%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV063^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:11 AM UTC 2026
% Result : Theorem 1.21s 1.15s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 114 ( 44 unt; 0 typ; 4 def)
% Number of atoms : 869 ( 104 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 2683 ( 79 ~; 65 |; 174 &;1755 @)
% ( 4 <=>; 237 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 232 ( 232 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 21 con; 0-2 aty)
% ( 369 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 484 ( 390 ^; 94 !; 0 ?; 484 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK2: a ).
thf(func_def_17,type,
sK3: a ).
thf(func_def_18,type,
sK4: a ).
thf(func_def_19,type,
sK5: a > a > $o ).
thf(func_def_20,type,
sK6: a > a > $o ).
thf(func_def_21,type,
sK7: a ).
thf(func_def_22,type,
sK8: a ).
thf(func_def_23,type,
sK9: a ).
thf(func_def_24,type,
sK10: a ).
thf(func_def_25,type,
sK11: a ).
thf(func_def_26,type,
sK12: a ).
thf(func_def_27,type,
sK13: a ).
thf(func_def_28,type,
sK14: a ).
thf(func_def_29,type,
sK15: a ).
thf(func_def_30,type,
sK16: a ).
thf(func_def_31,type,
sK17: a ).
thf(f414,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f80,f184,f201,f274,f413]) ).
thf(f413,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f412]) ).
thf(f412,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f411]) ).
thf(f411,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f410]) ).
thf(f410,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f403,f317]) ).
thf(f317,plain,
( ( ( sK6 @ sK13 @ sK15 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f311]) ).
thf(f311,plain,
( ( $true
= ( ( sK6 @ sK13 @ sK15 )
& ( sK6 @ sK15 @ sK12 ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f307]) ).
thf(f307,plain,
( ( $false
= ( ~ ( ( sK6 @ sK13 @ sK15 )
& ( sK6 @ sK15 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f306]) ).
thf(f306,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f293]) ).
thf(f293,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f291]) ).
thf(f291,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
=> $false ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f285,f288]) ).
thf(f288,plain,
( ( $false
= ( sK6 @ sK13 @ sK12 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f287]) ).
thf(f287,plain,
( ( ( ( ( sK6 @ sK13 @ sK14 )
& ( sK6 @ sK14 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f285]) ).
thf(f285,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f284]) ).
thf(f284,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK12 ) )
=> ( sK6 @ Y0 @ sK12 ) ) )
@ sK13 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f281]) ).
thf(f281,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK12 ) )
=> ( sK6 @ Y0 @ sK12 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f279]) ).
thf(f279,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f403,plain,
( ( $true
= ( ~ ( sK6 @ sK13 @ sK15 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f399]) ).
thf(f399,plain,
( ( ( ( sK6 @ sK13 @ sK15 )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f325,f288]) ).
thf(f325,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 @ sK15 )
=> ( sK6 @ X0 @ sK12 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f320]) ).
thf(f320,plain,
( ! [X0: a] :
( ( ( $true
& ( sK6 @ X0 @ sK15 ) )
=> ( sK6 @ X0 @ sK12 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f63,f319]) ).
thf(f319,plain,
( ( ( sK6 @ sK15 @ sK12 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f318]) ).
thf(f318,plain,
( ( ( $true
& ( sK6 @ sK15 @ sK12 ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f311,f317]) ).
thf(f63,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X2 @ X3 )
& ( sK6 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( X0 @ X6 @ X5 )
=> ( X4 @ X6 @ X5 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X8 )
& ( X4 @ X7 @ X9 ) )
=> ( X4 @ X7 @ X8 ) ) )
=> ( X4 @ X1 @ X3 ) )
& ! [X10: a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ( X10 @ X11 @ X13 )
& ( X10 @ X12 @ X11 ) )
=> ( X10 @ X12 @ X13 ) )
& ! [X14: a,X15: a] :
( ( X0 @ X14 @ X15 )
=> ( X10 @ X14 @ X15 ) ) )
=> ( X10 @ X3 @ X2 ) ) )
=> ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a,X19: a] :
( ( ( X16 @ X19 @ X18 )
& ( X16 @ X18 @ X17 ) )
=> ( X16 @ X19 @ X17 ) )
& ! [X20: a,X21: a] :
( ( X0 @ X20 @ X21 )
=> ( X16 @ X20 @ X21 ) ) )
=> ( X16 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a,X3: a,X2: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a,X3: a,X2: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KAFYM5Bwd8/DTF2THF_2338.p',cTHM136_pme) ).
thf(f274,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f273]) ).
thf(f273,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f271]) ).
thf(f271,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f263,f237]) ).
thf(f237,plain,
( ( $true
= ( sK6 @ sK11 @ sK9 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
( ( ( ( sK6 @ sK11 @ sK9 )
& ( sK6 @ sK9 @ sK10 ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $false
= ( ( ( sK6 @ sK11 @ sK9 )
& ( sK6 @ sK9 @ sK10 ) )
=> ( sK6 @ sK11 @ sK10 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f215]) ).
thf(f215,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK9 )
& ( sK6 @ sK9 @ sK10 ) )
=> ( sK6 @ Y0 @ sK10 ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK9 )
& ( sK6 @ sK9 @ sK10 ) )
=> ( sK6 @ Y0 @ sK10 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK9 )
& ( sK6 @ sK9 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK9 )
& ( sK6 @ sK9 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f208]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ sK9 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f182]) ).
thf(f182,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f263,plain,
( ( ( ~ ( sK6 @ sK11 @ sK9 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( ( ~ ( $true
& ( sK6 @ sK11 @ sK9 ) ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f230,f239]) ).
thf(f239,plain,
( ( $true
= ( sK6 @ sK9 @ sK10 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true
= ( $true
& ( sK6 @ sK9 @ sK10 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f218,f237]) ).
thf(f230,plain,
( ! [X0: a] :
( ( ~ ( ( sK6 @ X0 @ sK10 )
& ( sK6 @ sK11 @ X0 ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f223]) ).
thf(f223,plain,
( ! [X0: a] :
( $true
= ( ( ( sK6 @ X0 @ sK10 )
& ( sK6 @ sK11 @ X0 ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f63,f220]) ).
