%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM817^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:24:50 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 82 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 315 ( 40 ~; 22 |; 21 &; 184 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 36 ^; 59 !; 4 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
cEVEN1: $i > $o ).
thf(func_def_3,type,
cODD1: $i > $o ).
thf(func_def_15,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_16,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f371,plain,
$false,
inference(equality_resolution,[status(thm)],[f370]) ).
thf(f370,plain,
! [X0: $i] : ( c0 != X0 ),
inference(subsumption_resolution,[status(thm)],[f369,f16]) ).
thf(f16,plain,
! [X3: $i] :
( c0
!= ( cS @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( ( cS @ X1 )
!= ( cS @ X0 ) )
| ( X0 = X1 ) )
& ! [X2: $i] :
( $true
!= ( cODD1 @ X2 ) )
& ! [X3: $i] :
( c0
!= ( cS @ X3 ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
!= ( cS @ X1 ) )
| ( X1 = X2 ) )
& ! [X3: $i] :
( $true
!= ( cODD1 @ X3 ) )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X3: $i] :
( $true
!= ( cODD1 @ X3 ) )
& ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
!= ( cS @ X1 ) )
| ( X1 = X2 ) )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
= ( cS @ X1 ) )
=> ( X1 = X2 ) )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) )
=> ? [X3: $i] :
( $true
= ( cODD1 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( ! [X0: $i] :
( c0
!= ( cS @ X0 ) )
& ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
= ( cS @ X1 ) )
=> ( X1 = X2 ) ) )
=> ? [X3: $i] : ( cODD1 @ X3 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( ( ! [X3: $i] :
( c0
!= ( cS @ X3 ) )
& ! [X5: $i,X4: $i] :
( ( ( cS @ X4 )
= ( cS @ X5 ) )
=> ( X4 = X5 ) ) )
=> ? [X0: $i] : ( cODD1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( ( ! [X3: $i] :
( c0
!= ( cS @ X3 ) )
& ! [X5: $i,X4: $i] :
( ( ( cS @ X4 )
= ( cS @ X5 ) )
=> ( X4 = X5 ) ) )
=> ? [X0: $i] : ( cODD1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cTHM405) ).
thf(f369,plain,
! [X0: $i] :
( ( c0 != X0 )
| ( c0
= ( cS @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f352]) ).
thf(f352,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X1 )
!= X0 )
| ( c0 != X1 )
| ( c0 = X0 ) ),
inference(superposition,[status(thm)],[f16,f219]) ).
thf(f219,plain,
! [X0: $i,X1: $i] :
( ( ( cS
@ ( sK1
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X1 )
| ( c0 = X0 )
| ( ( cS @ X1 )
!= X0 ) ),
inference(superposition,[status(thm)],[f18,f170]) ).
thf(f170,plain,
! [X0: $i] :
( ( ( cS
@ ( cS
@ ( sK1
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 )
| ( c0 = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X0: $i] :
( ( ( cS
@ ( cS
@ ( sK1
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $true
= ( X0 = c0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: $i] :
( ( ( cS
@ ( cS
@ ( sK1
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $false
= ( X0 != c0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: $i] :
( ( ( cS
@ ( cS
@ ( sK1
@ ^ [Y0: $i] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $false
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ c0 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ ( cS @ ( cS @ ( sK1 @ X3 ) ) ) )
= $false )
| ( ( X3 @ c0 )
= $false )
| ( ( X3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ X2 )
= $true )
| ( ( X3 @ c0 )
= $false )
| ( $false
= ( ( X3 @ ( sK1 @ X3 ) )
=> ( X3 @ ( cS @ ( cS @ ( sK1 @ X3 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X3 @ Y0 )
=> ( X3 @ ( cS @ ( cS @ Y0 ) ) ) )
@ ( sK1 @ X3 ) ) )
| ( ( X3 @ c0 )
= $false )
| ( ( X3 @ X2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ c0 )
= $false )
| ( ( X3 @ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
=> ( X3 @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ X2 )
= $true )
| ( $false
= ( ( X3 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
=> ( X3 @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i > $o] :
( ( ( ( X3 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
=> ( X3 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
=> ( X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i] :
( $true
!= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i] :
( $true
!= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
@ X2 ) ),
inference(definition_unfolding,[status(thm)],[f17,f20]) ).
