%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV385^5 : 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 : n010.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 09:41:08 AM UTC 2026
% Result : Theorem 1.14s 1.14s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 231 equ; 15 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 475 ( 45 ~; 46 |; 34 &; 286 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 7 usr; 7 con; 0-2 aty)
% ( 16 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 142 ( 88 ^; 48 !; 6 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
x: b ).
thf(func_def_3,type,
y: a ).
thf(func_def_19,type,
sK1: ( b > a ) > a ).
thf(func_def_20,type,
sK2: ( b > a ) > b ).
thf(func_def_21,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK4: ( b > a ) > b > b ).
thf(func_def_23,type,
sK5: ( b > a ) > b > b ).
thf(f172,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f171,f33]) ).
thf(f33,plain,
( y
= ( sK1
@ ^ [Y0: b] : y ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( y
= ( sK1 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( y
= ( sK1 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ( y
= ( sK1 @ X1 ) )
=> ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: b > a] :
( ( ( y
= ( X1 @ ( sK2 @ X1 ) ) )
= $false )
| ( ( ( y
= ( sK1 @ X1 ) )
=> ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: b > a] :
( ( $false
= ( ( x
= ( sK2 @ X1 ) )
=> ( y
= ( X1 @ ( sK2 @ X1 ) ) ) ) )
| ( ( ( y
= ( sK1 @ X1 ) )
=> ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: b > a] :
( ( $false
= ( ^ [Y0: b] :
( ( x = Y0 )
=> ( y
= ( X1 @ Y0 ) ) )
@ ( sK2 @ X1 ) ) )
| ( ( ( y
= ( sK1 @ X1 ) )
=> ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: b > a] :
( ( ( !! @ b
@ ^ [Y0: b] :
( ( x = Y0 )
=> ( y
= ( X1 @ Y0 ) ) ) )
= $false )
| ( ( ( y
= ( sK1 @ X1 ) )
=> ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: b > a] :
( ( ( ^ [Y0: a] :
( ( y = Y0 )
=> ( ?? @ b
@ ^ [Y1: b] :
( ( (=) @ Y1 )
= ( ^ [Y2: b] :
( ( x = Y2 )
& ( ( X1 @ Y2 )
= Y0 ) ) ) ) ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( !! @ b
@ ^ [Y0: b] :
( ( x = Y0 )
=> ( y
= ( X1 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: b > a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( y = Y0 )
=> ( ?? @ b
@ ^ [Y1: b] :
( ( (=) @ Y1 )
= ( ^ [Y2: b] :
( ( x = Y2 )
& ( ( X1 @ Y2 )
= Y0 ) ) ) ) ) ) )
= $false )
| ( ( !! @ b
@ ^ [Y0: b] :
( ( x = Y0 )
=> ( y
= ( X1 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: b > a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( y = Y0 )
=> ( ?? @ b
@ ^ [Y1: b] :
( ( (=) @ Y1 )
= ( ^ [Y2: b] :
( ( x = Y2 )
& ( ( X1 @ Y2 )
= Y0 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( ( x = Y0 )
=> ( y
= ( X1 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: b > a] :
( ( ^ [Y0: b > a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( y = Y1 )
=> ( ?? @ b
@ ^ [Y2: b] :
( ( (=) @ Y2 )
= ( ^ [Y3: b] :
( ( x = Y3 )
& ( ( Y0 @ Y3 )
= Y1 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( ( x = Y1 )
=> ( y
= ( Y0 @ Y1 ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ?? @ ( b > a )
@ ^ [Y0: b > a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( y = Y1 )
=> ( ?? @ b
@ ^ [Y2: b] :
( ( (=) @ Y2 )
= ( ^ [Y3: b] :
( ( x = Y3 )
& ( ( Y0 @ Y3 )
= Y1 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( ( x = Y1 )
=> ( y
= ( Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ~ ( ?? @ ( b > a )
@ ^ [Y0: b > a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( y = Y1 )
=> ( ?? @ b
@ ^ [Y2: b] :
( ( (=) @ Y2 )
= ( ^ [Y3: b] :
( ( x = Y3 )
& ( ( Y0 @ Y3 )
= Y1 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( ( x = Y1 )
=> ( y
= ( Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ?? @ ( b > a )
@ ^ [Y0: b > a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( y = Y1 )
=> ( ?? @ b
@ ^ [Y2: b] :
( ( ^ [Y3: b,Y4: b] : ( Y3 = Y4 )
@ Y2 )
= ( ^ [Y3: b] :
( ( x = Y3 )
& ( ( Y0 @ Y3 )
= Y1 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( ( x = Y1 )
=> ( y
= ( Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ?? @ ( b > a )
@ ^ [Y0: b > a] :
( ( !! @ a
@ ^ [Y1: a] :
( ( y = Y1 )
=> ( ?? @ b
@ ^ [Y2: b] :
( ( ^ [Y3: b,Y4: b] : ( Y3 = Y4 )
@ Y2 )
= ( ^ [Y3: b] :
( ( x = Y3 )
& ( ( Y0 @ Y3 )
= Y1 ) ) ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( ( x = Y1 )
=> ( y
= ( Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: b > a] :
( ! [X1: b] :
( ( x = X1 )
=> ( y
= ( X0 @ X1 ) ) )
& ! [X2: a] :
( ( y = X2 )
=> ? [X3: b] :
( ( ^ [X4: b,X5: b] : ( X4 = X5 )
@ X3 )
= ( ^ [X6: b] :
( ( ( X0 @ X6 )
= X2 )
& ( x = X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: b > a] :
( ! [X1: b] :
( ( x = X1 )
=> ( y
= ( X0 @ X1 ) ) )
& ! [X2: a] :
( ( y = X2 )
=> ? [X3: b] :
( ( ^ [X5: b,X6: b] : ( X5 = X6 )
@ X3 )
= ( ^ [X4: b] :
( ( ( X0 @ X4 )
= X2 )
& ( x = X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: b > a] :
( ! [X1: b] :
( ( x = X1 )
=> ( y
= ( X0 @ X1 ) ) )
& ! [X2: a] :
( ( y = X2 )
=> ? [X3: b] :
( ( ^ [X5: b,X6: b] : ( X5 = X6 )
@ X3 )
= ( ^ [X4: b] :
( ( ( X0 @ X4 )
= X2 )
& ( x = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pDArOFEHlp/DTF2THF_27580.p',cX6004_pme) ).
