%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM636^2 : 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 : n015.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 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 246 ( 131 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 221 ( 66 ~; 56 |; 8 &; 82 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 9 ^; 61 !; 5 ?; 75 :)
% 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(f217,plain,
$false,
inference(equality_resolution,[status(thm)],[f215]) ).
thf(f215,plain,
! [X0: $i] : ( sK1 != X0 ),
inference(subsumption_resolution,[status(thm)],[f211,f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( succ @ X0 )
!= one ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( succ @ X0 )
!= one ),
file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',one_is_first) ).
thf(f211,plain,
! [X0: $i] :
( ( one
= ( succ @ one ) )
| ( sK1 != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: $i] :
( ( sK1 != X0 )
| ( sK1 != sK1 )
| ( one
= ( succ @ one ) ) ),
inference(superposition,[status(thm)],[f22,f173]) ).
thf(f173,plain,
! [X0: $i,X1: $i] :
( ( one = X0 )
| ( sK1 != X0 )
| ( X0 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: $i,X1: $i] :
( ( one = X0 )
| ( one = X0 )
| ( sK1 != X0 )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( X0 = one ) )
| ( one = X0 )
| ( sK1 != X0 )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
= $false )
| ( $true
= ( X0 = one ) )
| ( sK1 != X0 )
| ( one = X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X0: $i,X1: $i] :
( ( one = X0 )
| ( $true
= ( X0 != X1 ) )
| ( sK1 != X0 )
| ( $true
= ( X0 = one ) ) ),
inference(not_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( X0 != one ) )
| ( $true
= ( X0 != X1 ) )
| ( sK1 != X0 )
| ( one = X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f167]) ).
thf(f167,plain,
! [X0: $i,X1: $i] :
( ( sK1 != X0 )
| ( $true
!= ( X0 != one ) )
| ( sK1 != X0 )
| ( one = X0 )
| ( $true
= ( X0 != X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X0: $i,X1: $i] :
( ( one = X0 )
| ( $false
= ( X0 = sK1 ) )
| ( $true
= ( X0 != X1 ) )
| ( sK1 != X0 )
| ( $true
!= ( X0 != one ) ) ),
inference(not_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X0: $i,X1: $i] :
( ( ( X0 != sK1 )
= $true )
| ( one = X0 )
| ( sK1 != X0 )
| ( $true
= ( X0 != X1 ) )
| ( $true
!= ( X0 != one ) ) ),
inference(beta_eta_normalization,[status(thm)],[f162]) ).
thf(f162,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( ^ [Y0: $i] : ( X0 != Y0 )
@ one ) )
| ( one = X0 )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ sK1 ) )
| ( sK1 != X0 )
| ( $true
= ( ^ [Y0: $i] : ( X0 != Y0 )
@ X1 ) ) ),
inference(superposition,[status(thm)],[f19,f105]) ).
thf(f105,plain,
! [X0: $i] :
( ( ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) )
= sK1 )
| ( sK1 != X0 )
| ( one = X0 ) ),
inference(superposition,[status(thm)],[f24,f90]) ).
thf(f90,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( one = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( $true
= ( X0 = one ) ) ),
inference(not_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( $true
!= ( X0 != one ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( ( succ
@ ( sK0
@ ^ [Y0: $i] : ( X0 != Y0 ) ) )
= X0 )
| ( $true
!= ( ^ [Y0: $i] : ( X0 != Y0 )
@ one ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X0: $i > $o] :
( ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) )
| ( $true
!= ( X0 @ one ) )
| ( $true
= ( X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i > $o] :
( ( $true
!= ( X0 @ one ) )
| ( ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) )
& ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) )
| ! [X2: $i] :
( $true
= ( X0 @ X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f13]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( $true
!= ( X0 @ ( succ @ X1 ) ) )
& ( $true
= ( X0 @ X1 ) ) )
=> ( ( $true
!= ( X0 @ ( succ @ ( sK0 @ X0 ) ) ) )
& ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ( $true
!= ( X0 @ one ) )
| ? [X1: $i] :
( ( $true
!= ( X0 @ ( succ @ X1 ) ) )
& ( $true
= ( X0 @ X1 ) ) )
| ! [X2: $i] :
( $true
= ( X0 @ X2 ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ! [X2: $i] :
( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X0 @ one ) )
| ? [X1: $i] :
( ( $true
!= ( X0 @ ( succ @ X1 ) ) )
& ( $true
= ( X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ( ( $true
= ( X0 @ one ) )
& ! [X1: $i] :
( ( $true
= ( X0 @ X1 ) )
=> ( $true
= ( X0 @ ( succ @ X1 ) ) ) ) )
=> ! [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.dDnUcOoXu4/DTF2THF_23318.p',induction) ).
