%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV245^6 : TPTP v9.2.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 1.47s 1.65s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 325 ( 59 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 718 ( 4 ~; 18 |; 32 &; 472 @)
% ( 0 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 99 ( 99 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 70 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 166 ( 112 ^; 48 !; 6 ?; 166 :)
% 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 > $o ).
thf(func_def_17,type,
sK3: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_18,type,
sK4: a ).
thf(f333,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f332]) ).
thf(f332,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f298,f330]) ).
thf(f330,plain,
( ( sK2 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f324]) ).
thf(f324,plain,
( ( $false = $true )
| ( ( sK2 @ sK4 )
= $false ) ),
inference(superposition,[status(thm)],[f301,f21]) ).
thf(f21,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK2 @ sK1 )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ sK2 )
= $true ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK1 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
=> ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [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] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f8]) ).
thf(f8,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] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ 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] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ 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] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ 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] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X0 @ X3 ) ) )
=> ! [X4: a] :
( ? [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
=> ( cK @ X5 @ X6 ) )
& ( X5 @ X4 ) )
=> ( cK
@ ^ [X7: a] :
? [X8: a > $o] :
( ! [X9: a] :
( ( X8 @ X9 )
=> ( cK @ X8 @ X9 ) )
& ( X8 @ X7 ) )
@ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ? [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
& ( X3 @ X2 ) )
=> ( cK
@ ^ [X4: a] :
? [X3: a > $o] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( cK @ X3 @ X5 ) )
& ( X3 @ X4 ) )
@ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ X0 @ X2 )
=> ( cK @ X1 @ X2 ) ) )
=> ! [X2: a] :
( ? [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
& ( X3 @ X2 ) )
=> ( cK
@ ^ [X4: a] :
? [X3: a > $o] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( cK @ X3 @ X5 ) )
& ( X3 @ X4 ) )
@ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MUn0XpXtrW/DTF2THF_21380.p',cTHM116_2S) ).
thf(f301,plain,
! [X1: a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) )
| ( ( X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f300]) ).
thf(f300,plain,
! [X1: a > $o] :
( $false
= ( ( X1 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( cK @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f299]) ).
thf(f299,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f297]) ).
thf(f297,plain,
( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f296]) ).
thf(f296,plain,
( ( ( sK2 @ sK4 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK4 )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f295]) ).
thf(f295,plain,
( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f292]) ).
thf(f292,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f288,f22]) ).
thf(f22,plain,
( ( sK2 @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f288,plain,
( ( ( sK2 @ sK1 )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f287]) ).
thf(f287,plain,
( ( ( sK2 @ sK1 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f271]) ).
thf(f271,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ^ [Y1: a] :
( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( cK @ Y2 @ Y3 ) ) ) ) )
@ Y0 ) ) )
= $false )
| ( ( sK2 @ sK1 )
= $false )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f17,f54]) ).
thf(f54,plain,
! [X0: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( ( cK @ X1 @ X0 )
= $true )
| ( ( sK2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: a,X1: a > $o] :
( ( ( sK2 @ X0 )
= $false )
| ( $false = $true )
| ( ( cK @ X1 @ X0 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f28,f25]) ).
thf(f25,plain,
! [X1: a] :
( ( $true
= ( cK @ sK2 @ X1 ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a] :
( ( ( sK2 @ X1 )
=> ( cK @ sK2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cK @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f28,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false )
| ( ( cK @ X1 @ X3 )
= $false )
| ( ( cK @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false )
| ( ( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: a > $o,X3: a,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( cK @ X1 @ Y0 )
=> ( cK @ X2 @ Y0 ) )
@ X3 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: a > $o,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X1 @ Y0 )
=> ( cK @ X2 @ Y0 ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: a > $o,X1: a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( ( cK @ X1 @ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ X1 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: a > $o] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( ( cK @ X1 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f17,plain,
( $false
= ( cK
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f298,plain,
( ( sK2 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV245^6 : TPTP v9.2.1. Released v5.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:42:29 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEV245^6 : TPTP v9.2.1. Released v5.1.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0957 [Bro09]
% 0.28/0.47 % : tps_0964 [Bro09]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % 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, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 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 v5.1.0
% 0.28/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.28/0.47 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.28/0.47 % Number of connectives : 25 ( 0 ~; 0 |; 2 &; 16 @)
% 0.28/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 13 ( 13 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.28/0.47 % Number of variables : 10 ( 1 ^; 7 !; 2 ?; 10 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 % : Renamed from SYO319^5
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cK,type,
% 0.28/0.47 cK: ( a > $o ) > a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cTHM116_2S,conjecture,
% 0.28/0.47 ( ! [X: a > $o,Y: a > $o] :
% 0.28/0.47 ( ! [Xx: a] :
% 0.28/0.47 ( ( X @ Xx )
% 0.28/0.47 => ( Y @ Xx ) )
% 0.28/0.47 => ! [Xx: a] :
% 0.28/0.47 ( ( cK @ X @ Xx )
% 0.28/0.47 => ( cK @ Y @ Xx ) ) )
% 0.28/0.47 => ! [Xx: a] :
% 0.28/0.47 ( ? [S: a > $o] :
% 0.28/0.47 ( ! [Xx0: a] :
% 0.28/0.47 ( ( S @ Xx0 )
% 0.28/0.47 => ( cK @ S @ Xx0 ) )
% 0.28/0.47 & ( S @ Xx ) )
% 0.28/0.47 => ( cK
% 0.28/0.47 @ ^ [Xx0: a] :
% 0.28/0.47 ? [S: a > $o] :
% 0.28/0.47 ( ! [Xx1: a] :
% 0.28/0.47 ( ( S @ Xx1 )
% 0.28/0.47 => ( cK @ S @ Xx1 ) )
% 0.28/0.47 & ( S @ Xx0 ) )
% 0.28/0.47 @ Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.44/1.20 ---- Embedded in THF ---
% 1.44/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.20 %%% Generated on Tue Feb 24 12:42:30 EST 2026
% 1.44/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.20 %%% Logic specification used:
% 1.44/1.20 %%% thf(spec, logic, $$dhol).
