% 1.71/1.33 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.71/1.33 ! [V: mworld] :
% 1.71/1.33 ( ( mrel @ R @ W @ V )
% 1.71/1.33 => ( Phi @ V ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(mdia_type,type,
% 1.71/1.33 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(mdia_def,definition,
% 1.71/1.33 ( mdia
% 1.71/1.33 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.71/1.33 ? [V: mworld] :
% 1.71/1.33 ( ( mrel @ R @ W @ V )
% 1.71/1.33 & ( Phi @ V ) ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(acid_decl,type,
% 1.71/1.33 acid: mworld > $o ).
% 1.71/1.33
% 1.71/1.33 thf(pour_ab_make_axiom_1,axiom,
% 1.71/1.33 mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ acid ) ) @ ( mbox @ '#make_c' @ acid ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(pour_ab_make_axiom_2,axiom,
% 1.71/1.33 mlocal @ ( mimplies @ ( mbox @ '#pour_a' @ ( mbox @ '#pour_b' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(pour_ba_make_axiom_1,axiom,
% 1.71/1.33 mlocal @ ( mimplies @ ( mbox @ '#pour_b' @ ( mbox @ '#pour_a' @ acid ) ) @ ( mbox @ '#make_c' @ acid ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(pour_ba_make_axiom_2,axiom,
% 1.71/1.33 mlocal @ ( mimplies @ ( mbox @ '#pour_b' @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) ) @ ( mbox @ '#make_c' @ ( mnot @ acid ) ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(pour_a_acid,axiom,
% 1.71/1.33 mlocal @ ( mbox @ '#pour_a' @ ( mnot @ acid ) ) ).
% 1.71/1.33
% 1.71/1.33 thf(make_c_acid,axiom,
% 1.71/1.33 mlocal @ ( mdia @ '#make_c' @ acid ) ).
% 1.71/1.33
% 1.71/1.33 thf(conj,conjecture,
% 1.71/1.33 mlocal @ ( mand @ ( mdia @ '#pour_a' @ ( mnot @ acid ) ) @ ( mdia @ '#pour_a' @ ( mdia @ '#pour_b' @ acid ) ) ) ).
% 1.71/1.33 ------------------------
% 1.71/1.35 % (18713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18616 for (2999ds/183Mi)
% 1.71/1.35 % (18715)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18616 for (2999ds/27Mi)
% 1.71/1.35 % (18714)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18616 for (2999ds/4Mi)
% 1.71/1.35 % (18714)Instruction limit reached!
% 1.71/1.35 % (18714)------------------------------
% 1.71/1.35 % (18714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (18714)Termination reason: Unknown
% 1.71/1.35 % (18714)Termination phase: Function definition elimination
% 1.71/1.35
% 1.71/1.35 % (18714)Memory used [KB]: 1023
% 1.71/1.35 % (18714)Time elapsed: 0.002 s
% 1.71/1.35 % (18714)Instructions burned: 4 (million)
% 1.71/1.35 % (18714)------------------------------
% 1.71/1.35 % (18714)------------------------------
% 1.71/1.35 % (18713)First to succeed.
% 1.71/1.35 % (18718)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_18616 for (2999ds/275Mi)
% 1.71/1.36 % (18717)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_18616 for (2999ds/2Mi)
% 1.71/1.36 % (18713)Refutation found. Thanks to Tanya!
% 1.71/1.36 % SZS status Theorem for DTF2THF_18616
% 1.71/1.36 % SZS output start Proof for DTF2THF_18616
% 1.71/1.36 thf(type_def_5, type, mindex: $tType).
% 1.71/1.36 thf(type_def_6, type, mworld: $tType).
% 1.71/1.36 thf(func_def_0, type, mworld: $tType).
% 1.71/1.36 thf(func_def_1, type, mindex: $tType).
% 1.71/1.36 thf(func_def_2, type, mrel: mindex > mworld > mworld > $o).
% 1.71/1.36 thf(func_def_3, type, '#pour_b': mindex).
% 1.71/1.36 thf(func_def_4, type, '#make_c': mindex).
