%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV292^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 09:40:45 AM UTC 2026
% Result : Theorem 1.65s 1.33s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 32 unt; 0 typ; 2 def)
% Number of atoms : 627 ( 181 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 1814 ( 222 ~; 32 |; 288 &; 948 @)
% ( 2 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 536 ( 536 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 6 con; 0-2 aty)
% ( 63 !!; 171 ??; 0 @@+; 0 @@-)
% Number of variables : 425 ( 408 ^; 10 !; 7 ?; 425 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cONE: ( $i > $o ) > $o ).
thf(func_def_2,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_3,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK2: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_24,type,
sK3: ( ( $i > $o ) > $o ) > $o ).
thf(f103,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f45,f74,f102]) ).
thf(f102,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f99,f81]) ).
thf(f81,plain,
( ( ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK3 @ Y0 )
=> ( sK3
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK3
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK3 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_1
<=> ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f99,plain,
( ( ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( $true
=> ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( $true
=> ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 )
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f92,f87]) ).
thf(f87,plain,
( ( ( sK3
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK3 @ Y0 )
=> ( sK3
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK3
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f92,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( sK3 @ X1 )
=> ( sK3
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( sK3 @ Y0 )
=> ( sK3
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK3 @ Y0 )
=> ( sK3
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK3 @ Y0 )
=> ( sK3
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& $true )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f82,f87]) ).
thf(f74,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f69,f53]) ).
thf(f53,plain,
( ( $false
= ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 != Y3 )
& ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false
= ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 != Y3 )
& ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
@ sK2 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl0_2
<=> ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f69,plain,
( ( ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 != Y3 )
& ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( $true
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 != Y3 )
& ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( $true
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f64,f62]) ).
thf(f62,plain,
( ( ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( $true
& ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f54,f60]) ).
thf(f60,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f64,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( sK2 @ X1 )
=> ( sK2
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( X1
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( sK2
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f45,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f43,f40]) ).
thf(f38,plain,
( ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
& $true
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ~ ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f34,f30]) ).
thf(f30,plain,
( ( cP
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( ( cP
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 )
& ~ ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 != Y5 )
& ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( cP @ Y0 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ~ ( ( cP
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 )
& ~ ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 != Y5 )
& ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( cP @ Y0 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ~ ( ( cP
@ ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( ^ [Y1: ( $i > $o ) > $o,Y2: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y3: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y4: ( $i > $o ) > $o] :
( ( Y3 @ Y4 )
=> ( Y3
@ ( ^ [Y5: ( $i > $o ) > $o,Y6: $i > $o] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y6 @ Y7 )
& ( Y5
@ ^ [Y8: $i] :
( ( Y7 != Y8 )
& ( Y6 @ Y8 ) ) ) ) )
@ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y3 @ Y2 ) ) )
@ Y0
@ ( ^ [Y1: ( $i > $o ) > $o,Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ( ^ [Y1: ( $i > $o ) > $o,Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) )
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
& ( cP @ Y0 )
& ( ^ [Y1: ( $i > $o ) > $o,Y2: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y3: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y4: ( $i > $o ) > $o] :
( ( Y3 @ Y4 )
=> ( Y3
@ ( ^ [Y5: ( $i > $o ) > $o,Y6: $i > $o] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( Y6 @ Y7 )
& ( Y5
@ ^ [Y8: $i] :
( ( Y7 != Y8 )
& ( Y6 @ Y8 ) ) ) ) )
@ Y4 ) ) ) )
& ( Y3 @ Y1 ) )
=> ( Y3 @ Y2 ) ) )
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f22,f23,f17,f22,f23,f18]) ).
thf(f18,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cZERO_def) ).
thf(f17,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X2 != X3 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cSUCC
= ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X2
@ ^ [X3: $i] :
( ( X0 @ X3 )
& ( X1 != X3 ) ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cSUCC_def) ).
thf(f23,plain,
( c_less__eq_
= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2
@ ( ^ [Y4: ( $i > $o ) > $o,Y5: $i > $o] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4
@ ^ [Y7: $i] :
( ( Y6 != Y7 )
& ( Y5 @ Y7 ) ) ) ) )
@ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f17]) ).