% 1.44/1.20
% 1.44/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MUn0XpXtrW/DTF2DTF21380.p
% See solution above
% 1.44/1.20 ------------------------
% 1.44/1.21 ---- Cleaned THF ---
% 1.44/1.21 thf(a_type,type,
% 1.44/1.21 a: $tType ).
% 1.44/1.21
% 1.44/1.21 thf(cK,type,
% 1.44/1.21 cK: ( a > $o ) > a > $o ).
% 1.44/1.21
% 1.44/1.21 thf(cTHM116_2S,conjecture,
% 1.44/1.21 ( ! [X: a > $o,Y: a > $o] :
% 1.44/1.21 ( ! [Xx: a] :
% 1.44/1.21 ( ( X @ Xx )
% 1.44/1.21 => ( Y @ Xx ) )
% 1.44/1.21 => ! [Xx: a] :
% 1.44/1.21 ( ( cK @ X @ Xx )
% 1.44/1.21 => ( cK @ Y @ Xx ) ) )
% 1.44/1.21 => ! [Xx: a] :
% 1.44/1.21 ( ? [S: a > $o] :
% 1.44/1.21 ( ! [Xx0: a] :
% 1.44/1.21 ( ( S @ Xx0 )
% 1.44/1.21 => ( cK @ S @ Xx0 ) )
% 1.44/1.21 & ( S @ Xx ) )
% 1.44/1.21 => ( cK
% 1.44/1.21 @ ^ [Xx0: a] :
% 1.44/1.21 ? [S: a > $o] :
% 1.44/1.21 ( ! [Xx1: a] :
% 1.44/1.21 ( ( S @ Xx1 )
% 1.44/1.21 => ( cK @ S @ Xx1 ) )
% 1.44/1.21 & ( S @ Xx0 ) )
% 1.44/1.21 @ Xx ) ) ) ).
% 1.44/1.21 ------------------------
% 1.44/1.23 % (21478)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_21380 for (3000ds/4Mi)
% 1.44/1.23 % (21481)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_21380 for (3000ds/2Mi)
% 1.44/1.23 % (21481)Instruction limit reached!
% 1.44/1.23 % (21481)------------------------------
% 1.44/1.23 % (21481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.23 % (21481)Termination reason: Unknown
% 1.44/1.23 % (21481)Termination phase: Property scanning
% 1.44/1.23
% 1.44/1.23 % (21481)Memory used [KB]: 895
% 1.44/1.23 % (21481)Time elapsed: 0.002 s
% 1.44/1.23 % (21481)Instructions burned: 2 (million)
% 1.44/1.23 % (21481)------------------------------
% 1.44/1.23 % (21481)------------------------------
% 1.44/1.23 % (21482)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_21380 for (3000ds/275Mi)
% 1.44/1.23 % (21483)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21380 for (3000ds/18Mi)
% 1.44/1.23 % (21477)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21380 for (3000ds/183Mi)
% 1.44/1.24 % (21479)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_21380 for (3000ds/27Mi)
% 1.44/1.24 % (21478)Instruction limit reached!
% 1.44/1.24 % (21478)------------------------------
% 1.44/1.24 % (21478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (21478)Termination reason: Unknown
% 1.44/1.24 % (21478)Termination phase: Saturation
% 1.44/1.24
% 1.44/1.24 % (21478)Memory used [KB]: 5500
% 1.44/1.24 % (21478)Time elapsed: 0.005 s
% 1.44/1.24 % (21478)Instructions burned: 4 (million)
% 1.44/1.24 % (21478)------------------------------
% 1.44/1.24 % (21478)------------------------------
% 1.44/1.24 % (21483)Instruction limit reached!
% 1.44/1.24 % (21483)------------------------------
% 1.44/1.24 % (21483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (21483)Termination reason: Unknown
% 1.44/1.24 % (21483)Termination phase: Saturation
% 1.44/1.24
% 1.44/1.24 % (21483)Memory used [KB]: 5628
% 1.44/1.24 % (21483)Time elapsed: 0.011 s
% 1.44/1.24 % (21483)Instructions burned: 18 (million)
% 1.44/1.24 % (21483)------------------------------
% 1.44/1.24 % (21483)------------------------------
% 1.44/1.24 % (21480)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21380 for (3000ds/2Mi)
% 1.44/1.24 % (21480)Instruction limit reached!
% 1.44/1.24 % (21480)------------------------------
% 1.44/1.24 % (21480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (21480)Termination reason: Unknown
% 1.44/1.24 % (21480)Termination phase: Saturation
% 1.44/1.24
% 1.44/1.24 % (21480)Memory used [KB]: 5500
% 1.44/1.24 % (21480)Time elapsed: 0.003 s
% 1.44/1.24 % (21480)Instructions burned: 3 (million)
% 1.44/1.24 % (21480)------------------------------
% 1.44/1.24 % (21480)------------------------------
% 1.44/1.25 % (21479)Instruction limit reached!
% 1.44/1.25 % (21479)------------------------------
% 1.44/1.25 % (21479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.25 % (21479)Termination reason: Unknown
% 1.44/1.25 % (21479)Termination phase: Saturation
% 1.44/1.25
% 1.44/1.25 % (21479)Memory used [KB]: 5628
% 1.44/1.25 % (21479)Time elapsed: 0.012 s
% 1.44/1.25 % (21479)Instructions burned: 29 (million)
% 1.44/1.25 % (21479)------------------------------
% 1.44/1.25 % (21479)------------------------------
% 1.44/1.25 % (21484)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/3Mi)
% 1.44/1.25 % (21484)Instruction limit reached!
