%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV245^5 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:39 AM UTC 2026
% Result : Theorem 1.25s 1.47s
% Output : Refutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 61 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 832 ( 4 ~; 18 |; 36 &; 547 @)
% ( 0 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 145 ( 145 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 87 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 193 ( 136 ^; 51 !; 6 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_14,type,
ph0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK1: ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
sK3: $i > $o ).
thf(func_def_18,type,
sK4: ( $i > $o ) > ( $i > $o ) > $i ).
thf(f337,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f336]) ).
thf(f336,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f300,f331]) ).
thf(f331,plain,
( $false
= ( sK3 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f328]) ).
thf(f328,plain,
( ( $false
= ( sK3 @ sK5 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f23,f303]) ).
thf(f303,plain,
! [X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) ) ) )
| ( $false
= ( X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f302]) ).
thf(f302,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) ) )
& ( X1 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f301]) ).
thf(f301,plain,
! [X1: $i > $o] :
( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f299]) ).
thf(f299,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f298]) ).
thf(f298,plain,
( $false
= ( ( sK3 @ sK5 )
=> ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f297]) ).
thf(f297,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f296]) ).
thf(f296,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f295]) ).
thf(f295,plain,
( ( $false = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f282,f24]) ).
thf(f24,plain,
( $true
= ( sK3 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ( sK3 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK1 @ sK3 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) )
=> ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) ) ) )
=> ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK1 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) ) ) )
=> ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK1 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
=> ( sK1 @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) ) ) )
=> ( sK1
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK1 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( ( $i > $o ) > $i > $o )
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ?? @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X4: $i] :
( ( X0 @ X1 @ X4 )
=> ( X0 @ X2 @ X4 ) ) )
=> ! [X5: $i] :
( ? [X6: $i > $o] :
( ! [X7: $i] :
( ( X6 @ X7 )
=> ( X0 @ X6 @ X7 ) )
& ( X6 @ X5 ) )
=> ( X0
@ ^ [X8: $i] :
? [X9: $i > $o] :
( ( X9 @ X8 )
& ! [X10: $i] :
( ( X9 @ X10 )
=> ( X0 @ X9 @ X10 ) ) )
@ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
=> ! [X1: $i] :
( ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) )
& ( X4 @ X1 ) )
=> ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ( X4 @ X3 )
& ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) ) )
@ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X0 @ X1 @ X3 )
=> ( X0 @ X2 @ X3 ) ) )
=> ! [X1: $i] :
( ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X0 @ X4 @ X3 ) )
& ( X4 @ X1 ) )
=> ( X0
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ( X4 @ X3 )
& ! [X5: $i] :
( ( X4 @ X5 )
=> ( X0 @ X4 @ X5 ) ) )
@ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vglPP0fKg2/DTF2THF_22087.p',cTHM2A_TWO_pme) ).
thf(f282,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f281]) ).
thf(f281,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK1 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) )
| ( $false
= ( sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f273]) ).
thf(f273,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( sK1 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f19,f49]) ).
thf(f49,plain,
! [X0: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ X1 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ X1 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f30,f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK3 @ X1 ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ( sK3 @ X1 )
=> ( sK1 @ sK3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK1 @ sK3 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f30,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $true
= ( sK1 @ X1 @ X3 ) )
| ( $false
= ( sK1 @ X2 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( ( sK1 @ X2 @ X3 )
=> ( sK1 @ X1 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ X2 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ X2 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ X2 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK1 @ X1 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $o] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK1 @ X1 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
=> ( sK1 @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
=> ( sK1 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f19,plain,
( $false
= ( sK1
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK1 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK1 @ sK3 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f300,plain,
( $true
= ( sK3 @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV245^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 12:42:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.33 ---- Original DTF file ---
% 0.07/0.33 thf(spec,logic,$$dhol).
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 % File : SEV245^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.33 % Domain : Set Theory (Sets of sets)
% 0.07/0.33 % Problem : TPS problem from SETS-OF-SETS-THMS
% 0.07/0.33 % Version : Especial.
% 0.07/0.33 % English :
% 0.07/0.33
% 0.07/0.33 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.33 % Source : [Bro09]
% 0.07/0.33 % Names : tps_0976 [Bro09]
% 0.07/0.33
% 0.07/0.33 % Status : Theorem
% 0.07/0.33 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 0.33 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.07/0.33 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.07/0.33 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.07/0.33 % Maximal formula atoms : 0 ( 0 avg)
% 0.07/0.33 % Number of connectives : 25 ( 0 ~; 0 |; 2 &; 16 @)
% 0.07/0.33 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.07/0.33 % Maximal formula depth : 14 ( 14 avg)
% 0.07/0.33 % Number of types : 2 ( 0 usr)
% 0.07/0.33 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.07/0.33 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.07/0.33 % Number of variables : 11 ( 1 ^; 8 !; 2 ?; 11 :)
% 0.07/0.33 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.33
% 0.07/0.33 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.33 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.33 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.33 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 thf(cTHM2A_TWO_pme,conjecture,
% 0.07/0.33 ! [K: ( $i > $o ) > $i > $o] :
% 0.07/0.33 ( ! [Xx: $i > $o,Xy: $i > $o] :
% 0.07/0.33 ( ! [Xx0: $i] :
% 0.07/0.33 ( ( Xx @ Xx0 )
% 0.07/0.33 => ( Xy @ Xx0 ) )
% 0.07/0.33 => ! [Xx0: $i] :
% 0.07/0.33 ( ( K @ Xx @ Xx0 )
% 0.07/0.33 => ( K @ Xy @ Xx0 ) ) )
% 0.07/0.33 => ! [Xx: $i] :
% 0.07/0.33 ( ? [S: $i > $o] :
% 0.07/0.33 ( ! [Xx0: $i] :
% 0.07/0.33 ( ( S @ Xx0 )
% 0.07/0.33 => ( K @ S @ Xx0 ) )
% 0.07/0.33 & ( S @ Xx ) )
% 0.07/0.33 => ( K
% 0.07/0.33 @ ^ [Xx0: $i] :
% 0.07/0.33 ? [S: $i > $o] :
% 0.07/0.33 ( ! [Xx1: $i] :
% 0.07/0.33 ( ( S @ Xx1 )
% 0.07/0.33 => ( K @ S @ Xx1 ) )
% 0.07/0.33 & ( S @ Xx0 ) )
% 0.07/0.33 @ Xx ) ) ) ).
