%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN024^2 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 09:27:13 AM UTC 2026
% Result : Theorem 1.50s 1.28s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 294 ( 123 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 381 ( 58 ~; 37 |; 45 &; 224 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 96 ( 0 ^; 91 !; 5 ?; 96 :)
% 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_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f53,f59]) ).
thf(f59,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( zero != zero )
| ( ( s @ zero )
!= ( s @ zero ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f39,f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( zero != X0 ) ),
inference(forward_demodulation,[status(thm)],[f27,f16]) ).
thf(f16,plain,
! [X6: $i,X5: $i] :
( ( ite @ $true @ X6 @ X5 )
= X6 ),
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X6: $i,X4: $o,X5: $i] :
( ( ( ite @ X4 @ X6 @ X5 )
= X6 )
| ( $true != X4 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero )
= ( h @ X0 ) )
& ! [X1: $i,X2: $i,X3: $o] :
( ( $true = X3 )
| ( ( ite @ X3 @ X1 @ X2 )
= X2 ) )
& ! [X4: $o,X5: $i,X6: $i] :
( ( ( ite @ X4 @ X6 @ X5 )
= X6 )
| ( $true != X4 ) )
& ! [X7: $i > $i] :
( ( ( s @ zero )
!= ( X7 @ zero ) )
| ( zero
!= ( X7 @ ( s @ ( s @ zero ) ) ) )
| ( zero
!= ( X7 @ ( s @ zero ) ) ) )
& ! [X8: $i] :
( zero
!= ( s @ X8 ) )
& ! [X9: $i] :
( ( s @ X9 )
!= X9 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X5: $i,X6: $i,X7: $o] :
( ( $true = X7 )
| ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X0: $o,X1: $i,X2: $i] :
( ( ( ite @ X0 @ X2 @ X1 )
= X2 )
| ( $true != X0 ) )
& ! [X9: $i > $i] :
( ( ( s @ zero )
!= ( X9 @ zero ) )
| ( zero
!= ( X9 @ ( s @ ( s @ zero ) ) ) )
| ( zero
!= ( X9 @ ( s @ zero ) ) ) )
& ! [X4: $i] :
( zero
!= ( s @ X4 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X9: $i > $i] :
( ( ( s @ zero )
!= ( X9 @ zero ) )
| ( zero
!= ( X9 @ ( s @ ( s @ zero ) ) ) )
| ( zero
!= ( X9 @ ( s @ zero ) ) ) )
& ! [X5: $i,X6: $i,X7: $o] :
( ( $true = X7 )
| ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X4: $i] :
( zero
!= ( s @ X4 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 )
& ! [X0: $o,X1: $i,X2: $i] :
( ( ( ite @ X0 @ X2 @ X1 )
= X2 )
| ( $true != X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X5: $i,X6: $i,X7: $o] :
( ( $true != X7 )
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X4: $i] :
( zero
!= ( s @ X4 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 )
& ! [X0: $o,X1: $i,X2: $i] :
( ( $true = X0 )
=> ( ( ite @ X0 @ X2 @ X1 )
= X2 ) ) )
=> ? [X9: $i > $i] :
( ( ( s @ zero )
= ( X9 @ zero ) )
& ( zero
= ( X9 @ ( s @ zero ) ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( ( $true = X0 )
=> ( ( ite @ X0 @ X2 @ X1 )
= X2 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i] :
( zero
!= ( s @ X4 ) )
& ! [X5: $i,X6: $i,X7: $o] :
( ( $true != X7 )
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 ) )
=> ? [X9: $i > $i] :
( ( ( s @ zero )
= ( X9 @ zero ) )
& ( zero
= ( X9 @ ( s @ zero ) ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $o,X1: $i,X2: $i] :
( X0
=> ( ( ite @ X0 @ X2 @ X1 )
= X2 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X4: $i] :
( zero
!= ( s @ X4 ) )
& ! [X5: $i,X6: $i,X7: $o] :
( ~ X7
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 ) )
=> ? [X9: $i > $i] :
( ( zero
= ( X9 @ ( s @ zero ) ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X9 @ zero ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $o,X2: $i,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( zero
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $o,X2: $i,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite @ ( zero = X3 ) @ ( s @ zero ) @ zero ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( zero
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3LuQwmzfWt/DTF2THF_6508.p',n10) ).