% 1.44/1.25 % (21484)------------------------------
% 1.44/1.25 % (21484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.25 % (21484)Termination reason: Unknown
% 1.44/1.25 % (21484)Termination phase: Saturation
% 1.44/1.25
% 1.44/1.25 % (21484)Memory used [KB]: 5500
% 1.44/1.25 % (21484)Time elapsed: 0.003 s
% 1.44/1.25 % (21484)Instructions burned: 3 (million)
% 1.44/1.25 % (21484)------------------------------
% 1.44/1.25 % (21484)------------------------------
% 1.44/1.25 % (21485)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_21380 for (2999ds/37Mi)
% 1.44/1.25 % (21487)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_21380 for (2999ds/3Mi)
% 1.44/1.25 % (21487)Instruction limit reached!
% 1.44/1.25 % (21487)------------------------------
% 1.44/1.25 % (21487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.25 % (21487)Termination reason: Unknown
% 1.44/1.25 % (21487)Termination phase: Saturation
% 1.44/1.25
% 1.44/1.25 % (21487)Memory used [KB]: 5500
% 1.44/1.25 % (21487)Time elapsed: 0.003 s
% 1.44/1.25 % (21487)Instructions burned: 3 (million)
% 1.44/1.25 % (21487)------------------------------
% 1.44/1.25 % (21487)------------------------------
% 1.44/1.26 % (21488)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_21380 for (2999ds/1041Mi)
% 1.44/1.26 % (21489)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/7Mi)
% 1.44/1.26 % (21486)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_21380 for (2999ds/15Mi)
% 1.44/1.26 % (21489)Instruction limit reached!
% 1.44/1.26 % (21489)------------------------------
% 1.44/1.26 % (21489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.26 % (21489)Termination reason: Unknown
% 1.44/1.26 % (21489)Termination phase: Saturation
% 1.44/1.26
% 1.44/1.26 % (21489)Memory used [KB]: 1023
% 1.44/1.26 % (21489)Time elapsed: 0.004 s
% 1.44/1.26 % (21489)Instructions burned: 8 (million)
% 1.44/1.26 % (21489)------------------------------
% 1.44/1.26 % (21489)------------------------------
% 1.44/1.26 % (21490)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/16Mi)
% 1.44/1.27 % (21486)Instruction limit reached!
% 1.44/1.27 % (21486)------------------------------
% 1.44/1.27 % (21486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.27 % (21486)Termination reason: Unknown
% 1.44/1.27 % (21486)Termination phase: Saturation
% 1.44/1.27
% 1.44/1.27 % (21486)Memory used [KB]: 5628
% 1.44/1.27 % (21486)Time elapsed: 0.010 s
% 1.44/1.27 % (21486)Instructions burned: 16 (million)
% 1.44/1.27 % (21486)------------------------------
% 1.44/1.27 % (21486)------------------------------
% 1.44/1.27 % (21491)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_21380 for (2999ds/3Mi)
% 1.44/1.27 % (21485)Instruction limit reached!
% 1.44/1.27 % (21485)------------------------------
% 1.44/1.27 % (21485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.27 % (21485)Termination reason: Unknown
% 1.44/1.27 % (21485)Termination phase: Saturation
% 1.44/1.27
% 1.44/1.27 % (21485)Memory used [KB]: 6012
% 1.44/1.27 % (21485)Time elapsed: 0.019 s
% 1.44/1.27 % (21485)Instructions burned: 37 (million)
% 1.44/1.27 % (21485)------------------------------
% 1.44/1.27 % (21485)------------------------------
% 1.44/1.27 % (21491)Instruction limit reached!
% 1.44/1.27 % (21491)------------------------------
% 1.44/1.27 % (21491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.27 % (21491)Termination reason: Unknown
% 1.44/1.27 % (21491)Termination phase: Saturation
% 1.44/1.27
% 1.44/1.27 % (21491)Memory used [KB]: 5500
% 1.44/1.27 % (21491)Time elapsed: 0.002 s
% 1.44/1.27 % (21491)Instructions burned: 3 (million)
% 1.44/1.27 % (21491)------------------------------
% 1.44/1.27 % (21491)------------------------------
% 1.44/1.27 % (21490)Instruction limit reached!
% 1.44/1.27 % (21490)------------------------------
% 1.44/1.27 % (21490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.27 % (21490)Termination reason: Unknown
% 1.44/1.27 % (21490)Termination phase: Saturation
% 1.44/1.27
% 1.44/1.27 % (21490)Memory used [KB]: 5628
% 1.44/1.27 % (21490)Time elapsed: 0.008 s
% 1.44/1.27 % (21490)Instructions burned: 16 (million)
% 1.44/1.27 % (21490)------------------------------
% 1.44/1.27 % (21490)------------------------------
% 1.44/1.28 % (21493)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/7Mi)
% 1.44/1.28 % (21492)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_21380 for (2999ds/3Mi)
% 1.44/1.28 % (21493)Refutation not found, incomplete strategy
% 1.44/1.28 % (21493)------------------------------
% 1.44/1.28 % (21493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (21493)Termination reason: Refutation not found, incomplete strategy
% 1.44/1.28
% 1.44/1.28
% 1.44/1.28 % (21493)Memory used [KB]: 5500
% 1.44/1.28 % (21493)Time elapsed: 0.002 s
% 1.44/1.28 % (21493)Instructions burned: 3 (million)
% 1.44/1.28 % (21493)------------------------------
% 1.44/1.28 % (21493)------------------------------
% 1.44/1.28 % (21492)Instruction limit reached!
% 1.44/1.28 % (21492)------------------------------
% 1.44/1.28 % (21492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (21492)Termination reason: Unknown
% 1.44/1.28 % (21492)Termination phase: Saturation
% 1.44/1.28
% 1.44/1.28 % (21492)Memory used [KB]: 1023
% 1.44/1.28 % (21492)Time elapsed: 0.003 s
% 1.44/1.28 % (21492)Instructions burned: 4 (million)
% 1.44/1.28 % (21492)------------------------------
% 1.44/1.28 % (21492)------------------------------
% 1.44/1.29 % (21495)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/4Mi)
% 1.44/1.29 % (21494)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/3Mi)
% 1.44/1.29 % (21496)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/18Mi)
% 1.44/1.29 % (21495)Instruction limit reached!
