%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ108^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:28:30 AM UTC 2026
% Result : Theorem 1.62s 1.41s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of formulae : 53 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 372 ( 89 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 747 ( 12 ~; 40 |; 26 &; 545 @)
% ( 0 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-2 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 144 ( 114 ^; 30 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $o ).
thf(func_def_17,type,
sK3: $i > $o ).
thf(func_def_18,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_19,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f146,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f24,f139]) ).
thf(f139,plain,
( $false
= ( sK3 @ ( s @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $false = $true )
| ( $false
= ( sK3 @ ( s @ sK1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f137,f22]) ).
thf(f22,plain,
( $false
= ( sK3 @ ( s @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK3 @ ( s @ sK1 ) ) )
=> ( sK3 @ ( s @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK1 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK1 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( Y0 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK1 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ sK1 ) )
=> ( Y1 @ Y0 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ ( s @ sK1 ) ) )
=> ( Y1 @ ( s @ Y0 ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ sK1 ) )
=> ( Y1 @ Y0 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ ( s @ sK1 ) ) )
=> ( Y1 @ ( s @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y0 ) ) )
=> ( Y2 @ ( s @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y0 ) ) )
=> ( Y2 @ ( s @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y0 ) ) )
=> ( Y2 @ ( s @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
=> ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ ( s @ Y0 )
@ ( s @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f10,f9,f9]) ).
thf(f9,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox2/tmp/tmp.ZhDRJWFOcM/DTF2THF_19311.p',cCKB_E2_def) ).
thf(f10,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB_E2 @ Y0 @ Y1 )
=> ( cCKB_E2 @ ( s @ Y0 ) @ ( s @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB_E2 @ Y0 @ Y1 )
=> ( cCKB_E2 @ ( s @ Y0 ) @ ( s @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB_E2 @ X1 @ X0 )
=> ( cCKB_E2 @ ( s @ X1 ) @ ( s @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( cCKB_E2 @ X0 @ X1 )
=> ( cCKB_E2 @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i] :
( ( cCKB_E2 @ X0 @ X1 )
=> ( cCKB_E2 @ ( s @ X0 ) @ ( s @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZhDRJWFOcM/DTF2THF_19311.p',cCKB_L35000) ).
thf(f137,plain,
( ( $true
= ( sK3 @ ( s @ sK2 ) ) )
| ( $false
= ( sK3 @ ( s @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true
= ( sK3
@ ( s
@ ( ^ [Y0: $i] : Y0
@ sK2 ) ) ) )
| ( $false
= ( sK3
@ ( s
@ ( ^ [Y0: $i] : Y0
@ sK1 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: $i > $i] :
( ( ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) )
!= ( X0
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ ( X0 @ Y0 ) ) ) ) ) )
| ( $false
= ( sK3 @ ( s @ ( X0 @ sK1 ) ) ) )
| ( $true
= ( sK3 @ ( s @ ( X0 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: $i > $i] :
( ( $true
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK1 ) )
| ( ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) )
!= ( X0
@ ( sK4
@ ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: $i > $i] :
( ( ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) )
!= ( X0
@ ( sK4
@ ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK1 ) )
| ( $false = $true )
| ( $true
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X0 @ Y1 ) )
@ Y0 ) )
@ sK2 ) ) ),
inference(constrained_superposition,[status(thm)],[f36,f125]) ).
thf(f125,plain,
( ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) ) ) )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f123,f22]) ).
thf(f123,plain,
( ( $true
= ( sK3 @ ( s @ sK2 ) ) )
| ( ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false = $true )
| ( ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( sK3 @ ( s @ sK2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f121,f24]) ).