thf(f171,plain,
( y
!= ( sK1
@ ^ [Y0: b] : y ) ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ( y != y )
| ( y
!= ( sK1
@ ^ [Y0: b] : y ) ) ),
inference(beta_eta_normalization,[status(thm)],[f169]) ).
thf(f169,plain,
( ( ( ^ [Y0: b] : y
@ x )
!= ( sK1
@ ^ [Y0: b] : y ) )
| ( y
!= ( ^ [Y0: b] : y
@ ( sK2
@ ^ [Y0: b] : y ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( y
!= ( ^ [Y0: b] : y
@ ( sK2
@ ^ [Y0: b] : y ) ) )
| ( x != x )
| ( ( ^ [Y0: b] : y
@ x )
!= ( sK1
@ ^ [Y0: b] : y ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( x != x )
| ( ( ^ [Y0: b] : y
@ x )
!= ( sK1
@ ^ [Y0: b] : y ) )
| ( x != x )
| ( y
!= ( ^ [Y0: b] : y
@ ( sK2
@ ^ [Y0: b] : y ) ) ) ),
inference(superposition,[status(thm)],[f69,f166]) ).
thf(f166,plain,
( x
= ( sK5
@ ^ [Y0: b] : y
@ x ) ),
inference(equality_resolution,[status(thm)],[f161]) ).
thf(f161,plain,
! [X0: b] :
( ( x != X0 )
| ( x
= ( sK5
@ ^ [Y0: b] : y
@ X0 ) ) ),
inference(equality_factoring,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: b] :
( ( ( sK5
@ ^ [Y0: b] : y
@ X0 )
= X0 )
| ( x
= ( sK5
@ ^ [Y0: b] : y
@ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( sK5 @ X1 @ X2 )
= X2 )
| ( x
= ( sK5 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( x
= ( sK5 @ X1 @ X2 ) )
= $true )
| ( ( sK5 @ X1 @ X2 )
= X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: b,X1: b > a] :
( ( ( sK5 @ X1 @ X2 )
= X2 )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ( x
= ( sK5 @ X1 @ X2 ) )
& ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= ( sK1 @ X1 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X2
= ( sK5 @ X1 @ X2 ) )
= $true )
| ( ( ( x
= ( sK5 @ X1 @ X2 ) )
& ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= ( sK1 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ( x
= ( sK5 @ X1 @ X2 ) )
& ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= ( sK1 @ X1 ) ) )
!= ( X2
= ( sK5 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X2
= ( sK5 @ X1 @ X2 ) )
!= ( ^ [Y0: b] :
( ( x = Y0 )
& ( ( X1 @ Y0 )
= ( sK1 @ X1 ) ) )
@ ( sK5 @ X1 @ X2 ) ) ) ),
inference(negative_extensionality,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: b,X1: b > a] :
( ( ( (=) @ X2 )
!= ( ^ [Y0: b] :
( ( x = Y0 )
& ( ( X1 @ Y0 )
= ( sK1 @ X1 ) ) ) ) )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ( (=) @ X2 )
= ( ^ [Y0: b] :
( ( x = Y0 )
& ( ( X1 @ Y0 )
= ( sK1 @ X1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( (=) @ Y0 )
= ( ^ [Y1: b] :
( ( x = Y1 )
& ( ( X1 @ Y1 )
= ( sK1 @ X1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f69,plain,
! [X2: b,X1: b > a] :
( ( ( X1 @ ( sK5 @ X1 @ X2 ) )
!= ( sK1 @ X1 ) )
| ( x
!= ( sK5 @ X1 @ X2 ) )
| ( ( sK5 @ X1 @ X2 )
!= X2 )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: b,X1: b > a] :
( ( ( X1 @ ( sK5 @ X1 @ X2 ) )
!= ( sK1 @ X1 ) )
| ( $false
= ( X2
= ( sK5 @ X1 @ X2 ) ) )
| ( x
!= ( sK5 @ X1 @ X2 ) )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: b,X1: b > a] :
( ( ( x
= ( sK5 @ X1 @ X2 ) )
= $false )
| ( ( X1 @ ( sK5 @ X1 @ X2 ) )
!= ( sK1 @ X1 ) )
| ( $false
= ( X2
= ( sK5 @ X1 @ X2 ) ) )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: b,X1: b > a] :
( ( ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= ( sK1 @ X1 ) )
= $false )
| ( $false
= ( X2
= ( sK5 @ X1 @ X2 ) ) )
| ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( x
= ( sK5 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: b,X1: b > a] :
( ( y
!= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( ( x
= ( sK5 @ X1 @ X2 ) )
& ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= ( sK1 @ X1 ) ) )
= $false )
| ( $false
= ( X2
= ( sK5 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV385^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:45:33 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEV385^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : TPS problem X6004
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0248 [Bro09]
% 0.15/0.42 % : X6004 [TPS]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.20 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.15/0.42 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 4 ( 7 avg)
% 0.15/0.42 % Number of connectives : 7 ( 0 ~; 0 |; 2 &; 3 @)
% 0.15/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 6 ( 6 avg)
% 0.15/0.42 % Number of types : 2 ( 2 usr)
% 0.15/0.42 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.15/0.42 % Number of variables : 7 ( 3 ^; 2 !; 2 ?; 7 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 % : Polymorphic definitions expanded.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(b_type,type,
% 0.15/0.42 b: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(a_type,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(x,type,
% 0.15/0.42 x: b ).
% 0.15/0.42
% 0.15/0.42 thf(y,type,
% 0.15/0.42 y: a ).
