%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET597^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:31:51 AM UTC 2026
% Result : Theorem 1.74s 1.54s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 209 ( 14 unt; 0 typ; 18 def)
% Number of atoms : 1501 ( 359 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 2371 ( 376 ~; 368 |; 83 &;1050 @)
% ( 21 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 25 con; 0-2 aty)
% ( 196 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 367 ( 288 ^; 79 !; 0 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_18,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK2: a > $o ).
thf(func_def_20,type,
sK3: a > $o ).
thf(func_def_21,type,
sK4: a > $o ).
thf(func_def_22,type,
sK5: a ).
thf(func_def_23,type,
sK6: a > $o ).
thf(func_def_24,type,
sK7: a ).
thf(func_def_25,type,
sK8: a ).
thf(func_def_26,type,
sK9: a ).
thf(func_def_27,type,
sK10: ( a > $o ) > a ).
thf(func_def_28,type,
sK11: ( a > $o ) > a ).
thf(f635,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f32,f36,f52,f67,f73,f94,f143,f156,f170,f177,f181,f199,f241,f247,f528,f551,f571,f600,f608,f634]) ).
thf(f634,plain,
( spl0_26
| spl0_24
| ~ spl0_4
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[status(thm)],[f633,f523,f175,f30,f526,f549]) ).
thf(f549,definition,
( spl0_26
<=> ! [X0: a] :
( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition]) ).
thf(f526,definition,
( spl0_24
<=> ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f30,definition,
( spl0_4
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f175,definition,
( spl0_12
<=> ( ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f523,definition,
( spl0_23
<=> ( ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f633,plain,
( ! [X0: a] :
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f632]) ).
thf(f632,plain,
( ! [X0: a] :
( ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( $true = $false )
| ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f631]) ).
thf(f631,plain,
( ! [X0: a] :
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ~ $false ) = $false ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f615,f257]) ).
thf(f257,plain,
( ( ( sK3 @ sK9 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f175]) ).
thf(f615,plain,
( ! [X0: a] :
( ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( ( ~ ( sK3 @ sK9 ) )
= $false ) )
| ~ spl0_4
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f614]) ).
thf(f614,plain,
( ! [X0: a] :
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( ( ( sK3 @ sK9 )
=> $false )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) )
| ~ spl0_4
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f613]) ).
thf(f613,plain,
( ! [X0: a] :
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ( sK3 @ sK9 )
=> ~ $true )
= $false ) )
| ~ spl0_4
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f612]) ).
thf(f612,plain,
( ! [X0: a] :
( ( ( ( sK3 @ sK9 )
=> ( sK9 != sK9 ) )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f611]) ).
thf(f611,plain,
( ! [X0: a] :
( ( ( ( sK2 @ X0 )
=> ( ^ [Y0: a] : ( sK9 != Y0 )
@ X0 ) )
= $true )
| ( ( ( sK3 @ sK9 )
=> ( ^ [Y0: a] : ( sK9 != Y0 )
@ sK9 ) )
= $false )
| ( ( ^ [Y0: a] : ( sK9 != Y0 )
@ ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f313,f524]) ).
thf(f524,plain,
( ( ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f523]) ).
thf(f313,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( sK3 @ ( sK11 @ X1 ) )
=> ( X1 @ ( sK11 @ X1 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) )
| ( ( X1 @ ( sK10 @ X1 ) )
= $false ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f309]) ).
thf(f309,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( sK4 @ ( sK10 @ X1 ) )
=> ( X1 @ ( sK10 @ X1 ) ) )
= $false )
| ( ( ( sK3 @ ( sK11 @ X1 ) )
=> ( X1 @ ( sK11 @ X1 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( sK4 @ ( sK10 @ X1 ) )
=> ( X1 @ ( sK10 @ X1 ) ) )
= $false )
| ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f299]) ).
thf(f299,plain,
( ! [X2: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) )
| ( ( ( sK4 @ ( sK10 @ X1 ) )
=> ( X1 @ ( sK10 @ X1 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f287]) ).
thf(f287,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f285]) ).
thf(f285,plain,
( ! [X2: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f283]) ).
thf(f283,plain,
( ! [X2: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) )
@ X2 ) ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f206]) ).
thf(f206,plain,
( ( $true
= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f184,f205]) ).
thf(f205,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f608,plain,
( ~ spl0_12
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f607]) ).
thf(f607,plain,
( $false
| ~ spl0_12
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f606]) ).
thf(f606,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f604,f257]) ).
thf(f604,plain,
( ( $true
= ( sK3 @ sK9 ) )
| ~ spl0_23
| ~ spl0_25 ),
inference(backward_demodulation,[status(thm)],[f573,f524]) ).
thf(f573,plain,
( ( $true
= ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
| ~ spl0_25 ),
inference(binary_proxy_clausification,[status(thm)],[f547]) ).
thf(f547,plain,
( ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f546]) ).
thf(f546,definition,
( spl0_25
<=> ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f600,plain,
( spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[status(thm)],[f597,f546,f523]) ).
thf(f597,plain,
( ( ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 )
| ~ spl0_25 ),
inference(equality_proxy_clausification,[status(thm)],[f586]) ).
thf(f586,plain,
( ( $true
= ( sK9
= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
| ~ spl0_25 ),
inference(not_proxy_clausification,[status(thm)],[f575]) ).
thf(f575,plain,
( ( ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f574]) ).
thf(f574,plain,
( ( ( $true
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ~ spl0_25 ),
inference(backward_demodulation,[status(thm)],[f547,f573]) ).
thf(f571,plain,
( ~ spl0_10
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f570]) ).
thf(f570,plain,
( $false
| ~ spl0_10
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f569]) ).
thf(f569,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f568]) ).
thf(f568,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f567]) ).
thf(f567,plain,
( ( $true
= ( sK9 != sK9 ) )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f554]) ).
thf(f554,plain,
( ( $true
= ( $true
=> ( sK9 != sK9 ) ) )
| ~ spl0_10
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f550,f169]) ).
thf(f169,plain,
( ( $true
= ( sK2 @ sK9 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f168]) ).
thf(f168,definition,
( spl0_10
<=> ( $true
= ( sK2 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f550,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f549]) ).
thf(f551,plain,
( spl0_25
| spl0_26
| ~ spl0_4
| ~ spl0_12
| ~ spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f544,f526,f175,f30,f549,f546]) ).
thf(f544,plain,
( ! [X0: a] :
( ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f543]) ).
thf(f543,plain,
( ! [X0: a] :
( ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ( $true = $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f542]) ).
thf(f542,plain,
( ! [X0: a] :
( ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ~ $false ) = $false )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_24 ),
inference(forward_demodulation,[status(thm)],[f541,f259]) ).
thf(f259,plain,
( ( ( sK4 @ sK9 )
= $false )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( ( $false
| ( sK4 @ sK9 ) )
= $false )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f176,f257]) ).
thf(f541,plain,
( ! [X0: a] :
( ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( sK4 @ sK9 ) ) )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) )
| ~ spl0_4
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f540]) ).
thf(f540,plain,
( ! [X0: a] :
( ( ( ( sK4 @ sK9 )
=> $false )
= $false )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) ) )
| ~ spl0_4
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f539]) ).
thf(f539,plain,
( ! [X0: a] :
( ( ( ( sK4 @ sK9 )
=> ~ $true )
= $false )
| ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false ) )
| ~ spl0_4
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f538]) ).
thf(f538,plain,
( ! [X0: a] :
( ( $true
= ( ( sK2 @ X0 )
=> ( sK9 != X0 ) ) )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( sK9
!= ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ( ( ( sK4 @ sK9 )
=> ( sK9 != sK9 ) )
= $false ) )
| ~ spl0_4
| ~ spl0_24 ),
inference(beta_eta_normalization,[status(thm)],[f537]) ).
thf(f537,plain,
( ! [X0: a] :
( ( ( ( sK2 @ X0 )
=> ( ^ [Y0: a] : ( sK9 != Y0 )
@ X0 ) )
= $true )
| ( ( ( sK3
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
=> ( ^ [Y0: a] : ( sK9 != Y0 )
@ ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
= $false )
| ( ( ( sK4 @ sK9 )
=> ( ^ [Y0: a] : ( sK9 != Y0 )
@ sK9 ) )
= $false ) )
| ~ spl0_4
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f309,f532]) ).
thf(f532,plain,
( ( ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 )
| ~ spl0_24 ),
inference(equality_proxy_clausification,[status(thm)],[f529]) ).
thf(f529,plain,
( ( $true
= ( sK9
= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) ) )
| ~ spl0_24 ),
inference(not_proxy_clausification,[status(thm)],[f527]) ).
thf(f527,plain,
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f526]) ).
thf(f528,plain,
( spl0_23
| spl0_24
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f513,f168,f30,f526,f523]) ).
thf(f513,plain,
( ( ( sK9
!= ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ( ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 )
| ~ spl0_4
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f481]) ).
thf(f481,plain,
( ( ( sK11
@ ^ [Y0: a] : ( sK9 != Y0 ) )
= sK9 )
| ( ( ^ [Y0: a] : ( sK9 != Y0 )
@ ( sK10
@ ^ [Y0: a] : ( sK9 != Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_10 ),
inference(leibniz_equality_elimination,[status(thm)],[f352]) ).
