%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV417^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:41:12 AM UTC 2026
% Result : Theorem 1.66s 1.47s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 336 ( 79 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 457 ( 8 ~; 9 |; 91 &; 266 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 126 ^; 29 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: ( a > $o ) > $o ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a > $o ).
thf(func_def_18,type,
sK3: a > $o ).
thf(func_def_19,type,
sK4: a > $o ).
thf(func_def_20,type,
sK5: a ).
thf(f49,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
$false != $false,
inference(superposition,[status(thm)],[f34,f47]) ).
thf(f47,plain,
! [X0: a] :
( $false
= ( sK2 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: a] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: a] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f29,f41]) ).
thf(f41,plain,
! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( $false
= ( sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: a] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f26,f37]) ).
thf(f37,plain,
! [X1: a] :
( ( $false
= ( sK4 @ X1 ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a] :
( $false
= ( ( sK3 @ X1 )
& ( sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( cP
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( cP
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( cP
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( ( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( cP
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) )
=> ( ( cP
@ ^ [Y0: a] : $false )
& ( ( ^ [Y0: a] : $false )
= sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > $o] :
( ( ( ( ^ [Y1: a] :
( ( sK3 @ Y1 )
& ( Y0 @ Y1 ) ) )
= ( ^ [Y1: a] : $false ) )
& ( cP
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
& ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK3 @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: a] : $false )
& ( ( ^ [Y1: a] : $false )
= sK2 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( ( ^ [Y1: a] :
( ( sK3 @ Y1 )
& ( Y0 @ Y1 ) ) )
= ( ^ [Y1: a] : $false ) )
& ( cP
@ ^ [Y1: a] :
( ( sK3 @ Y1 )
& ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 )
=> ( sK3 @ Y1 ) ) ) )
=> ( ( cP
@ ^ [Y1: a] : $false )
& ( ( ^ [Y1: a] : $false )
= sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ( ^ [Y2: a] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
= ( ^ [Y2: a] : $false ) )
& ( cP
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0 @ Y2 ) ) ) )
=> ( ( cP
@ ^ [Y2: a] : $false )
& ( ( ^ [Y2: a] : $false )
= sK2 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( ( ^ [Y2: a] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
= ( ^ [Y2: a] : $false ) )
& ( cP
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 )
=> ( Y0 @ Y2 ) ) ) )
=> ( ( cP
@ ^ [Y2: a] : $false )
& ( ( ^ [Y2: a] : $false )
= sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( $false
= ( ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ( ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
= ( ^ [Y3: a] : $false ) )
& ( cP
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( ( cP
@ ^ [Y3: a] : $false )
& ( ( ^ [Y3: a] : $false )
= Y0 ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ( ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
= ( ^ [Y3: a] : $false ) )
& ( cP
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( ( cP
@ ^ [Y3: a] : $false )
& ( ( ^ [Y3: a] : $false )
= Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ( ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
= ( ^ [Y3: a] : $false ) )
& ( cP
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( ( cP
@ ^ [Y3: a] : $false )
& ( ( ^ [Y3: a] : $false )
= Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( ( ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
= ( ^ [Y3: a] : $false ) )
& ( cP
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 )
=> ( Y1 @ Y3 ) ) ) )
=> ( ( cP
@ ^ [Y3: a] : $false )
& ( ( ^ [Y3: a] : $false )
= Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) )
& ( cP
@ ^ [X5: a] :
( ( X0 @ X5 )
& ( X1 @ X5 ) ) )
& ( ( ^ [X6: a] :
( ( X0 @ X6 )
& ( X1 @ X6 ) ) )
= ( ^ [X7: a] : $false ) ) )
=> ( ( ( ^ [X8: a] : $false )
= X2 )
& ( cP
@ ^ [X9: a] : $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( cP
@ ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) )
=> ( ( ( ^ [X3: a] : $false )
= X0 )
& ( cP
@ ^ [X3: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( cP
@ ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
& ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) )
= ( ^ [X3: a] : $false ) ) )
=> ( ( ( ^ [X3: a] : $false )
= X0 )
& ( cP
@ ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GPyEAV34AC/DTF2THF_15675.p',cTHM502_pme) ).