% 0.07/0.33
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 ------------------------
% 1.19/1.03 ---- Embedded in THF ---
% 1.19/1.04 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.19/1.04 %%% Generated on Tue Feb 24 12:42:31 EST 2026
% 1.19/1.04 %%% using '$$dhol' embedding, version 1.3.0.
% 1.19/1.04 %%% Logic specification used:
% 1.19/1.04 %%% thf(spec, logic, $$dhol).
% 1.19/1.04
% 1.19/1.04 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vglPP0fKg2/DTF2DTF22087.p
% See solution above
% 1.19/1.04 ------------------------
% 1.19/1.04 ---- Cleaned THF ---
% 1.19/1.04 thf(cTHM2A_TWO_pme,conjecture,
% 1.19/1.04 ! [K: ( $i > $o ) > $i > $o] :
% 1.19/1.04 ( ! [Xx: $i > $o,Xy: $i > $o] :
% 1.19/1.04 ( ! [Xx0: $i] :
% 1.19/1.04 ( ( Xx @ Xx0 )
% 1.19/1.04 => ( Xy @ Xx0 ) )
% 1.19/1.04 => ! [Xx0: $i] :
% 1.19/1.04 ( ( K @ Xx @ Xx0 )
% 1.19/1.04 => ( K @ Xy @ Xx0 ) ) )
% 1.19/1.04 => ! [Xx: $i] :
% 1.19/1.04 ( ? [S: $i > $o] :
% 1.19/1.04 ( ! [Xx0: $i] :
% 1.19/1.04 ( ( S @ Xx0 )
% 1.19/1.04 => ( K @ S @ Xx0 ) )
% 1.19/1.04 & ( S @ Xx ) )
% 1.19/1.04 => ( K
% 1.19/1.04 @ ^ [Xx0: $i] :
% 1.19/1.04 ? [S: $i > $o] :
% 1.19/1.04 ( ! [Xx1: $i] :
% 1.19/1.04 ( ( S @ Xx1 )
% 1.19/1.04 => ( K @ S @ Xx1 ) )
% 1.19/1.04 & ( S @ Xx0 ) )
% 1.19/1.04 @ Xx ) ) ) ).
% 1.19/1.04 ------------------------
% 1.19/1.06 % (22185)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22087 for (3000ds/183Mi)
% 1.19/1.06 % (22187)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_22087 for (3000ds/27Mi)
% 1.19/1.06 % (22186)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_22087 for (3000ds/4Mi)
% 1.19/1.06 % (22188)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22087 for (3000ds/2Mi)
% 1.19/1.06 % (22189)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_22087 for (3000ds/2Mi)
% 1.19/1.06 % (22190)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_22087 for (3000ds/275Mi)
% 1.19/1.06 % (22191)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22087 for (3000ds/18Mi)
% 1.19/1.06 % (22188)Instruction limit reached!
% 1.19/1.06 % (22188)------------------------------
% 1.19/1.06 % (22188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.06 % (22189)Instruction limit reached!
% 1.19/1.06 % (22189)------------------------------
% 1.19/1.06 % (22189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.06 % (22188)Termination reason: Unknown
% 1.19/1.06 % (22188)Termination phase: Saturation
% 1.19/1.06
% 1.19/1.06 % (22188)Memory used [KB]: 5500
% 1.19/1.06 % (22188)Time elapsed: 0.003 s
% 1.19/1.06 % (22188)Instructions burned: 3 (million)
% 1.19/1.06 % (22188)------------------------------
% 1.19/1.06 % (22188)------------------------------
% 1.19/1.06 % (22189)Termination reason: Unknown
% 1.19/1.06 % (22189)Termination phase: Saturation
% 1.19/1.06
% 1.19/1.06 % (22189)Memory used [KB]: 5500
% 1.19/1.06 % (22189)Time elapsed: 0.003 s
% 1.19/1.06 % (22189)Instructions burned: 3 (million)
% 1.19/1.06 % (22189)------------------------------
% 1.19/1.06 % (22189)------------------------------
% 1.19/1.06 % (22186)Instruction limit reached!
% 1.19/1.06 % (22186)------------------------------
% 1.19/1.06 % (22186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.06 % (22186)Termination reason: Unknown
% 1.19/1.06 % (22186)Termination phase: Saturation
% 1.19/1.06
% 1.19/1.06 % (22186)Memory used [KB]: 5500
% 1.19/1.06 % (22186)Time elapsed: 0.004 s
% 1.19/1.06 % (22186)Instructions burned: 4 (million)
% 1.19/1.06 % (22186)------------------------------
% 1.19/1.06 % (22186)------------------------------
% 1.19/1.07 % (22191)Instruction limit reached!
% 1.19/1.07 % (22191)------------------------------
% 1.19/1.07 % (22191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.07 % (22191)Termination reason: Unknown
% 1.19/1.07 % (22191)Termination phase: Saturation
% 1.19/1.07
% 1.19/1.07 % (22191)Memory used [KB]: 5628
% 1.19/1.07 % (22191)Time elapsed: 0.011 s
% 1.19/1.07 % (22191)Instructions burned: 18 (million)
% 1.19/1.07 % (22191)------------------------------
% 1.19/1.07 % (22191)------------------------------
% 1.19/1.08 % (22187)Instruction limit reached!