thf(f121,plain,
( ( ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( sK3 @ ( s @ sK1 ) ) )
| ( $true
= ( sK3 @ ( s @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false
= ( sK3
@ ( s
@ ( ^ [Y0: $i] : Y0
@ sK1 ) ) ) )
| ( $true
= ( sK3
@ ( s
@ ( ^ [Y0: $i] : Y0
@ sK2 ) ) ) )
| ( $false
= ( sK3
@ ( s
@ ( sK4
@ ^ [Y0: $i] :
( sK3
@ ( s
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X1: $i > $i] :
( ( ( X1
@ ( s
@ ( s
@ ( sK4
@ ^ [Y0: $i] : ( sK3 @ ( s @ ( X1 @ Y0 ) ) ) ) ) ) )
!= ( s @ X2 ) )
| ( ( sK3 @ ( s @ ( X1 @ sK2 ) ) )
= $true )
| ( $false
= ( sK3 @ ( s @ ( X1 @ sK1 ) ) ) )
| ( ( sK3 @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i > $i] :
( ( $false
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) )
@ sK1 ) )
| ( ( X1
@ ( s
@ ( s
@ ( sK4
@ ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) ) ) ) ) )
!= ( s @ X2 ) )
| ( ( sK3 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i > $i] :
( ( ( X1
@ ( s
@ ( s
@ ( sK4
@ ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) ) ) ) ) )
!= ( s @ X2 ) )
| ( $false = $true )
| ( ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true )
| ( ( sK3 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( sK3
@ ( ^ [Y1: $i] : ( s @ ( X1 @ Y1 ) )
@ Y0 ) )
@ sK1 ) ) ),
inference(constrained_superposition,[status(thm)],[f35,f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ ( s @ ( s @ X1 ) ) ) )
| ( ( sK3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ ( s @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK3 @ ( s @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) ) )
| ( $false
= ( X1 @ sK1 ) )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK1 ) )
| ( ( ( X1 @ ( sK4 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK1 ) ) ),
inference(sigma_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK1 ) )
| ( $true
= ( X1 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( X1 @ sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( X1 @ sK1 ) )
=> ( X1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK1 ) )
=> ( Y0 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f36,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( X1 @ sK1 ) )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f24,plain,
( ( sK3 @ ( s @ sK1 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ108^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:33:36 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : PUZ108^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.27/0.47 % Domain : Puzzles
% 0.27/0.47 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0679 [Bro09]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.38 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.27/0.47 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.27/0.47 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.27/0.47 % Number of connectives : 16 ( 0 ~; 0 |; 1 &; 12 @)
% 0.27/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 7 ( 4 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.27/0.47 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(s_type,type,
% 0.27/0.47 s: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(cCKB_E2_type,type,
% 0.27/0.47 cCKB_E2: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(cCKB_E2_def,definition,
% 0.27/0.47 ( cCKB_E2
% 0.27/0.47 = ( ^ [Xx: $i,Xy: $i] :
% 0.27/0.47 ! [Xp: $i > $o] :
% 0.27/0.47 ( ( ( Xp @ Xx )
% 0.27/0.47 & ! [Xu: $i] :
% 0.27/0.47 ( ( Xp @ Xu )
% 0.27/0.47 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 0.27/0.47 => ( Xp @ Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cCKB_L35000,conjecture,
% 0.27/0.47 ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( cCKB_E2 @ Xx @ Xy )
% 0.27/0.47 => ( cCKB_E2 @ ( s @ Xx ) @ ( s @ Xy ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.44/1.29 ---- Embedded in THF ---
% 1.44/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.29 %%% Generated on Tue Feb 24 11:33:37 EST 2026
% 1.44/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.29 %%% Logic specification used:
% 1.44/1.29 %%% thf(spec, logic, $$dhol).
% 1.44/1.29
% 1.44/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZhDRJWFOcM/DTF2DTF19311.p
% See solution above
% 1.44/1.29 ------------------------
% 1.62/1.30 ---- Cleaned THF ---
% 1.62/1.30 thf(s_type,type,
% 1.62/1.30 s: $i > $i ).
% 1.62/1.30
% 1.62/1.30 thf(cCKB_E2_type,type,
% 1.62/1.30 cCKB_E2: $i > $i > $o ).
% 1.62/1.30
% 1.62/1.30 thf(cCKB_E2_def,definition,
% 1.62/1.30 ( cCKB_E2
% 1.62/1.30 = ( ^ [Xx: $i,Xy: $i] :
% 1.62/1.30 ! [Xp: $i > $o] :
% 1.62/1.30 ( ( ( Xp @ Xx )
% 1.62/1.30 & ! [Xu: $i] :
% 1.62/1.30 ( ( Xp @ Xu )
% 1.62/1.30 => ( Xp @ ( s @ ( s @ Xu ) ) ) ) )
% 1.62/1.30 => ( Xp @ Xy ) ) ) ) ).
% 1.62/1.30
% 1.62/1.30 thf(cCKB_L35000,conjecture,
% 1.62/1.30 ! [Xx: $i,Xy: $i] :
% 1.62/1.30 ( ( cCKB_E2 @ Xx @ Xy )
% 1.62/1.30 => ( cCKB_E2 @ ( s @ Xx ) @ ( s @ Xy ) ) ) ).
% 1.62/1.30 ------------------------
% 1.62/1.32 % (19531)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_19311 for (2999ds/4Mi)
% 1.62/1.32 % (19530)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/183Mi)
% 1.62/1.32 % (19531)Instruction limit reached!