thf(f19,plain,
( c_less__eq_
= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cSUCC @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( c_less__eq_
= ( ^ [Y0: ( $i > $o ) > $o,Y1: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y2: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y3: ( $i > $o ) > $o] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cSUCC @ Y3 ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( c_less__eq_
= ( ^ [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ( ( X2 @ X0 )
& ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cSUCC @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( c_less__eq_
= ( ^ [X1: ( $i > $o ) > $o,X4: ( $i > $o ) > $o] :
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ X1 )
& ! [X5: ( $i > $o ) > $o] :
( ( X0 @ X5 )
=> ( X0 @ ( cSUCC @ X5 ) ) ) )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',c_less__eq__def) ).
thf(f22,plain,
( cONE
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f17,f18]) ).
thf(f20,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( cONE
= ( cSUCC @ cZERO ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cONE_def) ).
thf(f21,plain,
( ( ~ ( ( cP @ cONE )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( c_less__eq_ @ Y0 @ ( cSUCC @ cONE ) )
& ( cP @ Y0 )
& ( c_less__eq_ @ cZERO @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ~ ( ( cP @ cONE )
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( c_less__eq_ @ Y0 @ ( cSUCC @ cONE ) )
& ( cP @ Y0 )
& ( c_less__eq_ @ cZERO @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( cP @ cONE )
=> ? [X0: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ X0 )
& ( cP @ X0 )
& ( c_less__eq_ @ X0 @ ( cSUCC @ cONE ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ( cP @ cONE )
=> ? [X1: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ X1 )
& ( cP @ X1 )
& ( c_less__eq_ @ X1 @ ( cSUCC @ cONE ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ( cP @ cONE )
=> ? [X1: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ X1 )
& ( cP @ X1 )
& ( c_less__eq_ @ X1 @ ( cSUCC @ cONE ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cBLEDSOE7A) ).
thf(f34,plain,
! [X1: ( $i > $o ) > $o] :
( $false
= ( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0 @ X1 ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 )
& ~ ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 != Y4 )
& ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( cP @ X1 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 )
& ~ ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 != Y5 )
& ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( cP @ Y0 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 )
& ~ ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 != Y5 )
& ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( cP @ Y0 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
= ( $true
=> ( ?? @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 )
& ~ ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 != Y5 )
& ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( cP @ Y0 )
& ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ^ [Y3: $i > $o] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2
@ ^ [Y5: $i] :
( ( Y4 != Y5 )
& ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f26,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV292^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:43:01 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.23/0.44 ---- Original DTF file ---
% 0.23/0.44 thf(spec,logic,$$dhol).
% 0.23/0.44 %------------------------------------------------------------------------------
% 0.23/0.44 % File : SEV292^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.23/0.44 % Domain : Set Theory
% 0.23/0.44 % Problem : TPS problem BLEDSOE7A
% 0.23/0.44 % Version : Especial.
% 0.23/0.44 % English :
% 0.23/0.44
% 0.23/0.44 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.23/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.44 % Source : [Bro09]
% 0.23/0.44 % Names : tps_0340 [Bro09]
% 0.23/0.44 % : BLEDSOE7A [TPS]
% 0.23/0.44
% 0.23/0.44 % Status : Theorem
% 0.23/0.44 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0
% 0.23/0.44 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 4 def)
% 0.23/0.44 % Number of atoms : 20 ( 5 equ; 0 cnn)
% 0.23/0.44 % Maximal formula atoms : 8 ( 4 avg)
% 0.23/0.44 % Number of connectives : 27 ( 2 ~; 0 |; 5 &; 17 @)
% 0.23/0.44 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.23/0.44 % Maximal formula depth : 7 ( 2 avg)
% 0.23/0.44 % Number of types : 2 ( 0 usr)
% 0.23/0.44 % Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% 0.23/0.44 % Number of symbols : 6 ( 5 usr; 0 con; 1-2 aty)
% 0.23/0.44 % Number of variables : 11 ( 6 ^; 2 !; 3 ?; 11 :)
% 0.23/0.44 % SPC : TH0_THM_EQU_NAR
% 0.23/0.44
% 0.23/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.23/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.23/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.23/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.23/0.44 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.23/0.44 % : v6.2.0 - Reordered definitions.
% 0.23/0.44 %------------------------------------------------------------------------------
% 0.23/0.44 thf(cP_type,type,
% 0.23/0.44 cP: ( ( $i > $o ) > $o ) > $o ).