% 1.19/1.08 % (22187)------------------------------
% 1.19/1.08 % (22187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.08 % (22187)Termination reason: Unknown
% 1.19/1.08 % (22187)Termination phase: Saturation
% 1.19/1.08
% 1.19/1.08 % (22187)Memory used [KB]: 5628
% 1.19/1.08 % (22187)Time elapsed: 0.016 s
% 1.19/1.08 % (22187)Instructions burned: 28 (million)
% 1.19/1.08 % (22187)------------------------------
% 1.19/1.08 % (22187)------------------------------
% 1.19/1.08 % (22192)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/3Mi)
% 1.19/1.08 % (22193)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_22087 for (2999ds/37Mi)
% 1.19/1.08 % (22194)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_22087 for (2999ds/15Mi)
% 1.19/1.08 % (22192)Instruction limit reached!
% 1.19/1.08 % (22192)------------------------------
% 1.19/1.08 % (22192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.08 % (22192)Termination reason: Unknown
% 1.19/1.08 % (22192)Termination phase: Saturation
% 1.19/1.08
% 1.19/1.08 % (22192)Memory used [KB]: 5500
% 1.19/1.08 % (22192)Time elapsed: 0.003 s
% 1.19/1.08 % (22192)Instructions burned: 3 (million)
% 1.19/1.08 % (22192)------------------------------
% 1.19/1.08 % (22192)------------------------------
% 1.19/1.09 % (22195)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_22087 for (2999ds/3Mi)
% 1.19/1.09 % (22194)Instruction limit reached!
% 1.19/1.09 % (22194)------------------------------
% 1.19/1.09 % (22194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.09 % (22194)Termination reason: Unknown
% 1.19/1.09 % (22194)Termination phase: Saturation
% 1.19/1.09
% 1.19/1.09 % (22194)Memory used [KB]: 5628
% 1.19/1.09 % (22194)Time elapsed: 0.009 s
% 1.19/1.09 % (22194)Instructions burned: 15 (million)
% 1.19/1.09 % (22194)------------------------------
% 1.19/1.09 % (22194)------------------------------
% 1.19/1.09 % (22195)Instruction limit reached!
% 1.19/1.09 % (22195)------------------------------
% 1.19/1.09 % (22195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.09 % (22195)Termination reason: Unknown
% 1.19/1.09 % (22195)Termination phase: Saturation
% 1.19/1.09
% 1.19/1.09 % (22195)Memory used [KB]: 5500
% 1.19/1.09 % (22195)Time elapsed: 0.003 s
% 1.19/1.09 % (22195)Instructions burned: 3 (million)
% 1.19/1.09 % (22195)------------------------------
% 1.19/1.09 % (22195)------------------------------
% 1.19/1.09 % (22196)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_22087 for (2999ds/1041Mi)
% 1.19/1.10 % (22197)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/7Mi)
% 1.19/1.10 % (22193)Instruction limit reached!
% 1.19/1.10 % (22193)------------------------------
% 1.19/1.10 % (22193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.10 % (22193)Termination reason: Unknown
% 1.19/1.10 % (22193)Termination phase: Saturation
% 1.19/1.10
% 1.19/1.10 % (22193)Memory used [KB]: 6140
% 1.19/1.10 % (22193)Time elapsed: 0.019 s
% 1.19/1.10 % (22193)Instructions burned: 38 (million)
% 1.19/1.10 % (22193)------------------------------
% 1.19/1.10 % (22193)------------------------------
% 1.19/1.10 % (22197)Instruction limit reached!
% 1.19/1.10 % (22197)------------------------------
% 1.19/1.10 % (22197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.10 % (22197)Termination reason: Unknown
% 1.19/1.10 % (22197)Termination phase: Saturation
% 1.19/1.10
% 1.19/1.10 % (22197)Memory used [KB]: 1023
% 1.19/1.10 % (22197)Time elapsed: 0.005 s
% 1.19/1.10 % (22197)Instructions burned: 7 (million)
% 1.19/1.10 % (22197)------------------------------
% 1.19/1.10 % (22197)------------------------------
% 1.19/1.10 % (22198)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/16Mi)
% 1.19/1.10 % (22199)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_22087 for (2999ds/3Mi)
% 1.19/1.11 % (22199)Instruction limit reached!
% 1.19/1.11 % (22199)------------------------------
% 1.19/1.11 % (22199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.11 % (22199)Termination reason: Unknown
% 1.19/1.11 % (22199)Termination phase: Saturation
% 1.19/1.11
% 1.19/1.11 % (22199)Memory used [KB]: 1023
% 1.19/1.11 % (22199)Time elapsed: 0.003 s
% 1.19/1.11 % (22199)Instructions burned: 3 (million)
% 1.19/1.11 % (22199)------------------------------
% 1.19/1.11 % (22199)------------------------------
% 1.19/1.11 % (22185)Instruction limit reached!
% 1.19/1.11 % (22185)------------------------------
% 1.19/1.11 % (22185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.11 % (22185)Termination reason: Unknown
% 1.19/1.11 % (22185)Termination phase: Saturation
% 1.19/1.11
% 1.19/1.11 % (22185)Memory used [KB]: 6780
% 1.19/1.11 % (22185)Time elapsed: 0.052 s
% 1.19/1.11 % (22185)Instructions burned: 185 (million)
% 1.19/1.11 % (22185)------------------------------
% 1.19/1.11 % (22185)------------------------------
% 1.19/1.11 % (22198)Instruction limit reached!
