%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV010^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 1.05s 1.00s
% Output : Refutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 165 ( 33 unt; 0 typ; 14 def)
% Number of atoms : 1238 ( 257 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2570 ( 167 ~; 163 |; 197 &;1490 @)
% ( 23 <=>; 185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 24 con; 0-2 aty)
% ( 255 !!; 90 ??; 0 @@+; 0 @@-)
% Number of variables : 393 ( 293 ^; 85 !; 15 ?; 393 :)
% 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 > $o ).
thf(func_def_22,type,
sK4: a ).
thf(func_def_23,type,
sK5: a ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a > $o ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a > $o ).
thf(func_def_29,type,
sK11: a ).
thf(f993,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f50,f91,f115,f133,f167,f174,f178,f263,f267,f307,f314,f607,f617,f867,f992]) ).
thf(f992,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f991]) ).
thf(f991,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f990]) ).
thf(f990,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f979,f163]) ).
thf(f163,plain,
( ( ( sK2 @ sK5 @ sK6 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f162]) ).
thf(f162,definition,
( spl0_7
<=> ( ( sK2 @ sK5 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f979,plain,
( ( $true
= ( sK2 @ sK5 @ sK6 ) )
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f975]) ).
thf(f975,plain,
( ( $true
= ( $true
=> ( sK2 @ sK5 @ sK6 ) ) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f902,f918]) ).
thf(f918,plain,
( ( $true
= ( sK2 @ sK5 @ sK4 ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f915]) ).
thf(f915,plain,
( ( $true
= ( $true
=> ( sK2 @ sK5 @ sK4 ) ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f60,f907]) ).
thf(f907,plain,
( ( $true
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f895]) ).
thf(f895,plain,
( ( ( ( sK2 @ sK4 @ sK5 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f890]) ).
thf(f890,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f60,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK2 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK2 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK2 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f20,f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f14,f17]) ).
thf(f17,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( ?? @ a @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( ?? @ a @ Y3 )
& ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) )
& ( Y2 @ Y1 )
& ( ?? @ a @ Y2 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( ?? @ a @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( ?? @ a @ Y3 )
& ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) )
& ( Y2 @ Y1 )
& ( ?? @ a @ Y2 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( ?? @ a @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( ?? @ a @ Y3 )
& ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) )
& ( Y2 @ Y1 )
& ( ?? @ a @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( ?? @ a
@ ^ [Y4: a] : ( Y3 @ Y4 ) )
& ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) )
& ( Y2 @ Y1 )
& ( ?? @ a
@ ^ [Y3: a] : ( 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] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( ?? @ a
@ ^ [Y4: a] : ( Y3 @ Y4 ) )
& ( Y3 @ Y1 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
= ( Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 = Y3 ) ) )
& ( Y2 @ Y1 )
& ( ?? @ a
@ ^ [Y3: a] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X2 @ X1 ) )
& ! [X4: a] : ( X0 @ X4 @ X4 )
& ! [X5: a,X6: a] :
( ( X0 @ X6 @ X5 )
=> ( X0 @ X5 @ X6 ) ) )
=> ( ! [X7: a] :
? [X8: a > $o] :
( ? [X9: a] : ( X8 @ X9 )
& ( X8 @ X7 )
& ! [X10: a > $o] :
( ( ! [X11: a] :
( ( X10 @ X11 )
=> ! [X12: a] :
( ( X0 @ X11 @ X12 )
<=> ( X10 @ X12 ) ) )
& ( X10 @ X7 )
& ? [X13: a] : ( X10 @ X13 ) )
=> ( X8 = X10 ) )
& ! [X14: a] :
( ( X8 @ X14 )
=> ! [X15: a] :
( ( X0 @ X14 @ X15 )
<=> ( X8 @ X15 ) ) ) )
& ! [X16: a > $o] :
( ( ! [X17: a] :
( ( X16 @ X17 )
=> ! [X18: a] :
( ( X0 @ X17 @ X18 )
<=> ( X16 @ X18 ) ) )
& ? [X19: a] : ( X16 @ X19 ) )
=> ? [X20: a] : ( X16 @ X20 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
=> ( ! [X1: a] :
? [X4: a > $o] :
( ? [X3: a] : ( X4 @ X3 )
& ( X4 @ X1 )
& ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X6 @ X2 ) ) )
& ( X6 @ X1 )
& ? [X3: a] : ( X6 @ X3 ) )
=> ( X4 = X6 ) )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X4 @ X2 ) ) ) )
& ! [X4: a > $o] :
( ( ! [X1: a] :
( ( X4 @ X1 )
=> ! [X2: a] :
( ( X0 @ X1 @ X2 )
<=> ( X4 @ X2 ) ) )
& ? [X3: a] : ( X4 @ X3 ) )
=> ? [X3: a] : ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 )
& ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
=> ( ! [X1: a] :
? [X4: a > $o] :
( ? [X3: a] : ( X4 @ X3 )
& ( X4 @ X1 )
& ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X6 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X6 @ X2 ) ) )
& ( X6 @ X1 )
& ? [X3: a] : ( X6 @ X3 ) )
=> ( X4 = X6 ) )
& ! [X5: a] :
( ( X4 @ X5 )
=> ! [X2: a] :
( ( X0 @ X5 @ X2 )
<=> ( X4 @ X2 ) ) ) )
& ! [X4: a > $o] :
( ( ! [X1: a] :
( ( X4 @ X1 )
=> ! [X2: a] :
( ( X0 @ X1 @ X2 )
<=> ( X4 @ X2 ) ) )
& ? [X3: a] : ( X4 @ X3 ) )
=> ? [X3: a] : ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uyw7pTFTpQ/DTF2THF_7187.p',cTHM260_pme) ).
thf(f902,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ X0 @ sK4 )
=> ( sK2 @ X0 @ sK6 ) ) )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f896]) ).
thf(f896,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK2 @ X0 @ sK4 ) )
=> ( sK2 @ X0 @ sK6 ) ) )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f74,f173]) ).
thf(f173,plain,
( ( $true
= ( sK2 @ sK4 @ sK6 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f172,definition,
( spl0_10
<=> ( $true
= ( sK2 @ sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f74,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X1 @ X3 )
& ( sK2 @ X2 @ X1 ) )
=> ( sK2 @ X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
& ( sK2 @ X2 @ X1 ) )
=> ( sK2 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
& ( sK2 @ X2 @ X1 ) )
=> ( sK2 @ X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ X1 @ Y1 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ X1 @ Y1 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f867,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f843,f312,f128,f309]) ).
thf(f309,definition,
( spl0_13
<=> ( ( sK7 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f128,definition,
( spl0_5
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f312,definition,
( spl0_14
<=> ( ( sK2 @ sK4 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f843,plain,
( ( ( sK7 @ sK8 )
= $false )
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f313,f763]) ).
thf(f763,plain,
( ! [X1: a] :
( ( sK7 @ X1 )
= ( sK2 @ sK4 @ X1 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f762]) ).
thf(f762,plain,
( ! [X1: a] :
( ( ( sK2 @ sK4 @ X1 )
= ( sK7 @ X1 ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f760]) ).
thf(f760,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
= ( sK7 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
= ( sK7 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f396]) ).
thf(f396,plain,
( ( $true
= ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
= ( sK7 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f375,f334]) ).
thf(f334,plain,
( ( $true
= ( sK7 @ sK4 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f333]) ).
thf(f333,plain,
( ( ( $true
& ( sK7 @ sK4 ) )
= $true )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f319,f332]) ).
thf(f332,plain,
( ( $true
= ( ?? @ a @ sK7 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f319]) ).
thf(f319,plain,
( ( $true
= ( ( ?? @ a @ sK7 )
& ( sK7 @ sK4 ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f318]) ).
thf(f318,plain,
( ( $true
= ( ( ?? @ a @ sK7 )
& ( sK7 @ sK4 )
& $true ) )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f294,f316]) ).
thf(f316,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK7 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK7 @ Y1 ) ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f294]) ).
thf(f294,plain,
( ( $true
= ( ( ?? @ a @ sK7 )
& ( sK7 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK7 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK7 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f272]) ).
thf(f272,plain,
( ( ( ( ( ?? @ a @ sK7 )
& ( sK7 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK7 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK7 @ Y1 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= sK7 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f270]) ).
thf(f270,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f375,plain,
( ! [X1: a] :
( $true
= ( ( sK7 @ X1 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
= ( sK7 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f373]) ).
thf(f373,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK7 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK7 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f316]) ).
thf(f313,plain,
( ( ( sK2 @ sK4 @ sK8 )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f312]) ).
thf(f617,plain,
( ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f616]) ).
thf(f616,plain,
( $false
| ~ spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f615]) ).
thf(f615,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_13 ),
inference(backward_demodulation,[status(thm)],[f303,f310]) ).
thf(f310,plain,
( ( ( sK7 @ sK8 )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f309]) ).
thf(f303,plain,
( ( $true
= ( sK7 @ sK8 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f302]) ).
thf(f302,definition,
( spl0_11
<=> ( $true
= ( sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f607,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f606]) ).
thf(f606,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f605]) ).
