%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM636^3 : 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 : n001.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 0.28s 1.24s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 212 ( 64 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 197 ( 39 ~; 32 |; 9 &; 104 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 39 !; 6 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
succ: $i > $i ).
thf(func_def_3,type,
m: $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f51,f56]) ).
thf(f56,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f30,f46]) ).
thf(f46,plain,
( ! [X0: $i] :
( ( m @ X0 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl2_2
<=> ! [X0: $i] :
( ( m @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f30,plain,
( ( m @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( m @ sK0 )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i] :
( ( m @ X0 )
!= $true )
=> ( ( m @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
? [X0: $i] :
( ( m @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ! [X0: $i] :
( ( m @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ! [X0: $i] : ( m @ X0 ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ! [X0: $i] : ( m @ X0 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
! [X0: $i] : ( m @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_all) ).
thf(f51,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f50,f41,f45]) ).
thf(f41,definition,
( spl2_1
<=> ( ( m @ ( sK1 @ m ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f50,plain,
( ! [X0: $i] :
( ( m @ X0 )
= $true )
| spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f49,f31]) ).
thf(f31,plain,
( ( m @ one )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( m @ one )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
m @ one,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
m @ one,
file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_one) ).
thf(f49,plain,
( ! [X0: $i] :
( ( ( m @ one )
!= $true )
| ( ( m @ X0 )
= $true ) )
| spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: $i] :
( ( ( m @ X0 )
= $true )
| ( $true != $true )
| ( ( m @ one )
!= $true ) )
| spl2_1 ),
inference(superposition,[status(thm)],[f43,f34]) ).
thf(f34,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK1 @ X0 ) )
= $true )
| ( ( X0 @ X1 )
= $true )
| ( ( X0 @ one )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ one )
!= $true )
| ( ( ( X0 @ ( succ @ ( sK1 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).
thf(f28,plain,
! [X0: $i > $o] :
( ? [X2: $i] :
( ( $true
!= ( X0 @ ( succ @ X2 ) ) )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( succ @ ( sK1 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ one )
!= $true )
| ? [X2: $i] :
( ( $true
!= ( X0 @ ( succ @ X2 ) ) )
& ( ( X0 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= $true )
| ( ( X0 @ one )
!= $true )
| ? [X1: $i] :
( ( ( X0 @ ( succ @ X1 ) )
!= $true )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= $true )
| ( ( X0 @ one )
!= $true )
| ? [X1: $i] :
( ( ( X0 @ ( succ @ X1 ) )
!= $true )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ one )
= $true )
& ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( succ @ X1 ) )
= $true ) ) )
=> ! [X2: $i] :
( ( X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,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.RvxFa77ogw/DTF2THF_30469.p',induction) ).
thf(f43,plain,
( ( ( m @ ( sK1 @ m ) )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f47,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f39,f45,f41]) ).
thf(f39,plain,
! [X0: $i] :
( ( ( m @ ( sK1 @ m ) )
!= $true )
| ( ( m @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f38,f31]) ).
thf(f38,plain,
! [X0: $i] :
( ( ( m @ one )
!= $true )
| ( ( m @ ( sK1 @ m ) )
!= $true )
| ( ( m @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i] :
( ( ( m @ X0 )
= $true )
| ( ( m @ ( sK1 @ m ) )
!= $true )
| ( $true != $true )
| ( ( m @ one )
!= $true ) ),
inference(superposition,[status(thm)],[f35,f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( ( m @ ( succ @ X0 ) )
= $true )
| ( ( m @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( m @ ( succ @ X0 ) )
= $true )
| ( ( m @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( m @ X0 )
= $true )
=> ( ( m @ ( succ @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( m @ X0 )
=> ( m @ ( succ @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: $i] :
( ( m @ X0 )
=> ( m @ ( succ @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_next) ).
