%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET598^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:31:51 AM UTC 2026
% Result : Theorem 1.72s 1.62s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 215 ( 14 unt; 0 typ; 23 def)
% Number of atoms : 1484 ( 330 equ; 36 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2244 ( 282 ~; 319 |; 117 &;1061 @)
% ( 26 <=>; 255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 33 usr; 30 con; 0-2 aty)
% ( 184 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 301 ( 225 ^; 76 !; 0 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > $o ).
thf(func_def_19,type,
sK3: a > $o ).
thf(func_def_20,type,
sK4: a > $o ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: ( a > $o ) > a ).
thf(func_def_26,type,
sK10: ( a > $o ) > a ).
thf(f2175,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f32,f57,f64,f68,f71,f92,f107,f125,f172,f263,f267,f1612,f1638,f1688,f1697,f1844,f1857,f1882,f1976,f2001,f2136,f2148,f2164,f2165,f2171,f2174]) ).
thf(f2174,plain,
( ~ spl0_32
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[status(thm)],[f2173]) ).
thf(f2173,plain,
( $false
| ~ spl0_32
| ~ spl0_33 ),
inference(trivial_inequality_removal,[status(thm)],[f2172]) ).
thf(f2172,plain,
( ( $true = $false )
| ~ spl0_32
| ~ spl0_33 ),
inference(backward_demodulation,[status(thm)],[f823,f820]) ).
thf(f820,plain,
( ( $false
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl0_32 ),
inference(avatar_component_clause,[status(thm)],[f819]) ).
thf(f819,definition,
( spl0_32
<=> ( $false
= ( sK2 @ ( sK9 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition]) ).
thf(f823,plain,
( ( $true
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[status(thm)],[f822]) ).
thf(f822,definition,
( spl0_33
<=> ( $true
= ( sK2 @ ( sK9 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_33])],[avatar_definition]) ).
thf(f2171,plain,
( spl0_32
| ~ spl0_1
| ~ spl0_37 ),
inference(avatar_split_clause,[status(thm)],[f2170,f1030,f20,f819]) ).
thf(f20,definition,
( spl0_1
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f1030,definition,
( spl0_37
<=> ( ( sK4 @ ( sK9 @ sK2 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_37])],[avatar_definition]) ).
thf(f2170,plain,
( ( $false
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f2169]) ).
thf(f2169,plain,
( ( ( $false
& ( sK3 @ ( sK9 @ sK2 ) ) )
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_37 ),
inference(superposition,[status(thm)],[f2088,f1031]) ).
thf(f1031,plain,
( ( ( sK4 @ ( sK9 @ sK2 ) )
= $false )
| ~ spl0_37 ),
inference(avatar_component_clause,[status(thm)],[f1030]) ).
thf(f2088,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ( sK4 @ X1 )
& ( sK3 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f2087]) ).
thf(f2087,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f2082]) ).
thf(f2082,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f2077]) ).
thf(f2077,plain,
( ( $false
!= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f16,f21]) ).
thf(f21,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f16,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK2 @ Y2 ) ) ) ) ) )
= ( sK2
= ( ^ [Y1: a] :
( ( Y0 @ Y1 )
& ( sK3 @ Y1 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( sK2 @ Y2 ) ) ) ) ) )
= ( sK2
= ( ^ [Y1: a] :
( ( Y0 @ Y1 )
& ( sK3 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( sK2 @ Y3 ) ) ) ) ) )
= ( sK2
= ( ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( sK2 @ Y3 ) ) ) ) ) )
= ( sK2
= ( ^ [Y2: a] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y1 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y1 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y1 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y1 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) )
= ( Y0
= ( ^ [Y3: a] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X0 @ X4 ) )
& ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 ) ) )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X2 @ X6 ) ) )
& ! [X7: a] :
( ( X2 @ X7 )
=> ( X1 @ X7 ) )
& ! [X8: a] :
( ( X2 @ X8 )
=> ( X0 @ X8 ) ) )
<=> ( X2
= ( ^ [X9: a] :
( ( X1 @ X9 )
& ( X0 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a > $o] :
( ( ! [X3: a] :
( ( X4 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X4 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( X4 @ X3 )
=> ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
<=> ( X0
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a > $o] :
( ( ! [X3: a] :
( ( X4 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X4 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( X4 @ X3 )
=> ( X0 @ X3 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
<=> ( X0
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4h05nG9iDq/DTF2THF_20557.p',cBOOL_PROP_57_pme) ).
thf(f2165,plain,
( spl0_37
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f2159,f120,f1030]) ).
thf(f120,definition,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f2159,plain,
( ( ( sK4 @ ( sK9 @ sK2 ) )
= $false )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f2155]) ).
thf(f2155,plain,
( ( $false
= ( ( sK2 @ ( sK9 @ sK2 ) )
=> ( sK4 @ ( sK9 @ sK2 ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f2154]) ).
thf(f2154,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) )
@ ( sK9 @ sK2 ) )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f120]) ).
thf(f2164,plain,
( spl0_33
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f2160,f120,f822]) ).
thf(f2160,plain,
( ( $true
= ( sK2 @ ( sK9 @ sK2 ) ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f2155]) ).
thf(f2148,plain,
( spl0_31
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f2147,f123,f816]) ).
thf(f816,definition,
( spl0_31
<=> ( $false
= ( sK3 @ ( sK10 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f123,definition,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f2147,plain,
( ( $false
= ( sK3 @ ( sK10 @ sK2 ) ) )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f2146]) ).
thf(f2146,plain,
( ( $false
= ( $true
=> ( sK3 @ ( sK10 @ sK2 ) ) ) )
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f2132,f2138]) ).
thf(f2138,plain,
( ( $true
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f2132]) ).
thf(f2132,plain,
( ( $false
= ( ( sK2 @ ( sK10 @ sK2 ) )
=> ( sK3 @ ( sK10 @ sK2 ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f2131]) ).
thf(f2131,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) )
@ ( sK10 @ sK2 ) )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f2136,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f2135]) ).
thf(f2135,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_31 ),
inference(trivial_inequality_removal,[status(thm)],[f2134]) ).
thf(f2134,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2133]) ).
thf(f2133,plain,
( ( ( $false
=> ( sK3 @ ( sK10 @ sK2 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f2132,f2102]) ).
thf(f2102,plain,
( ( ( sK2 @ ( sK10 @ sK2 ) )
= $false )
| ~ spl0_1
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2091]) ).
thf(f2091,plain,
( ( ( ( sK4 @ ( sK10 @ sK2 ) )
& $false )
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ~ spl0_1
| ~ spl0_31 ),
inference(superposition,[status(thm)],[f2088,f817]) ).
thf(f817,plain,
( ( $false
= ( sK3 @ ( sK10 @ sK2 ) ) )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f816]) ).
thf(f2001,plain,
( spl0_41
| spl0_39
| ~ spl0_2
| ~ spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[status(thm)],[f2000,f1610,f55,f23,f1607,f1630]) ).
thf(f1630,definition,
( spl0_41
<=> ! [X0: a] :
( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_41])],[avatar_definition]) ).
thf(f1607,definition,
( spl0_39
<=> ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition]) ).
thf(f23,definition,
( spl0_2
<=> ( $false
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f55,definition,
( spl0_6
<=> ( $true
= ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f1610,definition,
( spl0_40
<=> ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_40])],[avatar_definition]) ).
thf(f2000,plain,
( ! [X0: a] :
( ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false ) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_40 ),
inference(trivial_inequality_removal,[status(thm)],[f1999]) ).
thf(f1999,plain,
( ! [X0: a] :
( ( $true = $false )
| ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_40 ),
inference(forward_demodulation,[status(thm)],[f1947,f1907]) ).
thf(f1907,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f1947,plain,
( ! [X0: a] :
( ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( ( sK4 @ sK5 )
= $false ) )
| ~ spl0_2
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f1946]) ).
thf(f1946,plain,
( ! [X0: a] :
( ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( $true
=> ( sK4 @ sK5 ) )
= $false ) )
| ~ spl0_2
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f1934]) ).
thf(f1934,plain,
( ! [X0: a] :
( ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( ( sK5 = sK5 )
=> ( sK4 @ sK5 ) )
= $false )
| ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false ) )
| ~ spl0_2
| ~ spl0_40 ),
inference(superposition,[status(thm)],[f340,f1611]) ).
thf(f1611,plain,
( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
| ~ spl0_40 ),
inference(avatar_component_clause,[status(thm)],[f1610]) ).
thf(f340,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( X1 @ ( sK9 @ X1 ) )
=> ( sK4 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( sK3 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( X1 @ ( sK10 @ X1 ) )
=> ( sK3 @ ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) )
| ( ( ( X1 @ ( sK9 @ X1 ) )
=> ( sK4 @ ( sK9 @ X1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f327]) ).
thf(f327,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ( X1 @ ( sK9 @ X1 ) )
=> ( sK4 @ ( sK9 @ X1 ) ) )
= $false )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $false ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( ! [X2: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) )
| ( ( ( X1 @ ( sK9 @ X1 ) )
=> ( sK4 @ ( sK9 @ X1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f314]) ).
thf(f314,plain,
( ! [X2: a,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) )
@ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f312]) ).
thf(f312,plain,
( ! [X2: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f310]) ).
thf(f310,plain,
( ! [X2: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f299]) ).
thf(f299,plain,
( ! [X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $false
!= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
!= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f173,f175]) ).
thf(f175,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
!= $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f16,f24]) ).
thf(f24,plain,
( ( $false
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f1976,plain,
( ~ spl0_7
| ~ spl0_41 ),
inference(avatar_contradiction_clause,[status(thm)],[f1975]) ).
thf(f1975,plain,
( $false
| ~ spl0_7
| ~ spl0_41 ),
inference(trivial_inequality_removal,[status(thm)],[f1974]) ).
thf(f1974,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_41 ),
inference(boolean_simplification,[status(thm)],[f1973]) ).
thf(f1973,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_7
| ~ spl0_41 ),
inference(boolean_simplification,[status(thm)],[f1972]) ).
thf(f1972,plain,
( ( $true
= ( sK5 != sK5 ) )
| ~ spl0_7
| ~ spl0_41 ),
inference(boolean_simplification,[status(thm)],[f1956]) ).
thf(f1956,plain,
( ( $true
= ( ( sK5 = sK5 )
=> $false ) )
| ~ spl0_7
| ~ spl0_41 ),
inference(superposition,[status(thm)],[f1631,f60]) ).
thf(f60,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl0_7
<=> ( ( sK2 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1631,plain,
( ! [X0: a] :
( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ~ spl0_41 ),
inference(avatar_component_clause,[status(thm)],[f1630]) ).
thf(f1882,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1881]) ).