thf(f605,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f604,f310]) ).
thf(f604,plain,
( ( $true
= ( sK7 @ sK8 ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f603]) ).
thf(f603,plain,
( ( $true
= ( $true
=> ( sK7 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f602,f334]) ).
thf(f602,plain,
( ( $true
= ( ( sK7 @ sK4 )
=> ( sK7 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f593,f578]) ).
thf(f578,plain,
( ! [X1: a] :
( ( sK7 @ X1 )
= ( sK2 @ sK9 @ X1 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f577]) ).
thf(f577,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK9 @ X1 )
= ( sK7 @ X1 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f574]) ).
thf(f574,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK9 @ Y0 )
= ( sK7 @ Y0 ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f398]) ).
thf(f398,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK9 @ Y0 )
= ( sK7 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f397]) ).
thf(f397,plain,
( ( $true
= ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK9 @ Y0 )
= ( sK7 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f375,f341]) ).
thf(f341,plain,
( ( $true
= ( sK7 @ sK9 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f332]) ).
thf(f593,plain,
( ( $true
= ( ( sK2 @ sK9 @ sK4 )
=> ( sK7 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f330,f578]) ).
thf(f330,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ X0 @ sK4 )
=> ( sK2 @ X0 @ sK8 ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f321]) ).
thf(f321,plain,
( ! [X0: a] :
( ( ( $true
& ( sK2 @ X0 @ sK4 ) )
=> ( sK2 @ X0 @ sK8 ) )
= $true )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f74,f306]) ).
thf(f306,plain,
( ( ( sK2 @ sK4 @ sK8 )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f305]) ).
thf(f305,definition,
( spl0_12
<=> ( ( sK2 @ sK4 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f314,plain,
( spl0_13
| spl0_14
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f300,f128,f312,f309]) ).
thf(f300,plain,
( ( ( sK7 @ sK8 )
= $false )
| ( ( sK2 @ sK4 @ sK8 )
= $false )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f298]) ).
thf(f298,plain,
( ( ( sK2 @ sK4 @ sK8 )
!= ( sK7 @ sK8 ) )
| ~ spl0_5 ),
inference(negative_extensionality,[status(thm)],[f297]) ).
thf(f297,plain,
( ( sK7
!= ( sK2 @ sK4 ) )
| ~ spl0_5 ),
inference(equality_proxy_clausification,[status(thm)],[f296]) ).
thf(f296,plain,
( ( ( ( sK2 @ sK4 )
= sK7 )
= $false )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f295]) ).
thf(f295,plain,
( ( ( $true
=> ( ( sK2 @ sK4 )
= sK7 ) )
= $false )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f272,f294]) ).
thf(f307,plain,
( spl0_11
| spl0_12
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f299,f128,f305,f302]) ).
thf(f299,plain,
( ( ( sK2 @ sK4 @ sK8 )
= $true )
| ( $true
= ( sK7 @ sK8 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f298]) ).
thf(f267,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f266]) ).
thf(f266,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f265]) ).
thf(f265,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f173,f166]) ).
thf(f166,plain,
( ( ( sK2 @ sK4 @ sK6 )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f165,definition,
( spl0_8
<=> ( ( sK2 @ sK4 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f263,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f262]) ).
thf(f262,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f261]) ).
thf(f261,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f254,f170]) ).
thf(f170,plain,
( ( $true
= ( sK2 @ sK5 @ sK6 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f169,definition,
( spl0_9
<=> ( $true
= ( sK2 @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f254,plain,
( ( $true
= ( ~ ( sK2 @ sK5 @ sK6 ) ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $true
= ( ( sK2 @ sK5 @ sK6 )
=> $false ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f155,f166]) ).
thf(f155,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK5 @ X0 )
=> ( sK2 @ sK4 @ X0 ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK5 @ X0 )
& $true )
=> ( sK2 @ sK4 @ X0 ) ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f74,f143]) ).
thf(f143,plain,
( ( $true
= ( sK2 @ sK4 @ sK5 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ( sK2 @ sK4 @ sK5 )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f178,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f177]) ).
thf(f177,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f170,f163]) ).
thf(f174,plain,
( spl0_9
| spl0_10
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f159,f131,f172,f169]) ).
thf(f159,plain,
( ( $true
= ( sK2 @ sK5 @ sK6 ) )
| ( $true
= ( sK2 @ sK4 @ sK6 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( sK2 @ sK5 @ sK6 )
!= ( sK2 @ sK4 @ sK6 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( ( sK2 @ sK5 @ sK6 )
= ( sK2 @ sK4 @ sK6 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) )
@ sK6 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( $true
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
= ( sK2 @ sK4 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f141,f143]) ).
thf(f167,plain,
( spl0_7
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f160,f131,f165,f162]) ).
thf(f160,plain,
( ( ( sK2 @ sK5 @ sK6 )
= $false )
| ( ( sK2 @ sK4 @ sK6 )
= $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f133,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f123,f86,f131,f128]) ).
thf(f86,definition,
( spl0_3
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f123,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f115,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f114]) ).
thf(f114,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f94,f38]) ).
thf(f38,plain,
! [X1: a] :
( $true
= ( sK2 @ X1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] : ( sK2 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f94,plain,
( ! [X1: a] :
( ( sK2 @ sK4 @ X1 )
= $false )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( ?? @ a @ ( sK2 @ sK4 ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl0_4
<=> ( ( ?? @ a @ ( sK2 @ sK4 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f91,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f84,f23,f89,f86]) ).
thf(f23,definition,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f84,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) ) )
= $false )
| ( ( ?? @ a @ ( sK2 @ sK4 ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) )
& ( ?? @ a @ ( sK2 @ sK4 ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK2 @ sK4 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ( sK2 @ sK4 )
= Y0 ) ) )
& $true
& ( ?? @ a @ ( sK2 @ sK4 ) ) )
= $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f58,f38]) ).
thf(f58,plain,
( ! [X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( X1 @ Y1 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( X1 = Y0 ) ) )
& ( X1 @ sK4 )
& ( ?? @ a @ X1 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a @ Y1 )
& ( Y1 @ sK4 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 = Y1 ) ) )
& ( Y0 @ sK4 )
& ( ?? @ a @ Y0 ) )
@ X1 )
= $false )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ?? @ a @ Y1 )
& ( Y1 @ sK4 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 = Y1 ) ) )
& ( Y0 @ sK4 )
& ( ?? @ a @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) )
@ sK4 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f50,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f40,f39]) ).
thf(f39,plain,
( ( ( ?? @ a @ sK3 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( ( ?? @ a @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y1 ) ) ) ) ) )
=> ( ?? @ a @ sK3 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) )
@ sK3 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_2
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f40,plain,
( ( ( ( ?? @ a @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f28,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f26,f23]) ).
thf(f21,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ?? @ a @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ a @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ?? @ a @ Y2 )
& ( Y2 @ Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
= ( Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 = Y2 ) ) )
& ( Y1 @ Y0 )
& ( ?? @ a @ Y1 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f12,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV010^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:38:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEV010^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Set Theory (Relations)
% 0.07/0.31 % Problem : TPS problem THM260
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English : An equivalence relation defines a partition.
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0512 [Bro09]
% 0.07/0.31 % : THM260 [TPS]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.07/0.31 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.31 % Number of connectives : 51 ( 0 ~; 0 |; 10 &; 30 @)
% 0.07/0.31 % ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 19 ( 19 avg)
% 0.07/0.31 % Number of types : 2 ( 1 usr)
% 0.07/0.31 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.31 % Number of variables : 21 ( 0 ^; 16 !; 5 ?; 21 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 % : Polymorphic definitions expanded.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(a_type,type,
% 0.07/0.31 a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(cTHM260_pme,conjecture,
% 0.07/0.31 ! [R: a > a > $o] :
% 0.07/0.31 ( ( ! [Xx: a] : ( R @ Xx @ Xx )
% 0.07/0.31 & ! [Xx: a,Xy: a] :
% 0.07/0.31 ( ( R @ Xx @ Xy )
% 0.07/0.31 => ( R @ Xy @ Xx ) )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( ( R @ Xx @ Xy )
% 0.07/0.32 & ( R @ Xy @ Xz ) )
% 0.07/0.32 => ( R @ Xx @ Xz ) ) )
% 0.07/0.32 => ( ! [Xp: a > $o] :
% 0.07/0.32 ( ( ? [Xz: a] : ( Xp @ Xz )
% 0.07/0.32 & ! [Xx: a] :
% 0.07/0.32 ( ( Xp @ Xx )
% 0.07/0.32 => ! [Xy: a] :
% 0.07/0.32 ( ( Xp @ Xy )
% 0.07/0.32 <=> ( R @ Xx @ Xy ) ) ) )
% 0.07/0.32 => ? [Xz: a] : ( Xp @ Xz ) )
% 0.07/0.32 & ! [Xx: a] :
% 0.07/0.32 ? [Xp: a > $o] :
% 0.07/0.32 ( ? [Xz: a] : ( Xp @ Xz )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( Xp @ Xx0 )
% 0.07/0.32 => ! [Xy: a] :
% 0.07/0.32 ( ( Xp @ Xy )
% 0.07/0.32 <=> ( R @ Xx0 @ Xy ) ) )
% 0.07/0.32 & ( Xp @ Xx )
% 0.07/0.32 & ! [Xq: a > $o] :
% 0.07/0.32 ( ( ? [Xz: a] : ( Xq @ Xz )
% 0.07/0.32 & ! [Xx0: a] :
% 0.07/0.32 ( ( Xq @ Xx0 )
% 0.07/0.32 => ! [Xy: a] :
% 0.07/0.32 ( ( Xq @ Xy )
% 0.07/0.32 <=> ( R @ Xx0 @ Xy ) ) )
% 0.07/0.32 & ( Xq @ Xx ) )
% 0.07/0.32 => ( Xq = Xp ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.05/0.91 ---- Embedded in THF ---
% 1.05/0.91 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.05/0.91 %%% Generated on Tue Feb 24 12:38:16 EST 2026
% 1.05/0.91 %%% using '$$dhol' embedding, version 1.3.0.