% 0.15/0.42
% 0.15/0.42 thf(cX6004_pme,conjecture,
% 0.15/0.42 ? [Xs: b > a] :
% 0.15/0.42 ( ! [Xx_6: b] :
% 0.15/0.42 ( ( x = Xx_6 )
% 0.15/0.42 => ( y
% 0.15/0.42 = ( Xs @ Xx_6 ) ) )
% 0.15/0.42 & ! [Xy_56: a] :
% 0.15/0.42 ( ( y = Xy_56 )
% 0.15/0.42 => ? [Xy0: b] :
% 0.15/0.42 ( ( ^ [Xx_7: b] :
% 0.15/0.42 ( ( x = Xx_7 )
% 0.15/0.42 & ( Xy_56
% 0.15/0.42 = ( Xs @ Xx_7 ) ) ) )
% 0.15/0.42 = ( ^ [Xx: b,Xy: b] : ( Xx = Xy )
% 0.15/0.42 @ Xy0 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 0.93/1.01 ---- Embedded in THF ---
% 0.93/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.93/1.01 %%% Generated on Tue Feb 24 12:45:33 EST 2026
% 0.93/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 0.93/1.01 %%% Logic specification used:
% 0.93/1.01 %%% thf(spec, logic, $$dhol).
% 0.93/1.01
% 0.93/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pDArOFEHlp/DTF2DTF27580.p
% See solution above
% 0.93/1.01 ------------------------
% 0.93/1.02 ---- Cleaned THF ---
% 0.93/1.02 thf(b_type,type,
% 0.93/1.02 b: $tType ).
% 0.93/1.02
% 0.93/1.02 thf(a_type,type,
% 0.93/1.02 a: $tType ).
% 0.93/1.02
% 0.93/1.02 thf(x,type,
% 0.93/1.02 x: b ).
% 0.93/1.02
% 0.93/1.02 thf(y,type,
% 0.93/1.02 y: a ).
% 0.93/1.02
% 0.93/1.02 thf(cX6004_pme,conjecture,
% 0.93/1.02 ? [Xs: b > a] :
% 0.93/1.02 ( ! [Xx_6: b] :
% 0.93/1.02 ( ( x = Xx_6 )
% 0.93/1.02 => ( y
% 0.93/1.02 = ( Xs @ Xx_6 ) ) )
% 0.93/1.02 & ! [Xy_56: a] :
% 0.93/1.02 ( ( y = Xy_56 )
% 0.93/1.02 => ? [Xy0: b] :
% 0.93/1.02 ( ( ^ [Xx_7: b] :
% 0.93/1.02 ( ( x = Xx_7 )
% 0.93/1.02 & ( Xy_56
% 0.93/1.02 = ( Xs @ Xx_7 ) ) ) )
% 0.93/1.02 = ( ^ [Xx: b,Xy: b] : ( Xx = Xy )
% 0.93/1.02 @ Xy0 ) ) ) ) ).
% 0.93/1.02 ------------------------
% 1.14/1.03 % (27794)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_27580 for (2999ds/27Mi)
% 1.14/1.03 % (27792)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/183Mi)
% 1.14/1.04 % (27794)Refutation not found, incomplete strategy
% 1.14/1.04 % (27794)------------------------------
% 1.14/1.04 % (27794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.04 % (27794)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.04
% 1.14/1.04
% 1.14/1.04 % (27794)Memory used [KB]: 5500
% 1.14/1.04 % (27794)Time elapsed: 0.004 s
% 1.14/1.04 % (27794)Instructions burned: 7 (million)
% 1.14/1.04 % (27794)------------------------------
% 1.14/1.04 % (27794)------------------------------
% 1.14/1.04 % (27793)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_27580 for (2999ds/4Mi)
% 1.14/1.04 % (27795)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/2Mi)
% 1.14/1.04 % (27796)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_27580 for (2999ds/2Mi)
% 1.14/1.04 % (27797)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_27580 for (2999ds/275Mi)
% 1.14/1.04 % (27798)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/18Mi)
% 1.14/1.04 % (27795)Instruction limit reached!
% 1.14/1.04 % (27795)------------------------------
% 1.14/1.04 % (27795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.04 % (27795)Termination reason: Unknown
% 1.14/1.04 % (27795)Termination phase: Saturation
% 1.14/1.04
% 1.14/1.04 % (27795)Memory used [KB]: 895
% 1.14/1.04 % (27795)Time elapsed: 0.003 s
% 1.14/1.04 % (27795)Instructions burned: 2 (million)
% 1.14/1.04 % (27795)------------------------------
% 1.14/1.04 % (27795)------------------------------
% 1.14/1.04 % (27796)Instruction limit reached!
% 1.14/1.04 % (27796)------------------------------
% 1.14/1.04 % (27796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.04 % (27796)Termination reason: Unknown
% 1.14/1.04 % (27796)Termination phase: Property scanning
% 1.14/1.04
% 1.14/1.04 % (27796)Memory used [KB]: 895
% 1.14/1.04 % (27796)Time elapsed: 0.003 s
% 1.14/1.04 % (27796)Instructions burned: 2 (million)
% 1.14/1.04 % (27796)------------------------------
% 1.14/1.04 % (27796)------------------------------
% 1.14/1.04 % (27793)Instruction limit reached!
% 1.14/1.04 % (27793)------------------------------
% 1.14/1.04 % (27793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.04 % (27793)Termination reason: Unknown
% 1.14/1.04 % (27793)Termination phase: Saturation
% 1.14/1.04
% 1.14/1.04 % (27793)Memory used [KB]: 5500
% 1.14/1.04 % (27793)Time elapsed: 0.005 s
% 1.14/1.04 % (27793)Instructions burned: 4 (million)
% 1.14/1.04 % (27793)------------------------------
% 1.14/1.04 % (27793)------------------------------
% 1.14/1.05 % (27800)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/3Mi)
% 1.14/1.05 % (27800)Instruction limit reached!
% 1.14/1.05 % (27800)------------------------------
% 1.14/1.05 % (27800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.05 % (27800)Termination reason: Unknown
% 1.14/1.05 % (27800)Termination phase: Saturation
% 1.14/1.05
% 1.14/1.05 % (27800)Memory used [KB]: 5500
% 1.14/1.05 % (27800)Time elapsed: 0.002 s
% 1.14/1.05 % (27800)Instructions burned: 3 (million)
% 1.14/1.05 % (27800)------------------------------
% 1.14/1.05 % (27800)------------------------------
% 1.14/1.05 % (27797)Refutation not found, incomplete strategy
% 1.14/1.05 % (27797)------------------------------
% 1.14/1.05 % (27797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.05 % (27797)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.05
% 1.14/1.05
% 1.14/1.05 % (27797)Memory used [KB]: 5500
% 1.14/1.05 % (27797)Time elapsed: 0.008 s
% 1.14/1.05 % (27797)Instructions burned: 8 (million)
% 1.14/1.05 % (27797)------------------------------
% 1.14/1.05 % (27797)------------------------------
% 1.14/1.05 % (27798)Instruction limit reached!