% 1.44/1.29 % (21495)------------------------------
% 1.44/1.29 % (21495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.29 % (21495)Termination reason: Unknown
% 1.44/1.29 % (21495)Termination phase: Saturation
% 1.44/1.29
% 1.44/1.29 % (21495)Memory used [KB]: 5500
% 1.44/1.29 % (21495)Time elapsed: 0.027 s
% 1.44/1.29 % (21495)Instructions burned: 6 (million)
% 1.44/1.29 % (21495)------------------------------
% 1.44/1.29 % (21495)------------------------------
% 1.44/1.29 % (21494)Instruction limit reached!
% 1.44/1.29 % (21494)------------------------------
% 1.44/1.29 % (21494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.29 % (21494)Termination reason: Unknown
% 1.44/1.29 % (21494)Termination phase: Saturation
% 1.44/1.29
% 1.44/1.29 % (21494)Memory used [KB]: 5500
% 1.44/1.29 % (21494)Time elapsed: 0.004 s
% 1.44/1.29 % (21494)Instructions burned: 4 (million)
% 1.44/1.29 % (21494)------------------------------
% 1.44/1.29 % (21494)------------------------------
% 1.47/1.30 % (21496)Instruction limit reached!
% 1.47/1.30 % (21496)------------------------------
% 1.47/1.30 % (21496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (21496)Termination reason: Unknown
% 1.47/1.30 % (21496)Termination phase: Saturation
% 1.47/1.30
% 1.47/1.30 % (21496)Memory used [KB]: 5628
% 1.47/1.30 % (21496)Time elapsed: 0.009 s
% 1.47/1.30 % (21496)Instructions burned: 20 (million)
% 1.47/1.30 % (21496)------------------------------
% 1.47/1.30 % (21496)------------------------------
% 1.47/1.30 % (21498)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/6Mi)
% 1.47/1.31 % (21498)Instruction limit reached!
% 1.47/1.31 % (21498)------------------------------
% 1.47/1.31 % (21498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.31 % (21498)Termination reason: Unknown
% 1.47/1.31 % (21498)Termination phase: Saturation
% 1.47/1.31
% 1.47/1.31 % (21498)Memory used [KB]: 5500
% 1.47/1.31 % (21498)Time elapsed: 0.004 s
% 1.47/1.31 % (21498)Instructions burned: 8 (million)
% 1.47/1.31 % (21498)------------------------------
% 1.47/1.31 % (21498)------------------------------
% 1.47/1.31 % (21497)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/710Mi)
% 1.47/1.31 % (21499)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_21380 for (2999ds/902Mi)
% 1.47/1.31 % (21501)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21380 for (2999ds/5Mi)
% 1.47/1.32 % (21501)Instruction limit reached!
% 1.47/1.32 % (21501)------------------------------
% 1.47/1.32 % (21501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.32 % (21501)Termination reason: Unknown
% 1.47/1.32 % (21501)Termination phase: Saturation
% 1.47/1.32
% 1.47/1.32 % (21501)Memory used [KB]: 5500
% 1.47/1.32 % (21501)Time elapsed: 0.003 s
% 1.47/1.32 % (21501)Instructions burned: 6 (million)
% 1.47/1.32 % (21501)------------------------------
% 1.47/1.32 % (21501)------------------------------
% 1.47/1.32 % (21500)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_21380 for (2999ds/21Mi)
% 1.47/1.32 % (21477)Instruction limit reached!
% 1.47/1.32 % (21477)------------------------------
% 1.47/1.32 % (21477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.32 % (21477)Termination reason: Unknown
% 1.47/1.32 % (21477)Termination phase: Saturation
% 1.47/1.32
% 1.47/1.32 % (21477)Memory used [KB]: 6652
% 1.47/1.32 % (21477)Time elapsed: 0.091 s
% 1.47/1.32 % (21477)Instructions burned: 183 (million)
% 1.47/1.32 % (21477)------------------------------
% 1.47/1.32 % (21477)------------------------------
% 1.47/1.33 % (21502)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_21380 for (2998ds/6Mi)
% 1.47/1.33 % (21502)Instruction limit reached!
% 1.47/1.33 % (21502)------------------------------
% 1.47/1.33 % (21502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.33 % (21502)Termination reason: Unknown
% 1.47/1.33 % (21502)Termination phase: Saturation
% 1.47/1.33
% 1.47/1.33 % (21502)Memory used [KB]: 5500
% 1.47/1.33 % (21502)Time elapsed: 0.003 s
% 1.47/1.33 % (21502)Instructions burned: 7 (million)
% 1.47/1.33 % (21502)------------------------------
% 1.47/1.33 % (21502)------------------------------
% 1.47/1.33 % (21500)Instruction limit reached!
% 1.47/1.33 % (21500)------------------------------
% 1.47/1.33 % (21500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.33 % (21500)Termination reason: Unknown
% 1.47/1.33 % (21500)Termination phase: Saturation
% 1.47/1.33
% 1.47/1.33 % (21500)Memory used [KB]: 5628
% 1.47/1.33 % (21500)Time elapsed: 0.034 s
% 1.47/1.33 % (21500)Instructions burned: 21 (million)
% 1.47/1.33 % (21500)------------------------------
% 1.47/1.33 % (21500)------------------------------
% 1.47/1.34 % (21504)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_21380 for (2998ds/779Mi)
% 1.47/1.34 % (21503)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21380 for (2998ds/377Mi)
% 1.47/1.35 % (21505)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_21380 for (2998ds/19Mi)
% 1.47/1.36 % (21505)Instruction limit reached!
