%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV282^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:44 AM UTC 2026
% Result : Theorem 1.68s 1.34s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 279 ( 33 ~; 0 |; 30 &; 162 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 125 ( 125 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 4 con; 0-2 aty)
% ( 13 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 83 ( 75 ^; 4 !; 4 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK1: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_19,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f33,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f27,f25]) ).
thf(f25,plain,
( $false
= ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
& ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
=> ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0
@ ^ [Y2: $i > $o] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1
@ ^ [Y4: $i] :
( ( Y3 != Y4 )
& ( Y2 @ Y4 ) ) )
& ( Y2 @ Y3 ) ) ) ) ) )
& ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) )
=> ( Y0
@ ^ [Y1: $i > $o] :
~ ( ?? @ $i @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) )
& ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f16,f20,f19]) ).
thf(f19,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cZERO_def) ).
thf(f20,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1
@ ( ^ [Y3: ( $i > $o ) > $o,Y4: $i > $o] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( Y3
@ ^ [Y6: $i] :
( ( Y5 != Y6 )
& ( Y4 @ Y6 ) ) )
& ( Y4 @ Y5 ) ) )
@ Y2 ) ) ) )
& ( Y1
@ ^ [Y2: $i > $o] :
~ ( ?? @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f18,f19]) ).
thf(f18,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X2 != X3 ) ) ) ) )
= cSUCC ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: ( $i > $o ) > $o,X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ( X2
@ ^ [X3: $i] :
( ( X0 @ X3 )
& ( X1 != X3 ) ) ) ) )
= cSUCC ),
file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cSUCC_def) ).
thf(f17,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( cNAT
= ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cNAT
= ( ^ [X2: ( $i > $o ) > $o] :
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cNAT_def) ).
thf(f16,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( cNAT @ cZERO )
!= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( cNAT @ cZERO ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( cNAT @ cZERO ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
cNAT @ cZERO,
file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cTTTP6100) ).
thf(f27,plain,
( $true
= ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( sK1
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) )
& ( Y1 @ Y2 ) ) ) ) ) )
& ( sK1
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV282^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n022.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:43:06 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV282^5 : TPTP v9.2.1. Bugfixed v6.2.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem TTTP6100
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_000 [Bro09]
% 0.20/0.46 % : TTTP6100 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0
% 0.20/0.46 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 3 def)
% 0.20/0.46 % Number of atoms : 11 ( 4 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.46 % Number of connectives : 17 ( 2 ~; 0 |; 3 &; 10 @)
% 0.20/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 2 ( 1 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.20/0.46 % Number of variables : 9 ( 5 ^; 2 !; 2 ?; 9 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.20/0.46 % : v6.2.0 - Reordered definitions.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(cNAT_type,type,
% 0.20/0.46 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cSUCC_type,type,
% 0.20/0.46 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cZERO_type,type,
% 0.20/0.46 cZERO: ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cZERO_def,definition,
% 0.20/0.46 ( cZERO
% 0.20/0.46 = ( ^ [Xp: $i > $o] :
% 0.20/0.46 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cSUCC_def,definition,
% 0.20/0.46 ( cSUCC
% 0.20/0.46 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( Xp @ Xx )
% 0.20/0.47 & ( Xn
% 0.20/0.47 @ ^ [Xt: $i] :
% 0.20/0.47 ( ( Xt != Xx )
% 0.20/0.47 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cNAT_def,definition,
% 0.20/0.47 ( cNAT
% 0.20/0.47 = ( ^ [Xn: ( $i > $o ) > $o] :
% 0.20/0.47 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.20/0.47 ( ( ( Xp @ cZERO )
% 0.20/0.47 & ! [Xx: ( $i > $o ) > $o] :
% 0.20/0.47 ( ( Xp @ Xx )
% 0.20/0.47 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 0.20/0.47 => ( Xp @ Xn ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cTTTP6100,conjecture,
% 0.20/0.47 cNAT @ cZERO ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.68/1.31 ---- Embedded in THF ---
% 1.68/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.31 %%% Generated on Tue Feb 24 12:43:07 EST 2026
% 1.68/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.31 %%% Logic specification used:
% 1.68/1.31 %%% thf(spec, logic, $$dhol).