% 1.71/1.36 thf(func_def_5, type, '#pour_a': mindex).
% 1.71/1.36 thf(func_def_6, type, mactual: mworld).
% 1.71/1.36 thf(func_def_7, type, mlocal: (mworld > $o) > $o).
% 1.71/1.36 thf(func_def_9, type, mnot: (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_10, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_11, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_12, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_13, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_14, type, mbox: mindex > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_15, type, mdia: mindex > (mworld > $o) > mworld > $o).
% 1.71/1.36 thf(func_def_16, type, acid: mworld > $o).
% 1.71/1.36 thf(func_def_32, type, sK1: mworld).
% 1.71/1.36 thf(func_def_33, type, sK2: mworld).
% 1.71/1.36 thf(func_def_34, type, sK3: mworld).
% 1.71/1.36 thf(func_def_35, type, sK4: mworld).
% 1.71/1.36 thf(func_def_36, type, sK5: mworld).
% 1.71/1.36 thf(func_def_37, type, sK6: mworld).
% 1.71/1.36 thf(func_def_38, type, sK7: mworld).
% 1.71/1.36 thf(func_def_39, type, sK8: mworld).
% 1.71/1.36 thf(func_def_40, type, sK9: mworld).
% 1.71/1.36 thf(f272,plain,(
% 1.71/1.36 $false),
% 1.71/1.36 inference(avatar_sat_refutation,[status(thm)],[f212,f217,f222,f229,f243,f257,f271])).
% 1.71/1.36 thf(f271,plain,(
% 1.71/1.36 ~spl0_12 | ~spl0_13 | ~spl0_14 | ~spl0_16),
% 1.71/1.36 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 1.71/1.36 thf(f270,plain,(
% 1.71/1.36 $false | (~spl0_12 | ~spl0_13 | ~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f267])).
% 1.71/1.36 thf(f267,plain,(
% 1.71/1.36 ($true = $false) | (~spl0_12 | ~spl0_13 | ~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(superposition,[status(thm)],[f211,f265])).
% 1.71/1.36 thf(f265,plain,(
% 1.71/1.36 ((acid @ sK2) = $false) | (~spl0_13 | ~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f263])).
% 1.71/1.36 thf(f263,plain,(
% 1.71/1.36 ($true = $false) | ((acid @ sK2) = $false) | (~spl0_13 | ~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(superposition,[status(thm)],[f216,f261])).
% 1.71/1.36 thf(f261,plain,(
% 1.71/1.36 ( ! [X0 : mworld] : (((mrel @ '#pour_b' @ sK1 @ X0) = $false) | ((acid @ X0) = $false)) ) | (~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f259])).
% 1.71/1.36 thf(f259,plain,(
% 1.71/1.36 ( ! [X0 : mworld] : (($true = $false) | ((mrel @ '#pour_b' @ sK1 @ X0) = $false) | ((acid @ X0) = $false)) ) | (~spl0_14 | ~spl0_16)),
% 1.71/1.36 inference(superposition,[status(thm)],[f221,f228])).
% 1.71/1.36 thf(f228,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X3 : mworld] : (((mrel @ '#pour_a' @ mactual @ X2) = $false) | ((mrel @ '#pour_b' @ X2 @ X3) = $false) | ($false = (acid @ X3))) ) | ~spl0_16),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f227])).
% 1.71/1.36 thf(f227,definition,(
% 1.71/1.36 spl0_16 <=> ! [X2 : mworld,X3 : mworld] : (((mrel @ '#pour_a' @ mactual @ X2) = $false) | ($false = (acid @ X3)) | ((mrel @ '#pour_b' @ X2 @ X3) = $false))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.71/1.36 thf(f221,plain,(
% 1.71/1.36 ($true = (mrel @ '#pour_a' @ mactual @ sK1)) | ~spl0_14),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f219])).
% 1.71/1.36 thf(f219,definition,(
% 1.71/1.36 spl0_14 <=> ($true = (mrel @ '#pour_a' @ mactual @ sK1))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.71/1.36 thf(f216,plain,(
% 1.71/1.36 ($true = (mrel @ '#pour_b' @ sK1 @ sK2)) | ~spl0_13),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f214])).