% 1.05/0.91 %%% Logic specification used:
% 1.05/0.91 %%% thf(spec, logic, $$dhol).
% 1.05/0.91
% 1.05/0.91 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.uyw7pTFTpQ/DTF2DTF7187.p
% See solution above
% 1.05/0.91 ------------------------
% 1.05/0.91 ---- Cleaned THF ---
% 1.05/0.91 thf(a_type,type,
% 1.05/0.91 a: $tType ).
% 1.05/0.91
% 1.05/0.91 thf(cTHM260_pme,conjecture,
% 1.05/0.91 ! [R: a > a > $o] :
% 1.05/0.91 ( ( ! [Xx: a] : ( R @ Xx @ Xx )
% 1.05/0.91 & ! [Xx: a,Xy: a] :
% 1.05/0.91 ( ( R @ Xx @ Xy )
% 1.05/0.91 => ( R @ Xy @ Xx ) )
% 1.05/0.91 & ! [Xx: a,Xy: a,Xz: a] :
% 1.05/0.91 ( ( ( R @ Xx @ Xy )
% 1.05/0.91 & ( R @ Xy @ Xz ) )
% 1.05/0.91 => ( R @ Xx @ Xz ) ) )
% 1.05/0.91 => ( ! [Xp: a > $o] :
% 1.05/0.91 ( ( ? [Xz: a] : ( Xp @ Xz )
% 1.05/0.91 & ! [Xx: a] :
% 1.05/0.91 ( ( Xp @ Xx )
% 1.05/0.91 => ! [Xy: a] :
% 1.05/0.91 ( ( Xp @ Xy )
% 1.05/0.91 <=> ( R @ Xx @ Xy ) ) ) )
% 1.05/0.91 => ? [Xz: a] : ( Xp @ Xz ) )
% 1.05/0.91 & ! [Xx: a] :
% 1.05/0.91 ? [Xp: a > $o] :
% 1.05/0.91 ( ? [Xz: a] : ( Xp @ Xz )
% 1.05/0.91 & ! [Xx0: a] :
% 1.05/0.91 ( ( Xp @ Xx0 )
% 1.05/0.91 => ! [Xy: a] :
% 1.05/0.91 ( ( Xp @ Xy )
% 1.05/0.91 <=> ( R @ Xx0 @ Xy ) ) )
% 1.05/0.91 & ( Xp @ Xx )
% 1.05/0.91 & ! [Xq: a > $o] :
% 1.05/0.91 ( ( ? [Xz: a] : ( Xq @ Xz )
% 1.05/0.91 & ! [Xx0: a] :
% 1.05/0.91 ( ( Xq @ Xx0 )
% 1.05/0.91 => ! [Xy: a] :
% 1.05/0.91 ( ( Xq @ Xy )
% 1.05/0.91 <=> ( R @ Xx0 @ Xy ) ) )
% 1.05/0.91 & ( Xq @ Xx ) )
% 1.05/0.91 => ( Xq = Xp ) ) ) ) ) ).
% 1.05/0.91 ------------------------
% 1.05/0.93 % (7353)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_7187 for (3000ds/2Mi)
% 1.05/0.93 % (7354)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_7187 for (3000ds/275Mi)
% 1.05/0.93 % (7355)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/18Mi)
% 1.05/0.93 % (7351)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_7187 for (3000ds/27Mi)
% 1.05/0.93 % (7352)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/2Mi)
% 1.05/0.93 % (7349)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7187 for (3000ds/183Mi)
% 1.05/0.93 % (7350)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_7187 for (3000ds/4Mi)
% 1.05/0.93 % (7352)Instruction limit reached!
% 1.05/0.93 % (7352)------------------------------
% 1.05/0.93 % (7352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.93 % (7352)Termination reason: Unknown
% 1.05/0.93 % (7352)Termination phase: Preprocessing 3
% 1.05/0.93
% 1.05/0.93 % (7352)Memory used [KB]: 1023
% 1.05/0.93 % (7352)Time elapsed: 0.002 s
% 1.05/0.93 % (7352)Instructions burned: 2 (million)
% 1.05/0.93 % (7352)------------------------------
% 1.05/0.93 % (7352)------------------------------
% 1.05/0.93 % (7353)Instruction limit reached!
% 1.05/0.93 % (7353)------------------------------
% 1.05/0.93 % (7353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.93 % (7353)Termination reason: Unknown
% 1.05/0.93 % (7353)Termination phase: Property scanning
% 1.05/0.93
% 1.05/0.93 % (7353)Memory used [KB]: 1023
% 1.05/0.93 % (7353)Time elapsed: 0.002 s
% 1.05/0.93 % (7353)Instructions burned: 3 (million)
% 1.05/0.93 % (7353)------------------------------
% 1.05/0.93 % (7353)------------------------------
% 1.05/0.93 % (7350)Instruction limit reached!
% 1.05/0.93 % (7350)------------------------------
% 1.05/0.93 % (7350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.93 % (7350)Termination reason: Unknown
% 1.05/0.93 % (7350)Termination phase: Saturation
% 1.05/0.93
% 1.05/0.93 % (7350)Memory used [KB]: 5500
% 1.05/0.93 % (7350)Time elapsed: 0.003 s
% 1.05/0.93 % (7350)Instructions burned: 4 (million)
% 1.05/0.93 % (7350)------------------------------
% 1.05/0.93 % (7350)------------------------------
% 1.05/0.93 % (7355)Instruction limit reached!
% 1.05/0.93 % (7355)------------------------------
% 1.05/0.93 % (7355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.93 % (7355)Termination reason: Unknown
% 1.05/0.93 % (7355)Termination phase: Saturation
% 1.05/0.93
% 1.05/0.93 % (7355)Memory used [KB]: 5628
% 1.05/0.93 % (7355)Time elapsed: 0.007 s
% 1.05/0.93 % (7355)Instructions burned: 18 (million)
% 1.05/0.93 % (7355)------------------------------
% 1.05/0.93 % (7355)------------------------------
% 1.05/0.94 % (7351)Instruction limit reached!
% 1.05/0.94 % (7351)------------------------------
% 1.05/0.94 % (7351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.94 % (7351)Termination reason: Unknown
% 1.05/0.94 % (7351)Termination phase: Saturation
% 1.05/0.94
% 1.05/0.94 % (7351)Memory used [KB]: 5756
% 1.05/0.94 % (7351)Time elapsed: 0.011 s
% 1.05/0.94 % (7351)Instructions burned: 28 (million)
% 1.05/0.94 % (7351)------------------------------
% 1.05/0.94 % (7351)------------------------------
% 1.05/0.94 % (7356)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/3Mi)
% 1.05/0.94 % (7357)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_7187 for (2999ds/37Mi)
% 1.05/0.94 % (7358)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_7187 for (2999ds/15Mi)
% 1.05/0.94 % (7356)Instruction limit reached!
% 1.05/0.94 % (7356)------------------------------
% 1.05/0.94 % (7356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.94 % (7356)Termination reason: Unknown
% 1.05/0.94 % (7356)Termination phase: Saturation
% 1.05/0.94
% 1.05/0.94 % (7356)Memory used [KB]: 5500
% 1.05/0.94 % (7356)Time elapsed: 0.002 s
% 1.05/0.94 % (7356)Instructions burned: 3 (million)
% 1.05/0.94 % (7356)------------------------------
% 1.05/0.94 % (7356)------------------------------
% 1.05/0.94 % (7359)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_7187 for (2999ds/3Mi)
% 1.05/0.94 % (7358)Instruction limit reached!
% 1.05/0.94 % (7358)------------------------------
% 1.05/0.94 % (7358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.94 % (7358)Termination reason: Unknown
% 1.05/0.94 % (7358)Termination phase: Saturation
% 1.05/0.94
% 1.05/0.94 % (7358)Memory used [KB]: 5628
% 1.05/0.94 % (7358)Time elapsed: 0.006 s
% 1.05/0.94 % (7358)Instructions burned: 15 (million)
% 1.05/0.94 % (7358)------------------------------
% 1.05/0.94 % (7358)------------------------------
% 1.05/0.94 % (7359)Instruction limit reached!