thf(f26,plain,
! [X1: a] :
( ( $true
= ( sK4 @ X1 ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: a] :
( $true
= ( ( sK2 @ X1 )
=> ( sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK4 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f29,plain,
! [X1: a] :
( ( $true
= ( sK3 @ X1 ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: a] :
( $true
= ( ( sK2 @ X1 )
=> ( sK3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( sK3 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f34,plain,
( $false
!= ( sK2 @ sK5 ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ^ [Y0: a] : $false
@ sK5 )
!= ( sK2 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f32]) ).
thf(f32,plain,
( sK2
!= ( ^ [Y0: a] : $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
= ( ( ^ [Y0: a] : $false )
= sK2 ) ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( $true
& ( ( ^ [Y0: a] : $false )
= sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f14,f23]) ).
thf(f23,plain,
( $true
= ( cP
@ ^ [Y0: a] : $false ) ),
inference(forward_demodulation,[status(thm)],[f20,f22]) ).
thf(f20,plain,
( $true
= ( cP
@ ^ [Y0: a] :
( ( sK3 @ Y0 )
& ( sK4 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f14,plain,
( $false
= ( ( cP
@ ^ [Y0: a] : $false )
& ( ( ^ [Y0: a] : $false )
= sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV417^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n021.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:46:24 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SEV417^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.49 % Domain : Set Theory
% 0.32/0.49 % Problem : TPS problem from SETS-THMS
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Bro09]
% 0.32/0.49 % Names : tps_0953 [Bro09]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.27 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, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.32/0.49 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.32/0.49 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 5 ( 7 avg)
% 0.32/0.49 % Number of connectives : 19 ( 0 ~; 0 |; 6 &; 10 @)
% 0.32/0.49 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 12 ( 12 avg)
% 0.32/0.49 % Number of types : 2 ( 1 usr)
% 0.32/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.32/0.49 % Number of variables : 10 ( 5 ^; 5 !; 0 ?; 10 :)
% 0.32/0.49 % SPC : TH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(a_type,type,
% 0.32/0.49 a: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(cP,type,
% 0.32/0.49 cP: ( a > $o ) > $o ).
% 0.32/0.49
% 0.32/0.49 thf(cTHM502_pme,conjecture,
% 0.32/0.49 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.32/0.49 ( ( ! [Xx: a] :
% 0.32/0.49 ( ( X @ Xx )
% 0.32/0.49 => ( Y @ Xx ) )
% 0.32/0.49 & ! [Xx: a] :
% 0.32/0.49 ( ( X @ Xx )
% 0.32/0.49 => ( Z @ Xx ) )
% 0.32/0.49 & ( ( ^ [Xx: a] :
% 0.32/0.49 ( ( Y @ Xx )
% 0.32/0.49 & ( Z @ Xx ) ) )
% 0.32/0.49 = ( ^ [Xx: a] : $false ) )
% 0.32/0.49 & ( cP
% 0.32/0.49 @ ^ [Xx: a] :
% 0.32/0.49 ( ( Y @ Xx )
% 0.32/0.49 & ( Z @ Xx ) ) ) )
% 0.32/0.49 => ( ( X
% 0.32/0.49 = ( ^ [Xx: a] : $false ) )
% 0.32/0.49 & ( cP
% 0.32/0.49 @ ^ [Xx: a] : $false ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 12:46:25 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GPyEAV34AC/DTF2DTF15675.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(a_type,type,
% 1.66/1.43 a: $tType ).
% 1.66/1.43
% 1.66/1.43 thf(cP,type,
% 1.66/1.43 cP: ( a > $o ) > $o ).
