%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN023^2 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 09:27:12 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 231 ( 94 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 277 ( 34 ~; 28 |; 24 &; 173 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 0 ^; 74 !; 5 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
ite: $o > $i > $i > $i ).
thf(func_def_3,type,
h: $i > $i ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f74,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f21,f50,f72,f73]) ).
thf(f73,plain,
( ( zero
!= ( s @ zero ) )
| ( zero
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f72,plain,
( spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| spl0_3
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f70,f31]) ).
thf(f31,plain,
( ( zero
!= ( s @ zero ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_3
<=> ( zero
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f70,plain,
( ( zero
= ( s @ zero ) )
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( zero
= ( s @ zero ) )
| ( zero != zero )
| spl0_4 ),
inference(superposition,[status(thm)],[f49,f38]) ).
thf(f38,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( zero = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( ( zero = X0 )
= $true ) ),
inference(superposition,[status(thm)],[f11,f13]) ).
thf(f13,plain,
! [X2: $i,X0: $o,X1: $i] :
( ( ( ite @ X0 @ X1 @ X2 )
= X2 )
| ( $true = X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $o,X1: $i,X2: $i] :
( ( $true = X0 )
| ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i > $i] :
( ( zero
!= ( X3 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X3 @ zero ) ) )
& ! [X4: $i] :
( ( h @ X4 )
= ( ite @ ( zero = X4 ) @ ( s @ zero ) @ zero ) )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X7 @ X5 )
= X7 )
| ( $true != X6 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $o,X1: $i,X2: $i] :
( ( $true = X0 )
| ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X7: $i > $i] :
( ( zero
!= ( X7 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X7 @ zero ) ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i,X5: $o,X6: $i] :
( ( ( ite @ X5 @ X6 @ X4 )
= X6 )
| ( $true != X5 ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X7: $i > $i] :
( ( zero
!= ( X7 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X7 @ zero ) ) )
& ! [X0: $o,X1: $i,X2: $i] :
( ( $true = X0 )
| ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i,X5: $o,X6: $i] :
( ( ( ite @ X5 @ X6 @ X4 )
= X6 )
| ( $true != X5 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true != X0 )
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i,X5: $o,X6: $i] :
( ( $true = X5 )
=> ( ( ite @ X5 @ X6 @ X4 )
= X6 ) ) )
=> ? [X7: $i > $i] :
( ( ( s @ zero )
= ( X7 @ zero ) )
& ( zero
= ( X7 @ ( s @ zero ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true != X0 )
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i,X5: $o,X6: $i] :
( ( $true = X5 )
=> ( ( ite @ X5 @ X6 @ X4 )
= X6 ) ) )
=> ? [X7: $i > $i] :
( ( ( s @ zero )
= ( X7 @ zero ) )
& ( zero
= ( X7 @ ( s @ zero ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero )
= ( h @ X3 ) )
& ! [X4: $i,X5: $o,X6: $i] :
( X5
=> ( ( ite @ X5 @ X6 @ X4 )
= X6 ) ) )
=> ? [X7: $i > $i] :
( ( zero
= ( X7 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X7 @ zero ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero )
= ( h @ X3 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $o,X1: $i,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero )
= ( h @ X3 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vZqUbw50Uj/DTF2THF_30193.p',n10) ).
thf(f11,plain,
! [X4: $i] :
( ( h @ X4 )
= ( ite @ ( zero = X4 ) @ ( s @ zero ) @ zero ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f49,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_4
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f50,plain,
~ spl0_4,
inference(avatar_split_clause,[status(thm)],[f45,f47]) ).
thf(f45,plain,
( zero
!= ( h @ ( s @ zero ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( zero != zero )
| ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) ) ),
inference(superposition,[status(thm)],[f12,f40]) ).
thf(f40,plain,
! [X4: $i] :
( ( ( s @ zero )
= ( h @ X4 ) )
| ( zero != X4 ) ),
inference(forward_demodulation,[status(thm)],[f39,f14]) ).
thf(f14,plain,
! [X7: $i,X5: $i] :
( ( ite @ $true @ X7 @ X5 )
= X7 ),
inference(equality_resolution,[status(thm)],[f10]) ).
