%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV011^5 : 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 09:40:03 AM UTC 2026
% Result : Theorem 1.57s 1.28s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 36 unt; 0 typ; 6 def)
% Number of atoms : 710 ( 156 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1449 ( 98 ~; 88 |; 94 &; 875 @)
% ( 12 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 15 con; 0-2 aty)
% ( 160 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 255 ( 182 ^; 70 !; 3 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a ).
thf(func_def_23,type,
sK5: a ).
thf(func_def_24,type,
sK6: a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a ).
thf(f511,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f66,f113,f120,f171,f174,f230,f505,f510]) ).
thf(f510,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f509]) ).
thf(f509,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f508]) ).
thf(f508,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f109,f119]) ).
thf(f119,plain,
( ( ( sK2 @ sK3 @ sK5 )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f118,definition,
( spl0_6
<=> ( ( sK2 @ sK3 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f109,plain,
( ( $true
= ( sK2 @ sK3 @ sK5 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl0_3
<=> ( $true
= ( sK2 @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f505,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f504]) ).
thf(f504,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f264,f442]) ).
thf(f442,plain,
( ! [X1: a] :
( ( sK6 @ X1 )
= ( sK2 @ sK3 @ X1 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f441]) ).
thf(f441,plain,
( ! [X1: a] :
( ( ( sK2 @ sK3 @ X1 )
= ( sK6 @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f438]) ).
thf(f438,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f310]) ).
thf(f310,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK6 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f308]) ).
thf(f308,plain,
( ( ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK6 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f294,f289]) ).
thf(f289,plain,
( ( $true
= ( sK6 @ sK3 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f288]) ).
thf(f288,plain,
( ( $true
= ( ( sK6 @ sK3 )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f258,f286]) ).
thf(f286,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( ( ( sK6 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $false
= ( ( ( sK6 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK6 @ Y1 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= sK6 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f236]) ).
thf(f236,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) )
@ sK6 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f294,plain,
( ! [X1: a] :
( $true
= ( ( sK6 @ X1 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
= ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f293]) ).
thf(f293,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK6 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f286]) ).
thf(f264,plain,
( ( ( sK2 @ sK3 @ sK7 )
!= ( sK6 @ sK7 ) )
| ~ spl0_1 ),
inference(negative_extensionality,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ( sK2 @ sK3 )
!= sK6 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( ( sK2 @ sK3 )
= sK6 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f238]) ).
thf(f230,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f229]) ).
thf(f229,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f219,f112]) ).
thf(f112,plain,
( ( $true
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f111,definition,
( spl0_4
<=> ( $true
= ( sK2 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f219,plain,
( ( $true
= ( ~ ( sK2 @ sK4 @ sK5 ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f214]) ).
thf(f214,plain,
( ( $true
= ( ( sK2 @ sK4 @ sK5 )
=> $false ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f88,f119]) ).
thf(f88,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK4 @ X0 )
=> ( sK2 @ sK3 @ X0 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK2 @ sK4 @ X0 ) )
=> ( sK2 @ sK3 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f35,f75]) ).
thf(f75,plain,
( ( ( sK2 @ sK3 @ sK4 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false
= ( ( sK2 @ sK3 @ sK4 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) )
@ sK4 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f35,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f21,f22]) ).
thf(f22,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f13,f18]) ).
thf(f18,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
= ( sK2 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
= ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) )
& ! [X3: a] : ( X0 @ X3 @ X3 )
& ! [X4: a,X5: a,X6: a] :
( ( ( X0 @ X6 @ X5 )
& ( X0 @ X4 @ X6 ) )
=> ( X0 @ X4 @ X5 ) ) )
=> ! [X7: a] :
? [X8: a > $o] :
( ! [X9: a > $o] :
( ( ! [X10: a] :
( ( X9 @ X10 )
=> ! [X11: a] :
( ( X0 @ X10 @ X11 )
<=> ( X9 @ X11 ) ) )
& ( X9 @ X7 ) )
=> ( X8 = X9 ) )
& ! [X12: a] :
( ( X8 @ X12 )
=> ! [X13: a] :
( ( X8 @ X13 )
<=> ( X0 @ X12 @ X13 ) ) )
& ( X8 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a] :
? [X4: a > $o] :
( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X6 @ X2 ) ) )
& ( X6 @ X1 ) )
=> ( X4 = X6 ) )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X4 @ X2 )
<=> ( X0 @ X5 @ X2 ) ) )
& ( X4 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a] :
? [X4: a > $o] :
( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X6 @ X2 ) ) )
& ( X6 @ X1 ) )
=> ( X4 = X6 ) )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X4 @ X2 )
<=> ( X0 @ X5 @ X2 ) ) )
& ( X4 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIhcyDAlvr/DTF2THF_2982.p',cTHM260_B_pme) ).
thf(f174,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f173]) ).
thf(f173,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f112,f116]) ).
thf(f116,plain,
( ( $false
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f115,definition,
( spl0_5
<=> ( $false
= ( sK2 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f171,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f170]) ).
thf(f170,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f138,f167]) ).
thf(f167,plain,
( ( ( sK2 @ sK5 @ sK4 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( $true
=> ( sK2 @ sK5 @ sK4 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f87,f131]) ).
thf(f131,plain,
( ( $true
= ( sK2 @ sK5 @ sK3 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true
= ( $true
=> ( sK2 @ sK5 @ sK3 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f37,f109]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK2 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK2 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK2 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f87,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ X0 @ sK3 )
=> ( sK2 @ X0 @ sK4 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: a] :
( ( ( ( sK2 @ X0 @ sK3 )
& $true )
=> ( sK2 @ X0 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f35,f75]) ).