% 0.23/0.44
% 0.23/0.44 thf(cONE_type,type,
% 0.23/0.44 cONE: ( $i > $o ) > $o ).
% 0.23/0.44
% 0.23/0.44 thf(cSUCC_type,type,
% 0.23/0.44 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.23/0.44
% 0.23/0.44 thf(cZERO_type,type,
% 0.23/0.44 cZERO: ( $i > $o ) > $o ).
% 0.23/0.44
% 0.23/0.44 thf(c_less__eq__type,type,
% 0.23/0.44 c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 0.23/0.44
% 0.23/0.44 thf(cZERO_def,definition,
% 0.23/0.44 ( cZERO
% 0.23/0.44 = ( ^ [Xp: $i > $o] :
% 0.23/0.44 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.23/0.44
% 0.23/0.44 thf(cSUCC_def,definition,
% 0.23/0.44 ( cSUCC
% 0.23/0.44 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.23/0.44 ? [Xx: $i] :
% 0.23/0.44 ( ( Xp @ Xx )
% 0.23/0.44 & ( Xn
% 0.23/0.44 @ ^ [Xt: $i] :
% 0.23/0.44 ( ( Xt != Xx )
% 0.23/0.44 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.23/0.44
% 0.23/0.44 thf(cONE_def,definition,
% 0.23/0.44 ( cONE
% 0.23/0.44 = ( cSUCC @ cZERO ) ) ).
% 0.23/0.44
% 0.23/0.44 thf(c_less__eq__def,definition,
% 0.23/0.44 ( c_less__eq_
% 0.23/0.44 = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 0.23/0.44 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.23/0.44 ( ( ( Xp @ Xx )
% 0.23/0.44 & ! [Xz: ( $i > $o ) > $o] :
% 0.23/0.44 ( ( Xp @ Xz )
% 0.23/0.44 => ( Xp @ ( cSUCC @ Xz ) ) ) )
% 0.23/0.44 => ( Xp @ Xy ) ) ) ) ).
% 0.23/0.44
% 0.23/0.44 thf(cBLEDSOE7A,conjecture,
% 0.23/0.44 ( ( cP @ cONE )
% 0.23/0.44 => ? [Xx: ( $i > $o ) > $o] :
% 0.23/0.44 ( ( c_less__eq_ @ cZERO @ Xx )
% 0.23/0.44 & ( c_less__eq_ @ Xx @ ( cSUCC @ cONE ) )
% 0.23/0.44 & ( cP @ Xx ) ) ) ).
% 0.23/0.44
% 0.23/0.44 %------------------------------------------------------------------------------
% 0.23/0.44 ------------------------
% 1.54/1.25 ---- Embedded in THF ---
% 1.54/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.25 %%% Generated on Tue Feb 24 12:43:02 EST 2026
% 1.54/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.25 %%% Logic specification used:
% 1.54/1.25 %%% thf(spec, logic, $$dhol).
% 1.54/1.25
% 1.54/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2DTF4661.p
% See solution above
% 1.54/1.25 ------------------------
% 1.54/1.26 ---- Cleaned THF ---
% 1.54/1.26 thf(cP_type,type,
% 1.54/1.26 cP: ( ( $i > $o ) > $o ) > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cONE_type,type,
% 1.54/1.26 cONE: ( $i > $o ) > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cSUCC_type,type,
% 1.54/1.26 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cZERO_type,type,
% 1.54/1.26 cZERO: ( $i > $o ) > $o ).
% 1.54/1.26
% 1.54/1.26 thf(c_less__eq__type,type,
% 1.54/1.26 c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
% 1.54/1.26
% 1.54/1.26 thf(cZERO_def,definition,
% 1.54/1.26 ( cZERO
% 1.54/1.26 = ( ^ [Xp: $i > $o] :
% 1.54/1.26 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.54/1.26
% 1.54/1.26 thf(cSUCC_def,definition,
% 1.54/1.26 ( cSUCC
% 1.54/1.26 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.54/1.26 ? [Xx: $i] :
% 1.54/1.26 ( ( Xp @ Xx )
% 1.54/1.26 & ( Xn
% 1.54/1.26 @ ^ [Xt: $i] :
% 1.54/1.26 ( ( Xt != Xx )
% 1.54/1.26 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.54/1.26
% 1.54/1.26 thf(cONE_def,definition,
% 1.54/1.26 ( cONE
% 1.54/1.26 = ( cSUCC @ cZERO ) ) ).