% 1.19/1.11 % (22198)------------------------------
% 1.19/1.11 % (22198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.19/1.11 % (22198)Termination reason: Unknown
% 1.19/1.11 % (22198)Termination phase: Saturation
% 1.19/1.11
% 1.19/1.11 % (22198)Memory used [KB]: 5756
% 1.19/1.11 % (22198)Time elapsed: 0.010 s
% 1.19/1.11 % (22198)Instructions burned: 16 (million)
% 1.19/1.11 % (22198)------------------------------
% 1.19/1.11 % (22198)------------------------------
% 1.25/1.12 % (22200)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_22087 for (2999ds/3Mi)
% 1.25/1.12 % (22203)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/4Mi)
% 1.25/1.12 % (22201)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/7Mi)
% 1.25/1.12 % (22200)Instruction limit reached!
% 1.25/1.12 % (22200)------------------------------
% 1.25/1.12 % (22200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (22200)Termination reason: Unknown
% 1.25/1.12 % (22200)Termination phase: Saturation
% 1.25/1.12
% 1.25/1.12 % (22200)Memory used [KB]: 1023
% 1.25/1.12 % (22200)Time elapsed: 0.003 s
% 1.25/1.12 % (22200)Instructions burned: 3 (million)
% 1.25/1.12 % (22200)------------------------------
% 1.25/1.12 % (22200)------------------------------
% 1.25/1.12 % (22203)Instruction limit reached!
% 1.25/1.12 % (22203)------------------------------
% 1.25/1.12 % (22203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (22203)Termination reason: Unknown
% 1.25/1.12 % (22203)Termination phase: Saturation
% 1.25/1.12
% 1.25/1.12 % (22203)Memory used [KB]: 5500
% 1.25/1.12 % (22203)Time elapsed: 0.003 s
% 1.25/1.12 % (22203)Instructions burned: 5 (million)
% 1.25/1.12 % (22203)------------------------------
% 1.25/1.12 % (22203)------------------------------
% 1.25/1.12 % (22201)Refutation not found, incomplete strategy
% 1.25/1.12 % (22201)------------------------------
% 1.25/1.12 % (22201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (22201)Termination reason: Refutation not found, incomplete strategy
% 1.25/1.12
% 1.25/1.12
% 1.25/1.12 % (22201)Memory used [KB]: 5500
% 1.25/1.12 % (22201)Time elapsed: 0.003 s
% 1.25/1.12 % (22201)Instructions burned: 3 (million)
% 1.25/1.12 % (22201)------------------------------
% 1.25/1.12 % (22201)------------------------------
% 1.25/1.12 % (22202)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/3Mi)
% 1.25/1.12 % (22202)Instruction limit reached!
% 1.25/1.12 % (22202)------------------------------
% 1.25/1.12 % (22202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.12 % (22202)Termination reason: Unknown
% 1.25/1.12 % (22202)Termination phase: Saturation
% 1.25/1.12
% 1.25/1.12 % (22202)Memory used [KB]: 5500
% 1.25/1.12 % (22202)Time elapsed: 0.003 s
% 1.25/1.12 % (22202)Instructions burned: 3 (million)
% 1.25/1.12 % (22202)------------------------------
% 1.25/1.12 % (22202)------------------------------
% 1.25/1.13 % (22205)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/710Mi)
% 1.25/1.13 % (22204)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/18Mi)
% 1.25/1.13 % (22206)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/6Mi)
% 1.25/1.13 % (22207)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_22087 for (2999ds/902Mi)
% 1.25/1.14 % (22206)Instruction limit reached!
% 1.25/1.14 % (22206)------------------------------
% 1.25/1.14 % (22206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.14 % (22206)Termination reason: Unknown
% 1.25/1.14 % (22206)Termination phase: Saturation
% 1.25/1.14
% 1.25/1.14 % (22206)Memory used [KB]: 5500
% 1.25/1.14 % (22206)Time elapsed: 0.005 s
% 1.25/1.14 % (22206)Instructions burned: 6 (million)
% 1.25/1.14 % (22206)------------------------------
% 1.25/1.14 % (22206)------------------------------
% 1.25/1.14 % (22204)Instruction limit reached!
% 1.25/1.14 % (22204)------------------------------
% 1.25/1.14 % (22204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.14 % (22204)Termination reason: Unknown
% 1.25/1.14 % (22204)Termination phase: Saturation
% 1.25/1.14
% 1.25/1.14 % (22204)Memory used [KB]: 5628
% 1.25/1.14 % (22204)Time elapsed: 0.011 s
% 1.25/1.14 % (22204)Instructions burned: 18 (million)
% 1.25/1.14 % (22204)------------------------------
% 1.25/1.14 % (22204)------------------------------
% 1.25/1.14 % (22208)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_22087 for (2999ds/21Mi)
% 1.25/1.15 % (22208)Instruction limit reached!
% 1.25/1.15 % (22208)------------------------------
% 1.25/1.15 % (22208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.15 % (22208)Termination reason: Unknown
% 1.25/1.15 % (22208)Termination phase: Saturation
% 1.25/1.15
% 1.25/1.15 % (22208)Memory used [KB]: 5628
% 1.25/1.15 % (22208)Time elapsed: 0.013 s
% 1.25/1.15 % (22208)Instructions burned: 22 (million)
% 1.25/1.15 % (22208)------------------------------
% 1.25/1.15 % (22208)------------------------------
% 1.25/1.15 % (22209)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/5Mi)
% 1.25/1.15 % (22210)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_22087 for (2999ds/6Mi)
% 1.25/1.16 % (22209)Instruction limit reached!