thf(f352,plain,
( ! [X0: a > $o] :
( ( ( X0 @ ( sK11 @ X0 ) )
= $false )
| ( ( X0 @ ( sK10 @ X0 ) )
= $false )
| ( $true
= ( X0 @ sK9 ) ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f349]) ).
thf(f349,plain,
( ! [X0: a > $o] :
( ( ( X0 @ ( sK11 @ X0 ) )
= $false )
| ( ( X0 @ ( sK10 @ X0 ) )
= $false )
| ( $true
= ( $true
=> ( X0 @ sK9 ) ) ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f329,f169]) ).
thf(f329,plain,
( ! [X2: a,X1: a > $o] :
( ( $true
= ( ( sK2 @ X2 )
=> ( X1 @ X2 ) ) )
| ( ( X1 @ ( sK11 @ X1 ) )
= $false )
| ( ( X1 @ ( sK10 @ X1 ) )
= $false ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f313]) ).
thf(f247,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f246]) ).
thf(f246,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f195,f208]) ).
thf(f208,plain,
( ( ( sK3 @ sK9 )
= $false )
| ~ spl0_4
| ~ spl0_11 ),
inference(not_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ( ~ ( sK3 @ sK9 ) )
= $true )
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f190]) ).
thf(f190,plain,
( ( $true
= ( ( sK3 @ sK9 )
=> $false ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f188,f173]) ).
thf(f173,plain,
( ( ( sK2 @ sK9 )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f172,definition,
( spl0_11
<=> ( ( sK2 @ sK9 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f188,plain,
( ! [X1: a] :
( $true
= ( ( sK3 @ X1 )
=> ( sK2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f187]) ).
thf(f187,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f185]) ).
thf(f185,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f31,f184]) ).
thf(f195,plain,
( ( $true
= ( sK3 @ sK9 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f194]) ).
thf(f194,definition,
( spl0_13
<=> ( $true
= ( sK3 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f241,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f240]) ).
thf(f240,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f233,f173]) ).
thf(f233,plain,
( ( $true
= ( sK2 @ sK9 ) )
| ~ spl0_4
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $true
= ( $true
=> ( sK2 @ sK9 ) ) )
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f227,f198]) ).
thf(f198,plain,
( ( $true
= ( sK4 @ sK9 ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f197]) ).
thf(f197,definition,
( spl0_14
<=> ( $true
= ( sK4 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f227,plain,
( ! [X1: a] :
( $true
= ( ( sK4 @ X1 )
=> ( sK2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f223]) ).
thf(f223,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f205]) ).
thf(f199,plain,
( spl0_13
| spl0_14
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f192,f172,f23,f197,f194]) ).
thf(f23,definition,
( spl0_2
<=> ( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f192,plain,
( ( $true
= ( sK4 @ sK9 ) )
| ( $true
= ( sK3 @ sK9 ) )
| ~ spl0_2
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
( ( ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) )
!= $false )
| ~ spl0_2
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f161,f173]) ).
thf(f161,plain,
( ( ( sK2 @ sK9 )
!= ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
( ( ( sK2 @ sK9 )
!= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(negative_extensionality,[status(thm)],[f159]) ).
thf(f159,plain,
( ( sK2
!= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f181,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| ~ spl0_9
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $true = $false )
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f166,f176]) ).
thf(f166,plain,
( ( $true
= ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f165,definition,
( spl0_9
<=> ( $true
= ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f177,plain,
( spl0_11
| spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f163,f23,f175,f172]) ).
thf(f163,plain,
( ( ( sK2 @ sK9 )
= $false )
| ( ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f170,plain,
( spl0_9
| spl0_10
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f162,f23,f168,f165]) ).
thf(f162,plain,
( ( $true
= ( sK2 @ sK9 ) )
| ( $true
= ( ( sK3 @ sK9 )
| ( sK4 @ sK9 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f156,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f155]) ).
thf(f155,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f153,f151]) ).
thf(f151,plain,
( ( ( sK2 @ sK8 )
= $false )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ( $true
=> ( sK2 @ sK8 ) )
= $false )
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f147,f149]) ).
thf(f149,plain,
( ( $true
= ( sK4 @ sK8 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( ( sK4 @ sK8 )
=> ( sK2 @ sK8 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) )
@ sK8 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f153,plain,
( ( $true
= ( sK2 @ sK8 ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( ( sK3 @ sK8 )
| $true )
= ( sK2 @ sK8 ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f84,f149]) ).
thf(f84,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
| ( sK4 @ X1 ) )
= ( sK2 @ X1 ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) )
@ X1 )
= ( sK2 @ X1 ) )
| ~ spl0_6 ),
inference(argument_congruence,[status(thm)],[f78]) ).
thf(f78,plain,
( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
!= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
!= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f16,f51]) ).
thf(f51,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl0_6
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f16,plain,
( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
= ( sK2
= ( ^ [Y1: a] :
( ( sK3 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
= ( sK2
= ( ^ [Y1: a] :
( ( sK3 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK2 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( sK2 @ Y2 ) ) ) )
= ( sK2
= ( ^ [Y2: a] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK2 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( sK2 @ Y2 ) ) ) )
= ( sK2
= ( ^ [Y2: a] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y0 @ Y3 ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y0 @ Y3 ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y0 @ Y3 ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
=> ( Y0 @ Y3 ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a] :
( ( X0 @ X6 )
=> ( X4 @ X6 ) ) )
=> ! [X7: a] :
( ( X2 @ X7 )
=> ( X4 @ X7 ) ) )
& ! [X8: a] :
( ( X0 @ X8 )
=> ( X2 @ X8 ) ) )
<=> ( X2
= ( ^ [X9: a] :
( ( X0 @ X9 )
| ( X1 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) )
& ! [X5: a > $o] :
( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X5 @ X4 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X5 @ X4 ) ) )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( X5 @ X4 ) ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) ) )
<=> ( X0
= ( ^ [X3: a] :
( ( X2 @ X3 )
| ( X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X0 @ X4 ) )
& ! [X5: a > $o] :
( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X5 @ X4 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X5 @ X4 ) ) )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( X5 @ X4 ) ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) ) )
<=> ( X0
= ( ^ [X3: a] :
( ( X2 @ X3 )
| ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.flVDtHJC2k/DTF2THF_4962.p',cBOOL_PROP_56_pme) ).
thf(f143,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f142]) ).
thf(f142,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f135,f110]) ).
thf(f110,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ( $true
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f106,f108]) ).
thf(f108,plain,
( ( ( sK2 @ sK7 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( ( ( sK2 @ sK7 )
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK7 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
@ sK6 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_8
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f135,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true
= ( $true
=> ( sK6 @ sK7 ) ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f129,f127]) ).
thf(f127,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f126,f108]) ).
thf(f126,plain,
( ( ( sK2 @ sK7 )
= ( sK3 @ sK7 ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( sK2 @ sK7 )
= ( ( sK3 @ sK7 )
| $false ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f84,f120]) ).
thf(f120,plain,
( ( ( sK4 @ sK7 )
= $false )
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true
= ( ~ ( sK4 @ sK7 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f118]) ).
thf(f118,plain,
( ( ( ( sK4 @ sK7 )
=> $false )
= $true )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f116,f110]) ).
thf(f116,plain,
( ! [X1: a] :
( $true
= ( ( sK4 @ X1 )
=> ( sK6 @ X1 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& $true ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f100,f111]) ).
thf(f111,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f129,plain,
( ! [X1: a] :
( $true
= ( ( sK3 @ X1 )
=> ( sK6 @ X1 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK6 @ Y0 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f111]) ).
thf(f94,plain,
( spl0_7
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f87,f50,f92,f89]) ).
thf(f87,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
= $false )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f73,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& $false ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f31,f48]) ).
thf(f48,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f67,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f64,f57]) ).
thf(f57,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ( sK3 @ sK5 )
=> ( sK2 @ sK5 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) )
@ sK5 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f64,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( $true
| ( sK4 @ sK5 ) )
= ( sK2 @ sK5 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f42,f58]) ).
thf(f58,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f42,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
| ( sK4 @ X1 ) )
= ( sK2 @ X1 ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) )
@ X1 )
= ( sK2 @ X1 ) )
| ~ spl0_3 ),
inference(argument_congruence,[status(thm)],[f38]) ).
thf(f38,plain,
( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_3
<=> ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f52,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f45,f20,f50,f47]) ).
thf(f20,definition,
( spl0_1
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f45,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f36,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f28,f24]) ).
thf(f32,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f30,f27]) ).
thf(f17,plain,
( ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f23,f20]) ).
thf(f18,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 )
=> ( sK2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= $false )
| ( ( sK2
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET597^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n010.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 11:59:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SET597^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : TPS problem BOOL-PROP-56
% 0.32/0.48 % Version : Especial.
% 0.32/0.48 % English : Trybulec's 56th Boolean property of sets
% 0.32/0.48
% 0.32/0.48 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.32/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.48 % Source : [Bro09]
% 0.32/0.48 % Names : tps_0564 [Bro09]
% 0.32/0.48 % : BOOL-PROP-56 [TPS]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.32/0.48 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.32/0.48 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 1 ( 1 avg)
% 0.32/0.48 % Number of connectives : 23 ( 0 ~; 1 |; 3 &; 12 @)
% 0.32/0.48 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 13 ( 13 avg)
% 0.32/0.48 % Number of types : 2 ( 1 usr)
% 0.32/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.32/0.48 % Number of variables : 10 ( 1 ^; 9 !; 0 ?; 10 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.48 % : Polymorphic definitions expanded.
