%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO324^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:53:56 AM UTC 2026
% Result : Theorem 1.80s 1.57s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 62 ( 24 unt; 0 typ; 2 def)
% Number of atoms : 474 ( 106 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 1619 ( 223 ~; 144 |; 93 &; 965 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 389 ( 389 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 6 con; 0-3 aty)
% ( 83 !!; 106 ??; 0 @@+; 0 @@-)
% Number of variables : 288 ( 234 ^; 39 !; 15 ?; 288 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_19,type,
sK3: $i > $o ).
thf(func_def_20,type,
sK4: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
sK5: $i > $o ).
thf(f459,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f408,f412,f458]) ).
thf(f458,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f457]) ).
thf(f457,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f455]) ).
thf(f455,plain,
( ( $false
= ( ^ [Y0: $i > $o] : $true
@ sK5 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( $false
= ( $true
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( ( ~ $false
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
= $false )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f451,f418]) ).
thf(f418,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f417]) ).
thf(f417,plain,
( ( ( ~ ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f414]) ).
thf(f414,plain,
( ( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
!= $false )
= $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f391,f22]) ).
thf(f22,plain,
( ( sK3 @ ( sK2 @ sK3 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) ) ) )
& ~ ( Y0 @ ( sK2 @ sK3 ) ) ) )
| ( sK3 @ ( sK2 @ sK3 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1
@ ( sK2
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ ( sK2 @ Y3 ) )
& ( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ Y2 )
| ( Y4 @ ( sK2 @ Y3 ) ) ) ) ) ) ) )
& ~ ( Y1 @ ( sK2 @ Y0 ) ) ) )
| ( Y0 @ ( sK2 @ Y0 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1
@ ( sK2
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ ( sK2 @ Y3 ) )
& ( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ Y2 )
| ( Y4 @ ( sK2 @ Y3 ) ) ) ) ) ) ) )
& ~ ( Y1 @ ( sK2 @ Y0 ) ) ) )
| ( Y0 @ ( sK2 @ Y0 ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
| ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1
@ ( sK2
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ ( sK2 @ Y3 ) )
& ( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ Y2 )
| ( Y4 @ ( sK2 @ Y3 ) ) ) ) ) ) ) )
& ~ ( Y1 @ ( sK2 @ Y0 ) ) ) )
| ( Y0 @ ( sK2 @ Y0 ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f11,f13]) ).
thf(f13,plain,
( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
!= ( Y0 @ Y2 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ ( sK2 @ Y0 ) )
| ~ ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
!= ( Y0 @ Y2 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ ( sK2 @ Y0 ) )
| ~ ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) )
| ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1
@ ( sK2
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ ( sK2 @ Y3 ) )
& ( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ Y2 )
| ( Y4 @ ( sK2 @ Y3 ) ) ) ) ) ) ) )
& ~ ( Y1 @ ( sK2 @ Y0 ) ) ) )
| ( Y0 @ ( sK2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: ( $i > $o ) > $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
!= ( Y1 @ Y3 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ ( Y0 @ Y1 ) )
| ~ ( Y3 @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2
@ ( Y0
@ ^ [Y3: $i] :
( ?? @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ ( Y0 @ Y4 ) )
& ( !! @ ( $i > $o )
@ ^ [Y5: $i > $o] :
( ~ ( Y5 @ Y3 )
| ( Y5 @ ( Y0 @ Y4 ) ) ) ) ) ) ) )
& ~ ( Y2 @ ( Y0 @ Y1 ) ) ) )
| ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( ( $i > $o ) > $i )
@ ^ [Y0: ( $i > $o ) > $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
!= ( Y1 @ Y3 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ ( Y0 @ Y1 ) )
| ~ ( Y3 @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2
@ ( Y0
@ ^ [Y3: $i] :
( ?? @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ ( Y0 @ Y4 ) )
& ( !! @ ( $i > $o )
@ ^ [Y5: $i > $o] :
( ~ ( Y5 @ Y3 )
| ( Y5 @ ( Y0 @ Y4 ) ) ) ) ) ) ) )
& ~ ( Y2 @ ( Y0 @ Y1 ) ) ) )
| ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i )
@ ^ [Y0: ( $i > $o ) > $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
!= ( Y1 @ Y3 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ ( Y0 @ Y1 ) )
| ~ ( Y3 @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2
@ ( Y0
@ ^ [Y3: $i] :
( ?? @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ ( Y0 @ Y4 ) )
& ( !! @ ( $i > $o )
@ ^ [Y5: $i > $o] :
( ~ ( Y5 @ Y3 )
| ( Y5 @ ( Y0 @ Y4 ) ) ) ) ) ) ) )
& ~ ( Y2 @ ( Y0 @ Y1 ) ) ) )
| ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i )
@ ^ [Y0: ( $i > $o ) > $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
!= ( Y1 @ Y3 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( Y3 @ ( Y0 @ Y1 ) )
| ~ ( Y3 @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2
@ ( Y0
@ ^ [Y3: $i] :
( ?? @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ~ ( Y4 @ ( Y0 @ Y4 ) )
& ( !! @ ( $i > $o )
@ ^ [Y5: $i > $o] :
( ~ ( Y5 @ Y3 )
| ( Y5 @ ( Y0 @ Y4 ) ) ) ) ) ) ) )
& ~ ( Y2 @ ( Y0 @ Y1 ) ) ) )
| ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o] :
( ( X1 @ ( X0 @ X1 ) )
| ? [X2: $i > $o] :
( ~ ( X2 @ ( X0 @ X1 ) )
& ( X2
@ ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i > $o] :
( ( X5 @ ( X0 @ X4 ) )
| ~ ( X5 @ X3 ) )
& ~ ( X4 @ ( X0 @ X4 ) ) ) ) ) ) )
| ? [X6: $i > $o,X7: $i > $o] :
( ! [X8: $i > $o] :
( ~ ( X8 @ ( X0 @ X6 ) )
| ( X8 @ ( X0 @ X7 ) ) )
& ? [X9: $i] :
~ ( ( X6 @ X9 )
<=> ( X7 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X5: $i > $o] :
( ( X5 @ ( X0 @ X5 ) )
| ? [X2: $i > $o] :
( ~ ( X2 @ ( X0 @ X5 ) )
& ( X2
@ ( X0
@ ^ [X6: $i] :
? [X7: $i > $o] :
( ! [X8: $i > $o] :
( ( X8 @ ( X0 @ X7 ) )
| ~ ( X8 @ X6 ) )
& ~ ( X7 @ ( X0 @ X7 ) ) ) ) ) ) )
| ? [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X1 ) )
| ( X3 @ ( X0 @ X2 ) ) )
& ? [X4: $i] :
~ ( ( X1 @ X4 )
<=> ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
( ! [X5: $i > $o] :
( ( X5 @ ( X0 @ X5 ) )
| ? [X2: $i > $o] :
( ~ ( X2 @ ( X0 @ X5 ) )
& ( X2
@ ( X0
@ ^ [X6: $i] :
? [X7: $i > $o] :
( ! [X8: $i > $o] :
( ( X8 @ ( X0 @ X7 ) )
| ~ ( X8 @ X6 ) )
& ~ ( X7 @ ( X0 @ X7 ) ) ) ) ) ) )
| ? [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X1 ) )
| ( X3 @ ( X0 @ X2 ) ) )
& ? [X4: $i] :
~ ( ( X1 @ X4 )
<=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ok6vQgKaw6/DTF2THF_17427.p',cTHM143_EXPANDB) ).