% 1.71/1.36 thf(f214,definition,(
% 1.71/1.36 spl0_13 <=> ($true = (mrel @ '#pour_b' @ sK1 @ sK2))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.71/1.36 thf(f211,plain,(
% 1.71/1.36 ($true = (acid @ sK2)) | ~spl0_12),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f209])).
% 1.71/1.36 thf(f209,definition,(
% 1.71/1.36 spl0_12 <=> ($true = (acid @ sK2))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.71/1.36 thf(f257,plain,(
% 1.71/1.36 ~spl0_14 | ~spl0_15),
% 1.71/1.36 inference(avatar_contradiction_clause,[status(thm)],[f256])).
% 1.71/1.36 thf(f256,plain,(
% 1.71/1.36 $false | (~spl0_14 | ~spl0_15)),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f252])).
% 1.71/1.36 thf(f252,plain,(
% 1.71/1.36 ($true = $false) | (~spl0_14 | ~spl0_15)),
% 1.71/1.36 inference(superposition,[status(thm)],[f249,f251])).
% 1.71/1.36 thf(f251,plain,(
% 1.71/1.36 ((acid @ sK1) = $true) | (~spl0_14 | ~spl0_15)),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f247])).
% 1.71/1.36 thf(f247,plain,(
% 1.71/1.36 ((acid @ sK1) = $true) | ($true = $false) | (~spl0_14 | ~spl0_15)),
% 1.71/1.36 inference(superposition,[status(thm)],[f225,f221])).
% 1.71/1.36 thf(f225,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((acid @ X1) = $true)) ) | ~spl0_15),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f224])).
% 1.71/1.36 thf(f224,definition,(
% 1.71/1.36 spl0_15 <=> ! [X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((acid @ X1) = $true))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.71/1.36 thf(f249,plain,(
% 1.71/1.36 ((acid @ sK1) = $false) | ~spl0_14),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.71/1.36 thf(f246,plain,(
% 1.71/1.36 ($true = $false) | ((acid @ sK1) = $false) | ~spl0_14),
% 1.71/1.36 inference(superposition,[status(thm)],[f86,f221])).
% 1.71/1.36 thf(f86,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((acid @ X1) = $false)) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f85])).
% 1.71/1.36 thf(f85,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((~ (acid @ X1)) = $true) | ($false = (mrel @ '#pour_a' @ mactual @ X1))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.71/1.36 thf(f84,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = ((mrel @ '#pour_a' @ mactual @ X1) => (~ (acid @ X1))))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.71/1.36 thf(f83,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (~ (acid @ Y0)))) @ X1) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f82])).
% 1.71/1.36 thf(f82,plain,(
% 1.71/1.36 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (~ (acid @ Y0))))) = $true)),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.71/1.36 thf(f68,plain,(
% 1.71/1.36 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#pour_a' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ acid))))),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f61,f51,f59,f57])).
% 1.71/1.36 thf(f57,plain,(
% 1.71/1.36 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f44])).
% 1.71/1.36 thf(f44,plain,(
% 1.71/1.36 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f43])).
% 1.71/1.36 thf(f43,plain,(
% 1.71/1.36 ((^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))) = mnot)),
% 1.71/1.36 inference(rectify,[status(thm)],[f2])).
% 1.71/1.36 thf(f2,axiom,(
% 1.71/1.36 ((^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))) = mnot)),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mnot_def)).
% 1.71/1.36 thf(f59,plain,(
% 1.71/1.36 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f19,plain,(
% 1.71/1.36 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f18])).
% 1.71/1.36 thf(f18,plain,(
% 1.71/1.36 ((^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (! [X3 : mworld] : ((mrel @ X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 1.71/1.36 inference(rectify,[status(thm)],[f7])).
% 1.71/1.36 thf(f7,axiom,(
% 1.71/1.36 ((^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (! [X5 : mworld] : ((mrel @ X4 @ X2 @ X5) => (X0 @ X5)))) = mbox)),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mbox_def)).
% 1.71/1.36 thf(f51,plain,(
% 1.71/1.36 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f38])).
