%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM637^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:24:01 AM UTC 2026
% Result : Theorem 1.67s 1.45s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 135 ( 36 ~; 14 |; 12 &; 62 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 5 ^; 31 !; 8 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
succ: $i > $i ).
thf(func_def_5,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f168,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( sK1 != sK1 )
| ( one != one ) ),
inference(superposition,[status(thm)],[f23,f142]) ).
thf(f142,plain,
! [X0: $i] :
( ( one = X0 )
| ( sK1 != X0 ) ),
inference(superposition,[status(thm)],[f22,f73]) ).
thf(f73,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( one = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i] :
( ( ( X0 = one )
= $true )
| ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( ( X0 != one )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( ( ^ [Y0: $i] : ( X0 != Y0 )
@ one )
!= $true ) ),
inference(leibniz_equality_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X0: $i > $o] :
( ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) )
| ( ( X0 @ one )
!= $true )
| ( $true
= ( X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) ) )
| ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ( ( X0 @ one )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f14]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ ( succ @ X1 ) )
!= $true ) )
=> ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ ( succ @ X1 ) )
!= $true ) )
| ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ( ( X0 @ one )
!= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ( ( X0 @ one )
!= $true )
| ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ ( succ @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ one )
= $true )
& ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( succ @ X1 ) )
= $true ) ) )
=> ! [X2: $i] :
( $true
= ( X0 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( succ @ X1 ) ) )
& ( X0 @ one ) )
=> ! [X2: $i] : ( X0 @ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i > $o] :
( ( ! [X0: $i] :
( ( X2 @ X0 )
=> ( X2 @ ( succ @ X0 ) ) )
& ( X2 @ one ) )
=> ! [X1: $i] : ( X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.sWQpDrMQRX/DTF2THF_27035.p',induction) ).
thf(f22,plain,
! [X1: $i] :
( ( succ @ X1 )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( one != sK1 )
& ! [X1: $i] :
( ( succ @ X1 )
!= sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: $i] :
( ( one != X0 )
& ! [X1: $i] :
( ( succ @ X1 )
!= X0 ) )
=> ( ( one != sK1 )
& ! [X1: $i] :
( ( succ @ X1 )
!= sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $i] :
( ( one != X0 )
& ! [X1: $i] :
( ( succ @ X1 )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $i] :
( ( one != X0 )
=> ? [X1: $i] :
( ( succ @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $i] :
( ( one != X0 )
=> ? [X3: $i] :
( ( succ @ X3 )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $i] :
( ( one != X0 )
=> ? [X3: $i] :
( ( succ @ X3 )
= X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.sWQpDrMQRX/DTF2THF_27035.p',satz3) ).
thf(f23,plain,
one != sK1,
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM637^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:08:17 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
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : NUM637^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.48 % Domain : Number Theory
% 0.20/0.48 % Problem : Landau theorem 3
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [TPTP]
% 0.20/0.48 % Names : satz3 [Lan30]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % 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, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.20/0.48 % Syntax : Number of formulae : 6 ( 1 unt; 2 typ; 0 def)
% 0.20/0.48 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.48 % Number of connectives : 16 ( 2 ~; 0 |; 1 &; 9 @)
% 0.20/0.48 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 8 ( 5 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments :
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(one_type,type,
% 0.20/0.48 one: $i ).
% 0.20/0.48
% 0.20/0.48 thf(succ_type,type,
% 0.20/0.48 succ: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(one_is_first,axiom,
% 0.20/0.48 ! [X: $i] :
% 0.20/0.48 ( ( succ @ X )
% 0.20/0.48 != one ) ).