thf(f27,plain,
! [X0: $i] :
( ( ( h @ X0 )
= ( ite @ $true @ ( s @ zero ) @ zero ) )
| ( zero != X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( ( zero = X0 )
= $false )
| ( ( h @ X0 )
= ( ite @ $true @ ( s @ zero ) @ zero ) ) ),
inference(fool_paramodulation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero )
= ( h @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f39,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_2
<=> ( ( s @ zero )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f53,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f50,f11]) ).
thf(f11,plain,
! [X8: $i] :
( zero
!= ( s @ X8 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f50,plain,
( ( zero
= ( s @ zero ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( zero != zero )
| ( zero
= ( s @ zero ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f35,f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( zero = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( ( zero = X0 )
= $true ) ),
inference(superposition,[status(thm)],[f14,f15]) ).
thf(f14,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
| ( $true = X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f35,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_1
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f40,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f37,f33]) ).
thf(f31,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(subsumption_resolution,[status(thm)],[f30,f11]) ).
thf(f30,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| ( zero
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) )
| ( zero != zero ) ),
inference(superposition,[status(thm)],[f12,f26]) ).
thf(f12,plain,
! [X7: $i > $i] :
( ( zero
!= ( X7 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X7 @ zero ) )
| ( zero
!= ( X7 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN024^2 : TPTP v9.2.1. Released v6.4.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n017.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:18:11 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : NUN024^2 : TPTP v9.2.1. Released v6.4.0.
% 0.18/0.45 % Domain : Number Theory
% 0.18/0.45 % Problem : Function h s.t. h(0) = 1, h(1) = 0, h(2) = 0, with witness
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.18/0.45 % term that expresses the function H.
% 0.18/0.45
% 0.18/0.45 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [TPTP]
% 0.18/0.45 % Names : ntape6-1-with-witness.tptp [Rie16]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % 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, 0.29 v6.4.0
% 0.18/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.45 % Number of atoms : 9 ( 9 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 8 ( 9 avg)
% 0.18/0.45 % Number of connectives : 32 ( 3 ~; 0 |; 6 &; 20 @)
% 0.18/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-3 aty)
% 0.18/0.45 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(n6,type,
% 0.18/0.45 zero: $i ).
% 0.18/0.45
% 0.18/0.45 thf(n7,type,
% 0.18/0.45 s: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(n8,type,
% 0.18/0.45 ite: $o > $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(n9,type,
% 0.18/0.45 h: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(n10,conjecture,
% 0.18/0.45 ( ( ! [X100: $o,U: $i,V: $i] :
% 0.18/0.45 ( X100
% 0.18/0.45 => ( ( ite @ X100 @ U @ V )
% 0.18/0.45 = U ) )
% 0.18/0.45 & ! [X100: $o,U: $i,V: $i] :
% 0.18/0.45 ( ~ X100
% 0.18/0.45 => ( ( ite @ X100 @ U @ V )
% 0.18/0.45 = V ) )
% 0.18/0.45 & ! [X: $i] :
% 0.18/0.45 ( ( s @ X )
% 0.18/0.45 != zero )
% 0.18/0.45 & ! [X: $i] :
% 0.18/0.45 ( ( s @ X )
% 0.18/0.45 != X )
% 0.18/0.45 & ! [X: $i] :
% 0.18/0.45 ( ( h @ X )
% 0.18/0.45 = ( ite @ ( X = zero ) @ ( s @ zero ) @ zero ) ) )
% 0.18/0.45 => ? [H: $i > $i] :
% 0.18/0.45 ( ( ( H @ zero )
% 0.18/0.45 = ( s @ zero ) )
% 0.18/0.45 & ( ( H @ ( s @ zero ) )
% 0.18/0.45 = zero )
% 0.18/0.45 & ( ( H @ ( s @ ( s @ zero ) ) )
% 0.18/0.45 = zero ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.22 %%% Generated on Tue Feb 24 11:18:11 EST 2026
% 1.50/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.22 %%% Logic specification used:
% 1.50/1.22 %%% thf(spec, logic, $$dhol).
