%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU940^5 : 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 : n008.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 09:37:48 AM UTC 2026
% Result : Theorem 1.53s 1.30s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 107 equ; 32 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 528 ( 4 ~; 13 |; 58 &; 357 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 5 usr; 6 con; 0-2 aty)
% ( 42 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 182 ( 156 ^; 23 !; 3 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK2: $i > $o ).
thf(func_def_16,type,
sK3: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_17,type,
sK4: ( ( $i > $i ) > $o ) > $i > $i ).
thf(f109,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( ( sK2 @ sK5 )
=> ( sK2 @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f106,f83]) ).
thf(f83,plain,
! [X1: $i] :
( ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 )
@ X1 )
= X1 ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : Y0
@ X1 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false = $true )
| ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false
= ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
| ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
= $true )
| ( $false
= ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) ) ),
inference(superposition,[status(thm)],[f22,f28]) ).
thf(f28,plain,
( ( ^ [Y0: $i] : Y0 )
= ( sK3
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( X1 @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( ( X1 @ ( sK4 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) ) )
= $true )
| ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: ( $i > $i ) > $o] :
( ( ( ( ( X1 @ ( sK4 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) ) )
=> ( ( X1
@ ^ [Y0: $i] : ( sK4 @ X1 @ ( sK3 @ X1 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( sK4 @ X1 @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: ( $i > $i ) > $o] :
( ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) )
| ( $false
= ( ^ [Y0: $i > $i] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK3 @ X1 ) ) )
=> ( ( X1
@ ^ [Y1: $i] : ( Y0 @ ( sK3 @ X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( Y0 @ Y1 ) ) ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: ( $i > $i ) > $o] :
( ( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK3 @ X1 ) ) )
=> ( ( X1
@ ^ [Y1: $i] : ( Y0 @ ( sK3 @ X1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: ( $i > $i ) > $o] :
( ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) )
| ( $false
= ( ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y2 )
=> ( sK2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: ( $i > $i ) > $o] :
( ( $false
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y2 )
=> ( sK2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: ( $i > $i ) > $o] :
( $false
= ( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( ( X1
@ ^ [Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y2 )
=> ( sK2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ( X1
@ ^ [Y0: $i] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: ( $i > $i ) > $o] :
( $false
= ( ^ [Y0: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( ( Y0
@ ^ [Y3: $i] : ( Y2 @ ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( sK2 @ Y3 )
=> ( sK2 @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i] : Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( ( Y0
@ ^ [Y3: $i] : ( Y2 @ ( Y1 @ Y3 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( sK2 @ Y3 )
=> ( sK2 @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i] : Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ ( ( $i > $i ) > $o )
@ ^ [Y1: ( $i > $i ) > $o] :
( ( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( !! @ ( $i > $i )
@ ^ [Y3: $i > $i] :
( ( ( Y1 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( ( Y1
@ ^ [Y4: $i] : ( Y3 @ ( Y2 @ Y4 ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 )
=> ( Y0 @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( Y1
@ ^ [Y2: $i] : Y2 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X4 )
& ( X1 @ X3 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X6: $i] : ( X3 @ ( X4 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X4 )
& ( X1 @ X3 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X2: $i] : ( X3 @ ( X4 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
? [X1: ( $i > $i ) > $o] :
( ( X1
@ ^ [X2: $i] : X2 )
& ! [X3: $i > $i,X4: $i > $i] :
( ( ( X1 @ X4 )
& ( X1 @ X3 ) )
=> ( ! [X5: $i] :
( ( X0 @ X5 )
=> ( X0 @ ( X3 @ X5 ) ) )
& ( X1
@ ^ [X2: $i] : ( X3 @ ( X4 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.tduxh7xmv3/DTF2THF_27572.p',cTHM112A_pme) ).
thf(f106,plain,
( $false
= ( ( sK2 @ sK5 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 )
@ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
= ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
= ( $true
=> ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f49,f54]) ).
thf(f49,plain,
( $false
= ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
= ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& $true )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $false = $true )
| ( $false
= ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false
= ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
| ( $false
= ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false
= ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
| ( $false
= ( ( ( ( ^ [Y0: $i] : Y0 )
= ( sK4
@ ( (=)
@ ^ [Y0: $i] : Y0 ) ) )
& ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] : Y0 ) ) )
=> ( ( ( ^ [Y0: $i] : Y0 )
= ( ^ [Y0: $i] :
( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2
@ ( sK4
@ ( (=)
@ ^ [Y1: $i] : Y1 )
@ Y0 ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f20,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU940^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.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 12:36:39 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.45 ---- Original DTF file ---
% 0.26/0.45 thf(spec,logic,$$dhol).