thf(f10,plain,
! [X6: $o,X7: $i,X5: $i] :
( ( ( ite @ X6 @ X7 @ X5 )
= X7 )
| ( $true != X6 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f39,plain,
! [X4: $i] :
( ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ zero ) )
| ( zero != X4 ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X4: $i] :
( ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ zero ) )
| ( ( zero = X4 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X3: $i > $i] :
( ( ( s @ zero )
!= ( X3 @ zero ) )
| ( zero
!= ( X3 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f21,plain,
~ spl0_1,
inference(avatar_split_clause,[status(thm)],[f16,f18]) ).
thf(f18,definition,
( spl0_1
<=> ( zero
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( zero
!= ( s @ ( s @ zero ) ) ),
inference(equality_resolution,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN023^2 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n004.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 11:19:26 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NUN023^2 : TPTP v9.2.1. Released v6.4.0.
% 0.29/0.45 % Domain : Number Theory
% 0.29/0.45 % Problem : Function h s.t. h(0) = 1, h(1) = 0, with witness
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.29/0.45 % term that expresses the function H.
% 0.29/0.45
% 0.29/0.45 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [TPTP]
% 0.29/0.45 % Names : ntape6-0-with-witness.tptp [Rie16]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0
% 0.29/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.45 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 5 ( 6 avg)
% 0.29/0.45 % Number of connectives : 22 ( 1 ~; 0 |; 3 &; 15 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-3 aty)
% 0.29/0.45 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(n6,type,
% 0.29/0.45 zero: $i ).
% 0.29/0.45
% 0.29/0.45 thf(n7,type,
% 0.29/0.45 s: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(n8,type,
% 0.29/0.45 ite: $o > $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(n9,type,
% 0.29/0.45 h: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(n10,conjecture,
% 0.29/0.45 ( ( ! [X100: $o,U: $i,V: $i] :
% 0.29/0.45 ( X100
% 0.29/0.45 => ( ( ite @ X100 @ U @ V )
% 0.29/0.45 = U ) )
% 0.29/0.45 & ! [X100: $o,U: $i,V: $i] :
% 0.29/0.45 ( ~ X100
% 0.29/0.45 => ( ( ite @ X100 @ U @ V )
% 0.29/0.45 = V ) )
% 0.29/0.45 & ! [X: $i] :
% 0.29/0.45 ( ( h @ X )
% 0.29/0.45 = ( ite @ ( X = zero ) @ ( s @ zero ) @ zero ) ) )
% 0.29/0.45 => ? [H: $i > $i] :
% 0.29/0.45 ( ( ( H @ zero )
% 0.29/0.45 = ( s @ zero ) )
% 0.29/0.45 & ( ( H @ ( s @ zero ) )
% 0.29/0.45 = zero ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 11:19:27 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vZqUbw50Uj/DTF2DTF30193.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(n6,type,
% 1.49/1.26 zero: $i ).
% 1.49/1.26
% 1.49/1.26 thf(n7,type,
% 1.49/1.26 s: $i > $i ).
% 1.49/1.26
% 1.49/1.26 thf(n8,type,
% 1.49/1.26 ite: $o > $i > $i > $i ).
% 1.49/1.26
% 1.49/1.26 thf(n9,type,
% 1.49/1.26 h: $i > $i ).
% 1.49/1.26
% 1.49/1.26 thf(n10,conjecture,
% 1.49/1.26 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.49/1.26 ( X100
% 1.49/1.26 => ( ( ite @ X100 @ U @ V )
% 1.49/1.26 = U ) )
% 1.49/1.26 & ! [X100: $o,U: $i,V: $i] :
% 1.49/1.26 ( ~ X100
% 1.49/1.26 => ( ( ite @ X100 @ U @ V )
% 1.49/1.26 = V ) )
% 1.49/1.26 & ! [X: $i] :
% 1.49/1.26 ( ( h @ X )
% 1.49/1.26 = ( ite @ ( X = zero ) @ ( s @ zero ) @ zero ) ) )
% 1.49/1.26 => ? [H: $i > $i] :
% 1.49/1.26 ( ( ( H @ zero )
% 1.49/1.26 = ( s @ zero ) )
% 1.49/1.26 & ( ( H @ ( s @ zero ) )
% 1.49/1.26 = zero ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (30458)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30193 for (2999ds/2Mi)
% 1.49/1.27 % (30456)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_30193 for (2999ds/4Mi)
% 1.49/1.27 % (30458)Instruction limit reached!