% 1.71/1.36 thf(f38,plain,(
% 1.71/1.36 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f1])).
% 1.71/1.36 thf(f1,axiom,(
% 1.71/1.36 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mlocal_def)).
% 1.71/1.36 thf(f61,plain,(
% 1.71/1.36 ((mlocal @ (mbox @ '#pour_a' @ (mnot @ acid))) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f46])).
% 1.71/1.36 thf(f46,plain,(
% 1.71/1.36 ((mlocal @ (mbox @ '#pour_a' @ (mnot @ acid))) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f45])).
% 1.71/1.36 thf(f45,plain,(
% 1.71/1.36 (mlocal @ (mbox @ '#pour_a' @ (mnot @ acid)))),
% 1.71/1.36 inference(rectify,[status(thm)],[f13])).
% 1.71/1.36 thf(f13,axiom,(
% 1.71/1.36 (mlocal @ (mbox @ '#pour_a' @ (mnot @ acid)))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',pour_a_acid)).
% 1.71/1.36 thf(f243,plain,(
% 1.71/1.36 ~spl0_8),
% 1.71/1.36 inference(avatar_contradiction_clause,[status(thm)],[f242])).
% 1.71/1.36 thf(f242,plain,(
% 1.71/1.36 $false | ~spl0_8),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.71/1.36 thf(f238,plain,(
% 1.71/1.36 ($true = $false) | ~spl0_8),
% 1.71/1.36 inference(superposition,[status(thm)],[f237,f123])).
% 1.71/1.36 thf(f123,plain,(
% 1.71/1.36 ((acid @ sK5) = $true)),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.71/1.36 thf(f122,plain,(
% 1.71/1.36 (((mrel @ '#make_c' @ mactual @ sK5) & (acid @ sK5)) = $true)),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.71/1.36 thf(f121,plain,(
% 1.71/1.36 (((^[Y0 : mworld]: ((mrel @ '#make_c' @ mactual @ Y0) & (acid @ Y0))) @ sK5) = $true)),
% 1.71/1.36 inference(sigma_clausification,[status(thm)],[f120])).
% 1.71/1.36 thf(f120,plain,(
% 1.71/1.36 ($true = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#make_c' @ mactual @ Y0) & (acid @ Y0)))))),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.71/1.36 thf(f67,plain,(
% 1.71/1.36 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ '#make_c' @ acid)) = $true)),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f54,f51,f55])).
% 1.71/1.36 thf(f55,plain,(
% 1.71/1.36 (mdia = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f35])).
% 1.71/1.36 thf(f35,plain,(
% 1.71/1.36 (mdia = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f34])).
% 1.71/1.36 thf(f34,plain,(
% 1.71/1.36 ((^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (? [X3 : mworld] : ((X1 @ X3) & (mrel @ X0 @ X2 @ X3)))) = mdia)),
% 1.71/1.36 inference(rectify,[status(thm)],[f8])).
% 1.71/1.36 thf(f8,axiom,(
% 1.71/1.36 ((^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (? [X5 : mworld] : ((X0 @ X5) & (mrel @ X4 @ X2 @ X5)))) = mdia)),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mdia_def)).
% 1.71/1.36 thf(f54,plain,(
% 1.71/1.36 ((mlocal @ (mdia @ '#make_c' @ acid)) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f25])).
% 1.71/1.36 thf(f25,plain,(
% 1.71/1.36 ((mlocal @ (mdia @ '#make_c' @ acid)) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f24])).
% 1.71/1.36 thf(f24,plain,(
% 1.71/1.36 (mlocal @ (mdia @ '#make_c' @ acid))),
% 1.71/1.36 inference(rectify,[status(thm)],[f14])).
% 1.71/1.36 thf(f14,axiom,(
% 1.71/1.36 (mlocal @ (mdia @ '#make_c' @ acid))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',make_c_acid)).
% 1.71/1.36 thf(f237,plain,(
% 1.71/1.36 ((acid @ sK5) = $false) | ~spl0_8),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f235])).