% 1.14/1.05 % (27798)------------------------------
% 1.14/1.05 % (27798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.05 % (27798)Termination reason: Unknown
% 1.14/1.05 % (27798)Termination phase: Saturation
% 1.14/1.05
% 1.14/1.05 % (27798)Memory used [KB]: 5500
% 1.14/1.05 % (27798)Time elapsed: 0.014 s
% 1.14/1.05 % (27798)Instructions burned: 18 (million)
% 1.14/1.05 % (27798)------------------------------
% 1.14/1.05 % (27798)------------------------------
% 1.14/1.06 % (27814)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_27580 for (2999ds/1041Mi)
% 1.14/1.06 % (27808)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_27580 for (2999ds/37Mi)
% 1.14/1.06 % (27809)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_27580 for (2999ds/15Mi)
% 1.14/1.06 % (27810)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_27580 for (2999ds/3Mi)
% 1.14/1.06 % (27810)Instruction limit reached!
% 1.14/1.06 % (27810)------------------------------
% 1.14/1.06 % (27810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.06 % (27810)Termination reason: Unknown
% 1.14/1.06 % (27810)Termination phase: Saturation
% 1.14/1.06
% 1.14/1.06 % (27810)Memory used [KB]: 5500
% 1.14/1.06 % (27810)Time elapsed: 0.004 s
% 1.14/1.06 % (27810)Instructions burned: 3 (million)
% 1.14/1.06 % (27810)------------------------------
% 1.14/1.06 % (27810)------------------------------
% 1.14/1.07 % (27816)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/7Mi)
% 1.14/1.07 % (27809)Refutation not found, incomplete strategy
% 1.14/1.07 % (27809)------------------------------
% 1.14/1.07 % (27809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.07 % (27809)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.07
% 1.14/1.07
% 1.14/1.07 % (27809)Memory used [KB]: 5500
% 1.14/1.07 % (27809)Time elapsed: 0.009 s
% 1.14/1.07 % (27809)Instructions burned: 9 (million)
% 1.14/1.07 % (27809)------------------------------
% 1.14/1.07 % (27809)------------------------------
% 1.14/1.07 % (27820)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/16Mi)
% 1.14/1.07 % (27816)Instruction limit reached!
% 1.14/1.07 % (27816)------------------------------
% 1.14/1.07 % (27816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.07 % (27816)Termination reason: Unknown
% 1.14/1.07 % (27816)Termination phase: Saturation
% 1.14/1.07
% 1.14/1.07 % (27816)Memory used [KB]: 1023
% 1.14/1.07 % (27816)Time elapsed: 0.007 s
% 1.14/1.07 % (27816)Instructions burned: 8 (million)
% 1.14/1.07 % (27816)------------------------------
% 1.14/1.07 % (27816)------------------------------
% 1.14/1.07 % (27808)Instruction limit reached!
% 1.14/1.07 % (27808)------------------------------
% 1.14/1.07 % (27808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.07 % (27808)Termination reason: Unknown
% 1.14/1.07 % (27808)Termination phase: Saturation
% 1.14/1.07
% 1.14/1.07 % (27808)Memory used [KB]: 5756
% 1.14/1.07 % (27808)Time elapsed: 0.016 s
% 1.14/1.07 % (27808)Instructions burned: 39 (million)
% 1.14/1.07 % (27808)------------------------------
% 1.14/1.07 % (27808)------------------------------
% 1.14/1.07 % (27820)Instruction limit reached!
% 1.14/1.07 % (27820)------------------------------
% 1.14/1.07 % (27820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.07 % (27820)Termination reason: Unknown
% 1.14/1.07 % (27820)Termination phase: Saturation
% 1.14/1.07
% 1.14/1.07 % (27820)Memory used [KB]: 5628
% 1.14/1.07 % (27820)Time elapsed: 0.007 s
% 1.14/1.07 % (27820)Instructions burned: 17 (million)
% 1.14/1.07 % (27820)------------------------------
% 1.14/1.07 % (27820)------------------------------
% 1.14/1.07 % (27822)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_27580 for (2999ds/3Mi)
% 1.14/1.08 % (27822)Instruction limit reached!
% 1.14/1.08 % (27822)------------------------------
% 1.14/1.08 % (27822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.08 % (27822)Termination reason: Unknown
% 1.14/1.08 % (27822)Termination phase: Saturation
% 1.14/1.08
% 1.14/1.08 % (27822)Memory used [KB]: 5500
% 1.14/1.08 % (27822)Time elapsed: 0.003 s
% 1.14/1.08 % (27822)Instructions burned: 4 (million)
% 1.14/1.08 % (27822)------------------------------
% 1.14/1.08 % (27822)------------------------------
% 1.14/1.08 % (27828)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/3Mi)
% 1.14/1.08 % (27830)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/4Mi)
% 1.14/1.08 % (27828)Instruction limit reached!
% 1.14/1.08 % (27828)------------------------------
% 1.14/1.08 % (27828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.08 % (27828)Termination reason: Unknown
% 1.14/1.08 % (27828)Termination phase: Saturation
% 1.14/1.08
% 1.14/1.08 % (27828)Memory used [KB]: 5500
% 1.14/1.08 % (27828)Time elapsed: 0.002 s
% 1.14/1.08 % (27828)Instructions burned: 3 (million)
% 1.14/1.08 % (27828)------------------------------
% 1.14/1.08 % (27828)------------------------------
% 1.14/1.08 % (27830)Instruction limit reached!
% 1.14/1.08 % (27830)------------------------------
% 1.14/1.08 % (27830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.08 % (27830)Termination reason: Unknown
% 1.14/1.08 % (27830)Termination phase: Saturation
% 1.14/1.08
% 1.14/1.08 % (27830)Memory used [KB]: 5500
% 1.14/1.08 % (27830)Time elapsed: 0.003 s
% 1.14/1.08 % (27830)Instructions burned: 5 (million)
% 1.14/1.08 % (27830)------------------------------
% 1.14/1.08 % (27830)------------------------------
% 1.14/1.08 % (27824)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_27580 for (2999ds/3Mi)
% 1.14/1.09 % (27824)Instruction limit reached!