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % File : SEU940^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.45 % Domain : Set Theory (Functions)
% 0.26/0.45 % Problem : TPS problem THM112A
% 0.26/0.45 % Version : Especial.
% 0.26/0.45 % English :
% 0.26/0.45
% 0.26/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.45 % Source : [Bro09]
% 0.26/0.45 % Names : tps_0389 [Bro09]
% 0.26/0.45 % : THM112A [TPS]
% 0.26/0.45 % : THM112E [TPS]
% 0.26/0.45
% 0.26/0.45 % Status : Theorem
% 0.26/0.45 % Rating : 0.58 v9.1.0, 0.62 v9.0.0, 0.67 v8.2.0, 0.64 v8.1.0, 0.75 v7.4.0, 0.89 v7.3.0, 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 0.60 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% 0.26/0.45 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.26/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.26/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.26/0.45 % Number of connectives : 14 ( 0 ~; 0 |; 3 &; 9 @)
% 0.26/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.26/0.45 % Maximal formula depth : 12 ( 12 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.26/0.46 % Number of variables : 7 ( 2 ^; 4 !; 1 ?; 7 :)
% 0.26/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.46 % : Polymorphic definitions expanded.
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(cTHM112A_pme,conjecture,
% 0.26/0.46 ! [P: $i > $o] :
% 0.26/0.46 ? [M: ( $i > $i ) > $o] :
% 0.26/0.46 ( ( M
% 0.26/0.46 @ ^ [Xx: $i] : Xx )
% 0.26/0.46 & ! [G: $i > $i,H: $i > $i] :
% 0.26/0.46 ( ( ( M @ G )
% 0.26/0.46 & ( M @ H ) )
% 0.26/0.46 => ( ( M
% 0.26/0.46 @ ^ [Xx: $i] : ( G @ ( H @ Xx ) ) )
% 0.26/0.46 & ! [Y: $i] :
% 0.26/0.46 ( ( P @ Y )
% 0.26/0.46 => ( P @ ( G @ Y ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.48/1.22 ---- Embedded in THF ---
% 1.48/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.22 %%% Generated on Tue Feb 24 12:36:40 EST 2026
% 1.48/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.22 %%% Logic specification used:
% 1.48/1.22 %%% thf(spec, logic, $$dhol).
% 1.48/1.22
% 1.48/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tduxh7xmv3/DTF2DTF27572.p
% See solution above
% 1.48/1.22 ------------------------
% 1.48/1.23 ---- Cleaned THF ---
% 1.48/1.23 thf(cTHM112A_pme,conjecture,
% 1.48/1.23 ! [P: $i > $o] :
% 1.48/1.23 ? [M: ( $i > $i ) > $o] :
% 1.48/1.23 ( ( M
% 1.48/1.23 @ ^ [Xx: $i] : Xx )
% 1.48/1.23 & ! [G: $i > $i,H: $i > $i] :
% 1.48/1.23 ( ( ( M @ G )
% 1.48/1.23 & ( M @ H ) )
% 1.48/1.23 => ( ( M
% 1.48/1.23 @ ^ [Xx: $i] : ( G @ ( H @ Xx ) ) )
% 1.48/1.23 & ! [Y: $i] :
% 1.48/1.23 ( ( P @ Y )
% 1.48/1.23 => ( P @ ( G @ Y ) ) ) ) ) ) ).
% 1.48/1.23 ------------------------
% 1.48/1.24 % (27712)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27572 for (3000ds/2Mi)
% 1.48/1.24 % (27714)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_27572 for (3000ds/275Mi)
% 1.48/1.24 % (27712)Instruction limit reached!