thf(f391,plain,
( ! [X0: $i] :
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ X0 )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
!= ( sK3 @ X0 ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f390]) ).
thf(f390,definition,
( spl0_4
<=> ! [X0: $i] :
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ X0 )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
!= ( sK3 @ X0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f451,plain,
( ( ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f450]) ).
thf(f450,plain,
( ( ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ sK3 ) )
| ( Y0 @ ( sK2 @ sK3 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f436]) ).
thf(f436,plain,
( ( ( ~ ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ sK3 ) )
| ( Y0 @ ( sK2 @ sK3 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f434,f61]) ).
thf(f61,plain,
( ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) )
= ( sK2 @ sK3 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i > $o] :
( ( ( X1
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( X1 @ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i > $o] :
( ( ( X1
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( ( ~ ( X1 @ ( sK2 @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i > $o] :
( ( ( X1
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) )
& ~ ( X1 @ ( sK2 @ sK3 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) ) ) )
& ~ ( Y0 @ ( sK2 @ sK3 ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) ) ) )
& ~ ( Y0 @ ( sK2 @ sK3 ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0
@ ( sK2
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) ) ) )
& ~ ( Y0 @ ( sK2 @ sK3 ) ) ) )
| $false )
= $false ),
inference(backward_demodulation,[status(thm)],[f19,f22]) ).
thf(f434,plain,
( ! [X1: $i > $o] :
( ( ~ ( X1 @ ( sK2 @ X1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ sK3 ) )
| ( Y0 @ ( sK2 @ X1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f431]) ).
thf(f431,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ sK3 ) )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) )
@ X1 )
= $false )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f418]) ).
thf(f412,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f411,f387,f390]) ).
thf(f387,definition,
( spl0_3
<=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f411,plain,
( ! [X1: $i] :
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK2 @ Y0 ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ X1 )
| ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
!= ( sK3 @ X1 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f410]) ).
thf(f410,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) )
@ X1 )
= $false )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f388]) ).
thf(f388,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f387]) ).
thf(f408,plain,
spl0_3,
inference(avatar_split_clause,[status(thm)],[f367,f387]) ).
thf(f367,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f366]) ).
thf(f366,plain,
( ( $true = $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f365]) ).
thf(f365,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false )
| ( ( $true
| ~ ( sK4 @ sK3
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f364]) ).
thf(f364,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false )
| ( ( $true
| ~ ( sK4 @ sK3
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f359]) ).
thf(f359,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) )
@ Y0 )
!= ( sK3 @ Y0 ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( sK3 @ Y0 ) ) )
= $false )
| ( ( $true
| ~ ( sK4 @ sK3
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f37,f73]) ).
thf(f73,plain,
! [X0: $i > $o] :
( ( $true
= ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( X0 @ Y0 ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i > $o] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( X0 @ Y0 ) ) )
= $false )
| ( $true = $false )
| ( $true
= ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: $i > $o] :
( ( ( ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ X0 ) )
| $true )
= $false )
| ( $true
= ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( X0 @ Y0 ) ) )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: $i > $o] :
( ( ( ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ X0 ) )
| ~ $false )
= $false )
| ( $true
= ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
!= ( X0 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i > $o] :
( ( $true
= ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ sK3 ) ) )
| ( ( ( sK4 @ X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK2 @ Y1 ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ Y0 )
| ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ ( sK2 @ X0 ) )
| ~ $false )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK2 @ Y2 ) )
& ( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ~ ( Y3 @ Y1 )
| ( Y3 @ ( sK2 @ Y2 ) ) ) ) ) )
@ Y0 )
!= ( X0 @ Y0 ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f37,f39]) ).
