%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ103^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:28:29 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 76 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 325 ( 10 ~; 26 |; 18 &; 214 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 5 con; 0-2 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 30 ^; 19 !; 2 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_NUM: $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_16,type,
sK3: $i > $o ).
thf(func_def_17,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f59,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f57,f38]) ).
thf(f38,plain,
( ( sK3 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false = $true )
| ( ( sK3 @ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f29,f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ ( s @ X1 ) ) )
| ( ( sK3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( sK3 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( sK3 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ Y0 ) ) ) ) )
=> ( sK3 @ ( s @ sK0 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ ( s @ sK0 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ ( s @ sK0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( s @ sK0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f12,f14]) ).
thf(f14,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) )
= cCKB6_NUM ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ X0 ) ) )
= cCKB6_NUM ),
file('/export/starexec/sandbox2/tmp/tmp.Jxe6UyFypj/DTF2THF_30421.p',cCKB6_NUM_def) ).
thf(f12,plain,
( ( cCKB6_NUM @ ( s @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( cCKB6_NUM @ sK0 )
= $true )
& ( ( cCKB6_NUM @ ( s @ sK0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
& ( ( cCKB6_NUM @ ( s @ X0 ) )
!= $true ) )
=> ( ( ( cCKB6_NUM @ sK0 )
= $true )
& ( ( cCKB6_NUM @ ( s @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
& ( ( cCKB6_NUM @ ( s @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
=> ( ( cCKB6_NUM @ ( s @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jxe6UyFypj/DTF2THF_30421.p',cCKB6_L3000) ).
thf(f29,plain,
( ( sK3 @ ( s @ sK0 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f57,plain,
( ( sK3 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false = $true )
| ( ( sK3 @ sK0 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f55,f32]) ).
thf(f32,plain,
( ( sK3 @ c1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f55,plain,
( ( $false
= ( sK3 @ c1 ) )
| ( ( sK3 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( $false = $true )
| ( $false
= ( sK3 @ c1 ) ) ),
inference(superposition,[status(thm)],[f25,f47]) ).
thf(f47,plain,
( ( sK3 @ ( sK2 @ sK3 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( sK3 @ ( sK2 @ sK3 ) )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f45,f38]) ).
thf(f45,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( ( sK3 @ ( sK2 @ sK3 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( $false = $true )
| ( ( sK3 @ ( sK2 @ sK3 ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f43,f32]) ).
thf(f43,plain,
( ( $false
= ( sK3 @ c1 ) )
| ( ( sK3 @ sK0 )
= $true )
| ( ( sK3 @ ( sK2 @ sK3 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK3 @ sK0 )
= $true )
| ( ( sK3 @ ( sK2 @ sK3 ) )
= $false )
| ( $false = $true )
| ( $false
= ( sK3 @ c1 ) ) ),
inference(superposition,[status(thm)],[f24,f35]) ).
thf(f24,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK2 @ X1 ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( ( X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( $false
= ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( s @ ( sK2 @ X1 ) ) ) ) )
| ( ( X1 @ sK0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) )
@ ( sK2 @ X1 ) ) )
| ( ( X1 @ sK0 )
= $true )
| ( ( X1 @ c1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK0 )
= $true )
| ( ( X1 @ c1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ c1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) ) )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c1 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f13,plain,
( ( cCKB6_NUM @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f25,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X1 @ c1 )
= $false )
| ( ( X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ103^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:32:44 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : PUZ103^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.31/0.46 % Domain : Puzzles
% 0.31/0.46 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0623 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.31/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.31/0.46 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 1 &; 8 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(c1_type,type,
% 0.31/0.46 c1: $i ).
% 0.31/0.46
% 0.31/0.46 thf(s_type,type,
% 0.31/0.46 s: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(cCKB6_NUM_type,type,
% 0.31/0.46 cCKB6_NUM: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cCKB6_NUM_def,definition,
% 0.31/0.46 ( cCKB6_NUM
% 0.31/0.46 = ( ^ [Xx: $i] :
% 0.31/0.46 ! [Xp: $i > $o] :
% 0.31/0.46 ( ( ( Xp @ c1 )
% 0.31/0.46 & ! [Xw: $i] :
% 0.31/0.46 ( ( Xp @ Xw )
% 0.31/0.46 => ( Xp @ ( s @ Xw ) ) ) )
% 0.31/0.46 => ( Xp @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(cCKB6_L3000,conjecture,
% 0.31/0.46 ! [Xx: $i] :
% 0.31/0.46 ( ( cCKB6_NUM @ Xx )
% 0.31/0.46 => ( cCKB6_NUM @ ( s @ Xx ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 11:32:45 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Jxe6UyFypj/DTF2DTF30421.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(c1_type,type,
% 1.47/1.27 c1: $i ).