% 1.47/1.36 % (21505)------------------------------
% 1.47/1.36 % (21505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.36 % (21505)Termination reason: Unknown
% 1.47/1.36 % (21505)Termination phase: Saturation
% 1.47/1.36
% 1.47/1.36 % (21505)Memory used [KB]: 5628
% 1.47/1.36 % (21505)Time elapsed: 0.011 s
% 1.47/1.36 % (21505)Instructions burned: 19 (million)
% 1.47/1.36 % (21505)------------------------------
% 1.47/1.36 % (21505)------------------------------
% 1.47/1.36 % (21482)Instruction limit reached!
% 1.47/1.36 % (21482)------------------------------
% 1.47/1.36 % (21482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.36 % (21482)Termination reason: Unknown
% 1.47/1.36 % (21482)Termination phase: Saturation
% 1.47/1.36
% 1.47/1.36 % (21482)Memory used [KB]: 6140
% 1.47/1.36 % (21482)Time elapsed: 0.133 s
% 1.47/1.36 % (21482)Instructions burned: 276 (million)
% 1.47/1.36 % (21482)------------------------------
% 1.47/1.36 % (21482)------------------------------
% 1.47/1.37 % (21506)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21380 for (2998ds/879Mi)
% 1.47/1.37 % (21507)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21380 for (2998ds/17Mi)
% 1.47/1.38 % (21507)Instruction limit reached!
% 1.47/1.38 % (21507)------------------------------
% 1.47/1.38 % (21507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.38 % (21507)Termination reason: Unknown
% 1.47/1.38 % (21507)Termination phase: Saturation
% 1.47/1.38
% 1.47/1.38 % (21507)Memory used [KB]: 5628
% 1.47/1.38 % (21507)Time elapsed: 0.008 s
% 1.47/1.38 % (21507)Instructions burned: 19 (million)
% 1.47/1.38 % (21507)------------------------------
% 1.47/1.38 % (21507)------------------------------
% 1.47/1.39 % (21508)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21380 for (2998ds/3Mi)
% 1.47/1.39 % (21508)Instruction limit reached!
% 1.47/1.39 % (21508)------------------------------
% 1.47/1.39 % (21508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.39 % (21508)Termination reason: Unknown
% 1.47/1.39 % (21508)Termination phase: Saturation
% 1.47/1.39
% 1.47/1.39 % (21508)Memory used [KB]: 1023
% 1.47/1.39 % (21508)Time elapsed: 0.002 s
% 1.47/1.39 % (21508)Instructions burned: 3 (million)
% 1.47/1.39 % (21508)------------------------------
% 1.47/1.39 % (21508)------------------------------
% 1.47/1.40 % (21509)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21380 for (2998ds/30Mi)
% 1.47/1.41 % (21509)Instruction limit reached!
% 1.47/1.41 % (21509)------------------------------
% 1.47/1.41 % (21509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.41 % (21509)Termination reason: Unknown
% 1.47/1.41 % (21509)Termination phase: Saturation
% 1.47/1.41
% 1.47/1.41 % (21509)Memory used [KB]: 5628
% 1.47/1.41 % (21509)Time elapsed: 0.011 s
% 1.47/1.41 % (21509)Instructions burned: 30 (million)
% 1.47/1.41 % (21509)------------------------------
% 1.47/1.41 % (21509)------------------------------
% 1.47/1.42 % (21510)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21380 for (2997ds/127Mi)
% 1.47/1.46 % (21510)Instruction limit reached!
% 1.47/1.46 % (21510)------------------------------
% 1.47/1.46 % (21510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.46 % (21510)Termination reason: Unknown
% 1.47/1.46 % (21510)Termination phase: Saturation
% 1.47/1.46
% 1.47/1.46 % (21510)Memory used [KB]: 6012
% 1.47/1.46 % (21510)Time elapsed: 0.043 s
% 1.47/1.46 % (21510)Instructions burned: 128 (million)
% 1.47/1.46 % (21510)------------------------------
% 1.47/1.46 % (21510)------------------------------
% 1.47/1.47 % (21511)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21380 for (2997ds/100Mi)
% 1.47/1.51 % (21503)Instruction limit reached!
% 1.47/1.51 % (21503)------------------------------
% 1.47/1.51 % (21503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.51 % (21503)Termination reason: Unknown
% 1.47/1.51 % (21503)Termination phase: Saturation
% 1.47/1.51
% 1.47/1.51 % (21503)Memory used [KB]: 6140
% 1.47/1.51 % (21503)Time elapsed: 0.166 s
% 1.47/1.51 % (21503)Instructions burned: 377 (million)
% 1.47/1.51 % (21503)------------------------------
% 1.47/1.51 % (21503)------------------------------
% 1.47/1.51 % (21511)Instruction limit reached!
% 1.47/1.51 % (21511)------------------------------
% 1.47/1.51 % (21511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.51 % (21511)Termination reason: Unknown
% 1.47/1.51 % (21511)Termination phase: Saturation
% 1.47/1.51
% 1.47/1.51 % (21511)Memory used [KB]: 5756
% 1.47/1.51 % (21511)Time elapsed: 0.043 s
% 1.47/1.51 % (21511)Instructions burned: 100 (million)
% 1.47/1.51 % (21511)------------------------------
% 1.47/1.51 % (21511)------------------------------
% 1.47/1.52 % (21512)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_21380 for (2997ds/3Mi)
% 1.47/1.52 % (21512)Instruction limit reached!
% 1.47/1.52 % (21512)------------------------------
% 1.47/1.52 % (21512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.52 % (21512)Termination reason: Unknown
% 1.47/1.52 % (21512)Termination phase: Saturation
% 1.47/1.52
% 1.47/1.52 % (21512)Memory used [KB]: 5500
% 1.47/1.52 % (21512)Time elapsed: 0.003 s
% 1.47/1.52 % (21512)Instructions burned: 5 (million)
% 1.47/1.52 % (21512)------------------------------
% 1.47/1.52 % (21512)------------------------------
% 1.47/1.53 % (21513)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_21380 for (2996ds/20Mi)
% 1.47/1.53 % (21513)Instruction limit reached!