thf(f37,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ( sK4 @ X1 @ X2 @ ( sK2 @ X1 ) )
| ~ ( sK4 @ X1 @ X2 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
!= ( X1 @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
!= ( X1 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK2 @ X1 ) )
| ~ ( Y0 @ ( sK2 @ X2 ) ) )
@ ( sK4 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK2 @ X1 ) )
| ~ ( Y0 @ ( sK2 @ X2 ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
!= ( X1 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
!= ( X1 @ Y0 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK2 @ X1 ) )
| ~ ( Y0 @ ( sK2 @ X2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
!= ( X1 @ Y1 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ ( sK2 @ X1 ) )
| ~ ( Y1 @ ( sK2 @ Y0 ) ) ) ) )
@ X2 )
= $false ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
!= ( X1 @ Y1 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ ( sK2 @ X1 ) )
| ~ ( Y1 @ ( sK2 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
!= ( Y0 @ Y2 ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ ( sK2 @ Y0 ) )
| ~ ( Y2 @ ( sK2 @ Y1 ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO324^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:28:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SYO324^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.49 % Domain : Syntactic
% 0.33/0.49 % Problem : TPS problem from BASIC-HO-THMS
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro09]
% 0.33/0.49 % Names : tps_0983 [Bro09]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.25 v9.0.0, 0.33 v8.2.0, 0.36 v8.1.0, 0.42 v7.5.0, 0.50 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.33/0.49 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.33/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.33/0.49 % Number of connectives : 30 ( 5 ~; 4 |; 3 &; 17 @)
% 0.33/0.49 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 16 ( 16 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.33/0.49 % Number of variables : 10 ( 1 ^; 4 !; 5 ?; 10 :)
% 0.33/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(cTHM143_EXPANDB,conjecture,
% 0.33/0.49 ! [Xh: ( $i > $o ) > $i] :
% 0.33/0.49 ( ? [Xp: $i > $o,Xq: $i > $o] :
% 0.33/0.49 ( ! [Xq_31: $i > $o] :
% 0.33/0.49 ( ~ ( Xq_31 @ ( Xh @ Xp ) )
% 0.33/0.49 | ( Xq_31 @ ( Xh @ Xq ) ) )
% 0.33/0.49 & ? [Xx: $i] :
% 0.33/0.49 ~ ( ( Xp @ Xx )
% 0.33/0.49 <=> ( Xq @ Xx ) ) )
% 0.33/0.49 | ! [Xt: $i > $o] :
% 0.33/0.49 ( ( Xt @ ( Xh @ Xt ) )
% 0.33/0.49 | ? [Xq: $i > $o] :
% 0.33/0.49 ( ( Xq
% 0.33/0.49 @ ( Xh
% 0.33/0.49 @ ^ [Xz: $i] :
% 0.33/0.49 ? [Xt0: $i > $o] :
% 0.33/0.49 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.33/0.49 & ! [Xq0: $i > $o] :
% 0.33/0.49 ( ~ ( Xq0 @ Xz )
% 0.33/0.49 | ( Xq0 @ ( Xh @ Xt0 ) ) ) ) ) )
% 0.33/0.49 & ~ ( Xq @ ( Xh @ Xt ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.65/1.46 ---- Embedded in THF ---
% 1.65/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.46 %%% Generated on Tue Feb 24 14:28:13 EST 2026
% 1.65/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.46 %%% Logic specification used:
% 1.65/1.46 %%% thf(spec, logic, $$dhol).
% 1.65/1.46
% 1.65/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ok6vQgKaw6/DTF2DTF17427.p
% See solution above
% 1.65/1.46 ------------------------
% 1.65/1.47 ---- Cleaned THF ---
% 1.65/1.47 thf(cTHM143_EXPANDB,conjecture,
% 1.65/1.47 ! [Xh: ( $i > $o ) > $i] :
% 1.65/1.47 ( ? [Xp: $i > $o,Xq: $i > $o] :
% 1.65/1.47 ( ! [Xq_31: $i > $o] :
% 1.65/1.47 ( ~ ( Xq_31 @ ( Xh @ Xp ) )
% 1.65/1.47 | ( Xq_31 @ ( Xh @ Xq ) ) )
% 1.65/1.47 & ? [Xx: $i] :
% 1.65/1.47 ~ ( ( Xp @ Xx )
% 1.65/1.47 <=> ( Xq @ Xx ) ) )
% 1.65/1.47 | ! [Xt: $i > $o] :
% 1.65/1.47 ( ( Xt @ ( Xh @ Xt ) )
% 1.65/1.47 | ? [Xq: $i > $o] :
% 1.65/1.47 ( ( Xq
% 1.65/1.47 @ ( Xh
% 1.65/1.47 @ ^ [Xz: $i] :
% 1.65/1.47 ? [Xt0: $i > $o] :
% 1.65/1.47 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 1.65/1.47 & ! [Xq0: $i > $o] :
% 1.65/1.47 ( ~ ( Xq0 @ Xz )
% 1.65/1.47 | ( Xq0 @ ( Xh @ Xt0 ) ) ) ) ) )
% 1.65/1.47 & ~ ( Xq @ ( Xh @ Xt ) ) ) ) ) ).
% 1.65/1.47 ------------------------
% 1.65/1.49 % (17564)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_17427 for (2999ds/27Mi)
% 1.65/1.49 % (17562)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/183Mi)
% 1.65/1.49 % (17563)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_17427 for (2999ds/4Mi)
% 1.65/1.49 % (17565)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/2Mi)
% 1.65/1.49 % (17568)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/18Mi)
% 1.65/1.49 % (17567)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_17427 for (2999ds/275Mi)
% 1.65/1.49 % (17566)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_17427 for (2999ds/2Mi)
% 1.65/1.49 % (17565)Instruction limit reached!
% 1.65/1.49 % (17565)------------------------------
% 1.65/1.49 % (17565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (17565)Termination reason: Unknown
% 1.65/1.49 % (17565)Termination phase: Preprocessing 3
% 1.65/1.49
% 1.65/1.49 % (17566)Instruction limit reached!
% 1.65/1.49 % (17566)------------------------------
% 1.65/1.49 % (17566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (17566)Termination reason: Unknown
% 1.65/1.49 % (17566)Termination phase: Property scanning
% 1.65/1.49
% 1.65/1.49 % (17566)Memory used [KB]: 895
% 1.65/1.49 % (17566)Time elapsed: 0.003 s
% 1.65/1.49 % (17566)Instructions burned: 2 (million)
% 1.65/1.49 % (17566)------------------------------
% 1.65/1.49 % (17566)------------------------------
% 1.65/1.49 % (17565)Memory used [KB]: 895
% 1.65/1.49 % (17565)Time elapsed: 0.003 s
% 1.65/1.49 % (17565)Instructions burned: 2 (million)
% 1.65/1.49 % (17565)------------------------------
% 1.65/1.49 % (17565)------------------------------
% 1.65/1.50 % (17563)Instruction limit reached!