% 1.50/1.22
% 1.50/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3LuQwmzfWt/DTF2DTF6508.p
% See solution above
% 1.50/1.22 ------------------------
% 1.50/1.23 ---- Cleaned THF ---
% 1.50/1.23 thf(n6,type,
% 1.50/1.23 zero: $i ).
% 1.50/1.23
% 1.50/1.23 thf(n7,type,
% 1.50/1.23 s: $i > $i ).
% 1.50/1.23
% 1.50/1.23 thf(n8,type,
% 1.50/1.23 ite: $o > $i > $i > $i ).
% 1.50/1.23
% 1.50/1.23 thf(n9,type,
% 1.50/1.23 h: $i > $i ).
% 1.50/1.23
% 1.50/1.23 thf(n10,conjecture,
% 1.50/1.23 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.50/1.23 ( X100
% 1.50/1.23 => ( ( ite @ X100 @ U @ V )
% 1.50/1.23 = U ) )
% 1.50/1.23 & ! [X100: $o,U: $i,V: $i] :
% 1.50/1.23 ( ~ X100
% 1.50/1.23 => ( ( ite @ X100 @ U @ V )
% 1.50/1.23 = V ) )
% 1.50/1.23 & ! [X: $i] :
% 1.50/1.23 ( ( s @ X )
% 1.50/1.23 != zero )
% 1.50/1.23 & ! [X: $i] :
% 1.50/1.23 ( ( s @ X )
% 1.50/1.23 != X )
% 1.50/1.23 & ! [X: $i] :
% 1.50/1.23 ( ( h @ X )
% 1.50/1.23 = ( ite @ ( X = zero ) @ ( s @ zero ) @ zero ) ) )
% 1.50/1.23 => ? [H: $i > $i] :
% 1.50/1.23 ( ( ( H @ zero )
% 1.50/1.23 = ( s @ zero ) )
% 1.50/1.23 & ( ( H @ ( s @ zero ) )
% 1.50/1.23 = zero )
% 1.50/1.23 & ( ( H @ ( s @ ( s @ zero ) ) )
% 1.50/1.23 = zero ) ) ) ).
% 1.50/1.23 ------------------------
% 1.50/1.25 % (6788)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_6508 for (2999ds/4Mi)
% 1.50/1.25 % (6787)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/183Mi)
% 1.50/1.25 % (6788)Instruction limit reached!
% 1.50/1.25 % (6788)------------------------------
% 1.50/1.25 % (6788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (6788)Termination reason: Unknown
% 1.50/1.25 % (6788)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (6788)Memory used [KB]: 5500
% 1.50/1.25 % (6788)Time elapsed: 0.004 s
% 1.50/1.25 % (6788)Instructions burned: 5 (million)
% 1.50/1.25 % (6788)------------------------------
% 1.50/1.25 % (6788)------------------------------
% 1.50/1.25 % (6789)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_6508 for (2999ds/27Mi)
% 1.50/1.25 % (6790)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/2Mi)
% 1.50/1.25 % (6791)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_6508 for (2999ds/2Mi)
% 1.50/1.25 % (6792)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_6508 for (2999ds/275Mi)
% 1.50/1.25 % (6793)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/18Mi)
% 1.50/1.25 % (6791)Instruction limit reached!