thf(f138,plain,
( ( $true
= ( ~ ( sK2 @ sK5 @ sK4 ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true
= ( ( sK2 @ sK5 @ sK4 )
=> $false ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f37,f116]) ).
thf(f120,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f106,f64,f118,f115]) ).
thf(f106,plain,
( ( ( sK2 @ sK3 @ sK5 )
= $false )
| ( $false
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ( sK2 @ sK3 @ sK5 )
!= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( ( sK2 @ sK3 @ sK5 )
= ( sK2 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) )
@ sK5 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f113,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f105,f64,f111,f108]) ).
thf(f105,plain,
( ( $true
= ( sK2 @ sK3 @ sK5 ) )
| ( $true
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f66,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f59,f64,f61]) ).
thf(f59,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK3 )
= Y0 ) ) ) )
= $false ),
inference(superposition,[status(thm)],[f55,f27]) ).
thf(f27,plain,
! [X1: a] :
( $true
= ( sK2 @ X1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: a] :
( ( ^ [Y0: a] : ( sK2 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f55,plain,
! [X1: a > $o] :
( ( ( X1 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
= ( sK2 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( X1 = Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
= ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( Y1 @ sK3 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
= ( sK2 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
= ( sK2 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV011^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:38:03 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
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV011^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory (Relations)
% 0.20/0.46 % Problem : TPS problem THM260-B
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : An equivalence relation defines a partition.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0541 [Bro09]
% 0.20/0.46 % : THM260-B [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 36 ( 0 ~; 0 |; 6 &; 22 @)
% 0.20/0.46 % ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 16 ( 16 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.46 % Number of variables : 14 ( 0 ^; 13 !; 1 ?; 14 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % : Polymorphic definitions expanded.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM260_B_pme,conjecture,
% 0.20/0.46 ! [R: a > a > $o] :
% 0.20/0.46 ( ( ! [Xx: a] : ( R @ Xx @ Xx )
% 0.20/0.46 & ! [Xx: a,Xy: a] :
% 0.20/0.46 ( ( R @ Xx @ Xy )
% 0.20/0.46 => ( R @ Xy @ Xx ) )
% 0.20/0.46 & ! [Xx: a,Xy: a,Xz: a] :
% 0.20/0.46 ( ( ( R @ Xx @ Xy )
% 0.20/0.46 & ( R @ Xy @ Xz ) )
% 0.20/0.46 => ( R @ Xx @ Xz ) ) )
% 0.20/0.46 => ! [Xx: a] :
% 0.20/0.46 ? [Xp: a > $o] :
% 0.20/0.46 ( ! [Xx0: a] :
% 0.20/0.46 ( ( Xp @ Xx0 )
% 0.20/0.46 => ! [Xy: a] :
% 0.20/0.46 ( ( Xp @ Xy )
% 0.20/0.46 <=> ( R @ Xx0 @ Xy ) ) )
% 0.20/0.46 & ( Xp @ Xx )
% 0.20/0.46 & ! [Xq: a > $o] :
% 0.20/0.46 ( ( ! [Xx0: a] :
% 0.20/0.46 ( ( Xq @ Xx0 )
% 0.20/0.46 => ! [Xy: a] :
% 0.20/0.46 ( ( Xq @ Xy )
% 0.20/0.46 <=> ( R @ Xx0 @ Xy ) ) )
% 0.20/0.46 & ( Xq @ Xx ) )
% 0.20/0.46 => ( Xq = Xp ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.47/1.17 ---- Embedded in THF ---
% 1.47/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.17 %%% Generated on Tue Feb 24 12:38:04 EST 2026
% 1.47/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.17 %%% Logic specification used:
% 1.47/1.17 %%% thf(spec, logic, $$dhol).
% 1.47/1.17
% 1.47/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oIhcyDAlvr/DTF2DTF2982.p
% See solution above
% 1.47/1.17 ------------------------
% 1.47/1.18 ---- Cleaned THF ---
% 1.47/1.18 thf(a_type,type,
% 1.47/1.18 a: $tType ).
% 1.47/1.18
% 1.47/1.18 thf(cTHM260_B_pme,conjecture,
% 1.47/1.18 ! [R: a > a > $o] :
% 1.47/1.18 ( ( ! [Xx: a] : ( R @ Xx @ Xx )
% 1.47/1.18 & ! [Xx: a,Xy: a] :
% 1.47/1.18 ( ( R @ Xx @ Xy )
% 1.47/1.18 => ( R @ Xy @ Xx ) )
% 1.47/1.18 & ! [Xx: a,Xy: a,Xz: a] :
% 1.47/1.18 ( ( ( R @ Xx @ Xy )
% 1.47/1.18 & ( R @ Xy @ Xz ) )
% 1.47/1.18 => ( R @ Xx @ Xz ) ) )
% 1.47/1.18 => ! [Xx: a] :
% 1.47/1.18 ? [Xp: a > $o] :
% 1.47/1.18 ( ! [Xx0: a] :
% 1.47/1.18 ( ( Xp @ Xx0 )
% 1.47/1.18 => ! [Xy: a] :
% 1.47/1.18 ( ( Xp @ Xy )
% 1.47/1.18 <=> ( R @ Xx0 @ Xy ) ) )
% 1.47/1.18 & ( Xp @ Xx )
% 1.47/1.18 & ! [Xq: a > $o] :
% 1.47/1.18 ( ( ! [Xx0: a] :
% 1.47/1.18 ( ( Xq @ Xx0 )
% 1.47/1.18 => ! [Xy: a] :
% 1.47/1.18 ( ( Xq @ Xy )
% 1.47/1.18 <=> ( R @ Xx0 @ Xy ) ) )
% 1.47/1.18 & ( Xq @ Xx ) )
% 1.47/1.18 => ( Xq = Xp ) ) ) ) ).