thf(f35,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( succ @ ( sK1 @ X0 ) ) )
!= $true )
| ( ( X0 @ X1 )
= $true )
| ( ( X0 @ one )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM636^3 : 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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 11:09:50 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : NUM636^3 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.44 % Domain : Number Theory
% 0.18/0.44 % Problem : Landau theorem 2
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.18/0.44 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.18/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [TPTP]
% 0.18/0.44 % Names : satz2 [Lan30]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.45 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 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.18/0.44 % Syntax : Number of formulae : 10 ( 4 unt; 3 typ; 1 def)
% 0.18/0.44 % Number of atoms : 10 ( 5 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.44 % Number of connectives : 21 ( 2 ~; 0 |; 1 &; 14 @)
% 0.18/0.44 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 8 ( 4 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.18/0.44 % Number of variables : 9 ( 1 ^; 8 !; 0 ?; 9 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments :
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(one_type,type,
% 0.18/0.44 one: $i ).
% 0.18/0.44
% 0.18/0.44 thf(succ_type,type,
% 0.18/0.44 succ: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(one_is_first,axiom,
% 0.18/0.44 ! [X: $i] :
% 0.18/0.44 ( ( succ @ X )
% 0.18/0.44 != one ) ).
% 0.18/0.44
% 0.18/0.44 thf(succ_injective,axiom,
% 0.18/0.44 ! [X: $i,Y: $i] :
% 0.18/0.44 ( ( ( succ @ X )
% 0.18/0.44 = ( succ @ Y ) )
% 0.18/0.44 => ( X = Y ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(induction,axiom,
% 0.18/0.44 ! [M: $i > $o] :
% 0.18/0.44 ( ( ( M @ one )
% 0.18/0.44 & ! [X: $i] :
% 0.18/0.44 ( ( M @ X )
% 0.18/0.44 => ( M @ ( succ @ X ) ) ) )
% 0.18/0.44 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(m_type,type,
% 0.18/0.44 m: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(m_defn,definition,
% 0.18/0.44 ( m
% 0.18/0.44 = ( ^ [E: $i] :
% 0.18/0.44 ( ( succ @ E )
% 0.18/0.44 != E ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(m_is_one,lemma,
% 0.18/0.44 m @ one ).
% 0.18/0.44
% 0.18/0.44 thf(m_is_next,lemma,
% 0.18/0.44 ! [X: $i] :
% 0.18/0.44 ( ( m @ X )
% 0.18/0.44 => ( m @ ( succ @ X ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(m_is_all,conjecture,
% 0.18/0.44 ! [X: $i] : ( m @ X ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 0.28/1.20 ---- Embedded in THF ---
% 0.28/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.28/1.20 %%% Generated on Tue Feb 24 11:09:51 EST 2026
% 0.28/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.28/1.20 %%% Logic specification used:
% 0.28/1.20 %%% thf(spec, logic, $$dhol).
% 0.28/1.20
% 0.28/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2DTF30469.p
% See solution above
% 0.28/1.20 ------------------------
% 0.28/1.21 ---- Cleaned THF ---
% 0.28/1.21 thf(one_type,type,
% 0.28/1.21 one: $i ).
% 0.28/1.21
% 0.28/1.21 thf(succ_type,type,
% 0.28/1.21 succ: $i > $i ).
% 0.28/1.21
% 0.28/1.21 thf(one_is_first,axiom,
% 0.28/1.21 ! [X: $i] :
% 0.28/1.21 ( ( succ @ X )
% 0.28/1.21 != one ) ).
% 0.28/1.21
% 0.28/1.21 thf(succ_injective,axiom,
% 0.28/1.21 ! [X: $i,Y: $i] :
% 0.28/1.21 ( ( ( succ @ X )
% 0.28/1.21 = ( succ @ Y ) )
% 0.28/1.21 => ( X = Y ) ) ).