% 1.14/1.09 % (27824)------------------------------
% 1.14/1.09 % (27824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.09 % (27824)Termination reason: Unknown
% 1.14/1.09 % (27824)Termination phase: Property scanning
% 1.14/1.09
% 1.14/1.09 % (27824)Memory used [KB]: 895
% 1.14/1.09 % (27824)Time elapsed: 0.003 s
% 1.14/1.09 % (27824)Instructions burned: 3 (million)
% 1.14/1.09 % (27824)------------------------------
% 1.14/1.09 % (27824)------------------------------
% 1.14/1.09 % (27792)Instruction limit reached!
% 1.14/1.09 % (27792)------------------------------
% 1.14/1.09 % (27792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.09 % (27792)Termination reason: Unknown
% 1.14/1.09 % (27792)Termination phase: Saturation
% 1.14/1.09
% 1.14/1.09 % (27792)Memory used [KB]: 6524
% 1.14/1.09 % (27792)Time elapsed: 0.054 s
% 1.14/1.09 % (27792)Instructions burned: 186 (million)
% 1.14/1.09 % (27792)------------------------------
% 1.14/1.09 % (27792)------------------------------
% 1.14/1.09 % (27826)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/7Mi)
% 1.14/1.09 % (27826)Instruction limit reached!
% 1.14/1.09 % (27826)------------------------------
% 1.14/1.09 % (27826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.09 % (27826)Termination reason: Unknown
% 1.14/1.09 % (27826)Termination phase: Saturation
% 1.14/1.09
% 1.14/1.09 % (27826)Memory used [KB]: 5500
% 1.14/1.09 % (27826)Time elapsed: 0.004 s
% 1.14/1.09 % (27826)Instructions burned: 7 (million)
% 1.14/1.09 % (27826)------------------------------
% 1.14/1.09 % (27826)------------------------------
% 1.14/1.09 % (27837)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/710Mi)
% 1.14/1.09 % (27839)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/6Mi)
% 1.14/1.09 % (27833)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/18Mi)
% 1.14/1.09 % (27842)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_27580 for (2999ds/21Mi)
% 1.14/1.10 % (27839)Instruction limit reached!
% 1.14/1.10 % (27839)------------------------------
% 1.14/1.10 % (27839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.10 % (27839)Termination reason: Unknown
% 1.14/1.10 % (27839)Termination phase: Saturation
% 1.14/1.10
% 1.14/1.10 % (27839)Memory used [KB]: 5500
% 1.14/1.10 % (27839)Time elapsed: 0.004 s
% 1.14/1.10 % (27839)Instructions burned: 8 (million)
% 1.14/1.10 % (27839)------------------------------
% 1.14/1.10 % (27839)------------------------------
% 1.14/1.10 % (27844)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/5Mi)
% 1.14/1.10 % (27841)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_27580 for (2999ds/902Mi)
% 1.14/1.10 % (27844)Instruction limit reached!
% 1.14/1.10 % (27844)------------------------------
% 1.14/1.10 % (27844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.10 % (27844)Termination reason: Unknown
% 1.14/1.10 % (27844)Termination phase: Saturation
% 1.14/1.10
% 1.14/1.10 % (27844)Memory used [KB]: 5500
% 1.14/1.10 % (27844)Time elapsed: 0.003 s
% 1.14/1.10 % (27844)Instructions burned: 5 (million)
% 1.14/1.10 % (27844)------------------------------
% 1.14/1.10 % (27844)------------------------------
% 1.14/1.10 % (27833)Refutation not found, incomplete strategy
% 1.14/1.10 % (27833)------------------------------
% 1.14/1.10 % (27833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.10 % (27833)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.10
% 1.14/1.10
% 1.14/1.10 % (27833)Memory used [KB]: 5500
% 1.14/1.10 % (27833)Time elapsed: 0.010 s
% 1.14/1.10 % (27833)Instructions burned: 10 (million)
% 1.14/1.10 % (27833)------------------------------
% 1.14/1.10 % (27833)------------------------------
% 1.14/1.10 % (27842)Instruction limit reached!
% 1.14/1.10 % (27842)------------------------------
% 1.14/1.10 % (27842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.10 % (27842)Termination reason: Unknown
% 1.14/1.10 % (27842)Termination phase: Saturation
% 1.14/1.10
% 1.14/1.10 % (27842)Memory used [KB]: 5628
% 1.14/1.10 % (27842)Time elapsed: 0.009 s
% 1.14/1.10 % (27842)Instructions burned: 23 (million)
% 1.14/1.10 % (27842)------------------------------
% 1.14/1.10 % (27842)------------------------------
% 1.14/1.11 % (27847)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_27580 for (2999ds/6Mi)
% 1.14/1.11 % (27847)Instruction limit reached!
% 1.14/1.11 % (27847)------------------------------
% 1.14/1.11 % (27847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.11 % (27847)Termination reason: Unknown
% 1.14/1.11 % (27847)Termination phase: Saturation
% 1.14/1.11
% 1.14/1.11 % (27847)Memory used [KB]: 5500
% 1.14/1.11 % (27847)Time elapsed: 0.003 s
% 1.14/1.11 % (27847)Instructions burned: 6 (million)
% 1.14/1.11 % (27847)------------------------------
% 1.14/1.11 % (27847)------------------------------
% 1.14/1.11 % (27850)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/377Mi)
% 1.14/1.11 % (27850)Refutation not found, incomplete strategy
% 1.14/1.11 % (27850)------------------------------
% 1.14/1.11 % (27850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.11 % (27850)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.11
% 1.14/1.11
% 1.14/1.11 % (27850)Memory used [KB]: 5500
% 1.14/1.11 % (27850)Time elapsed: 0.004 s
% 1.14/1.11 % (27850)Instructions burned: 8 (million)
% 1.14/1.11 % (27850)------------------------------
% 1.14/1.11 % (27850)------------------------------
% 1.14/1.11 % (27854)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_27580 for (2999ds/19Mi)
% 1.14/1.12 % (27857)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/879Mi)
% 1.14/1.12 % (27852)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_27580 for (2999ds/779Mi)
% 1.14/1.12 % (27854)Instruction limit reached!