% 1.25/1.16 % (22209)------------------------------
% 1.25/1.16 % (22209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.16 % (22209)Termination reason: Unknown
% 1.25/1.16 % (22209)Termination phase: Saturation
% 1.25/1.16
% 1.25/1.16 % (22209)Memory used [KB]: 5500
% 1.25/1.16 % (22209)Time elapsed: 0.004 s
% 1.25/1.16 % (22209)Instructions burned: 5 (million)
% 1.25/1.16 % (22209)------------------------------
% 1.25/1.16 % (22209)------------------------------
% 1.25/1.16 % (22210)Instruction limit reached!
% 1.25/1.16 % (22210)------------------------------
% 1.25/1.16 % (22210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.16 % (22210)Termination reason: Unknown
% 1.25/1.16 % (22210)Termination phase: Saturation
% 1.25/1.16
% 1.25/1.16 % (22210)Memory used [KB]: 5500
% 1.25/1.16 % (22210)Time elapsed: 0.004 s
% 1.25/1.16 % (22210)Instructions burned: 6 (million)
% 1.25/1.16 % (22210)------------------------------
% 1.25/1.16 % (22210)------------------------------
% 1.25/1.17 % (22211)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22087 for (2999ds/377Mi)
% 1.25/1.17 % (22212)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_22087 for (2999ds/779Mi)
% 1.25/1.17 % (22213)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_22087 for (2999ds/19Mi)
% 1.25/1.18 % (22213)Instruction limit reached!
% 1.25/1.18 % (22213)------------------------------
% 1.25/1.18 % (22213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.18 % (22213)Termination reason: Unknown
% 1.25/1.18 % (22213)Termination phase: Saturation
% 1.25/1.18
% 1.25/1.18 % (22213)Memory used [KB]: 5628
% 1.25/1.18 % (22213)Time elapsed: 0.011 s
% 1.25/1.18 % (22213)Instructions burned: 20 (million)
% 1.25/1.18 % (22213)------------------------------
% 1.25/1.18 % (22213)------------------------------
% 1.25/1.19 % (22190)Instruction limit reached!
% 1.25/1.19 % (22190)------------------------------
% 1.25/1.19 % (22190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.19 % (22190)Termination reason: Unknown
% 1.25/1.19 % (22190)Termination phase: Saturation
% 1.25/1.19
% 1.25/1.19 % (22190)Memory used [KB]: 6140
% 1.25/1.19 % (22190)Time elapsed: 0.131 s
% 1.25/1.19 % (22190)Instructions burned: 275 (million)
% 1.25/1.19 % (22190)------------------------------
% 1.25/1.19 % (22190)------------------------------
% 1.25/1.20 % (22214)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22087 for (2998ds/879Mi)
% 1.25/1.21 % (22215)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22087 for (2998ds/17Mi)
% 1.25/1.22 % (22215)Instruction limit reached!
% 1.25/1.22 % (22215)------------------------------
% 1.25/1.22 % (22215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.22 % (22215)Termination reason: Unknown
% 1.25/1.22 % (22215)Termination phase: Saturation
% 1.25/1.22
% 1.25/1.22 % (22215)Memory used [KB]: 5628
% 1.25/1.22 % (22215)Time elapsed: 0.033 s
% 1.25/1.22 % (22215)Instructions burned: 18 (million)
% 1.25/1.22 % (22215)------------------------------
% 1.25/1.22 % (22215)------------------------------
% 1.25/1.23 % (22216)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22087 for (2998ds/3Mi)
% 1.25/1.23 % (22216)Instruction limit reached!
% 1.25/1.23 % (22216)------------------------------
% 1.25/1.23 % (22216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.23 % (22216)Termination reason: Unknown
% 1.25/1.23 % (22216)Termination phase: Saturation
% 1.25/1.23
% 1.25/1.23 % (22216)Memory used [KB]: 1023
% 1.25/1.23 % (22216)Time elapsed: 0.003 s
% 1.25/1.23 % (22216)Instructions burned: 3 (million)
% 1.25/1.23 % (22216)------------------------------
% 1.25/1.23 % (22216)------------------------------
% 1.25/1.25 % (22217)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22087 for (2998ds/30Mi)
% 1.25/1.27 % (22217)Instruction limit reached!
% 1.25/1.27 % (22217)------------------------------
% 1.25/1.27 % (22217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.27 % (22217)Termination reason: Unknown
% 1.25/1.27 % (22217)Termination phase: Saturation
% 1.25/1.27
% 1.25/1.27 % (22217)Memory used [KB]: 5628
% 1.25/1.27 % (22217)Time elapsed: 0.018 s
% 1.25/1.27 % (22217)Instructions burned: 31 (million)
% 1.25/1.27 % (22217)------------------------------
% 1.25/1.27 % (22217)------------------------------
% 1.25/1.28 % (22218)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22087 for (2997ds/127Mi)
% 1.25/1.35 % (22211)Instruction limit reached!
% 1.25/1.35 % (22211)------------------------------
% 1.25/1.35 % (22211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.35 % (22211)Termination reason: Unknown
% 1.25/1.35 % (22211)Termination phase: Saturation
% 1.25/1.35
% 1.25/1.35 % (22211)Memory used [KB]: 6268
% 1.25/1.35 % (22211)Time elapsed: 0.181 s
% 1.25/1.35 % (22211)Instructions burned: 378 (million)
% 1.25/1.35 % (22211)------------------------------
% 1.25/1.35 % (22211)------------------------------
% 1.25/1.35 % (22218)Instruction limit reached!
% 1.25/1.35 % (22218)------------------------------
% 1.25/1.35 % (22218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.35 % (22218)Termination reason: Unknown
% 1.25/1.35 % (22218)Termination phase: Saturation
% 1.25/1.35
% 1.25/1.35 % (22218)Memory used [KB]: 5884
% 1.25/1.35 % (22218)Time elapsed: 0.066 s
% 1.25/1.35 % (22218)Instructions burned: 127 (million)
% 1.25/1.35 % (22218)------------------------------
% 1.25/1.35 % (22218)------------------------------
% 1.25/1.35 % (22205)Instruction limit reached!