% 1.54/1.26
% 1.54/1.26 thf(c_less__eq__def,definition,
% 1.54/1.26 ( c_less__eq_
% 1.54/1.26 = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
% 1.54/1.26 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.54/1.26 ( ( ( Xp @ Xx )
% 1.54/1.26 & ! [Xz: ( $i > $o ) > $o] :
% 1.54/1.26 ( ( Xp @ Xz )
% 1.54/1.26 => ( Xp @ ( cSUCC @ Xz ) ) ) )
% 1.54/1.26 => ( Xp @ Xy ) ) ) ) ).
% 1.54/1.26
% 1.54/1.26 thf(cBLEDSOE7A,conjecture,
% 1.54/1.26 ( ( cP @ cONE )
% 1.54/1.26 => ? [Xx: ( $i > $o ) > $o] :
% 1.54/1.26 ( ( c_less__eq_ @ cZERO @ Xx )
% 1.54/1.26 & ( c_less__eq_ @ Xx @ ( cSUCC @ cONE ) )
% 1.54/1.26 & ( cP @ Xx ) ) ) ).
% 1.54/1.26 ------------------------
% 1.54/1.27 % (4815)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4661 for (2999ds/183Mi)
% 1.54/1.28 % (4820)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_4661 for (2999ds/275Mi)
% 1.54/1.28 % (4817)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_4661 for (2999ds/27Mi)
% 1.54/1.28 % (4820)Refutation not found, incomplete strategy
% 1.54/1.28 % (4820)------------------------------
% 1.54/1.28 % (4820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (4820)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.28
% 1.54/1.28
% 1.54/1.28 % (4820)Memory used [KB]: 5500
% 1.54/1.28 % (4820)Time elapsed: 0.002 s
% 1.54/1.28 % (4820)Instructions burned: 2 (million)
% 1.54/1.28 % (4820)------------------------------
% 1.54/1.28 % (4820)------------------------------
% 1.54/1.28 % (4819)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_4661 for (2999ds/2Mi)
% 1.54/1.28 % (4816)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_4661 for (2999ds/4Mi)
% 1.54/1.28 % (4819)Instruction limit reached!
% 1.54/1.28 % (4819)------------------------------
% 1.54/1.28 % (4819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (4819)Termination reason: Unknown
% 1.54/1.28 % (4819)Termination phase: Function definition elimination
% 1.54/1.28
% 1.54/1.28 % (4819)Memory used [KB]: 895
% 1.54/1.28 % (4819)Time elapsed: 0.003 s
% 1.54/1.28 % (4819)Instructions burned: 2 (million)
% 1.54/1.28 % (4819)------------------------------
% 1.54/1.28 % (4819)------------------------------
% 1.54/1.28 % (4816)Instruction limit reached!
% 1.54/1.28 % (4816)------------------------------
% 1.54/1.28 % (4816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.28 % (4816)Termination reason: Unknown
% 1.54/1.28 % (4816)Termination phase: Saturation
% 1.54/1.28
% 1.54/1.28 % (4816)Memory used [KB]: 5500
% 1.54/1.28 % (4816)Time elapsed: 0.004 s
% 1.54/1.28 % (4816)Instructions burned: 4 (million)
% 1.54/1.28 % (4816)------------------------------
% 1.54/1.28 % (4816)------------------------------
% 1.54/1.29 % (4821)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4661 for (2999ds/18Mi)
% 1.54/1.29 % (4818)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4661 for (2999ds/2Mi)
% 1.54/1.30 % (4817)Refutation not found, incomplete strategy
% 1.54/1.30 % (4817)------------------------------
% 1.54/1.30 % (4817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (4817)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.30
% 1.54/1.30
% 1.54/1.30 % (4817)Memory used [KB]: 5628
% 1.54/1.30 % (4817)Time elapsed: 0.015 s
% 1.54/1.30 % (4817)Instructions burned: 25 (million)
% 1.54/1.30 % (4817)------------------------------
% 1.54/1.30 % (4817)------------------------------
% 1.54/1.30 % (4818)Instruction limit reached!