% 1.66/1.43
% 1.66/1.43 thf(cTHM502_pme,conjecture,
% 1.66/1.43 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.66/1.43 ( ( ! [Xx: a] :
% 1.66/1.43 ( ( X @ Xx )
% 1.66/1.43 => ( Y @ Xx ) )
% 1.66/1.43 & ! [Xx: a] :
% 1.66/1.43 ( ( X @ Xx )
% 1.66/1.43 => ( Z @ Xx ) )
% 1.66/1.43 & ( ( ^ [Xx: a] :
% 1.66/1.43 ( ( Y @ Xx )
% 1.66/1.43 & ( Z @ Xx ) ) )
% 1.66/1.43 = ( ^ [Xx: a] : $false ) )
% 1.66/1.43 & ( cP
% 1.66/1.43 @ ^ [Xx: a] :
% 1.66/1.43 ( ( Y @ Xx )
% 1.66/1.43 & ( Z @ Xx ) ) ) )
% 1.66/1.43 => ( ( X
% 1.66/1.43 = ( ^ [Xx: a] : $false ) )
% 1.66/1.43 & ( cP
% 1.66/1.43 @ ^ [Xx: a] : $false ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (15802)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_15675 for (3000ds/4Mi)
% 1.66/1.45 % (15801)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15675 for (3000ds/183Mi)
% 1.66/1.45 % (15803)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_15675 for (3000ds/27Mi)
% 1.66/1.45 % (15806)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_15675 for (3000ds/275Mi)
% 1.66/1.45 % (15804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15675 for (3000ds/2Mi)
% 1.66/1.45 % (15805)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_15675 for (3000ds/2Mi)
% 1.66/1.45 % (15807)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15675 for (3000ds/18Mi)
% 1.66/1.45 % (15804)Instruction limit reached!
% 1.66/1.45 % (15804)------------------------------
% 1.66/1.45 % (15804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15804)Termination reason: Unknown
% 1.66/1.45 % (15804)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (15805)Instruction limit reached!
% 1.66/1.45 % (15805)------------------------------
% 1.66/1.45 % (15805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15805)Termination reason: Unknown
% 1.66/1.45 % (15805)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (15805)Memory used [KB]: 5500
% 1.66/1.45 % (15805)Time elapsed: 0.003 s
% 1.66/1.45 % (15805)Instructions burned: 3 (million)
% 1.66/1.45 % (15805)------------------------------
% 1.66/1.45 % (15805)------------------------------
% 1.66/1.45 % (15804)Memory used [KB]: 5500
% 1.66/1.45 % (15804)Time elapsed: 0.003 s
% 1.66/1.45 % (15804)Instructions burned: 2 (million)
% 1.66/1.45 % (15804)------------------------------
% 1.66/1.45 % (15804)------------------------------
% 1.66/1.45 % (15803)Refutation not found, incomplete strategy
% 1.66/1.45 % (15803)------------------------------
% 1.66/1.45 % (15803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15803)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (15803)Memory used [KB]: 5500
% 1.66/1.45 % (15803)Time elapsed: 0.003 s
% 1.66/1.45 % (15803)Instructions burned: 2 (million)
% 1.66/1.45 % (15803)------------------------------
% 1.66/1.45 % (15803)------------------------------
% 1.66/1.45 % (15802)Instruction limit reached!