thf(f1881,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1880]) ).
thf(f1880,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f1872,f91]) ).
thf(f91,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl0_10
<=> ( ( sK3 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f1872,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f1860]) ).
thf(f1860,plain,
( ( $true
= ( $true
=> ( sK3 @ sK5 ) ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f212,f53]) ).
thf(f53,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl0_5
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f212,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ X1 )
=> ( sK3 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f208]) ).
thf(f208,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f175,f207]) ).
thf(f207,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f1857,plain,
( spl0_9
| spl0_41
| spl0_42
| ~ spl0_2
| ~ spl0_39
| ~ spl0_40 ),
inference(avatar_split_clause,[status(thm)],[f1856,f1610,f1607,f23,f1633,f1630,f87]) ).
thf(f87,definition,
( spl0_9
<=> ( ( sK4 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1633,definition,
( spl0_42
<=> ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_42])],[avatar_definition]) ).
thf(f1856,plain,
( ! [X0: a] :
( ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( sK4 @ sK5 )
= $false ) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f1855]) ).
thf(f1855,plain,
( ! [X0: a] :
( ( ( $true
=> ( sK4 @ sK5 ) )
= $false )
| ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f1854]) ).
thf(f1854,plain,
( ! [X0: a] :
( ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( ( sK5 = sK5 )
=> ( sK4 @ sK5 ) )
= $false ) )
| ~ spl0_2
| ~ spl0_39
| ~ spl0_40 ),
inference(forward_demodulation,[status(thm)],[f1721,f1611]) ).
thf(f1721,plain,
( ! [X0: a] :
( ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false ) )
| ~ spl0_2
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f1709]) ).
thf(f1709,plain,
( ! [X0: a] :
( ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) )
| ( ( ( sK5
= ( sK10 @ ( (=) @ sK5 ) ) )
=> $false )
= $false ) )
| ~ spl0_2
| ~ spl0_39 ),
inference(superposition,[status(thm)],[f339,f1608]) ).
thf(f1608,plain,
( ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ~ spl0_39 ),
inference(avatar_component_clause,[status(thm)],[f1607]) ).
thf(f1844,plain,
( spl0_40
| ~ spl0_43 ),
inference(avatar_split_clause,[status(thm)],[f1831,f1636,f1610]) ).
thf(f1636,definition,
( spl0_43
<=> ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_43])],[avatar_definition]) ).
thf(f1831,plain,
( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
| ~ spl0_43 ),
inference(equality_proxy_clausification,[status(thm)],[f1750]) ).
thf(f1750,plain,
( ( $true
= ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) ) )
| ~ spl0_43 ),
inference(binary_proxy_clausification,[status(thm)],[f1637]) ).
thf(f1637,plain,
( ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false )
| ~ spl0_43 ),
inference(avatar_component_clause,[status(thm)],[f1636]) ).
thf(f1697,plain,
( ~ spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1696]) ).
thf(f1696,plain,
( $false
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1695]) ).
thf(f1695,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f288,f91]) ).
thf(f288,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f1688,plain,
( spl0_10
| ~ spl0_39
| ~ spl0_42 ),
inference(avatar_split_clause,[status(thm)],[f1680,f1633,f1607,f90]) ).
thf(f1680,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl0_39
| ~ spl0_42 ),
inference(backward_demodulation,[status(thm)],[f1608,f1671]) ).
thf(f1671,plain,
( ( sK5
= ( sK10 @ ( (=) @ sK5 ) ) )
| ~ spl0_42 ),
inference(equality_proxy_clausification,[status(thm)],[f1664]) ).
thf(f1664,plain,
( ( $true
= ( sK5
= ( sK10 @ ( (=) @ sK5 ) ) ) )
| ~ spl0_42 ),
inference(not_proxy_clausification,[status(thm)],[f1634]) ).
thf(f1634,plain,
( ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ~ spl0_42 ),
inference(avatar_component_clause,[status(thm)],[f1633]) ).
thf(f1638,plain,
( spl0_41
| spl0_42
| spl0_43
| ~ spl0_2
| ~ spl0_39 ),
inference(avatar_split_clause,[status(thm)],[f1626,f1607,f23,f1636,f1633,f1630]) ).
thf(f1626,plain,
( ! [X0: a] :
( ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false )
| ( ( sK5
!= ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f1614]) ).
thf(f1614,plain,
( ! [X0: a] :
( ( ( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
=> ( sK4 @ ( sK9 @ ( (=) @ sK5 ) ) ) )
= $false )
| ( ( ( sK5
= ( sK10 @ ( (=) @ sK5 ) ) )
=> $false )
= $false )
| ( $true
= ( ( sK5 = X0 )
=> ( sK2 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_39 ),
inference(superposition,[status(thm)],[f339,f1608]) ).
thf(f1612,plain,
( spl0_39
| spl0_40
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f1525,f59,f23,f1610,f1607]) ).
thf(f1525,plain,
( ( sK5
= ( sK9 @ ( (=) @ sK5 ) ) )
| ( ( sK3 @ ( sK10 @ ( (=) @ sK5 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(leibniz_equality_elimination,[status(thm)],[f1410]) ).
thf(f1410,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK9 @ X0 ) ) )
| ( ( sK3 @ ( sK10 @ X0 ) )
= $false )
| ( $false
= ( X0 @ sK5 ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(not_proxy_clausification,[status(thm)],[f726]) ).
thf(f726,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK9 @ X0 ) ) )
| ( ( sK3 @ ( sK10 @ X0 ) )
= $false )
| ( $true
= ( ~ ( X0 @ sK5 ) ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f698]) ).
thf(f698,plain,
( ! [X0: a > $o] :
( ( $true
= ( X0 @ ( sK9 @ X0 ) ) )
| ( ( sK3 @ ( sK10 @ X0 ) )
= $false )
| ( $true
= ( ( X0 @ sK5 )
=> $false ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f387,f60]) ).
thf(f387,plain,
( ! [X2: a,X1: a > $o] :
( ( $true
= ( ( X1 @ X2 )
=> ( sK2 @ X2 ) ) )
| ( $false
= ( sK3 @ ( sK10 @ X1 ) ) )
| ( $true
= ( X1 @ ( sK9 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f340]) ).
thf(f267,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f266]) ).
thf(f266,plain,
( $false
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f265]) ).
thf(f265,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f264]) ).
thf(f264,plain,
( ( $true
= ( $false
& ( sK3 @ sK5 ) ) )
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f56,f88]) ).
thf(f88,plain,
( ( ( sK4 @ sK5 )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f263,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f262]) ).
thf(f262,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f261]) ).
thf(f261,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f246,f88]) ).
thf(f246,plain,
( ( $true
= ( sK4 @ sK5 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f244]) ).
thf(f244,plain,
( ( $true
= ( $true
=> ( sK4 @ sK5 ) ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f236,f53]) ).
thf(f236,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ X1 )
=> ( sK4 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f234]) ).
thf(f234,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f207]) ).
thf(f172,plain,
( ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f171]) ).
thf(f171,plain,
( $false
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f168,f164]) ).
thf(f164,plain,
( ( ( sK4 @ sK7 )
= $false )
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f163,f148]) ).
thf(f148,plain,
( ( ( sK2 @ sK7 )
= $false )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( $true
=> ( sK2 @ sK7 ) )
= $false )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f144,f146]) ).
thf(f146,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( ( sK6 @ sK7 )
=> ( sK2 @ sK7 ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK2 @ Y0 ) )
@ sK7 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK2 @ Y0 ) ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) )
@ sK6 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f105,definition,
( spl0_12
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f163,plain,
( ( ( sK4 @ sK7 )
= ( sK2 @ sK7 ) )
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( sK2 @ sK7 )
= ( ( sK4 @ sK7 )
& $true ) )
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f99,f157]) ).
thf(f157,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true
= ( $true
=> ( sK3 @ sK7 ) ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f154,f146]) ).
thf(f154,plain,
( ! [X1: a] :
( $true
= ( ( sK6 @ X1 )
=> ( sK3 @ X1 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f153]) ).
thf(f153,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK3 @ Y0 ) )
@ X1 ) )
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& $true ) )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f138,f149]) ).
thf(f149,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK4 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f99,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ( sK4 @ X1 )
& ( sK3 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(argument_congruence,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_4
<=> ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f168,plain,
( ( $true
= ( sK4 @ sK7 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $true
= ( $true
=> ( sK4 @ sK7 ) ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f159,f146]) ).
thf(f159,plain,
( ! [X1: a] :
( $true
= ( ( sK6 @ X1 )
=> ( sK4 @ X1 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK6 @ Y0 )
=> ( sK4 @ Y0 ) )
@ X1 ) )
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f149]) ).
thf(f125,plain,
( spl0_13
| spl0_14
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f118,f102,f123,f120]) ).
thf(f102,definition,
( spl0_11
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f118,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
= $false )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f102]) ).
thf(f107,plain,
( spl0_11
| spl0_12
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f100,f20,f105,f102]) ).
thf(f100,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f92,plain,
( spl0_9
| spl0_10
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f85,f62,f90,f87]) ).
thf(f62,definition,
( spl0_8
<=> ( ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f85,plain,
( ( ( sK3 @ sK5 )
= $false )
| ( ( sK4 @ sK5 )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f71,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f53,f60]) ).
thf(f68,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f28,f21]) ).
thf(f28,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_3
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f64,plain,
( spl0_7
| spl0_8
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f50,f23,f62,f59]) ).
thf(f50,plain,
( ( ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) )
= $false )
| ( ( sK2 @ sK5 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( sK2 @ sK5 )
!= ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK2 @ sK5 )
!= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(negative_extensionality,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) )
!= sK2 )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f57,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f49,f23,f55,f52]) ).
thf(f49,plain,
( ( $true
= ( ( sK4 @ sK5 )
& ( sK3 @ sK5 ) ) )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f32,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f30,f27]) ).
thf(f17,plain,
( ( $true
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f23,f20]) ).
thf(f18,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK4 @ Y1 ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( sK2 @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( sK2
= ( ^ [Y0: a] :
( ( sK4 @ Y0 )
& ( sK3 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET598^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:00:12 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : SET598^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.49 % Domain : Set Theory
% 0.27/0.49 % Problem : TPS problem BOOL-PROP-57
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : Trybulec's 57th Boolean property of sets
% 0.27/0.49
% 0.27/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.27/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : tps_0566 [Bro09]
% 0.27/0.49 % : BOOL-PROP-57 [TPS]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.27/0.49 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.27/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.27/0.49 % Number of connectives : 23 ( 0 ~; 0 |; 4 &; 12 @)
% 0.27/0.49 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 13 ( 13 avg)
% 0.27/0.49 % Number of types : 2 ( 1 usr)
% 0.27/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.49 % Number of variables : 10 ( 1 ^; 9 !; 0 ?; 10 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.49 % : Polymorphic definitions expanded.