% 1.14/1.12 % (27854)------------------------------
% 1.14/1.12 % (27854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.12 % (27854)Termination reason: Unknown
% 1.14/1.12 % (27854)Termination phase: Saturation
% 1.14/1.12
% 1.14/1.12 % (27854)Memory used [KB]: 5500
% 1.14/1.12 % (27854)Time elapsed: 0.007 s
% 1.14/1.12 % (27854)Instructions burned: 19 (million)
% 1.14/1.12 % (27854)------------------------------
% 1.14/1.12 % (27854)------------------------------
% 1.14/1.12 % (27857)Refutation not found, incomplete strategy
% 1.14/1.12 % (27857)------------------------------
% 1.14/1.12 % (27857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.12 % (27857)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.12
% 1.14/1.12
% 1.14/1.12 % (27857)Memory used [KB]: 5500
% 1.14/1.12 % (27857)Time elapsed: 0.003 s
% 1.14/1.12 % (27857)Instructions burned: 6 (million)
% 1.14/1.12 % (27857)------------------------------
% 1.14/1.12 % (27857)------------------------------
% 1.14/1.12 % (27859)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/17Mi)
% 1.14/1.13 % (27862)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/3Mi)
% 1.14/1.13 % (27859)Instruction limit reached!
% 1.14/1.13 % (27859)------------------------------
% 1.14/1.13 % (27859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.13 % (27859)Termination reason: Unknown
% 1.14/1.13 % (27859)Termination phase: Saturation
% 1.14/1.13
% 1.14/1.13 % (27859)Memory used [KB]: 5500
% 1.14/1.13 % (27859)Time elapsed: 0.007 s
% 1.14/1.13 % (27859)Instructions burned: 19 (million)
% 1.14/1.13 % (27859)------------------------------
% 1.14/1.13 % (27859)------------------------------
% 1.14/1.13 % (27862)Instruction limit reached!
% 1.14/1.13 % (27862)------------------------------
% 1.14/1.13 % (27862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.13 % (27862)Termination reason: Unknown
% 1.14/1.13 % (27862)Termination phase: Saturation
% 1.14/1.13
% 1.14/1.13 % (27862)Memory used [KB]: 1023
% 1.14/1.13 % (27862)Time elapsed: 0.002 s
% 1.14/1.13 % (27862)Instructions burned: 3 (million)
% 1.14/1.13 % (27862)------------------------------
% 1.14/1.13 % (27862)------------------------------
% 1.14/1.13 % (27864)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27580 for (2999ds/30Mi)
% 1.14/1.13 % (27852)First to succeed.
% 1.14/1.14 % (27852)Refutation found. Thanks to Tanya!
% 1.14/1.14 % SZS status Theorem for DTF2THF_27580
% 1.14/1.14 % SZS output start Proof for DTF2THF_27580
% 1.14/1.14 thf(type_def_5, type, b: $tType).
% 1.14/1.14 thf(type_def_6, type, a: $tType).
% 1.14/1.14 thf(func_def_0, type, b: $tType).
% 1.14/1.14 thf(func_def_1, type, a: $tType).
% 1.14/1.14 thf(func_def_2, type, x: b).
% 1.14/1.14 thf(func_def_3, type, y: a).
% 1.14/1.14 thf(func_def_19, type, sK1: (b > a) > a).
% 1.14/1.14 thf(func_def_20, type, sK2: (b > a) > b).
% 1.14/1.14 thf(func_def_21, type, ph3: !>[X0: $tType]:(X0)).
% 1.14/1.14 thf(func_def_22, type, sK4: (b > a) > b > b).
% 1.14/1.14 thf(func_def_23, type, sK5: (b > a) > b > b).
% 1.14/1.14 thf(f172,plain,(
% 1.14/1.14 $false),
% 1.14/1.14 inference(subsumption_resolution,[status(thm)],[f171,f33])).
% 1.14/1.14 thf(f33,plain,(
% 1.14/1.14 (y = (sK1 @ (^[Y0 : b]: (y))))),
% 1.14/1.14 inference(equality_resolution,[status(thm)],[f31])).
% 1.14/1.14 thf(f31,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (y = (sK1 @ X1))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 1.14/1.14 thf(f27,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((y = (sK1 @ X1)) = $true)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.14/1.14 thf(f25,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (((y = (sK1 @ X1)) => (?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))))) = $false)) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.14/1.14 thf(f16,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : (((y = (X1 @ (sK2 @ X1))) = $false) | (((y = (sK1 @ X1)) => (?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))))) = $false)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.14/1.14 thf(f15,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : (($false = ((x = (sK2 @ X1)) => (y = (X1 @ (sK2 @ X1))))) | (((y = (sK1 @ X1)) => (?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))))) = $false)) )),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.14/1.14 thf(f14,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : (($false = ((^[Y0 : b]: ((x = Y0) => (y = (X1 @ Y0)))) @ (sK2 @ X1))) | (((y = (sK1 @ X1)) => (?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))))) = $false)) )),
% 1.14/1.14 inference(sigma_clausification,[status(thm)],[f13])).
% 1.14/1.14 thf(f13,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : (((!! @ b @ (^[Y0 : b]: ((x = Y0) => (y = (X1 @ Y0))))) = $false) | (((y = (sK1 @ X1)) => (?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))))) = $false)) )),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.14/1.14 thf(f12,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((((^[Y0 : a]: ((y = Y0) => (?? @ b @ (^[Y1 : b]: ((= @ Y1) = (^[Y2 : b]: ((x = Y2) & ((X1 @ Y2) = Y0)))))))) @ (sK1 @ X1)) = $false) | ((!! @ b @ (^[Y0 : b]: ((x = Y0) => (y = (X1 @ Y0))))) = $false)) )),
% 1.14/1.14 inference(sigma_clausification,[status(thm)],[f11])).