% 1.47/1.18 ------------------------
% 1.57/1.20 % (3080)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_2982 for (2999ds/4Mi)
% 1.57/1.20 % (3082)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/2Mi)
% 1.57/1.20 % (3080)Instruction limit reached!
% 1.57/1.20 % (3080)------------------------------
% 1.57/1.20 % (3080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.20 % (3080)Termination reason: Unknown
% 1.57/1.20 % (3080)Termination phase: Saturation
% 1.57/1.20
% 1.57/1.20 % (3080)Memory used [KB]: 5500
% 1.57/1.20 % (3080)Time elapsed: 0.003 s
% 1.57/1.20 % (3080)Instructions burned: 4 (million)
% 1.57/1.20 % (3080)------------------------------
% 1.57/1.20 % (3080)------------------------------
% 1.57/1.20 % (3082)Instruction limit reached!
% 1.57/1.20 % (3082)------------------------------
% 1.57/1.20 % (3082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.20 % (3082)Termination reason: Unknown
% 1.57/1.20 % (3082)Termination phase: Saturation
% 1.57/1.20
% 1.57/1.20 % (3082)Memory used [KB]: 5500
% 1.57/1.20 % (3082)Time elapsed: 0.002 s
% 1.57/1.20 % (3082)Instructions burned: 3 (million)
% 1.57/1.20 % (3082)------------------------------
% 1.57/1.20 % (3082)------------------------------
% 1.57/1.21 % (3079)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/183Mi)
% 1.57/1.21 % (3081)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_2982 for (2999ds/27Mi)
% 1.57/1.21 % (3083)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_2982 for (2999ds/2Mi)
% 1.57/1.21 % (3083)Instruction limit reached!
% 1.57/1.21 % (3083)------------------------------
% 1.57/1.21 % (3083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.21 % (3083)Termination reason: Unknown
% 1.57/1.21 % (3083)Termination phase: Unused predicate definition removal
% 1.57/1.21
% 1.57/1.21 % (3083)Memory used [KB]: 1023
% 1.57/1.21 % (3083)Time elapsed: 0.003 s
% 1.57/1.21 % (3083)Instructions burned: 2 (million)
% 1.57/1.21 % (3083)------------------------------
% 1.57/1.21 % (3083)------------------------------
% 1.57/1.21 % (3085)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/18Mi)
% 1.57/1.21 % (3087)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_2982 for (2999ds/37Mi)
% 1.57/1.21 % (3084)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_2982 for (2999ds/275Mi)
% 1.57/1.22 % (3085)Instruction limit reached!
% 1.57/1.22 % (3085)------------------------------
% 1.57/1.22 % (3085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (3085)Termination reason: Unknown
% 1.57/1.22 % (3085)Termination phase: Saturation
% 1.57/1.22
% 1.57/1.22 % (3085)Memory used [KB]: 5628
% 1.57/1.22 % (3085)Time elapsed: 0.007 s
% 1.57/1.22 % (3085)Instructions burned: 19 (million)
% 1.57/1.22 % (3085)------------------------------
% 1.57/1.22 % (3085)------------------------------
% 1.57/1.22 % (3086)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/3Mi)
% 1.57/1.22 % (3086)Instruction limit reached!
% 1.57/1.22 % (3086)------------------------------
% 1.57/1.22 % (3086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (3086)Termination reason: Unknown
% 1.57/1.22 % (3086)Termination phase: Saturation
% 1.57/1.22
% 1.57/1.22 % (3086)Memory used [KB]: 5500
% 1.57/1.22 % (3086)Time elapsed: 0.003 s
% 1.57/1.22 % (3086)Instructions burned: 3 (million)
% 1.57/1.22 % (3086)------------------------------
% 1.57/1.22 % (3086)------------------------------
% 1.57/1.22 % (3087)Instruction limit reached!
% 1.57/1.22 % (3087)------------------------------
% 1.57/1.22 % (3087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (3087)Termination reason: Unknown
% 1.57/1.22 % (3087)Termination phase: Saturation
% 1.57/1.22
% 1.57/1.22 % (3087)Memory used [KB]: 5756
% 1.57/1.22 % (3087)Time elapsed: 0.014 s
% 1.57/1.22 % (3087)Instructions burned: 38 (million)
% 1.57/1.22 % (3087)------------------------------
% 1.57/1.22 % (3087)------------------------------
% 1.57/1.22 % (3081)Instruction limit reached!
% 1.57/1.22 % (3081)------------------------------
% 1.57/1.22 % (3081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (3081)Termination reason: Unknown
% 1.57/1.22 % (3081)Termination phase: Saturation
% 1.57/1.22
% 1.57/1.22 % (3081)Memory used [KB]: 5628
% 1.57/1.22 % (3081)Time elapsed: 0.020 s
% 1.57/1.22 % (3081)Instructions burned: 27 (million)
% 1.57/1.22 % (3081)------------------------------
% 1.57/1.22 % (3081)------------------------------
% 1.57/1.22 % (3089)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_2982 for (2999ds/3Mi)
% 1.57/1.23 % (3088)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_2982 for (2999ds/15Mi)
% 1.57/1.23 % (3089)Instruction limit reached!