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(a_type,type,
% 0.27/0.49 a: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(cBOOL_PROP_57_pme,conjecture,
% 0.27/0.49 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.27/0.49 ( ( X
% 0.27/0.49 = ( ^ [Xx: a] :
% 0.27/0.49 ( ( Y @ Xx )
% 0.27/0.49 & ( Z @ Xx ) ) ) )
% 0.27/0.49 <=> ( ! [Xx: a] :
% 0.27/0.49 ( ( X @ Xx )
% 0.27/0.49 => ( Y @ Xx ) )
% 0.27/0.49 & ! [Xx: a] :
% 0.27/0.49 ( ( X @ Xx )
% 0.27/0.49 => ( Z @ Xx ) )
% 0.27/0.49 & ! [V: a > $o] :
% 0.27/0.49 ( ( ! [Xx: a] :
% 0.27/0.49 ( ( V @ Xx )
% 0.27/0.49 => ( Y @ Xx ) )
% 0.27/0.49 & ! [Xx: a] :
% 0.27/0.49 ( ( V @ Xx )
% 0.27/0.49 => ( Z @ Xx ) ) )
% 0.27/0.49 => ! [Xx: a] :
% 0.27/0.49 ( ( V @ Xx )
% 0.27/0.49 => ( X @ Xx ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.65/1.42 ---- Embedded in THF ---
% 1.65/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.42 %%% Generated on Tue Feb 24 12:00:13 EST 2026
% 1.65/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.42 %%% Logic specification used:
% 1.65/1.42 %%% thf(spec, logic, $$dhol).
% 1.65/1.42
% 1.65/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4h05nG9iDq/DTF2DTF20557.p
% See solution above
% 1.65/1.42 ------------------------
% 1.65/1.43 ---- Cleaned THF ---
% 1.65/1.43 thf(a_type,type,
% 1.65/1.43 a: $tType ).
% 1.65/1.43
% 1.65/1.43 thf(cBOOL_PROP_57_pme,conjecture,
% 1.65/1.43 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.65/1.43 ( ( X
% 1.65/1.43 = ( ^ [Xx: a] :
% 1.65/1.43 ( ( Y @ Xx )
% 1.65/1.43 & ( Z @ Xx ) ) ) )
% 1.65/1.43 <=> ( ! [Xx: a] :
% 1.65/1.43 ( ( X @ Xx )
% 1.65/1.43 => ( Y @ Xx ) )
% 1.65/1.43 & ! [Xx: a] :
% 1.65/1.43 ( ( X @ Xx )
% 1.65/1.43 => ( Z @ Xx ) )
% 1.65/1.43 & ! [V: a > $o] :
% 1.65/1.43 ( ( ! [Xx: a] :
% 1.65/1.43 ( ( V @ Xx )
% 1.65/1.43 => ( Y @ Xx ) )
% 1.65/1.43 & ! [Xx: a] :
% 1.65/1.43 ( ( V @ Xx )
% 1.65/1.43 => ( Z @ Xx ) ) )
% 1.65/1.43 => ! [Xx: a] :
% 1.65/1.43 ( ( V @ Xx )
% 1.65/1.43 => ( X @ Xx ) ) ) ) ) ).
% 1.65/1.43 ------------------------
% 1.65/1.45 % (20658)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20557 for (3000ds/2Mi)
% 1.65/1.45 % (20656)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_20557 for (3000ds/4Mi)
% 1.65/1.45 % (20657)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_20557 for (3000ds/27Mi)
% 1.65/1.45 % (20655)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20557 for (3000ds/183Mi)
% 1.65/1.45 % (20659)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_20557 for (3000ds/2Mi)
% 1.65/1.45 % (20660)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_20557 for (3000ds/275Mi)
% 1.65/1.45 % (20661)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20557 for (3000ds/18Mi)
% 1.65/1.45 % (20658)Instruction limit reached!
% 1.65/1.45 % (20658)------------------------------
% 1.65/1.45 % (20658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (20658)Termination reason: Unknown
% 1.65/1.45 % (20658)Termination phase: Property scanning
% 1.65/1.45 % (20659)Instruction limit reached!
% 1.65/1.45 % (20659)------------------------------
% 1.65/1.45 % (20659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (20659)Termination reason: Unknown
% 1.65/1.45 % (20659)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (20659)Memory used [KB]: 5500
% 1.65/1.45 % (20659)Time elapsed: 0.003 s
% 1.65/1.45 % (20659)Instructions burned: 3 (million)
% 1.65/1.45 % (20659)------------------------------
% 1.65/1.45 % (20659)------------------------------
% 1.65/1.45
% 1.65/1.45 % (20658)Memory used [KB]: 1023
% 1.65/1.45 % (20658)Time elapsed: 0.003 s
% 1.65/1.45 % (20658)Instructions burned: 3 (million)
% 1.65/1.45 % (20658)------------------------------
% 1.65/1.45 % (20658)------------------------------
% 1.65/1.45 % (20656)Instruction limit reached!
% 1.65/1.45 % (20656)------------------------------
% 1.65/1.45 % (20656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (20656)Termination reason: Unknown
% 1.65/1.45 % (20656)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (20656)Memory used [KB]: 5500
% 1.65/1.45 % (20656)Time elapsed: 0.004 s
% 1.65/1.45 % (20656)Instructions burned: 4 (million)
% 1.65/1.45 % (20656)------------------------------
% 1.65/1.45 % (20656)------------------------------
% 1.65/1.46 % (20660)Refutation not found, incomplete strategy
% 1.65/1.46 % (20660)------------------------------
% 1.65/1.46 % (20660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (20660)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (20660)Memory used [KB]: 5628
% 1.65/1.46 % (20660)Time elapsed: 0.009 s
% 1.65/1.46 % (20660)Instructions burned: 13 (million)
% 1.65/1.46 % (20660)------------------------------
% 1.65/1.46 % (20660)------------------------------
% 1.65/1.46 % (20661)Instruction limit reached!
% 1.65/1.46 % (20661)------------------------------
% 1.65/1.46 % (20661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (20661)Termination reason: Unknown
% 1.65/1.46 % (20661)Termination phase: Saturation
% 1.65/1.46
% 1.65/1.46 % (20661)Memory used [KB]: 5628
% 1.65/1.46 % (20661)Time elapsed: 0.012 s
% 1.65/1.46 % (20661)Instructions burned: 19 (million)
% 1.65/1.46 % (20661)------------------------------
% 1.65/1.46 % (20661)------------------------------
% 1.65/1.46 % (20657)Refutation not found, incomplete strategy
% 1.65/1.46 % (20657)------------------------------
% 1.65/1.46 % (20657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (20657)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.46
% 1.65/1.46
% 1.65/1.46 % (20657)Memory used [KB]: 5756
% 1.65/1.46 % (20657)Time elapsed: 0.017 s
% 1.65/1.46 % (20657)Instructions burned: 26 (million)
% 1.65/1.46 % (20657)------------------------------
% 1.65/1.46 % (20657)------------------------------
% 1.65/1.47 % (20662)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/3Mi)
% 1.65/1.47 % (20663)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_20557 for (2999ds/37Mi)
% 1.65/1.47 % (20664)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_20557 for (2999ds/15Mi)
% 1.65/1.47 % (20662)Instruction limit reached!
% 1.65/1.47 % (20662)------------------------------
% 1.65/1.47 % (20662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (20662)Termination reason: Unknown
% 1.65/1.47 % (20662)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (20662)Memory used [KB]: 5500
% 1.65/1.47 % (20662)Time elapsed: 0.003 s
% 1.65/1.47 % (20662)Instructions burned: 3 (million)
% 1.65/1.47 % (20662)------------------------------
% 1.65/1.47 % (20662)------------------------------
% 1.65/1.47 % (20665)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_20557 for (2999ds/3Mi)
% 1.65/1.47 % (20665)Instruction limit reached!
% 1.65/1.47 % (20665)------------------------------
% 1.65/1.47 % (20665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (20665)Termination reason: Unknown
% 1.65/1.47 % (20665)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (20665)Memory used [KB]: 5500
% 1.65/1.47 % (20665)Time elapsed: 0.003 s
% 1.65/1.47 % (20665)Instructions burned: 3 (million)
% 1.65/1.47 % (20665)------------------------------
% 1.65/1.47 % (20665)------------------------------
% 1.65/1.47 % (20666)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_20557 for (2999ds/1041Mi)
% 1.65/1.47 % (20664)Instruction limit reached!
% 1.65/1.47 % (20664)------------------------------
% 1.65/1.47 % (20664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (20664)Termination reason: Unknown
% 1.65/1.47 % (20664)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (20664)Memory used [KB]: 5756
% 1.65/1.47 % (20664)Time elapsed: 0.010 s
% 1.65/1.47 % (20664)Instructions burned: 16 (million)
% 1.65/1.47 % (20664)------------------------------
% 1.65/1.47 % (20664)------------------------------
% 1.65/1.48 % (20667)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/7Mi)
% 1.65/1.48 % (20668)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/16Mi)
% 1.65/1.48 % (20667)Instruction limit reached!
% 1.65/1.48 % (20667)------------------------------
% 1.65/1.48 % (20667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (20667)Termination reason: Unknown
% 1.65/1.48 % (20667)Termination phase: Saturation
% 1.65/1.48
% 1.65/1.48 % (20667)Memory used [KB]: 1023
% 1.65/1.48 % (20667)Time elapsed: 0.005 s
% 1.65/1.48 % (20667)Instructions burned: 7 (million)
% 1.65/1.48 % (20667)------------------------------
% 1.65/1.48 % (20667)------------------------------
% 1.65/1.48 % (20663)Instruction limit reached!
% 1.65/1.48 % (20663)------------------------------
% 1.65/1.48 % (20663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (20663)Termination reason: Unknown
% 1.65/1.48 % (20663)Termination phase: Saturation
% 1.65/1.48
% 1.65/1.48 % (20663)Memory used [KB]: 5628
% 1.65/1.48 % (20663)Time elapsed: 0.020 s
% 1.65/1.48 % (20663)Instructions burned: 37 (million)
% 1.65/1.48 % (20663)------------------------------
% 1.65/1.48 % (20663)------------------------------
% 1.65/1.49 % (20669)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_20557 for (2999ds/3Mi)
% 1.65/1.49 % (20670)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_20557 for (2999ds/3Mi)
% 1.65/1.49 % (20669)Instruction limit reached!