% 1.47/1.27
% 1.47/1.27 thf(s_type,type,
% 1.47/1.27 s: $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(cCKB6_NUM_type,type,
% 1.47/1.27 cCKB6_NUM: $i > $o ).
% 1.47/1.27
% 1.47/1.27 thf(cCKB6_NUM_def,definition,
% 1.47/1.27 ( cCKB6_NUM
% 1.47/1.27 = ( ^ [Xx: $i] :
% 1.47/1.27 ! [Xp: $i > $o] :
% 1.47/1.27 ( ( ( Xp @ c1 )
% 1.47/1.27 & ! [Xw: $i] :
% 1.47/1.27 ( ( Xp @ Xw )
% 1.47/1.27 => ( Xp @ ( s @ Xw ) ) ) )
% 1.47/1.27 => ( Xp @ Xx ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(cCKB6_L3000,conjecture,
% 1.47/1.27 ! [Xx: $i] :
% 1.47/1.27 ( ( cCKB6_NUM @ Xx )
% 1.47/1.27 => ( cCKB6_NUM @ ( s @ Xx ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (30643)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30421 for (2999ds/2Mi)
% 1.47/1.28 % (30643)Instruction limit reached!
% 1.47/1.28 % (30643)------------------------------
% 1.47/1.28 % (30643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (30643)Termination reason: Unknown
% 1.47/1.28 % (30643)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (30643)Memory used [KB]: 895
% 1.47/1.28 % (30643)Time elapsed: 0.002 s
% 1.47/1.28 % (30643)Instructions burned: 2 (million)
% 1.47/1.28 % (30643)------------------------------
% 1.47/1.28 % (30643)------------------------------
% 1.47/1.29 % (30641)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_30421 for (2999ds/4Mi)
% 1.47/1.29 % (30640)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30421 for (2999ds/183Mi)
% 1.47/1.29 % (30642)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_30421 for (2999ds/27Mi)
% 1.47/1.29 % (30644)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_30421 for (2999ds/2Mi)
% 1.47/1.29 % (30645)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_30421 for (2999ds/275Mi)
% 1.47/1.29 % (30646)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30421 for (2999ds/18Mi)
% 1.47/1.29 % (30644)Instruction limit reached!
% 1.47/1.29 % (30644)------------------------------
% 1.47/1.29 % (30644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30644)Termination reason: Unknown
% 1.47/1.29 % (30644)Termination phase: Function definition elimination
% 1.47/1.29
% 1.47/1.29 % (30644)Memory used [KB]: 895
% 1.47/1.29 % (30644)Time elapsed: 0.003 s
% 1.47/1.29 % (30644)Instructions burned: 2 (million)
% 1.47/1.29 % (30644)------------------------------
% 1.47/1.29 % (30644)------------------------------
% 1.47/1.29 % (30645)Refutation not found, incomplete strategy
% 1.47/1.29 % (30645)------------------------------
% 1.47/1.29 % (30645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30645)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (30645)Memory used [KB]: 5500
% 1.47/1.29 % (30645)Time elapsed: 0.003 s
% 1.47/1.29 % (30645)Instructions burned: 1 (million)
% 1.47/1.29 % (30645)------------------------------
% 1.47/1.29 % (30645)------------------------------
% 1.47/1.29 % (30647)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30421 for (2999ds/3Mi)
% 1.47/1.29 % (30641)Instruction limit reached!
% 1.47/1.29 % (30641)------------------------------
% 1.47/1.29 % (30641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30641)Termination reason: Unknown
% 1.47/1.29 % (30641)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (30641)Memory used [KB]: 5500
% 1.47/1.29 % (30641)Time elapsed: 0.005 s
% 1.47/1.29 % (30641)Instructions burned: 4 (million)
% 1.47/1.29 % (30641)------------------------------
% 1.47/1.29 % (30641)------------------------------
% 1.47/1.29 % (30647)Instruction limit reached!