thf(f24,plain,
! [X0: $i] :
( ( ( succ @ X0 )
!= sK1 )
| ( sK1 = X0 ) ),
inference(superposition,[status(thm)],[f21,f22]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( ( succ @ X0 )
!= ( succ @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( succ @ X0 )
!= ( succ @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( succ @ X0 )
= ( succ @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',succ_injective) ).
thf(f19,plain,
! [X2: $i,X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X0 @ one ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f22,plain,
( ( succ @ sK1 )
= sK1 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( succ @ sK1 )
= sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f16]) ).
thf(f16,plain,
( ? [X0: $i] :
( ( succ @ X0 )
= X0 )
=> ( ( succ @ sK1 )
= sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $i] :
( ( succ @ X0 )
= X0 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $i] :
( ( succ @ X0 )
!= X0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $i] :
( ( succ @ X0 )
!= X0 ),
file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',satz2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM636^2 : 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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:09:16 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUM636^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Number Theory
% 0.30/0.46 % Problem : Landau theorem 2
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [TPTP]
% 0.30/0.46 % Names : satz2 [Lan30]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.80 v5.2.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 6 ( 2 unt; 2 typ; 0 def)
% 0.30/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.46 % Number of connectives : 15 ( 2 ~; 0 |; 1 &; 9 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(one_type,type,
% 0.30/0.46 one: $i ).
% 0.30/0.46
% 0.30/0.46 thf(succ_type,type,
% 0.30/0.46 succ: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(one_is_first,axiom,
% 0.30/0.46 ! [X: $i] :
% 0.30/0.46 ( ( succ @ X )
% 0.30/0.46 != one ) ).
% 0.30/0.46
% 0.30/0.46 thf(succ_injective,axiom,
% 0.30/0.46 ! [X: $i,Y: $i] :
% 0.30/0.46 ( ( ( succ @ X )
% 0.30/0.46 = ( succ @ Y ) )
% 0.30/0.46 => ( X = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(induction,axiom,
% 0.30/0.46 ! [M: $i > $o] :
% 0.30/0.46 ( ( ( M @ one )
% 0.30/0.46 & ! [X: $i] :
% 0.30/0.46 ( ( M @ X )
% 0.30/0.46 => ( M @ ( succ @ X ) ) ) )
% 0.30/0.46 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz2,conjecture,
% 0.30/0.46 ! [X: $i] :
% 0.30/0.46 ( ( succ @ X )
% 0.30/0.46 != X ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 11:09:17 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2DTF23318.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(one_type,type,
% 1.51/1.25 one: $i ).
% 1.51/1.25
% 1.51/1.25 thf(succ_type,type,
% 1.51/1.25 succ: $i > $i ).
% 1.51/1.25
% 1.51/1.25 thf(one_is_first,axiom,
% 1.51/1.25 ! [X: $i] :
% 1.51/1.25 ( ( succ @ X )
% 1.51/1.25 != one ) ).
% 1.51/1.25
% 1.51/1.25 thf(succ_injective,axiom,
% 1.51/1.25 ! [X: $i,Y: $i] :
% 1.51/1.25 ( ( ( succ @ X )
% 1.51/1.25 = ( succ @ Y ) )
% 1.51/1.25 => ( X = Y ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(induction,axiom,
% 1.51/1.25 ! [M: $i > $o] :
% 1.51/1.25 ( ( ( M @ one )
% 1.51/1.25 & ! [X: $i] :
% 1.51/1.25 ( ( M @ X )
% 1.51/1.25 => ( M @ ( succ @ X ) ) ) )
% 1.51/1.25 => ! [Y: $i] : ( M @ Y ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(satz2,conjecture,
% 1.51/1.25 ! [X: $i] :
% 1.51/1.25 ( ( succ @ X )
% 1.51/1.25 != X ) ).
% 1.51/1.25 ------------------------
% 1.51/1.26 % (23621)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23318 for (2999ds/18Mi)
% 1.51/1.26 % (23615)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23318 for (2999ds/183Mi)
% 1.51/1.27 % (23621)Instruction limit reached!
% 1.51/1.27 % (23621)------------------------------
% 1.51/1.27 % (23621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (23621)Termination reason: Unknown
% 1.51/1.27 % (23621)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (23621)Memory used [KB]: 5628
% 1.51/1.27 % (23621)Time elapsed: 0.008 s
% 1.51/1.27 % (23621)Instructions burned: 18 (million)
% 1.51/1.27 % (23621)------------------------------
% 1.51/1.27 % (23621)------------------------------
% 1.51/1.27 % (23615)First to succeed.
