%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO325^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 09:53:56 AM UTC 2026
% Result : Theorem 1.56s 1.61s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 1
% Syntax : Number of formulae : 48 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 372 ( 63 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 832 ( 4 ~; 19 |; 38 &; 555 @)
% ( 0 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 7 con; 0-2 aty)
% ( 79 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 193 ( 139 ^; 48 !; 6 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cK: ( a > $o ) > a > $o ).
thf(func_def_14,type,
ph0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK1: a ).
thf(func_def_16,type,
sK2: a ).
thf(func_def_17,type,
sK3: a > $o ).
thf(func_def_18,type,
sK4: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_19,type,
sK5: a ).
thf(f383,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f382]) ).
thf(f382,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f348,f380]) ).
thf(f380,plain,
( $false
= ( sK3 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f376]) ).
thf(f376,plain,
( ( $false
= ( sK3 @ sK5 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f34,f351]) ).
thf(f351,plain,
! [X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) )
| ( $false
= ( X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f350]) ).
thf(f350,plain,
! [X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) )
& ( X1 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f349]) ).
thf(f349,plain,
! [X1: a > $o] :
( $false
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f346]) ).
thf(f346,plain,
( ( ( sK3 @ sK5 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) )
& ( Y0 @ sK5 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f345]) ).
thf(f345,plain,
( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f344]) ).
thf(f344,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f343]) ).
thf(f343,plain,
( ( $false = $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f327,f35]) ).
thf(f35,plain,
( $true
= ( sK3 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK3 @ sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( cK @ sK3 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
= ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
=> ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
= ( ^ [Y0: a] :
( ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false = $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f8,f14]) ).
thf(f14,plain,
! [X2: a > $o,X1: a > $o] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: a > $o,X1: a > $o] :
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( cK @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( cK @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( cK @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X3: a] :
( ( cK @ X0 @ X3 )
=> ( cK @ X1 @ X3 ) ) )
=> ! [X4: a] :
( ( cK
@ ^ [X5: a] :
? [X6: a > $o] :
( ! [X7: a] :
( ( X6 @ X7 )
=> ( cK @ X6 @ X7 ) )
& ( X6 @ X5 ) )
@ X4 )
=> ( cK
@ ( cK
@ ^ [X8: a] :
? [X9: a > $o] :
( ( X9 @ X8 )
& ! [X10: a] :
( ( X9 @ X10 )
=> ( cK @ X9 @ X10 ) ) ) )
@ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X2 )
=> ( cK
@ ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ( X4 @ X3 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) ) ) )
@ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X2 )
=> ( cK
@ ( cK
@ ^ [X3: a] :
? [X4: a > $o] :
( ( X4 @ X3 )
& ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) ) ) )
@ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P6xFd9fKlb/DTF2THF_14758.p',cTHM116_1SS) ).
thf(f8,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 )
=> ( cK
@ ( cK
@ ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f327,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f326]) ).
thf(f326,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f316]) ).
thf(f316,plain,
( ( $false
= ( sK3 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f30,f76]) ).
thf(f76,plain,
! [X0: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( cK @ X1 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: a,X1: a > $o] :
( ( $false = $true )
| ( $false
= ( sK3 @ X0 ) )
| ( $true
= ( cK @ X1 @ X0 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(superposition,[status(thm)],[f27,f38]) ).
thf(f38,plain,
! [X1: a] :
( ( $true
= ( cK @ sK3 @ X1 ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: a] :
( ( ( sK3 @ X1 )
=> ( cK @ sK3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( cK @ sK3 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f27,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $false
= ( cK @ X2 @ X3 ) )
| ( $true
= ( cK @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $true
= ( ( cK @ X2 @ X3 )
=> ( cK @ X1 @ X3 ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f14]) ).
thf(f30,plain,
( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f34,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
=> ( cK @ sK3 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f348,plain,
( $true
= ( sK3 @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO325^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:28:36 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SYO325^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.45 % Domain : Syntactic
% 0.31/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : tps_0986 [Bro09]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.33 v8.2.0, 0.36 v8.1.0, 0.50 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.31/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.45 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 7 ( 7 avg)
% 0.31/0.45 % Number of connectives : 28 ( 0 ~; 0 |; 2 &; 19 @)
% 0.31/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 14 ( 14 avg)
% 0.31/0.45 % Number of types : 2 ( 1 usr)
% 0.31/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.31/0.45 % Number of variables : 11 ( 2 ^; 7 !; 2 ?; 11 :)
% 0.31/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(a_type,type,
% 0.31/0.45 a: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(cK,type,
% 0.31/0.45 cK: ( a > $o ) > a > $o ).
% 0.31/0.45
% 0.31/0.45 thf(cTHM116_1SS,conjecture,
% 0.31/0.45 ( ! [X: a > $o,Y: a > $o] :
% 0.31/0.45 ( ! [Xx: a] :
% 0.31/0.45 ( ( X @ Xx )
% 0.31/0.45 => ( Y @ Xx ) )
% 0.31/0.45 => ! [Xx: a] :
% 0.31/0.45 ( ( cK @ X @ Xx )
% 0.31/0.45 => ( cK @ Y @ Xx ) ) )
% 0.31/0.45 => ! [Xx: a] :
% 0.31/0.45 ( ( cK
% 0.31/0.45 @ ^ [Xx0: a] :
% 0.31/0.45 ? [S: a > $o] :
% 0.31/0.45 ( ! [Xx1: a] :
% 0.31/0.45 ( ( S @ Xx1 )
% 0.31/0.45 => ( cK @ S @ Xx1 ) )
% 0.31/0.45 & ( S @ Xx0 ) )
% 0.31/0.45 @ Xx )
% 0.31/0.45 => ( cK
% 0.31/0.45 @ ( cK
% 0.31/0.45 @ ^ [Xx0: a] :
% 0.31/0.45 ? [S: a > $o] :
% 0.31/0.45 ( ! [Xx1: a] :
% 0.31/0.45 ( ( S @ Xx1 )
% 0.31/0.45 => ( cK @ S @ Xx1 ) )
% 0.31/0.45 & ( S @ Xx0 ) ) )
% 0.31/0.45 @ Xx ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.23 %%% Generated on Tue Feb 24 14:28:37 EST 2026
% 1.49/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.23 %%% Logic specification used:
% 1.49/1.23 %%% thf(spec, logic, $$dhol).