% 1.50/1.25 % (6791)------------------------------
% 1.50/1.25 % (6791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (6791)Termination reason: Unknown
% 1.50/1.25 % (6791)Termination phase: shuffling
% 1.50/1.25
% 1.50/1.25 % (6791)Memory used [KB]: 895
% 1.50/1.25 % (6791)Time elapsed: 0.003 s
% 1.50/1.25 % (6791)Instructions burned: 2 (million)
% 1.50/1.25 % (6791)------------------------------
% 1.50/1.25 % (6791)------------------------------
% 1.50/1.25 % (6790)Instruction limit reached!
% 1.50/1.25 % (6790)------------------------------
% 1.50/1.25 % (6790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (6790)Termination reason: Unknown
% 1.50/1.25 % (6790)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (6790)Memory used [KB]: 5500
% 1.50/1.25 % (6790)Time elapsed: 0.004 s
% 1.50/1.25 % (6790)Instructions burned: 2 (million)
% 1.50/1.25 % (6790)------------------------------
% 1.50/1.25 % (6790)------------------------------
% 1.50/1.26 % (6794)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/3Mi)
% 1.50/1.26 % (6789)Refutation not found, incomplete strategy
% 1.50/1.26 % (6789)------------------------------
% 1.50/1.26 % (6789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (6789)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.26
% 1.50/1.26
% 1.50/1.26 % (6789)Memory used [KB]: 5500
% 1.50/1.26 % (6789)Time elapsed: 0.006 s
% 1.50/1.26 % (6789)Instructions burned: 5 (million)
% 1.50/1.26 % (6789)------------------------------
% 1.50/1.26 % (6789)------------------------------
% 1.50/1.26 % (6792)Refutation not found, incomplete strategy
% 1.50/1.26 % (6792)------------------------------
% 1.50/1.26 % (6792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (6792)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.26
% 1.50/1.26
% 1.50/1.26 % (6792)Memory used [KB]: 5500
% 1.50/1.26 % (6792)Time elapsed: 0.006 s
% 1.50/1.26 % (6792)Instructions burned: 5 (million)
% 1.50/1.26 % (6792)------------------------------
% 1.50/1.26 % (6792)------------------------------
% 1.50/1.26 % (6794)Instruction limit reached!
% 1.50/1.26 % (6794)------------------------------
% 1.50/1.26 % (6794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (6794)Termination reason: Unknown
% 1.50/1.26 % (6794)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (6794)Memory used [KB]: 5500
% 1.50/1.26 % (6794)Time elapsed: 0.002 s
% 1.50/1.26 % (6794)Instructions burned: 3 (million)
% 1.50/1.26 % (6794)------------------------------
% 1.50/1.26 % (6794)------------------------------
% 1.50/1.27 % (6793)Instruction limit reached!
% 1.50/1.27 % (6793)------------------------------
% 1.50/1.27 % (6793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (6793)Termination reason: Unknown
% 1.50/1.27 % (6793)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (6793)Memory used [KB]: 5628
% 1.50/1.27 % (6793)Time elapsed: 0.014 s
% 1.50/1.27 % (6793)Instructions burned: 18 (million)
% 1.50/1.27 % (6793)------------------------------
% 1.50/1.27 % (6793)------------------------------
% 1.50/1.27 % (6797)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/3Mi)
% 1.50/1.27 % (6797)Instruction limit reached!
% 1.50/1.27 % (6797)------------------------------
% 1.50/1.27 % (6797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (6797)Termination reason: Unknown
% 1.50/1.27 % (6797)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (6797)Memory used [KB]: 5500
% 1.50/1.27 % (6797)Time elapsed: 0.002 s
% 1.50/1.27 % (6797)Instructions burned: 3 (million)
% 1.50/1.27 % (6797)------------------------------
% 1.50/1.27 % (6797)------------------------------
% 1.50/1.27 % (6795)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_6508 for (2999ds/37Mi)
% 1.50/1.27 % (6796)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_6508 for (2999ds/15Mi)
% 1.50/1.28 % (6798)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/1041Mi)
% 1.50/1.28 % (6799)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/7Mi)
% 1.50/1.28 % (6796)First to succeed.