% 0.20/0.48
% 0.20/0.48 thf(succ_injective,axiom,
% 0.20/0.48 ! [X: $i,Y: $i] :
% 0.20/0.48 ( ( ( succ @ X )
% 0.20/0.48 = ( succ @ Y ) )
% 0.20/0.48 => ( X = Y ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(induction,axiom,
% 0.20/0.48 ! [M: $i > $o] :
% 0.20/0.48 ( ( ( M @ one )
% 0.20/0.48 & ! [X: $i] :
% 0.20/0.48 ( ( M @ X )
% 0.20/0.48 => ( M @ ( succ @ X ) ) ) )
% 0.20/0.48 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(satz3,conjecture,
% 0.20/0.48 ! [X: $i] :
% 0.20/0.48 ( ( X != one )
% 0.20/0.48 => ? [U: $i] :
% 0.20/0.48 ( X
% 0.20/0.48 = ( succ @ U ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.67/1.41 ---- Embedded in THF ---
% 1.67/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.41 %%% Generated on Tue Feb 24 11:08:18 EST 2026
% 1.67/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.41 %%% Logic specification used:
% 1.67/1.41 %%% thf(spec, logic, $$dhol).
% 1.67/1.41
% 1.67/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sWQpDrMQRX/DTF2DTF27035.p
% See solution above
% 1.67/1.41 ------------------------
% 1.67/1.42 ---- Cleaned THF ---
% 1.67/1.42 thf(one_type,type,
% 1.67/1.42 one: $i ).
% 1.67/1.42
% 1.67/1.42 thf(succ_type,type,
% 1.67/1.42 succ: $i > $i ).
% 1.67/1.42
% 1.67/1.42 thf(one_is_first,axiom,
% 1.67/1.42 ! [X: $i] :
% 1.67/1.42 ( ( succ @ X )
% 1.67/1.42 != one ) ).
% 1.67/1.42
% 1.67/1.42 thf(succ_injective,axiom,
% 1.67/1.42 ! [X: $i,Y: $i] :
% 1.67/1.42 ( ( ( succ @ X )
% 1.67/1.42 = ( succ @ Y ) )
% 1.67/1.42 => ( X = Y ) ) ).
% 1.67/1.42
% 1.67/1.42 thf(induction,axiom,
% 1.67/1.42 ! [M: $i > $o] :
% 1.67/1.42 ( ( ( M @ one )
% 1.67/1.42 & ! [X: $i] :
% 1.67/1.42 ( ( M @ X )
% 1.67/1.42 => ( M @ ( succ @ X ) ) ) )
% 1.67/1.42 => ! [Y: $i] : ( M @ Y ) ) ).
% 1.67/1.42
% 1.67/1.42 thf(satz3,conjecture,
% 1.67/1.42 ! [X: $i] :
% 1.67/1.42 ( ( X != one )
% 1.67/1.42 => ? [U: $i] :
% 1.67/1.42 ( X
% 1.67/1.42 = ( succ @ U ) ) ) ).
% 1.67/1.42 ------------------------
% 1.67/1.44 % (27136)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27035 for (3000ds/2Mi)
% 1.67/1.44 % (27134)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_27035 for (3000ds/4Mi)
% 1.67/1.44 % (27133)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27035 for (3000ds/183Mi)
% 1.67/1.44 % (27135)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_27035 for (3000ds/27Mi)
% 1.67/1.44 % (27137)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_27035 for (3000ds/2Mi)
% 1.67/1.44 % (27138)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_27035 for (3000ds/275Mi)
% 1.67/1.44 % (27139)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27035 for (3000ds/18Mi)
% 1.67/1.44 % (27138)Refutation not found, incomplete strategy
% 1.67/1.44 % (27138)------------------------------
% 1.67/1.44 % (27138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (27138)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.44
% 1.67/1.44
% 1.67/1.44 % (27138)Memory used [KB]: 5373
% 1.67/1.44 % (27138)Time elapsed: 0.002 s
% 1.67/1.44 % (27138)Instructions burned: 1 (million)
% 1.67/1.44 % (27138)------------------------------
% 1.67/1.44 % (27138)------------------------------
% 1.67/1.44 % (27137)Instruction limit reached!