thf(f220,plain,
( ( $false
= ( sK6 @ sK11 @ sK10 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( $false
= ( $true
=> ( sK6 @ sK11 @ sK10 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f216,f218]) ).
thf(f201,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f200]) ).
thf(f200,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f196]) ).
thf(f196,plain,
( ( $false = $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f193,f43]) ).
thf(f43,plain,
! [X2: a,X1: a] :
( ( ( sK5 @ X2 @ X1 )
=> ( sK6 @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK5 @ Y0 @ X1 )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 @ X1 )
=> ( sK6 @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f27,f30]) ).
thf(f193,plain,
( ( ( ( sK5 @ sK7 @ sK8 )
=> ( sK6 @ sK7 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK6 @ sK7 @ Y0 ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK6 @ sK7 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f179,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f184,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f175,f78,f182,f179]) ).
thf(f78,definition,
( spl0_2
<=> ( ( sK6 @ sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f175,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f51,f112]) ).
thf(f112,plain,
( ( $false
= ( sK6 @ sK4 @ sK2 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true
= ( ~ ( sK6 @ sK4 @ sK2 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ( sK6 @ sK4 @ sK2 )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f91,f29]) ).
thf(f29,plain,
( ( sK6 @ sK4 @ sK3 )
= $false ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
= ( $true
=> ( sK6 @ sK4 @ sK3 ) ) ),
inference(backward_demodulation,[status(thm)],[f25,f27]) ).
thf(f91,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ X0 @ sK2 )
=> ( sK6 @ X0 @ sK3 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: a] :
( ( ( $true
& ( sK6 @ X0 @ sK2 ) )
=> ( sK6 @ X0 @ sK3 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f63,f79]) ).
thf(f79,plain,
( ( ( sK6 @ sK2 @ sK3 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f51,plain,
! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f80,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f73,f78,f75]) ).
thf(f73,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( sK6 @ sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK2 @ sK3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f41,f33]) ).
thf(f41,plain,
! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f19,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV063^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:45:59 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEV063^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory (Relations)
% 0.15/0.42 % Problem : TPS problem THM136
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English : The transitive closure of a relation is transitive.
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0372 [Bro09]
% 0.15/0.42 % : THM136 [TPS]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.15/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.15/0.42 % Number of connectives : 53 ( 0 ~; 0 |; 7 &; 36 @)
% 0.15/0.42 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 17 ( 17 avg)
% 0.15/0.42 % Number of types : 2 ( 1 usr)
% 0.15/0.42 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.15/0.42 % Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% 0.15/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 % : Polymorphic definitions expanded.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(a_type,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(cTHM136_pme,conjecture,
% 0.15/0.42 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 0.15/0.42 ( ( ! [Xp: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( Xr @ Xx0 @ Xy0 )
% 0.15/0.42 => ( Xp @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.15/0.42 & ( Xp @ Xy0 @ Xz0 ) )
% 0.15/0.42 => ( Xp @ Xx0 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp @ Xx @ Xy ) )
% 0.15/0.42 & ! [Xp: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( Xr @ Xx0 @ Xy0 )
% 0.15/0.42 => ( Xp @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.15/0.42 & ( Xp @ Xy0 @ Xz0 ) )
% 0.15/0.42 => ( Xp @ Xx0 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp @ Xy @ Xz ) ) )
% 0.15/0.42 => ! [Xp: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( Xr @ Xx0 @ Xy0 )
% 0.15/0.42 => ( Xp @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp @ Xx0 @ Xy0 )
% 0.15/0.42 & ( Xp @ Xy0 @ Xz0 ) )
% 0.15/0.42 => ( Xp @ Xx0 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp @ Xx @ Xz ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.12/1.06 ---- Embedded in THF ---
% 1.12/1.06 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.06 %%% Generated on Tue Feb 24 12:46:00 EST 2026
% 1.12/1.06 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.06 %%% Logic specification used:
% 1.12/1.06 %%% thf(spec, logic, $$dhol).
% 1.12/1.06
% 1.12/1.06 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KAFYM5Bwd8/DTF2DTF2338.p
% See solution above
% 1.12/1.06 ------------------------
% 1.12/1.06 ---- Cleaned THF ---
% 1.12/1.07 thf(a_type,type,
% 1.12/1.07 a: $tType ).
% 1.12/1.07
% 1.12/1.07 thf(cTHM136_pme,conjecture,
% 1.12/1.07 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 1.12/1.07 ( ( ! [Xp: a > a > $o] :
% 1.12/1.07 ( ( ! [Xx0: a,Xy0: a] :
% 1.12/1.07 ( ( Xr @ Xx0 @ Xy0 )
% 1.12/1.07 => ( Xp @ Xx0 @ Xy0 ) )
% 1.12/1.07 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.12/1.07 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.12/1.07 & ( Xp @ Xy0 @ Xz0 ) )
% 1.12/1.07 => ( Xp @ Xx0 @ Xz0 ) ) )
% 1.12/1.07 => ( Xp @ Xx @ Xy ) )
% 1.12/1.07 & ! [Xp: a > a > $o] :
% 1.12/1.07 ( ( ! [Xx0: a,Xy0: a] :
% 1.12/1.07 ( ( Xr @ Xx0 @ Xy0 )
% 1.12/1.07 => ( Xp @ Xx0 @ Xy0 ) )
% 1.12/1.07 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.12/1.07 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.12/1.07 & ( Xp @ Xy0 @ Xz0 ) )
% 1.12/1.07 => ( Xp @ Xx0 @ Xz0 ) ) )
% 1.12/1.07 => ( Xp @ Xy @ Xz ) ) )
% 1.12/1.07 => ! [Xp: a > a > $o] :
% 1.12/1.07 ( ( ! [Xx0: a,Xy0: a] :
% 1.12/1.07 ( ( Xr @ Xx0 @ Xy0 )
% 1.12/1.07 => ( Xp @ Xx0 @ Xy0 ) )
% 1.12/1.07 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.12/1.07 ( ( ( Xp @ Xx0 @ Xy0 )
% 1.12/1.07 & ( Xp @ Xy0 @ Xz0 ) )
% 1.12/1.07 => ( Xp @ Xx0 @ Xz0 ) ) )
% 1.12/1.07 => ( Xp @ Xx @ Xz ) ) ) ).