% 1.65/1.49 % (20669)------------------------------
% 1.65/1.49 % (20669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (20669)Termination reason: Unknown
% 1.65/1.49 % (20669)Termination phase: Twee Goal Transformation
% 1.65/1.49
% 1.65/1.49 % (20669)Memory used [KB]: 1023
% 1.65/1.49 % (20669)Time elapsed: 0.003 s
% 1.65/1.49 % (20669)Instructions burned: 3 (million)
% 1.65/1.49 % (20669)------------------------------
% 1.65/1.49 % (20669)------------------------------
% 1.65/1.49 % (20668)Instruction limit reached!
% 1.65/1.49 % (20668)------------------------------
% 1.65/1.49 % (20668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (20668)Termination reason: Unknown
% 1.65/1.49 % (20668)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (20668)Memory used [KB]: 5756
% 1.65/1.49 % (20668)Time elapsed: 0.010 s
% 1.65/1.49 % (20668)Instructions burned: 16 (million)
% 1.65/1.49 % (20668)------------------------------
% 1.65/1.49 % (20668)------------------------------
% 1.65/1.49 % (20670)Instruction limit reached!
% 1.65/1.49 % (20670)------------------------------
% 1.65/1.49 % (20670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (20670)Termination reason: Unknown
% 1.65/1.49 % (20670)Termination phase: Property scanning
% 1.65/1.49
% 1.65/1.49 % (20670)Memory used [KB]: 1023
% 1.65/1.49 % (20670)Time elapsed: 0.003 s
% 1.65/1.49 % (20670)Instructions burned: 3 (million)
% 1.65/1.49 % (20670)------------------------------
% 1.65/1.49 % (20670)------------------------------
% 1.72/1.50 % (20671)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/7Mi)
% 1.72/1.50 % (20672)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/3Mi)
% 1.72/1.50 % (20672)Instruction limit reached!
% 1.72/1.50 % (20672)------------------------------
% 1.72/1.50 % (20672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.50 % (20672)Termination reason: Unknown
% 1.72/1.50 % (20672)Termination phase: Saturation
% 1.72/1.50
% 1.72/1.50 % (20672)Memory used [KB]: 5500
% 1.72/1.50 % (20672)Time elapsed: 0.003 s
% 1.72/1.50 % (20672)Instructions burned: 3 (million)
% 1.72/1.50 % (20672)------------------------------
% 1.72/1.50 % (20672)------------------------------
% 1.72/1.50 % (20671)Instruction limit reached!
% 1.72/1.50 % (20671)------------------------------
% 1.72/1.50 % (20671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.50 % (20671)Termination reason: Unknown
% 1.72/1.50 % (20671)Termination phase: Saturation
% 1.72/1.50
% 1.72/1.50 % (20671)Memory used [KB]: 5500
% 1.72/1.50 % (20671)Time elapsed: 0.005 s
% 1.72/1.50 % (20671)Instructions burned: 7 (million)
% 1.72/1.50 % (20671)------------------------------
% 1.72/1.50 % (20671)------------------------------
% 1.72/1.51 % (20673)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/4Mi)
% 1.72/1.51 % (20674)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/18Mi)
% 1.72/1.51 % (20675)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/710Mi)
% 1.72/1.51 % (20673)Instruction limit reached!
% 1.72/1.51 % (20673)------------------------------
% 1.72/1.51 % (20673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.51 % (20673)Termination reason: Unknown
% 1.72/1.51 % (20673)Termination phase: Saturation
% 1.72/1.51
% 1.72/1.51 % (20673)Memory used [KB]: 5500
% 1.72/1.51 % (20673)Time elapsed: 0.004 s
% 1.72/1.51 % (20673)Instructions burned: 5 (million)
% 1.72/1.51 % (20673)------------------------------
% 1.72/1.51 % (20673)------------------------------
% 1.72/1.52 % (20676)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/6Mi)
% 1.72/1.52 % (20674)Instruction limit reached!
% 1.72/1.52 % (20674)------------------------------
% 1.72/1.52 % (20674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.52 % (20674)Termination reason: Unknown
% 1.72/1.52 % (20674)Termination phase: Saturation
% 1.72/1.52
% 1.72/1.52 % (20674)Memory used [KB]: 5628
% 1.72/1.52 % (20674)Time elapsed: 0.012 s
% 1.72/1.52 % (20674)Instructions burned: 18 (million)
% 1.72/1.52 % (20674)------------------------------
% 1.72/1.52 % (20674)------------------------------
% 1.72/1.52 % (20677)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_20557 for (2999ds/902Mi)
% 1.72/1.52 % (20676)Instruction limit reached!
% 1.72/1.52 % (20676)------------------------------
% 1.72/1.52 % (20676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.52 % (20676)Termination reason: Unknown
% 1.72/1.52 % (20676)Termination phase: Saturation
% 1.72/1.52
% 1.72/1.52 % (20676)Memory used [KB]: 5500
% 1.72/1.52 % (20676)Time elapsed: 0.005 s
% 1.72/1.52 % (20676)Instructions burned: 7 (million)
% 1.72/1.52 % (20676)------------------------------
% 1.72/1.52 % (20676)------------------------------
% 1.72/1.53 % (20678)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_20557 for (2999ds/21Mi)
% 1.72/1.53 % (20679)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/5Mi)
% 1.72/1.54 % (20679)Instruction limit reached!
% 1.72/1.54 % (20679)------------------------------
% 1.72/1.54 % (20679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.54 % (20679)Termination reason: Unknown
% 1.72/1.54 % (20679)Termination phase: Saturation
% 1.72/1.54
% 1.72/1.54 % (20679)Memory used [KB]: 5500
% 1.72/1.54 % (20679)Time elapsed: 0.004 s
% 1.72/1.54 % (20679)Instructions burned: 5 (million)
% 1.72/1.54 % (20679)------------------------------
% 1.72/1.54 % (20679)------------------------------
% 1.72/1.54 % (20680)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_20557 for (2999ds/6Mi)
% 1.72/1.54 % (20678)Instruction limit reached!
% 1.72/1.54 % (20678)------------------------------
% 1.72/1.54 % (20678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.54 % (20678)Termination reason: Unknown
% 1.72/1.54 % (20678)Termination phase: Saturation
% 1.72/1.54
% 1.72/1.54 % (20678)Memory used [KB]: 5756
% 1.72/1.54 % (20678)Time elapsed: 0.014 s
% 1.72/1.54 % (20678)Instructions burned: 22 (million)
% 1.72/1.54 % (20678)------------------------------
% 1.72/1.54 % (20678)------------------------------
% 1.72/1.54 % (20680)Instruction limit reached!
% 1.72/1.54 % (20680)------------------------------
% 1.72/1.54 % (20680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.54 % (20680)Termination reason: Unknown
% 1.72/1.54 % (20680)Termination phase: Saturation
% 1.72/1.54
% 1.72/1.54 % (20680)Memory used [KB]: 5500
% 1.72/1.54 % (20680)Time elapsed: 0.004 s
% 1.72/1.54 % (20680)Instructions burned: 6 (million)
% 1.72/1.54 % (20680)------------------------------
% 1.72/1.54 % (20680)------------------------------
% 1.72/1.54 % (20655)Instruction limit reached!
% 1.72/1.54 % (20655)------------------------------
% 1.72/1.54 % (20655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.54 % (20655)Termination reason: Unknown
% 1.72/1.54 % (20655)Termination phase: Saturation
% 1.72/1.54
% 1.72/1.54 % (20655)Memory used [KB]: 6780
% 1.72/1.54 % (20655)Time elapsed: 0.094 s
% 1.72/1.54 % (20655)Instructions burned: 185 (million)
% 1.72/1.54 % (20655)------------------------------
% 1.72/1.54 % (20655)------------------------------
% 1.72/1.55 % (20681)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/377Mi)
% 1.72/1.55 % (20682)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/779Mi)
% 1.72/1.56 % (20683)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/19Mi)
% 1.72/1.56 % (20684)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20557 for (2999ds/879Mi)
% 1.72/1.57 % (20683)Instruction limit reached!
% 1.72/1.57 % (20683)------------------------------
% 1.72/1.57 % (20683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.57 % (20683)Termination reason: Unknown
% 1.72/1.57 % (20683)Termination phase: Saturation
% 1.72/1.57
% 1.72/1.57 % (20683)Memory used [KB]: 5500
% 1.72/1.57 % (20683)Time elapsed: 0.011 s
% 1.72/1.57 % (20683)Instructions burned: 19 (million)
% 1.72/1.57 % (20683)------------------------------
% 1.72/1.57 % (20683)------------------------------
% 1.72/1.58 % (20685)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20557 for (2998ds/17Mi)
% 1.72/1.59 % (20685)Instruction limit reached!
% 1.72/1.59 % (20685)------------------------------
% 1.72/1.59 % (20685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.59 % (20685)Termination reason: Unknown
% 1.72/1.59 % (20685)Termination phase: Saturation
% 1.72/1.59
% 1.72/1.59 % (20685)Memory used [KB]: 5756
% 1.72/1.59 % (20685)Time elapsed: 0.012 s
% 1.72/1.59 % (20685)Instructions burned: 18 (million)
% 1.72/1.59 % (20685)------------------------------
% 1.72/1.59 % (20685)------------------------------
% 1.72/1.61 % (20686)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20557 for (2998ds/3Mi)
% 1.72/1.61 % (20686)Instruction limit reached!
% 1.72/1.61 % (20686)------------------------------
% 1.72/1.61 % (20686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.61 % (20686)Termination reason: Unknown
% 1.72/1.61 % (20686)Termination phase: Property scanning
% 1.72/1.61
% 1.72/1.61 % (20686)Memory used [KB]: 1023
% 1.72/1.61 % (20686)Time elapsed: 0.003 s
% 1.72/1.61 % (20686)Instructions burned: 3 (million)
% 1.72/1.61 % (20686)------------------------------
% 1.72/1.61 % (20686)------------------------------
% 1.72/1.61 % (20666)First to succeed.
% 1.72/1.62 % (20666)Refutation found. Thanks to Tanya!
% 1.72/1.62 % SZS status Theorem for DTF2THF_20557
% 1.72/1.62 % SZS output start Proof for DTF2THF_20557
% 1.72/1.62 thf(type_def_5, type, a: $tType).
% 1.72/1.62 thf(func_def_0, type, a: $tType).
% 1.72/1.62 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.72/1.62 thf(func_def_18, type, sK2: a > $o).
% 1.72/1.62 thf(func_def_19, type, sK3: a > $o).
% 1.72/1.62 thf(func_def_20, type, sK4: a > $o).
% 1.72/1.62 thf(func_def_21, type, sK5: a).
% 1.72/1.62 thf(func_def_22, type, sK6: a > $o).
