%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU861^5 : 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 : n011.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 09:37:36 AM UTC 2026
% Result : Theorem 1.57s 1.38s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 79 ( 32 unt; 0 typ; 2 def)
% Number of atoms : 622 ( 127 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1289 ( 75 ~; 98 |; 82 &; 681 @)
% ( 2 <=>; 171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 243 ( 243 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 9 con; 0-2 aty)
% ( 162 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 253 ( 177 ^; 70 !; 6 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cB: a > $o ).
thf(func_def_2,type,
cC: a > $o ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: ( a > $o ) > $o ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a > a ).
thf(func_def_23,type,
sK5: a > $o ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a > $o ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a > $o ).
thf(f187,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f72,f129,f186]) ).
thf(f186,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f185]) ).
thf(f185,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f183,f144]) ).
thf(f144,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( ( $true
=> ( sK2 @ sK5 ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f140,f142]) ).
thf(f142,plain,
( ( ( ( sK2 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( ( sK6 = Y0 )
| ( sK7 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $false
= ( ( ( sK2 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( ( sK6 = Y0 )
| ( sK7 @ Y0 ) ) ) ) )
=> ( sK2 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
=> ( ( sK6 = Y1 )
| ( Y0 @ Y1 ) ) ) ) )
=> ( sK2 @ sK5 ) )
@ sK7 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
=> ( ( sK6 = Y1 )
| ( Y0 @ Y1 ) ) ) ) )
=> ( sK2 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f137]) ).
thf(f137,plain,
( ( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 )
=> ( ( Y0 = Y2 )
| ( Y1 @ Y2 ) ) ) ) )
=> ( sK2 @ sK5 ) ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 )
=> ( ( Y0 = Y2 )
| ( Y1 @ Y2 ) ) ) ) )
=> ( sK2 @ sK5 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) )
@ sK5 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f183,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f182]) ).
thf(f182,plain,
( ( ( $true
=> ( sK2 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f181,f169]) ).
thf(f169,plain,
( ( ( sK2 @ sK9 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( ( ( sK2 @ sK9 )
& $true )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f163,f166]) ).
thf(f166,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( ( sK6 = Y0 )
| ( sK9 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $true
= ( ( sK2 @ sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( ( sK6 = Y0 )
| ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
( ( $false
= ( ~ ( ( sK2 @ sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 )
=> ( ( sK6 = Y0 )
| ( sK9 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: a > $o] :
~ ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
=> ( ( sK6 = Y1 )
| ( Y0 @ Y1 ) ) ) ) )
@ sK9 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
~ ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
=> ( ( sK6 = Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 )
=> ( ( sK6 = Y1 )
| ( Y0 @ Y1 ) ) ) ) )
=> $false ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f138,f144]) ).
thf(f181,plain,
( ( ( ( sK2 @ sK9 )
=> ( sK2 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( ( ( $true
& ( sK2 @ sK9 ) )
=> ( sK2 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f58,f166]) ).
thf(f58,plain,
! [X2: a > $o,X3: a > $o,X1: a] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X3 @ Y0 )
=> ( ( X1 = Y0 )
| ( X2 @ Y0 ) ) ) )
& ( sK2 @ X2 ) )
=> ( sK2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: a > $o,X3: a > $o,X1: a] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( X1 = Y1 )
| ( X2 @ Y1 ) ) ) )
& ( sK2 @ X2 ) )
=> ( sK2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: a > $o,X1: a] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( X1 = Y1 )
| ( X2 @ Y1 ) ) ) )
& ( sK2 @ X2 ) )
=> ( sK2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: a > $o,X1: a] :
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( ( X1 = Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( sK2 @ Y0 ) )
=> ( sK2 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: a] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( ( X1 = Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( sK2 @ Y0 ) )
=> ( sK2 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( ( Y0 = Y3 )
| ( Y1 @ Y3 ) ) ) )
& ( sK2 @ Y1 ) )
=> ( sK2 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( ( Y0 = Y3 )
| ( Y1 @ Y3 ) ) ) )
& ( sK2 @ Y1 ) )
=> ( sK2 @ Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( ( Y0 = Y3 )
| ( Y1 @ Y3 ) ) ) )
& ( sK2 @ Y1 ) )
=> ( sK2 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( ( Y0 = Y3 )
| ( Y1 @ Y3 ) ) ) )
& ( sK2 @ Y1 ) )
=> ( sK2 @ Y2 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
=> ( sK2 @ cB ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) )
=> ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( ( Y1 = Y4 )
| ( Y2 @ Y4 ) ) ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y3 ) ) ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ cB ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o,X2: a,X3: a > $o] :
( ( ! [X4: a] :
( ( X3 @ X4 )
=> ( ( X1 @ X4 )
| ( X2 = X4 ) ) )
& ( X0 @ X1 ) )
=> ( X0 @ X3 ) )
& ! [X5: a > $o] :
( ~ ? [X6: a] : ( X5 @ X6 )
=> ( X0 @ X5 ) ) )
=> ( X0 @ cC ) )
& ! [X7: a] :
( ( cB @ X7 )
=> ( cC @ X7 ) ) )
=> ! [X8: ( a > $o ) > $o] :
( ( ! [X9: a > $o] :
( ~ ? [X10: a] : ( X9 @ X10 )
=> ( X8 @ X9 ) )
& ! [X11: a > $o,X12: a > $o,X13: a] :
( ( ( X8 @ X12 )
& ! [X14: a] :
( ( X11 @ X14 )
=> ( ( X12 @ X14 )
| ( X13 = X14 ) ) ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ cB ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X6: a] :
( ( X5 @ X6 )
=> ( ( X3 @ X6 )
| ( X4 = X6 ) ) )
& ( X0 @ X3 ) )
=> ( X0 @ X5 ) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : ( X1 @ X2 )
=> ( X0 @ X1 ) ) )
=> ( X0 @ cC ) )
& ! [X4: a] :
( ( cB @ X4 )
=> ( cC @ X4 ) ) )
=> ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ~ ? [X2: a] : ( X1 @ X2 )
=> ( X0 @ X1 ) )
& ! [X5: a > $o,X3: a > $o,X4: a] :
( ( ( X0 @ X3 )
& ! [X7: a] :
( ( X5 @ X7 )
=> ( ( X3 @ X7 )
| ( X4 = X7 ) ) ) )
=> ( X0 @ X5 ) ) )
=> ( X0 @ cB ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X6: a] :
( ( X5 @ X6 )
=> ( ( X3 @ X6 )
| ( X4 = X6 ) ) )
& ( X0 @ X3 ) )
=> ( X0 @ X5 ) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : ( X1 @ X2 )
=> ( X0 @ X1 ) ) )
=> ( X0 @ cC ) )
& ! [X4: a] :
( ( cB @ X4 )
=> ( cC @ X4 ) ) )
=> ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ~ ? [X2: a] : ( X1 @ X2 )
=> ( X0 @ X1 ) )
& ! [X5: a > $o,X3: a > $o,X4: a] :
( ( ( X0 @ X3 )
& ! [X7: a] :
( ( X5 @ X7 )
=> ( ( X3 @ X7 )
| ( X4 = X7 ) ) ) )
=> ( X0 @ X5 ) ) )
=> ( X0 @ cB ) ) ),
file('/export/starexec/sandbox/tmp/tmp.33a7r4LH82/DTF2THF_7692.p',cTHM531E_pme) ).