% 1.47/1.29 % (30647)------------------------------
% 1.47/1.29 % (30647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (30647)Termination reason: Unknown
% 1.47/1.29 % (30647)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (30647)Memory used [KB]: 5500
% 1.47/1.29 % (30647)Time elapsed: 0.002 s
% 1.47/1.29 % (30647)Instructions burned: 3 (million)
% 1.47/1.29 % (30647)------------------------------
% 1.47/1.29 % (30647)------------------------------
% 1.47/1.29 % (30642)First to succeed.
% 1.61/1.30 % (30642)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_30421
% 1.61/1.30 % SZS output start Proof for DTF2THF_30421
% 1.61/1.30 thf(func_def_1, type, s: $i > $i).
% 1.61/1.30 thf(func_def_2, type, cCKB6_NUM: $i > $o).
% 1.61/1.30 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.30 thf(func_def_15, type, sK2: ($i > $o) > $i).
% 1.61/1.30 thf(func_def_16, type, sK3: $i > $o).
% 1.61/1.30 thf(func_def_17, type, ph4: !>[X0: $tType]:(X0)).
% 1.61/1.30 thf(f59,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.61/1.30 thf(f58,plain,(
% 1.61/1.30 ($false = $true)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f57,f38])).
% 1.61/1.30 thf(f38,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $false)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.61/1.30 thf(f37,plain,(
% 1.61/1.30 ($false = $true) | ((sK3 @ sK0) = $false)),
% 1.61/1.30 inference(superposition,[status(thm)],[f29,f35])).
% 1.61/1.30 thf(f35,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (($true = (sK3 @ (s @ X1))) | ((sK3 @ X1) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.61/1.30 thf(f34,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (($true = ((sK3 @ X1) => (sK3 @ (s @ X1))))) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.61/1.30 thf(f33,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0)))) @ X1))) )),
% 1.61/1.30 inference(pi_clausification,[status(thm)],[f31])).
% 1.61/1.30 thf(f31,plain,(
% 1.61/1.30 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0))))) = $true)),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.61/1.30 thf(f30,plain,(
% 1.61/1.30 (((sK3 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0)))))) = $true)),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.61/1.30 thf(f28,plain,(
% 1.61/1.30 ((((sK3 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK3 @ (s @ Y0)))))) => (sK3 @ (s @ sK0))) = $false)),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 (((^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ (s @ sK0)))) @ sK3) = $false)),
% 1.61/1.30 inference(sigma_clausification,[status(thm)],[f26])).
% 1.61/1.30 thf(f26,plain,(
% 1.61/1.30 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ (s @ sK0))))) != $true)),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))) @ (s @ sK0)) != $true)),
% 1.61/1.30 inference(definition_unfolding,[status(thm)],[f12,f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.30 thf(f6,plain,(
% 1.61/1.30 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,plain,(
% 1.61/1.30 ((^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2))) & (X1 @ c1)) => (X1 @ X0)))) = cCKB6_NUM)),
% 1.61/1.30 inference(rectify,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 ((^[X0 : $i] : (! [X1 : $i > $o] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2))) & (X1 @ c1)) => (X1 @ X0)))) = cCKB6_NUM)),
% 1.61/1.30 file('/export/starexec/sandbox2/tmp/tmp.Jxe6UyFypj/DTF2THF_30421.p',cCKB6_NUM_def)).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 ((cCKB6_NUM @ (s @ sK0)) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ((cCKB6_NUM @ sK0) = $true) & ((cCKB6_NUM @ (s @ sK0)) != $true)),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ? [X0 : $i] : (((cCKB6_NUM @ X0) = $true) & ((cCKB6_NUM @ (s @ X0)) != $true)) => (((cCKB6_NUM @ sK0) = $true) & ((cCKB6_NUM @ (s @ sK0)) != $true))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ? [X0 : $i] : (((cCKB6_NUM @ X0) = $true) & ((cCKB6_NUM @ (s @ X0)) != $true))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ~! [X0 : $i] : (((cCKB6_NUM @ X0) = $true) => ((cCKB6_NUM @ (s @ X0)) = $true))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.61/1.30 thf(f7,plain,(
% 1.61/1.30 ~! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ X0)))),
% 1.61/1.30 inference(rectify,[status(thm)],[f3])).