% 1.65/1.50 % (17563)------------------------------
% 1.65/1.50 % (17563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.50 % (17563)Termination reason: Unknown
% 1.65/1.50 % (17563)Termination phase: Saturation
% 1.65/1.50
% 1.65/1.50 % (17563)Memory used [KB]: 5500
% 1.65/1.50 % (17563)Time elapsed: 0.004 s
% 1.65/1.50 % (17563)Instructions burned: 4 (million)
% 1.65/1.50 % (17563)------------------------------
% 1.65/1.50 % (17563)------------------------------
% 1.80/1.50 % (17568)Instruction limit reached!
% 1.80/1.50 % (17568)------------------------------
% 1.80/1.50 % (17568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (17568)Termination reason: Unknown
% 1.80/1.50 % (17568)Termination phase: Saturation
% 1.80/1.50
% 1.80/1.50 % (17568)Memory used [KB]: 5628
% 1.80/1.50 % (17568)Time elapsed: 0.012 s
% 1.80/1.50 % (17568)Instructions burned: 19 (million)
% 1.80/1.50 % (17568)------------------------------
% 1.80/1.50 % (17568)------------------------------
% 1.80/1.51 % (17564)Instruction limit reached!
% 1.80/1.51 % (17564)------------------------------
% 1.80/1.51 % (17564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (17564)Termination reason: Unknown
% 1.80/1.51 % (17564)Termination phase: Saturation
% 1.80/1.51
% 1.80/1.51 % (17564)Memory used [KB]: 5628
% 1.80/1.51 % (17564)Time elapsed: 0.016 s
% 1.80/1.51 % (17564)Instructions burned: 27 (million)
% 1.80/1.51 % (17564)------------------------------
% 1.80/1.51 % (17564)------------------------------
% 1.80/1.51 % (17570)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_17427 for (2999ds/37Mi)
% 1.80/1.51 % (17569)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/3Mi)
% 1.80/1.51 % (17571)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_17427 for (2999ds/15Mi)
% 1.80/1.51 % (17569)Instruction limit reached!
% 1.80/1.51 % (17569)------------------------------
% 1.80/1.51 % (17569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (17569)Termination reason: Unknown
% 1.80/1.51 % (17569)Termination phase: Saturation
% 1.80/1.51
% 1.80/1.51 % (17569)Memory used [KB]: 5500
% 1.80/1.51 % (17569)Time elapsed: 0.004 s
% 1.80/1.51 % (17569)Instructions burned: 4 (million)
% 1.80/1.51 % (17569)------------------------------
% 1.80/1.51 % (17569)------------------------------
% 1.80/1.52 % (17572)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_17427 for (2999ds/3Mi)
% 1.80/1.52 % (17571)Instruction limit reached!
% 1.80/1.52 % (17571)------------------------------
% 1.80/1.52 % (17571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (17571)Termination reason: Unknown
% 1.80/1.52 % (17571)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (17571)Memory used [KB]: 5628
% 1.80/1.52 % (17571)Time elapsed: 0.010 s
% 1.80/1.52 % (17571)Instructions burned: 16 (million)
% 1.80/1.52 % (17571)------------------------------
% 1.80/1.52 % (17571)------------------------------
% 1.80/1.52 % (17572)Instruction limit reached!
% 1.80/1.52 % (17572)------------------------------
% 1.80/1.52 % (17572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (17572)Termination reason: Unknown
% 1.80/1.52 % (17572)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (17572)Memory used [KB]: 5500
% 1.80/1.52 % (17572)Time elapsed: 0.004 s
% 1.80/1.52 % (17572)Instructions burned: 4 (million)
% 1.80/1.52 % (17572)------------------------------
% 1.80/1.52 % (17572)------------------------------
% 1.80/1.52 % (17573)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_17427 for (2999ds/1041Mi)
% 1.80/1.53 % (17570)Instruction limit reached!
% 1.80/1.53 % (17570)------------------------------
% 1.80/1.53 % (17570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (17570)Termination reason: Unknown
% 1.80/1.53 % (17570)Termination phase: Saturation
% 1.80/1.53
% 1.80/1.53 % (17570)Memory used [KB]: 6140
% 1.80/1.53 % (17570)Time elapsed: 0.019 s
% 1.80/1.53 % (17570)Instructions burned: 37 (million)
% 1.80/1.53 % (17570)------------------------------
% 1.80/1.53 % (17570)------------------------------
% 1.80/1.53 % (17574)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/7Mi)
% 1.80/1.53 % (17574)Instruction limit reached!
% 1.80/1.53 % (17574)------------------------------
% 1.80/1.53 % (17574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (17574)Termination reason: Unknown
% 1.80/1.53 % (17574)Termination phase: Saturation
% 1.80/1.53
% 1.80/1.53 % (17574)Memory used [KB]: 1023
% 1.80/1.53 % (17574)Time elapsed: 0.006 s
% 1.80/1.53 % (17574)Instructions burned: 7 (million)
% 1.80/1.53 % (17574)------------------------------
% 1.80/1.53 % (17574)------------------------------
% 1.80/1.54 % (17575)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/16Mi)
% 1.80/1.54 % (17576)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_17427 for (2999ds/3Mi)
% 1.80/1.54 % (17576)Instruction limit reached!
% 1.80/1.54 % (17576)------------------------------
% 1.80/1.54 % (17576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.54 % (17576)Termination reason: Unknown
% 1.80/1.54 % (17576)Termination phase: Property scanning
% 1.80/1.54
% 1.80/1.54 % (17576)Memory used [KB]: 1023
% 1.80/1.54 % (17576)Time elapsed: 0.004 s
% 1.80/1.54 % (17576)Instructions burned: 3 (million)
% 1.80/1.54 % (17576)------------------------------
% 1.80/1.54 % (17576)------------------------------
% 1.80/1.54 % (17577)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_17427 for (2999ds/3Mi)
% 1.80/1.55 % (17577)Instruction limit reached!