thf(f20,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f19]) ).
thf(f19,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cEVEN1_def) ).
thf(f15,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cODD1_def) ).
thf(f17,plain,
! [X2: $i] :
( $true
!= ( cODD1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X1 )
!= ( cS @ X0 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM817^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:15:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : NUM817^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.29/0.47 % Domain : Number Theory (Induction on naturals)
% 0.29/0.47 % Problem : TPS problem from IND-THMS
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0823 [Bro09]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 1.00 v5.2.0
% 0.29/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.29/0.47 % Number of atoms : 9 ( 5 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.29/0.47 % Number of connectives : 19 ( 2 ~; 0 |; 2 &; 11 @)
% 0.29/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 6 ( 3 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 8 ( 2 ^; 5 !; 1 ?; 8 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % :
% 0.29/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(c0_type,type,
% 0.29/0.47 c0: $i ).
% 0.29/0.47
% 0.29/0.47 thf(cS_type,type,
% 0.29/0.47 cS: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(cEVEN1_type,type,
% 0.29/0.47 cEVEN1: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cODD1_type,type,
% 0.29/0.47 cODD1: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(cEVEN1_def,definition,
% 0.29/0.47 ( cEVEN1
% 0.29/0.47 = ( ^ [Xn: $i] :
% 0.29/0.47 ! [Xp: $i > $o] :
% 0.29/0.47 ( ( ( Xp @ c0 )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( Xp @ Xx )
% 0.29/0.47 => ( Xp @ ( cS @ ( cS @ Xx ) ) ) ) )
% 0.29/0.47 => ( Xp @ Xn ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cODD1_def,definition,
% 0.29/0.47 ( cODD1
% 0.29/0.47 = ( ^ [Xn: $i] :
% 0.29/0.47 ~ ( cEVEN1 @ Xn ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cTHM405,conjecture,
% 0.29/0.47 ( ( ! [Xu: $i] :
% 0.29/0.47 ( ( cS @ Xu )
% 0.29/0.47 != c0 )
% 0.29/0.47 & ! [Xv: $i,Xw: $i] :
% 0.29/0.47 ( ( ( cS @ Xv )
% 0.29/0.47 = ( cS @ Xw ) )
% 0.29/0.47 => ( Xv = Xw ) ) )
% 0.29/0.47 => ? [Xn: $i] : ( cODD1 @ Xn ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 11:15:43 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2DTF30729.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(c0_type,type,
% 1.47/1.28 c0: $i ).
% 1.47/1.28
% 1.47/1.28 thf(cS_type,type,
% 1.47/1.28 cS: $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(cEVEN1_type,type,
% 1.47/1.28 cEVEN1: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cODD1_type,type,
% 1.47/1.28 cODD1: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cEVEN1_def,definition,
% 1.47/1.28 ( cEVEN1
% 1.47/1.28 = ( ^ [Xn: $i] :
% 1.47/1.28 ! [Xp: $i > $o] :
% 1.47/1.28 ( ( ( Xp @ c0 )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ( Xp @ Xx )
% 1.47/1.28 => ( Xp @ ( cS @ ( cS @ Xx ) ) ) ) )
% 1.47/1.28 => ( Xp @ Xn ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cODD1_def,definition,
% 1.47/1.28 ( cODD1
% 1.47/1.28 = ( ^ [Xn: $i] :
% 1.47/1.28 ~ ( cEVEN1 @ Xn ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(cTHM405,conjecture,
% 1.47/1.28 ( ( ! [Xu: $i] :
% 1.47/1.28 ( ( cS @ Xu )
% 1.47/1.28 != c0 )
% 1.47/1.28 & ! [Xv: $i,Xw: $i] :
% 1.47/1.28 ( ( ( cS @ Xv )
% 1.47/1.28 = ( cS @ Xw ) )
% 1.47/1.28 => ( Xv = Xw ) ) )
% 1.47/1.28 => ? [Xn: $i] : ( cODD1 @ Xn ) ) ).
% 1.47/1.28 ------------------------
% 1.61/1.30 % (31033)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_30729 for (2999ds/4Mi)
% 1.61/1.30 % (31032)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30729 for (2999ds/183Mi)
% 1.61/1.30 % (31033)Instruction limit reached!