% 1.25/1.35 % (22205)------------------------------
% 1.25/1.35 % (22205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.35 % (22205)Termination reason: Unknown
% 1.25/1.35 % (22205)Termination phase: Saturation
% 1.25/1.35
% 1.25/1.35 % (22205)Memory used [KB]: 6780
% 1.25/1.35 % (22205)Time elapsed: 0.227 s
% 1.25/1.35 % (22205)Instructions burned: 710 (million)
% 1.25/1.35 % (22205)------------------------------
% 1.25/1.35 % (22205)------------------------------
% 1.25/1.36 % (22221)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/20Mi)
% 1.25/1.36 % (22219)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/100Mi)
% 1.25/1.36 % (22220)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/3Mi)
% 1.25/1.36 % (22220)Instruction limit reached!
% 1.25/1.36 % (22220)------------------------------
% 1.25/1.36 % (22220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.36 % (22220)Termination reason: Unknown
% 1.25/1.36 % (22220)Termination phase: Saturation
% 1.25/1.36
% 1.25/1.36 % (22220)Memory used [KB]: 5500
% 1.25/1.36 % (22220)Time elapsed: 0.003 s
% 1.25/1.36 % (22220)Instructions burned: 3 (million)
% 1.25/1.36 % (22220)------------------------------
% 1.25/1.36 % (22220)------------------------------
% 1.25/1.37 % (22221)Instruction limit reached!
% 1.25/1.37 % (22221)------------------------------
% 1.25/1.37 % (22221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.37 % (22221)Termination reason: Unknown
% 1.25/1.37 % (22221)Termination phase: Saturation
% 1.25/1.37
% 1.25/1.37 % (22221)Memory used [KB]: 5628
% 1.25/1.37 % (22221)Time elapsed: 0.008 s
% 1.25/1.37 % (22221)Instructions burned: 20 (million)
% 1.25/1.37 % (22221)------------------------------
% 1.25/1.37 % (22221)------------------------------
% 1.25/1.38 % (22223)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/107Mi)
% 1.25/1.38 % (22222)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/86Mi)
% 1.25/1.41 % (22223)Instruction limit reached!
% 1.25/1.41 % (22223)------------------------------
% 1.25/1.41 % (22223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.41 % (22223)Termination reason: Unknown
% 1.25/1.41 % (22223)Termination phase: Saturation
% 1.25/1.41
% 1.25/1.41 % (22223)Memory used [KB]: 5756
% 1.25/1.41 % (22223)Time elapsed: 0.033 s
% 1.25/1.41 % (22223)Instructions burned: 107 (million)
% 1.25/1.41 % (22223)------------------------------
% 1.25/1.41 % (22223)------------------------------
% 1.25/1.41 % (22219)Instruction limit reached!
% 1.25/1.41 % (22219)------------------------------
% 1.25/1.41 % (22219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.41 % (22219)Termination reason: Unknown
% 1.25/1.41 % (22219)Termination phase: Saturation
% 1.25/1.41
% 1.25/1.41 % (22219)Memory used [KB]: 5756
% 1.25/1.41 % (22219)Time elapsed: 0.050 s
% 1.25/1.41 % (22219)Instructions burned: 101 (million)
% 1.25/1.41 % (22219)------------------------------
% 1.25/1.41 % (22219)------------------------------
% 1.25/1.42 % (22224)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/39Mi)
% 1.25/1.42 % (22222)Instruction limit reached!
% 1.25/1.42 % (22222)------------------------------
% 1.25/1.42 % (22222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.42 % (22222)Termination reason: Unknown
% 1.25/1.42 % (22222)Termination phase: Saturation
% 1.25/1.42
% 1.25/1.42 % (22222)Memory used [KB]: 6140
% 1.25/1.42 % (22222)Time elapsed: 0.044 s
% 1.25/1.42 % (22222)Instructions burned: 86 (million)
% 1.25/1.42 % (22222)------------------------------
% 1.25/1.42 % (22222)------------------------------
% 1.25/1.43 % (22225)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/448Mi)
% 1.25/1.43 % (22224)Instruction limit reached!
% 1.25/1.43 % (22224)------------------------------
% 1.25/1.43 % (22224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.43 % (22224)Termination reason: Unknown
% 1.25/1.43 % (22224)Termination phase: Saturation
% 1.25/1.43
% 1.25/1.43 % (22224)Memory used [KB]: 5756
% 1.25/1.43 % (22224)Time elapsed: 0.014 s
% 1.25/1.43 % (22224)Instructions burned: 42 (million)
% 1.25/1.43 % (22224)------------------------------
% 1.25/1.43 % (22224)------------------------------
% 1.25/1.44 % (22226)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/46Mi)
% 1.25/1.44 % (22227)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_22087 for (2996ds/98Mi)
% 1.25/1.46 % (22226)Instruction limit reached!
% 1.25/1.46 % (22226)------------------------------
% 1.25/1.46 % (22226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.46 % (22226)Termination reason: Unknown
% 1.25/1.46 % (22226)Termination phase: Saturation
% 1.25/1.46
% 1.25/1.46 % (22226)Memory used [KB]: 5756
% 1.25/1.46 % (22226)Time elapsed: 0.026 s
% 1.25/1.46 % (22226)Instructions burned: 46 (million)
% 1.25/1.46 % (22226)------------------------------
% 1.25/1.46 % (22226)------------------------------
% 1.25/1.47 % (22227)First to succeed.