% 1.47/1.53 % (21513)------------------------------
% 1.47/1.53 % (21513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.53 % (21513)Termination reason: Unknown
% 1.47/1.53 % (21513)Termination phase: Saturation
% 1.47/1.53
% 1.47/1.53 % (21513)Memory used [KB]: 5628
% 1.47/1.53 % (21513)Time elapsed: 0.008 s
% 1.47/1.53 % (21513)Instructions burned: 21 (million)
% 1.47/1.53 % (21513)------------------------------
% 1.47/1.53 % (21513)------------------------------
% 1.47/1.54 % (21514)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_21380 for (2996ds/86Mi)
% 1.47/1.56 % (21515)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_21380 for (2996ds/107Mi)
% 1.47/1.56 % (21504)Instruction limit reached!
% 1.47/1.56 % (21504)------------------------------
% 1.47/1.56 % (21504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.56 % (21504)Termination reason: Unknown
% 1.47/1.56 % (21504)Termination phase: Saturation
% 1.47/1.56
% 1.47/1.56 % (21504)Memory used [KB]: 7164
% 1.47/1.56 % (21504)Time elapsed: 0.227 s
% 1.47/1.56 % (21504)Instructions burned: 780 (million)
% 1.47/1.56 % (21504)------------------------------
% 1.47/1.56 % (21504)------------------------------
% 1.47/1.57 % (21514)Instruction limit reached!
% 1.47/1.57 % (21514)------------------------------
% 1.47/1.57 % (21514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.57 % (21514)Termination reason: Unknown
% 1.47/1.57 % (21514)Termination phase: Saturation
% 1.47/1.57
% 1.47/1.57 % (21514)Memory used [KB]: 6140
% 1.47/1.57 % (21514)Time elapsed: 0.031 s
% 1.47/1.57 % (21514)Instructions burned: 87 (million)
% 1.47/1.57 % (21514)------------------------------
% 1.47/1.57 % (21514)------------------------------
% 1.47/1.57 % (21516)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_21380 for (2996ds/39Mi)
% 1.47/1.58 % (21517)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_21380 for (2996ds/448Mi)
% 1.47/1.59 % (21516)Instruction limit reached!
% 1.47/1.59 % (21516)------------------------------
% 1.47/1.59 % (21516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.59 % (21516)Termination reason: Unknown
% 1.47/1.59 % (21516)Termination phase: Saturation
% 1.47/1.59
% 1.47/1.59 % (21516)Memory used [KB]: 5756
% 1.47/1.59 % (21516)Time elapsed: 0.014 s
% 1.47/1.59 % (21516)Instructions burned: 42 (million)
% 1.47/1.59 % (21516)------------------------------
% 1.47/1.59 % (21516)------------------------------
% 1.47/1.60 % (21518)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_21380 for (2996ds/46Mi)
% 1.47/1.61 % (21518)Instruction limit reached!
% 1.47/1.61 % (21518)------------------------------
% 1.47/1.61 % (21518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.61 % (21518)Termination reason: Unknown
% 1.47/1.61 % (21518)Termination phase: Saturation
% 1.47/1.61
% 1.47/1.61 % (21518)Memory used [KB]: 5756
% 1.47/1.61 % (21518)Time elapsed: 0.017 s
% 1.47/1.61 % (21518)Instructions burned: 46 (million)
% 1.47/1.61 % (21518)------------------------------
% 1.47/1.61 % (21518)------------------------------
% 1.47/1.62 % (21519)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_21380 for (2996ds/98Mi)
% 1.47/1.62 % (21497)Instruction limit reached!
% 1.47/1.62 % (21497)------------------------------
% 1.47/1.62 % (21497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.62 % (21497)Termination reason: Unknown
% 1.47/1.62 % (21497)Termination phase: Saturation
% 1.47/1.62
% 1.47/1.62 % (21497)Memory used [KB]: 7164
% 1.47/1.62 % (21497)Time elapsed: 0.352 s
% 1.47/1.62 % (21497)Instructions burned: 712 (million)
% 1.47/1.62 % (21497)------------------------------
% 1.47/1.62 % (21497)------------------------------
% 1.47/1.63 % (21515)Instruction limit reached!
% 1.47/1.63 % (21515)------------------------------
% 1.47/1.63 % (21515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.63 % (21515)Termination reason: Unknown
% 1.47/1.63 % (21515)Termination phase: Saturation
% 1.47/1.63
% 1.47/1.63 % (21515)Memory used [KB]: 5756
% 1.47/1.63 % (21515)Time elapsed: 0.091 s
% 1.47/1.63 % (21515)Instructions burned: 107 (million)
% 1.47/1.63 % (21515)------------------------------
% 1.47/1.63 % (21515)------------------------------
% 1.47/1.63 % (21499)Instruction limit reached!
% 1.47/1.63 % (21499)------------------------------
% 1.47/1.63 % (21499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.63 % (21499)Termination reason: Unknown
% 1.47/1.63 % (21499)Termination phase: Saturation
% 1.47/1.63
% 1.47/1.63 % (21499)Memory used [KB]: 6780
% 1.47/1.63 % (21499)Time elapsed: 0.332 s
% 1.47/1.63 % (21499)Instructions burned: 902 (million)
% 1.47/1.63 % (21499)------------------------------
% 1.47/1.63 % (21499)------------------------------
% 1.47/1.64 % (21522)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21380 for (2995ds/39Mi)
% 1.47/1.65 % (21519)First to succeed.
% 1.47/1.65 % (21519)Refutation found. Thanks to Tanya!