% 1.49/1.23
% 1.49/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.P6xFd9fKlb/DTF2DTF14758.p
% See solution above
% 1.49/1.23 ------------------------
% 1.49/1.24 ---- Cleaned THF ---
% 1.49/1.24 thf(a_type,type,
% 1.49/1.24 a: $tType ).
% 1.49/1.24
% 1.49/1.24 thf(cK,type,
% 1.49/1.24 cK: ( a > $o ) > a > $o ).
% 1.49/1.24
% 1.49/1.24 thf(cTHM116_1SS,conjecture,
% 1.49/1.24 ( ! [X: a > $o,Y: a > $o] :
% 1.49/1.24 ( ! [Xx: a] :
% 1.49/1.24 ( ( X @ Xx )
% 1.49/1.24 => ( Y @ Xx ) )
% 1.49/1.24 => ! [Xx: a] :
% 1.49/1.24 ( ( cK @ X @ Xx )
% 1.49/1.24 => ( cK @ Y @ Xx ) ) )
% 1.49/1.24 => ! [Xx: a] :
% 1.49/1.24 ( ( cK
% 1.49/1.24 @ ^ [Xx0: a] :
% 1.49/1.24 ? [S: a > $o] :
% 1.49/1.24 ( ! [Xx1: a] :
% 1.49/1.24 ( ( S @ Xx1 )
% 1.49/1.24 => ( cK @ S @ Xx1 ) )
% 1.49/1.24 & ( S @ Xx0 ) )
% 1.49/1.24 @ Xx )
% 1.49/1.24 => ( cK
% 1.49/1.24 @ ( cK
% 1.49/1.24 @ ^ [Xx0: a] :
% 1.49/1.24 ? [S: a > $o] :
% 1.49/1.24 ( ! [Xx1: a] :
% 1.49/1.24 ( ( S @ Xx1 )
% 1.49/1.24 => ( cK @ S @ Xx1 ) )
% 1.49/1.24 & ( S @ Xx0 ) ) )
% 1.49/1.24 @ Xx ) ) ) ).
% 1.49/1.24 ------------------------
% 1.49/1.25 % (14974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14758 for (3000ds/2Mi)
% 1.49/1.26 % (14974)Instruction limit reached!
% 1.49/1.26 % (14974)------------------------------
% 1.49/1.26 % (14974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (14974)Termination reason: Unknown
% 1.49/1.26 % (14974)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (14974)Memory used [KB]: 5500
% 1.49/1.26 % (14974)Time elapsed: 0.002 s
% 1.49/1.26 % (14974)Instructions burned: 3 (million)
% 1.49/1.26 % (14974)------------------------------
% 1.49/1.26 % (14974)------------------------------
% 1.49/1.26 % (14971)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14758 for (3000ds/183Mi)
% 1.49/1.26 % (14972)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_14758 for (3000ds/4Mi)
% 1.49/1.26 % (14973)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_14758 for (3000ds/27Mi)
% 1.49/1.26 % (14975)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_14758 for (3000ds/2Mi)
% 1.49/1.26 % (14976)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_14758 for (3000ds/275Mi)
% 1.49/1.26 % (14977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14758 for (3000ds/18Mi)
% 1.49/1.26 % (14975)Instruction limit reached!
% 1.49/1.26 % (14975)------------------------------
% 1.49/1.26 % (14975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (14975)Termination reason: Unknown
% 1.49/1.26 % (14975)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (14975)Memory used [KB]: 895
% 1.49/1.26 % (14975)Time elapsed: 0.003 s
% 1.49/1.26 % (14975)Instructions burned: 2 (million)
% 1.49/1.26 % (14975)------------------------------
% 1.49/1.26 % (14975)------------------------------
% 1.49/1.26 % (14972)Instruction limit reached!
% 1.49/1.26 % (14972)------------------------------
% 1.49/1.26 % (14972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (14972)Termination reason: Unknown
% 1.49/1.26 % (14972)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (14972)Memory used [KB]: 5500
% 1.49/1.26 % (14972)Time elapsed: 0.005 s
% 1.49/1.26 % (14972)Instructions burned: 4 (million)
% 1.49/1.26 % (14972)------------------------------
% 1.49/1.26 % (14972)------------------------------
% 1.49/1.27 % (14978)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/3Mi)
% 1.49/1.27 % (14978)Instruction limit reached!
% 1.49/1.27 % (14978)------------------------------
% 1.49/1.27 % (14978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (14978)Termination reason: Unknown
% 1.49/1.27 % (14978)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (14978)Memory used [KB]: 5500
% 1.49/1.27 % (14978)Time elapsed: 0.003 s
% 1.49/1.27 % (14978)Instructions burned: 3 (million)
% 1.49/1.27 % (14978)------------------------------
% 1.49/1.27 % (14978)------------------------------
% 1.49/1.27 % (14977)Instruction limit reached!