% 1.48/1.24 % (27712)------------------------------
% 1.48/1.24 % (27712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (27712)Termination reason: Unknown
% 1.48/1.24 % (27712)Termination phase: Saturation
% 1.48/1.24
% 1.48/1.24 % (27712)Memory used [KB]: 5500
% 1.48/1.24 % (27712)Time elapsed: 0.002 s
% 1.48/1.24 % (27712)Instructions burned: 2 (million)
% 1.48/1.24 % (27712)------------------------------
% 1.48/1.24 % (27712)------------------------------
% 1.48/1.24 % (27711)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_27572 for (3000ds/27Mi)
% 1.48/1.24 % (27715)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27572 for (3000ds/18Mi)
% 1.48/1.25 % (27711)Refutation not found, incomplete strategy
% 1.48/1.25 % (27711)------------------------------
% 1.48/1.25 % (27711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (27711)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.25
% 1.48/1.25
% 1.48/1.25 % (27711)Memory used [KB]: 5500
% 1.48/1.25 % (27711)Time elapsed: 0.002 s
% 1.48/1.25 % (27711)Instructions burned: 2 (million)
% 1.48/1.25 % (27711)------------------------------
% 1.48/1.25 % (27711)------------------------------
% 1.48/1.25 % (27714)Refutation not found, incomplete strategy
% 1.48/1.25 % (27714)------------------------------
% 1.48/1.25 % (27714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (27714)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.25
% 1.48/1.25
% 1.48/1.25 % (27714)Memory used [KB]: 5628
% 1.48/1.25 % (27714)Time elapsed: 0.007 s
% 1.48/1.25 % (27714)Instructions burned: 17 (million)
% 1.48/1.25 % (27714)------------------------------
% 1.48/1.25 % (27714)------------------------------
% 1.48/1.25 % (27710)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_27572 for (3000ds/4Mi)
% 1.48/1.25 % (27715)Instruction limit reached!
% 1.48/1.25 % (27715)------------------------------
% 1.48/1.25 % (27715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (27715)Termination reason: Unknown
% 1.48/1.25 % (27715)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (27715)Memory used [KB]: 5500
% 1.48/1.25 % (27715)Time elapsed: 0.009 s
% 1.48/1.25 % (27715)Instructions burned: 19 (million)
% 1.48/1.25 % (27715)------------------------------
% 1.48/1.25 % (27715)------------------------------
% 1.48/1.25 % (27713)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_27572 for (3000ds/2Mi)
% 1.48/1.25 % (27710)Instruction limit reached!
% 1.48/1.25 % (27710)------------------------------
% 1.48/1.25 % (27710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (27710)Termination reason: Unknown
% 1.48/1.25 % (27710)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (27710)Memory used [KB]: 5500
% 1.48/1.25 % (27710)Time elapsed: 0.005 s
% 1.48/1.25 % (27710)Instructions burned: 4 (million)
% 1.48/1.25 % (27713)Instruction limit reached!
% 1.48/1.25 % (27713)------------------------------
% 1.48/1.25 % (27713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (27713)Termination reason: Unknown
% 1.48/1.25 % (27713)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (27713)Memory used [KB]: 5373
% 1.48/1.25 % (27713)Time elapsed: 0.004 s
% 1.48/1.25 % (27713)Instructions burned: 2 (million)
% 1.48/1.25 % (27713)------------------------------
% 1.48/1.25 % (27713)------------------------------
% 1.48/1.25 % (27710)------------------------------
% 1.48/1.25 % (27710)------------------------------
% 1.48/1.26 % (27709)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27572 for (3000ds/183Mi)
% 1.48/1.26 % (27719)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27572 for (2999ds/3Mi)
% 1.48/1.26 % (27719)Instruction limit reached!
% 1.48/1.26 % (27719)------------------------------
% 1.48/1.26 % (27719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (27719)Termination reason: Unknown
% 1.48/1.26 % (27719)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (27719)Memory used [KB]: 5500
% 1.48/1.26 % (27719)Time elapsed: 0.003 s
% 1.48/1.26 % (27719)Instructions burned: 3 (million)
% 1.48/1.26 % (27719)------------------------------
% 1.48/1.26 % (27719)------------------------------
% 1.48/1.27 % (27729)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_27572 for (2999ds/15Mi)
% 1.48/1.27 % (27730)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_27572 for (2999ds/3Mi)
% 1.48/1.27 % (27730)Instruction limit reached!