% 1.68/1.31
% 1.68/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2DTF29993.p
% See solution above
% 1.68/1.31 ------------------------
% 1.68/1.32 ---- Cleaned THF ---
% 1.68/1.32 thf(cNAT_type,type,
% 1.68/1.32 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 1.68/1.32
% 1.68/1.32 thf(cSUCC_type,type,
% 1.68/1.32 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 1.68/1.32
% 1.68/1.32 thf(cZERO_type,type,
% 1.68/1.32 cZERO: ( $i > $o ) > $o ).
% 1.68/1.32
% 1.68/1.32 thf(cZERO_def,definition,
% 1.68/1.32 ( cZERO
% 1.68/1.32 = ( ^ [Xp: $i > $o] :
% 1.68/1.32 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(cSUCC_def,definition,
% 1.68/1.32 ( cSUCC
% 1.68/1.32 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 1.68/1.32 ? [Xx: $i] :
% 1.68/1.32 ( ( Xp @ Xx )
% 1.68/1.32 & ( Xn
% 1.68/1.32 @ ^ [Xt: $i] :
% 1.68/1.32 ( ( Xt != Xx )
% 1.68/1.32 & ( Xp @ Xt ) ) ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(cNAT_def,definition,
% 1.68/1.32 ( cNAT
% 1.68/1.32 = ( ^ [Xn: ( $i > $o ) > $o] :
% 1.68/1.32 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 1.68/1.32 ( ( ( Xp @ cZERO )
% 1.68/1.32 & ! [Xx: ( $i > $o ) > $o] :
% 1.68/1.32 ( ( Xp @ Xx )
% 1.68/1.32 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 1.68/1.32 => ( Xp @ Xn ) ) ) ) ).
% 1.68/1.32
% 1.68/1.32 thf(cTTTP6100,conjecture,
% 1.68/1.32 cNAT @ cZERO ).
% 1.68/1.32 ------------------------
% 1.68/1.33 % (30184)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29993 for (2999ds/27Mi)
% 1.68/1.33 % (30186)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_29993 for (2999ds/2Mi)
% 1.68/1.34 % (30186)Instruction limit reached!
% 1.68/1.34 % (30186)------------------------------
% 1.68/1.34 % (30186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (30186)Termination reason: Unknown
% 1.68/1.34 % (30186)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (30186)Memory used [KB]: 1023
% 1.68/1.34 % (30186)Time elapsed: 0.002 s
% 1.68/1.34 % (30186)Instructions burned: 2 (million)
% 1.68/1.34 % (30186)------------------------------
% 1.68/1.34 % (30186)------------------------------
% 1.68/1.34 % (30184)First to succeed.
% 1.68/1.34 % (30184)Refutation found. Thanks to Tanya!
% 1.68/1.34 % SZS status Theorem for DTF2THF_29993
% 1.68/1.34 % SZS output start Proof for DTF2THF_29993
% 1.68/1.34 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 1.68/1.34 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 1.68/1.34 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 1.68/1.34 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.68/1.34 thf(func_def_18, type, sK1: (($i > $o) > $o) > $o).
% 1.68/1.34 thf(func_def_19, type, ph2: !>[X0: $tType]:(X0)).
% 1.68/1.34 thf(f33,plain,(
% 1.68/1.34 $false),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.68/1.34 thf(f32,plain,(
% 1.68/1.34 ($true = $false)),
% 1.68/1.34 inference(forward_demodulation,[status(thm)],[f27,f25])).