% 1.12/1.07 ------------------------
% 1.12/1.08 % (2541)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2338 for (3000ds/2Mi)
% 1.12/1.08 % (2539)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_2338 for (3000ds/4Mi)
% 1.12/1.08 % (2538)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2338 for (3000ds/183Mi)
% 1.12/1.08 % (2541)Instruction limit reached!
% 1.12/1.08 % (2541)------------------------------
% 1.12/1.08 % (2541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.08 % (2541)Termination reason: Unknown
% 1.12/1.08 % (2541)Termination phase: Preprocessing 3
% 1.12/1.08
% 1.12/1.08 % (2541)Memory used [KB]: 1023
% 1.12/1.08 % (2541)Time elapsed: 0.002 s
% 1.12/1.08 % (2541)Instructions burned: 2 (million)
% 1.12/1.08 % (2541)------------------------------
% 1.12/1.08 % (2541)------------------------------
% 1.12/1.08 % (2539)Instruction limit reached!
% 1.12/1.08 % (2539)------------------------------
% 1.12/1.08 % (2539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.08 % (2539)Termination reason: Unknown
% 1.12/1.08 % (2539)Termination phase: Saturation
% 1.12/1.08
% 1.12/1.08 % (2539)Memory used [KB]: 5500
% 1.12/1.08 % (2539)Time elapsed: 0.003 s
% 1.12/1.08 % (2539)Instructions burned: 4 (million)
% 1.12/1.08 % (2539)------------------------------
% 1.12/1.08 % (2539)------------------------------
% 1.12/1.09 % (2540)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_2338 for (3000ds/27Mi)
% 1.12/1.09 % (2542)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_2338 for (3000ds/2Mi)
% 1.12/1.09 % (2543)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_2338 for (3000ds/275Mi)
% 1.12/1.09 % (2544)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2338 for (3000ds/18Mi)
% 1.12/1.09 % (2542)Instruction limit reached!
% 1.12/1.09 % (2542)------------------------------
% 1.12/1.09 % (2542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.09 % (2542)Termination reason: Unknown
% 1.12/1.09 % (2542)Termination phase: shuffling
% 1.12/1.09
% 1.12/1.09 % (2542)Memory used [KB]: 1023
% 1.12/1.09 % (2542)Time elapsed: 0.003 s
% 1.12/1.09 % (2542)Instructions burned: 2 (million)
% 1.12/1.09 % (2542)------------------------------
% 1.12/1.09 % (2542)------------------------------
% 1.12/1.09 % (2551)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/3Mi)
% 1.12/1.09 % (2553)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_2338 for (2999ds/37Mi)
% 1.12/1.09 % (2551)Instruction limit reached!
% 1.12/1.09 % (2551)------------------------------
% 1.12/1.09 % (2551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.09 % (2551)Termination reason: Unknown
% 1.12/1.09 % (2551)Termination phase: Saturation
% 1.12/1.09
% 1.12/1.09 % (2551)Memory used [KB]: 5500
% 1.12/1.09 % (2551)Time elapsed: 0.002 s
% 1.12/1.09 % (2551)Instructions burned: 4 (million)
% 1.12/1.09 % (2551)------------------------------
% 1.12/1.09 % (2551)------------------------------
% 1.12/1.10 % (2544)Instruction limit reached!
% 1.12/1.10 % (2544)------------------------------
% 1.12/1.10 % (2544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (2544)Termination reason: Unknown
% 1.12/1.10 % (2544)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (2544)Memory used [KB]: 5628
% 1.12/1.10 % (2544)Time elapsed: 0.013 s
% 1.12/1.10 % (2544)Instructions burned: 18 (million)
% 1.12/1.10 % (2544)------------------------------
% 1.12/1.10 % (2544)------------------------------
% 1.12/1.10 % (2562)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_2338 for (2999ds/3Mi)
% 1.12/1.10 % (2562)Instruction limit reached!
% 1.12/1.10 % (2562)------------------------------
% 1.12/1.10 % (2562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (2562)Termination reason: Unknown
% 1.12/1.10 % (2562)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (2562)Memory used [KB]: 5500
% 1.12/1.10 % (2562)Time elapsed: 0.003 s
% 1.12/1.10 % (2562)Instructions burned: 5 (million)
% 1.12/1.10 % (2562)------------------------------
% 1.12/1.10 % (2562)------------------------------
% 1.12/1.10 % (2553)Instruction limit reached!
% 1.12/1.10 % (2553)------------------------------
% 1.12/1.10 % (2553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (2553)Termination reason: Unknown
% 1.12/1.10 % (2553)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (2553)Memory used [KB]: 5756
% 1.12/1.10 % (2553)Time elapsed: 0.013 s
% 1.12/1.10 % (2553)Instructions burned: 39 (million)
% 1.12/1.10 % (2553)------------------------------
% 1.12/1.10 % (2553)------------------------------
% 1.12/1.10 % (2540)Instruction limit reached!
% 1.12/1.10 % (2540)------------------------------
% 1.12/1.10 % (2540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (2540)Termination reason: Unknown
% 1.12/1.10 % (2540)Termination phase: Saturation
% 1.12/1.10
% 1.12/1.10 % (2540)Memory used [KB]: 5756
% 1.12/1.10 % (2540)Time elapsed: 0.020 s
% 1.12/1.10 % (2540)Instructions burned: 28 (million)
% 1.12/1.10 % (2540)------------------------------
% 1.12/1.10 % (2540)------------------------------
% 1.12/1.10 % (2559)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_2338 for (2999ds/15Mi)
% 1.12/1.11 % (2564)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/7Mi)
% 1.12/1.11 % (2565)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/16Mi)
% 1.12/1.11 % (2559)Instruction limit reached!
% 1.12/1.11 % (2559)------------------------------
% 1.12/1.11 % (2559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.11 % (2559)Termination reason: Unknown
% 1.12/1.11 % (2559)Termination phase: Saturation
% 1.12/1.11
% 1.12/1.11 % (2559)Memory used [KB]: 5756
% 1.12/1.11 % (2559)Time elapsed: 0.010 s
% 1.12/1.11 % (2559)Instructions burned: 16 (million)
% 1.12/1.11 % (2559)------------------------------
% 1.12/1.11 % (2559)------------------------------
% 1.12/1.11 % (2564)Instruction limit reached!