% 1.05/0.94 % (7359)------------------------------
% 1.05/0.94 % (7359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.94 % (7359)Termination reason: Unknown
% 1.05/0.94 % (7359)Termination phase: Saturation
% 1.05/0.94
% 1.05/0.94 % (7359)Memory used [KB]: 1023
% 1.05/0.94 % (7359)Time elapsed: 0.002 s
% 1.05/0.94 % (7359)Instructions burned: 3 (million)
% 1.05/0.94 % (7359)------------------------------
% 1.05/0.94 % (7359)------------------------------
% 1.05/0.95 % (7360)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_7187 for (2999ds/1041Mi)
% 1.05/0.95 % (7361)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/7Mi)
% 1.05/0.95 % (7357)Instruction limit reached!
% 1.05/0.95 % (7357)------------------------------
% 1.05/0.95 % (7357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.95 % (7357)Termination reason: Unknown
% 1.05/0.95 % (7357)Termination phase: Saturation
% 1.05/0.95
% 1.05/0.95 % (7357)Memory used [KB]: 5628
% 1.05/0.95 % (7357)Time elapsed: 0.013 s
% 1.05/0.95 % (7357)Instructions burned: 38 (million)
% 1.05/0.95 % (7357)------------------------------
% 1.05/0.95 % (7357)------------------------------
% 1.05/0.95 % (7361)Instruction limit reached!
% 1.05/0.95 % (7361)------------------------------
% 1.05/0.95 % (7361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.95 % (7361)Termination reason: Unknown
% 1.05/0.95 % (7361)Termination phase: Saturation
% 1.05/0.95
% 1.05/0.95 % (7361)Memory used [KB]: 1023
% 1.05/0.95 % (7361)Time elapsed: 0.004 s
% 1.05/0.95 % (7361)Instructions burned: 9 (million)
% 1.05/0.95 % (7361)------------------------------
% 1.05/0.95 % (7361)------------------------------
% 1.05/0.95 % (7362)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/16Mi)
% 1.05/0.95 % (7363)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_7187 for (2999ds/3Mi)
% 1.05/0.95 % (7363)Instruction limit reached!
% 1.05/0.95 % (7363)------------------------------
% 1.05/0.95 % (7363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.95 % (7363)Termination reason: Unknown
% 1.05/0.95 % (7363)Termination phase: Saturation
% 1.05/0.95
% 1.05/0.95 % (7363)Memory used [KB]: 5500
% 1.05/0.95 % (7363)Time elapsed: 0.003 s
% 1.05/0.95 % (7363)Instructions burned: 6 (million)
% 1.05/0.95 % (7363)------------------------------
% 1.05/0.95 % (7363)------------------------------
% 1.05/0.96 % (7362)Instruction limit reached!
% 1.05/0.96 % (7362)------------------------------
% 1.05/0.96 % (7362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.96 % (7362)Termination reason: Unknown
% 1.05/0.96 % (7362)Termination phase: Saturation
% 1.05/0.96
% 1.05/0.96 % (7362)Memory used [KB]: 5628
% 1.05/0.96 % (7362)Time elapsed: 0.007 s
% 1.05/0.96 % (7362)Instructions burned: 18 (million)
% 1.05/0.96 % (7362)------------------------------
% 1.05/0.96 % (7362)------------------------------
% 1.05/0.96 % (7364)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_7187 for (2999ds/3Mi)
% 1.05/0.96 % (7364)Instruction limit reached!
% 1.05/0.96 % (7364)------------------------------
% 1.05/0.96 % (7364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.96 % (7364)Termination reason: Unknown
% 1.05/0.96 % (7364)Termination phase: Property scanning
% 1.05/0.96
% 1.05/0.96 % (7364)Memory used [KB]: 1023
% 1.05/0.96 % (7364)Time elapsed: 0.002 s
% 1.05/0.96 % (7364)Instructions burned: 3 (million)
% 1.05/0.96 % (7364)------------------------------
% 1.05/0.96 % (7364)------------------------------
% 1.05/0.96 % (7366)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/3Mi)
% 1.05/0.96 % (7366)Instruction limit reached!
% 1.05/0.96 % (7366)------------------------------
% 1.05/0.96 % (7366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.96 % (7366)Termination reason: Unknown
% 1.05/0.96 % (7366)Termination phase: Saturation
% 1.05/0.96
% 1.05/0.96 % (7366)Memory used [KB]: 5500
% 1.05/0.96 % (7366)Time elapsed: 0.002 s
% 1.05/0.96 % (7366)Instructions burned: 3 (million)
% 1.05/0.96 % (7366)------------------------------
% 1.05/0.96 % (7366)------------------------------
% 1.05/0.97 % (7365)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/7Mi)
% 1.05/0.97 % (7367)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/4Mi)
% 1.05/0.97 % (7368)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/18Mi)
% 1.05/0.97 % (7367)Instruction limit reached!
% 1.05/0.97 % (7367)------------------------------
% 1.05/0.97 % (7367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.97 % (7367)Termination reason: Unknown
% 1.05/0.97 % (7367)Termination phase: Saturation
% 1.05/0.97
% 1.05/0.97 % (7367)Memory used [KB]: 5500
% 1.05/0.97 % (7367)Time elapsed: 0.003 s
% 1.05/0.97 % (7367)Instructions burned: 6 (million)
% 1.05/0.97 % (7367)------------------------------
% 1.05/0.97 % (7367)------------------------------
% 1.05/0.97 % (7365)Instruction limit reached!
% 1.05/0.97 % (7365)------------------------------
% 1.05/0.97 % (7365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.97 % (7365)Termination reason: Unknown
% 1.05/0.97 % (7365)Termination phase: Saturation
% 1.05/0.97
% 1.05/0.97 % (7365)Memory used [KB]: 5500
% 1.05/0.97 % (7365)Time elapsed: 0.006 s
% 1.05/0.97 % (7365)Instructions burned: 8 (million)
% 1.05/0.97 % (7365)------------------------------
% 1.05/0.97 % (7365)------------------------------
% 1.05/0.97 % (7369)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/710Mi)
% 1.05/0.97 % (7368)Instruction limit reached!
% 1.05/0.97 % (7368)------------------------------
% 1.05/0.97 % (7368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.97 % (7368)Termination reason: Unknown
% 1.05/0.97 % (7368)Termination phase: Saturation
% 1.05/0.97
% 1.05/0.97 % (7368)Memory used [KB]: 5628
% 1.05/0.97 % (7368)Time elapsed: 0.007 s
% 1.05/0.97 % (7368)Instructions burned: 18 (million)
% 1.05/0.97 % (7368)------------------------------
% 1.05/0.97 % (7368)------------------------------
% 1.05/0.98 % (7349)Instruction limit reached!
% 1.05/0.98 % (7349)------------------------------
% 1.05/0.98 % (7349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.98 % (7349)Termination reason: Unknown
% 1.05/0.98 % (7349)Termination phase: Saturation
% 1.05/0.98
% 1.05/0.98 % (7349)Memory used [KB]: 6524
% 1.05/0.98 % (7349)Time elapsed: 0.051 s
% 1.05/0.98 % (7349)Instructions burned: 184 (million)
% 1.05/0.98 % (7349)------------------------------
% 1.05/0.98 % (7349)------------------------------
% 1.05/0.98 % (7370)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/6Mi)
% 1.05/0.98 % (7371)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_7187 for (2999ds/902Mi)
% 1.05/0.98 % (7370)Instruction limit reached!
% 1.05/0.98 % (7370)------------------------------
% 1.05/0.98 % (7370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.98 % (7370)Termination reason: Unknown
% 1.05/0.98 % (7370)Termination phase: Saturation
% 1.05/0.98
% 1.05/0.98 % (7370)Memory used [KB]: 5500
% 1.05/0.98 % (7370)Time elapsed: 0.003 s
% 1.05/0.98 % (7370)Instructions burned: 6 (million)
% 1.05/0.98 % (7370)------------------------------
% 1.05/0.98 % (7370)------------------------------
% 1.05/0.98 % (7372)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_7187 for (2999ds/21Mi)
% 1.05/0.99 % (7373)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/5Mi)
% 1.05/0.99 % (7373)Instruction limit reached!
% 1.05/0.99 % (7373)------------------------------
% 1.05/0.99 % (7373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.99 % (7373)Termination reason: Unknown
% 1.05/0.99 % (7373)Termination phase: Saturation
% 1.05/0.99
% 1.05/0.99 % (7373)Memory used [KB]: 5500
% 1.05/0.99 % (7373)Time elapsed: 0.003 s
% 1.05/0.99 % (7373)Instructions burned: 7 (million)
% 1.05/0.99 % (7373)------------------------------
% 1.05/0.99 % (7373)------------------------------
% 1.05/0.99 % (7374)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7187 for (2999ds/6Mi)
% 1.05/0.99 % (7360)First to succeed.
% 1.05/0.99 % (7374)Instruction limit reached!