% 1.49/1.27 % (14977)------------------------------
% 1.49/1.27 % (14977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (14977)Termination reason: Unknown
% 1.49/1.27 % (14977)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (14977)Memory used [KB]: 5628
% 1.49/1.27 % (14977)Time elapsed: 0.014 s
% 1.49/1.27 % (14977)Instructions burned: 19 (million)
% 1.49/1.27 % (14977)------------------------------
% 1.49/1.27 % (14977)------------------------------
% 1.49/1.28 % (14981)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_14758 for (2999ds/3Mi)
% 1.49/1.28 % (14981)Instruction limit reached!
% 1.49/1.28 % (14981)------------------------------
% 1.49/1.28 % (14981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (14981)Termination reason: Unknown
% 1.49/1.28 % (14981)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (14981)Memory used [KB]: 5500
% 1.49/1.28 % (14981)Time elapsed: 0.003 s
% 1.49/1.28 % (14981)Instructions burned: 3 (million)
% 1.49/1.28 % (14981)------------------------------
% 1.49/1.28 % (14981)------------------------------
% 1.49/1.28 % (14973)Instruction limit reached!
% 1.49/1.28 % (14973)------------------------------
% 1.49/1.28 % (14973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (14973)Termination reason: Unknown
% 1.49/1.28 % (14973)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (14973)Memory used [KB]: 5628
% 1.49/1.28 % (14973)Time elapsed: 0.019 s
% 1.49/1.28 % (14973)Instructions burned: 28 (million)
% 1.49/1.28 % (14973)------------------------------
% 1.49/1.28 % (14973)------------------------------
% 1.49/1.28 % (14979)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_14758 for (2999ds/37Mi)
% 1.49/1.28 % (14980)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_14758 for (2999ds/15Mi)
% 1.49/1.29 % (14983)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/7Mi)
% 1.49/1.29 % (14982)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_14758 for (2999ds/1041Mi)
% 1.49/1.29 % (14983)Instruction limit reached!
% 1.49/1.29 % (14983)------------------------------
% 1.49/1.29 % (14983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (14983)Termination reason: Unknown
% 1.49/1.29 % (14983)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (14983)Memory used [KB]: 1023
% 1.49/1.29 % (14983)Time elapsed: 0.005 s
% 1.49/1.29 % (14983)Instructions burned: 9 (million)
% 1.49/1.29 % (14983)------------------------------
% 1.49/1.29 % (14983)------------------------------
% 1.49/1.29 % (14980)Instruction limit reached!
% 1.49/1.29 % (14980)------------------------------
% 1.49/1.29 % (14980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (14980)Termination reason: Unknown
% 1.49/1.29 % (14980)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (14980)Memory used [KB]: 5628
% 1.49/1.29 % (14980)Time elapsed: 0.012 s
% 1.49/1.29 % (14980)Instructions burned: 16 (million)
% 1.49/1.29 % (14980)------------------------------
% 1.49/1.29 % (14980)------------------------------
% 1.49/1.30 % (14984)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/16Mi)
% 1.56/1.30 % (14979)Instruction limit reached!
% 1.56/1.30 % (14979)------------------------------
% 1.56/1.30 % (14979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (14979)Termination reason: Unknown
% 1.56/1.30 % (14979)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (14979)Memory used [KB]: 6012
% 1.56/1.30 % (14979)Time elapsed: 0.021 s
% 1.56/1.30 % (14979)Instructions burned: 37 (million)
% 1.56/1.30 % (14979)------------------------------
% 1.56/1.30 % (14979)------------------------------
% 1.56/1.30 % (14985)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_14758 for (2999ds/3Mi)
% 1.56/1.30 % (14985)Instruction limit reached!
% 1.56/1.30 % (14985)------------------------------
% 1.56/1.30 % (14985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (14985)Termination reason: Unknown
% 1.56/1.30 % (14985)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (14985)Memory used [KB]: 5500
% 1.56/1.30 % (14985)Time elapsed: 0.003 s
% 1.56/1.30 % (14985)Instructions burned: 4 (million)
% 1.56/1.30 % (14985)------------------------------
% 1.56/1.30 % (14985)------------------------------
% 1.56/1.31 % (14984)Instruction limit reached!
% 1.56/1.31 % (14984)------------------------------
% 1.56/1.31 % (14984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (14984)Termination reason: Unknown
% 1.56/1.31 % (14984)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (14984)Memory used [KB]: 5756
% 1.56/1.31 % (14984)Time elapsed: 0.012 s
% 1.56/1.31 % (14984)Instructions burned: 18 (million)
% 1.56/1.31 % (14984)------------------------------
% 1.56/1.31 % (14984)------------------------------
% 1.56/1.31 % (14986)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_14758 for (2999ds/3Mi)
% 1.56/1.31 % (14986)Instruction limit reached!
% 1.56/1.31 % (14986)------------------------------
% 1.56/1.31 % (14986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (14986)Termination reason: Unknown
% 1.56/1.31 % (14986)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (14986)Memory used [KB]: 1023
% 1.56/1.31 % (14986)Time elapsed: 0.004 s
% 1.56/1.31 % (14986)Instructions burned: 4 (million)
% 1.56/1.31 % (14986)------------------------------
% 1.56/1.31 % (14986)------------------------------
% 1.56/1.31 % (14988)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/3Mi)
% 1.56/1.31 % (14988)Instruction limit reached!