% 1.68/1.34 thf(f25,plain,(
% 1.68/1.34 ($false = (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 1.68/1.34 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.68/1.34 thf(f24,plain,(
% 1.68/1.34 ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ Y0) => (sK1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.68/1.34 thf(f23,plain,(
% 1.68/1.34 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))) @ sK1))),
% 1.68/1.34 inference(sigma_clausification,[status(thm)],[f22])).
% 1.68/1.34 thf(f22,plain,(
% 1.68/1.34 ($true != (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4)))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))))),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.68/1.34 thf(f21,plain,(
% 1.68/1.34 (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) != $true)),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f16,f20,f19])).
% 1.68/1.34 thf(f19,plain,(
% 1.68/1.34 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.34 thf(f8,plain,(
% 1.68/1.34 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.68/1.34 thf(f7,plain,(
% 1.68/1.34 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.68/1.34 inference(rectify,[status(thm)],[f1])).
% 1.68/1.34 thf(f1,axiom,(
% 1.68/1.34 ((^[X0 : $i > $o] : (~? [X1 : $i] : (X0 @ X1))) = cZERO)),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cZERO_def)).
% 1.68/1.34 thf(f20,plain,(
% 1.68/1.34 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 1.68/1.34 inference(definition_unfolding,[status(thm)],[f17,f18,f19])).
% 1.68/1.34 thf(f18,plain,(
% 1.68/1.34 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f10,plain,(
% 1.68/1.34 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 1.68/1.34 thf(f9,plain,(
% 1.68/1.34 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3))))))) = cSUCC)),
% 1.68/1.34 inference(rectify,[status(thm)],[f2])).
% 1.68/1.34 thf(f2,axiom,(
% 1.68/1.34 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & (X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3))))))) = cSUCC)),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cSUCC_def)).
% 1.68/1.34 thf(f17,plain,(
% 1.68/1.34 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.68/1.34 thf(f12,plain,(
% 1.68/1.34 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.34 thf(f11,plain,(
% 1.68/1.34 (cNAT = (^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f3])).
% 1.68/1.34 thf(f3,axiom,(
% 1.68/1.34 (cNAT = (^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cNAT_def)).
% 1.68/1.34 thf(f16,plain,(
% 1.68/1.34 ((cNAT @ cZERO) != $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 1.68/1.34 thf(f15,plain,(
% 1.68/1.34 ((cNAT @ cZERO) != $true)),
% 1.68/1.34 inference(flattening,[status(thm)],[f14])).
% 1.68/1.34 thf(f14,plain,(
% 1.68/1.34 ~((cNAT @ cZERO) = $true)),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.68/1.34 thf(f13,plain,(
% 1.68/1.34 ~(cNAT @ cZERO)),
% 1.68/1.34 inference(rectify,[status(thm)],[f5])).
% 1.68/1.34 thf(f5,negated_conjecture,(
% 1.68/1.34 ~(cNAT @ cZERO)),
% 1.68/1.34 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.34 thf(f4,conjecture,(
% 1.68/1.34 (cNAT @ cZERO)),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.PIS9DFwbwx/DTF2THF_29993.p',cTTTP6100)).
% 1.68/1.34 thf(f27,plain,(
% 1.68/1.34 ($true = (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 1.68/1.34 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.68/1.34 thf(f26,plain,(
% 1.68/1.34 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ Y0) => (sK1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))) & (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true)),
% 1.68/1.34 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.68/1.34 % SZS output end Proof for DTF2THF_29993
% 1.68/1.34 % (30184)------------------------------
% 1.68/1.34 % (30184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (30184)Termination reason: Refutation
% 1.68/1.34
% 1.68/1.34 % (30184)Memory used [KB]: 5500
% 1.68/1.34 % (30184)Time elapsed: 0.003 s
% 1.68/1.34 % (30184)Instructions burned: 2 (million)
% 1.68/1.34 % (30184)------------------------------
% 1.68/1.34 % (30184)------------------------------
% 1.68/1.34 % (30181)Success in time 0.007 s
%------------------------------------------------------------------------------