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(a_type,type,
% 0.32/0.48 a: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(cBOOL_PROP_56_pme,conjecture,
% 0.32/0.48 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.32/0.48 ( ( X
% 0.32/0.48 = ( ^ [Xz: a] :
% 0.32/0.48 ( ( Y @ Xz )
% 0.32/0.48 | ( Z @ Xz ) ) ) )
% 0.32/0.48 <=> ( ! [Xx: a] :
% 0.32/0.48 ( ( Y @ Xx )
% 0.32/0.48 => ( X @ Xx ) )
% 0.32/0.48 & ! [Xx: a] :
% 0.32/0.48 ( ( Z @ Xx )
% 0.32/0.48 => ( X @ Xx ) )
% 0.32/0.48 & ! [V: a > $o] :
% 0.32/0.48 ( ( ! [Xx: a] :
% 0.32/0.48 ( ( Y @ Xx )
% 0.32/0.48 => ( V @ Xx ) )
% 0.32/0.48 & ! [Xx: a] :
% 0.32/0.48 ( ( Z @ Xx )
% 0.32/0.48 => ( V @ Xx ) ) )
% 0.32/0.48 => ! [Xx: a] :
% 0.32/0.48 ( ( X @ Xx )
% 0.32/0.48 => ( V @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.64/1.44 ---- Embedded in THF ---
% 1.64/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.44 %%% Generated on Tue Feb 24 11:59:49 EST 2026
% 1.64/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.44 %%% Logic specification used:
% 1.64/1.44 %%% thf(spec, logic, $$dhol).
% 1.64/1.44
% 1.64/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.flVDtHJC2k/DTF2DTF4962.p
% See solution above
% 1.64/1.44 ------------------------
% 1.64/1.45 ---- Cleaned THF ---
% 1.64/1.45 thf(a_type,type,
% 1.64/1.45 a: $tType ).
% 1.64/1.45
% 1.64/1.45 thf(cBOOL_PROP_56_pme,conjecture,
% 1.64/1.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.64/1.45 ( ( X
% 1.64/1.45 = ( ^ [Xz: a] :
% 1.64/1.45 ( ( Y @ Xz )
% 1.64/1.45 | ( Z @ Xz ) ) ) )
% 1.64/1.45 <=> ( ! [Xx: a] :
% 1.64/1.45 ( ( Y @ Xx )
% 1.64/1.45 => ( X @ Xx ) )
% 1.64/1.45 & ! [Xx: a] :
% 1.64/1.45 ( ( Z @ Xx )
% 1.64/1.45 => ( X @ Xx ) )
% 1.64/1.45 & ! [V: a > $o] :
% 1.64/1.45 ( ( ! [Xx: a] :
% 1.64/1.45 ( ( Y @ Xx )
% 1.64/1.45 => ( V @ Xx ) )
% 1.64/1.45 & ! [Xx: a] :
% 1.64/1.45 ( ( Z @ Xx )
% 1.64/1.45 => ( V @ Xx ) ) )
% 1.64/1.45 => ! [Xx: a] :
% 1.64/1.45 ( ( X @ Xx )
% 1.64/1.45 => ( V @ Xx ) ) ) ) ) ).
% 1.64/1.45 ------------------------
% 1.64/1.47 % (5061)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_4962 for (3000ds/4Mi)
% 1.64/1.47 % (5062)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_4962 for (3000ds/27Mi)
% 1.64/1.47 % (5060)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4962 for (3000ds/183Mi)
% 1.64/1.47 % (5063)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4962 for (3000ds/2Mi)
% 1.64/1.47 % (5064)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_4962 for (3000ds/2Mi)
% 1.64/1.47 % (5066)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4962 for (3000ds/18Mi)
% 1.64/1.47 % (5065)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_4962 for (3000ds/275Mi)
% 1.64/1.47 % (5063)Instruction limit reached!
% 1.64/1.47 % (5063)------------------------------
% 1.64/1.47 % (5063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (5063)Termination reason: Unknown
% 1.64/1.47 % (5063)Termination phase: Saturation
% 1.64/1.47 % (5064)Instruction limit reached!
% 1.64/1.47 % (5064)------------------------------
% 1.64/1.47 % (5064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (5064)Termination reason: Unknown
% 1.64/1.47 % (5064)Termination phase: Saturation
% 1.64/1.47
% 1.64/1.47 % (5064)Memory used [KB]: 5500
% 1.64/1.47 % (5064)Time elapsed: 0.003 s
% 1.64/1.47 % (5064)Instructions burned: 3 (million)
% 1.64/1.47 % (5064)------------------------------
% 1.64/1.47 % (5064)------------------------------
% 1.64/1.47
% 1.64/1.47 % (5063)Memory used [KB]: 1023
% 1.64/1.47 % (5063)Time elapsed: 0.003 s
% 1.64/1.47 % (5063)Instructions burned: 3 (million)
% 1.64/1.47 % (5063)------------------------------
% 1.64/1.47 % (5063)------------------------------
% 1.64/1.47 % (5061)Instruction limit reached!
% 1.64/1.47 % (5061)------------------------------
% 1.64/1.47 % (5061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (5061)Termination reason: Unknown
% 1.64/1.47 % (5061)Termination phase: Saturation
% 1.64/1.47
% 1.64/1.47 % (5061)Memory used [KB]: 5500
% 1.64/1.47 % (5061)Time elapsed: 0.004 s
% 1.64/1.47 % (5061)Instructions burned: 4 (million)
% 1.64/1.47 % (5061)------------------------------
% 1.64/1.47 % (5061)------------------------------
% 1.64/1.47 % (5065)Refutation not found, incomplete strategy
% 1.64/1.47 % (5065)------------------------------
% 1.64/1.47 % (5065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (5065)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.47
% 1.64/1.47
% 1.64/1.47 % (5065)Memory used [KB]: 5500
% 1.64/1.47 % (5065)Time elapsed: 0.007 s
% 1.64/1.47 % (5065)Instructions burned: 9 (million)
% 1.64/1.47 % (5065)------------------------------
% 1.64/1.47 % (5065)------------------------------
% 1.64/1.48 % (5066)Instruction limit reached!
% 1.64/1.48 % (5066)------------------------------
% 1.64/1.48 % (5066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.48 % (5066)Termination reason: Unknown
% 1.64/1.48 % (5066)Termination phase: Saturation
% 1.64/1.48
% 1.64/1.48 % (5066)Memory used [KB]: 5628
% 1.64/1.48 % (5066)Time elapsed: 0.011 s
% 1.64/1.48 % (5066)Instructions burned: 18 (million)
% 1.64/1.48 % (5066)------------------------------
% 1.64/1.48 % (5066)------------------------------
% 1.64/1.48 % (5062)Instruction limit reached!
% 1.64/1.48 % (5062)------------------------------
% 1.64/1.48 % (5062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.48 % (5062)Termination reason: Unknown
% 1.64/1.48 % (5062)Termination phase: Saturation
% 1.64/1.48
% 1.64/1.48 % (5062)Memory used [KB]: 5756
% 1.64/1.48 % (5062)Time elapsed: 0.018 s
% 1.64/1.48 % (5062)Instructions burned: 28 (million)
% 1.64/1.48 % (5062)------------------------------
% 1.64/1.48 % (5062)------------------------------
% 1.64/1.48 % (5067)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/3Mi)
% 1.64/1.48 % (5068)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/37Mi)
% 1.64/1.48 % (5069)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/15Mi)
% 1.64/1.48 % (5067)Instruction limit reached!
% 1.64/1.48 % (5067)------------------------------
% 1.64/1.48 % (5067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (5067)Termination reason: Unknown
% 1.64/1.49 % (5067)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (5067)Memory used [KB]: 5500
% 1.64/1.49 % (5067)Time elapsed: 0.003 s
% 1.64/1.49 % (5067)Instructions burned: 3 (million)
% 1.64/1.49 % (5067)------------------------------
% 1.64/1.49 % (5067)------------------------------
% 1.64/1.49 % (5070)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/3Mi)
% 1.64/1.49 % (5070)Instruction limit reached!
% 1.64/1.49 % (5070)------------------------------
% 1.64/1.49 % (5070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (5070)Termination reason: Unknown
% 1.64/1.49 % (5070)Termination phase: Property scanning
% 1.64/1.49
% 1.64/1.49 % (5070)Memory used [KB]: 1023
% 1.64/1.49 % (5070)Time elapsed: 0.003 s
% 1.64/1.49 % (5070)Instructions burned: 3 (million)
% 1.64/1.49 % (5070)------------------------------
% 1.64/1.49 % (5070)------------------------------
% 1.64/1.49 % (5071)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/1041Mi)
% 1.64/1.49 % (5069)Instruction limit reached!
% 1.64/1.49 % (5069)------------------------------
% 1.64/1.49 % (5069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (5069)Termination reason: Unknown
% 1.64/1.49 % (5069)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (5069)Memory used [KB]: 5756
% 1.64/1.49 % (5069)Time elapsed: 0.010 s
% 1.64/1.49 % (5069)Instructions burned: 16 (million)
% 1.64/1.49 % (5069)------------------------------
% 1.64/1.49 % (5069)------------------------------
% 1.74/1.50 % (5072)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/7Mi)
% 1.74/1.50 % (5073)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/16Mi)
% 1.74/1.50 % (5068)Instruction limit reached!