% 1.56/1.31 % (14988)------------------------------
% 1.56/1.31 % (14988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (14988)Termination reason: Unknown
% 1.56/1.31 % (14988)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (14988)Memory used [KB]: 5500
% 1.56/1.31 % (14988)Time elapsed: 0.003 s
% 1.56/1.31 % (14988)Instructions burned: 4 (million)
% 1.56/1.31 % (14988)------------------------------
% 1.56/1.31 % (14988)------------------------------
% 1.56/1.32 % (14987)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/7Mi)
% 1.56/1.32 % (14989)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/4Mi)
% 1.56/1.32 % (14989)Instruction limit reached!
% 1.56/1.32 % (14989)------------------------------
% 1.56/1.32 % (14989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (14989)Termination reason: Unknown
% 1.56/1.32 % (14989)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (14989)Memory used [KB]: 5500
% 1.56/1.32 % (14989)Time elapsed: 0.003 s
% 1.56/1.32 % (14989)Instructions burned: 5 (million)
% 1.56/1.32 % (14989)------------------------------
% 1.56/1.32 % (14989)------------------------------
% 1.56/1.32 % (14987)Refutation not found, incomplete strategy
% 1.56/1.32 % (14987)------------------------------
% 1.56/1.32 % (14987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (14987)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.32
% 1.56/1.32
% 1.56/1.32 % (14987)Memory used [KB]: 5500
% 1.56/1.32 % (14987)Time elapsed: 0.004 s
% 1.56/1.32 % (14987)Instructions burned: 3 (million)
% 1.56/1.32 % (14987)------------------------------
% 1.56/1.32 % (14987)------------------------------
% 1.56/1.32 % (14991)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/710Mi)
% 1.56/1.33 % (14992)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/6Mi)
% 1.56/1.33 % (14990)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/18Mi)
% 1.56/1.33 % (14992)Instruction limit reached!
% 1.56/1.33 % (14992)------------------------------
% 1.56/1.33 % (14992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (14992)Termination reason: Unknown
% 1.56/1.33 % (14992)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (14992)Memory used [KB]: 5500
% 1.56/1.33 % (14992)Time elapsed: 0.004 s
% 1.56/1.33 % (14992)Instructions burned: 6 (million)
% 1.56/1.33 % (14992)------------------------------
% 1.56/1.33 % (14992)------------------------------
% 1.56/1.33 % (14990)Refutation not found, incomplete strategy
% 1.56/1.33 % (14990)------------------------------
% 1.56/1.33 % (14990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (14990)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.33
% 1.56/1.33
% 1.56/1.33 % (14990)Memory used [KB]: 5500
% 1.56/1.33 % (14990)Time elapsed: 0.004 s
% 1.56/1.33 % (14990)Instructions burned: 3 (million)
% 1.56/1.33 % (14990)------------------------------
% 1.56/1.33 % (14990)------------------------------
% 1.56/1.34 % (14993)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_14758 for (2999ds/902Mi)
% 1.56/1.34 % (14994)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_14758 for (2999ds/21Mi)
% 1.56/1.35 % (14994)Instruction limit reached!
% 1.56/1.35 % (14994)------------------------------
% 1.56/1.35 % (14994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (14994)Termination reason: Unknown
% 1.56/1.35 % (14994)Termination phase: Saturation
% 1.56/1.35
% 1.56/1.35 % (14994)Memory used [KB]: 5628
% 1.56/1.35 % (14994)Time elapsed: 0.010 s
% 1.56/1.35 % (14994)Instructions burned: 23 (million)
% 1.56/1.35 % (14994)------------------------------
% 1.56/1.35 % (14994)------------------------------
% 1.56/1.35 % (14995)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/5Mi)
% 1.56/1.35 % (14995)Instruction limit reached!
% 1.56/1.35 % (14995)------------------------------
% 1.56/1.35 % (14995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (14995)Termination reason: Unknown
% 1.56/1.35 % (14995)Termination phase: Saturation
% 1.56/1.35
% 1.56/1.35 % (14995)Memory used [KB]: 5500
% 1.56/1.35 % (14995)Time elapsed: 0.005 s
% 1.56/1.35 % (14995)Instructions burned: 5 (million)
% 1.56/1.35 % (14995)------------------------------
% 1.56/1.35 % (14995)------------------------------
% 1.56/1.36 % (14996)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_14758 for (2999ds/6Mi)
% 1.56/1.36 % (14971)Instruction limit reached!
% 1.56/1.36 % (14971)------------------------------
% 1.56/1.36 % (14971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (14971)Termination reason: Unknown
% 1.56/1.36 % (14971)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (14971)Memory used [KB]: 6780
% 1.56/1.36 % (14971)Time elapsed: 0.100 s
% 1.56/1.36 % (14971)Instructions burned: 183 (million)
% 1.56/1.36 % (14971)------------------------------
% 1.56/1.36 % (14971)------------------------------
% 1.56/1.36 % (14996)Instruction limit reached!
% 1.56/1.36 % (14996)------------------------------
% 1.56/1.36 % (14996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (14996)Termination reason: Unknown
% 1.56/1.36 % (14996)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (14996)Memory used [KB]: 5500
% 1.56/1.36 % (14996)Time elapsed: 0.004 s
% 1.56/1.36 % (14996)Instructions burned: 8 (million)
% 1.56/1.36 % (14996)------------------------------
% 1.56/1.36 % (14996)------------------------------
% 1.56/1.37 % (14997)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14758 for (2999ds/377Mi)
% 1.56/1.37 % (14999)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_14758 for (2998ds/19Mi)
% 1.56/1.38 % (14998)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_14758 for (2998ds/779Mi)
% 1.56/1.38 % (14999)Instruction limit reached!