% 1.62/1.32 % (19531)------------------------------
% 1.62/1.32 % (19531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (19531)Termination reason: Unknown
% 1.62/1.32 % (19531)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (19531)Memory used [KB]: 5500
% 1.62/1.32 % (19531)Time elapsed: 0.003 s
% 1.62/1.32 % (19531)Instructions burned: 4 (million)
% 1.62/1.32 % (19531)------------------------------
% 1.62/1.32 % (19531)------------------------------
% 1.62/1.32 % (19532)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_19311 for (2999ds/27Mi)
% 1.62/1.32 % (19533)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/2Mi)
% 1.62/1.32 % (19534)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_19311 for (2999ds/2Mi)
% 1.62/1.32 % (19535)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_19311 for (2999ds/275Mi)
% 1.62/1.32 % (19536)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/18Mi)
% 1.62/1.33 % (19535)Refutation not found, incomplete strategy
% 1.62/1.33 % (19535)------------------------------
% 1.62/1.33 % (19535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (19535)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.33
% 1.62/1.33
% 1.62/1.33 % (19535)Memory used [KB]: 5500
% 1.62/1.33 % (19535)Time elapsed: 0.003 s
% 1.62/1.33 % (19535)Instructions burned: 1 (million)
% 1.62/1.33 % (19535)------------------------------
% 1.62/1.33 % (19535)------------------------------
% 1.62/1.33 % (19533)Instruction limit reached!
% 1.62/1.33 % (19533)------------------------------
% 1.62/1.33 % (19533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (19533)Termination reason: Unknown
% 1.62/1.33 % (19533)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (19533)Memory used [KB]: 5500
% 1.62/1.33 % (19533)Time elapsed: 0.004 s
% 1.62/1.33 % (19533)Instructions burned: 3 (million)
% 1.62/1.33 % (19533)------------------------------
% 1.62/1.33 % (19533)------------------------------
% 1.62/1.33 % (19534)Instruction limit reached!
% 1.62/1.33 % (19534)------------------------------
% 1.62/1.33 % (19534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (19534)Termination reason: Unknown
% 1.62/1.33 % (19534)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (19534)Memory used [KB]: 5500
% 1.62/1.33 % (19534)Time elapsed: 0.004 s
% 1.62/1.33 % (19534)Instructions burned: 3 (million)
% 1.62/1.33 % (19534)------------------------------
% 1.62/1.33 % (19534)------------------------------
% 1.62/1.33 % (19537)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/3Mi)
% 1.62/1.33 % (19532)Refutation not found, incomplete strategy
% 1.62/1.33 % (19532)------------------------------
% 1.62/1.33 % (19532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (19532)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.33
% 1.62/1.33
% 1.62/1.33 % (19532)Memory used [KB]: 5500
% 1.62/1.33 % (19532)Time elapsed: 0.006 s
% 1.62/1.33 % (19532)Instructions burned: 5 (million)
% 1.62/1.33 % (19532)------------------------------
% 1.62/1.33 % (19532)------------------------------
% 1.62/1.33 % (19537)Refutation not found, incomplete strategy
% 1.62/1.33 % (19537)------------------------------
% 1.62/1.33 % (19537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (19537)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.33
% 1.62/1.33
% 1.62/1.33 % (19537)Memory used [KB]: 5500
% 1.62/1.33 % (19537)Time elapsed: 0.002 s
% 1.62/1.33 % (19537)Instructions burned: 2 (million)
% 1.62/1.33 % (19537)------------------------------
% 1.62/1.33 % (19537)------------------------------
% 1.62/1.34 % (19536)Instruction limit reached!
% 1.62/1.34 % (19536)------------------------------
% 1.62/1.34 % (19536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (19536)Termination reason: Unknown
% 1.62/1.34 % (19536)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (19536)Memory used [KB]: 5628
% 1.62/1.34 % (19536)Time elapsed: 0.014 s
% 1.62/1.34 % (19536)Instructions burned: 18 (million)
% 1.62/1.34 % (19536)------------------------------
% 1.62/1.34 % (19536)------------------------------
% 1.62/1.34 % (19542)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/7Mi)
% 1.62/1.34 % (19542)Instruction limit reached!
% 1.62/1.34 % (19542)------------------------------
% 1.62/1.34 % (19542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (19542)Termination reason: Unknown
% 1.62/1.34 % (19542)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (19542)Memory used [KB]: 1023
% 1.62/1.34 % (19542)Time elapsed: 0.004 s
% 1.62/1.34 % (19542)Instructions burned: 9 (million)
% 1.62/1.34 % (19542)------------------------------
% 1.62/1.34 % (19542)------------------------------
% 1.62/1.34 % (19538)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_19311 for (2999ds/37Mi)
% 1.62/1.34 % (19539)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_19311 for (2999ds/15Mi)
% 1.62/1.34 % (19540)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_19311 for (2999ds/3Mi)
% 1.62/1.35 % (19540)Instruction limit reached!