% 1.74/1.50 % (5068)------------------------------
% 1.74/1.50 % (5068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (5068)Termination reason: Unknown
% 1.74/1.50 % (5068)Termination phase: Saturation
% 1.74/1.50
% 1.74/1.50 % (5068)Memory used [KB]: 5628
% 1.74/1.50 % (5068)Time elapsed: 0.020 s
% 1.74/1.50 % (5068)Instructions burned: 37 (million)
% 1.74/1.50 % (5068)------------------------------
% 1.74/1.50 % (5068)------------------------------
% 1.74/1.50 % (5072)Instruction limit reached!
% 1.74/1.50 % (5072)------------------------------
% 1.74/1.50 % (5072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (5072)Termination reason: Unknown
% 1.74/1.50 % (5072)Termination phase: Saturation
% 1.74/1.50
% 1.74/1.50 % (5072)Memory used [KB]: 1023
% 1.74/1.50 % (5072)Time elapsed: 0.006 s
% 1.74/1.50 % (5072)Instructions burned: 8 (million)
% 1.74/1.50 % (5072)------------------------------
% 1.74/1.50 % (5072)------------------------------
% 1.74/1.51 % (5074)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/3Mi)
% 1.74/1.51 % (5074)Instruction limit reached!
% 1.74/1.51 % (5074)------------------------------
% 1.74/1.51 % (5074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.51 % (5074)Termination reason: Unknown
% 1.74/1.51 % (5074)Termination phase: Twee Goal Transformation
% 1.74/1.51
% 1.74/1.51 % (5074)Memory used [KB]: 1023
% 1.74/1.51 % (5074)Time elapsed: 0.003 s
% 1.74/1.51 % (5074)Instructions burned: 3 (million)
% 1.74/1.51 % (5074)------------------------------
% 1.74/1.51 % (5074)------------------------------
% 1.74/1.51 % (5075)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/3Mi)
% 1.74/1.51 % (5075)Instruction limit reached!
% 1.74/1.51 % (5075)------------------------------
% 1.74/1.51 % (5075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.51 % (5075)Termination reason: Unknown
% 1.74/1.51 % (5075)Termination phase: Property scanning
% 1.74/1.51
% 1.74/1.51 % (5075)Memory used [KB]: 1023
% 1.74/1.51 % (5075)Time elapsed: 0.003 s
% 1.74/1.51 % (5075)Instructions burned: 3 (million)
% 1.74/1.51 % (5075)------------------------------
% 1.74/1.51 % (5075)------------------------------
% 1.74/1.51 % (5073)Instruction limit reached!
% 1.74/1.51 % (5073)------------------------------
% 1.74/1.51 % (5073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.51 % (5073)Termination reason: Unknown
% 1.74/1.51 % (5073)Termination phase: Saturation
% 1.74/1.51
% 1.74/1.51 % (5073)Memory used [KB]: 5756
% 1.74/1.51 % (5073)Time elapsed: 0.011 s
% 1.74/1.51 % (5073)Instructions burned: 17 (million)
% 1.74/1.51 % (5073)------------------------------
% 1.74/1.51 % (5073)------------------------------
% 1.74/1.52 % (5077)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/3Mi)
% 1.74/1.52 % (5076)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/7Mi)
% 1.74/1.52 % (5077)Instruction limit reached!
% 1.74/1.52 % (5077)------------------------------
% 1.74/1.52 % (5077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (5077)Termination reason: Unknown
% 1.74/1.52 % (5077)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (5077)Memory used [KB]: 5500
% 1.74/1.52 % (5077)Time elapsed: 0.003 s
% 1.74/1.52 % (5077)Instructions burned: 3 (million)
% 1.74/1.52 % (5077)------------------------------
% 1.74/1.52 % (5077)------------------------------
% 1.74/1.52 % (5078)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/4Mi)
% 1.74/1.52 % (5076)Instruction limit reached!
% 1.74/1.52 % (5076)------------------------------
% 1.74/1.52 % (5076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (5076)Termination reason: Unknown
% 1.74/1.52 % (5076)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (5076)Memory used [KB]: 5500
% 1.74/1.52 % (5076)Time elapsed: 0.006 s
% 1.74/1.52 % (5076)Instructions burned: 8 (million)
% 1.74/1.52 % (5076)------------------------------
% 1.74/1.52 % (5076)------------------------------
% 1.74/1.53 % (5078)Instruction limit reached!
% 1.74/1.53 % (5078)------------------------------
% 1.74/1.53 % (5078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.53 % (5078)Termination reason: Unknown
% 1.74/1.53 % (5078)Termination phase: Saturation
% 1.74/1.53
% 1.74/1.53 % (5078)Memory used [KB]: 5500
% 1.74/1.53 % (5078)Time elapsed: 0.004 s
% 1.74/1.53 % (5078)Instructions burned: 5 (million)
% 1.74/1.53 % (5078)------------------------------
% 1.74/1.53 % (5078)------------------------------
% 1.74/1.53 % (5079)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/18Mi)
% 1.74/1.53 % (5080)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/710Mi)
% 1.74/1.54 % (5071)First to succeed.
% 1.74/1.54 % (5081)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/6Mi)
% 1.74/1.54 % (5079)Instruction limit reached!
% 1.74/1.54 % (5079)------------------------------
% 1.74/1.54 % (5079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.54 % (5079)Termination reason: Unknown
% 1.74/1.54 % (5079)Termination phase: Saturation
% 1.74/1.54
% 1.74/1.54 % (5079)Memory used [KB]: 5628
% 1.74/1.54 % (5079)Time elapsed: 0.034 s
% 1.74/1.54 % (5079)Instructions burned: 19 (million)
% 1.74/1.54 % (5079)------------------------------
% 1.74/1.54 % (5079)------------------------------
% 1.74/1.54 % (5082)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/902Mi)
% 1.74/1.54 % (5081)Instruction limit reached!
% 1.74/1.54 % (5081)------------------------------
% 1.74/1.54 % (5081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.54 % (5060)Instruction limit reached!
% 1.74/1.54 % (5060)------------------------------
% 1.74/1.54 % (5060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.54 % (5060)Termination reason: Unknown
% 1.74/1.54 % (5060)Termination phase: Saturation
% 1.74/1.54
% 1.74/1.54 % (5060)Memory used [KB]: 6140
% 1.74/1.54 % (5060)Time elapsed: 0.076 s
% 1.74/1.54 % (5060)Instructions burned: 184 (million)
% 1.74/1.54 % (5060)------------------------------
% 1.74/1.54 % (5060)------------------------------
% 1.74/1.54 % (5081)Termination reason: Unknown
% 1.74/1.54 % (5081)Termination phase: Saturation
% 1.74/1.54
% 1.74/1.54 % (5081)Memory used [KB]: 5500
% 1.74/1.54 % (5081)Time elapsed: 0.005 s
% 1.74/1.54 % (5081)Instructions burned: 7 (million)
% 1.74/1.54 % (5081)------------------------------
% 1.74/1.54 % (5081)------------------------------
% 1.74/1.54 % (5083)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_4962 for (2999ds/21Mi)
% 1.74/1.54 % (5071)Refutation found. Thanks to Tanya!
% 1.74/1.54 % SZS status Theorem for DTF2THF_4962
% 1.74/1.54 % SZS output start Proof for DTF2THF_4962
% 1.74/1.54 thf(type_def_5, type, a: $tType).
% 1.74/1.54 thf(func_def_0, type, a: $tType).
% 1.74/1.54 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 1.74/1.54 thf(func_def_19, type, sK2: a > $o).
% 1.74/1.54 thf(func_def_20, type, sK3: a > $o).
% 1.74/1.54 thf(func_def_21, type, sK4: a > $o).
% 1.74/1.54 thf(func_def_22, type, sK5: a).
% 1.74/1.54 thf(func_def_23, type, sK6: a > $o).
% 1.74/1.54 thf(func_def_24, type, sK7: a).
% 1.74/1.54 thf(func_def_25, type, sK8: a).
% 1.74/1.54 thf(func_def_26, type, sK9: a).
% 1.74/1.54 thf(func_def_27, type, sK10: (a > $o) > a).
% 1.74/1.54 thf(func_def_28, type, sK11: (a > $o) > a).
% 1.74/1.54 thf(f635,plain,(
% 1.74/1.54 $false),
% 1.74/1.54 inference(avatar_sat_refutation,[status(thm)],[f25,f32,f36,f52,f67,f73,f94,f143,f156,f170,f177,f181,f199,f241,f247,f528,f551,f571,f600,f608,f634])).
% 1.74/1.54 thf(f634,plain,(
% 1.74/1.54 spl0_26 | spl0_24 | ~spl0_4 | ~spl0_12 | ~spl0_23),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f633,f523,f175,f30,f526,f549])).
% 1.74/1.54 thf(f549,definition,(
% 1.74/1.54 spl0_26 <=> ! [X0 : a] : ($true = ((sK2 @ X0) => (~ (sK9 = X0))))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])).