% 1.51/1.27 % (23616)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_23318 for (2999ds/4Mi)
% 1.51/1.27 % (23617)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_23318 for (2999ds/27Mi)
% 1.51/1.27 % (23618)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23318 for (2999ds/2Mi)
% 1.51/1.27 % (23619)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_23318 for (2999ds/2Mi)
% 1.51/1.27 % (23620)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_23318 for (2999ds/275Mi)
% 1.51/1.27 % (23615)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_23318
% 1.51/1.27 % SZS output start Proof for DTF2THF_23318
% 1.51/1.27 thf(func_def_1, type, succ: $i > $i).
% 1.51/1.27 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.51/1.27 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.51/1.27 thf(f217,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(equality_resolution,[status(thm)],[f215])).
% 1.51/1.27 thf(f215,plain,(
% 1.51/1.27 ( ! [X0 : $i] : ((sK1 != X0)) )),
% 1.51/1.27 inference(subsumption_resolution,[status(thm)],[f211,f18])).
% 1.51/1.27 thf(f18,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ X0) != one)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f1])).
% 1.51/1.27 thf(f1,axiom,(
% 1.51/1.27 ! [X0 : $i] : ((succ @ X0) != one)),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',one_is_first)).
% 1.51/1.27 thf(f211,plain,(
% 1.51/1.27 ( ! [X0 : $i] : ((one = (succ @ one)) | (sK1 != X0)) )),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.51/1.27 thf(f207,plain,(
% 1.51/1.27 ( ! [X0 : $i] : ((sK1 != X0) | (sK1 != sK1) | (one = (succ @ one))) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f22,f173])).
% 1.51/1.27 thf(f173,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : ((one = X0) | (sK1 != X0) | (X0 != X1)) )),
% 1.51/1.27 inference(duplicate_literal_removal,[status(thm)],[f172])).
% 1.51/1.27 thf(f172,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : ((one = X0) | (one = X0) | (sK1 != X0) | (X0 != X1)) )),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f171])).
% 1.51/1.27 thf(f171,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (($true = (X0 = one)) | (one = X0) | (sK1 != X0) | (X0 != X1)) )),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 1.51/1.27 thf(f170,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (((X0 = X1) = $false) | ($true = (X0 = one)) | (sK1 != X0) | (one = X0)) )),
% 1.51/1.27 inference(not_proxy_clausification,[status(thm)],[f169])).
% 1.51/1.27 thf(f169,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : ((one = X0) | ($true = (~ (X0 = X1))) | (sK1 != X0) | ($true = (X0 = one))) )),
% 1.51/1.27 inference(not_proxy_clausification,[status(thm)],[f168])).
% 1.51/1.27 thf(f168,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (($true != (~ (X0 = one))) | ($true = (~ (X0 = X1))) | (sK1 != X0) | (one = X0)) )),
% 1.51/1.27 inference(duplicate_literal_removal,[status(thm)],[f167])).
% 1.51/1.27 thf(f167,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : ((sK1 != X0) | ($true != (~ (X0 = one))) | (sK1 != X0) | (one = X0) | ($true = (~ (X0 = X1)))) )),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f166])).
% 1.51/1.27 thf(f166,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : ((one = X0) | ($false = (X0 = sK1)) | ($true = (~ (X0 = X1))) | (sK1 != X0) | ($true != (~ (X0 = one)))) )),
% 1.51/1.27 inference(not_proxy_clausification,[status(thm)],[f165])).
% 1.51/1.27 thf(f165,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (((~ (X0 = sK1)) = $true) | (one = X0) | (sK1 != X0) | ($true = (~ (X0 = X1))) | ($true != (~ (X0 = one)))) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f162])).
% 1.51/1.27 thf(f162,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (($true != ((^[Y0 : $i]: (~ (X0 = Y0))) @ one)) | (one = X0) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ sK1)) | (sK1 != X0) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X1))) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f19,f105])).
% 1.51/1.27 thf(f105,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: (~ (X0 = Y0)))) = sK1) | (sK1 != X0) | (one = X0)) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f24,f90])).
% 1.51/1.27 thf(f90,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | (one = X0)) )),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.51/1.27 thf(f89,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | ($true = (X0 = one))) )),
% 1.51/1.27 inference(not_proxy_clausification,[status(thm)],[f88])).
% 1.51/1.27 thf(f88,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | ($true != (~ (X0 = one)))) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.51/1.27 thf(f69,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ (sK0 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | ($true != ((^[Y0 : $i]: (~ (X0 = Y0))) @ one))) )),
% 1.51/1.27 inference(leibniz_equality_elimination,[status(thm)],[f20])).