% 1.71/1.36 thf(f235,plain,(
% 1.71/1.36 ((acid @ sK5) = $false) | ($true = $false) | ~spl0_8),
% 1.71/1.36 inference(superposition,[status(thm)],[f124,f192])).
% 1.71/1.36 thf(f192,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((mrel @ '#make_c' @ mactual @ X1) = $false) | ((acid @ X1) = $false)) ) | ~spl0_8),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f191])).
% 1.71/1.36 thf(f191,definition,(
% 1.71/1.36 spl0_8 <=> ! [X1 : mworld] : (((acid @ X1) = $false) | ((mrel @ '#make_c' @ mactual @ X1) = $false))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.71/1.36 thf(f124,plain,(
% 1.71/1.36 ($true = (mrel @ '#make_c' @ mactual @ sK5))),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.71/1.36 thf(f229,plain,(
% 1.71/1.36 spl0_15 | spl0_16),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f81,f227,f224])).
% 1.71/1.36 thf(f81,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((mrel @ '#pour_a' @ mactual @ X2) = $false) | ((mrel @ '#pour_b' @ X2 @ X3) = $false) | ((acid @ X1) = $true) | ($false = (acid @ X3))) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f80])).
% 1.71/1.36 thf(f80,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((~ (acid @ X1)) = $false) | ($false = (acid @ X3)) | ($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((mrel @ '#pour_a' @ mactual @ X2) = $false) | ((mrel @ '#pour_b' @ X2 @ X3) = $false)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.71/1.36 thf(f79,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((mrel @ '#pour_a' @ mactual @ X2) = $false) | (((mrel @ '#pour_b' @ X2 @ X3) & (acid @ X3)) = $false) | ((~ (acid @ X1)) = $false)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.71/1.36 thf(f78,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((~ (acid @ X1)) = $false) | ($false = ((^[Y0 : mworld]: ((mrel @ '#pour_b' @ X2 @ Y0) & (acid @ Y0))) @ X3)) | ($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((mrel @ '#pour_a' @ mactual @ X2) = $false)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f77])).
% 1.71/1.36 thf(f77,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X1 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_b' @ X2 @ Y0) & (acid @ Y0)))) = $false) | ($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((mrel @ '#pour_a' @ mactual @ X2) = $false) | ((~ (acid @ X1)) = $false)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.71/1.36 thf(f76,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ($false = ((mrel @ '#pour_a' @ mactual @ X2) & (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_b' @ X2 @ Y0) & (acid @ Y0)))))) | ((~ (acid @ X1)) = $false)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.71/1.36 thf(f75,plain,(
% 1.71/1.36 ( ! [X2 : mworld,X1 : mworld] : (((~ (acid @ X1)) = $false) | (((^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1)))))) @ X2) = $false) | ($false = (mrel @ '#pour_a' @ mactual @ X1))) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f74])).
% 1.71/1.36 thf(f74,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (mrel @ '#pour_a' @ mactual @ X1)) | ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1))))))) = $false) | ((~ (acid @ X1)) = $false)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.71/1.36 thf(f73,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : ((((mrel @ '#pour_a' @ mactual @ X1) & (~ (acid @ X1))) = $false) | ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1))))))) = $false)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.71/1.36 thf(f72,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1))))))) = $false) | (((^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (~ (acid @ Y0)))) @ X1) = $false)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f71])).
% 1.71/1.36 thf(f71,plain,(
% 1.71/1.36 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (~ (acid @ Y0))))) = $false) | ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1))))))) = $false)),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.71/1.36 thf(f70,plain,(
% 1.71/1.36 ($true != ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (~ (acid @ Y0))))) & (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) & (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) & (acid @ Y1)))))))))),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.71/1.36 thf(f65,plain,(
% 1.71/1.36 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ '#pour_a' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ acid)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ '#pour_a' @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ '#pour_b' @ acid)))))),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f52,f51,f60,f55,f57,f55,f55])).
% 1.71/1.36 thf(f60,plain,(
% 1.71/1.36 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f40])).
% 1.71/1.36 thf(f40,plain,(
% 1.71/1.36 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f39])).