% 1.74/1.54 thf(f526,definition,(
% 1.74/1.54 spl0_24 <=> ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.74/1.54 thf(f30,definition,(
% 1.74/1.54 spl0_4 <=> ($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.74/1.54 thf(f175,definition,(
% 1.74/1.54 spl0_12 <=> (((sK3 @ sK9) | (sK4 @ sK9)) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.74/1.54 thf(f523,definition,(
% 1.74/1.54 spl0_23 <=> ((sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 1.74/1.54 thf(f633,plain,(
% 1.74/1.54 ( ! [X0 : a] : (((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | (~spl0_4 | ~spl0_12 | ~spl0_23)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f632])).
% 1.74/1.54 thf(f632,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | ($true = $false) | ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false)) ) | (~spl0_4 | ~spl0_12 | ~spl0_23)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f631])).
% 1.74/1.54 thf(f631,plain,(
% 1.74/1.54 ( ! [X0 : a] : (((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | ((~ $false) = $false)) ) | (~spl0_4 | ~spl0_12 | ~spl0_23)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f615,f257])).
% 1.74/1.54 thf(f257,plain,(
% 1.74/1.54 ((sK3 @ sK9) = $false) | ~spl0_12),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f176])).
% 1.74/1.54 thf(f176,plain,(
% 1.74/1.54 (((sK3 @ sK9) | (sK4 @ sK9)) = $false) | ~spl0_12),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f175])).
% 1.74/1.54 thf(f615,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ((~ (sK3 @ sK9)) = $false)) ) | (~spl0_4 | ~spl0_23)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f614])).
% 1.74/1.54 thf(f614,plain,(
% 1.74/1.54 ( ! [X0 : a] : (((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | (((sK3 @ sK9) => $false) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | (~spl0_4 | ~spl0_23)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f613])).
% 1.74/1.54 thf(f613,plain,(
% 1.74/1.54 ( ! [X0 : a] : (((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | (((sK3 @ sK9) => (~ $true)) = $false)) ) | (~spl0_4 | ~spl0_23)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f612])).
% 1.74/1.54 thf(f612,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK3 @ sK9) => (~ (sK9 = sK9))) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false)) ) | (~spl0_4 | ~spl0_23)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f611])).
% 1.74/1.54 thf(f611,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK2 @ X0) => ((^[Y0 : a]: (~ (sK9 = Y0))) @ X0)) = $true) | (((sK3 @ sK9) => ((^[Y0 : a]: (~ (sK9 = Y0))) @ sK9)) = $false) | (((^[Y0 : a]: (~ (sK9 = Y0))) @ (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0))))) = $false)) ) | (~spl0_4 | ~spl0_23)),
% 1.74/1.54 inference(superposition,[status(thm)],[f313,f524])).
% 1.74/1.54 thf(f524,plain,(
% 1.74/1.54 ((sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9) | ~spl0_23),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f523])).
% 1.74/1.54 thf(f313,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : ((((sK3 @ (sK11 @ X1)) => (X1 @ (sK11 @ X1))) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2))) | ((X1 @ (sK10 @ X1)) = $false)) ) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f309])).
% 1.74/1.54 thf(f309,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : ((((sK4 @ (sK10 @ X1)) => (X1 @ (sK10 @ X1))) = $false) | (((sK3 @ (sK11 @ X1)) => (X1 @ (sK11 @ X1))) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2)))) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f300])).
% 1.74/1.54 thf(f300,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : ((((sK4 @ (sK10 @ X1)) => (X1 @ (sK10 @ X1))) = $false) | (((^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0))) @ (sK11 @ X1)) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2)))) ) | ~spl0_4),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f299])).
% 1.74/1.54 thf(f299,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2))) | (((sK4 @ (sK10 @ X1)) => (X1 @ (sK10 @ X1))) = $false)) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f287])).
% 1.74/1.54 thf(f287,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : ((((^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0))) @ (sK10 @ X1)) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2)))) ) | ~spl0_4),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f285])).
% 1.74/1.54 thf(f285,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))) = $false) | ($true = ((sK2 @ X2) => (X1 @ X2)))) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f283])).
% 1.74/1.54 thf(f283,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))) = $false) | ($true = ((^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0))) @ X2))) ) | ~spl0_4),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f269])).
% 1.74/1.54 thf(f269,plain,(
% 1.74/1.54 ( ! [X1 : a > $o] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))) = $false)) ) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f215])).
% 1.74/1.54 thf(f215,plain,(
% 1.74/1.54 ( ! [X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0))))) = $false) | ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0)))))) ) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f212])).
% 1.74/1.54 thf(f212,plain,(
% 1.74/1.54 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0))))) => (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0))))))) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.74/1.54 thf(f211,plain,(
% 1.74/1.54 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))) @ X1))) ) | ~spl0_4),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f207])).
% 1.74/1.54 thf(f207,plain,(
% 1.74/1.54 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) | ~spl0_4),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f206])).
% 1.74/1.54 thf(f206,plain,(
% 1.74/1.54 ($true = ($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))))))) | ~spl0_4),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f184,f205])).
% 1.74/1.54 thf(f205,plain,(
% 1.74/1.54 ($true = (!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0))))) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f184])).
% 1.74/1.54 thf(f184,plain,(
% 1.74/1.54 ($true = ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))))))) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.74/1.54 thf(f31,plain,(
% 1.74/1.54 ($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0)))))) | ~spl0_4),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.74/1.54 thf(f608,plain,(
% 1.74/1.54 ~spl0_12 | ~spl0_23 | ~spl0_25),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f607])).
% 1.74/1.54 thf(f607,plain,(
% 1.74/1.54 $false | (~spl0_12 | ~spl0_23 | ~spl0_25)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f606])).
% 1.74/1.54 thf(f606,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_12 | ~spl0_23 | ~spl0_25)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f604,f257])).
% 1.74/1.54 thf(f604,plain,(
% 1.74/1.54 ($true = (sK3 @ sK9)) | (~spl0_23 | ~spl0_25)),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f573,f524])).
% 1.74/1.54 thf(f573,plain,(
% 1.74/1.54 ($true = (sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) | ~spl0_25),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f547])).
% 1.74/1.54 thf(f547,plain,(
% 1.74/1.54 (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | ~spl0_25),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f546])).
% 1.74/1.54 thf(f546,definition,(
% 1.74/1.54 spl0_25 <=> (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 1.74/1.54 thf(f600,plain,(
% 1.74/1.54 spl0_23 | ~spl0_25),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f597,f546,f523])).
% 1.74/1.54 thf(f597,plain,(
% 1.74/1.54 ((sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9) | ~spl0_25),
% 1.74/1.54 inference(equality_proxy_clausification,[status(thm)],[f586])).
% 1.74/1.54 thf(f586,plain,(
% 1.74/1.54 ($true = (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) | ~spl0_25),
% 1.74/1.54 inference(not_proxy_clausification,[status(thm)],[f575])).
% 1.74/1.54 thf(f575,plain,(
% 1.74/1.54 ((~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ~spl0_25),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f574])).
% 1.74/1.54 thf(f574,plain,(
% 1.74/1.54 (($true => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | ~spl0_25),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f547,f573])).
% 1.74/1.54 thf(f571,plain,(
% 1.74/1.54 ~spl0_10 | ~spl0_26),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f570])).
% 1.74/1.54 thf(f570,plain,(
% 1.74/1.54 $false | (~spl0_10 | ~spl0_26)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f569])).
% 1.74/1.54 thf(f569,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_10 | ~spl0_26)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f568])).
% 1.74/1.54 thf(f568,plain,(
% 1.74/1.54 ($true = (~ $true)) | (~spl0_10 | ~spl0_26)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f567])).
% 1.74/1.54 thf(f567,plain,(
% 1.74/1.54 ($true = (~ (sK9 = sK9))) | (~spl0_10 | ~spl0_26)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f554])).
% 1.74/1.54 thf(f554,plain,(
% 1.74/1.54 ($true = ($true => (~ (sK9 = sK9)))) | (~spl0_10 | ~spl0_26)),
% 1.74/1.54 inference(superposition,[status(thm)],[f550,f169])).
% 1.74/1.54 thf(f169,plain,(
% 1.74/1.54 ($true = (sK2 @ sK9)) | ~spl0_10),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f168])).
% 1.74/1.54 thf(f168,definition,(
% 1.74/1.54 spl0_10 <=> ($true = (sK2 @ sK9))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.74/1.54 thf(f550,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | ~spl0_26),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f549])).
% 1.74/1.54 thf(f551,plain,(
% 1.74/1.54 spl0_25 | spl0_26 | ~spl0_4 | ~spl0_12 | ~spl0_24),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f544,f526,f175,f30,f549,f546])).
% 1.74/1.54 thf(f544,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false)) ) | (~spl0_4 | ~spl0_12 | ~spl0_24)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f543])).
% 1.74/1.54 thf(f543,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | ($true = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | (~spl0_4 | ~spl0_12 | ~spl0_24)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f542])).
% 1.74/1.54 thf(f542,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | ((~ $false) = $false) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false)) ) | (~spl0_4 | ~spl0_12 | ~spl0_24)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f541,f259])).
% 1.74/1.54 thf(f259,plain,(
% 1.74/1.54 ((sK4 @ sK9) = $false) | ~spl0_12),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f258])).
% 1.74/1.54 thf(f258,plain,(
% 1.74/1.54 (($false | (sK4 @ sK9)) = $false) | ~spl0_12),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f176,f257])).
% 1.74/1.54 thf(f541,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | ($false = (~ (sK4 @ sK9))) | ($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | (~spl0_4 | ~spl0_24)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f540])).