% 0.28/1.21
% 0.28/1.21 thf(induction,axiom,
% 0.28/1.21 ! [M: $i > $o] :
% 0.28/1.21 ( ( ( M @ one )
% 0.28/1.21 & ! [X: $i] :
% 0.28/1.21 ( ( M @ X )
% 0.28/1.21 => ( M @ ( succ @ X ) ) ) )
% 0.28/1.21 => ! [Y: $i] : ( M @ Y ) ) ).
% 0.28/1.21
% 0.28/1.21 thf(m_type,type,
% 0.28/1.21 m: $i > $o ).
% 0.28/1.21
% 0.28/1.21 thf(m_defn,definition,
% 0.28/1.21 ( m
% 0.28/1.21 = ( ^ [E: $i] :
% 0.28/1.21 ( ( succ @ E )
% 0.28/1.21 != E ) ) ) ).
% 0.28/1.21
% 0.28/1.21 thf(m_is_one,lemma,
% 0.28/1.21 m @ one ).
% 0.28/1.21
% 0.28/1.21 thf(m_is_next,lemma,
% 0.28/1.21 ! [X: $i] :
% 0.28/1.21 ( ( m @ X )
% 0.28/1.21 => ( m @ ( succ @ X ) ) ) ).
% 0.28/1.21
% 0.28/1.21 thf(m_is_all,conjecture,
% 0.28/1.21 ! [X: $i] : ( m @ X ) ).
% 0.28/1.21 ------------------------
% 0.28/1.22 % (30766)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_30469 for (2999ds/27Mi)
% 0.28/1.22 % (30765)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_30469 for (2999ds/4Mi)
% 0.28/1.23 % (30766)Refutation not found, incomplete strategy
% 0.28/1.23 % (30766)------------------------------
% 0.28/1.23 % (30766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.28/1.23 % (30766)Termination reason: Refutation not found, incomplete strategy
% 0.28/1.23
% 0.28/1.23
% 0.28/1.23 % (30766)Memory used [KB]: 5500
% 0.28/1.23 % (30766)Time elapsed: 0.003 s
% 0.28/1.23 % (30766)Instructions burned: 2 (million)
% 0.28/1.23 % (30766)------------------------------
% 0.28/1.23 % (30766)------------------------------
% 0.28/1.23 % (30765)Instruction limit reached!
% 0.28/1.23 % (30765)------------------------------
% 0.28/1.23 % (30765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.28/1.23 % (30765)Termination reason: Unknown
% 0.28/1.23 % (30765)Termination phase: Saturation
% 0.28/1.23
% 0.28/1.23 % (30765)Memory used [KB]: 5500
% 0.28/1.23 % (30765)Time elapsed: 0.003 s
% 0.28/1.23 % (30765)Instructions burned: 5 (million)
% 0.28/1.23 % (30765)------------------------------
% 0.28/1.23 % (30765)------------------------------
% 0.28/1.23 % (30764)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30469 for (2999ds/183Mi)
% 0.28/1.23 % (30767)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30469 for (2999ds/2Mi)
% 0.28/1.23 % (30768)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_30469 for (2999ds/2Mi)
% 0.28/1.23 % (30769)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_30469 for (2999ds/275Mi)
% 0.28/1.23 % (30770)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30469 for (2999ds/18Mi)
% 0.28/1.23 % (30768)Instruction limit reached!
% 0.28/1.23 % (30768)------------------------------
% 0.28/1.23 % (30768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.28/1.23 % (30768)Termination reason: Unknown
% 0.28/1.23 % (30768)Termination phase: Property scanning
% 0.28/1.23
% 0.28/1.23 % (30768)Memory used [KB]: 895
% 0.28/1.23 % (30768)Time elapsed: 0.003 s
% 0.28/1.23 % (30768)Instructions burned: 2 (million)
% 0.28/1.23 % (30768)------------------------------
% 0.28/1.23 % (30768)------------------------------
% 0.28/1.23 % (30767)Instruction limit reached!