% 1.14/1.14 thf(f11,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : (((!! @ a @ (^[Y0 : a]: ((y = Y0) => (?? @ b @ (^[Y1 : b]: ((= @ Y1) = (^[Y2 : b]: ((x = Y2) & ((X1 @ Y2) = Y0))))))))) = $false) | ((!! @ b @ (^[Y0 : b]: ((x = Y0) => (y = (X1 @ Y0))))) = $false)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.14/1.14 thf(f10,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((((!! @ a @ (^[Y0 : a]: ((y = Y0) => (?? @ b @ (^[Y1 : b]: ((= @ Y1) = (^[Y2 : b]: ((x = Y2) & ((X1 @ Y2) = Y0))))))))) & (!! @ b @ (^[Y0 : b]: ((x = Y0) => (y = (X1 @ Y0)))))) = $false)) )),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.14/1.14 thf(f9,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((((^[Y0 : b > a]: ((!! @ a @ (^[Y1 : a]: ((y = Y1) => (?? @ b @ (^[Y2 : b]: ((= @ Y2) = (^[Y3 : b]: ((x = Y3) & ((Y0 @ Y3) = Y1))))))))) & (!! @ b @ (^[Y1 : b]: ((x = Y1) => (y = (Y0 @ Y1))))))) @ X1) = $false)) )),
% 1.14/1.14 inference(pi_clausification,[status(thm)],[f8])).
% 1.14/1.14 thf(f8,plain,(
% 1.14/1.14 ((?? @ (b > a) @ (^[Y0 : b > a]: ((!! @ a @ (^[Y1 : a]: ((y = Y1) => (?? @ b @ (^[Y2 : b]: ((= @ Y2) = (^[Y3 : b]: ((x = Y3) & ((Y0 @ Y3) = Y1))))))))) & (!! @ b @ (^[Y1 : b]: ((x = Y1) => (y = (Y0 @ Y1)))))))) = $false)),
% 1.14/1.14 inference(not_proxy_clausification,[status(thm)],[f7])).
% 1.14/1.14 thf(f7,plain,(
% 1.14/1.14 ((~ (?? @ (b > a) @ (^[Y0 : b > a]: ((!! @ a @ (^[Y1 : a]: ((y = Y1) => (?? @ b @ (^[Y2 : b]: ((= @ Y2) = (^[Y3 : b]: ((x = Y3) & ((Y0 @ Y3) = Y1))))))))) & (!! @ b @ (^[Y1 : b]: ((x = Y1) => (y = (Y0 @ Y1))))))))) = $true)),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.14/1.14 thf(f6,plain,(
% 1.14/1.14 ((~ (?? @ (b > a) @ (^[Y0 : b > a]: ((!! @ a @ (^[Y1 : a]: ((y = Y1) => (?? @ b @ (^[Y2 : b]: (((^[Y3 : b]: ((^[Y4 : b]: (Y3 = Y4)))) @ Y2) = (^[Y3 : b]: ((x = Y3) & ((Y0 @ Y3) = Y1))))))))) & (!! @ b @ (^[Y1 : b]: ((x = Y1) => (y = (Y0 @ Y1))))))))) = $true)),
% 1.14/1.14 inference(cnf_transformation,[status(thm)],[f5])).
% 1.14/1.14 thf(f5,plain,(
% 1.14/1.14 ((~ (?? @ (b > a) @ (^[Y0 : b > a]: ((!! @ a @ (^[Y1 : a]: ((y = Y1) => (?? @ b @ (^[Y2 : b]: (((^[Y3 : b]: ((^[Y4 : b]: (Y3 = Y4)))) @ Y2) = (^[Y3 : b]: ((x = Y3) & ((Y0 @ Y3) = Y1))))))))) & (!! @ b @ (^[Y1 : b]: ((x = Y1) => (y = (Y0 @ Y1))))))))) = $true)),
% 1.14/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.14/1.14 thf(f4,plain,(
% 1.14/1.14 ~? [X0 : b > a] : (! [X1 : b] : ((x = X1) => (y = (X0 @ X1))) & ! [X2 : a] : ((y = X2) => ? [X3 : b] : (((^[X4 : b, X5 : b] : ((X4 = X5))) @ X3) = (^[X6 : b] : (((X0 @ X6) = X2) & (x = X6))))))),
% 1.14/1.14 inference(rectify,[status(thm)],[f2])).
% 1.14/1.14 thf(f2,negated_conjecture,(
% 1.14/1.14 ~? [X0 : b > a] : (! [X1 : b] : ((x = X1) => (y = (X0 @ X1))) & ! [X2 : a] : ((y = X2) => ? [X3 : b] : (((^[X5 : b, X6 : b] : ((X5 = X6))) @ X3) = (^[X4 : b] : (((X0 @ X4) = X2) & (x = X4))))))),
% 1.14/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.14/1.14 thf(f1,conjecture,(
% 1.14/1.14 ? [X0 : b > a] : (! [X1 : b] : ((x = X1) => (y = (X0 @ X1))) & ! [X2 : a] : ((y = X2) => ? [X3 : b] : (((^[X5 : b, X6 : b] : ((X5 = X6))) @ X3) = (^[X4 : b] : (((X0 @ X4) = X2) & (x = X4))))))),
% 1.14/1.14 file('/export/starexec/sandbox2/tmp/tmp.pDArOFEHlp/DTF2THF_27580.p',cX6004_pme)).
% 1.14/1.14 thf(f171,plain,(
% 1.14/1.14 (y != (sK1 @ (^[Y0 : b]: (y))))),
% 1.14/1.14 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.14/1.14 thf(f170,plain,(
% 1.14/1.14 (y != y) | (y != (sK1 @ (^[Y0 : b]: (y))))),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f169])).
% 1.14/1.14 thf(f169,plain,(
% 1.14/1.14 (((^[Y0 : b]: (y)) @ x) != (sK1 @ (^[Y0 : b]: (y)))) | (y != ((^[Y0 : b]: (y)) @ (sK2 @ (^[Y0 : b]: (y)))))),
% 1.14/1.14 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.14/1.14 thf(f168,plain,(
% 1.14/1.14 (y != ((^[Y0 : b]: (y)) @ (sK2 @ (^[Y0 : b]: (y))))) | (x != x) | (((^[Y0 : b]: (y)) @ x) != (sK1 @ (^[Y0 : b]: (y))))),
% 1.14/1.14 inference(duplicate_literal_removal,[status(thm)],[f167])).