% 1.12/1.11 % (2564)------------------------------
% 1.12/1.11 % (2564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.11 % (2564)Termination reason: Unknown
% 1.12/1.11 % (2564)Termination phase: Saturation
% 1.12/1.11
% 1.12/1.11 % (2564)Memory used [KB]: 1023
% 1.12/1.11 % (2564)Time elapsed: 0.004 s
% 1.12/1.11 % (2564)Instructions burned: 9 (million)
% 1.12/1.11 % (2564)------------------------------
% 1.12/1.11 % (2564)------------------------------
% 1.12/1.11 % (2563)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_2338 for (2999ds/1041Mi)
% 1.12/1.11 % (2565)Instruction limit reached!
% 1.12/1.11 % (2565)------------------------------
% 1.12/1.11 % (2565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.11 % (2565)Termination reason: Unknown
% 1.12/1.11 % (2565)Termination phase: Saturation
% 1.12/1.11
% 1.12/1.11 % (2565)Memory used [KB]: 5628
% 1.12/1.11 % (2565)Time elapsed: 0.006 s
% 1.12/1.11 % (2565)Instructions burned: 16 (million)
% 1.12/1.11 % (2565)------------------------------
% 1.12/1.11 % (2565)------------------------------
% 1.12/1.12 % (2567)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_2338 for (2999ds/3Mi)
% 1.12/1.12 % (2567)Instruction limit reached!
% 1.12/1.12 % (2567)------------------------------
% 1.12/1.12 % (2567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.12 % (2567)Termination reason: Unknown
% 1.12/1.12 % (2567)Termination phase: Twee Goal Transformation
% 1.12/1.12
% 1.12/1.12 % (2567)Memory used [KB]: 1023
% 1.12/1.12 % (2567)Time elapsed: 0.003 s
% 1.12/1.12 % (2567)Instructions burned: 6 (million)
% 1.12/1.12 % (2567)------------------------------
% 1.12/1.12 % (2567)------------------------------
% 1.12/1.12 % (2578)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/7Mi)
% 1.12/1.12 % (2577)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_2338 for (2999ds/3Mi)
% 1.12/1.12 % (2577)Instruction limit reached!
% 1.12/1.12 % (2577)------------------------------
% 1.12/1.12 % (2577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.12 % (2577)Termination reason: Unknown
% 1.12/1.12 % (2577)Termination phase: Saturation
% 1.12/1.12
% 1.12/1.12 % (2577)Memory used [KB]: 1023
% 1.12/1.12 % (2577)Time elapsed: 0.003 s
% 1.12/1.12 % (2577)Instructions burned: 5 (million)
% 1.12/1.12 % (2577)------------------------------
% 1.12/1.12 % (2577)------------------------------
% 1.12/1.12 % (2580)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/3Mi)
% 1.21/1.12 % (2578)Instruction limit reached!
% 1.21/1.12 % (2578)------------------------------
% 1.21/1.12 % (2578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.12 % (2578)Termination reason: Unknown
% 1.21/1.12 % (2578)Termination phase: Saturation
% 1.21/1.12
% 1.21/1.12 % (2578)Memory used [KB]: 5500
% 1.21/1.12 % (2578)Time elapsed: 0.004 s
% 1.21/1.12 % (2578)Instructions burned: 9 (million)
% 1.21/1.12 % (2578)------------------------------
% 1.21/1.12 % (2578)------------------------------
% 1.21/1.13 % (2580)Instruction limit reached!
% 1.21/1.13 % (2580)------------------------------
% 1.21/1.13 % (2580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.13 % (2580)Termination reason: Unknown
% 1.21/1.13 % (2580)Termination phase: Property scanning
% 1.21/1.13
% 1.21/1.13 % (2580)Memory used [KB]: 1023
% 1.21/1.13 % (2580)Time elapsed: 0.002 s
% 1.21/1.13 % (2580)Instructions burned: 3 (million)
% 1.21/1.13 % (2580)------------------------------
% 1.21/1.13 % (2580)------------------------------
% 1.21/1.13 % (2585)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/4Mi)
% 1.21/1.13 % (2538)Instruction limit reached!
% 1.21/1.13 % (2538)------------------------------
% 1.21/1.13 % (2538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.13 % (2538)Termination reason: Unknown
% 1.21/1.13 % (2538)Termination phase: Saturation
% 1.21/1.13
% 1.21/1.13 % (2538)Memory used [KB]: 6396
% 1.21/1.13 % (2538)Time elapsed: 0.053 s
% 1.21/1.13 % (2538)Instructions burned: 184 (million)
% 1.21/1.13 % (2538)------------------------------
% 1.21/1.13 % (2538)------------------------------
% 1.21/1.13 % (2585)Instruction limit reached!
% 1.21/1.13 % (2585)------------------------------
% 1.21/1.13 % (2585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.13 % (2585)Termination reason: Unknown
% 1.21/1.13 % (2585)Termination phase: Saturation
% 1.21/1.13
% 1.21/1.13 % (2585)Memory used [KB]: 5500
% 1.21/1.13 % (2585)Time elapsed: 0.003 s
% 1.21/1.13 % (2585)Instructions burned: 6 (million)
% 1.21/1.13 % (2585)------------------------------
% 1.21/1.13 % (2585)------------------------------
% 1.21/1.13 % (2586)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/18Mi)
% 1.21/1.13 % (2587)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/710Mi)
% 1.21/1.13 % (2588)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/6Mi)
% 1.21/1.14 % (2588)Instruction limit reached!
% 1.21/1.14 % (2588)------------------------------
% 1.21/1.14 % (2588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.14 % (2588)Termination reason: Unknown
% 1.21/1.14 % (2588)Termination phase: Saturation
% 1.21/1.14
% 1.21/1.14 % (2588)Memory used [KB]: 5500
% 1.21/1.14 % (2588)Time elapsed: 0.003 s
% 1.21/1.14 % (2588)Instructions burned: 7 (million)
% 1.21/1.14 % (2588)------------------------------
% 1.21/1.14 % (2588)------------------------------
% 1.21/1.14 % (2590)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_2338 for (2999ds/902Mi)
% 1.21/1.14 % (2591)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_2338 for (2999ds/21Mi)
% 1.21/1.14 % (2586)Instruction limit reached!