% 1.48/1.27 % (27730)------------------------------
% 1.48/1.27 % (27730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (27730)Termination reason: Unknown
% 1.48/1.27 % (27730)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (27730)Memory used [KB]: 5500
% 1.48/1.27 % (27730)Time elapsed: 0.004 s
% 1.48/1.27 % (27730)Instructions burned: 3 (million)
% 1.48/1.27 % (27730)------------------------------
% 1.48/1.27 % (27730)------------------------------
% 1.48/1.27 % (27729)Instruction limit reached!
% 1.48/1.27 % (27729)------------------------------
% 1.48/1.27 % (27729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (27729)Termination reason: Unknown
% 1.48/1.27 % (27729)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (27729)Memory used [KB]: 5628
% 1.48/1.27 % (27729)Time elapsed: 0.008 s
% 1.48/1.27 % (27729)Instructions burned: 15 (million)
% 1.48/1.27 % (27729)------------------------------
% 1.48/1.27 % (27729)------------------------------
% 1.48/1.27 % (27733)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27572 for (2999ds/16Mi)
% 1.48/1.28 % (27720)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_27572 for (2999ds/37Mi)
% 1.48/1.28 % (27731)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_27572 for (2999ds/1041Mi)
% 1.48/1.28 % (27733)Instruction limit reached!
% 1.48/1.28 % (27733)------------------------------
% 1.48/1.28 % (27733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (27733)Termination reason: Unknown
% 1.48/1.28 % (27733)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (27733)Memory used [KB]: 5628
% 1.48/1.28 % (27733)Time elapsed: 0.007 s
% 1.48/1.28 % (27733)Instructions burned: 17 (million)
% 1.48/1.28 % (27733)------------------------------
% 1.48/1.28 % (27733)------------------------------
% 1.48/1.28 % (27732)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27572 for (2999ds/7Mi)
% 1.48/1.29 % (27732)Instruction limit reached!
% 1.48/1.29 % (27732)------------------------------
% 1.48/1.29 % (27732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (27732)Termination reason: Unknown
% 1.48/1.29 % (27736)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_27572 for (2999ds/3Mi)
% 1.48/1.29 % (27732)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (27732)Memory used [KB]: 1023
% 1.48/1.29 % (27732)Time elapsed: 0.007 s
% 1.48/1.29 % (27732)Instructions burned: 7 (million)
% 1.48/1.29 % (27732)------------------------------
% 1.48/1.29 % (27732)------------------------------
% 1.48/1.29 % (27737)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_27572 for (2999ds/3Mi)
% 1.48/1.29 % (27736)Instruction limit reached!
% 1.48/1.29 % (27736)------------------------------
% 1.48/1.29 % (27736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (27736)Termination reason: Unknown
% 1.48/1.29 % (27736)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (27736)Memory used [KB]: 5500
% 1.48/1.29 % (27736)Time elapsed: 0.002 s
% 1.48/1.29 % (27736)Instructions burned: 3 (million)
% 1.48/1.29 % (27736)------------------------------
% 1.48/1.29 % (27736)------------------------------
% 1.48/1.29 % (27737)Instruction limit reached!
% 1.48/1.29 % (27737)------------------------------
% 1.48/1.29 % (27737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (27737)Termination reason: Unknown
% 1.48/1.29 % (27737)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (27737)Memory used [KB]: 1023
% 1.48/1.29 % (27737)Time elapsed: 0.003 s
% 1.48/1.29 % (27737)Instructions burned: 3 (million)
% 1.48/1.29 % (27737)------------------------------
% 1.48/1.29 % (27737)------------------------------
% 1.48/1.29 % (27731)First to succeed.
% 1.48/1.30 % (27738)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27572 for (2999ds/7Mi)
% 1.53/1.30 % (27731)Refutation found. Thanks to Tanya!
% 1.53/1.30 % SZS status Theorem for DTF2THF_27572
% 1.53/1.30 % SZS output start Proof for DTF2THF_27572
% 1.53/1.30 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.53/1.30 thf(func_def_15, type, sK2: $i > $o).