% 1.61/1.30 % (31033)------------------------------
% 1.61/1.30 % (31033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (31033)Termination reason: Unknown
% 1.61/1.30 % (31033)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (31033)Memory used [KB]: 5500
% 1.61/1.30 % (31033)Time elapsed: 0.004 s
% 1.61/1.30 % (31033)Instructions burned: 5 (million)
% 1.61/1.30 % (31033)------------------------------
% 1.61/1.30 % (31033)------------------------------
% 1.61/1.31 % (31035)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30729 for (2999ds/2Mi)
% 1.61/1.31 % (31034)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_30729 for (2999ds/27Mi)
% 1.61/1.31 % (31036)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_30729 for (2999ds/2Mi)
% 1.61/1.31 % (31037)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_30729 for (2999ds/275Mi)
% 1.61/1.31 % (31038)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30729 for (2999ds/18Mi)
% 1.61/1.31 % (31035)Instruction limit reached!
% 1.61/1.31 % (31035)------------------------------
% 1.61/1.31 % (31035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31035)Termination reason: Unknown
% 1.61/1.31 % (31035)Termination phase: Property scanning
% 1.61/1.31
% 1.61/1.31 % (31035)Memory used [KB]: 895
% 1.61/1.31 % (31035)Time elapsed: 0.003 s
% 1.61/1.31 % (31035)Instructions burned: 2 (million)
% 1.61/1.31 % (31035)------------------------------
% 1.61/1.31 % (31035)------------------------------
% 1.61/1.31 % (31036)Instruction limit reached!
% 1.61/1.31 % (31036)------------------------------
% 1.61/1.31 % (31036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31036)Termination reason: Unknown
% 1.61/1.31 % (31036)Termination phase: Property scanning
% 1.61/1.31
% 1.61/1.31 % (31036)Memory used [KB]: 895
% 1.61/1.31 % (31036)Time elapsed: 0.003 s
% 1.61/1.31 % (31036)Instructions burned: 2 (million)
% 1.61/1.31 % (31036)------------------------------
% 1.61/1.31 % (31036)------------------------------
% 1.61/1.31 % (31037)Refutation not found, incomplete strategy
% 1.61/1.31 % (31037)------------------------------
% 1.61/1.31 % (31037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31037)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (31037)Memory used [KB]: 5500
% 1.61/1.31 % (31037)Time elapsed: 0.003 s
% 1.61/1.31 % (31037)Instructions burned: 1 (million)
% 1.61/1.31 % (31037)------------------------------
% 1.61/1.31 % (31037)------------------------------
% 1.61/1.31 % (31034)Refutation not found, incomplete strategy
% 1.61/1.31 % (31034)------------------------------
% 1.61/1.31 % (31034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31034)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (31034)Memory used [KB]: 5500
% 1.61/1.31 % (31034)Time elapsed: 0.005 s
% 1.61/1.31 % (31034)Instructions burned: 4 (million)
% 1.61/1.31 % (31034)------------------------------
% 1.61/1.31 % (31034)------------------------------
% 1.61/1.31 % (31039)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30729 for (2999ds/3Mi)
% 1.61/1.31 % (31039)Refutation not found, incomplete strategy
% 1.61/1.31 % (31039)------------------------------
% 1.61/1.31 % (31039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31039)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (31039)Memory used [KB]: 5500
% 1.61/1.31 % (31039)Time elapsed: 0.002 s
% 1.61/1.31 % (31039)Instructions burned: 2 (million)
% 1.61/1.31 % (31039)------------------------------
% 1.61/1.31 % (31039)------------------------------
% 1.61/1.31 % (31032)First to succeed.
% 1.61/1.31 % (31032)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_30729
% 1.61/1.31 % SZS output start Proof for DTF2THF_30729
% 1.61/1.31 thf(func_def_1, type, cS: $i > $i).
% 1.61/1.31 thf(func_def_2, type, cEVEN1: $i > $o).
% 1.61/1.31 thf(func_def_3, type, cODD1: $i > $o).
% 1.61/1.31 thf(func_def_15, type, sK1: ($i > $o) > $i).
% 1.61/1.31 thf(func_def_16, type, ph2: !>[X0: $tType]:(X0)).
% 1.61/1.31 thf(f371,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(equality_resolution,[status(thm)],[f370])).