% 1.51/1.27 thf(f20,plain,(
% 1.51/1.27 ( ! [X2 : $i,X0 : $i > $o] : (($true != (X0 @ (succ @ (sK0 @ X0)))) | ($true != (X0 @ one)) | ($true = (X0 @ X2))) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : (($true != (X0 @ one)) | (($true != (X0 @ (succ @ (sK0 @ X0)))) & ($true = (X0 @ (sK0 @ X0)))) | ! [X2 : $i] : ($true = (X0 @ X2)))),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f13])).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : (? [X1 : $i] : (($true != (X0 @ (succ @ X1))) & ($true = (X0 @ X1))) => (($true != (X0 @ (succ @ (sK0 @ X0)))) & ($true = (X0 @ (sK0 @ X0)))))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : (($true != (X0 @ one)) | ? [X1 : $i] : (($true != (X0 @ (succ @ X1))) & ($true = (X0 @ X1))) | ! [X2 : $i] : ($true = (X0 @ X2)))),
% 1.51/1.27 inference(flattening,[status(thm)],[f9])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : (! [X2 : $i] : ($true = (X0 @ X2)) | (($true != (X0 @ one)) | ? [X1 : $i] : (($true != (X0 @ (succ @ X1))) & ($true = (X0 @ X1)))))),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f8])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : ((($true = (X0 @ one)) & ! [X1 : $i] : (($true = (X0 @ X1)) => ($true = (X0 @ (succ @ X1))))) => ! [X2 : $i] : ($true = (X0 @ X2)))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 1.51/1.27 inference(rectify,[status(thm)],[f3])).
% 1.51/1.27 thf(f3,axiom,(
% 1.51/1.27 ! [X2 : $i > $o] : ((! [X0 : $i] : ((X2 @ X0) => (X2 @ (succ @ X0))) & (X2 @ one)) => ! [X1 : $i] : (X2 @ X1))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',induction)).
% 1.51/1.27 thf(f24,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((succ @ X0) != sK1) | (sK1 = X0)) )),
% 1.51/1.27 inference(superposition,[status(thm)],[f21,f22])).
% 1.51/1.27 thf(f21,plain,(
% 1.51/1.27 ( ! [X0 : $i,X1 : $i] : (((succ @ X0) != (succ @ X1)) | (X0 = X1)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f15])).
% 1.51/1.27 thf(f15,plain,(
% 1.51/1.27 ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((succ @ X0) != (succ @ X1)))),
% 1.51/1.27 inference(rectify,[status(thm)],[f12])).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 ! [X1 : $i,X0 : $i] : ((X0 = X1) | ((succ @ X0) != (succ @ X1)))),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f2])).
% 1.51/1.27 thf(f2,axiom,(
% 1.51/1.27 ! [X1 : $i,X0 : $i] : (((succ @ X0) = (succ @ X1)) => (X0 = X1))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',succ_injective)).
% 1.51/1.27 thf(f19,plain,(
% 1.51/1.27 ( ! [X2 : $i,X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) | ($true = (X0 @ X2)) | ($true != (X0 @ one))) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 1.51/1.27 thf(f22,plain,(
% 1.51/1.27 ((succ @ sK1) = sK1)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f17])).
% 1.51/1.27 thf(f17,plain,(
% 1.51/1.27 ((succ @ sK1) = sK1)),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f16])).
% 1.51/1.27 thf(f16,plain,(
% 1.51/1.27 ? [X0 : $i] : ((succ @ X0) = X0) => ((succ @ sK1) = sK1)),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 ? [X0 : $i] : ((succ @ X0) = X0)),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,negated_conjecture,(
% 1.51/1.27 ~! [X0 : $i] : ((succ @ X0) != X0)),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.51/1.27 thf(f4,conjecture,(
% 1.51/1.27 ! [X0 : $i] : ((succ @ X0) != X0)),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.dDnUcOoXu4/DTF2THF_23318.p',satz2)).
% 1.51/1.27 % SZS output end Proof for DTF2THF_23318
% 1.51/1.27 % (23615)------------------------------
% 1.51/1.27 % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (23615)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (23615)Memory used [KB]: 5628
% 1.51/1.27 % (23615)Time elapsed: 0.008 s
% 1.51/1.27 % (23615)Instructions burned: 15 (million)
% 1.51/1.27 % (23615)------------------------------
% 1.51/1.27 % (23615)------------------------------
% 1.51/1.27 % (23614)Success in time 0.018 s
%------------------------------------------------------------------------------