% 1.25/1.47 % (22227)Refutation found. Thanks to Tanya!
% 1.25/1.47 % SZS status Theorem for DTF2THF_22087
% 1.25/1.47 % SZS output start Proof for DTF2THF_22087
% 1.25/1.47 thf(func_def_14, type, ph0: !>[X0: $tType]:(X0)).
% 1.25/1.47 thf(func_def_15, type, sK1: ($i > $o) > $i > $o).
% 1.25/1.47 thf(func_def_17, type, sK3: $i > $o).
% 1.25/1.47 thf(func_def_18, type, sK4: ($i > $o) > ($i > $o) > $i).
% 1.25/1.47 thf(f337,plain,(
% 1.25/1.47 $false),
% 1.25/1.47 inference(trivial_inequality_removal,[status(thm)],[f336])).
% 1.25/1.47 thf(f336,plain,(
% 1.25/1.47 ($false = $true)),
% 1.25/1.47 inference(backward_demodulation,[status(thm)],[f300,f331])).
% 1.25/1.47 thf(f331,plain,(
% 1.25/1.47 ($false = (sK3 @ sK5))),
% 1.25/1.47 inference(trivial_inequality_removal,[status(thm)],[f328])).
% 1.25/1.47 thf(f328,plain,(
% 1.25/1.47 ($false = (sK3 @ sK5)) | ($false = $true)),
% 1.25/1.47 inference(superposition,[status(thm)],[f23,f303])).
% 1.25/1.47 thf(f303,plain,(
% 1.25/1.47 ( ! [X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK1 @ X1 @ Y0))))) | ($false = (X1 @ sK5))) )),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f302])).
% 1.25/1.47 thf(f302,plain,(
% 1.25/1.47 ( ! [X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK1 @ X1 @ Y0)))) & (X1 @ sK5)) = $false)) )),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f301])).
% 1.25/1.47 thf(f301,plain,(
% 1.25/1.47 ( ! [X1 : $i > $o] : (($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))) & (Y0 @ sK5))) @ X1))) )),
% 1.25/1.47 inference(pi_clausification,[status(thm)],[f299])).
% 1.25/1.47 thf(f299,plain,(
% 1.25/1.47 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))) & (Y0 @ sK5)))) = $false)),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f298])).
% 1.25/1.47 thf(f298,plain,(
% 1.25/1.47 ($false = ((sK3 @ sK5) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))) & (Y0 @ sK5))))))),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f297])).
% 1.25/1.47 thf(f297,plain,(
% 1.25/1.47 ($false = ((^[Y0 : $i]: ((sK3 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK5))),
% 1.25/1.47 inference(sigma_clausification,[status(thm)],[f296])).
% 1.25/1.47 thf(f296,plain,(
% 1.25/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.25/1.47 inference(trivial_inequality_removal,[status(thm)],[f295])).
% 1.25/1.47 thf(f295,plain,(
% 1.25/1.47 ($false = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.25/1.47 inference(forward_demodulation,[status(thm)],[f282,f24])).
% 1.25/1.47 thf(f24,plain,(
% 1.25/1.47 ($true = (sK3 @ sK2))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.25/1.47 thf(f22,plain,(
% 1.25/1.47 ($true = ((sK3 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK1 @ sK3 @ Y0))))))),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.25/1.47 thf(f21,plain,(
% 1.25/1.47 ($true = ((^[Y0 : $i > $o]: ((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))))) @ sK3))),
% 1.25/1.47 inference(sigma_clausification,[status(thm)],[f20])).
% 1.25/1.47 thf(f20,plain,(
% 1.25/1.47 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1))))))) = $true)),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.25/1.47 thf(f18,plain,(
% 1.25/1.47 ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK2) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1))))))) => (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.25/1.47 thf(f17,plain,(
% 1.25/1.47 ($false = ((^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))) @ sK2))),
% 1.25/1.47 inference(sigma_clausification,[status(thm)],[f10])).
% 1.25/1.47 thf(f10,plain,(
% 1.25/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.25/1.47 thf(f9,plain,(
% 1.25/1.47 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (sK1 @ Y0 @ Y2))))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))))))),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.25/1.47 thf(f8,plain,(
% 1.25/1.47 ($false = ((^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))) @ sK1))),
% 1.25/1.47 inference(sigma_clausification,[status(thm)],[f7])).
% 1.25/1.47 thf(f7,plain,(
% 1.25/1.47 ($false = (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1))))))))),
% 1.25/1.47 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.25/1.47 thf(f6,plain,(
% 1.25/1.47 ($true = (~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))))))),
% 1.25/1.47 inference(cnf_transformation,[status(thm)],[f5])).
% 1.25/1.47 thf(f5,plain,(
% 1.25/1.47 ($true = (~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))))))),
% 1.25/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.25/1.47 thf(f4,plain,(
% 1.25/1.47 ~! [X0 : ($i > $o) > $i > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X4 : $i] : ((X0 @ X1 @ X4) => (X0 @ X2 @ X4))) => ! [X5 : $i] : (? [X6 : $i > $o] : (! [X7 : $i] : ((X6 @ X7) => (X0 @ X6 @ X7)) & (X6 @ X5)) => (X0 @ (^[X8 : $i] : (? [X9 : $i > $o] : ((X9 @ X8) & ! [X10 : $i] : ((X9 @ X10) => (X0 @ X9 @ X10))))) @ X5)))),
% 1.25/1.47 inference(rectify,[status(thm)],[f2])).