% 1.62/1.35 % (19540)------------------------------
% 1.62/1.35 % (19540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (19540)Termination reason: Unknown
% 1.62/1.35 % (19540)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (19540)Memory used [KB]: 5500
% 1.62/1.35 % (19540)Time elapsed: 0.004 s
% 1.62/1.35 % (19540)Instructions burned: 3 (million)
% 1.62/1.35 % (19540)------------------------------
% 1.62/1.35 % (19540)------------------------------
% 1.62/1.35 % (19541)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_19311 for (2999ds/1041Mi)
% 1.62/1.35 % (19544)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_19311 for (2999ds/3Mi)
% 1.62/1.35 % (19544)Instruction limit reached!
% 1.62/1.35 % (19544)------------------------------
% 1.62/1.35 % (19544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (19544)Termination reason: Unknown
% 1.62/1.35 % (19544)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (19544)Memory used [KB]: 5500
% 1.62/1.35 % (19544)Time elapsed: 0.002 s
% 1.62/1.35 % (19544)Instructions burned: 3 (million)
% 1.62/1.35 % (19544)------------------------------
% 1.62/1.35 % (19544)------------------------------
% 1.62/1.35 % (19539)Refutation not found, incomplete strategy
% 1.62/1.35 % (19539)------------------------------
% 1.62/1.35 % (19539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (19539)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.35
% 1.62/1.35
% 1.62/1.35 % (19539)Memory used [KB]: 5628
% 1.62/1.35 % (19539)Time elapsed: 0.011 s
% 1.62/1.35 % (19539)Instructions burned: 13 (million)
% 1.62/1.35 % (19539)------------------------------
% 1.62/1.35 % (19539)------------------------------
% 1.62/1.35 % (19543)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/16Mi)
% 1.62/1.36 % (19546)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/7Mi)
% 1.62/1.36 % (19543)Instruction limit reached!
% 1.62/1.36 % (19543)------------------------------
% 1.62/1.36 % (19543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (19543)Termination reason: Unknown
% 1.62/1.36 % (19543)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (19543)Memory used [KB]: 5756
% 1.62/1.36 % (19543)Time elapsed: 0.010 s
% 1.62/1.36 % (19543)Instructions burned: 16 (million)
% 1.62/1.36 % (19543)------------------------------
% 1.62/1.36 % (19543)------------------------------
% 1.62/1.36 % (19546)Refutation not found, incomplete strategy
% 1.62/1.36 % (19546)------------------------------
% 1.62/1.36 % (19546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (19546)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.36
% 1.62/1.36
% 1.62/1.36 % (19546)Memory used [KB]: 5500
% 1.62/1.36 % (19546)Time elapsed: 0.001 s
% 1.62/1.36 % (19546)------------------------------
% 1.62/1.36 % (19546)------------------------------
% 1.62/1.36 % (19545)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_19311 for (2999ds/3Mi)
% 1.62/1.36 % (19538)Instruction limit reached!
% 1.62/1.36 % (19538)------------------------------
% 1.62/1.36 % (19538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (19538)Termination reason: Unknown
% 1.62/1.36 % (19538)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (19538)Memory used [KB]: 5884
% 1.62/1.36 % (19538)Time elapsed: 0.023 s
% 1.62/1.36 % (19538)Instructions burned: 37 (million)
% 1.62/1.36 % (19538)------------------------------
% 1.62/1.36 % (19538)------------------------------
% 1.62/1.36 % (19545)Instruction limit reached!
% 1.62/1.36 % (19545)------------------------------
% 1.62/1.36 % (19545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (19545)Termination reason: Unknown
% 1.62/1.36 % (19545)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (19545)Memory used [KB]: 1023
% 1.62/1.36 % (19545)Time elapsed: 0.004 s
% 1.62/1.36 % (19545)Instructions burned: 3 (million)
% 1.62/1.36 % (19545)------------------------------
% 1.62/1.36 % (19545)------------------------------
% 1.62/1.37 % (19547)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/3Mi)
% 1.62/1.37 % (19549)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/18Mi)
% 1.62/1.37 % (19548)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/4Mi)
% 1.62/1.37 % (19547)Instruction limit reached!
% 1.62/1.37 % (19547)------------------------------
% 1.62/1.37 % (19547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (19547)Termination reason: Unknown
% 1.62/1.37 % (19547)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (19547)Memory used [KB]: 5500
% 1.62/1.37 % (19547)Time elapsed: 0.004 s
% 1.62/1.37 % (19547)Instructions burned: 3 (million)
% 1.62/1.37 % (19547)------------------------------
% 1.62/1.37 % (19547)------------------------------
% 1.62/1.37 % (19548)Instruction limit reached!
% 1.62/1.37 % (19548)------------------------------
% 1.62/1.37 % (19548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (19548)Termination reason: Unknown
% 1.62/1.37 % (19548)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (19548)Memory used [KB]: 5500
% 1.62/1.37 % (19548)Time elapsed: 0.003 s
% 1.62/1.37 % (19548)Instructions burned: 6 (million)
% 1.62/1.37 % (19548)------------------------------
% 1.62/1.37 % (19548)------------------------------
% 1.62/1.38 % (19549)Instruction limit reached!