% 1.80/1.55 % (17577)------------------------------
% 1.80/1.55 % (17577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (17577)Termination reason: Unknown
% 1.80/1.55 % (17577)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (17577)Memory used [KB]: 1023
% 1.80/1.55 % (17577)Time elapsed: 0.004 s
% 1.80/1.55 % (17577)Instructions burned: 4 (million)
% 1.80/1.55 % (17577)------------------------------
% 1.80/1.55 % (17577)------------------------------
% 1.80/1.55 % (17575)Instruction limit reached!
% 1.80/1.55 % (17575)------------------------------
% 1.80/1.55 % (17575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (17575)Termination reason: Unknown
% 1.80/1.55 % (17575)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (17575)Memory used [KB]: 5756
% 1.80/1.55 % (17575)Time elapsed: 0.012 s
% 1.80/1.55 % (17575)Instructions burned: 17 (million)
% 1.80/1.55 % (17575)------------------------------
% 1.80/1.55 % (17575)------------------------------
% 1.80/1.55 % (17578)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/7Mi)
% 1.80/1.55 % (17578)Instruction limit reached!
% 1.80/1.55 % (17578)------------------------------
% 1.80/1.55 % (17578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (17578)Termination reason: Unknown
% 1.80/1.55 % (17578)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (17578)Memory used [KB]: 5500
% 1.80/1.55 % (17578)Time elapsed: 0.006 s
% 1.80/1.55 % (17578)Instructions burned: 7 (million)
% 1.80/1.55 % (17578)------------------------------
% 1.80/1.55 % (17578)------------------------------
% 1.80/1.56 % (17579)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/3Mi)
% 1.80/1.56 % (17579)Instruction limit reached!
% 1.80/1.56 % (17579)------------------------------
% 1.80/1.56 % (17579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.56 % (17579)Termination reason: Unknown
% 1.80/1.56 % (17579)Termination phase: Saturation
% 1.80/1.56
% 1.80/1.56 % (17579)Memory used [KB]: 5500
% 1.80/1.56 % (17579)Time elapsed: 0.004 s
% 1.80/1.56 % (17579)Instructions burned: 3 (million)
% 1.80/1.56 % (17579)------------------------------
% 1.80/1.56 % (17579)------------------------------
% 1.80/1.56 % (17580)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/4Mi)
% 1.80/1.56 % (17581)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17427 for (2999ds/18Mi)
% 1.80/1.56 % (17580)Instruction limit reached!
% 1.80/1.56 % (17580)------------------------------
% 1.80/1.56 % (17580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.56 % (17580)Termination reason: Unknown
% 1.80/1.56 % (17580)Termination phase: Saturation
% 1.80/1.56
% 1.80/1.56 % (17580)Memory used [KB]: 5500
% 1.80/1.56 % (17580)Time elapsed: 0.004 s
% 1.80/1.57 % (17580)Instructions burned: 4 (million)
% 1.80/1.57 % (17580)------------------------------
% 1.80/1.57 % (17580)------------------------------
% 1.80/1.57 % (17573)First to succeed.
% 1.80/1.57 % (17573)Refutation found. Thanks to Tanya!
% 1.80/1.57 % SZS status Theorem for DTF2THF_17427
% 1.80/1.57 % SZS output start Proof for DTF2THF_17427
% 1.80/1.57 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.80/1.57 thf(func_def_18, type, sK2: ($i > $o) > $i).
% 1.80/1.57 thf(func_def_19, type, sK3: $i > $o).
% 1.80/1.57 thf(func_def_20, type, sK4: ($i > $o) > ($i > $o) > $i > $o).
% 1.80/1.57 thf(func_def_22, type, sK5: $i > $o).
% 1.80/1.57 thf(f459,plain,(
% 1.80/1.57 $false),
% 1.80/1.57 inference(avatar_sat_refutation,[status(thm)],[f408,f412,f458])).
% 1.80/1.57 thf(f458,plain,(
% 1.80/1.57 ~spl0_4),
% 1.80/1.57 inference(avatar_contradiction_clause,[status(thm)],[f457])).
% 1.80/1.57 thf(f457,plain,(
% 1.80/1.57 $false | ~spl0_4),
% 1.80/1.57 inference(trivial_inequality_removal,[status(thm)],[f456])).
% 1.80/1.57 thf(f456,plain,(
% 1.80/1.57 ($true = $false) | ~spl0_4),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f455])).
% 1.80/1.57 thf(f455,plain,(
% 1.80/1.57 ($false = ((^[Y0 : $i > $o]: ($true)) @ sK5)) | ~spl0_4),
% 1.80/1.57 inference(sigma_clausification,[status(thm)],[f454])).
% 1.80/1.57 thf(f454,plain,(
% 1.80/1.57 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) = $false) | ~spl0_4),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f453])).
% 1.80/1.57 thf(f453,plain,(
% 1.80/1.57 ($false = ($true & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))))) | ~spl0_4),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f452])).
% 1.80/1.57 thf(f452,plain,(
% 1.80/1.57 (((~ $false) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) = $false) | ~spl0_4),
% 1.80/1.57 inference(forward_demodulation,[status(thm)],[f451,f418])).
% 1.80/1.57 thf(f418,plain,(
% 1.80/1.57 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0)))))))) = $false) | ~spl0_4),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f417])).
% 1.80/1.57 thf(f417,plain,(
% 1.80/1.57 ((~ (~ (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0)))))))))) = $false) | ~spl0_4),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f414])).
% 1.80/1.57 thf(f414,plain,(
% 1.80/1.57 ((~ ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0)))))))) = $false)) = $false) | ~spl0_4),
% 1.80/1.57 inference(superposition,[status(thm)],[f391,f22])).