% 1.74/1.54 thf(f540,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK4 @ sK9) => $false) = $false) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0))))) ) | (~spl0_4 | ~spl0_24)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f539])).
% 1.74/1.54 thf(f539,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK4 @ sK9) => (~ $true)) = $false) | ($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false)) ) | (~spl0_4 | ~spl0_24)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f538])).
% 1.74/1.54 thf(f538,plain,(
% 1.74/1.54 ( ! [X0 : a] : (($true = ((sK2 @ X0) => (~ (sK9 = X0)))) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => (~ (sK9 = (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))))) = $false) | (((sK4 @ sK9) => (~ (sK9 = sK9))) = $false)) ) | (~spl0_4 | ~spl0_24)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f537])).
% 1.74/1.54 thf(f537,plain,(
% 1.74/1.54 ( ! [X0 : a] : ((((sK2 @ X0) => ((^[Y0 : a]: (~ (sK9 = Y0))) @ X0)) = $true) | (((sK3 @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0))))) => ((^[Y0 : a]: (~ (sK9 = Y0))) @ (sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | (((sK4 @ sK9) => ((^[Y0 : a]: (~ (sK9 = Y0))) @ sK9)) = $false)) ) | (~spl0_4 | ~spl0_24)),
% 1.74/1.54 inference(superposition,[status(thm)],[f309,f532])).
% 1.74/1.54 thf(f532,plain,(
% 1.74/1.54 ((sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9) | ~spl0_24),
% 1.74/1.54 inference(equality_proxy_clausification,[status(thm)],[f529])).
% 1.74/1.54 thf(f529,plain,(
% 1.74/1.54 ($true = (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) | ~spl0_24),
% 1.74/1.54 inference(not_proxy_clausification,[status(thm)],[f527])).
% 1.74/1.54 thf(f527,plain,(
% 1.74/1.54 ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ~spl0_24),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f526])).
% 1.74/1.54 thf(f528,plain,(
% 1.74/1.54 spl0_23 | spl0_24 | ~spl0_4 | ~spl0_10),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f513,f168,f30,f526,f523])).
% 1.74/1.54 thf(f513,plain,(
% 1.74/1.54 ((~ (sK9 = (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0)))))) = $false) | ((sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9) | (~spl0_4 | ~spl0_10)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f481])).
% 1.74/1.54 thf(f481,plain,(
% 1.74/1.54 ((sK11 @ (^[Y0 : a]: (~ (sK9 = Y0)))) = sK9) | (((^[Y0 : a]: (~ (sK9 = Y0))) @ (sK10 @ (^[Y0 : a]: (~ (sK9 = Y0))))) = $false) | (~spl0_4 | ~spl0_10)),
% 1.74/1.54 inference(leibniz_equality_elimination,[status(thm)],[f352])).
% 1.74/1.54 thf(f352,plain,(
% 1.74/1.54 ( ! [X0 : a > $o] : (((X0 @ (sK11 @ X0)) = $false) | ((X0 @ (sK10 @ X0)) = $false) | ($true = (X0 @ sK9))) ) | (~spl0_4 | ~spl0_10)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f349])).
% 1.74/1.54 thf(f349,plain,(
% 1.74/1.54 ( ! [X0 : a > $o] : (((X0 @ (sK11 @ X0)) = $false) | ((X0 @ (sK10 @ X0)) = $false) | ($true = ($true => (X0 @ sK9)))) ) | (~spl0_4 | ~spl0_10)),
% 1.74/1.54 inference(superposition,[status(thm)],[f329,f169])).
% 1.74/1.54 thf(f329,plain,(
% 1.74/1.54 ( ! [X2 : a,X1 : a > $o] : (($true = ((sK2 @ X2) => (X1 @ X2))) | ((X1 @ (sK11 @ X1)) = $false) | ((X1 @ (sK10 @ X1)) = $false)) ) | ~spl0_4),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f313])).
% 1.74/1.54 thf(f247,plain,(
% 1.74/1.54 ~spl0_4 | ~spl0_11 | ~spl0_13),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f246])).
% 1.74/1.54 thf(f246,plain,(
% 1.74/1.54 $false | (~spl0_4 | ~spl0_11 | ~spl0_13)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f245])).
% 1.74/1.54 thf(f245,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_4 | ~spl0_11 | ~spl0_13)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f195,f208])).
% 1.74/1.54 thf(f208,plain,(
% 1.74/1.54 ((sK3 @ sK9) = $false) | (~spl0_4 | ~spl0_11)),
% 1.74/1.54 inference(not_proxy_clausification,[status(thm)],[f191])).
% 1.74/1.54 thf(f191,plain,(
% 1.74/1.54 ((~ (sK3 @ sK9)) = $true) | (~spl0_4 | ~spl0_11)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f190])).
% 1.74/1.54 thf(f190,plain,(
% 1.74/1.54 ($true = ((sK3 @ sK9) => $false)) | (~spl0_4 | ~spl0_11)),
% 1.74/1.54 inference(superposition,[status(thm)],[f188,f173])).
% 1.74/1.54 thf(f173,plain,(
% 1.74/1.54 ((sK2 @ sK9) = $false) | ~spl0_11),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.74/1.54 thf(f172,definition,(
% 1.74/1.54 spl0_11 <=> ((sK2 @ sK9) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.74/1.54 thf(f188,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((sK3 @ X1) => (sK2 @ X1)))) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f187])).
% 1.74/1.54 thf(f187,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))) @ X1))) ) | ~spl0_4),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f186])).
% 1.74/1.54 thf(f186,plain,(
% 1.74/1.54 ($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) | ~spl0_4),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f185])).
% 1.74/1.54 thf(f185,plain,(
% 1.74/1.54 ($true = ($true & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0)))))) | ~spl0_4),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f31,f184])).
% 1.74/1.54 thf(f195,plain,(
% 1.74/1.54 ($true = (sK3 @ sK9)) | ~spl0_13),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f194])).
% 1.74/1.54 thf(f194,definition,(
% 1.74/1.54 spl0_13 <=> ($true = (sK3 @ sK9))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.74/1.54 thf(f241,plain,(
% 1.74/1.54 ~spl0_4 | ~spl0_11 | ~spl0_14),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f240])).
% 1.74/1.54 thf(f240,plain,(
% 1.74/1.54 $false | (~spl0_4 | ~spl0_11 | ~spl0_14)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.74/1.54 thf(f239,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_4 | ~spl0_11 | ~spl0_14)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f233,f173])).
% 1.74/1.54 thf(f233,plain,(
% 1.74/1.54 ($true = (sK2 @ sK9)) | (~spl0_4 | ~spl0_14)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f232])).
% 1.74/1.54 thf(f232,plain,(
% 1.74/1.54 ($true = ($true => (sK2 @ sK9))) | (~spl0_4 | ~spl0_14)),
% 1.74/1.54 inference(superposition,[status(thm)],[f227,f198])).
% 1.74/1.54 thf(f198,plain,(
% 1.74/1.54 ($true = (sK4 @ sK9)) | ~spl0_14),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f197])).
% 1.74/1.54 thf(f197,definition,(
% 1.74/1.54 spl0_14 <=> ($true = (sK4 @ sK9))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.74/1.54 thf(f227,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((sK4 @ X1) => (sK2 @ X1)))) ) | ~spl0_4),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f223])).
% 1.74/1.54 thf(f223,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0))) @ X1))) ) | ~spl0_4),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f205])).
% 1.74/1.54 thf(f199,plain,(
% 1.74/1.54 spl0_13 | spl0_14 | ~spl0_2 | ~spl0_11),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f192,f172,f23,f197,f194])).
% 1.74/1.54 thf(f23,definition,(
% 1.74/1.54 spl0_2 <=> ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.74/1.54 thf(f192,plain,(
% 1.74/1.54 ($true = (sK4 @ sK9)) | ($true = (sK3 @ sK9)) | (~spl0_2 | ~spl0_11)),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f182])).
% 1.74/1.54 thf(f182,plain,(
% 1.74/1.54 (((sK3 @ sK9) | (sK4 @ sK9)) != $false) | (~spl0_2 | ~spl0_11)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f161,f173])).
% 1.74/1.54 thf(f161,plain,(
% 1.74/1.54 ((sK2 @ sK9) != ((sK3 @ sK9) | (sK4 @ sK9))) | ~spl0_2),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.74/1.54 thf(f160,plain,(
% 1.74/1.54 ((sK2 @ sK9) != ((^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))) @ sK9)) | ~spl0_2),
% 1.74/1.54 inference(negative_extensionality,[status(thm)],[f159])).
% 1.74/1.54 thf(f159,plain,(
% 1.74/1.54 (sK2 != (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) | ~spl0_2),
% 1.74/1.54 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.74/1.54 thf(f24,plain,(
% 1.74/1.54 ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) = $false) | ~spl0_2),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.74/1.54 thf(f181,plain,(
% 1.74/1.54 ~spl0_9 | ~spl0_12),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 1.74/1.54 thf(f180,plain,(
% 1.74/1.54 $false | (~spl0_9 | ~spl0_12)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.74/1.54 thf(f179,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_9 | ~spl0_12)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f166,f176])).