% 1.54/1.30 % (4818)------------------------------
% 1.54/1.30 % (4818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (4818)Termination reason: Unknown
% 1.54/1.30 % (4818)Termination phase: Function definition elimination
% 1.54/1.30
% 1.54/1.30 % (4818)Memory used [KB]: 895
% 1.54/1.30 % (4818)Time elapsed: 0.004 s
% 1.54/1.30 % (4818)Instructions burned: 2 (million)
% 1.54/1.30 % (4818)------------------------------
% 1.54/1.30 % (4818)------------------------------
% 1.65/1.30 % (4821)Instruction limit reached!
% 1.65/1.30 % (4821)------------------------------
% 1.65/1.30 % (4821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (4821)Termination reason: Unknown
% 1.65/1.30 % (4821)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (4821)Memory used [KB]: 5500
% 1.65/1.30 % (4821)Time elapsed: 0.011 s
% 1.65/1.30 % (4821)Instructions burned: 18 (million)
% 1.65/1.30 % (4821)------------------------------
% 1.65/1.30 % (4821)------------------------------
% 1.65/1.30 % (4827)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_4661 for (2999ds/37Mi)
% 1.65/1.30 % (4828)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_4661 for (2999ds/15Mi)
% 1.65/1.31 % (4828)Instruction limit reached!
% 1.65/1.31 % (4828)------------------------------
% 1.65/1.31 % (4828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (4828)Termination reason: Unknown
% 1.65/1.31 % (4828)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (4828)Memory used [KB]: 5628
% 1.65/1.31 % (4828)Time elapsed: 0.010 s
% 1.65/1.31 % (4828)Instructions burned: 16 (million)
% 1.65/1.31 % (4828)------------------------------
% 1.65/1.31 % (4828)------------------------------
% 1.65/1.31 % (4826)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4661 for (2999ds/3Mi)
% 1.65/1.31 % (4832)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_4661 for (2999ds/1041Mi)
% 1.65/1.31 % (4834)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4661 for (2999ds/7Mi)
% 1.65/1.31 % (4826)Instruction limit reached!
% 1.65/1.31 % (4826)------------------------------
% 1.65/1.31 % (4826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (4826)Termination reason: Unknown
% 1.65/1.31 % (4826)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (4826)Memory used [KB]: 5500
% 1.65/1.31 % (4826)Time elapsed: 0.005 s
% 1.65/1.31 % (4826)Instructions burned: 3 (million)
% 1.65/1.31 % (4826)------------------------------
% 1.65/1.31 % (4826)------------------------------
% 1.65/1.32 % (4827)Instruction limit reached!
% 1.65/1.32 % (4827)------------------------------
% 1.65/1.32 % (4827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (4827)Termination reason: Unknown
% 1.65/1.32 % (4827)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (4827)Memory used [KB]: 5628
% 1.65/1.32 % (4827)Time elapsed: 0.019 s
% 1.65/1.32 % (4827)Instructions burned: 37 (million)
% 1.65/1.32 % (4827)------------------------------
% 1.65/1.32 % (4827)------------------------------
% 1.65/1.32 % (4834)Instruction limit reached!
% 1.65/1.32 % (4834)------------------------------
% 1.65/1.32 % (4834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (4834)Termination reason: Unknown
% 1.65/1.32 % (4834)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (4834)Memory used [KB]: 1023
% 1.65/1.32 % (4834)Time elapsed: 0.005 s
% 1.65/1.32 % (4834)Instructions burned: 8 (million)
% 1.65/1.32 % (4834)------------------------------
% 1.65/1.32 % (4834)------------------------------
% 1.65/1.32 % (4832)First to succeed.
% 1.65/1.33 % (4831)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_4661 for (2999ds/3Mi)
% 1.65/1.33 % (4832)Refutation found. Thanks to Tanya!
% 1.65/1.33 % SZS status Theorem for DTF2THF_4661
% 1.65/1.33 % SZS output start Proof for DTF2THF_4661
% 1.65/1.33 thf(func_def_0, type, cP: (($i > $o) > $o) > $o).
% 1.65/1.33 thf(func_def_1, type, cONE: ($i > $o) > $o).
% 1.65/1.33 thf(func_def_2, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.65/1.33 thf(func_def_3, type, cZERO: ($i > $o) > $o).
% 1.65/1.33 thf(func_def_4, type, c_less__eq_: (($i > $o) > $o) > (($i > $o) > $o) > $o).