% 1.21/1.14 % (2586)------------------------------
% 1.21/1.14 % (2586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.14 % (2586)Termination reason: Unknown
% 1.21/1.14 % (2586)Termination phase: Saturation
% 1.21/1.14
% 1.21/1.14 % (2586)Memory used [KB]: 5628
% 1.21/1.14 % (2586)Time elapsed: 0.007 s
% 1.21/1.14 % (2586)Instructions burned: 18 (million)
% 1.21/1.14 % (2586)------------------------------
% 1.21/1.14 % (2586)------------------------------
% 1.21/1.14 % (2563)First to succeed.
% 1.21/1.15 % (2594)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2338 for (2999ds/5Mi)
% 1.21/1.15 % (2543)Also succeeded, but the first one will report.
% 1.21/1.15 % (2563)Refutation found. Thanks to Tanya!
% 1.21/1.15 % SZS status Theorem for DTF2THF_2338
% 1.21/1.15 % SZS output start Proof for DTF2THF_2338
% 1.21/1.15 thf(type_def_5, type, a: $tType).
% 1.21/1.15 thf(func_def_0, type, a: $tType).
% 1.21/1.15 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.21/1.15 thf(func_def_16, type, sK2: a).
% 1.21/1.15 thf(func_def_17, type, sK3: a).
% 1.21/1.15 thf(func_def_18, type, sK4: a).
% 1.21/1.15 thf(func_def_19, type, sK5: a > a > $o).
% 1.21/1.15 thf(func_def_20, type, sK6: a > a > $o).
% 1.21/1.15 thf(func_def_21, type, sK7: a).
% 1.21/1.15 thf(func_def_22, type, sK8: a).
% 1.21/1.15 thf(func_def_23, type, sK9: a).
% 1.21/1.15 thf(func_def_24, type, sK10: a).
% 1.21/1.15 thf(func_def_25, type, sK11: a).
% 1.21/1.15 thf(func_def_26, type, sK12: a).
% 1.21/1.15 thf(func_def_27, type, sK13: a).
% 1.21/1.15 thf(func_def_28, type, sK14: a).
% 1.21/1.15 thf(func_def_29, type, sK15: a).
% 1.21/1.15 thf(func_def_30, type, sK16: a).
% 1.21/1.15 thf(func_def_31, type, sK17: a).
% 1.21/1.15 thf(f414,plain,(
% 1.21/1.15 $false),
% 1.21/1.15 inference(avatar_sat_refutation,[status(thm)],[f80,f184,f201,f274,f413])).
% 1.21/1.15 thf(f413,plain,(
% 1.21/1.15 ~spl0_1),
% 1.21/1.15 inference(avatar_contradiction_clause,[status(thm)],[f412])).
% 1.21/1.15 thf(f412,plain,(
% 1.21/1.15 $false | ~spl0_1),
% 1.21/1.15 inference(trivial_inequality_removal,[status(thm)],[f411])).
% 1.21/1.15 thf(f411,plain,(
% 1.21/1.15 ($false = $true) | ~spl0_1),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f410])).
% 1.21/1.15 thf(f410,plain,(
% 1.21/1.15 ((~ $true) = $true) | ~spl0_1),
% 1.21/1.15 inference(forward_demodulation,[status(thm)],[f403,f317])).
% 1.21/1.15 thf(f317,plain,(
% 1.21/1.15 ((sK6 @ sK13 @ sK15) = $true) | ~spl0_1),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f311])).
% 1.21/1.15 thf(f311,plain,(
% 1.21/1.15 ($true = ((sK6 @ sK13 @ sK15) & (sK6 @ sK15 @ sK12))) | ~spl0_1),
% 1.21/1.15 inference(not_proxy_clausification,[status(thm)],[f307])).
% 1.21/1.15 thf(f307,plain,(
% 1.21/1.15 ($false = (~ ((sK6 @ sK13 @ sK15) & (sK6 @ sK15 @ sK12)))) | ~spl0_1),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f306])).
% 1.21/1.15 thf(f306,plain,(
% 1.21/1.15 (((^[Y0 : a]: (~ ((sK6 @ sK13 @ Y0) & (sK6 @ Y0 @ sK12)))) @ sK15) = $false) | ~spl0_1),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f293])).
% 1.21/1.15 thf(f293,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK6 @ sK13 @ Y0) & (sK6 @ Y0 @ sK12)))))) | ~spl0_1),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f291])).
% 1.21/1.15 thf(f291,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK13 @ Y0) & (sK6 @ Y0 @ sK12)) => $false)))) | ~spl0_1),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f285,f288])).
% 1.21/1.15 thf(f288,plain,(
% 1.21/1.15 ($false = (sK6 @ sK13 @ sK12)) | ~spl0_1),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f287])).
% 1.21/1.15 thf(f287,plain,(
% 1.21/1.15 ((((sK6 @ sK13 @ sK14) & (sK6 @ sK14 @ sK12)) => (sK6 @ sK13 @ sK12)) = $false) | ~spl0_1),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f286])).
% 1.21/1.15 thf(f286,plain,(
% 1.21/1.15 (((^[Y0 : a]: (((sK6 @ sK13 @ Y0) & (sK6 @ Y0 @ sK12)) => (sK6 @ sK13 @ sK12))) @ sK14) = $false) | ~spl0_1),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f285])).
% 1.21/1.15 thf(f285,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK13 @ Y0) & (sK6 @ Y0 @ sK12)) => (sK6 @ sK13 @ sK12))))) | ~spl0_1),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f284])).
% 1.21/1.15 thf(f284,plain,(
% 1.21/1.15 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ sK12)) => (sK6 @ Y0 @ sK12))))) @ sK13) = $false) | ~spl0_1),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f281])).
% 1.21/1.15 thf(f281,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ sK12)) => (sK6 @ Y0 @ sK12))))))) | ~spl0_1),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f279])).
% 1.21/1.15 thf(f279,plain,(
% 1.21/1.15 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))) @ sK12) = $false) | ~spl0_1),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f76])).