% 1.56/1.38 % (14999)------------------------------
% 1.56/1.38 % (14999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (14999)Termination reason: Unknown
% 1.56/1.38 % (14999)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (14999)Memory used [KB]: 5628
% 1.56/1.38 % (14999)Time elapsed: 0.008 s
% 1.56/1.38 % (14999)Instructions burned: 19 (million)
% 1.56/1.38 % (14999)------------------------------
% 1.56/1.38 % (14999)------------------------------
% 1.56/1.39 % (15000)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14758 for (2998ds/879Mi)
% 1.56/1.39 % (14976)Instruction limit reached!
% 1.56/1.39 % (14976)------------------------------
% 1.56/1.39 % (14976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (14976)Termination reason: Unknown
% 1.56/1.39 % (14976)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (14976)Memory used [KB]: 5884
% 1.56/1.39 % (14976)Time elapsed: 0.133 s
% 1.56/1.39 % (14976)Instructions burned: 277 (million)
% 1.56/1.39 % (14976)------------------------------
% 1.56/1.39 % (14976)------------------------------
% 1.56/1.40 % (15001)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14758 for (2998ds/17Mi)
% 1.56/1.41 % (15001)Instruction limit reached!
% 1.56/1.41 % (15001)------------------------------
% 1.56/1.41 % (15001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (15001)Termination reason: Unknown
% 1.56/1.41 % (15001)Termination phase: Saturation
% 1.56/1.41
% 1.56/1.41 % (15001)Memory used [KB]: 5628
% 1.56/1.41 % (15001)Time elapsed: 0.007 s
% 1.56/1.41 % (15001)Instructions burned: 17 (million)
% 1.56/1.41 % (15001)------------------------------
% 1.56/1.41 % (15001)------------------------------
% 1.56/1.42 % (15002)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14758 for (2998ds/3Mi)
% 1.56/1.42 % (15002)Instruction limit reached!
% 1.56/1.42 % (15002)------------------------------
% 1.56/1.42 % (15002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (15002)Termination reason: Unknown
% 1.56/1.42 % (15002)Termination phase: Saturation
% 1.56/1.42
% 1.56/1.42 % (15002)Memory used [KB]: 1023
% 1.56/1.42 % (15002)Time elapsed: 0.003 s
% 1.56/1.42 % (15002)Instructions burned: 4 (million)
% 1.56/1.42 % (15002)------------------------------
% 1.56/1.42 % (15002)------------------------------
% 1.56/1.43 % (15003)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14758 for (2998ds/30Mi)
% 1.56/1.44 % (15003)Instruction limit reached!
% 1.56/1.44 % (15003)------------------------------
% 1.56/1.44 % (15003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (15003)Termination reason: Unknown
% 1.56/1.44 % (15003)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (15003)Memory used [KB]: 5628
% 1.56/1.44 % (15003)Time elapsed: 0.012 s
% 1.56/1.44 % (15003)Instructions burned: 30 (million)
% 1.56/1.44 % (15003)------------------------------
% 1.56/1.44 % (15003)------------------------------
% 1.56/1.45 % (15004)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14758 for (2998ds/127Mi)
% 1.56/1.49 % (15004)Instruction limit reached!
% 1.56/1.49 % (15004)------------------------------
% 1.56/1.49 % (15004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.49 % (15004)Termination reason: Unknown
% 1.56/1.49 % (15004)Termination phase: Saturation
% 1.56/1.49
% 1.56/1.49 % (15004)Memory used [KB]: 6012
% 1.56/1.49 % (15004)Time elapsed: 0.043 s
% 1.56/1.49 % (15004)Instructions burned: 127 (million)
% 1.56/1.49 % (15004)------------------------------
% 1.56/1.49 % (15004)------------------------------
% 1.56/1.49 % (14997)Instruction limit reached!
% 1.56/1.49 % (14997)------------------------------
% 1.56/1.49 % (14997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.49 % (14997)Termination reason: Unknown
% 1.56/1.49 % (14997)Termination phase: Saturation
% 1.56/1.49
% 1.56/1.49 % (14997)Memory used [KB]: 6268
% 1.56/1.49 % (14997)Time elapsed: 0.126 s
% 1.56/1.49 % (14997)Instructions burned: 380 (million)
% 1.56/1.49 % (14997)------------------------------
% 1.56/1.49 % (14997)------------------------------
% 1.56/1.50 % (15005)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14758 for (2997ds/100Mi)
% 1.56/1.50 % (15006)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_14758 for (2997ds/3Mi)
% 1.56/1.50 % (15005)Refutation not found, incomplete strategy
% 1.56/1.50 % (15005)------------------------------
% 1.56/1.50 % (15005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.50 % (15005)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.50
% 1.56/1.50
% 1.56/1.50 % (15005)Memory used [KB]: 5500
% 1.56/1.50 % (15005)Time elapsed: 0.002 s
% 1.56/1.50 % (15005)Instructions burned: 3 (million)
% 1.56/1.50 % (15005)------------------------------
% 1.56/1.50 % (15005)------------------------------
% 1.56/1.50 % (15006)Instruction limit reached!
% 1.56/1.50 % (15006)------------------------------
% 1.56/1.50 % (15006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.50 % (15006)Termination reason: Unknown
% 1.56/1.50 % (15006)Termination phase: Saturation
% 1.56/1.50
% 1.56/1.50 % (15006)Memory used [KB]: 5500
% 1.56/1.50 % (15006)Time elapsed: 0.003 s
% 1.56/1.50 % (15006)Instructions burned: 4 (million)
% 1.56/1.50 % (15006)------------------------------
% 1.56/1.50 % (15006)------------------------------
% 1.56/1.51 % (15007)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_14758 for (2997ds/20Mi)
% 1.56/1.52 % (15008)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_14758 for (2997ds/86Mi)
% 1.56/1.52 % (15007)Instruction limit reached!