% 1.72/1.62 thf(func_def_23, type, sK7: a).
% 1.72/1.62 thf(func_def_24, type, sK8: a).
% 1.72/1.62 thf(func_def_25, type, sK9: (a > $o) > a).
% 1.72/1.62 thf(func_def_26, type, sK10: (a > $o) > a).
% 1.72/1.62 thf(f2175,plain,(
% 1.72/1.62 $false),
% 1.72/1.62 inference(avatar_sat_refutation,[status(thm)],[f25,f32,f57,f64,f68,f71,f92,f107,f125,f172,f263,f267,f1612,f1638,f1688,f1697,f1844,f1857,f1882,f1976,f2001,f2136,f2148,f2164,f2165,f2171,f2174])).
% 1.72/1.62 thf(f2174,plain,(
% 1.72/1.62 ~spl0_32 | ~spl0_33),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f2173])).
% 1.72/1.62 thf(f2173,plain,(
% 1.72/1.62 $false | (~spl0_32 | ~spl0_33)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f2172])).
% 1.72/1.62 thf(f2172,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_32 | ~spl0_33)),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f823,f820])).
% 1.72/1.62 thf(f820,plain,(
% 1.72/1.62 ($false = (sK2 @ (sK9 @ sK2))) | ~spl0_32),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f819])).
% 1.72/1.62 thf(f819,definition,(
% 1.72/1.62 spl0_32 <=> ($false = (sK2 @ (sK9 @ sK2)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition])).
% 1.72/1.62 thf(f823,plain,(
% 1.72/1.62 ($true = (sK2 @ (sK9 @ sK2))) | ~spl0_33),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f822])).
% 1.72/1.62 thf(f822,definition,(
% 1.72/1.62 spl0_33 <=> ($true = (sK2 @ (sK9 @ sK2)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_33])],[avatar_definition])).
% 1.72/1.62 thf(f2171,plain,(
% 1.72/1.62 spl0_32 | ~spl0_1 | ~spl0_37),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f2170,f1030,f20,f819])).
% 1.72/1.62 thf(f20,definition,(
% 1.72/1.62 spl0_1 <=> ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.72/1.62 thf(f1030,definition,(
% 1.72/1.62 spl0_37 <=> ((sK4 @ (sK9 @ sK2)) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_37])],[avatar_definition])).
% 1.72/1.62 thf(f2170,plain,(
% 1.72/1.62 ($false = (sK2 @ (sK9 @ sK2))) | (~spl0_1 | ~spl0_37)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f2169])).
% 1.72/1.62 thf(f2169,plain,(
% 1.72/1.62 (($false & (sK3 @ (sK9 @ sK2))) = (sK2 @ (sK9 @ sK2))) | (~spl0_1 | ~spl0_37)),
% 1.72/1.62 inference(superposition,[status(thm)],[f2088,f1031])).
% 1.72/1.62 thf(f1031,plain,(
% 1.72/1.62 ((sK4 @ (sK9 @ sK2)) = $false) | ~spl0_37),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1030])).
% 1.72/1.62 thf(f2088,plain,(
% 1.72/1.62 ( ! [X1 : a] : (((sK2 @ X1) = ((sK4 @ X1) & (sK3 @ X1)))) ) | ~spl0_1),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f2087])).
% 1.72/1.62 thf(f2087,plain,(
% 1.72/1.62 ( ! [X1 : a] : (((sK2 @ X1) = ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) @ X1))) ) | ~spl0_1),
% 1.72/1.62 inference(argument_congruence,[status(thm)],[f2082])).
% 1.72/1.62 thf(f2082,plain,(
% 1.72/1.62 ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) = sK2) | ~spl0_1),
% 1.72/1.62 inference(equality_proxy_clausification,[status(thm)],[f2077])).
% 1.72/1.62 thf(f2077,plain,(
% 1.72/1.62 ($false != (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))))) | ~spl0_1),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f16,f21])).
% 1.72/1.62 thf(f21,plain,(
% 1.72/1.62 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) = $false) | ~spl0_1),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.72/1.62 thf(f16,plain,(
% 1.72/1.62 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) != (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0)))))),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.72/1.62 thf(f15,plain,(
% 1.72/1.62 ($false = ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))))))),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.72/1.62 thf(f14,plain,(
% 1.72/1.62 (((^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (sK3 @ Y1))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK3 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2))))) => (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK2 @ Y2)))))))) = (sK2 = (^[Y1 : a]: ((Y0 @ Y1) & (sK3 @ Y1)))))) @ sK4) = $false)),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f13])).
% 1.72/1.62 thf(f13,plain,(
% 1.72/1.62 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((((!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (sK3 @ Y1))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK3 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2))))) => (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (sK2 @ Y2)))))))) = (sK2 = (^[Y1 : a]: ((Y0 @ Y1) & (sK3 @ Y1))))))) = $false)),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.72/1.62 thf(f12,plain,(
% 1.72/1.62 (((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y0 @ Y2))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y1 @ Y3))))) => (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (sK2 @ Y3)))))))) = (sK2 = (^[Y2 : a]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) @ sK3) = $false)),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f11])).
% 1.72/1.62 thf(f11,plain,(
% 1.72/1.62 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y0 @ Y2))))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y0 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y1 @ Y3))))) => (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (sK2 @ Y3)))))))) = (sK2 = (^[Y2 : a]: ((Y1 @ Y2) & (Y0 @ Y2))))))))))),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.72/1.62 thf(f10,plain,(
% 1.72/1.62 (((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y1 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y2 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y0 @ Y4)))))))) = (Y0 = (^[Y3 : a]: ((Y2 @ Y3) & (Y1 @ Y3)))))))))) @ sK2) = $false)),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f7])).
% 1.72/1.62 thf(f7,plain,(
% 1.72/1.62 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y1 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y2 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y0 @ Y4)))))))) = (Y0 = (^[Y3 : a]: ((Y2 @ Y3) & (Y1 @ Y3))))))))))) = $false)),
% 1.72/1.62 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.72/1.62 thf(f6,plain,(
% 1.72/1.62 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y1 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y2 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y0 @ Y4)))))))) = (Y0 = (^[Y3 : a]: ((Y2 @ Y3) & (Y1 @ Y3)))))))))))))),
% 1.72/1.62 inference(cnf_transformation,[status(thm)],[f5])).
% 1.72/1.62 thf(f5,plain,(
% 1.72/1.62 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y1 @ Y4)))) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y2 @ Y4))))) => (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y0 @ Y4)))))))) = (Y0 = (^[Y3 : a]: ((Y2 @ Y3) & (Y1 @ Y3)))))))))))))),
% 1.72/1.62 inference(fool_elimination,[status(thm)],[f4])).
% 1.72/1.62 thf(f4,plain,(
% 1.72/1.62 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a > $o] : ((! [X4 : a] : ((X3 @ X4) => (X0 @ X4)) & ! [X5 : a] : ((X3 @ X5) => (X1 @ X5))) => ! [X6 : a] : ((X3 @ X6) => (X2 @ X6))) & ! [X7 : a] : ((X2 @ X7) => (X1 @ X7)) & ! [X8 : a] : ((X2 @ X8) => (X0 @ X8))) <=> (X2 = (^[X9 : a] : ((X1 @ X9) & (X0 @ X9)))))),
% 1.72/1.62 inference(rectify,[status(thm)],[f2])).
% 1.72/1.62 thf(f2,negated_conjecture,(
% 1.72/1.62 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X4 : a > $o] : ((! [X3 : a] : ((X4 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X4 @ X3) => (X1 @ X3))) => ! [X3 : a] : ((X4 @ X3) => (X0 @ X3))) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) <=> (X0 = (^[X3 : a] : ((X1 @ X3) & (X2 @ X3)))))),
% 1.72/1.62 inference(negated_conjecture,[status(cth)],[f1])).
% 1.72/1.62 thf(f1,conjecture,(
% 1.72/1.62 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X4 : a > $o] : ((! [X3 : a] : ((X4 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X4 @ X3) => (X1 @ X3))) => ! [X3 : a] : ((X4 @ X3) => (X0 @ X3))) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) <=> (X0 = (^[X3 : a] : ((X1 @ X3) & (X2 @ X3)))))),
% 1.72/1.62 file('/export/starexec/sandbox/tmp/tmp.4h05nG9iDq/DTF2THF_20557.p',cBOOL_PROP_57_pme)).
% 1.72/1.62 thf(f2165,plain,(
% 1.72/1.62 spl0_37 | ~spl0_13),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f2159,f120,f1030])).
% 1.72/1.62 thf(f120,definition,(
% 1.72/1.62 spl0_13 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.72/1.62 thf(f2159,plain,(
% 1.72/1.62 ((sK4 @ (sK9 @ sK2)) = $false) | ~spl0_13),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f2155])).
% 1.72/1.62 thf(f2155,plain,(
% 1.72/1.62 ($false = ((sK2 @ (sK9 @ sK2)) => (sK4 @ (sK9 @ sK2)))) | ~spl0_13),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f2154])).
% 1.72/1.62 thf(f2154,plain,(
% 1.72/1.62 (((^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))) @ (sK9 @ sK2)) = $false) | ~spl0_13),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f121])).
% 1.72/1.62 thf(f121,plain,(
% 1.72/1.62 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) = $false) | ~spl0_13),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f120])).
% 1.72/1.62 thf(f2164,plain,(
% 1.72/1.62 spl0_33 | ~spl0_13),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f2160,f120,f822])).
% 1.72/1.62 thf(f2160,plain,(
% 1.72/1.62 ($true = (sK2 @ (sK9 @ sK2))) | ~spl0_13),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f2155])).
% 1.72/1.62 thf(f2148,plain,(
% 1.72/1.62 spl0_31 | ~spl0_14),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f2147,f123,f816])).
% 1.72/1.62 thf(f816,definition,(
% 1.72/1.62 spl0_31 <=> ($false = (sK3 @ (sK10 @ sK2)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 1.72/1.62 thf(f123,definition,(
% 1.72/1.62 spl0_14 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0)))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.72/1.62 thf(f2147,plain,(
% 1.72/1.62 ($false = (sK3 @ (sK10 @ sK2))) | ~spl0_14),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f2146])).
% 1.72/1.62 thf(f2146,plain,(
% 1.72/1.62 ($false = ($true => (sK3 @ (sK10 @ sK2)))) | ~spl0_14),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f2132,f2138])).
% 1.72/1.62 thf(f2138,plain,(
% 1.72/1.62 ($true = (sK2 @ (sK10 @ sK2))) | ~spl0_14),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f2132])).
% 1.72/1.62 thf(f2132,plain,(
% 1.72/1.62 ($false = ((sK2 @ (sK10 @ sK2)) => (sK3 @ (sK10 @ sK2)))) | ~spl0_14),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f2131])).