% 1.49/1.27 % (30458)------------------------------
% 1.49/1.27 % (30458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (30458)Termination reason: Unknown
% 1.49/1.27 % (30458)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (30458)Memory used [KB]: 5500
% 1.49/1.27 % (30458)Time elapsed: 0.002 s
% 1.49/1.27 % (30458)Instructions burned: 2 (million)
% 1.49/1.27 % (30458)------------------------------
% 1.49/1.27 % (30458)------------------------------
% 1.49/1.27 % (30459)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_30193 for (2999ds/2Mi)
% 1.49/1.27 % (30459)Instruction limit reached!
% 1.49/1.27 % (30459)------------------------------
% 1.49/1.27 % (30459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (30459)Termination reason: Unknown
% 1.49/1.27 % (30459)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (30459)Memory used [KB]: 5500
% 1.49/1.27 % (30459)Time elapsed: 0.002 s
% 1.49/1.27 % (30459)Instructions burned: 3 (million)
% 1.49/1.27 % (30459)------------------------------
% 1.49/1.27 % (30459)------------------------------
% 1.49/1.28 % (30456)Instruction limit reached!
% 1.49/1.28 % (30456)------------------------------
% 1.49/1.28 % (30456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (30456)Termination reason: Unknown
% 1.49/1.28 % (30456)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (30456)Memory used [KB]: 5500
% 1.49/1.28 % (30456)Time elapsed: 0.003 s
% 1.49/1.28 % (30456)Instructions burned: 5 (million)
% 1.49/1.28 % (30456)------------------------------
% 1.49/1.28 % (30456)------------------------------
% 1.49/1.28 % (30455)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30193 for (2999ds/183Mi)
% 1.49/1.28 % (30457)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_30193 for (2999ds/27Mi)
% 1.49/1.28 % (30461)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30193 for (2999ds/18Mi)
% 1.49/1.28 % (30460)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_30193 for (2999ds/275Mi)
% 1.49/1.28 % (30462)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30193 for (2999ds/3Mi)
% 1.49/1.28 % (30462)Instruction limit reached!
% 1.49/1.28 % (30462)------------------------------
% 1.49/1.28 % (30462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (30462)Termination reason: Unknown
% 1.49/1.28 % (30462)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (30462)Memory used [KB]: 5500
% 1.49/1.28 % (30462)Time elapsed: 0.002 s
% 1.49/1.28 % (30462)Instructions burned: 3 (million)
% 1.49/1.28 % (30462)------------------------------
% 1.49/1.28 % (30462)------------------------------
% 1.49/1.28 % (30463)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_30193 for (2999ds/37Mi)
% 1.49/1.29 % (30460)Refutation not found, incomplete strategy
% 1.49/1.29 % (30460)------------------------------
% 1.49/1.29 % (30460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (30460)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (30460)Memory used [KB]: 5500
% 1.49/1.29 % (30460)Time elapsed: 0.006 s
% 1.49/1.29 % (30460)Instructions burned: 5 (million)
% 1.49/1.29 % (30460)------------------------------
% 1.49/1.29 % (30460)------------------------------
% 1.49/1.29 % (30457)Refutation not found, incomplete strategy
% 1.49/1.29 % (30457)------------------------------
% 1.49/1.29 % (30457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (30457)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (30457)Memory used [KB]: 5500
% 1.49/1.29 % (30457)Time elapsed: 0.006 s
% 1.49/1.29 % (30457)Instructions burned: 5 (million)
% 1.49/1.29 % (30457)------------------------------
% 1.49/1.29 % (30457)------------------------------
% 1.49/1.29 % (30464)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30193 for (2999ds/15Mi)
% 1.49/1.29 % (30464)First to succeed.
% 1.49/1.29 % (30464)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_30193
% 1.49/1.29 % SZS output start Proof for DTF2THF_30193
% 1.49/1.29 thf(func_def_1, type, s: $i > $i).
% 1.49/1.29 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.49/1.29 thf(func_def_3, type, h: $i > $i).
% 1.49/1.29 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.29 thf(f74,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(avatar_sat_refutation,[status(thm)],[f21,f50,f72,f73])).
% 1.49/1.29 thf(f73,plain,(
% 1.49/1.29 (zero != (s @ zero)) | (zero = (s @ (s @ zero)))),
% 1.49/1.29 introduced(definition,[],[theory_tautology_sat_conflict])).