% 1.47/1.65 % SZS status Theorem for DTF2THF_21380
% 1.47/1.65 % SZS output start Proof for DTF2THF_21380
% 1.47/1.65 thf(type_def_5, type, a: $tType).
% 1.47/1.65 thf(func_def_0, type, a: $tType).
% 1.47/1.65 thf(func_def_1, type, cK: (a > $o) > a > $o).
% 1.47/1.65 thf(func_def_14, type, ph0: !>[X0: $tType]:(X0)).
% 1.47/1.65 thf(func_def_15, type, sK1: a).
% 1.47/1.65 thf(func_def_16, type, sK2: a > $o).
% 1.47/1.65 thf(func_def_17, type, sK3: (a > $o) > (a > $o) > a).
% 1.47/1.65 thf(func_def_18, type, sK4: a).
% 1.47/1.65 thf(f333,plain,(
% 1.47/1.65 $false),
% 1.47/1.65 inference(trivial_inequality_removal,[status(thm)],[f332])).
% 1.47/1.65 thf(f332,plain,(
% 1.47/1.65 ($false = $true)),
% 1.47/1.65 inference(backward_demodulation,[status(thm)],[f298,f330])).
% 1.47/1.65 thf(f330,plain,(
% 1.47/1.65 ((sK2 @ sK4) = $false)),
% 1.47/1.65 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 1.47/1.65 thf(f324,plain,(
% 1.47/1.65 ($false = $true) | ((sK2 @ sK4) = $false)),
% 1.47/1.65 inference(superposition,[status(thm)],[f301,f21])).
% 1.47/1.65 thf(f21,plain,(
% 1.47/1.65 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cK @ sK2 @ Y0)))) = $true)),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.47/1.65 thf(f20,plain,(
% 1.47/1.65 (((sK2 @ sK1) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cK @ sK2 @ Y0))))) = $true)),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.47/1.65 thf(f19,plain,(
% 1.47/1.65 (((^[Y0 : a > $o]: ((Y0 @ sK1) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))))) @ sK2) = $true)),
% 1.47/1.65 inference(sigma_clausification,[status(thm)],[f18])).
% 1.47/1.65 thf(f18,plain,(
% 1.47/1.65 ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK1) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1))))))) = $true)),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.47/1.65 thf(f16,plain,(
% 1.47/1.65 ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK1) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1))))))) => (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK1)))),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.47/1.65 thf(f15,plain,(
% 1.47/1.65 (((^[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]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0))) @ sK1) = $false)),
% 1.47/1.65 inference(sigma_clausification,[status(thm)],[f8])).
% 1.47/1.65 thf(f8,plain,(
% 1.47/1.65 ($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]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0)))))),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.47/1.65 thf(f7,plain,(
% 1.47/1.65 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ 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]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0))))) = $false)),
% 1.47/1.65 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.47/1.65 thf(f6,plain,(
% 1.47/1.65 ($true = (~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ 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 > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0)))))))),
% 1.47/1.65 inference(cnf_transformation,[status(thm)],[f5])).
% 1.47/1.65 thf(f5,plain,(
% 1.47/1.65 ($true = (~ ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) => (!! @ 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]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0)))))))),
% 1.47/1.65 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.65 thf(f4,plain,(
% 1.47/1.65 ~(! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : a] : ((cK @ X1 @ X3) => (cK @ X0 @ X3))) => ! [X4 : a] : (? [X5 : a > $o] : (! [X6 : a] : ((X5 @ X6) => (cK @ X5 @ X6)) & (X5 @ X4)) => (cK @ (^[X7 : a] : (? [X8 : a > $o] : (! [X9 : a] : ((X8 @ X9) => (cK @ X8 @ X9)) & (X8 @ X7)))) @ X4)))),
% 1.47/1.65 inference(rectify,[status(thm)],[f2])).
% 1.47/1.65 thf(f2,negated_conjecture,(
% 1.47/1.65 ~(! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : (? [X3 : a > $o] : (! [X4 : a] : ((X3 @ X4) => (cK @ X3 @ X4)) & (X3 @ X2)) => (cK @ (^[X4 : a] : (? [X3 : a > $o] : (! [X5 : a] : ((X3 @ X5) => (cK @ X3 @ X5)) & (X3 @ X4)))) @ X2)))),
% 1.47/1.65 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.65 thf(f1,conjecture,(
% 1.47/1.65 ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cK @ X0 @ X2) => (cK @ X1 @ X2))) => ! [X2 : a] : (? [X3 : a > $o] : (! [X4 : a] : ((X3 @ X4) => (cK @ X3 @ X4)) & (X3 @ X2)) => (cK @ (^[X4 : a] : (? [X3 : a > $o] : (! [X5 : a] : ((X3 @ X5) => (cK @ X3 @ X5)) & (X3 @ X4)))) @ X2))),
% 1.47/1.65 file('/export/starexec/sandbox/tmp/tmp.MUn0XpXtrW/DTF2THF_21380.p',cTHM116_2S)).
% 1.47/1.65 thf(f301,plain,(
% 1.47/1.65 ( ! [X1 : a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cK @ X1 @ Y0))))) | ((X1 @ sK4) = $false)) )),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f300])).
% 1.47/1.65 thf(f300,plain,(
% 1.47/1.65 ( ! [X1 : a > $o] : (($false = ((X1 @ sK4) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cK @ X1 @ Y0))))))) )),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f299])).
% 1.47/1.65 thf(f299,plain,(
% 1.47/1.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: ((Y0 @ sK4) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))))) @ X1) = $false)) )),
% 1.47/1.65 inference(pi_clausification,[status(thm)],[f297])).
% 1.47/1.65 thf(f297,plain,(
% 1.47/1.65 ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1))))))))),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f296])).
% 1.47/1.65 thf(f296,plain,(
% 1.47/1.65 (((sK2 @ sK4) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cK @ Y0 @ Y1)))))))) = $false)),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f295])).