% 1.62/1.38 % (19549)------------------------------
% 1.62/1.38 % (19549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (19549)Termination reason: Unknown
% 1.62/1.38 % (19549)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (19549)Memory used [KB]: 5500
% 1.62/1.38 % (19549)Time elapsed: 0.007 s
% 1.62/1.38 % (19549)Instructions burned: 18 (million)
% 1.62/1.38 % (19549)------------------------------
% 1.62/1.38 % (19549)------------------------------
% 1.62/1.38 % (19530)Instruction limit reached!
% 1.62/1.38 % (19530)------------------------------
% 1.62/1.38 % (19530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (19530)Termination reason: Unknown
% 1.62/1.38 % (19530)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (19530)Memory used [KB]: 6268
% 1.62/1.38 % (19530)Time elapsed: 0.062 s
% 1.62/1.38 % (19530)Instructions burned: 184 (million)
% 1.62/1.38 % (19530)------------------------------
% 1.62/1.38 % (19530)------------------------------
% 1.62/1.38 % (19550)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/710Mi)
% 1.62/1.38 % (19551)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/6Mi)
% 1.62/1.38 % (19553)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/21Mi)
% 1.62/1.39 % (19551)Instruction limit reached!
% 1.62/1.39 % (19551)------------------------------
% 1.62/1.39 % (19551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (19551)Termination reason: Unknown
% 1.62/1.39 % (19551)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (19551)Memory used [KB]: 5500
% 1.62/1.39 % (19551)Time elapsed: 0.006 s
% 1.62/1.39 % (19551)Instructions burned: 6 (million)
% 1.62/1.39 % (19551)------------------------------
% 1.62/1.39 % (19551)------------------------------
% 1.62/1.39 % (19554)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/5Mi)
% 1.62/1.39 % (19555)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/6Mi)
% 1.62/1.39 % (19554)Instruction limit reached!
% 1.62/1.39 % (19554)------------------------------
% 1.62/1.39 % (19554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (19554)Termination reason: Unknown
% 1.62/1.39 % (19554)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (19554)Memory used [KB]: 5500
% 1.62/1.39 % (19554)Time elapsed: 0.003 s
% 1.62/1.39 % (19554)Instructions burned: 6 (million)
% 1.62/1.39 % (19554)------------------------------
% 1.62/1.39 % (19554)------------------------------
% 1.62/1.39 % (19555)Refutation not found, incomplete strategy
% 1.62/1.39 % (19555)------------------------------
% 1.62/1.39 % (19555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (19555)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.39
% 1.62/1.39
% 1.62/1.39 % (19555)Memory used [KB]: 5500
% 1.62/1.39 % (19555)Time elapsed: 0.002 s
% 1.62/1.39 % (19555)Instructions burned: 1 (million)
% 1.62/1.39 % (19555)------------------------------
% 1.62/1.39 % (19555)------------------------------
% 1.62/1.39 % (19552)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/902Mi)
% 1.62/1.39 % (19552)Refutation not found, incomplete strategy
% 1.62/1.39 % (19552)------------------------------
% 1.62/1.39 % (19552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (19552)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.39
% 1.62/1.39
% 1.62/1.39 % (19552)Memory used [KB]: 5500
% 1.62/1.39 % (19552)Time elapsed: 0.003 s
% 1.62/1.39 % (19552)Instructions burned: 2 (million)
% 1.62/1.39 % (19552)------------------------------
% 1.62/1.39 % (19552)------------------------------
% 1.62/1.39 % (19553)Instruction limit reached!
% 1.62/1.39 % (19553)------------------------------
% 1.62/1.39 % (19553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (19553)Termination reason: Unknown
% 1.62/1.39 % (19553)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (19553)Memory used [KB]: 5628
% 1.62/1.39 % (19553)Time elapsed: 0.010 s
% 1.62/1.39 % (19553)Instructions burned: 22 (million)
% 1.62/1.39 % (19553)------------------------------
% 1.62/1.39 % (19553)------------------------------
% 1.62/1.40 % (19557)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/779Mi)
% 1.62/1.40 % (19558)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/19Mi)
% 1.62/1.40 % (19558)Refutation not found, incomplete strategy
% 1.62/1.40 % (19558)------------------------------
% 1.62/1.40 % (19558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (19558)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.40
% 1.62/1.40
% 1.62/1.40 % (19558)Memory used [KB]: 5500
% 1.62/1.40 % (19558)Time elapsed: 0.002 s
% 1.62/1.40 % (19558)Instructions burned: 1 (million)
% 1.62/1.40 % (19558)------------------------------
% 1.62/1.40 % (19558)------------------------------
% 1.62/1.40 % (19560)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/17Mi)
% 1.62/1.40 % (19556)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19311 for (2999ds/377Mi)
% 1.62/1.41 % (19557)First to succeed.