% 1.61/1.31 thf(f370,plain,(
% 1.61/1.31 ( ! [X0 : $i] : ((c0 != X0)) )),
% 1.61/1.31 inference(subsumption_resolution,[status(thm)],[f369,f16])).
% 1.61/1.31 thf(f16,plain,(
% 1.61/1.31 ( ! [X3 : $i] : ((c0 != (cS @ X3))) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.31 thf(f14,plain,(
% 1.61/1.31 ! [X0 : $i,X1 : $i] : (((cS @ X1) != (cS @ X0)) | (X0 = X1)) & ! [X2 : $i] : ($true != (cODD1 @ X2)) & ! [X3 : $i] : (c0 != (cS @ X3))),
% 1.61/1.31 inference(rectify,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 ! [X1 : $i,X2 : $i] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) & ! [X3 : $i] : ($true != (cODD1 @ X3)) & ! [X0 : $i] : (c0 != (cS @ X0))),
% 1.61/1.31 inference(flattening,[status(thm)],[f12])).
% 1.61/1.31 thf(f12,plain,(
% 1.61/1.31 ! [X3 : $i] : ($true != (cODD1 @ X3)) & (! [X1 : $i,X2 : $i] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) & ! [X0 : $i] : (c0 != (cS @ X0)))),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 ~((! [X1 : $i,X2 : $i] : (((cS @ X2) = (cS @ X1)) => (X1 = X2)) & ! [X0 : $i] : (c0 != (cS @ X0))) => ? [X3 : $i] : ($true = (cODD1 @ X3)))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 ~((! [X0 : $i] : (c0 != (cS @ X0)) & ! [X1 : $i,X2 : $i] : (((cS @ X2) = (cS @ X1)) => (X1 = X2))) => ? [X3 : $i] : (cODD1 @ X3))),
% 1.61/1.31 inference(rectify,[status(thm)],[f4])).
% 1.61/1.31 thf(f4,negated_conjecture,(
% 1.61/1.31 ~((! [X3 : $i] : (c0 != (cS @ X3)) & ! [X5 : $i,X4 : $i] : (((cS @ X4) = (cS @ X5)) => (X4 = X5))) => ? [X0 : $i] : (cODD1 @ X0))),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.61/1.31 thf(f3,conjecture,(
% 1.61/1.31 (! [X3 : $i] : (c0 != (cS @ X3)) & ! [X5 : $i,X4 : $i] : (((cS @ X4) = (cS @ X5)) => (X4 = X5))) => ? [X0 : $i] : (cODD1 @ X0)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cTHM405)).
% 1.61/1.31 thf(f369,plain,(
% 1.61/1.31 ( ! [X0 : $i] : ((c0 != X0) | (c0 = (cS @ X0))) )),
% 1.61/1.31 inference(equality_resolution,[status(thm)],[f352])).
% 1.61/1.31 thf(f352,plain,(
% 1.61/1.31 ( ! [X0 : $i,X1 : $i] : (((cS @ X1) != X0) | (c0 != X1) | (c0 = X0)) )),
% 1.61/1.31 inference(superposition,[status(thm)],[f16,f219])).
% 1.61/1.31 thf(f219,plain,(
% 1.61/1.31 ( ! [X0 : $i,X1 : $i] : (((cS @ (sK1 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X1) | (c0 = X0) | ((cS @ X1) != X0)) )),
% 1.61/1.31 inference(superposition,[status(thm)],[f18,f170])).
% 1.61/1.31 thf(f170,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | (c0 = X0)) )),
% 1.61/1.31 inference(equality_proxy_clausification,[status(thm)],[f169])).
% 1.61/1.31 thf(f169,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | ($true = (X0 = c0))) )),
% 1.61/1.31 inference(not_proxy_clausification,[status(thm)],[f168])).
% 1.61/1.31 thf(f168,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | ($false = (~ (X0 = c0)))) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.61/1.31 thf(f130,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | ($false = ((^[Y0 : $i]: (~ (X0 = Y0))) @ c0))) )),
% 1.61/1.31 inference(leibniz_equality_elimination,[status(thm)],[f30])).