% 1.66/1.45 % (15802)------------------------------
% 1.66/1.45 % (15802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15802)Termination reason: Unknown
% 1.66/1.45 % (15802)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (15802)Memory used [KB]: 5500
% 1.66/1.45 % (15802)Time elapsed: 0.004 s
% 1.66/1.45 % (15802)Instructions burned: 4 (million)
% 1.66/1.45 % (15802)------------------------------
% 1.66/1.45 % (15802)------------------------------
% 1.66/1.45 % (15806)Refutation not found, incomplete strategy
% 1.66/1.45 % (15806)------------------------------
% 1.66/1.45 % (15806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15806)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (15806)Memory used [KB]: 5500
% 1.66/1.45 % (15806)Time elapsed: 0.004 s
% 1.66/1.45 % (15806)Instructions burned: 4 (million)
% 1.66/1.45 % (15806)------------------------------
% 1.66/1.45 % (15806)------------------------------
% 1.66/1.45 % (15801)Refutation not found, incomplete strategy
% 1.66/1.45 % (15801)------------------------------
% 1.66/1.45 % (15801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15801)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (15801)Memory used [KB]: 5500
% 1.66/1.45 % (15801)Time elapsed: 0.005 s
% 1.66/1.45 % (15801)Instructions burned: 5 (million)
% 1.66/1.45 % (15801)------------------------------
% 1.66/1.45 % (15801)------------------------------
% 1.66/1.45 % (15807)Refutation not found, incomplete strategy
% 1.66/1.45 % (15807)------------------------------
% 1.66/1.45 % (15807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (15807)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (15807)Memory used [KB]: 5500
% 1.66/1.45 % (15807)Time elapsed: 0.005 s
% 1.66/1.45 % (15807)Instructions burned: 5 (million)
% 1.66/1.45 % (15807)------------------------------
% 1.66/1.45 % (15807)------------------------------
% 1.66/1.46 % (15808)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15675 for (2999ds/3Mi)
% 1.66/1.46 % (15809)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_15675 for (2999ds/37Mi)
% 1.66/1.46 % (15810)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_15675 for (2999ds/15Mi)
% 1.66/1.46 % (15811)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_15675 for (2999ds/3Mi)
% 1.66/1.46 % (15812)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_15675 for (2999ds/1041Mi)
% 1.66/1.46 % (15813)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15675 for (2999ds/7Mi)
% 1.66/1.47 % (15808)Refutation not found, incomplete strategy
% 1.66/1.47 % (15808)------------------------------
% 1.66/1.47 % (15808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15808)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.47
% 1.66/1.47
% 1.66/1.47 % (15808)Memory used [KB]: 5500
% 1.66/1.47 % (15808)Time elapsed: 0.003 s
% 1.66/1.47 % (15808)Instructions burned: 2 (million)
% 1.66/1.47 % (15808)------------------------------
% 1.66/1.47 % (15808)------------------------------
% 1.66/1.47 % (15814)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15675 for (2999ds/16Mi)
% 1.66/1.47 % (15811)Refutation not found, incomplete strategy
% 1.66/1.47 % (15811)------------------------------
% 1.66/1.47 % (15811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15811)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.47
% 1.66/1.47
% 1.66/1.47 % (15811)Memory used [KB]: 5500
% 1.66/1.47 % (15811)Time elapsed: 0.003 s
% 1.66/1.47 % (15811)Instructions burned: 2 (million)
% 1.66/1.47 % (15811)------------------------------
% 1.66/1.47 % (15811)------------------------------
% 1.66/1.47 % (15813)Refutation not found, incomplete strategy
% 1.66/1.47 % (15813)------------------------------
% 1.66/1.47 % (15813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15813)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.47
% 1.66/1.47
% 1.66/1.47 % (15813)Memory used [KB]: 1023
% 1.66/1.47 % (15813)Time elapsed: 0.003 s
% 1.66/1.47 % (15813)Instructions burned: 3 (million)
% 1.66/1.47 % (15813)------------------------------
% 1.66/1.47 % (15813)------------------------------
% 1.66/1.47 % (15809)First to succeed.
% 1.66/1.47 % (15810)Refutation not found, incomplete strategy
% 1.66/1.47 % (15810)------------------------------
% 1.66/1.47 % (15810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15810)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.47
% 1.66/1.47
% 1.66/1.47 % (15810)Memory used [KB]: 5628
% 1.66/1.47 % (15810)Time elapsed: 0.006 s
% 1.66/1.47 % (15810)Instructions burned: 7 (million)
% 1.66/1.47 % (15810)------------------------------
% 1.66/1.47 % (15810)------------------------------
% 1.66/1.47 % (15809)Refutation found. Thanks to Tanya!