thf(f129,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f126,f121]) ).
thf(f121,plain,
( ! [X0: a] :
( $false
= ( cC @ ( sK4 @ X0 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: a] :
( $false
= ( ( X0
= ( sK4 @ X0 ) )
| ( cC @ ( sK4 @ X0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X0: a] :
( $false
= ( $true
=> ( ( X0
= ( sK4 @ X0 ) )
| ( cC @ ( sK4 @ X0 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f107,f118]) ).
thf(f118,plain,
( ! [X0: a] :
( ( cB @ ( sK4 @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ! [X0: a] :
( $false
= ( ( cB @ ( sK4 @ X0 ) )
=> ( ( X0
= ( sK4 @ X0 ) )
| ( cC @ ( sK4 @ X0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
( ! [X0: a] :
( $false
= ( ^ [Y0: a] :
( ( cB @ Y0 )
=> ( ( X0 = Y0 )
| ( cC @ Y0 ) ) )
@ ( sK4 @ X0 ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( ( X0 = Y0 )
| ( cC @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ! [X0: a] :
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( ( X0 = Y0 )
| ( cC @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( ( X0 = Y0 )
| ( cC @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f79,f22]) ).
thf(f22,plain,
( $false
= ( sK2 @ cB ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( $true
=> ( sK2 @ cB ) ) ),
inference(backward_demodulation,[status(thm)],[f18,f20]) ).
thf(f79,plain,
( ! [X0: a > $o,X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( ( X1 = Y0 )
| ( cC @ Y0 ) ) ) )
=> ( sK2 @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: a > $o,X1: a] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( ( X1 = Y0 )
| ( cC @ Y0 ) ) ) )
& $true )
=> ( sK2 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f58,f71]) ).
thf(f71,plain,
( ( $true
= ( sK2 @ cC ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_2
<=> ( $true
= ( sK2 @ cC ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f126,plain,
( ! [X0: a] :
( ( cC @ ( sK4 @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f125]) ).
thf(f125,plain,
( ! [X0: a] :
( ( $true
=> ( cC @ ( sK4 @ X0 ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f32,f118]) ).
thf(f32,plain,
! [X1: a] :
( ( ( cB @ X1 )
=> ( cC @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f12,f27]) ).
thf(f27,plain,
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cB @ Y0 )
=> ( cC @ Y0 ) ) )
& ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f72,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f70,f67]) ).
thf(f65,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( sK2 @ cC ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) )
=> ( sK2 @ cC ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( sK2 @ Y0 ) ) ) ) ) )
=> ( sK2 @ cC ) )
= $true ),
inference(superposition,[status(thm)],[f45,f26]) ).
thf(f26,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( sK2 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f20,f24]) ).
thf(f45,plain,
! [X1: ( a > $o ) > $o] :
( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ~ ( ?? @ a @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( ( Y1 = Y3 )
| ( Y2 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 ) ) ) ) ) )
=> ( X1 @ cC ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: ( a > $o ) > $o] :
( $true
= ( ^ [Y0: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ~ ( ?? @ a @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 )
=> ( ( Y2 = Y4 )
| ( Y3 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( Y0 @ cC ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU861^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n011.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:35:32 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU861^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.38 % Domain : Set Theory (Finite sets)
% 0.17/0.38 % Problem : TPS problem THM531E
% 0.17/0.38 % Version : Especial.
% 0.17/0.38 % English : Subset of a finite set is finite.
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.38 % Source : [Bro09]
% 0.17/0.38 % Names : tps_0532 [Bro09]
% 0.17/0.38 % : THM531E [TPS]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.38 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.38 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 6 ( 6 avg)
% 0.17/0.38 % Number of connectives : 35 ( 2 ~; 2 |; 5 &; 16 @)
% 0.17/0.38 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 15 ( 15 avg)
% 0.17/0.38 % Number of types : 2 ( 1 usr)
% 0.17/0.38 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.38 % Number of variables : 15 ( 0 ^; 13 !; 2 ?; 15 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.38 % : Polymorphic definitions expanded.
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(a_type,type,
% 0.17/0.38 a: $tType ).
% 0.17/0.38
% 0.17/0.38 thf(cB,type,
% 0.17/0.38 cB: a > $o ).
% 0.17/0.38
% 0.17/0.38 thf(cC,type,
% 0.17/0.38 cC: a > $o ).