% 0.28/1.23 % (30767)------------------------------
% 0.28/1.23 % (30767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.28/1.23 % (30767)Termination reason: Unknown
% 0.28/1.23 % (30767)Termination phase: Saturation
% 0.28/1.23
% 0.28/1.23 % (30767)Memory used [KB]: 5500
% 0.28/1.23 % (30767)Time elapsed: 0.004 s
% 0.28/1.23 % (30767)Instructions burned: 3 (million)
% 0.28/1.23 % (30767)------------------------------
% 0.28/1.23 % (30767)------------------------------
% 0.28/1.23 % (30769)First to succeed.
% 0.28/1.24 % (30772)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30469 for (2999ds/37Mi)
% 0.28/1.24 % (30771)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30469 for (2999ds/3Mi)
% 0.28/1.24 % (30769)Refutation found. Thanks to Tanya!
% 0.28/1.24 % SZS status Theorem for DTF2THF_30469
% 0.28/1.24 % SZS output start Proof for DTF2THF_30469
% 0.28/1.24 thf(func_def_1, type, succ: $i > $i).
% 0.28/1.24 thf(func_def_3, type, m: $i > $o).
% 0.28/1.24 thf(func_def_11, type, sK1: ($i > $o) > $i).
% 0.28/1.24 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 0.28/1.24 thf(f60,plain,(
% 0.28/1.24 $false),
% 0.28/1.24 inference(avatar_sat_refutation,[status(thm)],[f47,f51,f56])).
% 0.28/1.24 thf(f56,plain,(
% 0.28/1.24 ~spl2_2),
% 0.28/1.24 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 0.28/1.24 thf(f55,plain,(
% 0.28/1.24 $false | ~spl2_2),
% 0.28/1.24 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 0.28/1.24 thf(f53,plain,(
% 0.28/1.24 ($true != $true) | ~spl2_2),
% 0.28/1.24 inference(superposition,[status(thm)],[f30,f46])).
% 0.28/1.24 thf(f46,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ X0) = $true)) ) | ~spl2_2),
% 0.28/1.24 inference(avatar_component_clause,[status(thm)],[f45])).
% 0.28/1.24 thf(f45,definition,(
% 0.28/1.24 spl2_2 <=> ! [X0 : $i] : ((m @ X0) = $true)),
% 0.28/1.24 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 0.28/1.24 thf(f30,plain,(
% 0.28/1.24 ((m @ sK0) != $true)),
% 0.28/1.24 inference(cnf_transformation,[status(thm)],[f26])).
% 0.28/1.24 thf(f26,plain,(
% 0.28/1.24 ((m @ sK0) != $true)),
% 0.28/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25])).
% 0.28/1.24 thf(f25,plain,(
% 0.28/1.24 ? [X0 : $i] : ((m @ X0) != $true) => ((m @ sK0) != $true)),
% 0.28/1.24 introduced(definition,[],[choice_axiom])).
% 0.28/1.24 thf(f24,plain,(
% 0.28/1.24 ? [X0 : $i] : ((m @ X0) != $true)),
% 0.28/1.24 inference(ennf_transformation,[status(thm)],[f17])).
% 0.28/1.24 thf(f17,plain,(
% 0.28/1.24 ~! [X0 : $i] : ((m @ X0) = $true)),
% 0.28/1.24 inference(fool_elimination,[status(thm)],[f16])).
% 0.28/1.24 thf(f16,plain,(
% 0.28/1.24 ~! [X0 : $i] : (m @ X0)),
% 0.28/1.24 inference(rectify,[status(thm)],[f8])).
% 0.28/1.24 thf(f8,negated_conjecture,(
% 0.28/1.24 ~! [X0 : $i] : (m @ X0)),
% 0.28/1.24 inference(negated_conjecture,[status(cth)],[f7])).
% 0.28/1.24 thf(f7,conjecture,(
% 0.28/1.24 ! [X0 : $i] : (m @ X0)),
% 0.28/1.24 file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_all)).