% 1.66/1.47 % SZS status Theorem for DTF2THF_15675
% 1.66/1.47 % SZS output start Proof for DTF2THF_15675
% 1.66/1.47 thf(type_def_5, type, a: $tType).
% 1.66/1.47 thf(func_def_0, type, a: $tType).
% 1.66/1.47 thf(func_def_1, type, cP: (a > $o) > $o).
% 1.66/1.47 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.47 thf(func_def_17, type, sK2: a > $o).
% 1.66/1.47 thf(func_def_18, type, sK3: a > $o).
% 1.66/1.47 thf(func_def_19, type, sK4: a > $o).
% 1.66/1.47 thf(func_def_20, type, sK5: a).
% 1.66/1.47 thf(f49,plain,(
% 1.66/1.47 $false),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.66/1.47 thf(f48,plain,(
% 1.66/1.47 ($false != $false)),
% 1.66/1.47 inference(superposition,[status(thm)],[f34,f47])).
% 1.66/1.47 thf(f47,plain,(
% 1.66/1.47 ( ! [X0 : a] : (($false = (sK2 @ X0))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.66/1.47 thf(f46,plain,(
% 1.66/1.47 ( ! [X0 : a] : (($false = (sK2 @ X0)) | ($true = $false)) )),
% 1.66/1.47 inference(duplicate_literal_removal,[status(thm)],[f43])).
% 1.66/1.47 thf(f43,plain,(
% 1.66/1.47 ( ! [X0 : a] : (($false = (sK2 @ X0)) | ($true = $false) | ($false = (sK2 @ X0))) )),
% 1.66/1.47 inference(superposition,[status(thm)],[f29,f41])).
% 1.66/1.47 thf(f41,plain,(
% 1.66/1.47 ( ! [X0 : a] : (($false = (sK3 @ X0)) | ($false = (sK2 @ X0))) )),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.66/1.47 thf(f39,plain,(
% 1.66/1.47 ( ! [X0 : a] : (($true = $false) | ($false = (sK2 @ X0)) | ($false = (sK3 @ X0))) )),
% 1.66/1.47 inference(superposition,[status(thm)],[f26,f37])).
% 1.66/1.47 thf(f37,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($false = (sK4 @ X1)) | ($false = (sK3 @ X1))) )),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.66/1.47 thf(f36,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($false = ((sK3 @ X1) & (sK4 @ X1)))) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.66/1.47 thf(f35,plain,(
% 1.66/1.47 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) @ X1))) )),
% 1.66/1.47 inference(argument_congruence,[status(thm)],[f22])).
% 1.66/1.47 thf(f22,plain,(
% 1.66/1.47 ((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false)))),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.66/1.47 thf(f21,plain,(
% 1.66/1.47 ($true = ((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.66/1.47 thf(f19,plain,(
% 1.66/1.47 ($true = (((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false))) & (cP @ (^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.66/1.47 thf(f17,plain,(
% 1.66/1.47 ($true = ((((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false))) & (cP @ (^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.66/1.47 thf(f15,plain,(
% 1.66/1.47 ($true = (((((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false))) & (cP @ (^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.66/1.47 thf(f13,plain,(
% 1.66/1.47 ($false = ((((((^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))) = (^[Y0 : a]: ($false))) & (cP @ (^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))))) => ((cP @ (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) = sK2))))),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.66/1.47 thf(f12,plain,(
% 1.66/1.47 ($false = ((^[Y0 : a > $o]: ((((((^[Y1 : a]: ((sK3 @ Y1) & (Y0 @ Y1))) = (^[Y1 : a]: ($false))) & (cP @ (^[Y1 : a]: ((sK3 @ Y1) & (Y0 @ Y1))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (sK3 @ Y1))))) => ((cP @ (^[Y1 : a]: ($false))) & ((^[Y1 : a]: ($false)) = sK2)))) @ sK4))),
% 1.66/1.47 inference(sigma_clausification,[status(thm)],[f11])).