% 0.17/0.38
% 0.17/0.38 thf(cTHM531E_pme,conjecture,
% 0.17/0.38 ( ( ! [P: ( a > $o ) > $o] :
% 0.17/0.38 ( ( ! [E: a > $o] :
% 0.17/0.38 ( ~ ? [Xt: a] : ( E @ Xt )
% 0.17/0.38 => ( P @ E ) )
% 0.17/0.38 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 0.17/0.38 ( ( ( P @ Y )
% 0.17/0.38 & ! [Xx_27: a] :
% 0.17/0.38 ( ( Z @ Xx_27 )
% 0.17/0.38 => ( ( Y @ Xx_27 )
% 0.17/0.38 | ( Xx_27 = Xx ) ) ) )
% 0.17/0.38 => ( P @ Z ) ) )
% 0.17/0.38 => ( P @ cC ) )
% 0.17/0.38 & ! [Xx: a] :
% 0.17/0.38 ( ( cB @ Xx )
% 0.17/0.38 => ( cC @ Xx ) ) )
% 0.17/0.38 => ! [P: ( a > $o ) > $o] :
% 0.17/0.38 ( ( ! [E: a > $o] :
% 0.17/0.38 ( ~ ? [Xt: a] : ( E @ Xt )
% 0.17/0.38 => ( P @ E ) )
% 0.17/0.38 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 0.17/0.38 ( ( ( P @ Y )
% 0.17/0.38 & ! [Xx_28: a] :
% 0.17/0.38 ( ( Z @ Xx_28 )
% 0.17/0.38 => ( ( Y @ Xx_28 )
% 0.17/0.38 | ( Xx_28 = Xx ) ) ) )
% 0.17/0.38 => ( P @ Z ) ) )
% 0.17/0.38 => ( P @ cB ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.39/1.29 ---- Embedded in THF ---
% 1.39/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.29 %%% Generated on Tue Feb 24 12:35:33 EST 2026
% 1.39/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.29 %%% Logic specification used:
% 1.39/1.29 %%% thf(spec, logic, $$dhol).
% 1.39/1.29
% 1.39/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.33a7r4LH82/DTF2DTF7692.p
% See solution above
% 1.39/1.29 ------------------------
% 1.57/1.30 ---- Cleaned THF ---
% 1.57/1.30 thf(a_type,type,
% 1.57/1.30 a: $tType ).
% 1.57/1.30
% 1.57/1.30 thf(cB,type,
% 1.57/1.30 cB: a > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cC,type,
% 1.57/1.30 cC: a > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cTHM531E_pme,conjecture,
% 1.57/1.30 ( ( ! [P: ( a > $o ) > $o] :
% 1.57/1.30 ( ( ! [E: a > $o] :
% 1.57/1.30 ( ~ ? [Xt: a] : ( E @ Xt )
% 1.57/1.30 => ( P @ E ) )
% 1.57/1.30 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 1.57/1.30 ( ( ( P @ Y )
% 1.57/1.30 & ! [Xx_27: a] :
% 1.57/1.30 ( ( Z @ Xx_27 )
% 1.57/1.30 => ( ( Y @ Xx_27 )
% 1.57/1.30 | ( Xx_27 = Xx ) ) ) )
% 1.57/1.30 => ( P @ Z ) ) )
% 1.57/1.30 => ( P @ cC ) )
% 1.57/1.30 & ! [Xx: a] :
% 1.57/1.30 ( ( cB @ Xx )
% 1.57/1.30 => ( cC @ Xx ) ) )
% 1.57/1.30 => ! [P: ( a > $o ) > $o] :
% 1.57/1.30 ( ( ! [E: a > $o] :
% 1.57/1.30 ( ~ ? [Xt: a] : ( E @ Xt )
% 1.57/1.30 => ( P @ E ) )
% 1.57/1.30 & ! [Y: a > $o,Xx: a,Z: a > $o] :
% 1.57/1.30 ( ( ( P @ Y )
% 1.57/1.30 & ! [Xx_28: a] :
% 1.57/1.30 ( ( Z @ Xx_28 )
% 1.57/1.30 => ( ( Y @ Xx_28 )
% 1.57/1.30 | ( Xx_28 = Xx ) ) ) )
% 1.57/1.30 => ( P @ Z ) ) )
% 1.57/1.30 => ( P @ cB ) ) ) ).
% 1.57/1.30 ------------------------
% 1.57/1.32 % (7795)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_7692 for (2999ds/275Mi)
% 1.57/1.32 % (7790)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/183Mi)
% 1.57/1.32 % (7794)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_7692 for (2999ds/2Mi)
% 1.57/1.32 % (7793)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/2Mi)
% 1.57/1.32 % (7796)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/18Mi)
% 1.57/1.32 % (7792)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_7692 for (2999ds/27Mi)
% 1.57/1.32 % (7791)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_7692 for (2999ds/4Mi)
% 1.57/1.32 % (7793)Instruction limit reached!
% 1.57/1.32 % (7793)------------------------------
% 1.57/1.32 % (7793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (7793)Termination reason: Unknown
% 1.57/1.32 % (7794)Instruction limit reached!
% 1.57/1.32 % (7794)------------------------------
% 1.57/1.32 % (7794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (7794)Termination reason: Unknown
% 1.57/1.32 % (7794)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (7794)Memory used [KB]: 1023
% 1.57/1.32 % (7794)Time elapsed: 0.003 s
% 1.57/1.32 % (7794)Instructions burned: 3 (million)
% 1.57/1.32 % (7794)------------------------------
% 1.57/1.32 % (7794)------------------------------
% 1.57/1.32 % (7793)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (7793)Memory used [KB]: 1023
% 1.57/1.32 % (7793)Time elapsed: 0.003 s
% 1.57/1.32 % (7793)Instructions burned: 2 (million)
% 1.57/1.32 % (7793)------------------------------
% 1.57/1.32 % (7793)------------------------------
% 1.57/1.32 % (7791)Instruction limit reached!