% 0.28/1.24 thf(f51,plain,(
% 0.28/1.24 spl2_2 | spl2_1),
% 0.28/1.24 inference(avatar_split_clause,[status(thm)],[f50,f41,f45])).
% 0.28/1.24 thf(f41,definition,(
% 0.28/1.24 spl2_1 <=> ((m @ (sK1 @ m)) = $true)),
% 0.28/1.24 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 0.28/1.24 thf(f50,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ X0) = $true)) ) | spl2_1),
% 0.28/1.24 inference(subsumption_resolution,[status(thm)],[f49,f31])).
% 0.28/1.24 thf(f31,plain,(
% 0.28/1.24 ((m @ one) = $true)),
% 0.28/1.24 inference(cnf_transformation,[status(thm)],[f15])).
% 0.28/1.24 thf(f15,plain,(
% 0.28/1.24 ((m @ one) = $true)),
% 0.28/1.24 inference(fool_elimination,[status(thm)],[f14])).
% 0.28/1.24 thf(f14,plain,(
% 0.28/1.24 (m @ one)),
% 0.28/1.24 inference(rectify,[status(thm)],[f5])).
% 0.28/1.24 thf(f5,axiom,(
% 0.28/1.24 (m @ one)),
% 0.28/1.24 file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_one)).
% 0.28/1.24 thf(f49,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ one) != $true) | ((m @ X0) = $true)) ) | spl2_1),
% 0.28/1.24 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 0.28/1.24 thf(f48,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ X0) = $true) | ($true != $true) | ((m @ one) != $true)) ) | spl2_1),
% 0.28/1.24 inference(superposition,[status(thm)],[f43,f34])).
% 0.28/1.24 thf(f34,plain,(
% 0.28/1.24 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (sK1 @ X0)) = $true) | ((X0 @ X1) = $true) | ((X0 @ one) != $true)) )),
% 0.28/1.24 inference(cnf_transformation,[status(thm)],[f29])).
% 0.28/1.24 thf(f29,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ((X0 @ one) != $true) | (((X0 @ (succ @ (sK1 @ X0))) != $true) & ((X0 @ (sK1 @ X0)) = $true)))),
% 0.28/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28])).
% 0.28/1.24 thf(f28,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : (? [X2 : $i] : (($true != (X0 @ (succ @ X2))) & ((X0 @ X2) = $true)) => (((X0 @ (succ @ (sK1 @ X0))) != $true) & ((X0 @ (sK1 @ X0)) = $true)))),
% 0.28/1.24 introduced(definition,[],[choice_axiom])).
% 0.28/1.24 thf(f27,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ((X0 @ one) != $true) | ? [X2 : $i] : (($true != (X0 @ (succ @ X2))) & ((X0 @ X2) = $true)))),
% 0.28/1.24 inference(rectify,[status(thm)],[f22])).
% 0.28/1.24 thf(f22,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) = $true) | ((X0 @ one) != $true) | ? [X1 : $i] : (((X0 @ (succ @ X1)) != $true) & ((X0 @ X1) = $true)))),
% 0.28/1.24 inference(flattening,[status(thm)],[f21])).
% 0.28/1.24 thf(f21,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) = $true) | (((X0 @ one) != $true) | ? [X1 : $i] : (((X0 @ (succ @ X1)) != $true) & ((X0 @ X1) = $true))))),
% 0.28/1.24 inference(ennf_transformation,[status(thm)],[f19])).
% 0.28/1.24 thf(f19,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : ((((X0 @ one) = $true) & ! [X1 : $i] : (((X0 @ X1) = $true) => ((X0 @ (succ @ X1)) = $true))) => ! [X2 : $i] : ((X0 @ X2) = $true))),
% 0.28/1.24 inference(fool_elimination,[status(thm)],[f18])).
% 0.28/1.24 thf(f18,plain,(
% 0.28/1.24 ! [X0 : $i > $o] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.28/1.24 inference(rectify,[status(thm)],[f3])).