% 1.49/1.29 thf(f72,plain,(
% 1.49/1.29 spl0_3 | spl0_4),
% 1.49/1.29 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.49/1.29 thf(f71,plain,(
% 1.49/1.29 $false | (spl0_3 | spl0_4)),
% 1.49/1.29 inference(subsumption_resolution,[status(thm)],[f70,f31])).
% 1.49/1.29 thf(f31,plain,(
% 1.49/1.29 (zero != (s @ zero)) | spl0_3),
% 1.49/1.29 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.49/1.29 thf(f29,definition,(
% 1.49/1.29 spl0_3 <=> (zero = (s @ zero))),
% 1.49/1.29 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.49/1.29 thf(f70,plain,(
% 1.49/1.29 (zero = (s @ zero)) | spl0_4),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.49/1.29 thf(f68,plain,(
% 1.49/1.29 (zero = (s @ zero)) | (zero != zero) | spl0_4),
% 1.49/1.29 inference(superposition,[status(thm)],[f49,f38])).
% 1.49/1.29 thf(f38,plain,(
% 1.49/1.29 ( ! [X0 : $i] : ((zero = (h @ X0)) | (zero = X0)) )),
% 1.49/1.29 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.49/1.29 thf(f34,plain,(
% 1.49/1.29 ( ! [X0 : $i] : ((zero = (h @ X0)) | ((zero = X0) = $true)) )),
% 1.49/1.29 inference(superposition,[status(thm)],[f11,f13])).
% 1.49/1.29 thf(f13,plain,(
% 1.49/1.29 ( ! [X2 : $i,X0 : $o,X1 : $i] : (((ite @ X0 @ X1 @ X2) = X2) | ($true = X0)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 ! [X0 : $o,X1 : $i,X2 : $i] : (($true = X0) | ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i > $i] : ((zero != (X3 @ (s @ zero))) | ((s @ zero) != (X3 @ zero))) & ! [X4 : $i] : ((h @ X4) = (ite @ (zero = X4) @ (s @ zero) @ zero)) & ! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X7 @ X5) = X7) | ($true != X6))),
% 1.49/1.29 inference(rectify,[status(thm)],[f8])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 ! [X0 : $o,X1 : $i,X2 : $i] : (($true = X0) | ((ite @ X0 @ X1 @ X2) = X2)) & ! [X7 : $i > $i] : ((zero != (X7 @ (s @ zero))) | ((s @ zero) != (X7 @ zero))) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i,X5 : $o,X6 : $i] : (((ite @ X5 @ X6 @ X4) = X6) | ($true != X5))),
% 1.49/1.29 inference(flattening,[status(thm)],[f7])).
% 1.49/1.29 thf(f7,plain,(
% 1.49/1.29 ! [X7 : $i > $i] : ((zero != (X7 @ (s @ zero))) | ((s @ zero) != (X7 @ zero))) & (! [X0 : $o,X1 : $i,X2 : $i] : (($true = X0) | ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i,X5 : $o,X6 : $i] : (((ite @ X5 @ X6 @ X4) = X6) | ($true != X5)))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.29 thf(f6,plain,(
% 1.49/1.29 ~((! [X0 : $o,X1 : $i,X2 : $i] : (($true != X0) => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i,X5 : $o,X6 : $i] : (($true = X5) => ((ite @ X5 @ X6 @ X4) = X6))) => ? [X7 : $i > $i] : (((s @ zero) = (X7 @ zero)) & (zero = (X7 @ (s @ zero)))))),
% 1.49/1.29 inference(flattening,[status(thm)],[f5])).
% 1.49/1.29 thf(f5,plain,(
% 1.49/1.29 ~((! [X0 : $o,X1 : $i,X2 : $i] : (~($true = X0) => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i,X5 : $o,X6 : $i] : (($true = X5) => ((ite @ X5 @ X6 @ X4) = X6))) => ? [X7 : $i > $i] : (((s @ zero) = (X7 @ zero)) & (zero = (X7 @ (s @ zero)))))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,plain,(
% 1.49/1.29 ~((! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((ite @ (zero = X3) @ (s @ zero) @ zero) = (h @ X3)) & ! [X4 : $i,X5 : $o,X6 : $i] : (X5 => ((ite @ X5 @ X6 @ X4) = X6))) => ? [X7 : $i > $i] : ((zero = (X7 @ (s @ zero))) & ((s @ zero) = (X7 @ zero))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f2])).