% 1.57/1.32 % (7791)------------------------------
% 1.57/1.32 % (7791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (7791)Termination reason: Unknown
% 1.57/1.32 % (7791)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (7791)Memory used [KB]: 5500
% 1.57/1.32 % (7791)Time elapsed: 0.004 s
% 1.57/1.32 % (7791)Instructions burned: 4 (million)
% 1.57/1.32 % (7791)------------------------------
% 1.57/1.32 % (7791)------------------------------
% 1.57/1.33 % (7796)Instruction limit reached!
% 1.57/1.33 % (7796)------------------------------
% 1.57/1.33 % (7796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (7796)Termination reason: Unknown
% 1.57/1.33 % (7796)Termination phase: Saturation
% 1.57/1.33
% 1.57/1.33 % (7796)Memory used [KB]: 5628
% 1.57/1.33 % (7796)Time elapsed: 0.011 s
% 1.57/1.33 % (7796)Instructions burned: 18 (million)
% 1.57/1.33 % (7796)------------------------------
% 1.57/1.33 % (7796)------------------------------
% 1.57/1.33 % (7792)Instruction limit reached!
% 1.57/1.33 % (7792)------------------------------
% 1.57/1.33 % (7792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (7792)Termination reason: Unknown
% 1.57/1.33 % (7792)Termination phase: Saturation
% 1.57/1.33
% 1.57/1.33 % (7792)Memory used [KB]: 5628
% 1.57/1.33 % (7792)Time elapsed: 0.017 s
% 1.57/1.33 % (7792)Instructions burned: 27 (million)
% 1.57/1.33 % (7792)------------------------------
% 1.57/1.33 % (7792)------------------------------
% 1.57/1.34 % (7797)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/3Mi)
% 1.57/1.34 % (7798)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_7692 for (2999ds/37Mi)
% 1.57/1.34 % (7799)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_7692 for (2999ds/15Mi)
% 1.57/1.34 % (7797)Instruction limit reached!
% 1.57/1.34 % (7797)------------------------------
% 1.57/1.34 % (7797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (7797)Termination reason: Unknown
% 1.57/1.34 % (7797)Termination phase: Saturation
% 1.57/1.34
% 1.57/1.34 % (7797)Memory used [KB]: 5500
% 1.57/1.34 % (7797)Time elapsed: 0.003 s
% 1.57/1.34 % (7797)Instructions burned: 3 (million)
% 1.57/1.34 % (7797)------------------------------
% 1.57/1.34 % (7797)------------------------------
% 1.57/1.34 % (7800)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_7692 for (2999ds/3Mi)
% 1.57/1.35 % (7799)Instruction limit reached!
% 1.57/1.35 % (7799)------------------------------
% 1.57/1.35 % (7799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (7799)Termination reason: Unknown
% 1.57/1.35 % (7799)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (7799)Memory used [KB]: 5628
% 1.57/1.35 % (7799)Time elapsed: 0.010 s
% 1.57/1.35 % (7799)Instructions burned: 16 (million)
% 1.57/1.35 % (7799)------------------------------
% 1.57/1.35 % (7799)------------------------------
% 1.57/1.35 % (7800)Instruction limit reached!
% 1.57/1.35 % (7800)------------------------------
% 1.57/1.35 % (7800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (7800)Termination reason: Unknown
% 1.57/1.35 % (7800)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (7800)Memory used [KB]: 5500
% 1.57/1.35 % (7800)Time elapsed: 0.003 s
% 1.57/1.35 % (7800)Instructions burned: 3 (million)
% 1.57/1.35 % (7800)------------------------------
% 1.57/1.35 % (7800)------------------------------
% 1.57/1.35 % (7801)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_7692 for (2999ds/1041Mi)
% 1.57/1.35 % (7802)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/7Mi)
% 1.57/1.35 % (7798)Instruction limit reached!
% 1.57/1.35 % (7798)------------------------------
% 1.57/1.35 % (7798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (7798)Termination reason: Unknown
% 1.57/1.35 % (7798)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (7798)Memory used [KB]: 5756
% 1.57/1.35 % (7798)Time elapsed: 0.019 s
% 1.57/1.35 % (7798)Instructions burned: 37 (million)
% 1.57/1.35 % (7798)------------------------------
% 1.57/1.35 % (7798)------------------------------
% 1.57/1.36 % (7802)Instruction limit reached!
% 1.57/1.36 % (7802)------------------------------
% 1.57/1.36 % (7802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (7802)Termination reason: Unknown
% 1.57/1.36 % (7802)Termination phase: Saturation
% 1.57/1.36
% 1.57/1.36 % (7802)Memory used [KB]: 1023
% 1.57/1.36 % (7802)Time elapsed: 0.005 s
% 1.57/1.36 % (7802)Instructions burned: 7 (million)
% 1.57/1.36 % (7802)------------------------------
% 1.57/1.36 % (7802)------------------------------
% 1.57/1.36 % (7803)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/16Mi)
% 1.57/1.36 % (7804)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_7692 for (2999ds/3Mi)
% 1.57/1.36 % (7804)Instruction limit reached!
% 1.57/1.36 % (7804)------------------------------
% 1.57/1.36 % (7804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (7804)Termination reason: Unknown
% 1.57/1.36 % (7804)Termination phase: Twee Goal Transformation
% 1.57/1.36
% 1.57/1.36 % (7804)Memory used [KB]: 1023
% 1.57/1.36 % (7804)Time elapsed: 0.003 s
% 1.57/1.36 % (7804)Instructions burned: 4 (million)
% 1.57/1.36 % (7804)------------------------------
% 1.57/1.36 % (7804)------------------------------
% 1.57/1.37 % (7805)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_7692 for (2999ds/3Mi)
% 1.57/1.37 % (7803)Instruction limit reached!