% 1.72/1.62 thf(f2131,plain,(
% 1.72/1.62 (((^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))) @ (sK10 @ sK2)) = $false) | ~spl0_14),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f124])).
% 1.72/1.62 thf(f124,plain,(
% 1.72/1.62 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0)))) = $false) | ~spl0_14),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.72/1.62 thf(f2136,plain,(
% 1.72/1.62 ~spl0_1 | ~spl0_14 | ~spl0_31),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f2135])).
% 1.72/1.62 thf(f2135,plain,(
% 1.72/1.62 $false | (~spl0_1 | ~spl0_14 | ~spl0_31)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f2134])).
% 1.72/1.62 thf(f2134,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_1 | ~spl0_14 | ~spl0_31)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f2133])).
% 1.72/1.62 thf(f2133,plain,(
% 1.72/1.62 (($false => (sK3 @ (sK10 @ sK2))) = $false) | (~spl0_1 | ~spl0_14 | ~spl0_31)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f2132,f2102])).
% 1.72/1.62 thf(f2102,plain,(
% 1.72/1.62 ((sK2 @ (sK10 @ sK2)) = $false) | (~spl0_1 | ~spl0_31)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f2091])).
% 1.72/1.62 thf(f2091,plain,(
% 1.72/1.62 (((sK4 @ (sK10 @ sK2)) & $false) = (sK2 @ (sK10 @ sK2))) | (~spl0_1 | ~spl0_31)),
% 1.72/1.62 inference(superposition,[status(thm)],[f2088,f817])).
% 1.72/1.62 thf(f817,plain,(
% 1.72/1.62 ($false = (sK3 @ (sK10 @ sK2))) | ~spl0_31),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f816])).
% 1.72/1.62 thf(f2001,plain,(
% 1.72/1.62 spl0_41 | spl0_39 | ~spl0_2 | ~spl0_6 | ~spl0_40),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f2000,f1610,f55,f23,f1607,f1630])).
% 1.72/1.62 thf(f1630,definition,(
% 1.72/1.62 spl0_41 <=> ! [X0 : a] : ($true = ((sK5 = X0) => (sK2 @ X0)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_41])],[avatar_definition])).
% 1.72/1.62 thf(f1607,definition,(
% 1.72/1.62 spl0_39 <=> ((sK3 @ (sK10 @ (= @ sK5))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition])).
% 1.72/1.62 thf(f23,definition,(
% 1.72/1.62 spl0_2 <=> ($false = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0)))))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.72/1.62 thf(f55,definition,(
% 1.72/1.62 spl0_6 <=> ($true = ((sK4 @ sK5) & (sK3 @ sK5)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.72/1.62 thf(f1610,definition,(
% 1.72/1.62 spl0_40 <=> (sK5 = (sK9 @ (= @ sK5)))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_40])],[avatar_definition])).
% 1.72/1.62 thf(f2000,plain,(
% 1.72/1.62 ( ! [X0 : a] : (($true = ((sK5 = X0) => (sK2 @ X0))) | ((sK3 @ (sK10 @ (= @ sK5))) = $false)) ) | (~spl0_2 | ~spl0_6 | ~spl0_40)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f1999])).
% 1.72/1.62 thf(f1999,plain,(
% 1.72/1.62 ( ! [X0 : a] : (($true = $false) | ((sK3 @ (sK10 @ (= @ sK5))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0)))) ) | (~spl0_2 | ~spl0_6 | ~spl0_40)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f1947,f1907])).
% 1.72/1.62 thf(f1907,plain,(
% 1.72/1.62 ($true = (sK4 @ sK5)) | ~spl0_6),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.72/1.62 thf(f56,plain,(
% 1.72/1.62 ($true = ((sK4 @ sK5) & (sK3 @ sK5))) | ~spl0_6),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.72/1.62 thf(f1947,plain,(
% 1.72/1.62 ( ! [X0 : a] : (($true = ((sK5 = X0) => (sK2 @ X0))) | ((sK3 @ (sK10 @ (= @ sK5))) = $false) | ((sK4 @ sK5) = $false)) ) | (~spl0_2 | ~spl0_40)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1946])).
% 1.72/1.62 thf(f1946,plain,(
% 1.72/1.62 ( ! [X0 : a] : (((sK3 @ (sK10 @ (= @ sK5))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0))) | (($true => (sK4 @ sK5)) = $false)) ) | (~spl0_2 | ~spl0_40)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1934])).
% 1.72/1.62 thf(f1934,plain,(
% 1.72/1.62 ( ! [X0 : a] : (($true = ((sK5 = X0) => (sK2 @ X0))) | (((sK5 = sK5) => (sK4 @ sK5)) = $false) | ((sK3 @ (sK10 @ (= @ sK5))) = $false)) ) | (~spl0_2 | ~spl0_40)),
% 1.72/1.62 inference(superposition,[status(thm)],[f340,f1611])).
% 1.72/1.62 thf(f1611,plain,(
% 1.72/1.62 (sK5 = (sK9 @ (= @ sK5))) | ~spl0_40),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1610])).
% 1.72/1.62 thf(f340,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : ((((X1 @ (sK9 @ X1)) => (sK4 @ (sK9 @ X1))) = $false) | ($false = (sK3 @ (sK10 @ X1))) | ($true = ((X1 @ X2) => (sK2 @ X2)))) ) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f339])).
% 1.72/1.62 thf(f339,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : ((((X1 @ (sK10 @ X1)) => (sK3 @ (sK10 @ X1))) = $false) | ($true = ((X1 @ X2) => (sK2 @ X2))) | (((X1 @ (sK9 @ X1)) => (sK4 @ (sK9 @ X1))) = $false)) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f327])).
% 1.72/1.62 thf(f327,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : ((((X1 @ (sK9 @ X1)) => (sK4 @ (sK9 @ X1))) = $false) | ($true = ((X1 @ X2) => (sK2 @ X2))) | (((^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0))) @ (sK10 @ X1)) = $false)) ) | ~spl0_2),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f320])).
% 1.72/1.62 thf(f320,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0))))) | ($true = ((X1 @ X2) => (sK2 @ X2))) | (((X1 @ (sK9 @ X1)) => (sK4 @ (sK9 @ X1))) = $false)) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f314])).
% 1.72/1.62 thf(f314,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : ((((^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0))) @ (sK9 @ X1)) = $false) | ($true = ((X1 @ X2) => (sK2 @ X2))) | ($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0)))))) ) | ~spl0_2),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f312])).
% 1.72/1.62 thf(f312,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0))))) | ($true = ((X1 @ X2) => (sK2 @ X2)))) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f310])).
% 1.72/1.62 thf(f310,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0))))) | ($true = ((^[Y0 : a]: ((X1 @ Y0) => (sK2 @ Y0))) @ X2)) | ($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0)))))) ) | ~spl0_2),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f299])).
% 1.72/1.62 thf(f299,plain,(
% 1.72/1.62 ( ! [X1 : a > $o] : (($true = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0)))))) ) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f185])).
% 1.72/1.62 thf(f185,plain,(
% 1.72/1.62 ( ! [X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0))))) = $false) | ($true = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ Y0)))))) ) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f182])).
% 1.72/1.62 thf(f182,plain,(
% 1.72/1.62 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK4 @ Y0))))) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ Y0))))))) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f181])).
% 1.72/1.62 thf(f181,plain,(
% 1.72/1.62 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))) @ X1))) ) | ~spl0_2),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f178])).
% 1.72/1.62 thf(f178,plain,(
% 1.72/1.62 ($false != (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) | ~spl0_2),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f176])).
% 1.72/1.62 thf(f176,plain,(
% 1.72/1.62 ($false != ($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1))))))))) | ~spl0_2),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f173,f175])).
% 1.72/1.62 thf(f175,plain,(
% 1.72/1.62 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) = $true) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.72/1.62 thf(f173,plain,(
% 1.72/1.62 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) != $false) | ~spl0_2),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f16,f24])).
% 1.72/1.62 thf(f24,plain,(
% 1.72/1.62 ($false = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))))) | ~spl0_2),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.72/1.62 thf(f1976,plain,(
% 1.72/1.62 ~spl0_7 | ~spl0_41),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f1975])).
% 1.72/1.62 thf(f1975,plain,(
% 1.72/1.62 $false | (~spl0_7 | ~spl0_41)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f1974])).
% 1.72/1.62 thf(f1974,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_7 | ~spl0_41)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1973])).
% 1.72/1.62 thf(f1973,plain,(
% 1.72/1.62 ($true = (~ $true)) | (~spl0_7 | ~spl0_41)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1972])).
% 1.72/1.62 thf(f1972,plain,(
% 1.72/1.62 ($true = (~ (sK5 = sK5))) | (~spl0_7 | ~spl0_41)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1956])).
% 1.72/1.62 thf(f1956,plain,(
% 1.72/1.62 ($true = ((sK5 = sK5) => $false)) | (~spl0_7 | ~spl0_41)),
% 1.72/1.62 inference(superposition,[status(thm)],[f1631,f60])).
% 1.72/1.62 thf(f60,plain,(
% 1.72/1.62 ((sK2 @ sK5) = $false) | ~spl0_7),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.72/1.62 thf(f59,definition,(
% 1.72/1.62 spl0_7 <=> ((sK2 @ sK5) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.72/1.62 thf(f1631,plain,(
% 1.72/1.62 ( ! [X0 : a] : (($true = ((sK5 = X0) => (sK2 @ X0)))) ) | ~spl0_41),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1630])).
% 1.72/1.62 thf(f1882,plain,(
% 1.72/1.62 ~spl0_2 | ~spl0_5 | ~spl0_10),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f1881])).
% 1.72/1.62 thf(f1881,plain,(
% 1.72/1.62 $false | (~spl0_2 | ~spl0_5 | ~spl0_10)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f1880])).
% 1.72/1.62 thf(f1880,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_10)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f1872,f91])).
% 1.72/1.62 thf(f91,plain,(
% 1.72/1.62 ((sK3 @ sK5) = $false) | ~spl0_10),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.72/1.62 thf(f90,definition,(
% 1.72/1.62 spl0_10 <=> ((sK3 @ sK5) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.72/1.62 thf(f1872,plain,(
% 1.72/1.62 ($true = (sK3 @ sK5)) | (~spl0_2 | ~spl0_5)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1860])).
% 1.72/1.62 thf(f1860,plain,(
% 1.72/1.62 ($true = ($true => (sK3 @ sK5))) | (~spl0_2 | ~spl0_5)),
% 1.72/1.62 inference(superposition,[status(thm)],[f212,f53])).