% 1.50/1.28 % (6801)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_6508 for (2999ds/3Mi)
% 1.50/1.28 % (6801)Instruction limit reached!
% 1.50/1.28 % (6801)------------------------------
% 1.50/1.28 % (6801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (6801)Termination reason: Unknown
% 1.50/1.28 % (6801)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (6801)Memory used [KB]: 5500
% 1.50/1.28 % (6801)Time elapsed: 0.002 s
% 1.50/1.28 % (6801)Instructions burned: 3 (million)
% 1.50/1.28 % (6801)------------------------------
% 1.50/1.28 % (6801)------------------------------
% 1.50/1.28 % (6796)Refutation found. Thanks to Tanya!
% 1.50/1.28 % SZS status Theorem for DTF2THF_6508
% 1.50/1.28 % SZS output start Proof for DTF2THF_6508
% 1.50/1.28 thf(func_def_1, type, s: $i > $i).
% 1.50/1.28 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.50/1.28 thf(func_def_3, type, h: $i > $i).
% 1.50/1.28 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.50/1.28 thf(f60,plain,(
% 1.50/1.28 $false),
% 1.50/1.28 inference(avatar_sat_refutation,[status(thm)],[f40,f53,f59])).
% 1.50/1.28 thf(f59,plain,(
% 1.50/1.28 spl0_2),
% 1.50/1.28 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.50/1.28 thf(f58,plain,(
% 1.50/1.28 $false | spl0_2),
% 1.50/1.28 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.50/1.28 thf(f56,plain,(
% 1.50/1.28 (zero != zero) | ((s @ zero) != (s @ zero)) | spl0_2),
% 1.50/1.28 inference(superposition,[status(thm)],[f39,f28])).
% 1.50/1.28 thf(f28,plain,(
% 1.50/1.28 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | (zero != X0)) )),
% 1.50/1.28 inference(forward_demodulation,[status(thm)],[f27,f16])).
% 1.50/1.28 thf(f16,plain,(
% 1.50/1.28 ( ! [X6 : $i,X5 : $i] : (((ite @ $true @ X6 @ X5) = X6)) )),
% 1.50/1.28 inference(equality_resolution,[status(thm)],[f13])).
% 1.50/1.28 thf(f13,plain,(
% 1.50/1.28 ( ! [X6 : $i,X4 : $o,X5 : $i] : (((ite @ X4 @ X6 @ X5) = X6) | ($true != X4)) )),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.28 thf(f9,plain,(
% 1.50/1.28 ! [X0 : $i] : ((ite @ (zero = X0) @ (s @ zero) @ zero) = (h @ X0)) & ! [X1 : $i,X2 : $i,X3 : $o] : (($true = X3) | ((ite @ X3 @ X1 @ X2) = X2)) & ! [X4 : $o,X5 : $i,X6 : $i] : (((ite @ X4 @ X6 @ X5) = X6) | ($true != X4)) & ! [X7 : $i > $i] : (((s @ zero) != (X7 @ zero)) | (zero != (X7 @ (s @ (s @ zero)))) | (zero != (X7 @ (s @ zero)))) & ! [X8 : $i] : (zero != (s @ X8)) & ! [X9 : $i] : ((s @ X9) != X9)),
% 1.50/1.28 inference(rectify,[status(thm)],[f8])).
% 1.50/1.28 thf(f8,plain,(
% 1.50/1.28 ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X5 : $i,X6 : $i,X7 : $o] : (($true = X7) | ((ite @ X7 @ X5 @ X6) = X6)) & ! [X0 : $o,X1 : $i,X2 : $i] : (((ite @ X0 @ X2 @ X1) = X2) | ($true != X0)) & ! [X9 : $i > $i] : (((s @ zero) != (X9 @ zero)) | (zero != (X9 @ (s @ (s @ zero)))) | (zero != (X9 @ (s @ zero)))) & ! [X4 : $i] : (zero != (s @ X4)) & ! [X8 : $i] : ((s @ X8) != X8)),
% 1.50/1.28 inference(flattening,[status(thm)],[f7])).