% 1.67/1.44 % (27137)------------------------------
% 1.67/1.44 % (27137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (27137)Termination reason: Unknown
% 1.67/1.44 % (27137)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (27137)Memory used [KB]: 5500
% 1.67/1.44 % (27137)Time elapsed: 0.003 s
% 1.67/1.44 % (27137)Instructions burned: 3 (million)
% 1.67/1.44 % (27137)------------------------------
% 1.67/1.44 % (27137)------------------------------
% 1.67/1.44 % (27135)Refutation not found, incomplete strategy
% 1.67/1.44 % (27135)------------------------------
% 1.67/1.44 % (27135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (27135)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.44
% 1.67/1.44
% 1.67/1.44 % (27135)Memory used [KB]: 5500
% 1.67/1.44 % (27135)Time elapsed: 0.003 s
% 1.67/1.44 % (27135)Instructions burned: 2 (million)
% 1.67/1.44 % (27135)------------------------------
% 1.67/1.44 % (27135)------------------------------
% 1.67/1.44 % (27134)Instruction limit reached!
% 1.67/1.44 % (27134)------------------------------
% 1.67/1.44 % (27134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (27134)Termination reason: Unknown
% 1.67/1.44 % (27134)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (27134)Memory used [KB]: 5500
% 1.67/1.44 % (27134)Time elapsed: 0.004 s
% 1.67/1.44 % (27134)Instructions burned: 4 (million)
% 1.67/1.44 % (27136)Instruction limit reached!
% 1.67/1.44 % (27136)------------------------------
% 1.67/1.44 % (27136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (27136)Termination reason: Unknown
% 1.67/1.44 % (27136)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (27136)Memory used [KB]: 5500
% 1.67/1.44 % (27136)Time elapsed: 0.004 s
% 1.67/1.44 % (27136)Instructions burned: 2 (million)
% 1.67/1.44 % (27136)------------------------------
% 1.67/1.44 % (27136)------------------------------
% 1.67/1.44 % (27134)------------------------------
% 1.67/1.44 % (27134)------------------------------
% 1.67/1.45 % (27133)First to succeed.
% 1.67/1.45 % (27133)Refutation found. Thanks to Tanya!
% 1.67/1.45 % SZS status Theorem for DTF2THF_27035
% 1.67/1.45 % SZS output start Proof for DTF2THF_27035
% 1.67/1.45 thf(func_def_1, type, succ: $i > $i).
% 1.67/1.45 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.67/1.45 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.67/1.45 thf(f168,plain,(
% 1.67/1.45 $false),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.67/1.45 thf(f167,plain,(
% 1.67/1.45 (sK1 != sK1) | (one != one)),
% 1.67/1.45 inference(superposition,[status(thm)],[f23,f142])).
% 1.67/1.45 thf(f142,plain,(
% 1.67/1.45 ( ! [X0 : $i] : ((one = X0) | (sK1 != X0)) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f22,f73])).
% 1.67/1.45 thf(f73,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | (one = X0)) )),
% 1.67/1.45 inference(equality_proxy_clausification,[status(thm)],[f72])).
% 1.67/1.45 thf(f72,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((X0 = one) = $true) | ((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 1.67/1.45 inference(not_proxy_clausification,[status(thm)],[f71])).
% 1.67/1.45 thf(f71,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | ((~ (X0 = one)) != $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.67/1.45 thf(f64,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | (((^[Y0 : $i]: (~ (X0 = Y0))) @ one) != $true)) )),
% 1.67/1.45 inference(leibniz_equality_elimination,[status(thm)],[f20])).
% 1.67/1.45 thf(f20,plain,(
% 1.67/1.45 ( ! [X2 : $i,X0 : $i > $o] : (($true != (X0 @ (succ @ (sK0 @ X0)))) | ((X0 @ one) != $true) | ($true = (X0 @ X2))) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.45 thf(f15,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : ((((X0 @ (sK0 @ X0)) = $true) & ($true != (X0 @ (succ @ (sK0 @ X0))))) | ! [X2 : $i] : ($true = (X0 @ X2)) | ((X0 @ one) != $true))),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f14])).