% 1.57/1.37 % (7803)------------------------------
% 1.57/1.37 % (7803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.37 % (7803)Termination reason: Unknown
% 1.57/1.37 % (7803)Termination phase: Saturation
% 1.57/1.37
% 1.57/1.37 % (7803)Memory used [KB]: 5628
% 1.57/1.37 % (7803)Time elapsed: 0.010 s
% 1.57/1.37 % (7803)Instructions burned: 17 (million)
% 1.57/1.37 % (7803)------------------------------
% 1.57/1.37 % (7803)------------------------------
% 1.57/1.37 % (7805)Instruction limit reached!
% 1.57/1.37 % (7805)------------------------------
% 1.57/1.37 % (7805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.37 % (7805)Termination reason: Unknown
% 1.57/1.37 % (7805)Termination phase: Saturation
% 1.57/1.37
% 1.57/1.37 % (7805)Memory used [KB]: 1023
% 1.57/1.37 % (7805)Time elapsed: 0.003 s
% 1.57/1.37 % (7805)Instructions burned: 3 (million)
% 1.57/1.37 % (7805)------------------------------
% 1.57/1.37 % (7805)------------------------------
% 1.57/1.37 % (7801)First to succeed.
% 1.57/1.37 % (7806)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7692 for (2999ds/7Mi)
% 1.57/1.38 % (7801)Refutation found. Thanks to Tanya!
% 1.57/1.38 % SZS status Theorem for DTF2THF_7692
% 1.57/1.38 % SZS output start Proof for DTF2THF_7692
% 1.57/1.38 thf(type_def_5, type, a: $tType).
% 1.57/1.38 thf(func_def_0, type, a: $tType).
% 1.57/1.38 thf(func_def_1, type, cB: a > $o).
% 1.57/1.38 thf(func_def_2, type, cC: a > $o).
% 1.57/1.38 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.57/1.38 thf(func_def_20, type, sK2: (a > $o) > $o).
% 1.57/1.38 thf(func_def_21, type, sK3: a).
% 1.57/1.38 thf(func_def_22, type, sK4: a > a).
% 1.57/1.38 thf(func_def_23, type, sK5: a > $o).
% 1.57/1.38 thf(func_def_24, type, sK6: a).
% 1.57/1.38 thf(func_def_25, type, sK7: a > $o).
% 1.57/1.38 thf(func_def_26, type, sK8: a).
% 1.57/1.38 thf(func_def_27, type, sK9: a > $o).
% 1.57/1.38 thf(f187,plain,(
% 1.57/1.38 $false),
% 1.57/1.38 inference(avatar_sat_refutation,[status(thm)],[f72,f129,f186])).
% 1.57/1.38 thf(f186,plain,(
% 1.57/1.38 ~spl0_1),
% 1.57/1.38 inference(avatar_contradiction_clause,[status(thm)],[f185])).
% 1.57/1.38 thf(f185,plain,(
% 1.57/1.38 $false | ~spl0_1),
% 1.57/1.38 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.57/1.38 thf(f184,plain,(
% 1.57/1.38 ($false = $true) | ~spl0_1),
% 1.57/1.38 inference(forward_demodulation,[status(thm)],[f183,f144])).
% 1.57/1.38 thf(f144,plain,(
% 1.57/1.38 ($false = (sK2 @ sK5)) | ~spl0_1),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f143])).
% 1.57/1.38 thf(f143,plain,(
% 1.57/1.38 (($true => (sK2 @ sK5)) = $false) | ~spl0_1),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f140,f142])).
% 1.57/1.38 thf(f142,plain,(
% 1.57/1.38 (((sK2 @ sK7) & (!! @ a @ (^[Y0 : a]: ((sK5 @ Y0) => ((sK6 = Y0) | (sK7 @ Y0)))))) = $true) | ~spl0_1),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.57/1.38 thf(f140,plain,(
% 1.57/1.38 ($false = (((sK2 @ sK7) & (!! @ a @ (^[Y0 : a]: ((sK5 @ Y0) => ((sK6 = Y0) | (sK7 @ Y0)))))) => (sK2 @ sK5))) | ~spl0_1),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.57/1.38 thf(f139,plain,(
% 1.57/1.38 ($false = ((^[Y0 : a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1) => ((sK6 = Y1) | (Y0 @ Y1)))))) => (sK2 @ sK5))) @ sK7)) | ~spl0_1),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f138])).
% 1.57/1.38 thf(f138,plain,(
% 1.57/1.38 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1) => ((sK6 = Y1) | (Y0 @ Y1)))))) => (sK2 @ sK5))))) | ~spl0_1),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f137])).
% 1.57/1.38 thf(f137,plain,(
% 1.57/1.38 (((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2) => ((Y0 = Y2) | (Y1 @ Y2)))))) => (sK2 @ sK5))))) @ sK6) = $false) | ~spl0_1),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f134])).
% 1.57/1.38 thf(f134,plain,(
% 1.57/1.38 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2) => ((Y0 = Y2) | (Y1 @ Y2)))))) => (sK2 @ sK5))))))) | ~spl0_1),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f132])).
% 1.57/1.38 thf(f132,plain,(
% 1.57/1.38 ($false = ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0))))))) @ sK5)) | ~spl0_1),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f68])).
% 1.57/1.38 thf(f68,plain,(
% 1.57/1.38 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0)))))))) = $false) | ~spl0_1),
% 1.57/1.38 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.57/1.38 thf(f67,definition,(
% 1.57/1.38 spl0_1 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0)))))))) = $false)),
% 1.57/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.57/1.38 thf(f183,plain,(
% 1.57/1.38 ($true = (sK2 @ sK5)) | ~spl0_1),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f182])).
% 1.57/1.38 thf(f182,plain,(
% 1.57/1.38 (($true => (sK2 @ sK5)) = $true) | ~spl0_1),
% 1.57/1.38 inference(forward_demodulation,[status(thm)],[f181,f169])).