% 1.21/1.15 thf(f76,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false) | ~spl0_1),
% 1.21/1.15 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.21/1.15 thf(f75,definition,(
% 1.21/1.15 spl0_1 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false)),
% 1.21/1.15 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.21/1.15 thf(f403,plain,(
% 1.21/1.15 ($true = (~ (sK6 @ sK13 @ sK15))) | ~spl0_1),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f399])).
% 1.21/1.15 thf(f399,plain,(
% 1.21/1.15 (((sK6 @ sK13 @ sK15) => $false) = $true) | ~spl0_1),
% 1.21/1.15 inference(superposition,[status(thm)],[f325,f288])).
% 1.21/1.15 thf(f325,plain,(
% 1.21/1.15 ( ! [X0 : a] : ((((sK6 @ X0 @ sK15) => (sK6 @ X0 @ sK12)) = $true)) ) | ~spl0_1),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f320])).
% 1.21/1.15 thf(f320,plain,(
% 1.21/1.15 ( ! [X0 : a] : (((($true & (sK6 @ X0 @ sK15)) => (sK6 @ X0 @ sK12)) = $true)) ) | ~spl0_1),
% 1.21/1.15 inference(superposition,[status(thm)],[f63,f319])).
% 1.21/1.15 thf(f319,plain,(
% 1.21/1.15 ((sK6 @ sK15 @ sK12) = $true) | ~spl0_1),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f318])).
% 1.21/1.15 thf(f318,plain,(
% 1.21/1.15 (($true & (sK6 @ sK15 @ sK12)) = $true) | ~spl0_1),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f311,f317])).
% 1.21/1.15 thf(f63,plain,(
% 1.21/1.15 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK6 @ X2 @ X3) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ X3)) = $true)) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.21/1.15 thf(f62,plain,(
% 1.21/1.15 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ Y0))) @ X3) = $true)) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f61])).
% 1.21/1.15 thf(f61,plain,(
% 1.21/1.15 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ Y0)))))) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.21/1.15 thf(f60,plain,(
% 1.21/1.15 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ X1 @ Y0)) => (sK6 @ X1 @ Y1))))) @ X2) = $true)) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f59])).
% 1.21/1.15 thf(f59,plain,(
% 1.21/1.15 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ X1 @ Y0)) => (sK6 @ X1 @ Y1)))))) = $true)) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.21/1.15 thf(f58,plain,(
% 1.21/1.15 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))) @ X1))) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f30])).
% 1.21/1.15 thf(f30,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $true)),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.21/1.15 thf(f27,plain,(
% 1.21/1.15 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))))) = $true)),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.21/1.15 thf(f25,plain,(
% 1.21/1.15 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))))) => (sK6 @ sK4 @ sK3)) = $false)),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.21/1.15 thf(f24,plain,(
% 1.21/1.15 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK4 @ sK3))) @ sK6) = $false)),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f18])).
% 1.21/1.15 thf(f18,plain,(
% 1.21/1.15 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK4 @ sK3)))))),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.21/1.15 thf(f17,plain,(
% 1.21/1.15 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK4 @ sK3))))))),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.21/1.15 thf(f16,plain,(
% 1.21/1.15 (((^[Y0 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK4 @ sK3)))))) @ sK5) = $false)),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f15])).
% 1.21/1.15 thf(f15,plain,(
% 1.21/1.15 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK4 @ sK3))))))))),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.21/1.15 thf(f14,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ sK3)))))))) @ sK4))),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f13])).
% 1.21/1.15 thf(f13,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ sK3))))))))) = $false)),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.21/1.15 thf(f12,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ sK2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK3))),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f11])).
% 1.21/1.15 thf(f11,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ sK2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ sK2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y0))))))))))))),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.21/1.15 thf(f10,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y1)))))))))))) @ sK2))),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f7])).
% 1.21/1.15 thf(f7,plain,(
% 1.21/1.15 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y1))))))))))))))),
% 1.21/1.15 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.21/1.15 thf(f6,plain,(
% 1.21/1.15 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y1)))))))))))))))),
% 1.21/1.15 inference(cnf_transformation,[status(thm)],[f5])).
% 1.21/1.15 thf(f5,plain,(
% 1.21/1.15 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y1)))))))))))))))),
% 1.21/1.15 inference(fool_elimination,[status(thm)],[f4])).
% 1.21/1.15 thf(f4,plain,(
% 1.21/1.15 ~! [X0 : a > a > $o,X1 : a,X2 : a,X3 : a] : ((! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((X0 @ X6 @ X5) => (X4 @ X6 @ X5)) & ! [X7 : a,X8 : a,X9 : a] : (((X4 @ X9 @ X8) & (X4 @ X7 @ X9)) => (X4 @ X7 @ X8))) => (X4 @ X1 @ X3)) & ! [X10 : a > a > $o] : ((! [X11 : a,X12 : a,X13 : a] : (((X10 @ X11 @ X13) & (X10 @ X12 @ X11)) => (X10 @ X12 @ X13)) & ! [X14 : a,X15 : a] : ((X0 @ X14 @ X15) => (X10 @ X14 @ X15))) => (X10 @ X3 @ X2))) => ! [X16 : a > a > $o] : ((! [X17 : a,X18 : a,X19 : a] : (((X16 @ X19 @ X18) & (X16 @ X18 @ X17)) => (X16 @ X19 @ X17)) & ! [X20 : a,X21 : a] : ((X0 @ X20 @ X21) => (X16 @ X20 @ X21))) => (X16 @ X1 @ X2)))),
% 1.21/1.15 inference(rectify,[status(thm)],[f2])).
% 1.21/1.15 thf(f2,negated_conjecture,(
% 1.21/1.15 ~! [X0 : a > a > $o,X1 : a,X3 : a,X2 : a] : ((! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6)) & ! [X5 : a,X7 : a,X6 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2)) & ! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))) => ! [X4 : a > a > $o] : ((! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6))) => (X4 @ X1 @ X3)))),
% 1.21/1.15 inference(negated_conjecture,[status(cth)],[f1])).