% 1.61/1.31 thf(f30,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (((X3 @ (cS @ (cS @ (sK1 @ X3)))) = $false) | ((X3 @ c0) = $false) | ((X3 @ X2) = $true)) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.61/1.31 thf(f29,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (((X3 @ X2) = $true) | ((X3 @ c0) = $false) | ($false = ((X3 @ (sK1 @ X3)) => (X3 @ (cS @ (cS @ (sK1 @ X3))))))) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.61/1.31 thf(f28,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (($false = ((^[Y0 : $i]: ((X3 @ Y0) => (X3 @ (cS @ (cS @ Y0))))) @ (sK1 @ X3))) | ((X3 @ c0) = $false) | ((X3 @ X2) = $true)) )),
% 1.61/1.31 inference(sigma_clausification,[status(thm)],[f27])).
% 1.61/1.31 thf(f27,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (((X3 @ c0) = $false) | ((X3 @ X2) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) => (X3 @ (cS @ (cS @ Y0)))))))) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.61/1.31 thf(f26,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (((X3 @ X2) = $true) | ($false = ((X3 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) => (X3 @ (cS @ (cS @ Y0))))))))) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.61/1.31 thf(f25,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : (((((X3 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) => (X3 @ (cS @ (cS @ Y0))))))) => (X3 @ X2)) = $true)) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.61/1.31 thf(f24,plain,(
% 1.61/1.31 ( ! [X2 : $i,X3 : $i > $o] : ((((^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X2))) @ X3) = $true)) )),
% 1.61/1.31 inference(pi_clausification,[status(thm)],[f23])).
% 1.61/1.31 thf(f23,plain,(
% 1.61/1.31 ( ! [X2 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X2)))))) )),
% 1.61/1.31 inference(not_proxy_clausification,[status(thm)],[f22])).
% 1.61/1.31 thf(f22,plain,(
% 1.61/1.31 ( ! [X2 : $i] : (($true != (~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1))))))) => (Y0 @ X2))))))) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.61/1.31 thf(f21,plain,(
% 1.61/1.31 ( ! [X2 : $i] : (($true != ((^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ c0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3))))))) => (Y2 @ Y1))))) @ Y0))) @ X2))) )),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f17,f20])).
% 1.61/1.31 thf(f20,plain,(
% 1.61/1.31 (cODD1 = (^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ c0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3))))))) => (Y2 @ Y1))))) @ Y0))))),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f15,f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2))))))) => (Y1 @ Y0))))))),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.61/1.31 thf(f7,plain,(
% 1.61/1.31 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2))))))) => (Y1 @ Y0))))))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.61/1.31 thf(f6,plain,(
% 1.61/1.31 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2)))) & (X1 @ c0)) => (X1 @ X0)))))),
% 1.61/1.31 inference(rectify,[status(thm)],[f1])).
% 1.61/1.31 thf(f1,axiom,(
% 1.61/1.31 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2)))) & (X1 @ c0)) => (X1 @ X0)))))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cEVEN1_def)).
% 1.61/1.31 thf(f15,plain,(
% 1.61/1.31 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.31 thf(f11,plain,(
% 1.61/1.31 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.61/1.31 thf(f10,plain,(
% 1.61/1.31 (cODD1 = (^[X0 : $i] : (~(cEVEN1 @ X0))))),
% 1.61/1.31 inference(rectify,[status(thm)],[f2])).
% 1.61/1.31 thf(f2,axiom,(
% 1.61/1.31 (cODD1 = (^[X0 : $i] : (~(cEVEN1 @ X0))))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.y280w42KKN/DTF2THF_30729.p',cODD1_def)).
% 1.61/1.31 thf(f17,plain,(
% 1.61/1.31 ( ! [X2 : $i] : (($true != (cODD1 @ X2))) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.31 thf(f18,plain,(
% 1.61/1.31 ( ! [X0 : $i,X1 : $i] : (((cS @ X1) != (cS @ X0)) | (X0 = X1)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.31 % SZS output end Proof for DTF2THF_30729
% 1.61/1.31 % (31032)------------------------------
% 1.61/1.31 % (31032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (31032)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (31032)Memory used [KB]: 5628
% 1.61/1.31 % (31032)Time elapsed: 0.014 s
% 1.61/1.31 % (31032)Instructions burned: 33 (million)
% 1.61/1.31 % (31032)------------------------------
% 1.61/1.31 % (31032)------------------------------
% 1.61/1.31 % (31031)Success in time 0.022 s
%------------------------------------------------------------------------------