% 1.57/1.23 % (3089)------------------------------
% 1.57/1.23 % (3089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.23 % (3089)Termination reason: Unknown
% 1.57/1.23 % (3089)Termination phase: Saturation
% 1.57/1.23
% 1.57/1.23 % (3089)Memory used [KB]: 5500
% 1.57/1.23 % (3089)Time elapsed: 0.002 s
% 1.57/1.23 % (3089)Instructions burned: 3 (million)
% 1.57/1.23 % (3089)------------------------------
% 1.57/1.23 % (3089)------------------------------
% 1.57/1.23 % (3091)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/7Mi)
% 1.57/1.23 % (3090)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_2982 for (2999ds/1041Mi)
% 1.57/1.23 % (3088)Instruction limit reached!
% 1.57/1.23 % (3088)------------------------------
% 1.57/1.23 % (3088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.23 % (3088)Termination reason: Unknown
% 1.57/1.23 % (3088)Termination phase: Saturation
% 1.57/1.23
% 1.57/1.23 % (3088)Memory used [KB]: 5628
% 1.57/1.23 % (3088)Time elapsed: 0.010 s
% 1.57/1.23 % (3088)Instructions burned: 15 (million)
% 1.57/1.23 % (3088)------------------------------
% 1.57/1.23 % (3088)------------------------------
% 1.57/1.23 % (3093)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_2982 for (2999ds/3Mi)
% 1.57/1.23 % (3091)Instruction limit reached!
% 1.57/1.23 % (3091)------------------------------
% 1.57/1.23 % (3091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.23 % (3091)Termination reason: Unknown
% 1.57/1.23 % (3091)Termination phase: Saturation
% 1.57/1.23
% 1.57/1.23 % (3091)Memory used [KB]: 1023
% 1.57/1.23 % (3091)Time elapsed: 0.004 s
% 1.57/1.23 % (3091)Instructions burned: 7 (million)
% 1.57/1.23 % (3091)------------------------------
% 1.57/1.23 % (3091)------------------------------
% 1.57/1.24 % (3093)Instruction limit reached!
% 1.57/1.24 % (3093)------------------------------
% 1.57/1.24 % (3093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.24 % (3093)Termination reason: Unknown
% 1.57/1.24 % (3093)Termination phase: Saturation
% 1.57/1.24
% 1.57/1.24 % (3093)Memory used [KB]: 1023
% 1.57/1.24 % (3093)Time elapsed: 0.002 s
% 1.57/1.24 % (3093)Instructions burned: 4 (million)
% 1.57/1.24 % (3093)------------------------------
% 1.57/1.24 % (3093)------------------------------
% 1.57/1.24 % (3092)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/16Mi)
% 1.57/1.24 % (3095)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/7Mi)
% 1.57/1.25 % (3096)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/3Mi)
% 1.57/1.25 % (3096)Instruction limit reached!
% 1.57/1.25 % (3096)------------------------------
% 1.57/1.25 % (3096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (3096)Termination reason: Unknown
% 1.57/1.25 % (3096)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (3096)Memory used [KB]: 5500
% 1.57/1.25 % (3096)Time elapsed: 0.002 s
% 1.57/1.25 % (3096)Instructions burned: 4 (million)
% 1.57/1.25 % (3096)------------------------------
% 1.57/1.25 % (3096)------------------------------
% 1.57/1.25 % (3094)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_2982 for (2999ds/3Mi)
% 1.57/1.25 % (3095)Instruction limit reached!
% 1.57/1.25 % (3095)------------------------------
% 1.57/1.25 % (3095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (3095)Termination reason: Unknown
% 1.57/1.25 % (3095)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (3095)Memory used [KB]: 5500
% 1.57/1.25 % (3095)Time elapsed: 0.005 s
% 1.57/1.25 % (3095)Instructions burned: 9 (million)
% 1.57/1.25 % (3095)------------------------------
% 1.57/1.25 % (3095)------------------------------
% 1.57/1.25 % (3094)Instruction limit reached!
% 1.57/1.25 % (3094)------------------------------
% 1.57/1.25 % (3094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (3094)Termination reason: Unknown
% 1.57/1.25 % (3094)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (3094)Memory used [KB]: 5500
% 1.57/1.25 % (3094)Time elapsed: 0.003 s
% 1.57/1.25 % (3094)Instructions burned: 5 (million)
% 1.57/1.25 % (3094)------------------------------
% 1.57/1.25 % (3094)------------------------------
% 1.57/1.25 % (3092)Instruction limit reached!
% 1.57/1.25 % (3092)------------------------------
% 1.57/1.25 % (3092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (3092)Termination reason: Unknown
% 1.57/1.25 % (3092)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (3092)Memory used [KB]: 5628
% 1.57/1.25 % (3092)Time elapsed: 0.012 s
% 1.57/1.25 % (3092)Instructions burned: 17 (million)
% 1.57/1.25 % (3092)------------------------------
% 1.57/1.25 % (3092)------------------------------
% 1.57/1.26 % (3097)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/4Mi)
% 1.57/1.26 % (3097)Instruction limit reached!
% 1.57/1.26 % (3097)------------------------------
% 1.57/1.26 % (3097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (3097)Termination reason: Unknown
% 1.57/1.26 % (3097)Termination phase: Saturation
% 1.57/1.26
% 1.57/1.26 % (3097)Memory used [KB]: 5500
% 1.57/1.26 % (3097)Time elapsed: 0.003 s
% 1.57/1.26 % (3097)Instructions burned: 4 (million)
% 1.57/1.26 % (3097)------------------------------
% 1.57/1.26 % (3097)------------------------------
% 1.57/1.26 % (3098)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/18Mi)
% 1.57/1.26 % (3098)Instruction limit reached!