% 1.80/1.57 thf(f22,plain,(
% 1.80/1.57 ((sK3 @ (sK2 @ sK3)) = $false)),
% 1.80/1.57 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.80/1.57 thf(f19,plain,(
% 1.80/1.57 (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK2 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))))) & (~ (Y0 @ (sK2 @ sK3)))))) | (sK3 @ (sK2 @ sK3))) = $false)),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.80/1.57 thf(f18,plain,(
% 1.80/1.57 (((^[Y0 : $i > $o]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ (sK2 @ Y3))) & (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ Y2)) | (Y4 @ (sK2 @ Y3))))))))))) & (~ (Y1 @ (sK2 @ Y0)))))) | (Y0 @ (sK2 @ Y0)))) @ sK3) = $false)),
% 1.80/1.57 inference(sigma_clausification,[status(thm)],[f15])).
% 1.80/1.57 thf(f15,plain,(
% 1.80/1.57 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ (sK2 @ Y3))) & (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ Y2)) | (Y4 @ (sK2 @ Y3))))))))))) & (~ (Y1 @ (sK2 @ Y0)))))) | (Y0 @ (sK2 @ Y0))))) = $false)),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f14])).
% 1.80/1.57 thf(f14,plain,(
% 1.80/1.57 (($false | (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ (sK2 @ Y3))) & (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ Y2)) | (Y4 @ (sK2 @ Y3))))))))))) & (~ (Y1 @ (sK2 @ Y0)))))) | (Y0 @ (sK2 @ Y0)))))) = $false)),
% 1.80/1.57 inference(backward_demodulation,[status(thm)],[f11,f13])).
% 1.80/1.57 thf(f13,plain,(
% 1.80/1.57 ($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (~ ((Y1 @ Y2) = (Y0 @ Y2))))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (sK2 @ Y0)) | (~ (Y2 @ (sK2 @ Y1))))))))))))),
% 1.80/1.57 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.80/1.57 thf(f11,plain,(
% 1.80/1.57 ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (~ ((Y1 @ Y2) = (Y0 @ Y2))))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (sK2 @ Y0)) | (~ (Y2 @ (sK2 @ Y1))))))))))) | (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ (sK2 @ Y3))) & (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ Y2)) | (Y4 @ (sK2 @ Y3))))))))))) & (~ (Y1 @ (sK2 @ Y0)))))) | (Y0 @ (sK2 @ Y0)))))))),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.80/1.57 thf(f10,plain,(
% 1.80/1.57 (((^[Y0 : ($i > $o) > $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (~ ((Y2 @ Y3) = (Y1 @ Y3))))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ (Y0 @ Y1)) | (~ (Y3 @ (Y0 @ Y2))))))))))) | (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ (Y0 @ Y4))) & (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((~ (Y5 @ Y3)) | (Y5 @ (Y0 @ Y4))))))))))) & (~ (Y2 @ (Y0 @ Y1)))))) | (Y1 @ (Y0 @ Y1))))))) @ sK2) = $false)),
% 1.80/1.57 inference(sigma_clausification,[status(thm)],[f7])).
% 1.80/1.57 thf(f7,plain,(
% 1.80/1.57 ($false = (!! @ (($i > $o) > $i) @ (^[Y0 : ($i > $o) > $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (~ ((Y2 @ Y3) = (Y1 @ Y3))))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ (Y0 @ Y1)) | (~ (Y3 @ (Y0 @ Y2))))))))))) | (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ (Y0 @ Y4))) & (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((~ (Y5 @ Y3)) | (Y5 @ (Y0 @ Y4))))))))))) & (~ (Y2 @ (Y0 @ Y1)))))) | (Y1 @ (Y0 @ Y1)))))))))),
% 1.80/1.57 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.80/1.57 thf(f6,plain,(
% 1.80/1.57 ($true = (~ (!! @ (($i > $o) > $i) @ (^[Y0 : ($i > $o) > $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (~ ((Y2 @ Y3) = (Y1 @ Y3))))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ (Y0 @ Y1)) | (~ (Y3 @ (Y0 @ Y2))))))))))) | (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ (Y0 @ Y4))) & (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((~ (Y5 @ Y3)) | (Y5 @ (Y0 @ Y4))))))))))) & (~ (Y2 @ (Y0 @ Y1)))))) | (Y1 @ (Y0 @ Y1))))))))))),
% 1.80/1.57 inference(cnf_transformation,[status(thm)],[f5])).
% 1.80/1.57 thf(f5,plain,(
% 1.80/1.57 ($true = (~ (!! @ (($i > $o) > $i) @ (^[Y0 : ($i > $o) > $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (~ ((Y2 @ Y3) = (Y1 @ Y3))))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ (Y0 @ Y1)) | (~ (Y3 @ (Y0 @ Y2))))))))))) | (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((~ (Y4 @ (Y0 @ Y4))) & (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((~ (Y5 @ Y3)) | (Y5 @ (Y0 @ Y4))))))))))) & (~ (Y2 @ (Y0 @ Y1)))))) | (Y1 @ (Y0 @ Y1))))))))))),
% 1.80/1.57 inference(fool_elimination,[status(thm)],[f4])).
% 1.80/1.57 thf(f4,plain,(
% 1.80/1.57 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o] : ((X1 @ (X0 @ X1)) | ? [X2 : $i > $o] : (~(X2 @ (X0 @ X1)) & (X2 @ (X0 @ (^[X3 : $i] : (? [X4 : $i > $o] : (! [X5 : $i > $o] : ((X5 @ (X0 @ X4)) | ~(X5 @ X3)) & ~(X4 @ (X0 @ X4))))))))) | ? [X6 : $i > $o,X7 : $i > $o] : (! [X8 : $i > $o] : (~(X8 @ (X0 @ X6)) | (X8 @ (X0 @ X7))) & ? [X9 : $i] : ~((X6 @ X9) <=> (X7 @ X9))))),
% 1.80/1.57 inference(rectify,[status(thm)],[f2])).