% 1.25/1.47 thf(f2,negated_conjecture,(
% 1.25/1.47 ~! [X0 : ($i > $o) > $i > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X3 : $i] : ((X0 @ X1 @ X3) => (X0 @ X2 @ X3))) => ! [X1 : $i] : (? [X4 : $i > $o] : (! [X3 : $i] : ((X4 @ X3) => (X0 @ X4 @ X3)) & (X4 @ X1)) => (X0 @ (^[X3 : $i] : (? [X4 : $i > $o] : ((X4 @ X3) & ! [X5 : $i] : ((X4 @ X5) => (X0 @ X4 @ X5))))) @ X1)))),
% 1.25/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.25/1.47 thf(f1,conjecture,(
% 1.25/1.47 ! [X0 : ($i > $o) > $i > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X3 : $i] : ((X0 @ X1 @ X3) => (X0 @ X2 @ X3))) => ! [X1 : $i] : (? [X4 : $i > $o] : (! [X3 : $i] : ((X4 @ X3) => (X0 @ X4 @ X3)) & (X4 @ X1)) => (X0 @ (^[X3 : $i] : (? [X4 : $i > $o] : ((X4 @ X3) & ! [X5 : $i] : ((X4 @ X5) => (X0 @ X4 @ X5))))) @ X1)))),
% 1.25/1.47 file('/export/starexec/sandbox/tmp/tmp.vglPP0fKg2/DTF2THF_22087.p',cTHM2A_TWO_pme)).
% 1.25/1.47 thf(f282,plain,(
% 1.25/1.47 ($false = (sK3 @ sK2)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f281])).
% 1.25/1.47 thf(f281,plain,(
% 1.25/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))))) | ($false = (sK3 @ sK2))),
% 1.25/1.47 inference(trivial_inequality_removal,[status(thm)],[f273])).
% 1.25/1.47 thf(f273,plain,(
% 1.25/1.47 ($false = (sK3 @ sK2)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))))) | ($false = $true)),
% 1.25/1.47 inference(superposition,[status(thm)],[f19,f49])).
% 1.25/1.47 thf(f49,plain,(
% 1.25/1.47 ( ! [X0 : $i,X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (X1 @ Y0))))) | ($true = (sK1 @ X1 @ X0)) | ($false = (sK3 @ X0))) )),
% 1.25/1.47 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.25/1.47 thf(f34,plain,(
% 1.25/1.47 ( ! [X0 : $i,X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (X1 @ Y0))))) | ($true = (sK1 @ X1 @ X0)) | ($false = $true) | ($false = (sK3 @ X0))) )),
% 1.25/1.47 inference(superposition,[status(thm)],[f30,f27])).
% 1.25/1.47 thf(f27,plain,(
% 1.25/1.47 ( ! [X1 : $i] : (($true = (sK1 @ sK3 @ X1)) | ($false = (sK3 @ X1))) )),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.25/1.47 thf(f26,plain,(
% 1.25/1.47 ( ! [X1 : $i] : (($true = ((sK3 @ X1) => (sK1 @ sK3 @ X1)))) )),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.25/1.47 thf(f25,plain,(
% 1.25/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) => (sK1 @ sK3 @ Y0))) @ X1))) )),
% 1.25/1.47 inference(pi_clausification,[status(thm)],[f23])).
% 1.25/1.47 thf(f30,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $o] : (($true = (sK1 @ X1 @ X3)) | ($false = (sK1 @ X2 @ X3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0)))))) )),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.25/1.47 thf(f29,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0))))) | ($true = ((sK1 @ X2 @ X3) => (sK1 @ X1 @ X3)))) )),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.25/1.47 thf(f28,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0))))) | ($true = ((^[Y0 : $i]: ((sK1 @ X2 @ Y0) => (sK1 @ X1 @ Y0))) @ X3))) )),
% 1.25/1.47 inference(pi_clausification,[status(thm)],[f16])).
% 1.25/1.47 thf(f16,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ X2 @ Y0) => (sK1 @ X1 @ Y0))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0)))))) )),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.25/1.47 thf(f15,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X1 : $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ X2 @ Y0) => (sK1 @ X1 @ Y0))))))) )),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.25/1.47 thf(f14,plain,(
% 1.25/1.47 ( ! [X2 : $i > $o,X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ X1 @ Y1)))))) @ X2))) )),
% 1.25/1.47 inference(pi_clausification,[status(thm)],[f13])).
% 1.25/1.47 thf(f13,plain,(
% 1.25/1.47 ( ! [X1 : $i > $o] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ X1 @ Y1))))))))) )),
% 1.25/1.47 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.25/1.47 thf(f12,plain,(
% 1.25/1.47 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (sK1 @ Y0 @ Y2)))))))) @ X1))) )),
% 1.25/1.47 inference(pi_clausification,[status(thm)],[f11])).
% 1.25/1.47 thf(f11,plain,(
% 1.25/1.47 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (sK1 @ Y0 @ Y2))))))))))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.25/1.47 thf(f19,plain,(
% 1.25/1.47 ($false = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.25/1.47 thf(f23,plain,(
% 1.25/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK1 @ sK3 @ Y0)))))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.25/1.47 thf(f300,plain,(
% 1.25/1.47 ($true = (sK3 @ sK5))),
% 1.25/1.47 inference(binary_proxy_clausification,[status(thm)],[f298])).
% 1.25/1.47 % SZS output end Proof for DTF2THF_22087
% 1.25/1.47 % (22227)------------------------------
% 1.25/1.47 % (22227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.25/1.47 % (22227)Termination reason: Refutation
% 1.25/1.47
% 1.25/1.47 % (22227)Memory used [KB]: 1279
% 1.25/1.47 % (22227)Time elapsed: 0.026 s
% 1.25/1.47 % (22227)Instructions burned: 76 (million)
% 1.25/1.47 % (22227)------------------------------
% 1.25/1.47 % (22227)------------------------------
% 1.25/1.47 % (22184)Success in time 0.423 s
%------------------------------------------------------------------------------