% 1.65/1.33 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.33 thf(func_def_23, type, sK2: (($i > $o) > $o) > $o).
% 1.65/1.33 thf(func_def_24, type, sK3: (($i > $o) > $o) > $o).
% 1.65/1.33 thf(f103,plain,(
% 1.65/1.33 $false),
% 1.65/1.33 inference(avatar_sat_refutation,[status(thm)],[f45,f74,f102])).
% 1.65/1.33 thf(f102,plain,(
% 1.65/1.33 ~spl0_1),
% 1.65/1.33 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.65/1.33 thf(f101,plain,(
% 1.65/1.33 $false | ~spl0_1),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.65/1.33 thf(f100,plain,(
% 1.65/1.33 ($false = $true) | ~spl0_1),
% 1.65/1.33 inference(forward_demodulation,[status(thm)],[f99,f81])).
% 1.65/1.33 thf(f81,plain,(
% 1.65/1.33 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $false) | ~spl0_1),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.65/1.33 thf(f80,plain,(
% 1.65/1.33 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $false) | ~spl0_1),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.65/1.33 thf(f77,plain,(
% 1.65/1.33 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) @ sK3)) | ~spl0_1),
% 1.65/1.33 inference(sigma_clausification,[status(thm)],[f41])).
% 1.65/1.33 thf(f41,plain,(
% 1.65/1.33 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))) | ~spl0_1),
% 1.65/1.33 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.65/1.33 thf(f40,definition,(
% 1.65/1.33 spl0_1 <=> ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))),
% 1.65/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.33 thf(f99,plain,(
% 1.65/1.33 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_1),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f98])).
% 1.65/1.33 thf(f98,plain,(
% 1.65/1.33 (($true => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_1),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.65/1.33 thf(f94,plain,(
% 1.65/1.33 (($true => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & ((^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))) @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_1),
% 1.65/1.33 inference(superposition,[status(thm)],[f92,f87])).
% 1.65/1.33 thf(f87,plain,(
% 1.65/1.33 ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true) | ~spl0_1),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.65/1.33 thf(f82,plain,(
% 1.65/1.33 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true) | ~spl0_1),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.65/1.33 thf(f92,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : ((((sK3 @ X1) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) ) | ~spl0_1),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.65/1.33 thf(f91,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1) = $true)) ) | ~spl0_1),
% 1.65/1.33 inference(pi_clausification,[status(thm)],[f90])).
% 1.65/1.33 thf(f90,plain,(
% 1.65/1.33 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true) | ~spl0_1),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f89])).
% 1.65/1.33 thf(f89,plain,(
% 1.65/1.33 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & $true) = $true) | ~spl0_1),
% 1.65/1.33 inference(backward_demodulation,[status(thm)],[f82,f87])).
% 1.65/1.33 thf(f74,plain,(
% 1.65/1.33 ~spl0_2),
% 1.65/1.33 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.65/1.33 thf(f73,plain,(
% 1.65/1.33 $false | ~spl0_2),
% 1.65/1.33 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.65/1.33 thf(f72,plain,(
% 1.65/1.33 ($false = $true) | ~spl0_2),
% 1.65/1.33 inference(forward_demodulation,[status(thm)],[f69,f53])).
% 1.65/1.33 thf(f53,plain,(
% 1.65/1.33 ($false = (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))) | ~spl0_2),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.65/1.33 thf(f52,plain,(
% 1.65/1.33 ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ~spl0_2),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.65/1.33 thf(f48,plain,(
% 1.65/1.33 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))) @ sK2)) | ~spl0_2),
% 1.65/1.33 inference(sigma_clausification,[status(thm)],[f44])).
% 1.65/1.33 thf(f44,plain,(
% 1.65/1.33 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))))) | ~spl0_2),
% 1.65/1.33 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.65/1.33 thf(f43,definition,(
% 1.65/1.33 spl0_2 <=> ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))))),
% 1.65/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.33 thf(f69,plain,(
% 1.65/1.33 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f68])).
% 1.65/1.33 thf(f68,plain,(
% 1.65/1.33 (($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.65/1.33 thf(f66,plain,(
% 1.65/1.33 (($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))) @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(superposition,[status(thm)],[f64,f62])).
% 1.65/1.33 thf(f62,plain,(
% 1.65/1.33 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f61])).