% 1.49/1.29 thf(f2,negated_conjecture,(
% 1.49/1.29 ~((! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((ite @ (zero = X3) @ (s @ zero) @ zero) = (h @ X3)) & ! [X2 : $i,X0 : $o,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero))))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.29 thf(f1,conjecture,(
% 1.49/1.29 (! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((ite @ (zero = X3) @ (s @ zero) @ zero) = (h @ X3)) & ! [X2 : $i,X0 : $o,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.vZqUbw50Uj/DTF2THF_30193.p',n10)).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ( ! [X4 : $i] : (((h @ X4) = (ite @ (zero = X4) @ (s @ zero) @ zero))) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.29 thf(f49,plain,(
% 1.49/1.29 (zero != (h @ (s @ zero))) | spl0_4),
% 1.49/1.29 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.49/1.29 thf(f47,definition,(
% 1.49/1.29 spl0_4 <=> (zero = (h @ (s @ zero)))),
% 1.49/1.29 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.49/1.29 thf(f50,plain,(
% 1.49/1.29 ~spl0_4),
% 1.49/1.29 inference(avatar_split_clause,[status(thm)],[f45,f47])).
% 1.49/1.29 thf(f45,plain,(
% 1.49/1.29 (zero != (h @ (s @ zero)))),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.49/1.29 thf(f44,plain,(
% 1.49/1.29 (zero != zero) | ((s @ zero) != (s @ zero)) | (zero != (h @ (s @ zero)))),
% 1.49/1.29 inference(superposition,[status(thm)],[f12,f40])).
% 1.49/1.29 thf(f40,plain,(
% 1.49/1.29 ( ! [X4 : $i] : (((s @ zero) = (h @ X4)) | (zero != X4)) )),
% 1.49/1.29 inference(forward_demodulation,[status(thm)],[f39,f14])).
% 1.49/1.29 thf(f14,plain,(
% 1.49/1.29 ( ! [X7 : $i,X5 : $i] : (((ite @ $true @ X7 @ X5) = X7)) )),
% 1.49/1.29 inference(equality_resolution,[status(thm)],[f10])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 ( ! [X6 : $o,X7 : $i,X5 : $i] : (((ite @ X6 @ X7 @ X5) = X7) | ($true != X6)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.29 thf(f39,plain,(
% 1.49/1.29 ( ! [X4 : $i] : (((h @ X4) = (ite @ $true @ (s @ zero) @ zero)) | (zero != X4)) )),
% 1.49/1.29 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.49/1.29 thf(f33,plain,(
% 1.49/1.29 ( ! [X4 : $i] : (((h @ X4) = (ite @ $true @ (s @ zero) @ zero)) | ((zero = X4) = $false)) )),
% 1.49/1.29 inference(fool_paramodulation,[status(thm)],[f11])).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 ( ! [X3 : $i > $i] : (((s @ zero) != (X3 @ zero)) | (zero != (X3 @ (s @ zero)))) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.49/1.29 thf(f21,plain,(
% 1.49/1.29 ~spl0_1),
% 1.49/1.29 inference(avatar_split_clause,[status(thm)],[f16,f18])).
% 1.49/1.29 thf(f18,definition,(
% 1.49/1.29 spl0_1 <=> (zero = (s @ (s @ zero)))),
% 1.49/1.29 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.29 thf(f16,plain,(
% 1.49/1.29 (zero != (s @ (s @ zero)))),
% 1.49/1.29 inference(equality_resolution,[status(thm)],[f12])).
% 1.49/1.29 % SZS output end Proof for DTF2THF_30193
% 1.49/1.29 % (30464)------------------------------
% 1.49/1.29 % (30464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (30464)Termination reason: Refutation
% 1.49/1.29
% 1.49/1.29 % (30464)Memory used [KB]: 5500
% 1.49/1.29 % (30464)Time elapsed: 0.005 s
% 1.49/1.29 % (30464)Instructions burned: 5 (million)
% 1.49/1.29 % (30464)------------------------------
% 1.49/1.29 % (30464)------------------------------
% 1.49/1.29 % (30454)Success in time 0.023 s
%------------------------------------------------------------------------------