% 1.05/0.99 % (7374)------------------------------
% 1.05/0.99 % (7374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.99 % (7374)Termination reason: Unknown
% 1.05/0.99 % (7374)Termination phase: Saturation
% 1.05/0.99
% 1.05/0.99 % (7374)Memory used [KB]: 5500
% 1.05/0.99 % (7374)Time elapsed: 0.003 s
% 1.05/0.99 % (7374)Instructions burned: 8 (million)
% 1.05/0.99 % (7374)------------------------------
% 1.05/0.99 % (7374)------------------------------
% 1.05/0.99 % (7372)Instruction limit reached!
% 1.05/0.99 % (7372)------------------------------
% 1.05/0.99 % (7372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/0.99 % (7372)Termination reason: Unknown
% 1.05/0.99 % (7372)Termination phase: Saturation
% 1.05/0.99
% 1.05/0.99 % (7372)Memory used [KB]: 5628
% 1.05/0.99 % (7372)Time elapsed: 0.009 s
% 1.05/0.99 % (7372)Instructions burned: 24 (million)
% 1.05/0.99 % (7372)------------------------------
% 1.05/0.99 % (7372)------------------------------
% 1.05/1.00 % (7360)Refutation found. Thanks to Tanya!
% 1.05/1.00 % SZS status Theorem for DTF2THF_7187
% 1.05/1.00 % SZS output start Proof for DTF2THF_7187
% 1.05/1.00 thf(type_def_5, type, a: $tType).
% 1.05/1.00 thf(func_def_0, type, a: $tType).
% 1.05/1.00 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.05/1.00 thf(func_def_20, type, sK2: a > a > $o).
% 1.05/1.00 thf(func_def_21, type, sK3: a > $o).
% 1.05/1.00 thf(func_def_22, type, sK4: a).
% 1.05/1.00 thf(func_def_23, type, sK5: a).
% 1.05/1.00 thf(func_def_24, type, sK6: a).
% 1.05/1.00 thf(func_def_25, type, sK7: a > $o).
% 1.05/1.00 thf(func_def_26, type, sK8: a).
% 1.05/1.00 thf(func_def_27, type, sK9: a).
% 1.05/1.00 thf(func_def_28, type, sK10: a > $o).
% 1.05/1.00 thf(func_def_29, type, sK11: a).
% 1.05/1.00 thf(f993,plain,(
% 1.05/1.00 $false),
% 1.05/1.00 inference(avatar_sat_refutation,[status(thm)],[f28,f50,f91,f115,f133,f167,f174,f178,f263,f267,f307,f314,f607,f617,f867,f992])).
% 1.05/1.00 thf(f992,plain,(
% 1.05/1.00 ~spl0_6 | ~spl0_7 | ~spl0_10),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f991])).
% 1.05/1.00 thf(f991,plain,(
% 1.05/1.00 $false | (~spl0_6 | ~spl0_7 | ~spl0_10)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f990])).
% 1.05/1.00 thf(f990,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_6 | ~spl0_7 | ~spl0_10)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f979,f163])).
% 1.05/1.00 thf(f163,plain,(
% 1.05/1.00 ((sK2 @ sK5 @ sK6) = $false) | ~spl0_7),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.05/1.00 thf(f162,definition,(
% 1.05/1.00 spl0_7 <=> ((sK2 @ sK5 @ sK6) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.05/1.00 thf(f979,plain,(
% 1.05/1.00 ($true = (sK2 @ sK5 @ sK6)) | (~spl0_6 | ~spl0_10)),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f975])).
% 1.05/1.00 thf(f975,plain,(
% 1.05/1.00 ($true = ($true => (sK2 @ sK5 @ sK6))) | (~spl0_6 | ~spl0_10)),
% 1.05/1.00 inference(superposition,[status(thm)],[f902,f918])).
% 1.05/1.00 thf(f918,plain,(
% 1.05/1.00 ($true = (sK2 @ sK5 @ sK4)) | ~spl0_6),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f915])).
% 1.05/1.00 thf(f915,plain,(
% 1.05/1.00 ($true = ($true => (sK2 @ sK5 @ sK4))) | ~spl0_6),
% 1.05/1.00 inference(superposition,[status(thm)],[f60,f907])).
% 1.05/1.00 thf(f907,plain,(
% 1.05/1.00 ($true = (sK2 @ sK4 @ sK5)) | ~spl0_6),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f895])).
% 1.05/1.00 thf(f895,plain,(
% 1.05/1.00 (((sK2 @ sK4 @ sK5) => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) = (sK2 @ sK4 @ Y0))))) = $false) | ~spl0_6),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f890])).
% 1.05/1.00 thf(f890,plain,(
% 1.05/1.00 (((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1)))))) @ sK5) = $false) | ~spl0_6),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f132])).
% 1.05/1.00 thf(f132,plain,(
% 1.05/1.00 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) = $false) | ~spl0_6),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.05/1.00 thf(f131,definition,(
% 1.05/1.00 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.05/1.00 thf(f60,plain,(
% 1.05/1.00 ( ! [X2 : a,X1 : a] : (($true = ((sK2 @ X1 @ X2) => (sK2 @ X2 @ X1)))) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.05/1.00 thf(f59,plain,(
% 1.05/1.00 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1))) @ X2))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f56])).
% 1.05/1.00 thf(f56,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1)))))) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.05/1.00 thf(f55,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))) @ X1))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f34])).
% 1.05/1.00 thf(f34,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))))),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f33])).
% 1.05/1.00 thf(f33,plain,(
% 1.05/1.00 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & $true) = $true)),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f20,f31])).
% 1.05/1.00 thf(f31,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0))))),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.05/1.00 thf(f20,plain,(
% 1.05/1.00 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))))),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f19])).
% 1.05/1.00 thf(f19,plain,(
% 1.05/1.00 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & $true))),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f14,f17])).
% 1.05/1.00 thf(f17,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ Y2)))))))))),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.05/1.00 thf(f14,plain,(
% 1.05/1.00 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ Y2))))))))))),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.05/1.00 thf(f12,plain,(
% 1.05/1.00 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (sK2 @ Y0 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ Y2))))))))) => ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) & (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1)))))))) = $false)),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.05/1.00 thf(f11,plain,(
% 1.05/1.00 (((^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((?? @ a @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (?? @ a @ Y1)))) & (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) = (Y2 @ Y4))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((((?? @ a @ Y3) & (Y3 @ Y1)) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))) & (Y2 @ Y1)) & (?? @ a @ Y2))))))))) @ sK2) = $false)),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f8])).
% 1.05/1.00 thf(f8,plain,(
% 1.05/1.00 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((?? @ a @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (?? @ a @ Y1)))) & (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) = (Y2 @ Y4))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((((?? @ a @ Y3) & (Y3 @ Y1)) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))) & (Y2 @ Y1)) & (?? @ a @ Y2)))))))))) = $false)),
% 1.05/1.00 inference(not_proxy_clausification,[status(thm)],[f7])).
% 1.05/1.00 thf(f7,plain,(
% 1.05/1.00 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((?? @ a @ Y1) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (?? @ a @ Y1)))) & (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) = (Y2 @ Y4))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((((?? @ a @ Y3) & (Y3 @ Y1)) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))) & (Y2 @ Y1)) & (?? @ a @ Y2))))))))))))),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.05/1.00 thf(f6,plain,(
% 1.05/1.00 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((?? @ a @ (^[Y2 : a]: (Y1 @ Y2))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) = (Y2 @ Y4))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((((?? @ a @ (^[Y4 : a]: (Y3 @ Y4))) & (Y3 @ Y1)) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))) & (Y2 @ Y1)) & (?? @ a @ (^[Y3 : a]: (Y2 @ Y3))))))))))))))),
% 1.05/1.00 inference(cnf_transformation,[status(thm)],[f5])).
% 1.05/1.00 thf(f5,plain,(
% 1.05/1.00 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (Y0 @ Y1 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((?? @ a @ (^[Y2 : a]: (Y1 @ Y2))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) = (Y2 @ Y4))))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((((?? @ a @ (^[Y4 : a]: (Y3 @ Y4))) & (Y3 @ Y1)) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) = (Y3 @ Y5)))))))) => (Y2 = Y3))))) & (Y2 @ Y1)) & (?? @ a @ (^[Y3 : a]: (Y2 @ Y3))))))))))))))),
% 1.05/1.00 inference(fool_elimination,[status(thm)],[f4])).
% 1.05/1.00 thf(f4,plain,(
% 1.05/1.00 ~! [X0 : a > a > $o] : ((! [X1 : a,X2 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)) & ! [X4 : a] : (X0 @ X4 @ X4) & ! [X5 : a,X6 : a] : ((X0 @ X6 @ X5) => (X0 @ X5 @ X6))) => (! [X7 : a] : ? [X8 : a > $o] : (? [X9 : a] : (X8 @ X9) & (X8 @ X7) & ! [X10 : a > $o] : ((! [X11 : a] : ((X10 @ X11) => ! [X12 : a] : ((X0 @ X11 @ X12) <=> (X10 @ X12))) & (X10 @ X7) & ? [X13 : a] : (X10 @ X13)) => (X8 = X10)) & ! [X14 : a] : ((X8 @ X14) => ! [X15 : a] : ((X0 @ X14 @ X15) <=> (X8 @ X15)))) & ! [X16 : a > $o] : ((! [X17 : a] : ((X16 @ X17) => ! [X18 : a] : ((X0 @ X17 @ X18) <=> (X16 @ X18))) & ? [X19 : a] : (X16 @ X19)) => ? [X20 : a] : (X16 @ X20))))),
% 1.05/1.00 inference(rectify,[status(thm)],[f2])).