% 1.57/1.38 thf(f169,plain,(
% 1.57/1.38 ((sK2 @ sK9) = $true) | ~spl0_1),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f168])).
% 1.57/1.38 thf(f168,plain,(
% 1.57/1.38 (((sK2 @ sK9) & $true) = $true) | ~spl0_1),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f163,f166])).
% 1.57/1.38 thf(f166,plain,(
% 1.57/1.38 ((!! @ a @ (^[Y0 : a]: ((sK5 @ Y0) => ((sK6 = Y0) | (sK9 @ Y0))))) = $true) | ~spl0_1),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.57/1.38 thf(f163,plain,(
% 1.57/1.38 ($true = ((sK2 @ sK9) & (!! @ a @ (^[Y0 : a]: ((sK5 @ Y0) => ((sK6 = Y0) | (sK9 @ Y0))))))) | ~spl0_1),
% 1.57/1.38 inference(not_proxy_clausification,[status(thm)],[f162])).
% 1.57/1.38 thf(f162,plain,(
% 1.57/1.38 ($false = (~ ((sK2 @ sK9) & (!! @ a @ (^[Y0 : a]: ((sK5 @ Y0) => ((sK6 = Y0) | (sK9 @ Y0)))))))) | ~spl0_1),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f161])).
% 1.57/1.38 thf(f161,plain,(
% 1.57/1.38 ($false = ((^[Y0 : a > $o]: (~ ((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1) => ((sK6 = Y1) | (Y0 @ Y1)))))))) @ sK9)) | ~spl0_1),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f146])).
% 1.57/1.38 thf(f146,plain,(
% 1.57/1.38 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (~ ((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1) => ((sK6 = Y1) | (Y0 @ Y1)))))))))) | ~spl0_1),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f145])).
% 1.57/1.38 thf(f145,plain,(
% 1.57/1.38 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1) => ((sK6 = Y1) | (Y0 @ Y1)))))) => $false)))) | ~spl0_1),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f138,f144])).
% 1.57/1.38 thf(f181,plain,(
% 1.57/1.38 (((sK2 @ sK9) => (sK2 @ sK5)) = $true) | ~spl0_1),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f179])).
% 1.57/1.38 thf(f179,plain,(
% 1.57/1.38 ((($true & (sK2 @ sK9)) => (sK2 @ sK5)) = $true) | ~spl0_1),
% 1.57/1.38 inference(superposition,[status(thm)],[f58,f166])).
% 1.57/1.38 thf(f58,plain,(
% 1.57/1.38 ( ! [X2 : a > $o,X3 : a > $o,X1 : a] : (($true = (((!! @ a @ (^[Y0 : a]: ((X3 @ Y0) => ((X1 = Y0) | (X2 @ Y0))))) & (sK2 @ X2)) => (sK2 @ X3)))) )),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.57/1.38 thf(f57,plain,(
% 1.57/1.38 ( ! [X2 : a > $o,X3 : a > $o,X1 : a] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((X1 = Y1) | (X2 @ Y1))))) & (sK2 @ X2)) => (sK2 @ Y0))) @ X3) = $true)) )),
% 1.57/1.38 inference(pi_clausification,[status(thm)],[f56])).
% 1.57/1.38 thf(f56,plain,(
% 1.57/1.38 ( ! [X2 : a > $o,X1 : a] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((X1 = Y1) | (X2 @ Y1))))) & (sK2 @ X2)) => (sK2 @ Y0)))) = $true)) )),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.57/1.38 thf(f55,plain,(
% 1.57/1.38 ( ! [X2 : a > $o,X1 : a] : ((((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => ((X1 = Y2) | (Y0 @ Y2))))) & (sK2 @ Y0)) => (sK2 @ Y1))))) @ X2) = $true)) )),
% 1.57/1.38 inference(pi_clausification,[status(thm)],[f54])).
% 1.57/1.38 thf(f54,plain,(
% 1.57/1.38 ( ! [X1 : a] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => ((X1 = Y2) | (Y0 @ Y2))))) & (sK2 @ Y0)) => (sK2 @ Y1)))))) = $true)) )),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.57/1.38 thf(f53,plain,(
% 1.57/1.38 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => ((Y0 = Y3) | (Y1 @ Y3))))) & (sK2 @ Y1)) => (sK2 @ Y2))))))) @ X1))) )),
% 1.57/1.38 inference(pi_clausification,[status(thm)],[f24])).
% 1.57/1.38 thf(f24,plain,(
% 1.57/1.38 ((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => ((Y0 = Y3) | (Y1 @ Y3))))) & (sK2 @ Y1)) => (sK2 @ Y2)))))))) = $true)),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.57/1.38 thf(f20,plain,(
% 1.57/1.38 (((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => ((Y0 = Y3) | (Y1 @ Y3))))) & (sK2 @ Y1)) => (sK2 @ Y2)))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0))))) = $true)),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.57/1.38 thf(f18,plain,(
% 1.57/1.38 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => ((Y0 = Y3) | (Y1 @ Y3))))) & (sK2 @ Y1)) => (sK2 @ Y2)))))))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0))))) => (sK2 @ cB)))),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.57/1.38 thf(f17,plain,(
% 1.57/1.38 (((^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1))))) => (Y0 @ cB))) @ sK2) = $false)),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f11])).
% 1.57/1.38 thf(f11,plain,(
% 1.57/1.38 ($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1))))) => (Y0 @ cB)))))),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.57/1.38 thf(f8,plain,(
% 1.57/1.38 ($false = (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1))))) => (Y0 @ cB))))))),
% 1.57/1.38 inference(not_proxy_clausification,[status(thm)],[f7])).
% 1.57/1.38 thf(f7,plain,(
% 1.57/1.38 ($true = (~ (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1))))) => (Y0 @ cB)))))))),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.57/1.38 thf(f6,plain,(
% 1.57/1.38 ((~ (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1))))) => (Y0 @ cB)))))) = $true)),
% 1.57/1.38 inference(cnf_transformation,[status(thm)],[f5])).