% 1.80/1.57 thf(f2,negated_conjecture,(
% 1.80/1.57 ~! [X0 : ($i > $o) > $i] : (! [X5 : $i > $o] : ((X5 @ (X0 @ X5)) | ? [X2 : $i > $o] : (~(X2 @ (X0 @ X5)) & (X2 @ (X0 @ (^[X6 : $i] : (? [X7 : $i > $o] : (! [X8 : $i > $o] : ((X8 @ (X0 @ X7)) | ~(X8 @ X6)) & ~(X7 @ (X0 @ X7))))))))) | ? [X1 : $i > $o,X2 : $i > $o] : (! [X3 : $i > $o] : (~(X3 @ (X0 @ X1)) | (X3 @ (X0 @ X2))) & ? [X4 : $i] : ~((X1 @ X4) <=> (X2 @ X4))))),
% 1.80/1.57 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.57 thf(f1,conjecture,(
% 1.80/1.57 ! [X0 : ($i > $o) > $i] : (! [X5 : $i > $o] : ((X5 @ (X0 @ X5)) | ? [X2 : $i > $o] : (~(X2 @ (X0 @ X5)) & (X2 @ (X0 @ (^[X6 : $i] : (? [X7 : $i > $o] : (! [X8 : $i > $o] : ((X8 @ (X0 @ X7)) | ~(X8 @ X6)) & ~(X7 @ (X0 @ X7))))))))) | ? [X1 : $i > $o,X2 : $i > $o] : (! [X3 : $i > $o] : (~(X3 @ (X0 @ X1)) | (X3 @ (X0 @ X2))) & ? [X4 : $i] : ~((X1 @ X4) <=> (X2 @ X4))))),
% 1.80/1.57 file('/export/starexec/sandbox/tmp/tmp.ok6vQgKaw6/DTF2THF_17427.p',cTHM143_EXPANDB)).
% 1.80/1.57 thf(f391,plain,(
% 1.80/1.57 ( ! [X0 : $i] : (((~ ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ X0)) | (Y1 @ (sK2 @ Y0)))))))) = (sK3 @ X0))) = $false)) ) | ~spl0_4),
% 1.80/1.57 inference(avatar_component_clause,[status(thm)],[f390])).
% 1.80/1.57 thf(f390,definition,(
% 1.80/1.57 spl0_4 <=> ! [X0 : $i] : ((~ ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ X0)) | (Y1 @ (sK2 @ Y0)))))))) = (sK3 @ X0))) = $false)),
% 1.80/1.57 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.80/1.57 thf(f451,plain,(
% 1.80/1.57 (((~ (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) = $false) | ~spl0_4),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f450])).
% 1.80/1.57 thf(f450,plain,(
% 1.80/1.57 (((~ (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ sK3))) | (Y0 @ (sK2 @ sK3)))))) = $false) | ~spl0_4),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f436])).
% 1.80/1.57 thf(f436,plain,(
% 1.80/1.57 (((~ ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ sK3))) | (Y0 @ (sK2 @ sK3)))))) = $false) | ~spl0_4),
% 1.80/1.57 inference(superposition,[status(thm)],[f434,f61])).
% 1.80/1.57 thf(f61,plain,(
% 1.80/1.57 ((sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))))) = (sK2 @ sK3))),
% 1.80/1.57 inference(leibniz_equality_elimination,[status(thm)],[f39])).
% 1.80/1.57 thf(f39,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : (((X1 @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))) = $false) | ($true = (X1 @ (sK2 @ sK3)))) )),
% 1.80/1.57 inference(not_proxy_clausification,[status(thm)],[f29])).
% 1.80/1.57 thf(f29,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : (((X1 @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))) = $false) | ((~ (X1 @ (sK2 @ sK3))) = $false)) )),
% 1.80/1.57 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.80/1.57 thf(f27,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : ((((X1 @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))) & (~ (X1 @ (sK2 @ sK3)))) = $false)) )),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.80/1.57 thf(f26,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((Y0 @ (sK2 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))))) & (~ (Y0 @ (sK2 @ sK3))))) @ X1) = $false)) )),
% 1.80/1.57 inference(pi_clausification,[status(thm)],[f25])).
% 1.80/1.57 thf(f25,plain,(
% 1.80/1.57 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK2 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))))) & (~ (Y0 @ (sK2 @ sK3)))))) = $false)),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f24])).
% 1.80/1.57 thf(f24,plain,(
% 1.80/1.57 (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK2 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))))) & (~ (Y0 @ (sK2 @ sK3)))))) | $false) = $false)),
% 1.80/1.57 inference(backward_demodulation,[status(thm)],[f19,f22])).
% 1.80/1.57 thf(f434,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : ((((~ (X1 @ (sK2 @ X1))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ sK3))) | (Y0 @ (sK2 @ X1)))))) = $false)) ) | ~spl0_4),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f431])).
% 1.80/1.57 thf(f431,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ sK3))) | (Y1 @ (sK2 @ Y0))))))) @ X1) = $false)) ) | ~spl0_4),
% 1.80/1.57 inference(pi_clausification,[status(thm)],[f418])).
% 1.80/1.57 thf(f412,plain,(
% 1.80/1.57 spl0_4 | ~spl0_3),
% 1.80/1.57 inference(avatar_split_clause,[status(thm)],[f411,f387,f390])).
% 1.80/1.57 thf(f387,definition,(
% 1.80/1.57 spl0_3 <=> ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false)),
% 1.80/1.57 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.80/1.57 thf(f411,plain,(
% 1.80/1.57 ( ! [X1 : $i] : (((~ ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK2 @ Y0))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ X1)) | (Y1 @ (sK2 @ Y0)))))))) = (sK3 @ X1))) = $false)) ) | ~spl0_3),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f410])).
% 1.80/1.57 thf(f410,plain,(
% 1.80/1.57 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0)))) @ X1) = $false)) ) | ~spl0_3),
% 1.80/1.57 inference(pi_clausification,[status(thm)],[f388])).