% 1.05/1.00 thf(f2,negated_conjecture,(
% 1.05/1.00 ~! [X0 : a > a > $o] : ((! [X3 : a,X1 : a,X2 : a] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : a] : (X0 @ X1 @ X1) & ! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1))) => (! [X1 : a] : ? [X4 : a > $o] : (? [X3 : a] : (X4 @ X3) & (X4 @ X1) & ! [X6 : a > $o] : ((! [X5 : a] : ((X6 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X6 @ X2))) & (X6 @ X1) & ? [X3 : a] : (X6 @ X3)) => (X4 = X6)) & ! [X5 : a] : ((X4 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X4 @ X2)))) & ! [X4 : a > $o] : ((! [X1 : a] : ((X4 @ X1) => ! [X2 : a] : ((X0 @ X1 @ X2) <=> (X4 @ X2))) & ? [X3 : a] : (X4 @ X3)) => ? [X3 : a] : (X4 @ X3))))),
% 1.05/1.00 inference(negated_conjecture,[status(cth)],[f1])).
% 1.05/1.00 thf(f1,conjecture,(
% 1.05/1.00 ! [X0 : a > a > $o] : ((! [X3 : a,X1 : a,X2 : a] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : a] : (X0 @ X1 @ X1) & ! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1))) => (! [X1 : a] : ? [X4 : a > $o] : (? [X3 : a] : (X4 @ X3) & (X4 @ X1) & ! [X6 : a > $o] : ((! [X5 : a] : ((X6 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X6 @ X2))) & (X6 @ X1) & ? [X3 : a] : (X6 @ X3)) => (X4 = X6)) & ! [X5 : a] : ((X4 @ X5) => ! [X2 : a] : ((X0 @ X5 @ X2) <=> (X4 @ X2)))) & ! [X4 : a > $o] : ((! [X1 : a] : ((X4 @ X1) => ! [X2 : a] : ((X0 @ X1 @ X2) <=> (X4 @ X2))) & ? [X3 : a] : (X4 @ X3)) => ? [X3 : a] : (X4 @ X3))))),
% 1.05/1.00 file('/export/starexec/sandbox2/tmp/tmp.uyw7pTFTpQ/DTF2THF_7187.p',cTHM260_pme)).
% 1.05/1.00 thf(f902,plain,(
% 1.05/1.00 ( ! [X0 : a] : (($true = ((sK2 @ X0 @ sK4) => (sK2 @ X0 @ sK6)))) ) | ~spl0_10),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f896])).
% 1.05/1.00 thf(f896,plain,(
% 1.05/1.00 ( ! [X0 : a] : (($true = (($true & (sK2 @ X0 @ sK4)) => (sK2 @ X0 @ sK6)))) ) | ~spl0_10),
% 1.05/1.00 inference(superposition,[status(thm)],[f74,f173])).
% 1.05/1.00 thf(f173,plain,(
% 1.05/1.00 ($true = (sK2 @ sK4 @ sK6)) | ~spl0_10),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.05/1.00 thf(f172,definition,(
% 1.05/1.00 spl0_10 <=> ($true = (sK2 @ sK4 @ sK6))),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.05/1.00 thf(f74,plain,(
% 1.05/1.00 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK2 @ X1 @ X3) & (sK2 @ X2 @ X1)) => (sK2 @ X2 @ X3)) = $true)) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.05/1.00 thf(f73,plain,(
% 1.05/1.00 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK2 @ X1 @ Y0) & (sK2 @ X2 @ X1)) => (sK2 @ X2 @ Y0))) @ X3))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f72])).
% 1.05/1.00 thf(f72,plain,(
% 1.05/1.00 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ X1 @ Y0) & (sK2 @ X2 @ X1)) => (sK2 @ X2 @ Y0)))))) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.05/1.00 thf(f71,plain,(
% 1.05/1.00 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ X1 @ Y1) & (sK2 @ Y0 @ X1)) => (sK2 @ Y0 @ Y1))))) @ X2))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f70])).
% 1.05/1.00 thf(f70,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ X1 @ Y1) & (sK2 @ Y0 @ X1)) => (sK2 @ Y0 @ Y1)))))))) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.05/1.00 thf(f69,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ Y2))))))) @ X1))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f17])).
% 1.05/1.00 thf(f867,plain,(
% 1.05/1.00 spl0_13 | ~spl0_5 | ~spl0_14),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f843,f312,f128,f309])).
% 1.05/1.00 thf(f309,definition,(
% 1.05/1.00 spl0_13 <=> ((sK7 @ sK8) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.05/1.00 thf(f128,definition,(
% 1.05/1.00 spl0_5 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0)))) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.05/1.00 thf(f312,definition,(
% 1.05/1.00 spl0_14 <=> ((sK2 @ sK4 @ sK8) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.05/1.00 thf(f843,plain,(
% 1.05/1.00 ((sK7 @ sK8) = $false) | (~spl0_5 | ~spl0_14)),
% 1.05/1.00 inference(superposition,[status(thm)],[f313,f763])).
% 1.05/1.00 thf(f763,plain,(
% 1.05/1.00 ( ! [X1 : a] : (((sK7 @ X1) = (sK2 @ sK4 @ X1))) ) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f762])).
% 1.05/1.00 thf(f762,plain,(
% 1.05/1.00 ( ! [X1 : a] : ((((sK2 @ sK4 @ X1) = (sK7 @ X1)) = $true)) ) | ~spl0_5),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f760])).
% 1.05/1.00 thf(f760,plain,(
% 1.05/1.00 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK2 @ sK4 @ Y0) = (sK7 @ Y0))) @ X1) = $true)) ) | ~spl0_5),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f400])).
% 1.05/1.00 thf(f400,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) = (sK7 @ Y0))))) | ~spl0_5),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f396])).
% 1.05/1.00 thf(f396,plain,(
% 1.05/1.00 ($true = ($true => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) = (sK7 @ Y0)))))) | ~spl0_5),
% 1.05/1.00 inference(superposition,[status(thm)],[f375,f334])).
% 1.05/1.00 thf(f334,plain,(
% 1.05/1.00 ($true = (sK7 @ sK4)) | ~spl0_5),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f333])).
% 1.05/1.00 thf(f333,plain,(
% 1.05/1.00 (($true & (sK7 @ sK4)) = $true) | ~spl0_5),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f319,f332])).
% 1.05/1.00 thf(f332,plain,(
% 1.05/1.00 ($true = (?? @ a @ sK7)) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f319])).
% 1.05/1.00 thf(f319,plain,(
% 1.05/1.00 ($true = ((?? @ a @ sK7) & (sK7 @ sK4))) | ~spl0_5),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f318])).
% 1.05/1.00 thf(f318,plain,(
% 1.05/1.00 ($true = (((?? @ a @ sK7) & (sK7 @ sK4)) & $true)) | ~spl0_5),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f294,f316])).
% 1.05/1.00 thf(f316,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: ((sK7 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK7 @ Y1)))))))) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f294])).
% 1.05/1.00 thf(f294,plain,(
% 1.05/1.00 ($true = (((?? @ a @ sK7) & (sK7 @ sK4)) & (!! @ a @ (^[Y0 : a]: ((sK7 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK7 @ Y1))))))))) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f272])).
% 1.05/1.00 thf(f272,plain,(
% 1.05/1.00 (((((?? @ a @ sK7) & (sK7 @ sK4)) & (!! @ a @ (^[Y0 : a]: ((sK7 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK7 @ Y1)))))))) => ((sK2 @ sK4) = sK7)) = $false) | ~spl0_5),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f270])).
% 1.05/1.00 thf(f270,plain,(
% 1.05/1.00 (((^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))) @ sK7) = $false) | ~spl0_5),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f129])).
% 1.05/1.00 thf(f129,plain,(
% 1.05/1.00 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0)))) = $false) | ~spl0_5),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f128])).
% 1.05/1.00 thf(f375,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((sK7 @ X1) => (!! @ a @ (^[Y0 : a]: ((sK2 @ X1 @ Y0) = (sK7 @ Y0))))))) ) | ~spl0_5),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f373])).
% 1.05/1.00 thf(f373,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK7 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK7 @ Y1)))))) @ X1))) ) | ~spl0_5),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f316])).
% 1.05/1.00 thf(f313,plain,(
% 1.05/1.00 ((sK2 @ sK4 @ sK8) = $false) | ~spl0_14),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f312])).
% 1.05/1.00 thf(f617,plain,(
% 1.05/1.00 ~spl0_11 | ~spl0_13),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f616])).
% 1.05/1.00 thf(f616,plain,(
% 1.05/1.00 $false | (~spl0_11 | ~spl0_13)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f615])).