% 1.56/1.52 % (15007)------------------------------
% 1.56/1.52 % (15007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.52 % (15007)Termination reason: Unknown
% 1.56/1.52 % (15007)Termination phase: Saturation
% 1.56/1.52
% 1.56/1.52 % (15007)Memory used [KB]: 5628
% 1.56/1.52 % (15007)Time elapsed: 0.009 s
% 1.56/1.52 % (15007)Instructions burned: 21 (million)
% 1.56/1.52 % (15007)------------------------------
% 1.56/1.52 % (15007)------------------------------
% 1.56/1.53 % (15009)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_14758 for (2997ds/107Mi)
% 1.56/1.54 % (15008)Instruction limit reached!
% 1.56/1.54 % (15008)------------------------------
% 1.56/1.54 % (15008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.54 % (15008)Termination reason: Unknown
% 1.56/1.54 % (15008)Termination phase: Saturation
% 1.56/1.54
% 1.56/1.54 % (15008)Memory used [KB]: 6012
% 1.56/1.54 % (15008)Time elapsed: 0.052 s
% 1.56/1.54 % (15008)Instructions burned: 86 (million)
% 1.56/1.54 % (15008)------------------------------
% 1.56/1.54 % (15008)------------------------------
% 1.56/1.55 % (14991)Instruction limit reached!
% 1.56/1.55 % (14991)------------------------------
% 1.56/1.55 % (14991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.55 % (14991)Termination reason: Unknown
% 1.56/1.55 % (14991)Termination phase: Saturation
% 1.56/1.55
% 1.56/1.55 % (14991)Memory used [KB]: 7164
% 1.56/1.55 % (14991)Time elapsed: 0.225 s
% 1.56/1.55 % (14991)Instructions burned: 711 (million)
% 1.56/1.55 % (14991)------------------------------
% 1.56/1.55 % (14991)------------------------------
% 1.56/1.55 % (15010)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_14758 for (2997ds/39Mi)
% 1.56/1.56 % (15011)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_14758 for (2997ds/448Mi)
% 1.56/1.57 % (15009)Instruction limit reached!
% 1.56/1.57 % (15009)------------------------------
% 1.56/1.57 % (15009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.57 % (15009)Termination reason: Unknown
% 1.56/1.57 % (15009)Termination phase: Saturation
% 1.56/1.57
% 1.56/1.57 % (15009)Memory used [KB]: 5756
% 1.56/1.57 % (15009)Time elapsed: 0.057 s
% 1.56/1.57 % (15009)Instructions burned: 107 (million)
% 1.56/1.57 % (15009)------------------------------
% 1.56/1.57 % (15009)------------------------------
% 1.56/1.57 % (15010)Instruction limit reached!
% 1.56/1.57 % (15010)------------------------------
% 1.56/1.57 % (15010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.57 % (15010)Termination reason: Unknown
% 1.56/1.57 % (15010)Termination phase: Saturation
% 1.56/1.57
% 1.56/1.57 % (15010)Memory used [KB]: 5756
% 1.56/1.57 % (15010)Time elapsed: 0.036 s
% 1.56/1.57 % (15010)Instructions burned: 39 (million)
% 1.56/1.57 % (15010)------------------------------
% 1.56/1.57 % (15010)------------------------------
% 1.56/1.58 % (15012)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_14758 for (2996ds/46Mi)
% 1.56/1.58 % (15013)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_14758 for (2996ds/98Mi)
% 1.56/1.59 % (15012)Instruction limit reached!
% 1.56/1.59 % (15012)------------------------------
% 1.56/1.59 % (15012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.59 % (15012)Termination reason: Unknown
% 1.56/1.59 % (15012)Termination phase: Saturation
% 1.56/1.59
% 1.56/1.59 % (15012)Memory used [KB]: 5756
% 1.56/1.59 % (15012)Time elapsed: 0.041 s
% 1.56/1.59 % (15012)Instructions burned: 47 (million)
% 1.56/1.59 % (15012)------------------------------
% 1.56/1.59 % (15012)------------------------------
% 1.56/1.60 % (15014)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14758 for (2996ds/507Mi)
% 1.56/1.61 % (15013)First to succeed.
% 1.56/1.61 % (15013)Refutation found. Thanks to Tanya!
% 1.56/1.61 % SZS status Theorem for DTF2THF_14758
% 1.56/1.61 % SZS output start Proof for DTF2THF_14758
% 1.56/1.61 thf(type_def_5, type, a: $tType).
% 1.56/1.61 thf(func_def_0, type, a: $tType).
% 1.56/1.61 thf(func_def_1, type, cK: (a > $o) > a > $o).
% 1.56/1.61 thf(func_def_14, type, ph0: !>[X0: $tType]:(X0)).
% 1.56/1.61 thf(func_def_15, type, sK1: a).
% 1.56/1.61 thf(func_def_16, type, sK2: a).
% 1.56/1.61 thf(func_def_17, type, sK3: a > $o).
% 1.56/1.61 thf(func_def_18, type, sK4: (a > $o) > (a > $o) > a).
% 1.56/1.61 thf(func_def_19, type, sK5: a).
% 1.56/1.61 thf(f383,plain,(
% 1.56/1.61 $false),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f382])).
% 1.56/1.61 thf(f382,plain,(
% 1.56/1.61 ($false = $true)),
% 1.56/1.61 inference(backward_demodulation,[status(thm)],[f348,f380])).