% 1.57/1.26 % (3098)------------------------------
% 1.57/1.26 % (3098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (3098)Termination reason: Unknown
% 1.57/1.26 % (3098)Termination phase: Saturation
% 1.57/1.26
% 1.57/1.26 % (3098)Memory used [KB]: 5500
% 1.57/1.26 % (3098)Time elapsed: 0.008 s
% 1.57/1.26 % (3098)Instructions burned: 18 (million)
% 1.57/1.26 % (3098)------------------------------
% 1.57/1.26 % (3098)------------------------------
% 1.57/1.26 % (3100)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/6Mi)
% 1.57/1.27 % (3099)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/710Mi)
% 1.57/1.27 % (3101)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_2982 for (2999ds/902Mi)
% 1.57/1.27 % (3100)Instruction limit reached!
% 1.57/1.27 % (3100)------------------------------
% 1.57/1.27 % (3100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (3100)Termination reason: Unknown
% 1.57/1.27 % (3100)Termination phase: Saturation
% 1.57/1.27
% 1.57/1.27 % (3100)Memory used [KB]: 5500
% 1.57/1.27 % (3100)Time elapsed: 0.005 s
% 1.57/1.27 % (3100)Instructions burned: 7 (million)
% 1.57/1.27 % (3100)------------------------------
% 1.57/1.27 % (3100)------------------------------
% 1.57/1.27 % (3090)First to succeed.
% 1.57/1.27 % (3102)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_2982 for (2999ds/21Mi)
% 1.57/1.28 % (3103)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2982 for (2999ds/5Mi)
% 1.57/1.28 % (3090)Refutation found. Thanks to Tanya!
% 1.57/1.28 % SZS status Theorem for DTF2THF_2982
% 1.57/1.28 % SZS output start Proof for DTF2THF_2982
% 1.57/1.28 thf(type_def_5, type, a: $tType).
% 1.57/1.28 thf(func_def_0, type, a: $tType).
% 1.57/1.28 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.57/1.28 thf(func_def_20, type, sK2: a > a > $o).
% 1.57/1.28 thf(func_def_21, type, sK3: a).
% 1.57/1.28 thf(func_def_22, type, sK4: a).
% 1.57/1.28 thf(func_def_23, type, sK5: a).
% 1.57/1.28 thf(func_def_24, type, sK6: a > $o).
% 1.57/1.28 thf(func_def_25, type, sK7: a).
% 1.57/1.28 thf(func_def_26, type, sK8: a).
% 1.57/1.28 thf(f511,plain,(
% 1.57/1.28 $false),
% 1.57/1.28 inference(avatar_sat_refutation,[status(thm)],[f66,f113,f120,f171,f174,f230,f505,f510])).
% 1.57/1.28 thf(f510,plain,(
% 1.57/1.28 ~spl0_3 | ~spl0_6),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f509])).
% 1.57/1.28 thf(f509,plain,(
% 1.57/1.28 $false | (~spl0_3 | ~spl0_6)),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f508])).
% 1.57/1.28 thf(f508,plain,(
% 1.57/1.28 ($true = $false) | (~spl0_3 | ~spl0_6)),
% 1.57/1.28 inference(forward_demodulation,[status(thm)],[f109,f119])).
% 1.57/1.28 thf(f119,plain,(
% 1.57/1.28 ((sK2 @ sK3 @ sK5) = $false) | ~spl0_6),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.57/1.28 thf(f118,definition,(
% 1.57/1.28 spl0_6 <=> ((sK2 @ sK3 @ sK5) = $false)),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.57/1.28 thf(f109,plain,(
% 1.57/1.28 ($true = (sK2 @ sK3 @ sK5)) | ~spl0_3),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.57/1.28 thf(f108,definition,(
% 1.57/1.28 spl0_3 <=> ($true = (sK2 @ sK3 @ sK5))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.57/1.28 thf(f505,plain,(
% 1.57/1.28 ~spl0_1),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f504])).
% 1.57/1.28 thf(f504,plain,(
% 1.57/1.28 $false | ~spl0_1),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f264,f442])).
% 1.57/1.28 thf(f442,plain,(
% 1.57/1.28 ( ! [X1 : a] : (((sK6 @ X1) = (sK2 @ sK3 @ X1))) ) | ~spl0_1),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f441])).
% 1.57/1.28 thf(f441,plain,(
% 1.57/1.28 ( ! [X1 : a] : ((((sK2 @ sK3 @ X1) = (sK6 @ X1)) = $true)) ) | ~spl0_1),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f438])).
% 1.57/1.28 thf(f438,plain,(
% 1.57/1.28 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK6 @ Y0))) @ X1) = $true)) ) | ~spl0_1),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f310])).
% 1.57/1.28 thf(f310,plain,(
% 1.57/1.28 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK6 @ Y0))))) | ~spl0_1),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f308])).
% 1.57/1.28 thf(f308,plain,(
% 1.57/1.28 (($true => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK6 @ Y0))))) = $true) | ~spl0_1),
% 1.57/1.28 inference(superposition,[status(thm)],[f294,f289])).
% 1.57/1.28 thf(f289,plain,(
% 1.57/1.28 ($true = (sK6 @ sK3)) | ~spl0_1),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f288])).
% 1.57/1.28 thf(f288,plain,(
% 1.57/1.28 ($true = ((sK6 @ sK3) & $true)) | ~spl0_1),
% 1.57/1.28 inference(backward_demodulation,[status(thm)],[f258,f286])).
% 1.57/1.28 thf(f286,plain,(
% 1.57/1.28 ($true = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK6 @ Y1)))))))) | ~spl0_1),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 1.57/1.28 thf(f258,plain,(
% 1.57/1.28 (((sK6 @ sK3) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK6 @ Y1)))))))) = $true) | ~spl0_1),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.57/1.28 thf(f238,plain,(
% 1.57/1.28 ($false = (((sK6 @ sK3) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK6 @ Y1)))))))) => ((sK2 @ sK3) = sK6))) | ~spl0_1),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f236])).