% 1.57/1.38 thf(f5,plain,(
% 1.57/1.38 ((~ (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))) => (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => ((Y1 = Y4) | (Y2 @ Y4))))) & (Y0 @ Y2)) => (Y0 @ Y3)))))))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ (^[Y2 : a]: (Y1 @ Y2)))) => (Y0 @ Y1))))) => (Y0 @ cB)))))) = $true)),
% 1.57/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.38 thf(f4,plain,(
% 1.57/1.38 ~((! [X0 : (a > $o) > $o] : ((! [X1 : a > $o,X2 : a,X3 : a > $o] : ((! [X4 : a] : ((X3 @ X4) => ((X1 @ X4) | (X2 = X4))) & (X0 @ X1)) => (X0 @ X3)) & ! [X5 : a > $o] : (~? [X6 : a] : (X5 @ X6) => (X0 @ X5))) => (X0 @ cC)) & ! [X7 : a] : ((cB @ X7) => (cC @ X7))) => ! [X8 : (a > $o) > $o] : ((! [X9 : a > $o] : (~? [X10 : a] : (X9 @ X10) => (X8 @ X9)) & ! [X11 : a > $o,X12 : a > $o,X13 : a] : (((X8 @ X12) & ! [X14 : a] : ((X11 @ X14) => ((X12 @ X14) | (X13 = X14)))) => (X8 @ X11))) => (X8 @ cB)))),
% 1.57/1.38 inference(rectify,[status(thm)],[f2])).
% 1.57/1.38 thf(f2,negated_conjecture,(
% 1.57/1.38 ~((! [X0 : (a > $o) > $o] : ((! [X3 : a > $o,X4 : a,X5 : a > $o] : ((! [X6 : a] : ((X5 @ X6) => ((X3 @ X6) | (X4 = X6))) & (X0 @ X3)) => (X0 @ X5)) & ! [X1 : a > $o] : (~? [X2 : a] : (X1 @ X2) => (X0 @ X1))) => (X0 @ cC)) & ! [X4 : a] : ((cB @ X4) => (cC @ X4))) => ! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : (~? [X2 : a] : (X1 @ X2) => (X0 @ X1)) & ! [X5 : a > $o,X3 : a > $o,X4 : a] : (((X0 @ X3) & ! [X7 : a] : ((X5 @ X7) => ((X3 @ X7) | (X4 = X7)))) => (X0 @ X5))) => (X0 @ cB)))),
% 1.57/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.38 thf(f1,conjecture,(
% 1.57/1.38 (! [X0 : (a > $o) > $o] : ((! [X3 : a > $o,X4 : a,X5 : a > $o] : ((! [X6 : a] : ((X5 @ X6) => ((X3 @ X6) | (X4 = X6))) & (X0 @ X3)) => (X0 @ X5)) & ! [X1 : a > $o] : (~? [X2 : a] : (X1 @ X2) => (X0 @ X1))) => (X0 @ cC)) & ! [X4 : a] : ((cB @ X4) => (cC @ X4))) => ! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : (~? [X2 : a] : (X1 @ X2) => (X0 @ X1)) & ! [X5 : a > $o,X3 : a > $o,X4 : a] : (((X0 @ X3) & ! [X7 : a] : ((X5 @ X7) => ((X3 @ X7) | (X4 = X7)))) => (X0 @ X5))) => (X0 @ cB))),
% 1.57/1.38 file('/export/starexec/sandbox/tmp/tmp.33a7r4LH82/DTF2THF_7692.p',cTHM531E_pme)).
% 1.57/1.38 thf(f129,plain,(
% 1.57/1.38 ~spl0_2),
% 1.57/1.38 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.57/1.38 thf(f128,plain,(
% 1.57/1.38 $false | ~spl0_2),
% 1.57/1.38 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.57/1.38 thf(f127,plain,(
% 1.57/1.38 ($false = $true) | ~spl0_2),
% 1.57/1.38 inference(forward_demodulation,[status(thm)],[f126,f121])).
% 1.57/1.38 thf(f121,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($false = (cC @ (sK4 @ X0)))) ) | ~spl0_2),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.57/1.38 thf(f120,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($false = ((X0 = (sK4 @ X0)) | (cC @ (sK4 @ X0))))) ) | ~spl0_2),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f119])).
% 1.57/1.38 thf(f119,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($false = ($true => ((X0 = (sK4 @ X0)) | (cC @ (sK4 @ X0)))))) ) | ~spl0_2),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f107,f118])).
% 1.57/1.38 thf(f118,plain,(
% 1.57/1.38 ( ! [X0 : a] : (((cB @ (sK4 @ X0)) = $true)) ) | ~spl0_2),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.57/1.38 thf(f107,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($false = ((cB @ (sK4 @ X0)) => ((X0 = (sK4 @ X0)) | (cC @ (sK4 @ X0)))))) ) | ~spl0_2),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.57/1.38 thf(f101,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($false = ((^[Y0 : a]: ((cB @ Y0) => ((X0 = Y0) | (cC @ Y0)))) @ (sK4 @ X0)))) ) | ~spl0_2),
% 1.57/1.38 inference(sigma_clausification,[status(thm)],[f88])).
% 1.57/1.38 thf(f88,plain,(
% 1.57/1.38 ( ! [X0 : a] : (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => ((X0 = Y0) | (cC @ Y0))))) = $false)) ) | ~spl0_2),
% 1.57/1.38 inference(not_proxy_clausification,[status(thm)],[f86])).
% 1.57/1.38 thf(f86,plain,(
% 1.57/1.38 ( ! [X0 : a] : (($true = (~ (!! @ a @ (^[Y0 : a]: ((cB @ Y0) => ((X0 = Y0) | (cC @ Y0)))))))) ) | ~spl0_2),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f85])).