% 1.50/1.28 thf(f7,plain,(
% 1.50/1.28 ! [X9 : $i > $i] : (((s @ zero) != (X9 @ zero)) | (zero != (X9 @ (s @ (s @ zero)))) | (zero != (X9 @ (s @ zero)))) & (! [X5 : $i,X6 : $i,X7 : $o] : (($true = X7) | ((ite @ X7 @ X5 @ X6) = X6)) & ! [X4 : $i] : (zero != (s @ X4)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X8 : $i] : ((s @ X8) != X8) & ! [X0 : $o,X1 : $i,X2 : $i] : (((ite @ X0 @ X2 @ X1) = X2) | ($true != X0)))),
% 1.50/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.50/1.28 thf(f6,plain,(
% 1.50/1.28 ~((! [X5 : $i,X6 : $i,X7 : $o] : (($true != X7) => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X4 : $i] : (zero != (s @ X4)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X8 : $i] : ((s @ X8) != X8) & ! [X0 : $o,X1 : $i,X2 : $i] : (($true = X0) => ((ite @ X0 @ X2 @ X1) = X2))) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & (zero = (X9 @ (s @ (s @ zero))))))),
% 1.50/1.28 inference(flattening,[status(thm)],[f5])).
% 1.50/1.28 thf(f5,plain,(
% 1.50/1.28 ~((! [X0 : $o,X1 : $i,X2 : $i] : (($true = X0) => ((ite @ X0 @ X2 @ X1) = X2)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i] : (zero != (s @ X4)) & ! [X5 : $i,X6 : $i,X7 : $o] : (~($true = X7) => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X8 : $i] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & (zero = (X9 @ (s @ (s @ zero))))))),
% 1.50/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.28 thf(f4,plain,(
% 1.50/1.28 ~((! [X0 : $o,X1 : $i,X2 : $i] : (X0 => ((ite @ X0 @ X2 @ X1) = X2)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X4 : $i] : (zero != (s @ X4)) & ! [X5 : $i,X6 : $i,X7 : $o] : (~X7 => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X8 : $i] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : ((zero = (X9 @ (s @ zero))) & (zero = (X9 @ (s @ (s @ zero)))) & ((s @ zero) = (X9 @ zero))))),
% 1.50/1.28 inference(rectify,[status(thm)],[f2])).
% 1.50/1.28 thf(f2,negated_conjecture,(
% 1.50/1.28 ~((! [X0 : $o,X2 : $i,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & (zero = (X4 @ (s @ (s @ zero)))) & ((s @ zero) = (X4 @ zero))))),
% 1.50/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.28 thf(f1,conjecture,(
% 1.50/1.28 (! [X0 : $o,X2 : $i,X1 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((h @ X3) = (ite @ (zero = X3) @ (s @ zero) @ zero)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & (zero = (X4 @ (s @ (s @ zero)))) & ((s @ zero) = (X4 @ zero)))),
% 1.50/1.28 file('/export/starexec/sandbox/tmp/tmp.3LuQwmzfWt/DTF2THF_6508.p',n10)).
% 1.50/1.28 thf(f27,plain,(
% 1.50/1.28 ( ! [X0 : $i] : (((h @ X0) = (ite @ $true @ (s @ zero) @ zero)) | (zero != X0)) )),
% 1.50/1.28 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.50/1.28 thf(f22,plain,(
% 1.50/1.28 ( ! [X0 : $i] : (((zero = X0) = $false) | ((h @ X0) = (ite @ $true @ (s @ zero) @ zero))) )),
% 1.50/1.28 inference(fool_paramodulation,[status(thm)],[f15])).