% 1.14/1.14 thf(f167,plain,(
% 1.14/1.14 (x != x) | (((^[Y0 : b]: (y)) @ x) != (sK1 @ (^[Y0 : b]: (y)))) | (x != x) | (y != ((^[Y0 : b]: (y)) @ (sK2 @ (^[Y0 : b]: (y)))))),
% 1.14/1.14 inference(superposition,[status(thm)],[f69,f166])).
% 1.14/1.14 thf(f166,plain,(
% 1.14/1.14 (x = (sK5 @ (^[Y0 : b]: (y)) @ x))),
% 1.14/1.14 inference(equality_resolution,[status(thm)],[f161])).
% 1.14/1.14 thf(f161,plain,(
% 1.14/1.14 ( ! [X0 : b] : ((x != X0) | (x = (sK5 @ (^[Y0 : b]: (y)) @ X0))) )),
% 1.14/1.14 inference(equality_factoring,[status(thm)],[f76])).
% 1.14/1.14 thf(f76,plain,(
% 1.14/1.14 ( ! [X0 : b] : (((sK5 @ (^[Y0 : b]: (y)) @ X0) = X0) | (x = (sK5 @ (^[Y0 : b]: (y)) @ X0))) )),
% 1.14/1.14 inference(equality_resolution,[status(thm)],[f64])).
% 1.14/1.14 thf(f64,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((sK5 @ X1 @ X2) = X2) | (x = (sK5 @ X1 @ X2))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 1.14/1.14 thf(f63,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((x = (sK5 @ X1 @ X2)) = $true) | ((sK5 @ X1 @ X2) = X2)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.14/1.14 thf(f61,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : (((sK5 @ X1 @ X2) = X2) | (y != (X1 @ (sK2 @ X1))) | (((x = (sK5 @ X1 @ X2)) & ((X1 @ (sK5 @ X1 @ X2)) = (sK1 @ X1))) = $true)) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f59])).
% 1.14/1.14 thf(f59,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((X2 = (sK5 @ X1 @ X2)) = $true) | (((x = (sK5 @ X1 @ X2)) & ((X1 @ (sK5 @ X1 @ X2)) = (sK1 @ X1))) = $true)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.14/1.14 thf(f58,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (((x = (sK5 @ X1 @ X2)) & ((X1 @ (sK5 @ X1 @ X2)) = (sK1 @ X1))) != (X2 = (sK5 @ X1 @ X2)))) )),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.14/1.14 thf(f57,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((X2 = (sK5 @ X1 @ X2)) != ((^[Y0 : b]: ((x = Y0) & ((X1 @ Y0) = (sK1 @ X1)))) @ (sK5 @ X1 @ X2)))) )),
% 1.14/1.14 inference(negative_extensionality,[status(thm)],[f30])).
% 1.14/1.14 thf(f30,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : (((= @ X2) != (^[Y0 : b]: ((x = Y0) & ((X1 @ Y0) = (sK1 @ X1))))) | (y != (X1 @ (sK2 @ X1)))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.14/1.14 thf(f29,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (((= @ X2) = (^[Y0 : b]: ((x = Y0) & ((X1 @ Y0) = (sK1 @ X1))))) = $false)) )),
% 1.14/1.14 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.14/1.14 thf(f28,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (((^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1)))))) @ X2) = $false)) )),
% 1.14/1.14 inference(pi_clausification,[status(thm)],[f26])).
% 1.14/1.14 thf(f26,plain,(
% 1.14/1.14 ( ! [X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | ((?? @ b @ (^[Y0 : b]: ((= @ Y0) = (^[Y1 : b]: ((x = Y1) & ((X1 @ Y1) = (sK1 @ X1))))))) = $false)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.14/1.14 thf(f69,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : (((X1 @ (sK5 @ X1 @ X2)) != (sK1 @ X1)) | (x != (sK5 @ X1 @ X2)) | ((sK5 @ X1 @ X2) != X2) | (y != (X1 @ (sK2 @ X1)))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 1.14/1.14 thf(f68,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : (((X1 @ (sK5 @ X1 @ X2)) != (sK1 @ X1)) | ($false = (X2 = (sK5 @ X1 @ X2))) | (x != (sK5 @ X1 @ X2)) | (y != (X1 @ (sK2 @ X1)))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f67])).
% 1.14/1.14 thf(f67,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : (((x = (sK5 @ X1 @ X2)) = $false) | ((X1 @ (sK5 @ X1 @ X2)) != (sK1 @ X1)) | ($false = (X2 = (sK5 @ X1 @ X2))) | (y != (X1 @ (sK2 @ X1)))) )),
% 1.14/1.14 inference(equality_proxy_clausification,[status(thm)],[f66])).
% 1.14/1.14 thf(f66,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((((X1 @ (sK5 @ X1 @ X2)) = (sK1 @ X1)) = $false) | ($false = (X2 = (sK5 @ X1 @ X2))) | (y != (X1 @ (sK2 @ X1))) | ((x = (sK5 @ X1 @ X2)) = $false)) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.14/1.14 thf(f60,plain,(
% 1.14/1.14 ( ! [X2 : b,X1 : b > a] : ((y != (X1 @ (sK2 @ X1))) | (((x = (sK5 @ X1 @ X2)) & ((X1 @ (sK5 @ X1 @ X2)) = (sK1 @ X1))) = $false) | ($false = (X2 = (sK5 @ X1 @ X2)))) )),
% 1.14/1.14 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.14/1.14 % SZS output end Proof for DTF2THF_27580
% 1.14/1.14 % (27852)------------------------------
% 1.14/1.14 % (27852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.14 % (27852)Termination reason: Refutation
% 1.14/1.14
% 1.14/1.14 % (27852)Memory used [KB]: 5628
% 1.14/1.14 % (27852)Time elapsed: 0.019 s
% 1.14/1.14 % (27852)Instructions burned: 38 (million)
% 1.14/1.14 % (27852)------------------------------
% 1.14/1.14 % (27852)------------------------------
% 1.14/1.14 % (27789)Success in time 0.097 s
%------------------------------------------------------------------------------