% 1.62/1.41 % (19557)Refutation found. Thanks to Tanya!
% 1.62/1.41 % SZS status Theorem for DTF2THF_19311
% 1.62/1.41 % SZS output start Proof for DTF2THF_19311
% 1.62/1.41 thf(func_def_0, type, s: $i > $i).
% 1.62/1.41 thf(func_def_1, type, cCKB_E2: $i > $i > $o).
% 1.62/1.41 thf(func_def_17, type, sK3: $i > $o).
% 1.62/1.41 thf(func_def_18, type, sK4: ($i > $o) > $i).
% 1.62/1.41 thf(func_def_19, type, ph5: !>[X0: $tType]:(X0)).
% 1.62/1.41 thf(f146,plain,(
% 1.62/1.41 $false),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.62/1.41 thf(f140,plain,(
% 1.62/1.41 ($false = $true)),
% 1.62/1.41 inference(backward_demodulation,[status(thm)],[f24,f139])).
% 1.62/1.41 thf(f139,plain,(
% 1.62/1.41 ($false = (sK3 @ (s @ sK1)))),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.62/1.41 thf(f138,plain,(
% 1.62/1.41 ($false = $true) | ($false = (sK3 @ (s @ sK1)))),
% 1.62/1.41 inference(forward_demodulation,[status(thm)],[f137,f22])).
% 1.62/1.41 thf(f22,plain,(
% 1.62/1.41 ($false = (sK3 @ (s @ sK2)))),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.62/1.41 thf(f21,plain,(
% 1.62/1.41 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ (s @ Y0)))))) & (sK3 @ (s @ sK1))) => (sK3 @ (s @ sK2))))),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.62/1.41 thf(f20,plain,(
% 1.62/1.41 (((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ (s @ sK1))) => (Y0 @ (s @ sK2)))) @ sK3) = $false)),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f18])).
% 1.62/1.41 thf(f18,plain,(
% 1.62/1.41 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ (s @ sK1))) => (Y0 @ (s @ sK2))))))),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.62/1.41 thf(f17,plain,(
% 1.62/1.41 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ sK1)) => (Y0 @ sK2)))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ (s @ sK1))) => (Y0 @ (s @ sK2)))))))),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.62/1.41 thf(f16,plain,(
% 1.62/1.41 ($false = ((^[Y0 : $i]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ (s @ Y2)))))) & (Y1 @ sK1)) => (Y1 @ Y0)))) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ (s @ Y2)))))) & (Y1 @ (s @ sK1))) => (Y1 @ (s @ Y0))))))) @ sK2))),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f15])).
% 1.62/1.41 thf(f15,plain,(
% 1.62/1.41 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ (s @ Y2)))))) & (Y1 @ sK1)) => (Y1 @ Y0)))) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ (s @ Y2)))))) & (Y1 @ (s @ sK1))) => (Y1 @ (s @ Y0)))))))) = $false)),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.62/1.41 thf(f14,plain,(
% 1.62/1.41 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1)))) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ (s @ Y0))) => (Y2 @ (s @ Y1))))))))) @ sK1))),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f13])).
% 1.62/1.41 thf(f13,plain,(
% 1.62/1.41 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1)))) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ (s @ Y0))) => (Y2 @ (s @ Y1)))))))))))),
% 1.62/1.41 inference(not_proxy_clausification,[status(thm)],[f12])).
% 1.62/1.41 thf(f12,plain,(
% 1.62/1.41 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1)))) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ (s @ Y0))) => (Y2 @ (s @ Y1))))))))))) = $true)),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.62/1.41 thf(f11,plain,(
% 1.62/1.41 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y4 @ (s @ (s @ Y5)))))) & (Y4 @ Y2)) => (Y4 @ Y3))))))) @ Y0 @ Y1) => ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y4 @ (s @ (s @ Y5)))))) & (Y4 @ Y2)) => (Y4 @ Y3))))))) @ (s @ Y0) @ (s @ Y1)))))))) = $true)),
% 1.62/1.41 inference(definition_unfolding,[status(thm)],[f10,f9,f9])).
% 1.62/1.41 thf(f9,plain,(
% 1.62/1.41 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f6])).
% 1.62/1.41 thf(f6,plain,(
% 1.62/1.41 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3)))))) & (Y2 @ Y0)) => (Y2 @ Y1))))))))),
% 1.62/1.41 inference(fool_elimination,[status(thm)],[f5])).
% 1.62/1.41 thf(f5,plain,(
% 1.62/1.41 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : (((X2 @ X0) & ! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3))))) => (X2 @ X1)))) = cCKB_E2)),
% 1.62/1.41 inference(rectify,[status(thm)],[f1])).