% 1.71/1.36 thf(f39,plain,(
% 1.71/1.36 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f3])).
% 1.71/1.36 thf(f3,axiom,(
% 1.71/1.36 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mand_def)).
% 1.71/1.36 thf(f52,plain,(
% 1.71/1.36 ((mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid)))) != $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f47])).
% 1.71/1.36 thf(f47,plain,(
% 1.71/1.36 ((mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid)))) != $true)),
% 1.71/1.36 inference(flattening,[status(thm)],[f29])).
% 1.71/1.36 thf(f29,plain,(
% 1.71/1.36 ~((mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid)))) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f28])).
% 1.71/1.36 thf(f28,plain,(
% 1.71/1.36 ~(mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f16])).
% 1.71/1.36 thf(f16,negated_conjecture,(
% 1.71/1.36 ~(mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid))))),
% 1.71/1.36 inference(negated_conjecture,[status(cth)],[f15])).
% 1.71/1.36 thf(f15,conjecture,(
% 1.71/1.36 (mlocal @ (mand @ (mdia @ '#pour_a' @ (mnot @ acid)) @ (mdia @ '#pour_a' @ (mdia @ '#pour_b' @ acid))))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',conj)).
% 1.71/1.36 thf(f222,plain,(
% 1.71/1.36 spl0_14 | spl0_8),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f96,f191,f219])).
% 1.71/1.36 thf(f96,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = (mrel @ '#pour_a' @ mactual @ sK1)) | ((mrel @ '#make_c' @ mactual @ X1) = $false) | ((acid @ X1) = $false)) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f95])).
% 1.71/1.36 thf(f95,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((mrel @ '#make_c' @ mactual @ X1) = $false) | ((~ (acid @ X1)) = $true) | ($true = (mrel @ '#pour_a' @ mactual @ sK1))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.71/1.36 thf(f94,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1)))) | ($true = (mrel @ '#pour_a' @ mactual @ sK1))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.71/1.36 thf(f92,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = ((mrel @ '#pour_a' @ mactual @ sK1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_b' @ sK1 @ Y0) => (~ (acid @ Y0))))))) | ($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1))))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.71/1.36 thf(f91,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1)))) | ($false = ((^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) => (~ (acid @ Y1))))))) @ sK1))) )),
% 1.71/1.36 inference(sigma_clausification,[status(thm)],[f90])).
% 1.71/1.36 thf(f90,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) => (~ (acid @ Y1))))))))) | ($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1))))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.71/1.36 thf(f89,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#make_c' @ mactual @ Y0) => (~ (acid @ Y0)))) @ X1) = $true) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) => (~ (acid @ Y1)))))))))) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f88])).
% 1.71/1.36 thf(f88,plain,(
% 1.71/1.36 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#make_c' @ mactual @ Y0) => (~ (acid @ Y0)))))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) => (~ (acid @ Y1)))))))))),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.71/1.36 thf(f87,plain,(
% 1.71/1.36 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_a' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#pour_b' @ Y0 @ Y1) => (~ (acid @ Y1)))))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#make_c' @ mactual @ Y0) => (~ (acid @ Y0)))))))),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.71/1.36 thf(f66,plain,(
% 1.71/1.36 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#pour_a' @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#pour_b' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ acid))) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#make_c' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ acid)))) = $true)),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f53,f51,f48,f59,f59,f57,f59,f57])).
% 1.71/1.36 thf(f48,plain,(
% 1.71/1.36 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f42])).
% 1.71/1.36 thf(f42,plain,(
% 1.71/1.36 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f41])).
% 1.71/1.36 thf(f41,plain,(
% 1.71/1.36 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f5])).
% 1.71/1.36 thf(f5,axiom,(
% 1.71/1.36 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',mimplies_def)).
% 1.71/1.36 thf(f53,plain,(
% 1.71/1.36 ((mlocal @ (mimplies @ (mbox @ '#pour_a' @ (mbox @ '#pour_b' @ (mnot @ acid))) @ (mbox @ '#make_c' @ (mnot @ acid)))) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f31])).