% 1.65/1.33 thf(f61,plain,(
% 1.65/1.33 (($true & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(backward_demodulation,[status(thm)],[f54,f60])).
% 1.65/1.33 thf(f60,plain,(
% 1.65/1.33 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.65/1.33 thf(f54,plain,(
% 1.65/1.33 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $true) | ~spl0_2),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.65/1.33 thf(f64,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : ((((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)) ) | ~spl0_2),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.65/1.33 thf(f63,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1) = $true)) ) | ~spl0_2),
% 1.65/1.33 inference(pi_clausification,[status(thm)],[f60])).
% 1.65/1.33 thf(f45,plain,(
% 1.65/1.33 spl0_1 | spl0_2),
% 1.65/1.33 inference(avatar_split_clause,[status(thm)],[f38,f43,f40])).
% 1.65/1.33 thf(f38,plain,(
% 1.65/1.33 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))))) | ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.65/1.33 thf(f37,plain,(
% 1.65/1.33 (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))) = $false)),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f36])).
% 1.65/1.33 thf(f36,plain,(
% 1.65/1.33 ($false = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) & $true) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))))),
% 1.65/1.33 inference(superposition,[status(thm)],[f34,f30])).
% 1.65/1.33 thf(f30,plain,(
% 1.65/1.33 ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) = $true)),
% 1.65/1.33 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.65/1.33 thf(f26,plain,(
% 1.65/1.33 ($false = ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5))))))))))))))))) & (cP @ Y0)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))))))),
% 1.65/1.33 inference(not_proxy_clausification,[status(thm)],[f25])).
% 1.65/1.33 thf(f25,plain,(
% 1.65/1.33 ((~ ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5))))))))))))))))) & (cP @ Y0)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))))))) = $true)),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.65/1.33 thf(f24,plain,(
% 1.65/1.33 ((~ ((cP @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((((^[Y1 : ($i > $o) > $o]: ((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))))))))) @ Y4))))) & (Y3 @ Y1)) => (Y3 @ Y2))))))) @ Y0 @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))) @ ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))) @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))))))) & (cP @ Y0)) & ((^[Y1 : ($i > $o) > $o]: ((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((~ (Y7 = Y8)) & (Y6 @ Y8)))))))))) @ Y4))))) & (Y3 @ Y1)) => (Y3 @ Y2))))))) @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))) @ Y0)))))) = $true)),
% 1.65/1.33 inference(definition_unfolding,[status(thm)],[f21,f22,f23,f17,f22,f23,f18])).
% 1.65/1.33 thf(f18,plain,(
% 1.65/1.33 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.33 thf(f9,plain,(
% 1.65/1.33 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.65/1.33 thf(f8,plain,(
% 1.65/1.33 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.65/1.33 inference(rectify,[status(thm)],[f1])).
% 1.65/1.33 thf(f1,axiom,(
% 1.65/1.33 (cZERO = (^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cZERO_def)).
% 1.65/1.33 thf(f17,plain,(
% 1.65/1.33 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.33 thf(f16,plain,(
% 1.65/1.33 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f15])).
% 1.65/1.33 thf(f15,plain,(
% 1.65/1.33 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))))),
% 1.65/1.33 inference(rectify,[status(thm)],[f2])).
% 1.65/1.33 thf(f2,axiom,(
% 1.65/1.33 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cSUCC_def)).
% 1.65/1.33 thf(f23,plain,(
% 1.65/1.33 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.65/1.33 inference(definition_unfolding,[status(thm)],[f19,f17])).
% 1.65/1.33 thf(f19,plain,(
% 1.65/1.33 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.33 thf(f14,plain,(
% 1.65/1.33 (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f13])).
% 1.65/1.33 thf(f13,plain,(
% 1.65/1.33 (c_less__eq_ = (^[X0 : ($i > $o) > $o, X1 : ($i > $o) > $o] : (! [X2 : (($i > $o) > $o) > $o] : (((X2 @ X0) & ! [X3 : ($i > $o) > $o] : ((X2 @ X3) => (X2 @ (cSUCC @ X3)))) => (X2 @ X1)))))),
% 1.65/1.33 inference(rectify,[status(thm)],[f4])).