% 1.74/1.54 thf(f166,plain,(
% 1.74/1.54 ($true = ((sK3 @ sK9) | (sK4 @ sK9))) | ~spl0_9),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.74/1.54 thf(f165,definition,(
% 1.74/1.54 spl0_9 <=> ($true = ((sK3 @ sK9) | (sK4 @ sK9)))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.74/1.54 thf(f177,plain,(
% 1.74/1.54 spl0_11 | spl0_12 | ~spl0_2),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f163,f23,f175,f172])).
% 1.74/1.54 thf(f163,plain,(
% 1.74/1.54 ((sK2 @ sK9) = $false) | (((sK3 @ sK9) | (sK4 @ sK9)) = $false) | ~spl0_2),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.74/1.54 thf(f170,plain,(
% 1.74/1.54 spl0_9 | spl0_10 | ~spl0_2),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f162,f23,f168,f165])).
% 1.74/1.54 thf(f162,plain,(
% 1.74/1.54 ($true = (sK2 @ sK9)) | ($true = ((sK3 @ sK9) | (sK4 @ sK9))) | ~spl0_2),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.74/1.54 thf(f156,plain,(
% 1.74/1.54 ~spl0_6 | ~spl0_7),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f155])).
% 1.74/1.54 thf(f155,plain,(
% 1.74/1.54 $false | (~spl0_6 | ~spl0_7)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.74/1.54 thf(f154,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_6 | ~spl0_7)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f153,f151])).
% 1.74/1.54 thf(f151,plain,(
% 1.74/1.54 ((sK2 @ sK8) = $false) | ~spl0_7),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f150])).
% 1.74/1.54 thf(f150,plain,(
% 1.74/1.54 (($true => (sK2 @ sK8)) = $false) | ~spl0_7),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f147,f149])).
% 1.74/1.54 thf(f149,plain,(
% 1.74/1.54 ($true = (sK4 @ sK8)) | ~spl0_7),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.74/1.54 thf(f147,plain,(
% 1.74/1.54 (((sK4 @ sK8) => (sK2 @ sK8)) = $false) | ~spl0_7),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.74/1.54 thf(f146,plain,(
% 1.74/1.54 (((^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0))) @ sK8) = $false) | ~spl0_7),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f90])).
% 1.74/1.54 thf(f90,plain,(
% 1.74/1.54 ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) = $false) | ~spl0_7),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.74/1.54 thf(f89,definition,(
% 1.74/1.54 spl0_7 <=> ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.74/1.54 thf(f153,plain,(
% 1.74/1.54 ($true = (sK2 @ sK8)) | (~spl0_6 | ~spl0_7)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f152])).
% 1.74/1.54 thf(f152,plain,(
% 1.74/1.54 (((sK3 @ sK8) | $true) = (sK2 @ sK8)) | (~spl0_6 | ~spl0_7)),
% 1.74/1.54 inference(superposition,[status(thm)],[f84,f149])).
% 1.74/1.54 thf(f84,plain,(
% 1.74/1.54 ( ! [X1 : a] : ((((sK3 @ X1) | (sK4 @ X1)) = (sK2 @ X1))) ) | ~spl0_6),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.74/1.54 thf(f83,plain,(
% 1.74/1.54 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))) @ X1) = (sK2 @ X1))) ) | ~spl0_6),
% 1.74/1.54 inference(argument_congruence,[status(thm)],[f78])).
% 1.74/1.54 thf(f78,plain,(
% 1.74/1.54 (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) | ~spl0_6),
% 1.74/1.54 inference(equality_proxy_clausification,[status(thm)],[f75])).
% 1.74/1.54 thf(f75,plain,(
% 1.74/1.54 ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) != $false) | ~spl0_6),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f74])).
% 1.74/1.54 thf(f74,plain,(
% 1.74/1.54 ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) != ($false & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0)))))) | ~spl0_6),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f16,f51])).
% 1.74/1.54 thf(f51,plain,(
% 1.74/1.54 (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) = $false) | ~spl0_6),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.74/1.54 thf(f50,definition,(
% 1.74/1.54 spl0_6 <=> (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.74/1.54 thf(f16,plain,(
% 1.74/1.54 ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) != (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))))),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.74/1.54 thf(f15,plain,(
% 1.74/1.54 (((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) = (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))))) = $false)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.74/1.54 thf(f14,plain,(
% 1.74/1.54 (((^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2) => (Y1 @ Y2))))) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (sK2 @ Y1))))) = (sK2 = (^[Y1 : a]: ((sK3 @ Y1) | (Y0 @ Y1)))))) @ sK4) = $false)),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f13])).
% 1.74/1.54 thf(f13,plain,(
% 1.74/1.54 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2) => (Y1 @ Y2))))) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (sK2 @ Y1))))) = (sK2 = (^[Y1 : a]: ((sK3 @ Y1) | (Y0 @ Y1))))))) = $false)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.74/1.54 thf(f12,plain,(
% 1.74/1.54 (((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK2 @ Y2)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3) => (Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (sK2 @ Y2))))) = (sK2 = (^[Y2 : a]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) @ sK3) = $false)),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f11])).
% 1.74/1.54 thf(f11,plain,(
% 1.74/1.54 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK2 @ Y2)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3) => (Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (sK2 @ Y2))))) = (sK2 = (^[Y2 : a]: ((Y0 @ Y2) | (Y1 @ Y2))))))))) = $false)),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.74/1.54 thf(f10,plain,(
% 1.74/1.54 (((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y3 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4) => (Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y0 @ Y3))))) = (Y0 = (^[Y3 : a]: ((Y1 @ Y3) | (Y2 @ Y3)))))))))) @ sK2) = $false)),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f7])).
% 1.74/1.54 thf(f7,plain,(
% 1.74/1.54 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y3 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4) => (Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y0 @ Y3))))) = (Y0 = (^[Y3 : a]: ((Y1 @ Y3) | (Y2 @ Y3))))))))))) = $false)),
% 1.74/1.54 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.74/1.54 thf(f6,plain,(
% 1.74/1.54 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y3 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4) => (Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y0 @ Y3))))) = (Y0 = (^[Y3 : a]: ((Y1 @ Y3) | (Y2 @ Y3)))))))))))))),
% 1.74/1.54 inference(cnf_transformation,[status(thm)],[f5])).
% 1.74/1.54 thf(f5,plain,(
% 1.74/1.54 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y3 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4) => (Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) => (Y0 @ Y3))))) = (Y0 = (^[Y3 : a]: ((Y1 @ Y3) | (Y2 @ Y3)))))))))))))),
% 1.74/1.54 inference(fool_elimination,[status(thm)],[f4])).
% 1.74/1.54 thf(f4,plain,(
% 1.74/1.54 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X4 : a > $o] : ((! [X5 : a] : ((X1 @ X5) => (X4 @ X5)) & ! [X6 : a] : ((X0 @ X6) => (X4 @ X6))) => ! [X7 : a] : ((X2 @ X7) => (X4 @ X7))) & ! [X8 : a] : ((X0 @ X8) => (X2 @ X8))) <=> (X2 = (^[X9 : a] : ((X0 @ X9) | (X1 @ X9)))))),
% 1.74/1.54 inference(rectify,[status(thm)],[f2])).
% 1.74/1.54 thf(f2,negated_conjecture,(
% 1.74/1.54 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X5 : a > $o] : ((! [X4 : a] : ((X1 @ X4) => (X5 @ X4)) & ! [X4 : a] : ((X2 @ X4) => (X5 @ X4))) => ! [X4 : a] : ((X0 @ X4) => (X5 @ X4))) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4))) <=> (X0 = (^[X3 : a] : ((X2 @ X3) | (X1 @ X3)))))),
% 1.74/1.54 inference(negated_conjecture,[status(cth)],[f1])).
% 1.74/1.54 thf(f1,conjecture,(
% 1.74/1.54 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X5 : a > $o] : ((! [X4 : a] : ((X1 @ X4) => (X5 @ X4)) & ! [X4 : a] : ((X2 @ X4) => (X5 @ X4))) => ! [X4 : a] : ((X0 @ X4) => (X5 @ X4))) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4))) <=> (X0 = (^[X3 : a] : ((X2 @ X3) | (X1 @ X3)))))),
% 1.74/1.54 file('/export/starexec/sandbox/tmp/tmp.flVDtHJC2k/DTF2THF_4962.p',cBOOL_PROP_56_pme)).
% 1.74/1.54 thf(f143,plain,(
% 1.74/1.54 ~spl0_6 | ~spl0_8),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f142])).
% 1.74/1.54 thf(f142,plain,(
% 1.74/1.54 $false | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.74/1.54 thf(f141,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f135,f110])).
% 1.74/1.54 thf(f110,plain,(
% 1.74/1.54 ((sK6 @ sK7) = $false) | ~spl0_8),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f109])).
% 1.74/1.54 thf(f109,plain,(
% 1.74/1.54 (($true => (sK6 @ sK7)) = $false) | ~spl0_8),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f106,f108])).
% 1.74/1.54 thf(f108,plain,(
% 1.74/1.54 ((sK2 @ sK7) = $true) | ~spl0_8),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.74/1.54 thf(f106,plain,(
% 1.74/1.54 (((sK2 @ sK7) => (sK6 @ sK7)) = $false) | ~spl0_8),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.74/1.54 thf(f105,plain,(
% 1.74/1.54 (((^[Y0 : a]: ((sK2 @ Y0) => (sK6 @ Y0))) @ sK7) = $false) | ~spl0_8),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f99])).