% 1.56/1.61 thf(f380,plain,(
% 1.56/1.61 ($false = (sK3 @ sK5))),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.56/1.61 thf(f376,plain,(
% 1.56/1.61 ($false = (sK3 @ sK5)) | ($false = $true)),
% 1.56/1.61 inference(superposition,[status(thm)],[f34,f351])).
% 1.56/1.61 thf(f351,plain,(
% 1.56/1.61 ( ! [X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cK @ X1 @ Y0))))) | ($false = (X1 @ sK5))) )),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f350])).
% 1.56/1.61 thf(f350,plain,(
% 1.56/1.61 ( ! [X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cK @ X1 @ Y0)))) & (X1 @ sK5)) = $false)) )),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f349])).
% 1.56/1.61 thf(f349,plain,(
% 1.56/1.61 ( ! [X1 : a > $o] : (($false = ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))) & (Y0 @ sK5))) @ X1))) )),
% 1.56/1.61 inference(pi_clausification,[status(thm)],[f347])).
% 1.56/1.61 thf(f347,plain,(
% 1.56/1.61 ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))) & (Y0 @ sK5)))))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f346])).
% 1.56/1.61 thf(f346,plain,(
% 1.56/1.61 (((sK3 @ sK5) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))) & (Y0 @ sK5))))) = $false)),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f345])).
% 1.56/1.61 thf(f345,plain,(
% 1.56/1.61 (((^[Y0 : a]: ((sK3 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK5) = $false)),
% 1.56/1.61 inference(sigma_clausification,[status(thm)],[f344])).
% 1.56/1.61 thf(f344,plain,(
% 1.56/1.61 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f343])).
% 1.56/1.61 thf(f343,plain,(
% 1.56/1.61 ($false = $true) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.56/1.61 inference(forward_demodulation,[status(thm)],[f327,f35])).
% 1.56/1.61 thf(f35,plain,(
% 1.56/1.61 ($true = (sK3 @ sK2))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.56/1.61 thf(f33,plain,(
% 1.56/1.61 (((sK3 @ sK2) & (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (cK @ sK3 @ Y0))))) = $true)),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.56/1.61 thf(f32,plain,(
% 1.56/1.61 ($true = ((^[Y0 : a > $o]: ((Y0 @ sK2) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))))) @ sK3))),
% 1.56/1.61 inference(sigma_clausification,[status(thm)],[f31])).
% 1.56/1.61 thf(f31,plain,(
% 1.56/1.61 ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1))))))))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.56/1.61 thf(f29,plain,(
% 1.56/1.61 ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1))))))) => (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.56/1.61 thf(f28,plain,(
% 1.56/1.61 ($false = ((^[Y0 : a]: ((?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2))))))) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))) @ sK2))),
% 1.56/1.61 inference(sigma_clausification,[status(thm)],[f25])).
% 1.56/1.61 thf(f25,plain,(
% 1.56/1.61 ($false = (!! @ a @ (^[Y0 : a]: ((?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2))))))) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.56/1.61 thf(f24,plain,(
% 1.56/1.61 ($false = (!! @ a @ (^[Y0 : a]: (((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.56/1.61 thf(f21,plain,(
% 1.56/1.61 ($false = $true) | ($false = (!! @ a @ (^[Y0 : a]: (((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.56/1.61 inference(superposition,[status(thm)],[f8,f14])).
% 1.56/1.61 thf(f14,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X1 : a > $o] : (($true = (!! @ a @ (^[Y0 : a]: ((cK @ X2 @ Y0) => (cK @ X1 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: ((X2 @ Y0) => (X1 @ Y0)))))) )),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.56/1.61 thf(f13,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X1 : a > $o] : (($true = ((!! @ a @ (^[Y0 : a]: ((X2 @ Y0) => (X1 @ Y0)))) => (!! @ a @ (^[Y0 : a]: ((cK @ X2 @ Y0) => (cK @ X1 @ Y0))))))) )),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.56/1.61 thf(f12,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X1 : a > $o] : ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ Y0 @ Y1) => (cK @ X1 @ Y1)))))) @ X2) = $true)) )),
% 1.56/1.61 inference(pi_clausification,[status(thm)],[f11])).
% 1.56/1.61 thf(f11,plain,(
% 1.56/1.61 ( ! [X1 : a > $o] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ Y0 @ Y1) => (cK @ X1 @ Y1))))))) = $true)) )),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.56/1.61 thf(f10,plain,(
% 1.56/1.61 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y1 @ Y2) => (cK @ Y0 @ Y2)))))))) @ X1))) )),
% 1.56/1.61 inference(pi_clausification,[status(thm)],[f9])).
% 1.56/1.61 thf(f9,plain,(
% 1.56/1.61 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y1 @ Y2) => (cK @ Y0 @ Y2))))))))))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.56/1.61 thf(f7,plain,(
% 1.56/1.61 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y1 @ Y2) => (cK @ Y0 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1)))))) @ Y0))))))),
% 1.56/1.61 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.56/1.61 thf(f6,plain,(
% 1.56/1.61 ($true = (~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y1 @ Y2) => (cK @ Y0 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1)))))) @ Y0)))))))),
% 1.56/1.61 inference(cnf_transformation,[status(thm)],[f5])).