% 1.50/1.28 thf(f15,plain,(
% 1.50/1.28 ( ! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero) = (h @ X0))) )),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.28 thf(f39,plain,(
% 1.50/1.28 ((s @ zero) != (h @ zero)) | spl0_2),
% 1.50/1.28 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.50/1.28 thf(f37,definition,(
% 1.50/1.28 spl0_2 <=> ((s @ zero) = (h @ zero))),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.50/1.28 thf(f53,plain,(
% 1.50/1.28 spl0_1),
% 1.50/1.28 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.50/1.28 thf(f52,plain,(
% 1.50/1.28 $false | spl0_1),
% 1.50/1.28 inference(subsumption_resolution,[status(thm)],[f50,f11])).
% 1.50/1.28 thf(f11,plain,(
% 1.50/1.28 ( ! [X8 : $i] : ((zero != (s @ X8))) )),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.28 thf(f50,plain,(
% 1.50/1.28 (zero = (s @ zero)) | spl0_1),
% 1.50/1.28 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.50/1.28 thf(f49,plain,(
% 1.50/1.28 (zero != zero) | (zero = (s @ zero)) | spl0_1),
% 1.50/1.28 inference(superposition,[status(thm)],[f35,f26])).
% 1.50/1.28 thf(f26,plain,(
% 1.50/1.28 ( ! [X0 : $i] : ((zero = (h @ X0)) | (zero = X0)) )),
% 1.50/1.28 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.50/1.28 thf(f24,plain,(
% 1.50/1.28 ( ! [X0 : $i] : ((zero = (h @ X0)) | ((zero = X0) = $true)) )),
% 1.50/1.28 inference(superposition,[status(thm)],[f14,f15])).
% 1.50/1.28 thf(f14,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X1 @ X2) = X2) | ($true = X3)) )),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.28 thf(f35,plain,(
% 1.50/1.28 (zero != (h @ (s @ zero))) | spl0_1),
% 1.50/1.28 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.50/1.28 thf(f33,definition,(
% 1.50/1.28 spl0_1 <=> (zero = (h @ (s @ zero)))),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.50/1.28 thf(f40,plain,(
% 1.50/1.28 ~spl0_1 | ~spl0_2),
% 1.50/1.28 inference(avatar_split_clause,[status(thm)],[f31,f37,f33])).
% 1.50/1.28 thf(f31,plain,(
% 1.50/1.28 (zero != (h @ (s @ zero))) | ((s @ zero) != (h @ zero))),
% 1.50/1.28 inference(subsumption_resolution,[status(thm)],[f30,f11])).
% 1.50/1.28 thf(f30,plain,(
% 1.50/1.28 (zero = (s @ (s @ zero))) | (zero != (h @ (s @ zero))) | ((s @ zero) != (h @ zero))),
% 1.50/1.28 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.50/1.28 thf(f29,plain,(
% 1.50/1.28 (zero != (h @ (s @ zero))) | (zero = (s @ (s @ zero))) | ((s @ zero) != (h @ zero)) | (zero != zero)),
% 1.50/1.28 inference(superposition,[status(thm)],[f12,f26])).
% 1.50/1.28 thf(f12,plain,(
% 1.50/1.28 ( ! [X7 : $i > $i] : ((zero != (X7 @ (s @ (s @ zero)))) | ((s @ zero) != (X7 @ zero)) | (zero != (X7 @ (s @ zero)))) )),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.28 % SZS output end Proof for DTF2THF_6508
% 1.50/1.28 % (6796)------------------------------
% 1.50/1.28 % (6796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (6796)Termination reason: Refutation
% 1.50/1.28
% 1.50/1.28 % (6796)Memory used [KB]: 5500
% 1.50/1.28 % (6796)Time elapsed: 0.008 s
% 1.50/1.28 % (6796)Instructions burned: 7 (million)
% 1.50/1.28 % (6796)------------------------------
% 1.50/1.28 % (6796)------------------------------
% 1.50/1.28 % (6786)Success in time 0.04 s
%------------------------------------------------------------------------------