% 1.74/1.54 thf(f99,plain,(
% 1.74/1.54 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_8),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.74/1.54 thf(f98,plain,(
% 1.74/1.54 ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK6 @ Y0))))) => (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK6 @ Y0))))) = $false) | ~spl0_8),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.74/1.54 thf(f97,plain,(
% 1.74/1.54 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))) @ sK6) = $false) | ~spl0_8),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f93])).
% 1.74/1.54 thf(f93,plain,(
% 1.74/1.54 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))))) = $false) | ~spl0_8),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.74/1.54 thf(f92,definition,(
% 1.74/1.54 spl0_8 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.74/1.54 thf(f135,plain,(
% 1.74/1.54 ($true = (sK6 @ sK7)) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f134])).
% 1.74/1.54 thf(f134,plain,(
% 1.74/1.54 ($true = ($true => (sK6 @ sK7))) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(superposition,[status(thm)],[f129,f127])).
% 1.74/1.54 thf(f127,plain,(
% 1.74/1.54 ($true = (sK3 @ sK7)) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f126,f108])).
% 1.74/1.54 thf(f126,plain,(
% 1.74/1.54 ((sK2 @ sK7) = (sK3 @ sK7)) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f124])).
% 1.74/1.54 thf(f124,plain,(
% 1.74/1.54 ((sK2 @ sK7) = ((sK3 @ sK7) | $false)) | (~spl0_6 | ~spl0_8)),
% 1.74/1.54 inference(superposition,[status(thm)],[f84,f120])).
% 1.74/1.54 thf(f120,plain,(
% 1.74/1.54 ((sK4 @ sK7) = $false) | ~spl0_8),
% 1.74/1.54 inference(not_proxy_clausification,[status(thm)],[f119])).
% 1.74/1.54 thf(f119,plain,(
% 1.74/1.54 ($true = (~ (sK4 @ sK7))) | ~spl0_8),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f118])).
% 1.74/1.54 thf(f118,plain,(
% 1.74/1.54 (((sK4 @ sK7) => $false) = $true) | ~spl0_8),
% 1.74/1.54 inference(superposition,[status(thm)],[f116,f110])).
% 1.74/1.54 thf(f116,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((sK4 @ X1) => (sK6 @ X1)))) ) | ~spl0_8),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.74/1.54 thf(f115,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK4 @ Y0) => (sK6 @ Y0))) @ X1))) ) | ~spl0_8),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f114])).
% 1.74/1.54 thf(f114,plain,(
% 1.74/1.54 ($true = (!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK6 @ Y0))))) | ~spl0_8),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f113])).
% 1.74/1.54 thf(f113,plain,(
% 1.74/1.54 ($true = ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK6 @ Y0)))) & $true)) | ~spl0_8),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f100,f111])).
% 1.74/1.54 thf(f111,plain,(
% 1.74/1.54 ($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK6 @ Y0))))) | ~spl0_8),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.74/1.54 thf(f100,plain,(
% 1.74/1.54 ($true = ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK6 @ Y0)))))) | ~spl0_8),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.74/1.54 thf(f129,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((sK3 @ X1) => (sK6 @ X1)))) ) | ~spl0_8),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.74/1.54 thf(f128,plain,(
% 1.74/1.54 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0) => (sK6 @ Y0))) @ X1))) ) | ~spl0_8),
% 1.74/1.54 inference(pi_clausification,[status(thm)],[f111])).
% 1.74/1.54 thf(f94,plain,(
% 1.74/1.54 spl0_7 | spl0_8 | ~spl0_6),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f87,f50,f92,f89])).
% 1.74/1.54 thf(f87,plain,(
% 1.74/1.54 ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) = $false) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))))) = $false) | ~spl0_6),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.74/1.54 thf(f73,plain,(
% 1.74/1.54 ~spl0_4 | ~spl0_5),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.74/1.54 thf(f72,plain,(
% 1.74/1.54 $false | (~spl0_4 | ~spl0_5)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.74/1.54 thf(f71,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_4 | ~spl0_5)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f70])).
% 1.74/1.54 thf(f70,plain,(
% 1.74/1.54 ($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & $false)) | (~spl0_4 | ~spl0_5)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f31,f48])).
% 1.74/1.54 thf(f48,plain,(
% 1.74/1.54 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) | ~spl0_5),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.74/1.54 thf(f47,definition,(
% 1.74/1.54 spl0_5 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0)))))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.74/1.54 thf(f67,plain,(
% 1.74/1.54 ~spl0_3 | ~spl0_5),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.74/1.54 thf(f66,plain,(
% 1.74/1.54 $false | (~spl0_3 | ~spl0_5)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.74/1.54 thf(f65,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_3 | ~spl0_5)),
% 1.74/1.54 inference(forward_demodulation,[status(thm)],[f64,f57])).
% 1.74/1.54 thf(f57,plain,(
% 1.74/1.54 ((sK2 @ sK5) = $false) | ~spl0_5),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.74/1.54 thf(f56,plain,(
% 1.74/1.54 (((sK3 @ sK5) => (sK2 @ sK5)) = $false) | ~spl0_5),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.74/1.54 thf(f55,plain,(
% 1.74/1.54 (((^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))) @ sK5) = $false) | ~spl0_5),
% 1.74/1.54 inference(sigma_clausification,[status(thm)],[f48])).
% 1.74/1.54 thf(f64,plain,(
% 1.74/1.54 ($true = (sK2 @ sK5)) | (~spl0_3 | ~spl0_5)),
% 1.74/1.54 inference(boolean_simplification,[status(thm)],[f63])).
% 1.74/1.54 thf(f63,plain,(
% 1.74/1.54 (($true | (sK4 @ sK5)) = (sK2 @ sK5)) | (~spl0_3 | ~spl0_5)),
% 1.74/1.54 inference(superposition,[status(thm)],[f42,f58])).
% 1.74/1.54 thf(f58,plain,(
% 1.74/1.54 ($true = (sK3 @ sK5)) | ~spl0_5),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.74/1.54 thf(f42,plain,(
% 1.74/1.54 ( ! [X1 : a] : ((((sK3 @ X1) | (sK4 @ X1)) = (sK2 @ X1))) ) | ~spl0_3),
% 1.74/1.54 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.74/1.54 thf(f41,plain,(
% 1.74/1.54 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))) @ X1) = (sK2 @ X1))) ) | ~spl0_3),
% 1.74/1.54 inference(argument_congruence,[status(thm)],[f38])).
% 1.74/1.54 thf(f38,plain,(
% 1.74/1.54 (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) | ~spl0_3),
% 1.74/1.54 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.74/1.54 thf(f28,plain,(
% 1.74/1.54 ($true = (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))))) | ~spl0_3),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.74/1.54 thf(f27,definition,(
% 1.74/1.54 spl0_3 <=> ($true = (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))))),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.74/1.54 thf(f52,plain,(
% 1.74/1.54 spl0_5 | spl0_6 | ~spl0_1),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f45,f20,f50,f47])).
% 1.74/1.54 thf(f20,definition,(
% 1.74/1.54 spl0_1 <=> ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) = $false)),
% 1.74/1.54 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.74/1.54 thf(f45,plain,(
% 1.74/1.54 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) | (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) = $false) | ~spl0_1),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.74/1.54 thf(f21,plain,(
% 1.74/1.54 ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) = $false) | ~spl0_1),
% 1.74/1.54 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.74/1.54 thf(f36,plain,(
% 1.74/1.54 ~spl0_2 | ~spl0_3),
% 1.74/1.54 inference(avatar_contradiction_clause,[status(thm)],[f35])).
% 1.74/1.54 thf(f35,plain,(
% 1.74/1.54 $false | (~spl0_2 | ~spl0_3)),
% 1.74/1.54 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.74/1.54 thf(f34,plain,(
% 1.74/1.54 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.74/1.54 inference(backward_demodulation,[status(thm)],[f28,f24])).
% 1.74/1.54 thf(f32,plain,(
% 1.74/1.54 spl0_3 | spl0_4),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f17,f30,f27])).
% 1.74/1.54 thf(f17,plain,(
% 1.74/1.54 ($true = (sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0))))) | ($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))))),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.74/1.54 thf(f25,plain,(
% 1.74/1.54 spl0_1 | spl0_2),
% 1.74/1.54 inference(avatar_split_clause,[status(thm)],[f18,f23,f20])).
% 1.74/1.54 thf(f18,plain,(
% 1.74/1.54 ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (sK2 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1) => (Y0 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (sK2 @ Y0))))) = $false) | ((sK2 = (^[Y0 : a]: ((sK3 @ Y0) | (sK4 @ Y0)))) = $false)),
% 1.74/1.54 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.74/1.54 % SZS output end Proof for DTF2THF_4962
% 1.74/1.54 % (5071)------------------------------
% 1.74/1.54 % (5071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.54 % (5071)Termination reason: Refutation
% 1.74/1.54
% 1.74/1.54 % (5071)Memory used [KB]: 5884
% 1.74/1.54 % (5071)Time elapsed: 0.051 s
% 1.74/1.54 % (5071)Instructions burned: 78 (million)
% 1.74/1.54 % (5071)------------------------------
% 1.74/1.54 % (5071)------------------------------
% 1.74/1.54 % (5059)Success in time 0.097 s
%------------------------------------------------------------------------------