% 1.65/1.33 thf(f4,axiom,(
% 1.65/1.33 (c_less__eq_ = (^[X1 : ($i > $o) > $o, X4 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ X1) & ! [X5 : ($i > $o) > $o] : ((X0 @ X5) => (X0 @ (cSUCC @ X5)))) => (X0 @ X4)))))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',c_less__eq__def)).
% 1.65/1.33 thf(f22,plain,(
% 1.65/1.33 (cONE = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.65/1.33 inference(definition_unfolding,[status(thm)],[f20,f17,f18])).
% 1.65/1.33 thf(f20,plain,(
% 1.65/1.33 (cONE = (cSUCC @ cZERO))),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.33 thf(f10,plain,(
% 1.65/1.33 (cONE = (cSUCC @ cZERO))),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f3])).
% 1.65/1.33 thf(f3,axiom,(
% 1.65/1.33 (cONE = (cSUCC @ cZERO))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cONE_def)).
% 1.65/1.33 thf(f21,plain,(
% 1.65/1.33 ((~ ((cP @ cONE) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((c_less__eq_ @ Y0 @ (cSUCC @ cONE)) & (cP @ Y0)) & (c_less__eq_ @ cZERO @ Y0)))))) = $true)),
% 1.65/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.33 thf(f12,plain,(
% 1.65/1.33 ((~ ((cP @ cONE) => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((c_less__eq_ @ Y0 @ (cSUCC @ cONE)) & (cP @ Y0)) & (c_less__eq_ @ cZERO @ Y0)))))) = $true)),
% 1.65/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.33 thf(f11,plain,(
% 1.65/1.33 ~((cP @ cONE) => ? [X0 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X0) & (cP @ X0) & (c_less__eq_ @ X0 @ (cSUCC @ cONE))))),
% 1.65/1.33 inference(rectify,[status(thm)],[f6])).
% 1.65/1.33 thf(f6,negated_conjecture,(
% 1.65/1.33 ~((cP @ cONE) => ? [X1 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X1) & (cP @ X1) & (c_less__eq_ @ X1 @ (cSUCC @ cONE))))),
% 1.65/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 1.65/1.33 thf(f5,conjecture,(
% 1.65/1.33 (cP @ cONE) => ? [X1 : ($i > $o) > $o] : ((c_less__eq_ @ cZERO @ X1) & (cP @ X1) & (c_less__eq_ @ X1 @ (cSUCC @ cONE)))),
% 1.65/1.33 file('/export/starexec/sandbox2/tmp/tmp.hwPzrCpAh2/DTF2THF_4661.p',cBLEDSOE7A)).
% 1.65/1.33 thf(f34,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : (($false = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ X1)) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))) & (cP @ X1)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ X1))))))) )),
% 1.65/1.33 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.65/1.33 thf(f33,plain,(
% 1.65/1.33 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5))))))))))))))))) & (cP @ Y0)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) @ X1) = $false)) )),
% 1.65/1.33 inference(pi_clausification,[status(thm)],[f32])).
% 1.65/1.33 thf(f32,plain,(
% 1.65/1.33 ((?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5))))))))))))))))) & (cP @ Y0)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))))) = $false)),
% 1.65/1.33 inference(boolean_simplification,[status(thm)],[f31])).
% 1.65/1.33 thf(f31,plain,(
% 1.65/1.33 ($false = ($true => (?? @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ Y0)) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (?? @ $i @ (^[Y4 : $i]: (((~ (Y3 = Y4)) & (Y2 @ Y4)) & (~ (?? @ $i @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & ((~ (Y3 = Y5)) & (Y2 @ Y5))))))))))))))))) & (cP @ Y0)) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((~ (Y4 = Y5)) & (Y3 @ Y5)))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))))))),
% 1.65/1.33 inference(backward_demodulation,[status(thm)],[f26,f30])).
% 1.65/1.33 % SZS output end Proof for DTF2THF_4661
% 1.65/1.33 % (4832)------------------------------
% 1.65/1.33 % (4832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (4832)Termination reason: Refutation
% 1.65/1.33
% 1.65/1.33 % (4832)Memory used [KB]: 5756
% 1.65/1.33 % (4832)Time elapsed: 0.037 s
% 1.65/1.33 % (4832)Instructions burned: 35 (million)
% 1.65/1.33 % (4832)------------------------------
% 1.65/1.33 % (4832)------------------------------
% 1.65/1.33 % (4813)Success in time 0.069 s
%------------------------------------------------------------------------------