% 1.62/1.41 thf(f1,axiom,(
% 1.62/1.41 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : (((X2 @ X0) & ! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3))))) => (X2 @ X1)))) = cCKB_E2)),
% 1.62/1.41 file('/export/starexec/sandbox2/tmp/tmp.ZhDRJWFOcM/DTF2THF_19311.p',cCKB_E2_def)).
% 1.62/1.41 thf(f10,plain,(
% 1.62/1.41 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cCKB_E2 @ Y0 @ Y1) => (cCKB_E2 @ (s @ Y0) @ (s @ Y1)))))))))),
% 1.62/1.41 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.41 thf(f8,plain,(
% 1.62/1.41 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cCKB_E2 @ Y0 @ Y1) => (cCKB_E2 @ (s @ Y0) @ (s @ Y1)))))))))),
% 1.62/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.62/1.41 thf(f7,plain,(
% 1.62/1.41 ~! [X0 : $i,X1 : $i] : ((cCKB_E2 @ X1 @ X0) => (cCKB_E2 @ (s @ X1) @ (s @ X0)))),
% 1.62/1.41 inference(rectify,[status(thm)],[f3])).
% 1.62/1.41 thf(f3,negated_conjecture,(
% 1.62/1.41 ~! [X1 : $i,X0 : $i] : ((cCKB_E2 @ X0 @ X1) => (cCKB_E2 @ (s @ X0) @ (s @ X1)))),
% 1.62/1.41 inference(negated_conjecture,[status(cth)],[f2])).
% 1.62/1.41 thf(f2,conjecture,(
% 1.62/1.41 ! [X1 : $i,X0 : $i] : ((cCKB_E2 @ X0 @ X1) => (cCKB_E2 @ (s @ X0) @ (s @ X1)))),
% 1.62/1.41 file('/export/starexec/sandbox2/tmp/tmp.ZhDRJWFOcM/DTF2THF_19311.p',cCKB_L35000)).
% 1.62/1.41 thf(f137,plain,(
% 1.62/1.41 ($true = (sK3 @ (s @ sK2))) | ($false = (sK3 @ (s @ sK1)))),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.62/1.41 thf(f134,plain,(
% 1.62/1.41 ($true = (sK3 @ (s @ ((^[Y0 : $i]: (Y0)) @ sK2)))) | ($false = (sK3 @ (s @ ((^[Y0 : $i]: (Y0)) @ sK1))))),
% 1.62/1.41 inference(equality_resolution,[status(thm)],[f130])).
% 1.62/1.41 thf(f130,plain,(
% 1.62/1.41 ( ! [X0 : $i > $i] : (((sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))) != (X0 @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ (X0 @ Y0))))))) | ($false = (sK3 @ (s @ (X0 @ sK1)))) | ($true = (sK3 @ (s @ (X0 @ sK2))))) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f129])).
% 1.62/1.41 thf(f129,plain,(
% 1.62/1.41 ( ! [X0 : $i > $i] : (($true = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0))) @ sK2)) | ($false = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0))) @ sK1)) | ((sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))) != (X0 @ (sK4 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0))))))) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.62/1.41 thf(f128,plain,(
% 1.62/1.41 ( ! [X0 : $i > $i] : (((sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))) != (X0 @ (sK4 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0)))))) | ($false = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0))) @ sK1)) | ($false = $true) | ($true = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X0 @ Y1))) @ Y0))) @ sK2))) )),
% 1.62/1.41 inference(constrained_superposition,[status(thm)],[f36,f125])).
% 1.62/1.41 thf(f125,plain,(
% 1.62/1.41 ((sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))))) = $false)),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.62/1.41 thf(f124,plain,(
% 1.62/1.41 ((sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))))) = $false) | ($false = $true)),
% 1.62/1.41 inference(forward_demodulation,[status(thm)],[f123,f22])).
% 1.62/1.41 thf(f123,plain,(
% 1.62/1.41 ($true = (sK3 @ (s @ sK2))) | ((sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))))) = $false)),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.62/1.41 thf(f122,plain,(
% 1.62/1.41 ($false = $true) | ((sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))))) = $false) | ($true = (sK3 @ (s @ sK2)))),
% 1.62/1.41 inference(forward_demodulation,[status(thm)],[f121,f24])).
% 1.62/1.41 thf(f121,plain,(
% 1.62/1.41 ((sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ Y0)))))) = $false) | ($false = (sK3 @ (s @ sK1))) | ($true = (sK3 @ (s @ sK2)))),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.62/1.41 thf(f118,plain,(
% 1.62/1.41 ($false = (sK3 @ (s @ ((^[Y0 : $i]: (Y0)) @ sK1)))) | ($true = (sK3 @ (s @ ((^[Y0 : $i]: (Y0)) @ sK2)))) | ($false = (sK3 @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ ((^[Y1 : $i]: (Y1)) @ Y0))))))))),
% 1.62/1.41 inference(equality_resolution,[status(thm)],[f76])).