% 0.28/1.24 thf(f3,axiom,(
% 0.28/1.24 ! [X2 : $i > $o] : ((! [X0 : $i] : ((X2 @ X0) => (X2 @ (succ @ X0))) & (X2 @ one)) => ! [X1 : $i] : (X2 @ X1))),
% 0.28/1.24 file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',induction)).
% 0.28/1.24 thf(f43,plain,(
% 0.28/1.24 ((m @ (sK1 @ m)) != $true) | spl2_1),
% 0.28/1.24 inference(avatar_component_clause,[status(thm)],[f41])).
% 0.28/1.24 thf(f47,plain,(
% 0.28/1.24 ~spl2_1 | spl2_2),
% 0.28/1.24 inference(avatar_split_clause,[status(thm)],[f39,f45,f41])).
% 0.28/1.24 thf(f39,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ (sK1 @ m)) != $true) | ((m @ X0) = $true)) )),
% 0.28/1.24 inference(subsumption_resolution,[status(thm)],[f38,f31])).
% 0.28/1.24 thf(f38,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ one) != $true) | ((m @ (sK1 @ m)) != $true) | ((m @ X0) = $true)) )),
% 0.28/1.24 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 0.28/1.24 thf(f37,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ X0) = $true) | ((m @ (sK1 @ m)) != $true) | ($true != $true) | ((m @ one) != $true)) )),
% 0.28/1.24 inference(superposition,[status(thm)],[f35,f36])).
% 0.28/1.24 thf(f36,plain,(
% 0.28/1.24 ( ! [X0 : $i] : (((m @ (succ @ X0)) = $true) | ((m @ X0) != $true)) )),
% 0.28/1.24 inference(cnf_transformation,[status(thm)],[f23])).
% 0.28/1.24 thf(f23,plain,(
% 0.28/1.24 ! [X0 : $i] : (((m @ (succ @ X0)) = $true) | ((m @ X0) != $true))),
% 0.28/1.24 inference(ennf_transformation,[status(thm)],[f13])).
% 0.28/1.24 thf(f13,plain,(
% 0.28/1.24 ! [X0 : $i] : (((m @ X0) = $true) => ((m @ (succ @ X0)) = $true))),
% 0.28/1.24 inference(fool_elimination,[status(thm)],[f12])).
% 0.28/1.24 thf(f12,plain,(
% 0.28/1.24 ! [X0 : $i] : ((m @ X0) => (m @ (succ @ X0)))),
% 0.28/1.24 inference(rectify,[status(thm)],[f6])).
% 0.28/1.24 thf(f6,axiom,(
% 0.28/1.24 ! [X0 : $i] : ((m @ X0) => (m @ (succ @ X0)))),
% 0.28/1.24 file('/export/starexec/sandbox/tmp/tmp.RvxFa77ogw/DTF2THF_30469.p',m_is_next)).
% 0.28/1.24 thf(f35,plain,(
% 0.28/1.24 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (succ @ (sK1 @ X0))) != $true) | ((X0 @ X1) = $true) | ((X0 @ one) != $true)) )),
% 0.28/1.24 inference(cnf_transformation,[status(thm)],[f29])).
% 0.28/1.24 % SZS output end Proof for DTF2THF_30469
% 0.28/1.24 % (30769)------------------------------
% 0.28/1.24 % (30769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.28/1.24 % (30769)Termination reason: Refutation
% 0.28/1.24
% 0.28/1.24 % (30769)Memory used [KB]: 5500
% 0.28/1.24 % (30769)Time elapsed: 0.006 s
% 0.28/1.24 % (30769)Instructions burned: 3 (million)
% 0.28/1.24 % (30769)------------------------------
% 0.28/1.24 % (30769)------------------------------
% 0.28/1.24 % (30763)Success in time 0.022 s
%------------------------------------------------------------------------------