% 1.57/1.28 thf(f236,plain,(
% 1.57/1.28 ($false = ((^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0))) @ sK6)) | ~spl0_1),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f62])).
% 1.57/1.28 thf(f62,plain,(
% 1.57/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0)))) = $false) | ~spl0_1),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.57/1.28 thf(f61,definition,(
% 1.57/1.28 spl0_1 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0)))) = $false)),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.57/1.28 thf(f294,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = ((sK6 @ X1) => (!! @ a @ (^[Y0 : a]: ((sK2 @ X1 @ Y0) = (sK6 @ Y0))))))) ) | ~spl0_1),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f293])).
% 1.57/1.28 thf(f293,plain,(
% 1.57/1.28 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK6 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK6 @ Y1)))))) @ X1) = $true)) ) | ~spl0_1),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f286])).
% 1.57/1.28 thf(f264,plain,(
% 1.57/1.28 ((sK2 @ sK3 @ sK7) != (sK6 @ sK7)) | ~spl0_1),
% 1.57/1.28 inference(negative_extensionality,[status(thm)],[f263])).
% 1.57/1.28 thf(f263,plain,(
% 1.57/1.28 ((sK2 @ sK3) != sK6) | ~spl0_1),
% 1.57/1.28 inference(equality_proxy_clausification,[status(thm)],[f257])).
% 1.57/1.28 thf(f257,plain,(
% 1.57/1.28 (((sK2 @ sK3) = sK6) = $false) | ~spl0_1),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f238])).
% 1.57/1.28 thf(f230,plain,(
% 1.57/1.28 ~spl0_2 | ~spl0_4 | ~spl0_6),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f229])).
% 1.57/1.28 thf(f229,plain,(
% 1.57/1.28 $false | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.57/1.28 thf(f228,plain,(
% 1.57/1.28 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f227])).
% 1.57/1.28 thf(f227,plain,(
% 1.57/1.28 ($true = (~ $true)) | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 1.57/1.28 inference(forward_demodulation,[status(thm)],[f219,f112])).
% 1.57/1.28 thf(f112,plain,(
% 1.57/1.28 ($true = (sK2 @ sK4 @ sK5)) | ~spl0_4),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f111])).
% 1.57/1.28 thf(f111,definition,(
% 1.57/1.28 spl0_4 <=> ($true = (sK2 @ sK4 @ sK5))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.57/1.28 thf(f219,plain,(
% 1.57/1.28 ($true = (~ (sK2 @ sK4 @ sK5))) | (~spl0_2 | ~spl0_6)),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f214])).
% 1.57/1.28 thf(f214,plain,(
% 1.57/1.28 ($true = ((sK2 @ sK4 @ sK5) => $false)) | (~spl0_2 | ~spl0_6)),
% 1.57/1.28 inference(superposition,[status(thm)],[f88,f119])).
% 1.57/1.28 thf(f88,plain,(
% 1.57/1.28 ( ! [X0 : a] : (($true = ((sK2 @ sK4 @ X0) => (sK2 @ sK3 @ X0)))) ) | ~spl0_2),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f82])).
% 1.57/1.28 thf(f82,plain,(
% 1.57/1.28 ( ! [X0 : a] : (($true = (($true & (sK2 @ sK4 @ X0)) => (sK2 @ sK3 @ X0)))) ) | ~spl0_2),
% 1.57/1.28 inference(superposition,[status(thm)],[f35,f75])).
% 1.57/1.28 thf(f75,plain,(
% 1.57/1.28 ((sK2 @ sK3 @ sK4) = $true) | ~spl0_2),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.57/1.28 thf(f71,plain,(
% 1.57/1.28 ($false = ((sK2 @ sK3 @ sK4) => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK2 @ sK4 @ Y0)))))) | ~spl0_2),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.57/1.28 thf(f69,plain,(
% 1.57/1.28 ($false = ((^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1)))))) @ sK4)) | ~spl0_2),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f65])).
% 1.57/1.28 thf(f65,plain,(
% 1.57/1.28 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1)))))))) | ~spl0_2),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.57/1.28 thf(f64,definition,(
% 1.57/1.28 spl0_2 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1))))))))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.57/1.28 thf(f35,plain,(
% 1.57/1.28 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK2 @ X3 @ X1) & (sK2 @ X1 @ X2)) => (sK2 @ X3 @ X2)) = $true)) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.57/1.28 thf(f34,plain,(
% 1.57/1.28 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK2 @ Y0 @ X1) & (sK2 @ X1 @ X2)) => (sK2 @ Y0 @ X2))) @ X3))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f31])).
% 1.57/1.28 thf(f31,plain,(
% 1.57/1.28 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) & (sK2 @ X1 @ X2)) => (sK2 @ Y0 @ X2)))))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.57/1.28 thf(f30,plain,(
% 1.57/1.28 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ X1) & (sK2 @ X1 @ Y0)) => (sK2 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f29])).
% 1.57/1.28 thf(f29,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ X1) & (sK2 @ X1 @ Y0)) => (sK2 @ Y1 @ Y0)))))))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.57/1.28 thf(f28,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1))))))) @ X1))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f25])).
% 1.57/1.28 thf(f25,plain,(
% 1.57/1.28 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f24])).
% 1.57/1.28 thf(f24,plain,(
% 1.57/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))) & $true))),
% 1.57/1.28 inference(backward_demodulation,[status(thm)],[f21,f22])).
% 1.57/1.28 thf(f22,plain,(
% 1.57/1.28 ($true = (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.57/1.28 thf(f21,plain,(
% 1.57/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f20])).