% 1.21/1.15 thf(f1,conjecture,(
% 1.21/1.15 ! [X0 : a > a > $o,X1 : a,X3 : a,X2 : a] : ((! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6)) & ! [X5 : a,X7 : a,X6 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2)) & ! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))) => ! [X4 : a > a > $o] : ((! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X4 @ X5 @ X6))) => (X4 @ X1 @ X3)))),
% 1.21/1.15 file('/export/starexec/sandbox2/tmp/tmp.KAFYM5Bwd8/DTF2THF_2338.p',cTHM136_pme)).
% 1.21/1.15 thf(f274,plain,(
% 1.21/1.15 ~spl0_4),
% 1.21/1.15 inference(avatar_contradiction_clause,[status(thm)],[f273])).
% 1.21/1.15 thf(f273,plain,(
% 1.21/1.15 $false | ~spl0_4),
% 1.21/1.15 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.21/1.15 thf(f272,plain,(
% 1.21/1.15 ($false = $true) | ~spl0_4),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f271])).
% 1.21/1.15 thf(f271,plain,(
% 1.21/1.15 ((~ $true) = $true) | ~spl0_4),
% 1.21/1.15 inference(forward_demodulation,[status(thm)],[f263,f237])).
% 1.21/1.15 thf(f237,plain,(
% 1.21/1.15 ($true = (sK6 @ sK11 @ sK9)) | ~spl0_4),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f218])).
% 1.21/1.15 thf(f218,plain,(
% 1.21/1.15 (((sK6 @ sK11 @ sK9) & (sK6 @ sK9 @ sK10)) = $true) | ~spl0_4),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f216])).
% 1.21/1.15 thf(f216,plain,(
% 1.21/1.15 ($false = (((sK6 @ sK11 @ sK9) & (sK6 @ sK9 @ sK10)) => (sK6 @ sK11 @ sK10))) | ~spl0_4),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f215])).
% 1.21/1.15 thf(f215,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: (((sK6 @ Y0 @ sK9) & (sK6 @ sK9 @ sK10)) => (sK6 @ Y0 @ sK10))) @ sK11)) | ~spl0_4),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f214])).
% 1.21/1.15 thf(f214,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK9) & (sK6 @ sK9 @ sK10)) => (sK6 @ Y0 @ sK10)))) = $false) | ~spl0_4),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f213])).
% 1.21/1.15 thf(f213,plain,(
% 1.21/1.15 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK9) & (sK6 @ sK9 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK10) = $false) | ~spl0_4),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f212])).
% 1.21/1.15 thf(f212,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK9) & (sK6 @ sK9 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ~spl0_4),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f208])).
% 1.21/1.15 thf(f208,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))) @ sK9)) | ~spl0_4),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f183])).
% 1.21/1.15 thf(f183,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false) | ~spl0_4),
% 1.21/1.15 inference(avatar_component_clause,[status(thm)],[f182])).
% 1.21/1.15 thf(f182,definition,(
% 1.21/1.15 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false)),
% 1.21/1.15 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.21/1.15 thf(f263,plain,(
% 1.21/1.15 ((~ (sK6 @ sK11 @ sK9)) = $true) | ~spl0_4),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f260])).
% 1.21/1.15 thf(f260,plain,(
% 1.21/1.15 ((~ ($true & (sK6 @ sK11 @ sK9))) = $true) | ~spl0_4),
% 1.21/1.15 inference(superposition,[status(thm)],[f230,f239])).
% 1.21/1.15 thf(f239,plain,(
% 1.21/1.15 ($true = (sK6 @ sK9 @ sK10)) | ~spl0_4),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f238])).
% 1.21/1.15 thf(f238,plain,(
% 1.21/1.15 ($true = ($true & (sK6 @ sK9 @ sK10))) | ~spl0_4),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f218,f237])).
% 1.21/1.15 thf(f230,plain,(
% 1.21/1.15 ( ! [X0 : a] : (((~ ((sK6 @ X0 @ sK10) & (sK6 @ sK11 @ X0))) = $true)) ) | ~spl0_4),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f223])).
% 1.21/1.15 thf(f223,plain,(
% 1.21/1.15 ( ! [X0 : a] : (($true = (((sK6 @ X0 @ sK10) & (sK6 @ sK11 @ X0)) => $false))) ) | ~spl0_4),
% 1.21/1.15 inference(superposition,[status(thm)],[f63,f220])).
% 1.21/1.15 thf(f220,plain,(
% 1.21/1.15 ($false = (sK6 @ sK11 @ sK10)) | ~spl0_4),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f219])).
% 1.21/1.15 thf(f219,plain,(
% 1.21/1.15 ($false = ($true => (sK6 @ sK11 @ sK10))) | ~spl0_4),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f216,f218])).
% 1.21/1.15 thf(f201,plain,(
% 1.21/1.15 ~spl0_3),
% 1.21/1.15 inference(avatar_contradiction_clause,[status(thm)],[f200])).
% 1.21/1.15 thf(f200,plain,(
% 1.21/1.15 $false | ~spl0_3),
% 1.21/1.15 inference(trivial_inequality_removal,[status(thm)],[f196])).
% 1.21/1.15 thf(f196,plain,(
% 1.21/1.15 ($false = $true) | ~spl0_3),
% 1.21/1.15 inference(superposition,[status(thm)],[f193,f43])).
% 1.21/1.15 thf(f43,plain,(
% 1.21/1.15 ( ! [X2 : a,X1 : a] : ((((sK5 @ X2 @ X1) => (sK6 @ X2 @ X1)) = $true)) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.21/1.15 thf(f42,plain,(
% 1.21/1.15 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK5 @ Y0 @ X1) => (sK6 @ Y0 @ X1))) @ X2) = $true)) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f39])).
% 1.21/1.15 thf(f39,plain,(
% 1.21/1.15 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK5 @ Y0 @ X1) => (sK6 @ Y0 @ X1)))) = $true)) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.21/1.15 thf(f38,plain,(
% 1.21/1.15 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))) @ X1))) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f33])).
% 1.21/1.15 thf(f33,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) = $true)),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f32])).
% 1.21/1.15 thf(f32,plain,(
% 1.21/1.15 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & $true) = $true)),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f27,f30])).
% 1.21/1.15 thf(f193,plain,(
% 1.21/1.15 (((sK5 @ sK7 @ sK8) => (sK6 @ sK7 @ sK8)) = $false) | ~spl0_3),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.21/1.15 thf(f192,plain,(
% 1.21/1.15 ($false = ((^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ sK7 @ Y0))) @ sK8)) | ~spl0_3),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f191])).