% 1.62/1.41 thf(f76,plain,(
% 1.62/1.41 ( ! [X2 : $i,X1 : $i > $i] : (((X1 @ (s @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ (s @ (X1 @ Y0)))))))) != (s @ X2)) | ((sK3 @ (s @ (X1 @ sK2))) = $true) | ($false = (sK3 @ (s @ (X1 @ sK1)))) | ((sK3 @ X2) = $false)) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.62/1.41 thf(f75,plain,(
% 1.62/1.41 ( ! [X2 : $i,X1 : $i > $i] : (($false = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))) @ sK1)) | ((X1 @ (s @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))))))) != (s @ X2)) | ((sK3 @ X2) = $false) | (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))) @ sK2) = $true)) )),
% 1.62/1.41 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.62/1.41 thf(f60,plain,(
% 1.62/1.41 ( ! [X2 : $i,X1 : $i > $i] : (((X1 @ (s @ (s @ (sK4 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))))))) != (s @ X2)) | ($false = $true) | (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))) @ sK2) = $true) | ((sK3 @ X2) = $false) | ($false = ((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (s @ (X1 @ Y1))) @ Y0))) @ sK1))) )),
% 1.62/1.41 inference(constrained_superposition,[status(thm)],[f35,f28])).
% 1.62/1.41 thf(f28,plain,(
% 1.62/1.41 ( ! [X1 : $i] : (($true = (sK3 @ (s @ (s @ X1)))) | ((sK3 @ X1) = $false)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.62/1.41 thf(f27,plain,(
% 1.62/1.41 ( ! [X1 : $i] : ((((sK3 @ X1) => (sK3 @ (s @ (s @ X1)))) = $true)) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.62/1.41 thf(f26,plain,(
% 1.62/1.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ (s @ Y0))))) @ X1) = $true)) )),
% 1.62/1.41 inference(pi_clausification,[status(thm)],[f25])).
% 1.62/1.41 thf(f25,plain,(
% 1.62/1.41 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ (s @ Y0)))))))),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.62/1.41 thf(f23,plain,(
% 1.62/1.41 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ (s @ Y0)))))) & (sK3 @ (s @ sK1))))),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.62/1.41 thf(f35,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($false = (X1 @ (s @ (s @ (sK4 @ X1))))) | ($false = (X1 @ sK1)) | ($true = (X1 @ sK2))) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.41 thf(f34,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ sK2)) | ($false = (X1 @ sK1)) | (((X1 @ (sK4 @ X1)) => (X1 @ (s @ (s @ (sK4 @ X1))))) = $false)) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.62/1.41 thf(f33,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ sK2)) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))) @ (sK4 @ X1)) = $false) | ($false = (X1 @ sK1))) )),
% 1.62/1.41 inference(sigma_clausification,[status(thm)],[f32])).
% 1.62/1.41 thf(f32,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($false = (X1 @ sK1)) | ($true = (X1 @ sK2)) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))) = $false)) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.62/1.41 thf(f31,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ sK2)) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))) & (X1 @ sK1)))) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.62/1.41 thf(f30,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))) & (X1 @ sK1)) => (X1 @ sK2)))) )),
% 1.62/1.41 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.62/1.41 thf(f29,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ sK1)) => (Y0 @ sK2))) @ X1))) )),
% 1.62/1.41 inference(pi_clausification,[status(thm)],[f19])).
% 1.62/1.41 thf(f19,plain,(
% 1.62/1.41 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1)))))) & (Y0 @ sK1)) => (Y0 @ sK2)))))),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.62/1.41 thf(f36,plain,(
% 1.62/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ (sK4 @ X1))) | ($false = (X1 @ sK1)) | ($true = (X1 @ sK2))) )),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.41 thf(f24,plain,(
% 1.62/1.41 ((sK3 @ (s @ sK1)) = $true)),
% 1.62/1.41 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.62/1.41 % SZS output end Proof for DTF2THF_19311
% 1.62/1.41 % (19557)------------------------------
% 1.62/1.41 % (19557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (19557)Termination reason: Refutation
% 1.62/1.41
% 1.62/1.41 % (19557)Memory used [KB]: 5628
% 1.62/1.41 % (19557)Time elapsed: 0.009 s
% 1.62/1.41 % (19557)Instructions burned: 21 (million)
% 1.62/1.41 % (19557)------------------------------
% 1.62/1.41 % (19557)------------------------------
% 1.62/1.41 % (19529)Success in time 0.089 s
%------------------------------------------------------------------------------