% 1.47/1.65 thf(f295,plain,(
% 1.47/1.65 ($false = ((^[Y0 : a]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2))))))))) @ sK4))),
% 1.47/1.65 inference(sigma_clausification,[status(thm)],[f292])).
% 1.47/1.65 thf(f292,plain,(
% 1.47/1.65 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))))))),
% 1.47/1.65 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.47/1.65 thf(f291,plain,(
% 1.47/1.65 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2))))))))))) | ($false = $true)),
% 1.47/1.65 inference(forward_demodulation,[status(thm)],[f288,f22])).
% 1.47/1.65 thf(f22,plain,(
% 1.47/1.65 ((sK2 @ sK1) = $true)),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.47/1.65 thf(f288,plain,(
% 1.47/1.65 ((sK2 @ sK1) = $false) | ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))))))),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f287])).
% 1.47/1.65 thf(f287,plain,(
% 1.47/1.65 ((sK2 @ sK1) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0)))) = $false)),
% 1.47/1.65 inference(trivial_inequality_removal,[status(thm)],[f271])).
% 1.47/1.65 thf(f271,plain,(
% 1.47/1.65 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((^[Y1 : a]: (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y1) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (cK @ Y2 @ Y3)))))))) @ Y0)))) = $false) | ((sK2 @ sK1) = $false) | ($false = $true)),
% 1.47/1.65 inference(superposition,[status(thm)],[f17,f54])).
% 1.47/1.65 thf(f54,plain,(
% 1.47/1.65 ( ! [X0 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0)))) = $false) | ((cK @ X1 @ X0) = $true) | ((sK2 @ X0) = $false)) )),
% 1.47/1.65 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.47/1.65 thf(f32,plain,(
% 1.47/1.65 ( ! [X0 : a,X1 : a > $o] : (((sK2 @ X0) = $false) | ($false = $true) | ((cK @ X1 @ X0) = $true) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (X1 @ Y0)))) = $false)) )),
% 1.47/1.65 inference(superposition,[status(thm)],[f28,f25])).
% 1.47/1.65 thf(f25,plain,(
% 1.47/1.65 ( ! [X1 : a] : (($true = (cK @ sK2 @ X1)) | ((sK2 @ X1) = $false)) )),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.47/1.65 thf(f24,plain,(
% 1.47/1.65 ( ! [X1 : a] : ((((sK2 @ X1) => (cK @ sK2 @ X1)) = $true)) )),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.47/1.65 thf(f23,plain,(
% 1.47/1.65 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0) => (cK @ sK2 @ Y0))) @ X1) = $true)) )),
% 1.47/1.65 inference(pi_clausification,[status(thm)],[f21])).
% 1.47/1.65 thf(f28,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) = $false) | ((cK @ X1 @ X3) = $false) | ((cK @ X2 @ X3) = $true)) )),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.47/1.65 thf(f27,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) = $false) | (((cK @ X1 @ X3) => (cK @ X2 @ X3)) = $true)) )),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.47/1.65 thf(f26,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X3 : a,X1 : a > $o] : ((((^[Y0 : a]: ((cK @ X1 @ Y0) => (cK @ X2 @ Y0))) @ X3) = $true) | ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) = $false)) )),
% 1.47/1.65 inference(pi_clausification,[status(thm)],[f14])).
% 1.47/1.65 thf(f14,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X1 : a > $o] : (((!! @ a @ (^[Y0 : a]: ((cK @ X1 @ Y0) => (cK @ X2 @ Y0)))) = $true) | ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) = $false)) )),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.47/1.65 thf(f13,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X1 : a > $o] : ((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (X2 @ Y0)))) => (!! @ a @ (^[Y0 : a]: ((cK @ X1 @ Y0) => (cK @ X2 @ Y0))))) = $true)) )),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.47/1.65 thf(f12,plain,(
% 1.47/1.65 ( ! [X2 : a > $o,X1 : a > $o] : ((((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (Y0 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ X1 @ Y1) => (cK @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 1.47/1.65 inference(pi_clausification,[status(thm)],[f11])).
% 1.47/1.65 thf(f11,plain,(
% 1.47/1.65 ( ! [X1 : a > $o] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (Y0 @ Y1)))) => (!! @ a @ (^[Y1 : a]: ((cK @ X1 @ Y1) => (cK @ Y0 @ Y1))))))) = $true)) )),
% 1.47/1.65 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.47/1.65 thf(f10,plain,(
% 1.47/1.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2)))))))) @ X1) = $true)) )),
% 1.47/1.65 inference(pi_clausification,[status(thm)],[f9])).
% 1.47/1.65 thf(f9,plain,(
% 1.47/1.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y0 @ Y2) => (Y1 @ Y2)))) => (!! @ a @ (^[Y2 : a]: ((cK @ Y0 @ Y2) => (cK @ Y1 @ Y2))))))))) = $true)),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.47/1.65 thf(f17,plain,(
% 1.47/1.65 ($false = (cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))))))) @ sK1))),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.47/1.65 thf(f298,plain,(
% 1.47/1.65 ((sK2 @ sK4) = $true)),
% 1.47/1.65 inference(binary_proxy_clausification,[status(thm)],[f296])).
% 1.47/1.65 % SZS output end Proof for DTF2THF_21380
% 1.47/1.65 % (21519)------------------------------
% 1.47/1.65 % (21519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.65 % (21519)Termination reason: Refutation
% 1.47/1.65
% 1.47/1.65 % (21519)Memory used [KB]: 1279
% 1.47/1.65 % (21519)Time elapsed: 0.027 s
% 1.47/1.65 % (21519)Instructions burned: 77 (million)
% 1.47/1.65 % (21519)------------------------------
% 1.47/1.65 % (21519)------------------------------
% 1.47/1.65 % (21476)Success in time 0.432 s
%------------------------------------------------------------------------------