% 1.05/1.00 thf(f615,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_11 | ~spl0_13)),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f303,f310])).
% 1.05/1.00 thf(f310,plain,(
% 1.05/1.00 ((sK7 @ sK8) = $false) | ~spl0_13),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f309])).
% 1.05/1.00 thf(f303,plain,(
% 1.05/1.00 ($true = (sK7 @ sK8)) | ~spl0_11),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f302])).
% 1.05/1.00 thf(f302,definition,(
% 1.05/1.00 spl0_11 <=> ($true = (sK7 @ sK8))),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.05/1.00 thf(f607,plain,(
% 1.05/1.00 ~spl0_5 | ~spl0_12 | ~spl0_13),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f606])).
% 1.05/1.00 thf(f606,plain,(
% 1.05/1.00 $false | (~spl0_5 | ~spl0_12 | ~spl0_13)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f605])).
% 1.05/1.00 thf(f605,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_5 | ~spl0_12 | ~spl0_13)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f604,f310])).
% 1.05/1.00 thf(f604,plain,(
% 1.05/1.00 ($true = (sK7 @ sK8)) | (~spl0_5 | ~spl0_12)),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f603])).
% 1.05/1.00 thf(f603,plain,(
% 1.05/1.00 ($true = ($true => (sK7 @ sK8))) | (~spl0_5 | ~spl0_12)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f602,f334])).
% 1.05/1.00 thf(f602,plain,(
% 1.05/1.00 ($true = ((sK7 @ sK4) => (sK7 @ sK8))) | (~spl0_5 | ~spl0_12)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f593,f578])).
% 1.05/1.00 thf(f578,plain,(
% 1.05/1.00 ( ! [X1 : a] : (((sK7 @ X1) = (sK2 @ sK9 @ X1))) ) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f577])).
% 1.05/1.00 thf(f577,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((sK2 @ sK9 @ X1) = (sK7 @ X1)))) ) | ~spl0_5),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f574])).
% 1.05/1.00 thf(f574,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ sK9 @ Y0) = (sK7 @ Y0))) @ X1))) ) | ~spl0_5),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f398])).
% 1.05/1.00 thf(f398,plain,(
% 1.05/1.00 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK9 @ Y0) = (sK7 @ Y0))))) | ~spl0_5),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f397])).
% 1.05/1.00 thf(f397,plain,(
% 1.05/1.00 ($true = ($true => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK9 @ Y0) = (sK7 @ Y0)))))) | ~spl0_5),
% 1.05/1.00 inference(superposition,[status(thm)],[f375,f341])).
% 1.05/1.00 thf(f341,plain,(
% 1.05/1.00 ($true = (sK7 @ sK9)) | ~spl0_5),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f332])).
% 1.05/1.00 thf(f593,plain,(
% 1.05/1.00 ($true = ((sK2 @ sK9 @ sK4) => (sK7 @ sK8))) | (~spl0_5 | ~spl0_12)),
% 1.05/1.00 inference(superposition,[status(thm)],[f330,f578])).
% 1.05/1.00 thf(f330,plain,(
% 1.05/1.00 ( ! [X0 : a] : (($true = ((sK2 @ X0 @ sK4) => (sK2 @ X0 @ sK8)))) ) | ~spl0_12),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f321])).
% 1.05/1.00 thf(f321,plain,(
% 1.05/1.00 ( ! [X0 : a] : (((($true & (sK2 @ X0 @ sK4)) => (sK2 @ X0 @ sK8)) = $true)) ) | ~spl0_12),
% 1.05/1.00 inference(superposition,[status(thm)],[f74,f306])).
% 1.05/1.00 thf(f306,plain,(
% 1.05/1.00 ((sK2 @ sK4 @ sK8) = $true) | ~spl0_12),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f305])).
% 1.05/1.00 thf(f305,definition,(
% 1.05/1.00 spl0_12 <=> ((sK2 @ sK4 @ sK8) = $true)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.05/1.00 thf(f314,plain,(
% 1.05/1.00 spl0_13 | spl0_14 | ~spl0_5),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f300,f128,f312,f309])).
% 1.05/1.00 thf(f300,plain,(
% 1.05/1.00 ((sK7 @ sK8) = $false) | ((sK2 @ sK4 @ sK8) = $false) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f298])).
% 1.05/1.00 thf(f298,plain,(
% 1.05/1.00 ((sK2 @ sK4 @ sK8) != (sK7 @ sK8)) | ~spl0_5),
% 1.05/1.00 inference(negative_extensionality,[status(thm)],[f297])).
% 1.05/1.00 thf(f297,plain,(
% 1.05/1.00 (sK7 != (sK2 @ sK4)) | ~spl0_5),
% 1.05/1.00 inference(equality_proxy_clausification,[status(thm)],[f296])).
% 1.05/1.00 thf(f296,plain,(
% 1.05/1.00 (((sK2 @ sK4) = sK7) = $false) | ~spl0_5),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f295])).
% 1.05/1.00 thf(f295,plain,(
% 1.05/1.00 (($true => ((sK2 @ sK4) = sK7)) = $false) | ~spl0_5),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f272,f294])).
% 1.05/1.00 thf(f307,plain,(
% 1.05/1.00 spl0_11 | spl0_12 | ~spl0_5),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f299,f128,f305,f302])).
% 1.05/1.00 thf(f299,plain,(
% 1.05/1.00 ((sK2 @ sK4 @ sK8) = $true) | ($true = (sK7 @ sK8)) | ~spl0_5),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f298])).
% 1.05/1.00 thf(f267,plain,(
% 1.05/1.00 ~spl0_8 | ~spl0_10),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f266])).
% 1.05/1.00 thf(f266,plain,(
% 1.05/1.00 $false | (~spl0_8 | ~spl0_10)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f265])).
% 1.05/1.00 thf(f265,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_8 | ~spl0_10)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f173,f166])).
% 1.05/1.00 thf(f166,plain,(
% 1.05/1.00 ((sK2 @ sK4 @ sK6) = $false) | ~spl0_8),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.05/1.00 thf(f165,definition,(
% 1.05/1.00 spl0_8 <=> ((sK2 @ sK4 @ sK6) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.05/1.00 thf(f263,plain,(
% 1.05/1.00 ~spl0_6 | ~spl0_8 | ~spl0_9),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f262])).
% 1.05/1.00 thf(f262,plain,(
% 1.05/1.00 $false | (~spl0_6 | ~spl0_8 | ~spl0_9)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f261])).
% 1.05/1.00 thf(f261,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_6 | ~spl0_8 | ~spl0_9)),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f260])).
% 1.05/1.00 thf(f260,plain,(
% 1.05/1.00 ($true = (~ $true)) | (~spl0_6 | ~spl0_8 | ~spl0_9)),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f254,f170])).
% 1.05/1.00 thf(f170,plain,(
% 1.05/1.00 ($true = (sK2 @ sK5 @ sK6)) | ~spl0_9),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.05/1.00 thf(f169,definition,(
% 1.05/1.00 spl0_9 <=> ($true = (sK2 @ sK5 @ sK6))),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.05/1.00 thf(f254,plain,(
% 1.05/1.00 ($true = (~ (sK2 @ sK5 @ sK6))) | (~spl0_6 | ~spl0_8)),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f247])).
% 1.05/1.00 thf(f247,plain,(
% 1.05/1.00 ($true = ((sK2 @ sK5 @ sK6) => $false)) | (~spl0_6 | ~spl0_8)),
% 1.05/1.00 inference(superposition,[status(thm)],[f155,f166])).
% 1.05/1.00 thf(f155,plain,(
% 1.05/1.00 ( ! [X0 : a] : (($true = ((sK2 @ sK5 @ X0) => (sK2 @ sK4 @ X0)))) ) | ~spl0_6),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f150])).
% 1.05/1.00 thf(f150,plain,(
% 1.05/1.00 ( ! [X0 : a] : (($true = (((sK2 @ sK5 @ X0) & $true) => (sK2 @ sK4 @ X0)))) ) | ~spl0_6),
% 1.05/1.00 inference(superposition,[status(thm)],[f74,f143])).
% 1.05/1.00 thf(f143,plain,(
% 1.05/1.00 ($true = (sK2 @ sK4 @ sK5)) | ~spl0_6),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.05/1.00 thf(f141,plain,(
% 1.05/1.00 (((sK2 @ sK4 @ sK5) => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) = (sK2 @ sK4 @ Y0))))) = $false) | ~spl0_6),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f136])).
% 1.05/1.00 thf(f136,plain,(
% 1.05/1.00 (((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1)))))) @ sK5) = $false) | ~spl0_6),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f132])).
% 1.05/1.00 thf(f178,plain,(
% 1.05/1.00 ~spl0_7 | ~spl0_9),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f177])).
% 1.05/1.00 thf(f177,plain,(
% 1.05/1.00 $false | (~spl0_7 | ~spl0_9)),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.05/1.00 thf(f176,plain,(
% 1.05/1.00 ($true = $false) | (~spl0_7 | ~spl0_9)),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f170,f163])).