% 1.66/1.47 thf(f11,plain,(
% 1.66/1.47 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((((((^[Y1 : a]: ((sK3 @ Y1) & (Y0 @ Y1))) = (^[Y1 : a]: ($false))) & (cP @ (^[Y1 : a]: ((sK3 @ Y1) & (Y0 @ Y1))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (Y0 @ Y1))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1) => (sK3 @ Y1))))) => ((cP @ (^[Y1 : a]: ($false))) & ((^[Y1 : a]: ($false)) = sK2))))))),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.66/1.47 thf(f10,plain,(
% 1.66/1.47 ($false = ((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((((^[Y2 : a]: ((Y0 @ Y2) & (Y1 @ Y2))) = (^[Y2 : a]: ($false))) & (cP @ (^[Y2 : a]: ((Y0 @ Y2) & (Y1 @ Y2))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y0 @ Y2))))) => ((cP @ (^[Y2 : a]: ($false))) & ((^[Y2 : a]: ($false)) = sK2)))))) @ sK3))),
% 1.66/1.47 inference(sigma_clausification,[status(thm)],[f9])).
% 1.66/1.47 thf(f9,plain,(
% 1.66/1.47 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((((((^[Y2 : a]: ((Y0 @ Y2) & (Y1 @ Y2))) = (^[Y2 : a]: ($false))) & (cP @ (^[Y2 : a]: ((Y0 @ Y2) & (Y1 @ Y2))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y1 @ Y2))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2) => (Y0 @ Y2))))) => ((cP @ (^[Y2 : a]: ($false))) & ((^[Y2 : a]: ($false)) = sK2))))))))),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.66/1.47 thf(f8,plain,(
% 1.66/1.47 ($false = ((^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((((^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))) = (^[Y3 : a]: ($false))) & (cP @ (^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) => ((cP @ (^[Y3 : a]: ($false))) & ((^[Y3 : a]: ($false)) = Y0)))))))) @ sK2))),
% 1.66/1.47 inference(sigma_clausification,[status(thm)],[f7])).
% 1.66/1.47 thf(f7,plain,(
% 1.66/1.47 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((((^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))) = (^[Y3 : a]: ($false))) & (cP @ (^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) => ((cP @ (^[Y3 : a]: ($false))) & ((^[Y3 : a]: ($false)) = Y0))))))))))),
% 1.66/1.47 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.66/1.47 thf(f6,plain,(
% 1.66/1.47 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((((^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))) = (^[Y3 : a]: ($false))) & (cP @ (^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) => ((cP @ (^[Y3 : a]: ($false))) & ((^[Y3 : a]: ($false)) = Y0)))))))))))),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.47 thf(f5,plain,(
% 1.66/1.47 ($true = (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((((((^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))) = (^[Y3 : a]: ($false))) & (cP @ (^[Y3 : a]: ((Y1 @ Y3) & (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y2 @ Y3))))) & (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ Y3))))) => ((cP @ (^[Y3 : a]: ($false))) & ((^[Y3 : a]: ($false)) = Y0)))))))))))),
% 1.66/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.47 thf(f4,plain,(
% 1.66/1.47 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X1 @ X3)) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4)) & (cP @ (^[X5 : a] : ((X0 @ X5) & (X1 @ X5)))) & ((^[X6 : a] : ((X0 @ X6) & (X1 @ X6))) = (^[X7 : a] : ($false)))) => (((^[X8 : a] : ($false)) = X2) & (cP @ (^[X9 : a] : ($false)))))),
% 1.66/1.47 inference(rectify,[status(thm)],[f2])).