% 1.67/1.45 thf(f14,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : (? [X1 : $i] : (((X0 @ X1) = $true) & ((X0 @ (succ @ X1)) != $true)) => (((X0 @ (sK0 @ X0)) = $true) & ($true != (X0 @ (succ @ (sK0 @ X0))))))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f11,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : (? [X1 : $i] : (((X0 @ X1) = $true) & ((X0 @ (succ @ X1)) != $true)) | ! [X2 : $i] : ($true = (X0 @ X2)) | ((X0 @ one) != $true))),
% 1.67/1.45 inference(flattening,[status(thm)],[f10])).
% 1.67/1.45 thf(f10,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : (! [X2 : $i] : ($true = (X0 @ X2)) | (((X0 @ one) != $true) | ? [X1 : $i] : (((X0 @ X1) = $true) & ((X0 @ (succ @ X1)) != $true))))),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f8])).
% 1.67/1.45 thf(f8,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : ((((X0 @ one) = $true) & ! [X1 : $i] : (((X0 @ X1) = $true) => ((X0 @ (succ @ X1)) = $true))) => ! [X2 : $i] : ($true = (X0 @ X2)))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.45 thf(f7,plain,(
% 1.67/1.45 ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 1.67/1.45 inference(rectify,[status(thm)],[f3])).
% 1.67/1.45 thf(f3,axiom,(
% 1.67/1.45 ! [X2 : $i > $o] : ((! [X0 : $i] : ((X2 @ X0) => (X2 @ (succ @ X0))) & (X2 @ one)) => ! [X1 : $i] : (X2 @ X1))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.sWQpDrMQRX/DTF2THF_27035.p',induction)).
% 1.67/1.45 thf(f22,plain,(
% 1.67/1.45 ( ! [X1 : $i] : (((succ @ X1) != sK1)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.45 thf(f17,plain,(
% 1.67/1.45 (one != sK1) & ! [X1 : $i] : ((succ @ X1) != sK1)),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f16])).
% 1.67/1.45 thf(f16,plain,(
% 1.67/1.45 ? [X0 : $i] : ((one != X0) & ! [X1 : $i] : ((succ @ X1) != X0)) => ((one != sK1) & ! [X1 : $i] : ((succ @ X1) != sK1))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f13,plain,(
% 1.67/1.45 ? [X0 : $i] : ((one != X0) & ! [X1 : $i] : ((succ @ X1) != X0))),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.45 thf(f9,plain,(
% 1.67/1.45 ~! [X0 : $i] : ((one != X0) => ? [X1 : $i] : ((succ @ X1) = X0))),
% 1.67/1.45 inference(rectify,[status(thm)],[f5])).
% 1.67/1.45 thf(f5,negated_conjecture,(
% 1.67/1.45 ~! [X0 : $i] : ((one != X0) => ? [X3 : $i] : ((succ @ X3) = X0))),
% 1.67/1.45 inference(negated_conjecture,[status(cth)],[f4])).
% 1.67/1.45 thf(f4,conjecture,(
% 1.67/1.45 ! [X0 : $i] : ((one != X0) => ? [X3 : $i] : ((succ @ X3) = X0))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.sWQpDrMQRX/DTF2THF_27035.p',satz3)).
% 1.67/1.45 thf(f23,plain,(
% 1.67/1.45 (one != sK1)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.45 % SZS output end Proof for DTF2THF_27035
% 1.67/1.45 % (27133)------------------------------
% 1.67/1.45 % (27133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (27133)Termination reason: Refutation
% 1.67/1.45
% 1.67/1.45 % (27133)Memory used [KB]: 5500
% 1.67/1.45 % (27133)Time elapsed: 0.009 s
% 1.67/1.45 % (27133)Instructions burned: 10 (million)
% 1.67/1.45 % (27133)------------------------------
% 1.67/1.45 % (27133)------------------------------
% 1.67/1.45 % (27132)Success in time 0.023 s
%------------------------------------------------------------------------------