% 1.56/1.61 thf(f5,plain,(
% 1.56/1.61 ($true = (~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y1 @ Y2) => (cK @ Y0 @ Y2))))))))) => (!! @ a @ (^[Y0 : a]: ((cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1)))))) @ Y0)))))))),
% 1.56/1.61 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.61 thf(f4,plain,(
% 1.56/1.61 ~(! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X3 : a] : ((cK @ X0 @ X3) => (cK @ X1 @ X3))) => ! [X4 : a] : ((cK @ (^[X5 : a] : (? [X6 : a > $o] : (! [X7 : a] : ((X6 @ X7) => (cK @ X6 @ X7)) & (X6 @ X5)))) @ X4) => (cK @ (cK @ (^[X8 : a] : (? [X9 : a > $o] : ((X9 @ X8) & ! [X10 : a] : ((X9 @ X10) => (cK @ X9 @ X10)))))) @ X4)))),
% 1.56/1.61 inference(rectify,[status(thm)],[f2])).
% 1.56/1.61 thf(f2,negated_conjecture,(
% 1.56/1.61 ~(! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ (^[X3 : a] : (? [X4 : a > $o] : (! [X5 : a] : ((X4 @ X5) => (cK @ X4 @ X5)) & (X4 @ X3)))) @ X2) => (cK @ (cK @ (^[X3 : a] : (? [X4 : a > $o] : ((X4 @ X3) & ! [X5 : a] : ((X4 @ X5) => (cK @ X4 @ X5)))))) @ X2)))),
% 1.56/1.61 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.61 thf(f1,conjecture,(
% 1.56/1.61 ! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : ((cK @ (^[X3 : a] : (? [X4 : a > $o] : (! [X5 : a] : ((X4 @ X5) => (cK @ X4 @ X5)) & (X4 @ X3)))) @ X2) => (cK @ (cK @ (^[X3 : a] : (? [X4 : a > $o] : ((X4 @ X3) & ! [X5 : a] : ((X4 @ X5) => (cK @ X4 @ X5)))))) @ X2))),
% 1.56/1.61 file('/export/starexec/sandbox2/tmp/tmp.P6xFd9fKlb/DTF2THF_14758.p',cTHM116_1SS)).
% 1.56/1.61 thf(f8,plain,(
% 1.56/1.61 ($false = (!! @ a @ (^[Y0 : a]: ((cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0) => (cK @ (cK @ (^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1)))))) @ Y0)))))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.56/1.61 thf(f327,plain,(
% 1.56/1.61 ($false = (sK3 @ sK2)) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))))))),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f326])).
% 1.56/1.61 thf(f326,plain,(
% 1.56/1.61 ($false = (sK3 @ sK2)) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => ((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f316])).
% 1.56/1.61 thf(f316,plain,(
% 1.56/1.61 ($false = (sK3 @ sK2)) | ($false = $true) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => ((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 1.56/1.61 inference(superposition,[status(thm)],[f30,f76])).
% 1.56/1.61 thf(f76,plain,(
% 1.56/1.61 ( ! [X0 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0))))) | ($true = (cK @ X1 @ X0)) | ($false = (sK3 @ X0))) )),
% 1.56/1.61 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.56/1.61 thf(f74,plain,(
% 1.56/1.61 ( ! [X0 : a,X1 : a > $o] : (($false = $true) | ($false = (sK3 @ X0)) | ($true = (cK @ X1 @ X0)) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (X1 @ Y0)))))) )),
% 1.56/1.61 inference(superposition,[status(thm)],[f27,f38])).
% 1.56/1.61 thf(f38,plain,(
% 1.56/1.61 ( ! [X1 : a] : (($true = (cK @ sK3 @ X1)) | ($false = (sK3 @ X1))) )),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.56/1.61 thf(f37,plain,(
% 1.56/1.61 ( ! [X1 : a] : ((((sK3 @ X1) => (cK @ sK3 @ X1)) = $true)) )),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.56/1.61 thf(f36,plain,(
% 1.56/1.61 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0) => (cK @ sK3 @ Y0))) @ X1))) )),
% 1.56/1.61 inference(pi_clausification,[status(thm)],[f34])).
% 1.56/1.61 thf(f27,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X2 @ Y0) => (X1 @ Y0))))) | ($false = (cK @ X2 @ X3)) | ($true = (cK @ X1 @ X3))) )),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.56/1.61 thf(f26,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($true = ((cK @ X2 @ X3) => (cK @ X1 @ X3))) | ($false = (!! @ a @ (^[Y0 : a]: ((X2 @ Y0) => (X1 @ Y0)))))) )),
% 1.56/1.61 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.56/1.61 thf(f19,plain,(
% 1.56/1.61 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X2 @ Y0) => (X1 @ Y0))))) | (((^[Y0 : a]: ((cK @ X2 @ Y0) => (cK @ X1 @ Y0))) @ X3) = $true)) )),
% 1.56/1.61 inference(pi_clausification,[status(thm)],[f14])).
% 1.56/1.61 thf(f30,plain,(
% 1.56/1.61 ($false = (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.56/1.61 thf(f34,plain,(
% 1.56/1.61 ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0) => (cK @ sK3 @ Y0)))) = $true)),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.56/1.61 thf(f348,plain,(
% 1.56/1.61 ($true = (sK3 @ sK5))),
% 1.56/1.61 inference(binary_proxy_clausification,[status(thm)],[f346])).
% 1.56/1.61 % SZS output end Proof for DTF2THF_14758
% 1.56/1.61 % (15013)------------------------------
% 1.56/1.61 % (15013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.61 % (15013)Termination reason: Refutation
% 1.56/1.61
% 1.56/1.61 % (15013)Memory used [KB]: 1279
% 1.56/1.61 % (15013)Time elapsed: 0.056 s
% 1.56/1.61 % (15013)Instructions burned: 90 (million)
% 1.56/1.61 % (15013)------------------------------
% 1.56/1.61 % (15013)------------------------------
% 1.56/1.61 % (14970)Success in time 0.345 s
%------------------------------------------------------------------------------