% 1.05/1.00 thf(f174,plain,(
% 1.05/1.00 spl0_9 | spl0_10 | ~spl0_6),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f159,f131,f172,f169])).
% 1.05/1.00 thf(f159,plain,(
% 1.05/1.00 ($true = (sK2 @ sK5 @ sK6)) | ($true = (sK2 @ sK4 @ sK6)) | ~spl0_6),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.05/1.00 thf(f148,plain,(
% 1.05/1.00 ((sK2 @ sK5 @ sK6) != (sK2 @ sK4 @ sK6)) | ~spl0_6),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.05/1.00 thf(f147,plain,(
% 1.05/1.00 (((sK2 @ sK5 @ sK6) = (sK2 @ sK4 @ sK6)) = $false) | ~spl0_6),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.05/1.00 thf(f146,plain,(
% 1.05/1.00 (((^[Y0 : a]: ((sK2 @ sK5 @ Y0) = (sK2 @ sK4 @ Y0))) @ sK6) = $false) | ~spl0_6),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f145])).
% 1.05/1.00 thf(f145,plain,(
% 1.05/1.00 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) = (sK2 @ sK4 @ Y0)))) = $false) | ~spl0_6),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f144])).
% 1.05/1.00 thf(f144,plain,(
% 1.05/1.00 (($true => (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) = (sK2 @ sK4 @ Y0))))) = $false) | ~spl0_6),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f141,f143])).
% 1.05/1.00 thf(f167,plain,(
% 1.05/1.00 spl0_7 | spl0_8 | ~spl0_6),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f160,f131,f165,f162])).
% 1.05/1.00 thf(f160,plain,(
% 1.05/1.00 ((sK2 @ sK5 @ sK6) = $false) | ((sK2 @ sK4 @ sK6) = $false) | ~spl0_6),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.05/1.00 thf(f133,plain,(
% 1.05/1.00 spl0_5 | spl0_6 | ~spl0_3),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f123,f86,f131,f128])).
% 1.05/1.00 thf(f86,definition,(
% 1.05/1.00 spl0_3 <=> (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))))) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.05/1.00 thf(f123,plain,(
% 1.05/1.00 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) = $false) | ~spl0_3),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.05/1.00 thf(f87,plain,(
% 1.05/1.00 (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))))) = $false) | ~spl0_3),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.05/1.00 thf(f115,plain,(
% 1.05/1.00 ~spl0_4),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f114])).
% 1.05/1.00 thf(f114,plain,(
% 1.05/1.00 $false | ~spl0_4),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.05/1.00 thf(f97,plain,(
% 1.05/1.00 ($true = $false) | ~spl0_4),
% 1.05/1.00 inference(superposition,[status(thm)],[f94,f38])).
% 1.05/1.00 thf(f38,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = (sK2 @ X1 @ X1))) )),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.05/1.00 thf(f37,plain,(
% 1.05/1.00 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (sK2 @ Y0 @ Y0)) @ X1))) )),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f31])).
% 1.05/1.00 thf(f94,plain,(
% 1.05/1.00 ( ! [X1 : a] : (((sK2 @ sK4 @ X1) = $false)) ) | ~spl0_4),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f90])).
% 1.05/1.00 thf(f90,plain,(
% 1.05/1.00 ((?? @ a @ (sK2 @ sK4)) = $false) | ~spl0_4),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.05/1.00 thf(f89,definition,(
% 1.05/1.00 spl0_4 <=> ((?? @ a @ (sK2 @ sK4)) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.05/1.00 thf(f91,plain,(
% 1.05/1.00 spl0_3 | spl0_4 | ~spl0_1),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f84,f23,f89,f86])).
% 1.05/1.00 thf(f23,definition,(
% 1.05/1.00 spl0_1 <=> ((!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1)))))) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.05/1.00 thf(f84,plain,(
% 1.05/1.00 (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))))) = $false) | ((?? @ a @ (sK2 @ sK4)) = $false) | ~spl0_1),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.05/1.00 thf(f63,plain,(
% 1.05/1.00 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))))) & (?? @ a @ (sK2 @ sK4))) = $false) | ~spl0_1),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f62])).
% 1.05/1.00 thf(f62,plain,(
% 1.05/1.00 (((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK2 @ sK4 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => ((sK2 @ sK4) = Y0))))) & $true) & (?? @ a @ (sK2 @ sK4))) = $false) | ~spl0_1),
% 1.05/1.00 inference(superposition,[status(thm)],[f58,f38])).
% 1.05/1.00 thf(f58,plain,(
% 1.05/1.00 ( ! [X1 : a > $o] : ((((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (X1 @ Y1))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((?? @ a @ Y0) & (Y0 @ sK4)) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (X1 = Y0))))) & (X1 @ sK4)) & (?? @ a @ X1)) = $false)) ) | ~spl0_1),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.05/1.00 thf(f57,plain,(
% 1.05/1.00 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((?? @ a @ Y1) & (Y1 @ sK4)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (Y0 = Y1))))) & (Y0 @ sK4)) & (?? @ a @ Y0))) @ X1) = $false)) ) | ~spl0_1),
% 1.05/1.00 inference(pi_clausification,[status(thm)],[f54])).
% 1.05/1.00 thf(f54,plain,(
% 1.05/1.00 ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((?? @ a @ Y1) & (Y1 @ sK4)) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3)))))))) => (Y0 = Y1))))) & (Y0 @ sK4)) & (?? @ a @ Y0)))) = $false) | ~spl0_1),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.05/1.00 thf(f53,plain,(
% 1.05/1.00 (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1))))) @ sK4) = $false) | ~spl0_1),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f24])).
% 1.05/1.00 thf(f24,plain,(
% 1.05/1.00 ((!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1)))))) = $false) | ~spl0_1),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.05/1.00 thf(f50,plain,(
% 1.05/1.00 ~spl0_2),
% 1.05/1.00 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.05/1.00 thf(f49,plain,(
% 1.05/1.00 $false | ~spl0_2),
% 1.05/1.00 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.05/1.00 thf(f48,plain,(
% 1.05/1.00 ($true = $false) | ~spl0_2),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f47])).
% 1.05/1.00 thf(f47,plain,(
% 1.05/1.00 ($true = ($false & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK3 @ Y1))))))))) | ~spl0_2),
% 1.05/1.00 inference(forward_demodulation,[status(thm)],[f40,f39])).
% 1.05/1.00 thf(f39,plain,(
% 1.05/1.00 ((?? @ a @ sK3) = $false) | ~spl0_2),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.05/1.00 thf(f36,plain,(
% 1.05/1.00 ((((?? @ a @ sK3) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK3 @ Y1)))))))) => (?? @ a @ sK3)) = $false) | ~spl0_2),
% 1.05/1.00 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.05/1.00 thf(f35,plain,(
% 1.05/1.00 (((^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0))) @ sK3) = $false) | ~spl0_2),
% 1.05/1.00 inference(sigma_clausification,[status(thm)],[f27])).
% 1.05/1.00 thf(f27,plain,(
% 1.05/1.00 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) = $false) | ~spl0_2),
% 1.05/1.00 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.05/1.00 thf(f26,definition,(
% 1.05/1.00 spl0_2 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) = $false)),
% 1.05/1.00 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.05/1.00 thf(f40,plain,(
% 1.05/1.00 (((?? @ a @ sK3) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) = (sK3 @ Y1)))))))) = $true) | ~spl0_2),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.05/1.00 thf(f28,plain,(
% 1.05/1.00 spl0_1 | spl0_2),
% 1.05/1.00 inference(avatar_split_clause,[status(thm)],[f21,f26,f23])).
% 1.05/1.00 thf(f21,plain,(
% 1.05/1.00 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1)))))) = $false)),
% 1.05/1.00 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.05/1.00 thf(f16,plain,(
% 1.05/1.00 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) & (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1))))))) = $false)),
% 1.05/1.00 inference(boolean_simplification,[status(thm)],[f15])).
% 1.05/1.00 thf(f15,plain,(
% 1.05/1.00 (($true => ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((?? @ a @ Y0) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) = (Y0 @ Y2)))))))) => (?? @ a @ Y0)))) & (!! @ a @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) = (Y1 @ Y3))))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((?? @ a @ Y2) & (Y2 @ Y0)) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) = (Y2 @ Y4)))))))) => (Y1 = Y2))))) & (Y1 @ Y0)) & (?? @ a @ Y1)))))))) = $false)),
% 1.05/1.00 inference(backward_demodulation,[status(thm)],[f12,f14])).
% 1.05/1.00 % SZS output end Proof for DTF2THF_7187
% 1.05/1.00 % (7360)------------------------------
% 1.05/1.00 % (7360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.05/1.00 % (7360)Termination reason: Refutation
% 1.05/1.00
% 1.05/1.00 % (7360)Memory used [KB]: 6140
% 1.05/1.00 % (7360)Time elapsed: 0.050 s
% 1.05/1.00 % (7360)Instructions burned: 137 (million)
% 1.05/1.00 % (7360)------------------------------
% 1.05/1.00 % (7360)------------------------------
% 1.05/1.00 % (7348)Success in time 0.07 s
%------------------------------------------------------------------------------