% 1.57/1.38 thf(f85,plain,(
% 1.57/1.38 ( ! [X0 : a] : ((((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => ((X0 = Y0) | (cC @ Y0))))) => $false) = $true)) ) | ~spl0_2),
% 1.57/1.38 inference(superposition,[status(thm)],[f79,f22])).
% 1.57/1.38 thf(f22,plain,(
% 1.57/1.38 ($false = (sK2 @ cB))),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f21])).
% 1.57/1.38 thf(f21,plain,(
% 1.57/1.38 ($false = ($true => (sK2 @ cB)))),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f18,f20])).
% 1.57/1.38 thf(f79,plain,(
% 1.57/1.38 ( ! [X0 : a > $o,X1 : a] : ((((!! @ a @ (^[Y0 : a]: ((X0 @ Y0) => ((X1 = Y0) | (cC @ Y0))))) => (sK2 @ X0)) = $true)) ) | ~spl0_2),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f75])).
% 1.57/1.38 thf(f75,plain,(
% 1.57/1.38 ( ! [X0 : a > $o,X1 : a] : (($true = (((!! @ a @ (^[Y0 : a]: ((X0 @ Y0) => ((X1 = Y0) | (cC @ Y0))))) & $true) => (sK2 @ X0)))) ) | ~spl0_2),
% 1.57/1.38 inference(superposition,[status(thm)],[f58,f71])).
% 1.57/1.38 thf(f71,plain,(
% 1.57/1.38 ($true = (sK2 @ cC)) | ~spl0_2),
% 1.57/1.38 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.57/1.38 thf(f70,definition,(
% 1.57/1.38 spl0_2 <=> ($true = (sK2 @ cC))),
% 1.57/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.57/1.38 thf(f126,plain,(
% 1.57/1.38 ( ! [X0 : a] : (((cC @ (sK4 @ X0)) = $true)) ) | ~spl0_2),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f125])).
% 1.57/1.38 thf(f125,plain,(
% 1.57/1.38 ( ! [X0 : a] : ((($true => (cC @ (sK4 @ X0))) = $true)) ) | ~spl0_2),
% 1.57/1.38 inference(superposition,[status(thm)],[f32,f118])).
% 1.57/1.38 thf(f32,plain,(
% 1.57/1.38 ( ! [X1 : a] : ((((cB @ X1) => (cC @ X1)) = $true)) )),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.57/1.38 thf(f31,plain,(
% 1.57/1.38 ( ! [X1 : a] : ((((^[Y0 : a]: ((cB @ Y0) => (cC @ Y0))) @ X1) = $true)) )),
% 1.57/1.38 inference(pi_clausification,[status(thm)],[f30])).
% 1.57/1.38 thf(f30,plain,(
% 1.57/1.38 ($true = (!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))))),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f29])).
% 1.57/1.38 thf(f29,plain,(
% 1.57/1.38 ($true = ((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & $true))),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f12,f27])).
% 1.57/1.38 thf(f27,plain,(
% 1.57/1.38 ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC)))) = $true)),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.57/1.38 thf(f12,plain,(
% 1.57/1.38 (((!! @ a @ (^[Y0 : a]: ((cB @ Y0) => (cC @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))))) = $true)),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.57/1.38 thf(f72,plain,(
% 1.57/1.38 spl0_1 | spl0_2),
% 1.57/1.38 inference(avatar_split_clause,[status(thm)],[f65,f70,f67])).
% 1.57/1.38 thf(f65,plain,(
% 1.57/1.38 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0)))))))) = $false) | ($true = (sK2 @ cC))),
% 1.57/1.38 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.57/1.38 thf(f50,plain,(
% 1.57/1.38 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0)))))))) => (sK2 @ cC)) = $true)),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f49])).
% 1.57/1.38 thf(f49,plain,(
% 1.57/1.38 ((($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (sK2 @ Y0))))))))) => (sK2 @ cC)) = $true)),
% 1.57/1.38 inference(superposition,[status(thm)],[f45,f26])).
% 1.57/1.38 thf(f26,plain,(
% 1.57/1.38 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0)))) = $true)),
% 1.57/1.38 inference(boolean_simplification,[status(thm)],[f25])).
% 1.57/1.38 thf(f25,plain,(
% 1.57/1.38 (($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (sK2 @ Y0))))) = $true)),
% 1.57/1.38 inference(backward_demodulation,[status(thm)],[f20,f24])).
% 1.57/1.38 thf(f45,plain,(
% 1.57/1.38 ( ! [X1 : (a > $o) > $o] : (($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((~ (?? @ a @ Y0)) => (X1 @ Y0)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((X1 @ Y2) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => ((Y1 = Y3) | (Y2 @ Y3)))))) => (X1 @ Y0))))))))) => (X1 @ cC)))) )),
% 1.57/1.38 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.57/1.38 thf(f44,plain,(
% 1.57/1.38 ( ! [X1 : (a > $o) > $o] : (($true = ((^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((~ (?? @ a @ Y1)) => (Y0 @ Y1)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y0 @ Y3) & (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => ((Y2 = Y4) | (Y3 @ Y4)))))) => (Y0 @ Y1))))))))) => (Y0 @ cC))) @ X1))) )),
% 1.57/1.38 inference(pi_clausification,[status(thm)],[f27])).
% 1.57/1.38 % SZS output end Proof for DTF2THF_7692
% 1.57/1.38 % (7801)------------------------------
% 1.57/1.38 % (7801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (7801)Termination reason: Refutation
% 1.57/1.38
% 1.57/1.38 % (7801)Memory used [KB]: 5756
% 1.57/1.38 % (7801)Time elapsed: 0.027 s
% 1.57/1.38 % (7801)Instructions burned: 41 (million)
% 1.57/1.38 % (7801)------------------------------
% 1.57/1.38 % (7801)------------------------------
% 1.57/1.38 % (7789)Success in time 0.067 s
%------------------------------------------------------------------------------