% 1.57/1.28 thf(f20,plain,(
% 1.57/1.28 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & $true))),
% 1.57/1.28 inference(backward_demodulation,[status(thm)],[f13,f18])).
% 1.57/1.28 thf(f18,plain,(
% 1.57/1.28 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.57/1.28 thf(f13,plain,(
% 1.57/1.28 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.57/1.28 thf(f11,plain,(
% 1.57/1.28 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK2 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) => (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) = (sK2 @ Y2 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2)))))))))) = $false)),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.57/1.28 thf(f10,plain,(
% 1.57/1.28 ($false = ((^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) = (Y0 @ Y3 @ Y4)))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))))))))) @ sK2))),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f7])).
% 1.57/1.28 thf(f7,plain,(
% 1.57/1.28 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) = (Y0 @ Y3 @ Y4)))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3)))))))))))) = $false)),
% 1.57/1.28 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.57/1.28 thf(f6,plain,(
% 1.57/1.28 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) = (Y0 @ Y3 @ Y4)))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))))))))))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f5])).
% 1.57/1.28 thf(f5,plain,(
% 1.57/1.28 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4) = (Y0 @ Y3 @ Y4)))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))))))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.28 thf(f4,plain,(
% 1.57/1.28 ~! [X0 : a > a > $o] : ((! [X1 : a,X2 : a] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)) & ! [X3 : a] : (X0 @ X3 @ X3) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X6 @ X5) & (X0 @ X4 @ X6)) => (X0 @ X4 @ X5))) => ! [X7 : a] : ? [X8 : a > $o] : (! [X9 : a > $o] : ((! [X10 : a] : ((X9 @ X10) => ! [X11 : a] : ((X0 @ X10 @ X11) <=> (X9 @ X11))) & (X9 @ X7)) => (X8 = X9)) & ! [X12 : a] : ((X8 @ X12) => ! [X13 : a] : ((X8 @ X13) <=> (X0 @ X12 @ X13))) & (X8 @ X7)))),
% 1.57/1.28 inference(rectify,[status(thm)],[f2])).
% 1.57/1.28 thf(f2,negated_conjecture,(
% 1.57/1.28 ~! [X0 : a > a > $o] : ((! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & ! [X1 : a] : (X0 @ X1 @ X1) & ! [X1 : a,X3 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3))) => ! [X1 : a] : ? [X4 : a > $o] : (! [X6 : a > $o] : ((! [X5 : a] : ((X6 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X6 @ X2))) & (X6 @ X1)) => (X4 = X6)) & ! [X5 : a] : ((X4 @ X5) => ! [X2 : a] : ((X4 @ X2) <=> (X0 @ X5 @ X2))) & (X4 @ X1)))),
% 1.57/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.28 thf(f1,conjecture,(
% 1.57/1.28 ! [X0 : a > a > $o] : ((! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & ! [X1 : a] : (X0 @ X1 @ X1) & ! [X1 : a,X3 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3))) => ! [X1 : a] : ? [X4 : a > $o] : (! [X6 : a > $o] : ((! [X5 : a] : ((X6 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X6 @ X2))) & (X6 @ X1)) => (X4 = X6)) & ! [X5 : a] : ((X4 @ X5) => ! [X2 : a] : ((X4 @ X2) <=> (X0 @ X5 @ X2))) & (X4 @ X1)))),
% 1.57/1.28 file('/export/starexec/sandbox/tmp/tmp.oIhcyDAlvr/DTF2THF_2982.p',cTHM260_B_pme)).
% 1.57/1.28 thf(f174,plain,(
% 1.57/1.28 ~spl0_4 | ~spl0_5),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f173])).
% 1.57/1.28 thf(f173,plain,(
% 1.57/1.28 $false | (~spl0_4 | ~spl0_5)),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.57/1.28 thf(f172,plain,(
% 1.57/1.28 ($true = $false) | (~spl0_4 | ~spl0_5)),
% 1.57/1.28 inference(forward_demodulation,[status(thm)],[f112,f116])).
% 1.57/1.28 thf(f116,plain,(
% 1.57/1.28 ($false = (sK2 @ sK4 @ sK5)) | ~spl0_5),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.57/1.28 thf(f115,definition,(
% 1.57/1.28 spl0_5 <=> ($false = (sK2 @ sK4 @ sK5))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.57/1.28 thf(f171,plain,(
% 1.57/1.28 ~spl0_2 | ~spl0_3 | ~spl0_5),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f170])).
% 1.57/1.28 thf(f170,plain,(
% 1.57/1.28 $false | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.57/1.28 thf(f169,plain,(
% 1.57/1.28 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f168])).
% 1.57/1.28 thf(f168,plain,(
% 1.57/1.28 ($true = (~ $true)) | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 1.57/1.28 inference(backward_demodulation,[status(thm)],[f138,f167])).
% 1.57/1.28 thf(f167,plain,(
% 1.57/1.28 ((sK2 @ sK5 @ sK4) = $true) | (~spl0_2 | ~spl0_3)),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f161])).
% 1.57/1.28 thf(f161,plain,(
% 1.57/1.28 (($true => (sK2 @ sK5 @ sK4)) = $true) | (~spl0_2 | ~spl0_3)),
% 1.57/1.28 inference(superposition,[status(thm)],[f87,f131])).
% 1.57/1.28 thf(f131,plain,(
% 1.57/1.28 ($true = (sK2 @ sK5 @ sK3)) | ~spl0_3),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f123])).
% 1.57/1.28 thf(f123,plain,(
% 1.57/1.28 ($true = ($true => (sK2 @ sK5 @ sK3))) | ~spl0_3),
% 1.57/1.28 inference(superposition,[status(thm)],[f37,f109])).