% 1.53/1.30 thf(func_def_16, type, sK3: (($i > $i) > $o) > $i > $i).
% 1.53/1.30 thf(func_def_17, type, sK4: (($i > $i) > $o) > $i > $i).
% 1.53/1.30 thf(f109,plain,(
% 1.53/1.30 $false),
% 1.53/1.30 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.53/1.30 thf(f108,plain,(
% 1.53/1.30 ($false = $true)),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f107])).
% 1.53/1.30 thf(f107,plain,(
% 1.53/1.30 ($false = ((sK2 @ sK5) => (sK2 @ sK5)))),
% 1.53/1.30 inference(forward_demodulation,[status(thm)],[f106,f83])).
% 1.53/1.30 thf(f83,plain,(
% 1.53/1.30 ( ! [X1 : $i] : (((sK4 @ (= @ (^[Y0 : $i]: (Y0))) @ X1) = X1)) )),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.53/1.30 thf(f80,plain,(
% 1.53/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (Y0)) @ X1) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))) @ X1))) )),
% 1.53/1.30 inference(argument_congruence,[status(thm)],[f61])).
% 1.53/1.30 thf(f61,plain,(
% 1.53/1.30 ((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0)))))),
% 1.53/1.30 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.53/1.30 thf(f54,plain,(
% 1.53/1.30 (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) = $true)),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f53])).
% 1.53/1.30 thf(f53,plain,(
% 1.53/1.30 ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & $true) = $true)),
% 1.53/1.30 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.53/1.30 thf(f52,plain,(
% 1.53/1.30 ($false = $true) | ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & $true) = $true)),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f51])).
% 1.53/1.30 thf(f51,plain,(
% 1.53/1.30 ($false = ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) | ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & $true) = $true)),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f43])).
% 1.53/1.30 thf(f43,plain,(
% 1.53/1.30 ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) = $true) | ($false = ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0))))),
% 1.53/1.30 inference(superposition,[status(thm)],[f22,f28])).
% 1.53/1.30 thf(f28,plain,(
% 1.53/1.30 ((^[Y0 : $i]: (Y0)) = (sK3 @ (= @ (^[Y0 : $i]: (Y0)))))),
% 1.53/1.30 inference(leibniz_equality_elimination,[status(thm)],[f23])).
% 1.53/1.30 thf(f23,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (((X1 @ (sK3 @ X1)) = $true) | ($false = (X1 @ (^[Y0 : $i]: (Y0))))) )),
% 1.53/1.30 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.53/1.30 thf(f22,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : ((((X1 @ (sK4 @ X1)) & (X1 @ (sK3 @ X1))) = $true) | ($false = (X1 @ (^[Y0 : $i]: (Y0))))) )),
% 1.53/1.30 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.53/1.30 thf(f20,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (((((X1 @ (sK4 @ X1)) & (X1 @ (sK3 @ X1))) => ((X1 @ (^[Y0 : $i]: (sK4 @ X1 @ (sK3 @ X1 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ X1 @ Y0))))))) = $false) | ($false = (X1 @ (^[Y0 : $i]: (Y0))))) )),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.53/1.30 thf(f19,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = (X1 @ (^[Y0 : $i]: (Y0)))) | ($false = ((^[Y0 : $i > $i]: (((X1 @ Y0) & (X1 @ (sK3 @ X1))) => ((X1 @ (^[Y1 : $i]: (Y0 @ (sK3 @ X1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) => (sK2 @ (Y0 @ Y1)))))))) @ (sK4 @ X1)))) )),
% 1.53/1.30 inference(sigma_clausification,[status(thm)],[f18])).
% 1.53/1.30 thf(f18,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (((X1 @ Y0) & (X1 @ (sK3 @ X1))) => ((X1 @ (^[Y1 : $i]: (Y0 @ (sK3 @ X1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) => (sK2 @ (Y0 @ Y1)))))))))) | ($false = (X1 @ (^[Y0 : $i]: (Y0))))) )),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.53/1.30 thf(f15,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = (X1 @ (^[Y0 : $i]: (Y0)))) | ($false = ((^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (((X1 @ Y1) & (X1 @ Y0)) => ((X1 @ (^[Y2 : $i]: (Y1 @ (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) => (sK2 @ (Y1 @ Y2)))))))))) @ (sK3 @ X1)))) )),
% 1.53/1.30 inference(sigma_clausification,[status(thm)],[f14])).