% 1.71/1.36 thf(f31,plain,(
% 1.71/1.36 ((mlocal @ (mimplies @ (mbox @ '#pour_a' @ (mbox @ '#pour_b' @ (mnot @ acid))) @ (mbox @ '#make_c' @ (mnot @ acid)))) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f30])).
% 1.71/1.36 thf(f30,plain,(
% 1.71/1.36 (mlocal @ (mimplies @ (mbox @ '#pour_a' @ (mbox @ '#pour_b' @ (mnot @ acid))) @ (mbox @ '#make_c' @ (mnot @ acid))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f10])).
% 1.71/1.36 thf(f10,axiom,(
% 1.71/1.36 (mlocal @ (mimplies @ (mbox @ '#pour_a' @ (mbox @ '#pour_b' @ (mnot @ acid))) @ (mbox @ '#make_c' @ (mnot @ acid))))),
% 1.71/1.36 file('/export/starexec/sandbox2/tmp/tmp.y7e734VIi9/DTF2THF_18616.p',pour_ab_make_axiom_2)).
% 1.71/1.36 thf(f217,plain,(
% 1.71/1.36 spl0_13 | spl0_8),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f102,f191,f214])).
% 1.71/1.36 thf(f102,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = (mrel @ '#pour_b' @ sK1 @ sK2)) | ((acid @ X1) = $false) | ((mrel @ '#make_c' @ mactual @ X1) = $false)) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f101])).
% 1.71/1.36 thf(f101,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = (mrel @ '#pour_b' @ sK1 @ sK2)) | ((~ (acid @ X1)) = $true) | ((mrel @ '#make_c' @ mactual @ X1) = $false)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.71/1.36 thf(f99,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((mrel @ '#make_c' @ mactual @ X1) = $false) | (((mrel @ '#pour_b' @ sK1 @ sK2) => (~ (acid @ sK2))) = $false) | ((~ (acid @ X1)) = $true)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.71/1.36 thf(f98,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1)))) | (((mrel @ '#pour_b' @ sK1 @ sK2) => (~ (acid @ sK2))) = $false)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.71/1.36 thf(f97,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1)))) | (((^[Y0 : mworld]: ((mrel @ '#pour_b' @ sK1 @ Y0) => (~ (acid @ Y0)))) @ sK2) = $false)) )),
% 1.71/1.36 inference(sigma_clausification,[status(thm)],[f93])).
% 1.71/1.36 thf(f93,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#pour_b' @ sK1 @ Y0) => (~ (acid @ Y0)))))) | ($true = ((mrel @ '#make_c' @ mactual @ X1) => (~ (acid @ X1))))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.71/1.36 thf(f212,plain,(
% 1.71/1.36 spl0_12 | spl0_8),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f104,f191,f209])).
% 1.71/1.36 thf(f104,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($true = (acid @ sK2)) | ((mrel @ '#make_c' @ mactual @ X1) = $false) | ((acid @ X1) = $false)) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f103])).
% 1.71/1.36 thf(f103,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (((~ (acid @ X1)) = $true) | ((mrel @ '#make_c' @ mactual @ X1) = $false) | ($true = (acid @ sK2))) )),
% 1.71/1.36 inference(not_proxy_clausification,[status(thm)],[f100])).
% 1.71/1.36 thf(f100,plain,(
% 1.71/1.36 ( ! [X1 : mworld] : (($false = (~ (acid @ sK2))) | ((~ (acid @ X1)) = $true) | ((mrel @ '#make_c' @ mactual @ X1) = $false)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.71/1.36 % SZS output end Proof for DTF2THF_18616
% 1.71/1.36 % (18713)------------------------------
% 1.71/1.36 % (18713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.36 % (18713)Termination reason: Refutation
% 1.71/1.36
% 1.71/1.36 % (18713)Memory used [KB]: 5756
% 1.71/1.36 % (18713)Time elapsed: 0.009 s
% 1.71/1.36 % (18713)Instructions burned: 16 (million)
% 1.71/1.36 % (18713)------------------------------
% 1.71/1.36 % (18713)------------------------------
% 1.71/1.36 % (18712)Success in time 0.018 s
%------------------------------------------------------------------------------