% 1.57/1.28 thf(f37,plain,(
% 1.57/1.28 ( ! [X2 : a,X1 : a] : (($true = ((sK2 @ X1 @ X2) => (sK2 @ X2 @ X1)))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.57/1.28 thf(f36,plain,(
% 1.57/1.28 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1))) @ X2))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f33])).
% 1.57/1.28 thf(f33,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1)))))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.57/1.28 thf(f32,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))) @ X1))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f18])).
% 1.57/1.28 thf(f87,plain,(
% 1.57/1.28 ( ! [X0 : a] : (($true = ((sK2 @ X0 @ sK3) => (sK2 @ X0 @ sK4)))) ) | ~spl0_2),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f83])).
% 1.57/1.28 thf(f83,plain,(
% 1.57/1.28 ( ! [X0 : a] : (((((sK2 @ X0 @ sK3) & $true) => (sK2 @ X0 @ sK4)) = $true)) ) | ~spl0_2),
% 1.57/1.28 inference(superposition,[status(thm)],[f35,f75])).
% 1.57/1.28 thf(f138,plain,(
% 1.57/1.28 ($true = (~ (sK2 @ sK5 @ sK4))) | ~spl0_5),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f134])).
% 1.57/1.28 thf(f134,plain,(
% 1.57/1.28 ($true = ((sK2 @ sK5 @ sK4) => $false)) | ~spl0_5),
% 1.57/1.28 inference(superposition,[status(thm)],[f37,f116])).
% 1.57/1.28 thf(f120,plain,(
% 1.57/1.28 spl0_5 | spl0_6 | ~spl0_2),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f106,f64,f118,f115])).
% 1.57/1.28 thf(f106,plain,(
% 1.57/1.28 ((sK2 @ sK3 @ sK5) = $false) | ($false = (sK2 @ sK4 @ sK5)) | ~spl0_2),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.57/1.28 thf(f104,plain,(
% 1.57/1.28 ((sK2 @ sK3 @ sK5) != (sK2 @ sK4 @ sK5)) | ~spl0_2),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.57/1.28 thf(f103,plain,(
% 1.57/1.28 (((sK2 @ sK3 @ sK5) = (sK2 @ sK4 @ sK5)) = $false) | ~spl0_2),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.57/1.28 thf(f102,plain,(
% 1.57/1.28 (((^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK2 @ sK4 @ Y0))) @ sK5) = $false) | ~spl0_2),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f74])).
% 1.57/1.28 thf(f74,plain,(
% 1.57/1.28 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) = (sK2 @ sK4 @ Y0)))) = $false) | ~spl0_2),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.57/1.28 thf(f113,plain,(
% 1.57/1.28 spl0_3 | spl0_4 | ~spl0_2),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f105,f64,f111,f108])).
% 1.57/1.28 thf(f105,plain,(
% 1.57/1.28 ($true = (sK2 @ sK3 @ sK5)) | ($true = (sK2 @ sK4 @ sK5)) | ~spl0_2),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.57/1.28 thf(f66,plain,(
% 1.57/1.28 spl0_1 | spl0_2),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f59,f64,f61])).
% 1.57/1.28 thf(f59,plain,(
% 1.57/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0)))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1))))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.57/1.28 thf(f58,plain,(
% 1.57/1.28 (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0))))) = $false)),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f57])).
% 1.57/1.28 thf(f57,plain,(
% 1.57/1.28 ((($true & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) = (sK2 @ Y0 @ Y1)))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK3) = Y0))))) = $false)),
% 1.57/1.28 inference(superposition,[status(thm)],[f55,f27])).
% 1.57/1.28 thf(f27,plain,(
% 1.57/1.28 ( ! [X1 : a] : (($true = (sK2 @ X1 @ X1))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.57/1.28 thf(f26,plain,(
% 1.57/1.28 ( ! [X1 : a] : ((((^[Y0 : a]: (sK2 @ Y0 @ Y0)) @ X1) = $true)) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f22])).
% 1.57/1.28 thf(f55,plain,(
% 1.57/1.28 ( ! [X1 : a > $o] : (((((X1 @ sK3) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) = (sK2 @ Y0 @ Y1)))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (X1 = Y0))))) = $false)) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.57/1.28 thf(f54,plain,(
% 1.57/1.28 ( ! [X1 : a > $o] : (($false = ((^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) = (sK2 @ Y1 @ Y2)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (Y0 = Y1)))))) @ X1))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f53])).
% 1.57/1.28 thf(f53,plain,(
% 1.57/1.28 ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: (((Y0 @ sK3) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) = (sK2 @ Y1 @ Y2)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK3) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (Y0 = Y1))))))))),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.57/1.28 thf(f52,plain,(
% 1.57/1.28 ($false = ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) = (sK2 @ Y2 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2)))))))) @ sK3))),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f12])).
% 1.57/1.28 thf(f12,plain,(
% 1.57/1.28 ($false = (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3) = (sK2 @ Y2 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.57/1.28 % SZS output end Proof for DTF2THF_2982
% 1.57/1.28 % (3090)------------------------------
% 1.57/1.28 % (3090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (3090)Termination reason: Refutation
% 1.57/1.28
% 1.57/1.28 % (3090)Memory used [KB]: 5884
% 1.57/1.28 % (3090)Time elapsed: 0.046 s
% 1.57/1.28 % (3090)Instructions burned: 76 (million)
% 1.57/1.28 % (3090)------------------------------
% 1.57/1.28 % (3090)------------------------------
% 1.57/1.28 % (3078)Success in time 0.098 s
%------------------------------------------------------------------------------