% 1.21/1.15 thf(f191,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ sK7 @ Y0)))) = $false) | ~spl0_3),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f187])).
% 1.21/1.15 thf(f187,plain,(
% 1.21/1.15 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))) @ sK7) = $false) | ~spl0_3),
% 1.21/1.15 inference(sigma_clausification,[status(thm)],[f180])).
% 1.21/1.15 thf(f180,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_3),
% 1.21/1.15 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.21/1.15 thf(f179,definition,(
% 1.21/1.15 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false)),
% 1.21/1.15 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.21/1.15 thf(f184,plain,(
% 1.21/1.15 spl0_3 | spl0_4 | ~spl0_2),
% 1.21/1.15 inference(avatar_split_clause,[status(thm)],[f175,f78,f182,f179])).
% 1.21/1.15 thf(f78,definition,(
% 1.21/1.15 spl0_2 <=> ((sK6 @ sK2 @ sK3) = $true)),
% 1.21/1.15 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.21/1.15 thf(f175,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false) | ~spl0_2),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f169])).
% 1.21/1.15 thf(f169,plain,(
% 1.21/1.15 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) = $false) | ~spl0_2),
% 1.21/1.15 inference(not_proxy_clausification,[status(thm)],[f136])).
% 1.21/1.15 thf(f136,plain,(
% 1.21/1.15 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))))) = $true) | ~spl0_2),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f130])).
% 1.21/1.15 thf(f130,plain,(
% 1.21/1.15 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) => $false) = $true) | ~spl0_2),
% 1.21/1.15 inference(superposition,[status(thm)],[f51,f112])).
% 1.21/1.15 thf(f112,plain,(
% 1.21/1.15 ($false = (sK6 @ sK4 @ sK2)) | ~spl0_2),
% 1.21/1.15 inference(not_proxy_clausification,[status(thm)],[f99])).
% 1.21/1.15 thf(f99,plain,(
% 1.21/1.15 ($true = (~ (sK6 @ sK4 @ sK2))) | ~spl0_2),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f97])).
% 1.21/1.15 thf(f97,plain,(
% 1.21/1.15 (((sK6 @ sK4 @ sK2) => $false) = $true) | ~spl0_2),
% 1.21/1.15 inference(superposition,[status(thm)],[f91,f29])).
% 1.21/1.15 thf(f29,plain,(
% 1.21/1.15 ((sK6 @ sK4 @ sK3) = $false)),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f28])).
% 1.21/1.15 thf(f28,plain,(
% 1.21/1.15 ($false = ($true => (sK6 @ sK4 @ sK3)))),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f25,f27])).
% 1.21/1.15 thf(f91,plain,(
% 1.21/1.15 ( ! [X0 : a] : (($true = ((sK6 @ X0 @ sK2) => (sK6 @ X0 @ sK3)))) ) | ~spl0_2),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f83])).
% 1.21/1.15 thf(f83,plain,(
% 1.21/1.15 ( ! [X0 : a] : (((($true & (sK6 @ X0 @ sK2)) => (sK6 @ X0 @ sK3)) = $true)) ) | ~spl0_2),
% 1.21/1.15 inference(superposition,[status(thm)],[f63,f79])).
% 1.21/1.15 thf(f79,plain,(
% 1.21/1.15 ((sK6 @ sK2 @ sK3) = $true) | ~spl0_2),
% 1.21/1.15 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.21/1.15 thf(f51,plain,(
% 1.21/1.15 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK4 @ sK2)))) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.21/1.15 thf(f50,plain,(
% 1.21/1.15 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK2))) @ X1) = $true)) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f34])).
% 1.21/1.15 thf(f34,plain,(
% 1.21/1.15 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK2)))) = $true)),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.21/1.15 thf(f19,plain,(
% 1.21/1.15 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK2 @ sK3)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK2))))) = $true)),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.21/1.15 thf(f80,plain,(
% 1.21/1.15 spl0_1 | spl0_2),
% 1.21/1.15 inference(avatar_split_clause,[status(thm)],[f73,f78,f75])).
% 1.21/1.15 thf(f73,plain,(
% 1.21/1.15 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false) | ((sK6 @ sK2 @ sK3) = $true)),
% 1.21/1.15 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.21/1.15 thf(f46,plain,(
% 1.21/1.15 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) => (sK6 @ sK2 @ sK3)) = $true)),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f45])).
% 1.21/1.15 thf(f45,plain,(
% 1.21/1.15 ($true = (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) => (sK6 @ sK2 @ sK3)))),
% 1.21/1.15 inference(superposition,[status(thm)],[f41,f33])).
% 1.21/1.15 thf(f41,plain,(
% 1.21/1.15 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0))))))))) => (X1 @ sK2 @ sK3)) = $true)) )),
% 1.21/1.15 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.21/1.15 thf(f40,plain,(
% 1.21/1.15 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK2 @ sK3))) @ X1) = $true)) )),
% 1.21/1.15 inference(pi_clausification,[status(thm)],[f37])).
% 1.21/1.15 thf(f37,plain,(
% 1.21/1.15 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK2 @ sK3)))) = $true)),
% 1.21/1.15 inference(boolean_simplification,[status(thm)],[f36])).
% 1.21/1.15 thf(f36,plain,(
% 1.21/1.15 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK2 @ sK3)))) & $true) = $true)),
% 1.21/1.15 inference(backward_demodulation,[status(thm)],[f19,f34])).
% 1.21/1.15 % SZS output end Proof for DTF2THF_2338
% 1.21/1.15 % (2563)------------------------------
% 1.21/1.15 % (2563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.21/1.15 % (2563)Termination reason: Refutation
% 1.21/1.15
% 1.21/1.15 % (2563)Memory used [KB]: 6012
% 1.21/1.15 % (2563)Time elapsed: 0.034 s
% 1.21/1.15 % (2563)Instructions burned: 87 (million)
% 1.21/1.15 % (2563)------------------------------
% 1.21/1.15 % (2563)------------------------------
% 1.21/1.15 % (2535)Success in time 0.07 s
%------------------------------------------------------------------------------