% 1.80/1.57 thf(f388,plain,(
% 1.80/1.57 ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false) | ~spl0_3),
% 1.80/1.57 inference(avatar_component_clause,[status(thm)],[f387])).
% 1.80/1.57 thf(f408,plain,(
% 1.80/1.57 spl0_3),
% 1.80/1.57 inference(avatar_split_clause,[status(thm)],[f367,f387])).
% 1.80/1.57 thf(f367,plain,(
% 1.80/1.57 ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false)),
% 1.80/1.57 inference(trivial_inequality_removal,[status(thm)],[f366])).
% 1.80/1.57 thf(f366,plain,(
% 1.80/1.57 ($true = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false)),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f365])).
% 1.80/1.57 thf(f365,plain,(
% 1.80/1.57 ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false) | (($true | (~ (sK4 @ sK3 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))))) = $false)),
% 1.80/1.57 inference(duplicate_literal_removal,[status(thm)],[f364])).
% 1.80/1.57 thf(f364,plain,(
% 1.80/1.57 ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false) | (($true | (~ (sK4 @ sK3 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false)),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f359])).
% 1.80/1.57 thf(f359,plain,(
% 1.80/1.57 ((?? @ $i @ (^[Y0 : $i]: (~ (((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))) @ Y0) = (sK3 @ Y0))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (sK3 @ Y0))))) = $false) | (($true | (~ (sK4 @ sK3 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))))))) = $false)),
% 1.80/1.57 inference(superposition,[status(thm)],[f37,f73])).
% 1.80/1.57 thf(f73,plain,(
% 1.80/1.57 ( ! [X0 : $i > $o] : (($true = (sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3))) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (X0 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.80/1.57 thf(f72,plain,(
% 1.80/1.57 ( ! [X0 : $i > $o] : (((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (X0 @ Y0))))) = $false) | ($true = $false) | ($true = (sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3)))) )),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f71])).
% 1.80/1.57 thf(f71,plain,(
% 1.80/1.57 ( ! [X0 : $i > $o] : ((((sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ X0)) | $true) = $false) | ($true = (sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3))) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (X0 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(boolean_simplification,[status(thm)],[f70])).
% 1.80/1.57 thf(f70,plain,(
% 1.80/1.57 ( ! [X0 : $i > $o] : ((((sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ X0)) | (~ $false)) = $false) | ($true = (sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3))) | ((?? @ $i @ (^[Y0 : $i]: (~ ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1)))))))) = (X0 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.80/1.57 thf(f67,plain,(
% 1.80/1.57 ( ! [X0 : $i > $o] : (($true = (sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ sK3))) | (((sK4 @ X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK2 @ Y1))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y0)) | (Y2 @ (sK2 @ Y1))))))))) @ (sK2 @ X0)) | (~ $false)) = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ (((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK2 @ Y2))) & (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((~ (Y3 @ Y1)) | (Y3 @ (sK2 @ Y2))))))))) @ Y0) = (X0 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(superposition,[status(thm)],[f37,f39])).
% 1.80/1.57 thf(f37,plain,(
% 1.80/1.57 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((sK4 @ X1 @ X2 @ (sK2 @ X1)) | (~ (sK4 @ X1 @ X2 @ (sK2 @ X2)))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ ((X2 @ Y0) = (X1 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.80/1.57 thf(f35,plain,(
% 1.80/1.57 ( ! [X2 : $i > $o,X1 : $i > $o] : (((?? @ $i @ (^[Y0 : $i]: (~ ((X2 @ Y0) = (X1 @ Y0))))) = $false) | (((^[Y0 : $i > $o]: ((Y0 @ (sK2 @ X1)) | (~ (Y0 @ (sK2 @ X2))))) @ (sK4 @ X1 @ X2)) = $false)) )),
% 1.80/1.57 inference(sigma_clausification,[status(thm)],[f28])).
% 1.80/1.57 thf(f28,plain,(
% 1.80/1.57 ( ! [X2 : $i > $o,X1 : $i > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK2 @ X1)) | (~ (Y0 @ (sK2 @ X2)))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: (~ ((X2 @ Y0) = (X1 @ Y0))))) = $false)) )),
% 1.80/1.57 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.80/1.57 thf(f21,plain,(
% 1.80/1.57 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((?? @ $i @ (^[Y0 : $i]: (~ ((X2 @ Y0) = (X1 @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK2 @ X1)) | (~ (Y0 @ (sK2 @ X2))))))) = $false)) )),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.80/1.57 thf(f20,plain,(
% 1.80/1.57 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (~ ((Y0 @ Y1) = (X1 @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ X1)) | (~ (Y1 @ (sK2 @ Y0)))))))) @ X2) = $false)) )),
% 1.80/1.57 inference(pi_clausification,[status(thm)],[f17])).
% 1.80/1.57 thf(f17,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (~ ((Y0 @ Y1) = (X1 @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ (sK2 @ X1)) | (~ (Y1 @ (sK2 @ Y0))))))))) = $false)) )),
% 1.80/1.57 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.80/1.57 thf(f16,plain,(
% 1.80/1.57 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (~ ((Y1 @ Y2) = (Y0 @ Y2))))) & (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ (sK2 @ Y0)) | (~ (Y2 @ (sK2 @ Y1)))))))))) @ X1) = $false)) )),
% 1.80/1.57 inference(pi_clausification,[status(thm)],[f13])).
% 1.80/1.57 % SZS output end Proof for DTF2THF_17427
% 1.80/1.57 % (17573)------------------------------
% 1.80/1.57 % (17573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.57 % (17573)Termination reason: Refutation
% 1.80/1.57
% 1.80/1.57 % (17573)Memory used [KB]: 5884
% 1.80/1.57 % (17573)Time elapsed: 0.048 s
% 1.80/1.57 % (17573)Instructions burned: 83 (million)
% 1.80/1.57 % (17573)------------------------------
% 1.80/1.57 % (17573)------------------------------
% 1.80/1.57 % (17561)Success in time 0.083 s
%------------------------------------------------------------------------------