% 1.72/1.62 thf(f53,plain,(
% 1.72/1.62 ($true = (sK2 @ sK5)) | ~spl0_5),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.72/1.62 thf(f52,definition,(
% 1.72/1.62 spl0_5 <=> ($true = (sK2 @ sK5))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.72/1.62 thf(f212,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((sK2 @ X1) => (sK3 @ X1)))) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f210])).
% 1.72/1.62 thf(f210,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))) @ X1))) ) | ~spl0_2),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f209])).
% 1.72/1.62 thf(f209,plain,(
% 1.72/1.62 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) | ~spl0_2),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f208])).
% 1.72/1.62 thf(f208,plain,(
% 1.72/1.62 ($true = ($true & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0)))))) | ~spl0_2),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f175,f207])).
% 1.72/1.62 thf(f207,plain,(
% 1.72/1.62 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))))) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.72/1.62 thf(f1857,plain,(
% 1.72/1.62 spl0_9 | spl0_41 | spl0_42 | ~spl0_2 | ~spl0_39 | ~spl0_40),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f1856,f1610,f1607,f23,f1633,f1630,f87])).
% 1.72/1.62 thf(f87,definition,(
% 1.72/1.62 spl0_9 <=> ((sK4 @ sK5) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.72/1.62 thf(f1633,definition,(
% 1.72/1.62 spl0_42 <=> ((~ (sK5 = (sK10 @ (= @ sK5)))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_42])],[avatar_definition])).
% 1.72/1.62 thf(f1856,plain,(
% 1.72/1.62 ( ! [X0 : a] : (((~ (sK5 = (sK10 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0))) | ((sK4 @ sK5) = $false)) ) | (~spl0_2 | ~spl0_39 | ~spl0_40)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1855])).
% 1.72/1.62 thf(f1855,plain,(
% 1.72/1.62 ( ! [X0 : a] : ((($true => (sK4 @ sK5)) = $false) | ((~ (sK5 = (sK10 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0)))) ) | (~spl0_2 | ~spl0_39 | ~spl0_40)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1854])).
% 1.72/1.62 thf(f1854,plain,(
% 1.72/1.62 ( ! [X0 : a] : (((~ (sK5 = (sK10 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0))) | (((sK5 = sK5) => (sK4 @ sK5)) = $false)) ) | (~spl0_2 | ~spl0_39 | ~spl0_40)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f1721,f1611])).
% 1.72/1.62 thf(f1721,plain,(
% 1.72/1.62 ( ! [X0 : a] : ((((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0))) | ((~ (sK5 = (sK10 @ (= @ sK5)))) = $false)) ) | (~spl0_2 | ~spl0_39)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1709])).
% 1.72/1.62 thf(f1709,plain,(
% 1.72/1.62 ( ! [X0 : a] : ((((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0))) | (((sK5 = (sK10 @ (= @ sK5))) => $false) = $false)) ) | (~spl0_2 | ~spl0_39)),
% 1.72/1.62 inference(superposition,[status(thm)],[f339,f1608])).
% 1.72/1.62 thf(f1608,plain,(
% 1.72/1.62 ((sK3 @ (sK10 @ (= @ sK5))) = $false) | ~spl0_39),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1607])).
% 1.72/1.62 thf(f1844,plain,(
% 1.72/1.62 spl0_40 | ~spl0_43),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f1831,f1636,f1610])).
% 1.72/1.62 thf(f1636,definition,(
% 1.72/1.62 spl0_43 <=> (((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_43])],[avatar_definition])).
% 1.72/1.62 thf(f1831,plain,(
% 1.72/1.62 (sK5 = (sK9 @ (= @ sK5))) | ~spl0_43),
% 1.72/1.62 inference(equality_proxy_clausification,[status(thm)],[f1750])).
% 1.72/1.62 thf(f1750,plain,(
% 1.72/1.62 ($true = (sK5 = (sK9 @ (= @ sK5)))) | ~spl0_43),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f1637])).
% 1.72/1.62 thf(f1637,plain,(
% 1.72/1.62 (((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false) | ~spl0_43),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1636])).
% 1.72/1.62 thf(f1697,plain,(
% 1.72/1.62 ~spl0_6 | ~spl0_10),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f1696])).
% 1.72/1.62 thf(f1696,plain,(
% 1.72/1.62 $false | (~spl0_6 | ~spl0_10)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f1695])).
% 1.72/1.62 thf(f1695,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_6 | ~spl0_10)),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f288,f91])).
% 1.72/1.62 thf(f288,plain,(
% 1.72/1.62 ($true = (sK3 @ sK5)) | ~spl0_6),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.72/1.62 thf(f1688,plain,(
% 1.72/1.62 spl0_10 | ~spl0_39 | ~spl0_42),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f1680,f1633,f1607,f90])).
% 1.72/1.62 thf(f1680,plain,(
% 1.72/1.62 ((sK3 @ sK5) = $false) | (~spl0_39 | ~spl0_42)),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f1608,f1671])).
% 1.72/1.62 thf(f1671,plain,(
% 1.72/1.62 (sK5 = (sK10 @ (= @ sK5))) | ~spl0_42),
% 1.72/1.62 inference(equality_proxy_clausification,[status(thm)],[f1664])).
% 1.72/1.62 thf(f1664,plain,(
% 1.72/1.62 ($true = (sK5 = (sK10 @ (= @ sK5)))) | ~spl0_42),
% 1.72/1.62 inference(not_proxy_clausification,[status(thm)],[f1634])).
% 1.72/1.62 thf(f1634,plain,(
% 1.72/1.62 ((~ (sK5 = (sK10 @ (= @ sK5)))) = $false) | ~spl0_42),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f1633])).
% 1.72/1.62 thf(f1638,plain,(
% 1.72/1.62 spl0_41 | spl0_42 | spl0_43 | ~spl0_2 | ~spl0_39),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f1626,f1607,f23,f1636,f1633,f1630])).
% 1.72/1.62 thf(f1626,plain,(
% 1.72/1.62 ( ! [X0 : a] : ((((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false) | ((~ (sK5 = (sK10 @ (= @ sK5)))) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0)))) ) | (~spl0_2 | ~spl0_39)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f1614])).
% 1.72/1.62 thf(f1614,plain,(
% 1.72/1.62 ( ! [X0 : a] : ((((sK5 = (sK9 @ (= @ sK5))) => (sK4 @ (sK9 @ (= @ sK5)))) = $false) | (((sK5 = (sK10 @ (= @ sK5))) => $false) = $false) | ($true = ((sK5 = X0) => (sK2 @ X0)))) ) | (~spl0_2 | ~spl0_39)),
% 1.72/1.62 inference(superposition,[status(thm)],[f339,f1608])).
% 1.72/1.62 thf(f1612,plain,(
% 1.72/1.62 spl0_39 | spl0_40 | ~spl0_2 | ~spl0_7),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f1525,f59,f23,f1610,f1607])).
% 1.72/1.62 thf(f1525,plain,(
% 1.72/1.62 (sK5 = (sK9 @ (= @ sK5))) | ((sK3 @ (sK10 @ (= @ sK5))) = $false) | (~spl0_2 | ~spl0_7)),
% 1.72/1.62 inference(leibniz_equality_elimination,[status(thm)],[f1410])).
% 1.72/1.62 thf(f1410,plain,(
% 1.72/1.62 ( ! [X0 : a > $o] : (($true = (X0 @ (sK9 @ X0))) | ((sK3 @ (sK10 @ X0)) = $false) | ($false = (X0 @ sK5))) ) | (~spl0_2 | ~spl0_7)),
% 1.72/1.62 inference(not_proxy_clausification,[status(thm)],[f726])).
% 1.72/1.62 thf(f726,plain,(
% 1.72/1.62 ( ! [X0 : a > $o] : (($true = (X0 @ (sK9 @ X0))) | ((sK3 @ (sK10 @ X0)) = $false) | ($true = (~ (X0 @ sK5)))) ) | (~spl0_2 | ~spl0_7)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f698])).
% 1.72/1.62 thf(f698,plain,(
% 1.72/1.62 ( ! [X0 : a > $o] : (($true = (X0 @ (sK9 @ X0))) | ((sK3 @ (sK10 @ X0)) = $false) | ($true = ((X0 @ sK5) => $false))) ) | (~spl0_2 | ~spl0_7)),
% 1.72/1.62 inference(superposition,[status(thm)],[f387,f60])).
% 1.72/1.62 thf(f387,plain,(
% 1.72/1.62 ( ! [X2 : a,X1 : a > $o] : (($true = ((X1 @ X2) => (sK2 @ X2))) | ($false = (sK3 @ (sK10 @ X1))) | ($true = (X1 @ (sK9 @ X1)))) ) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f340])).
% 1.72/1.62 thf(f267,plain,(
% 1.72/1.62 ~spl0_6 | ~spl0_9),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f266])).
% 1.72/1.62 thf(f266,plain,(
% 1.72/1.62 $false | (~spl0_6 | ~spl0_9)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f265])).
% 1.72/1.62 thf(f265,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_6 | ~spl0_9)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f264])).
% 1.72/1.62 thf(f264,plain,(
% 1.72/1.62 ($true = ($false & (sK3 @ sK5))) | (~spl0_6 | ~spl0_9)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f56,f88])).
% 1.72/1.62 thf(f88,plain,(
% 1.72/1.62 ((sK4 @ sK5) = $false) | ~spl0_9),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.72/1.62 thf(f263,plain,(
% 1.72/1.62 ~spl0_2 | ~spl0_5 | ~spl0_9),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f262])).
% 1.72/1.62 thf(f262,plain,(
% 1.72/1.62 $false | (~spl0_2 | ~spl0_5 | ~spl0_9)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f261])).
% 1.72/1.62 thf(f261,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_9)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f246,f88])).
% 1.72/1.62 thf(f246,plain,(
% 1.72/1.62 ($true = (sK4 @ sK5)) | (~spl0_2 | ~spl0_5)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f244])).
% 1.72/1.62 thf(f244,plain,(
% 1.72/1.62 ($true = ($true => (sK4 @ sK5))) | (~spl0_2 | ~spl0_5)),
% 1.72/1.62 inference(superposition,[status(thm)],[f236,f53])).
% 1.72/1.62 thf(f236,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((sK2 @ X1) => (sK4 @ X1)))) ) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f234])).
% 1.72/1.62 thf(f234,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))) @ X1))) ) | ~spl0_2),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f207])).
% 1.72/1.62 thf(f172,plain,(
% 1.72/1.62 ~spl0_4 | ~spl0_12),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f171])).
% 1.72/1.62 thf(f171,plain,(
% 1.72/1.62 $false | (~spl0_4 | ~spl0_12)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.72/1.62 thf(f170,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_4 | ~spl0_12)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f168,f164])).