% 1.53/1.30 thf(f14,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (((X1 @ Y1) & (X1 @ Y0)) => ((X1 @ (^[Y2 : $i]: (Y1 @ (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) => (sK2 @ (Y1 @ Y2)))))))))))) | ($false = (X1 @ (^[Y0 : $i]: (Y0))))) )),
% 1.53/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.53/1.30 thf(f13,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (((X1 @ Y1) & (X1 @ Y0)) => ((X1 @ (^[Y2 : $i]: (Y1 @ (Y0 @ Y2)))) & (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) => (sK2 @ (Y1 @ Y2))))))))))) & (X1 @ (^[Y0 : $i]: (Y0)))))) )),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.53/1.30 thf(f12,plain,(
% 1.53/1.30 ( ! [X1 : ($i > $i) > $o] : (($false = ((^[Y0 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (((Y0 @ Y2) & (Y0 @ Y1)) => ((Y0 @ (^[Y3 : $i]: (Y2 @ (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) => (sK2 @ (Y2 @ Y3))))))))))) & (Y0 @ (^[Y1 : $i]: (Y1))))) @ X1))) )),
% 1.53/1.30 inference(pi_clausification,[status(thm)],[f11])).
% 1.53/1.30 thf(f11,plain,(
% 1.53/1.30 ($false = (?? @ (($i > $i) > $o) @ (^[Y0 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (((Y0 @ Y2) & (Y0 @ Y1)) => ((Y0 @ (^[Y3 : $i]: (Y2 @ (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) => (sK2 @ (Y2 @ Y3))))))))))) & (Y0 @ (^[Y1 : $i]: (Y1)))))))),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.53/1.30 thf(f10,plain,(
% 1.53/1.30 ($false = ((^[Y0 : $i > $o]: (?? @ (($i > $i) > $o) @ (^[Y1 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (((Y1 @ Y3) & (Y1 @ Y2)) => ((Y1 @ (^[Y4 : $i]: (Y3 @ (Y2 @ Y4)))) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) => (Y0 @ (Y3 @ Y4))))))))))) & (Y1 @ (^[Y2 : $i]: (Y2))))))) @ sK2))),
% 1.53/1.30 inference(sigma_clausification,[status(thm)],[f7])).
% 1.53/1.30 thf(f7,plain,(
% 1.53/1.30 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ (($i > $i) > $o) @ (^[Y1 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (((Y1 @ Y3) & (Y1 @ Y2)) => ((Y1 @ (^[Y4 : $i]: (Y3 @ (Y2 @ Y4)))) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) => (Y0 @ (Y3 @ Y4))))))))))) & (Y1 @ (^[Y2 : $i]: (Y2)))))))))),
% 1.53/1.30 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.53/1.30 thf(f6,plain,(
% 1.53/1.30 ((~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ (($i > $i) > $o) @ (^[Y1 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (((Y1 @ Y3) & (Y1 @ Y2)) => ((Y1 @ (^[Y4 : $i]: (Y3 @ (Y2 @ Y4)))) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) => (Y0 @ (Y3 @ Y4))))))))))) & (Y1 @ (^[Y2 : $i]: (Y2))))))))) = $true)),
% 1.53/1.30 inference(cnf_transformation,[status(thm)],[f5])).
% 1.53/1.30 thf(f5,plain,(
% 1.53/1.30 ((~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ (($i > $i) > $o) @ (^[Y1 : ($i > $i) > $o]: ((!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i) @ (^[Y3 : $i > $i]: (((Y1 @ Y3) & (Y1 @ Y2)) => ((Y1 @ (^[Y4 : $i]: (Y3 @ (Y2 @ Y4)))) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) => (Y0 @ (Y3 @ Y4))))))))))) & (Y1 @ (^[Y2 : $i]: (Y2))))))))) = $true)),
% 1.53/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.30 thf(f4,plain,(
% 1.53/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ((X1 @ (^[X2 : $i] : (X2))) & ! [X3 : $i > $i,X4 : $i > $i] : (((X1 @ X4) & (X1 @ X3)) => (! [X5 : $i] : ((X0 @ X5) => (X0 @ (X3 @ X5))) & (X1 @ (^[X6 : $i] : (X3 @ (X4 @ X6)))))))),
% 1.53/1.30 inference(rectify,[status(thm)],[f2])).