% 1.61/1.30 thf(f3,negated_conjecture,(
% 1.61/1.30 ~! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ X0)))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.61/1.30 thf(f2,conjecture,(
% 1.61/1.30 ! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ X0)))),
% 1.61/1.30 file('/export/starexec/sandbox2/tmp/tmp.Jxe6UyFypj/DTF2THF_30421.p',cCKB6_L3000)).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 ((sK3 @ (s @ sK0)) = $false)),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.61/1.30 thf(f57,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $true)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.61/1.30 thf(f56,plain,(
% 1.61/1.30 ($false = $true) | ((sK3 @ sK0) = $true)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f55,f32])).
% 1.61/1.30 thf(f32,plain,(
% 1.61/1.30 ((sK3 @ c1) = $true)),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.61/1.30 thf(f55,plain,(
% 1.61/1.30 ($false = (sK3 @ c1)) | ((sK3 @ sK0) = $true)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.61/1.30 thf(f53,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $true) | ($false = $true) | ($false = (sK3 @ c1))),
% 1.61/1.30 inference(superposition,[status(thm)],[f25,f47])).
% 1.61/1.30 thf(f47,plain,(
% 1.61/1.30 ((sK3 @ (sK2 @ sK3)) = $false)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.61/1.30 thf(f46,plain,(
% 1.61/1.30 ((sK3 @ (sK2 @ sK3)) = $false) | ($false = $true)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f45,f38])).
% 1.61/1.30 thf(f45,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $true) | ((sK3 @ (sK2 @ sK3)) = $false)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.61/1.30 thf(f44,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $true) | ($false = $true) | ((sK3 @ (sK2 @ sK3)) = $false)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f43,f32])).
% 1.61/1.30 thf(f43,plain,(
% 1.61/1.30 ($false = (sK3 @ c1)) | ((sK3 @ sK0) = $true) | ((sK3 @ (sK2 @ sK3)) = $false)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.61/1.30 thf(f40,plain,(
% 1.61/1.30 ((sK3 @ sK0) = $true) | ((sK3 @ (sK2 @ sK3)) = $false) | ($false = $true) | ($false = (sK3 @ c1))),
% 1.61/1.30 inference(superposition,[status(thm)],[f24,f35])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (((X1 @ (s @ (sK2 @ X1))) = $false) | ((X1 @ c1) = $false) | ((X1 @ sK0) = $true)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (((X1 @ c1) = $false) | ($false = ((X1 @ (sK2 @ X1)) => (X1 @ (s @ (sK2 @ X1))))) | ((X1 @ sK0) = $true)) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.61/1.30 thf(f22,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (($false = ((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))) @ (sK2 @ X1))) | ((X1 @ sK0) = $true) | ((X1 @ c1) = $false)) )),
% 1.61/1.30 inference(sigma_clausification,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (((X1 @ sK0) = $true) | ((X1 @ c1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0))))) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.61/1.30 thf(f20,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : ((((X1 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))))) = $false) | ((X1 @ sK0) = $true)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (($true = (((X1 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))))) => (X1 @ sK0)))) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ sK0))) @ X1) = $true)) )),
% 1.61/1.30 inference(pi_clausification,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ sK0)))) = $true)),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.61/1.30 thf(f15,plain,(
% 1.61/1.30 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))) @ sK0) = $true)),
% 1.61/1.30 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ((cCKB6_NUM @ sK0) = $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f25,plain,(
% 1.61/1.30 ( ! [X1 : $i > $o] : (($true = (X1 @ (sK2 @ X1))) | ((X1 @ c1) = $false) | ((X1 @ sK0) = $true)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_30421
% 1.61/1.30 % (30642)------------------------------
% 1.61/1.30 % (30642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (30642)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (30642)Memory used [KB]: 5500
% 1.61/1.30 % (30642)Time elapsed: 0.007 s
% 1.61/1.30 % (30642)Instructions burned: 5 (million)
% 1.61/1.30 % (30642)------------------------------
% 1.61/1.30 % (30642)------------------------------
% 1.61/1.30 % (30639)Success in time 0.023 s
%------------------------------------------------------------------------------