% 1.72/1.62 thf(f164,plain,(
% 1.72/1.62 ((sK4 @ sK7) = $false) | (~spl0_4 | ~spl0_12)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f163,f148])).
% 1.72/1.62 thf(f148,plain,(
% 1.72/1.62 ((sK2 @ sK7) = $false) | ~spl0_12),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f147])).
% 1.72/1.62 thf(f147,plain,(
% 1.72/1.62 (($true => (sK2 @ sK7)) = $false) | ~spl0_12),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f144,f146])).
% 1.72/1.62 thf(f146,plain,(
% 1.72/1.62 ($true = (sK6 @ sK7)) | ~spl0_12),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.72/1.62 thf(f144,plain,(
% 1.72/1.62 (((sK6 @ sK7) => (sK2 @ sK7)) = $false) | ~spl0_12),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.72/1.62 thf(f143,plain,(
% 1.72/1.62 ($false = ((^[Y0 : a]: ((sK6 @ Y0) => (sK2 @ Y0))) @ sK7)) | ~spl0_12),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f137])).
% 1.72/1.62 thf(f137,plain,(
% 1.72/1.62 ($false = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK2 @ Y0))))) | ~spl0_12),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.72/1.62 thf(f136,plain,(
% 1.72/1.62 ($false = (((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK3 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK4 @ Y0))))) => (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK2 @ Y0)))))) | ~spl0_12),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.72/1.62 thf(f135,plain,(
% 1.72/1.62 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))) @ sK6) = $false) | ~spl0_12),
% 1.72/1.62 inference(sigma_clausification,[status(thm)],[f106])).
% 1.72/1.62 thf(f106,plain,(
% 1.72/1.62 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) | ~spl0_12),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.72/1.62 thf(f105,definition,(
% 1.72/1.62 spl0_12 <=> ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1))))))))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.72/1.62 thf(f163,plain,(
% 1.72/1.62 ((sK4 @ sK7) = (sK2 @ sK7)) | (~spl0_4 | ~spl0_12)),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f161])).
% 1.72/1.62 thf(f161,plain,(
% 1.72/1.62 ((sK2 @ sK7) = ((sK4 @ sK7) & $true)) | (~spl0_4 | ~spl0_12)),
% 1.72/1.62 inference(superposition,[status(thm)],[f99,f157])).
% 1.72/1.62 thf(f157,plain,(
% 1.72/1.62 ($true = (sK3 @ sK7)) | ~spl0_12),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f156])).
% 1.72/1.62 thf(f156,plain,(
% 1.72/1.62 ($true = ($true => (sK3 @ sK7))) | ~spl0_12),
% 1.72/1.62 inference(superposition,[status(thm)],[f154,f146])).
% 1.72/1.62 thf(f154,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((sK6 @ X1) => (sK3 @ X1)))) ) | ~spl0_12),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f153])).
% 1.72/1.62 thf(f153,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK6 @ Y0) => (sK3 @ Y0))) @ X1))) ) | ~spl0_12),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f152])).
% 1.72/1.62 thf(f152,plain,(
% 1.72/1.62 ($true = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK3 @ Y0))))) | ~spl0_12),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f151])).
% 1.72/1.62 thf(f151,plain,(
% 1.72/1.62 ($true = ((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK3 @ Y0)))) & $true)) | ~spl0_12),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f138,f149])).
% 1.72/1.62 thf(f149,plain,(
% 1.72/1.62 ($true = (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK4 @ Y0))))) | ~spl0_12),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 1.72/1.62 thf(f138,plain,(
% 1.72/1.62 ($true = ((!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK3 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK6 @ Y0) => (sK4 @ Y0)))))) | ~spl0_12),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.72/1.62 thf(f99,plain,(
% 1.72/1.62 ( ! [X1 : a] : (((sK2 @ X1) = ((sK4 @ X1) & (sK3 @ X1)))) ) | ~spl0_4),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.72/1.62 thf(f98,plain,(
% 1.72/1.62 ( ! [X1 : a] : (((sK2 @ X1) = ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) @ X1))) ) | ~spl0_4),
% 1.72/1.62 inference(argument_congruence,[status(thm)],[f95])).
% 1.72/1.62 thf(f95,plain,(
% 1.72/1.62 ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) = sK2) | ~spl0_4),
% 1.72/1.62 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.72/1.62 thf(f31,plain,(
% 1.72/1.62 ($true = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))))) | ~spl0_4),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.72/1.62 thf(f30,definition,(
% 1.72/1.62 spl0_4 <=> ($true = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0)))))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.72/1.62 thf(f168,plain,(
% 1.72/1.62 ($true = (sK4 @ sK7)) | ~spl0_12),
% 1.72/1.62 inference(boolean_simplification,[status(thm)],[f167])).
% 1.72/1.62 thf(f167,plain,(
% 1.72/1.62 ($true = ($true => (sK4 @ sK7))) | ~spl0_12),
% 1.72/1.62 inference(superposition,[status(thm)],[f159,f146])).
% 1.72/1.62 thf(f159,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((sK6 @ X1) => (sK4 @ X1)))) ) | ~spl0_12),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f158])).
% 1.72/1.62 thf(f158,plain,(
% 1.72/1.62 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK6 @ Y0) => (sK4 @ Y0))) @ X1))) ) | ~spl0_12),
% 1.72/1.62 inference(pi_clausification,[status(thm)],[f149])).
% 1.72/1.62 thf(f125,plain,(
% 1.72/1.62 spl0_13 | spl0_14 | ~spl0_11),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f118,f102,f123,f120])).
% 1.72/1.62 thf(f102,definition,(
% 1.72/1.62 spl0_11 <=> (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.72/1.62 thf(f118,plain,(
% 1.72/1.62 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) = $false) | ~spl0_11),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.72/1.62 thf(f103,plain,(
% 1.72/1.62 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) = $false) | ~spl0_11),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.72/1.62 thf(f107,plain,(
% 1.72/1.62 spl0_11 | spl0_12 | ~spl0_1),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f100,f20,f105,f102])).
% 1.72/1.62 thf(f100,plain,(
% 1.72/1.62 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) = $false) | ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) | ~spl0_1),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.72/1.62 thf(f92,plain,(
% 1.72/1.62 spl0_9 | spl0_10 | ~spl0_8),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f85,f62,f90,f87])).
% 1.72/1.62 thf(f62,definition,(
% 1.72/1.62 spl0_8 <=> (((sK4 @ sK5) & (sK3 @ sK5)) = $false)),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.72/1.62 thf(f85,plain,(
% 1.72/1.62 ((sK3 @ sK5) = $false) | ((sK4 @ sK5) = $false) | ~spl0_8),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.72/1.62 thf(f63,plain,(
% 1.72/1.62 (((sK4 @ sK5) & (sK3 @ sK5)) = $false) | ~spl0_8),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.72/1.62 thf(f71,plain,(
% 1.72/1.62 ~spl0_5 | ~spl0_7),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 1.72/1.62 thf(f70,plain,(
% 1.72/1.62 $false | (~spl0_5 | ~spl0_7)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.72/1.62 thf(f69,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_5 | ~spl0_7)),
% 1.72/1.62 inference(backward_demodulation,[status(thm)],[f53,f60])).
% 1.72/1.62 thf(f68,plain,(
% 1.72/1.62 ~spl0_1 | ~spl0_3),
% 1.72/1.62 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.72/1.62 thf(f67,plain,(
% 1.72/1.62 $false | (~spl0_1 | ~spl0_3)),
% 1.72/1.62 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.72/1.62 thf(f66,plain,(
% 1.72/1.62 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 1.72/1.62 inference(forward_demodulation,[status(thm)],[f28,f21])).
% 1.72/1.62 thf(f28,plain,(
% 1.72/1.62 ($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1))))))))) | ~spl0_3),
% 1.72/1.62 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.72/1.62 thf(f27,definition,(
% 1.72/1.62 spl0_3 <=> ($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))))),
% 1.72/1.62 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.72/1.62 thf(f64,plain,(
% 1.72/1.62 spl0_7 | spl0_8 | ~spl0_2),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f50,f23,f62,f59])).
% 1.72/1.62 thf(f50,plain,(
% 1.72/1.62 (((sK4 @ sK5) & (sK3 @ sK5)) = $false) | ((sK2 @ sK5) = $false) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.72/1.62 thf(f42,plain,(
% 1.72/1.62 ((sK2 @ sK5) != ((sK4 @ sK5) & (sK3 @ sK5))) | ~spl0_2),
% 1.72/1.62 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.72/1.62 thf(f41,plain,(
% 1.72/1.62 ((sK2 @ sK5) != ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) @ sK5)) | ~spl0_2),
% 1.72/1.62 inference(negative_extensionality,[status(thm)],[f34])).
% 1.72/1.62 thf(f34,plain,(
% 1.72/1.62 ((^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))) != sK2) | ~spl0_2),
% 1.72/1.62 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.72/1.62 thf(f57,plain,(
% 1.72/1.62 spl0_5 | spl0_6 | ~spl0_2),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f49,f23,f55,f52])).
% 1.72/1.62 thf(f49,plain,(
% 1.72/1.62 ($true = ((sK4 @ sK5) & (sK3 @ sK5))) | ($true = (sK2 @ sK5)) | ~spl0_2),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.72/1.62 thf(f32,plain,(
% 1.72/1.62 spl0_3 | spl0_4),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f17,f30,f27])).
% 1.72/1.62 thf(f17,plain,(
% 1.72/1.62 ($true = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0))))) | ($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))))),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.72/1.62 thf(f25,plain,(
% 1.72/1.62 spl0_1 | spl0_2),
% 1.72/1.62 inference(avatar_split_clause,[status(thm)],[f18,f23,f20])).
% 1.72/1.62 thf(f18,plain,(
% 1.72/1.62 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK3 @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK4 @ Y1))))) => (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (sK2 @ Y1)))))))) = $false) | ($false = (sK2 = (^[Y0 : a]: ((sK4 @ Y0) & (sK3 @ Y0)))))),
% 1.72/1.62 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.72/1.62 % SZS output end Proof for DTF2THF_20557
% 1.72/1.62 % (20666)------------------------------
% 1.72/1.62 % (20666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.62 % (20666)Termination reason: Refutation
% 1.72/1.62
% 1.72/1.62 % (20666)Memory used [KB]: 6396
% 1.72/1.62 % (20666)Time elapsed: 0.144 s
% 1.72/1.62 % (20666)Instructions burned: 265 (million)
% 1.72/1.62 % (20666)------------------------------
% 1.72/1.62 % (20666)------------------------------
% 1.72/1.62 % (20654)Success in time 0.191 s
%------------------------------------------------------------------------------