% 1.53/1.30 thf(f2,negated_conjecture,(
% 1.53/1.30 ~! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ((X1 @ (^[X2 : $i] : (X2))) & ! [X3 : $i > $i,X4 : $i > $i] : (((X1 @ X4) & (X1 @ X3)) => (! [X5 : $i] : ((X0 @ X5) => (X0 @ (X3 @ X5))) & (X1 @ (^[X2 : $i] : (X3 @ (X4 @ X2)))))))),
% 1.53/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.30 thf(f1,conjecture,(
% 1.53/1.30 ! [X0 : $i > $o] : ? [X1 : ($i > $i) > $o] : ((X1 @ (^[X2 : $i] : (X2))) & ! [X3 : $i > $i,X4 : $i > $i] : (((X1 @ X4) & (X1 @ X3)) => (! [X5 : $i] : ((X0 @ X5) => (X0 @ (X3 @ X5))) & (X1 @ (^[X2 : $i] : (X3 @ (X4 @ X2)))))))),
% 1.53/1.30 file('/export/starexec/sandbox2/tmp/tmp.tduxh7xmv3/DTF2THF_27572.p',cTHM112A_pme)).
% 1.53/1.30 thf(f106,plain,(
% 1.53/1.30 ($false = ((sK2 @ sK5) => (sK2 @ (sK4 @ (= @ (^[Y0 : $i]: (Y0))) @ sK5))))),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.53/1.30 thf(f100,plain,(
% 1.53/1.30 ($false = ((^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0)))) @ sK5))),
% 1.53/1.30 inference(sigma_clausification,[status(thm)],[f60])).
% 1.53/1.30 thf(f60,plain,(
% 1.53/1.30 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f59])).
% 1.53/1.30 thf(f59,plain,(
% 1.53/1.30 ($false = ($true & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0)))))))),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f58])).
% 1.53/1.30 thf(f58,plain,(
% 1.53/1.30 ($false = ($true => ($true & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(forward_demodulation,[status(thm)],[f49,f54])).
% 1.53/1.30 thf(f49,plain,(
% 1.53/1.30 ($false = (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) => (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f48])).
% 1.53/1.30 thf(f48,plain,(
% 1.53/1.30 ($false = ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & $true) => (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f47])).
% 1.53/1.30 thf(f47,plain,(
% 1.53/1.30 ($false = ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) => (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.53/1.30 thf(f46,plain,(
% 1.53/1.30 ($false = $true) | ($false = ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) => (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(boolean_simplification,[status(thm)],[f45])).
% 1.53/1.30 thf(f45,plain,(
% 1.53/1.30 ($false = ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) | ($false = ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) => (((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.53/1.30 thf(f42,plain,(
% 1.53/1.30 ($false = ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) | ($false = ((((^[Y0 : $i]: (Y0)) = (sK4 @ (= @ (^[Y0 : $i]: (Y0))))) & ((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (Y0)))) => (((^[Y0 : $i]: (Y0)) = (^[Y0 : $i]: (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ ((^[Y1 : $i]: (Y1)) @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (sK4 @ (= @ (^[Y1 : $i]: (Y1))) @ Y0))))))))),
% 1.53/1.30 inference(superposition,[status(thm)],[f20,f28])).
% 1.53/1.30 % SZS output end Proof for DTF2THF_27572
% 1.53/1.30 % (27731)------------------------------
% 1.53/1.30 % (27731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (27731)Termination reason: Refutation
% 1.53/1.30
% 1.53/1.30 % (27731)Memory used [KB]: 5628
% 1.53/1.30 % (27731)Time elapsed: 0.025 s
% 1.53/1.30 % (27731)Instructions burned: 20 (million)
% 1.53/1.30 % (27731)------------------------------
% 1.53/1.30 % (27731)------------------------------
% 1.53/1.30 % (27706)Success in time 0.068 s
%------------------------------------------------------------------------------