% 1.66/1.47 thf(f2,negated_conjecture,(
% 1.66/1.47 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & (cP @ (^[X3 : a] : ((X1 @ X3) & (X2 @ X3)))) & ((^[X3 : a] : ((X1 @ X3) & (X2 @ X3))) = (^[X3 : a] : ($false)))) => (((^[X3 : a] : ($false)) = X0) & (cP @ (^[X3 : a] : ($false)))))),
% 1.66/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.47 thf(f1,conjecture,(
% 1.66/1.47 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & (cP @ (^[X3 : a] : ((X1 @ X3) & (X2 @ X3)))) & ((^[X3 : a] : ((X1 @ X3) & (X2 @ X3))) = (^[X3 : a] : ($false)))) => (((^[X3 : a] : ($false)) = X0) & (cP @ (^[X3 : a] : ($false)))))),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.GPyEAV34AC/DTF2THF_15675.p',cTHM502_pme)).
% 1.66/1.47 thf(f26,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = (sK4 @ X1)) | ((sK2 @ X1) = $false)) )),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.66/1.47 thf(f25,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = ((sK2 @ X1) => (sK4 @ X1)))) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.66/1.47 thf(f24,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0))) @ X1))) )),
% 1.66/1.47 inference(pi_clausification,[status(thm)],[f18])).
% 1.66/1.47 thf(f18,plain,(
% 1.66/1.47 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK4 @ Y0)))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.66/1.47 thf(f29,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = (sK3 @ X1)) | ((sK2 @ X1) = $false)) )),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.66/1.47 thf(f28,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = ((sK2 @ X1) => (sK3 @ X1)))) )),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.66/1.47 thf(f27,plain,(
% 1.66/1.47 ( ! [X1 : a] : (($true = ((^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0))) @ X1))) )),
% 1.66/1.47 inference(pi_clausification,[status(thm)],[f16])).
% 1.66/1.47 thf(f16,plain,(
% 1.66/1.47 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (sK3 @ Y0)))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.66/1.47 thf(f34,plain,(
% 1.66/1.47 ($false != (sK2 @ sK5))),
% 1.66/1.47 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.66/1.47 thf(f33,plain,(
% 1.66/1.47 (((^[Y0 : a]: ($false)) @ sK5) != (sK2 @ sK5))),
% 1.66/1.47 inference(negative_extensionality,[status(thm)],[f32])).
% 1.66/1.47 thf(f32,plain,(
% 1.66/1.47 (sK2 != (^[Y0 : a]: ($false)))),
% 1.66/1.47 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.66/1.47 thf(f31,plain,(
% 1.66/1.47 ($false = ((^[Y0 : a]: ($false)) = sK2))),
% 1.66/1.47 inference(boolean_simplification,[status(thm)],[f30])).
% 1.66/1.47 thf(f30,plain,(
% 1.66/1.47 ($false = ($true & ((^[Y0 : a]: ($false)) = sK2)))),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f14,f23])).
% 1.66/1.47 thf(f23,plain,(
% 1.66/1.47 ($true = (cP @ (^[Y0 : a]: ($false))))),
% 1.66/1.47 inference(forward_demodulation,[status(thm)],[f20,f22])).
% 1.66/1.47 thf(f20,plain,(
% 1.66/1.47 ($true = (cP @ (^[Y0 : a]: ((sK3 @ Y0) & (sK4 @ Y0)))))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.66/1.47 thf(f14,plain,(
% 1.66/1.47 ($false = ((cP @ (^[Y0 : a]: ($false))) & ((^[Y0 : a]: ($false)) = sK2)))),
% 1.66/1.47 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.66/1.47 % SZS output end Proof for DTF2THF_15675
% 1.66/1.47 % (15809)------------------------------
% 1.66/1.47 % (15809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15809)Termination reason: Refutation
% 1.66/1.47
% 1.66/1.47 % (15809)Memory used [KB]: 5500
% 1.66/1.47 % (15809)Time elapsed: 0.007 s
% 1.66/1.47 % (15809)Instructions burned: 6 (million)
% 1.66/1.47 % (15809)------------------------------
% 1.66/1.47 % (15809)------------------------------
% 1.66/1.47 % (15800)Success in time 0.035 s
%------------------------------------------------------------------------------