%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN025^2 : 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 : n009.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 1.65s 1.34s
% Output : Refutation 1.65s
% 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 : 277 ( 115 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 387 ( 50 ~; 37 |; 37 &; 246 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 88 ( 0 ^; 83 !; 5 ?; 88 :)
% 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(f59,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f50,f58]) ).
thf(f58,plain,
spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f56,f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( s @ X1 )
!= X1 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X2: $i,X3: $o,X4: $i] :
( ( ( ite @ X3 @ X2 @ X4 )
= X2 )
| ( $true != X3 ) )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X7 @ X5 )
= X5 )
| ( $true = X6 ) )
& ! [X8: $i > $i] :
( ( zero
!= ( X8 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X3: $i] :
( ( h @ X3 )
= ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X5 @ X7 )
= X5 )
| ( $true != X6 ) )
& ! [X0: $i,X1: $o,X2: $i] :
( ( ( ite @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 ) )
& ! [X8: $i > $i] :
( ( zero
!= ( X8 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X8: $i > $i] :
( ( zero
!= ( X8 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X5 @ X7 )
= X5 )
| ( $true != X6 ) )
& ! [X0: $i,X1: $o,X2: $i] :
( ( ( ite @ X1 @ X2 @ X0 )
= X0 )
| ( $true = X1 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X5: $i,X6: $o,X7: $i] :
( ( $true = X6 )
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) )
& ! [X0: $i,X1: $o,X2: $i] :
( ( $true != X1 )
=> ( ( ite @ X1 @ X2 @ X0 )
= X0 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) ) )
=> ? [X8: $i > $i] :
( ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) )
& ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i,X1: $o,X2: $i] :
( ( $true != X1 )
=> ( ( ite @ X1 @ X2 @ X0 )
= X0 ) )
& ! [X3: $i] :
( ( h @ X3 )
= ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X5: $i,X6: $o,X7: $i] :
( ( $true = X6 )
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) ) )
=> ? [X8: $i > $i] :
( ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) )
& ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $o,X2: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X0 )
= X0 ) )
& ! [X3: $i] :
( ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) )
= ( h @ X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X5: $i,X6: $o,X7: $i] :
( X6
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) ) )
=> ? [X8: $i > $i] :
( ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i,X0: $o,X1: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) )
= ( h @ X3 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X1: $i,X0: $o,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i,X0: $o,X1: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) )
= ( h @ X3 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X1: $i,X0: $o,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) )
& ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a8iTFgKtnd/DTF2THF_3053.p',n10) ).
thf(f56,plain,
( ( zero
= ( s @ zero ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
= ( s @ zero ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f42,f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( ( s @ zero )
= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( ( s @ zero )
= X0 )
= $true )
| ( ( s @ zero )
= ( h @ X0 ) ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X6: $o,X7: $i,X5: $i] :
( ( ( ite @ X6 @ X7 @ X5 )
= X5 )
| ( $true = X6 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f42,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_2
<=> ( ( s @ zero )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f50,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( s @ zero )
!= ( s @ zero ) )
| ( zero != zero )
| spl0_1 ),
inference(superposition,[status(thm)],[f38,f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( ( s @ zero )
!= X0 ) ),
inference(forward_demodulation,[status(thm)],[f27,f15]) ).
thf(f15,plain,
! [X2: $i,X4: $i] :
( ( ite @ $true @ X2 @ X4 )
= X2 ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i,X3: $o,X4: $i] :
( ( ( ite @ X3 @ X2 @ X4 )
= X2 )
| ( $true != X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( s @ zero )
!= X0 )
| ( ( h @ X0 )
= ( ite @ $true @ zero @ ( s @ zero ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( ( h @ X0 )
= ( ite @ $true @ zero @ ( s @ zero ) ) )
| ( $false
= ( ( s @ zero )
= X0 ) ) ),
inference(fool_paramodulation,[status(thm)],[f14]) ).
thf(f38,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_1
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f43,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f40,f36]) ).
thf(f34,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(subsumption_resolution,[status(thm)],[f33,f13]) ).
thf(f33,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( s @ zero ) ) ),
inference(superposition,[status(thm)],[f10,f26]) ).
thf(f10,plain,
! [X8: $i > $i] :
( ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( zero
!= ( X8 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN025^2 : 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
% 0.14/0.33 % Computer : n009.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 11:19:40 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
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NUN025^2 : 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, h(2) = 1, 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 : ntape6-2-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, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 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 : 8 ( 8 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 7 ( 8 avg)
% 0.29/0.45 % Number of connectives : 31 ( 2 ~; 0 |; 5 &; 21 @)
% 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 : 9 ( 0 ^; 8 !; 1 ?; 9 :)
% 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 ( ( s @ X )
% 0.29/0.45 != X )
% 0.29/0.45 & ! [X: $i] :
% 0.29/0.45 ( ( h @ X )
% 0.29/0.45 = ( ite
% 0.29/0.45 @ ( X
% 0.29/0.45 = ( s @ zero ) )
% 0.29/0.45 @ zero
% 0.29/0.45 @ ( s @ 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 & ( ( H @ ( s @ ( s @ zero ) ) )
% 0.29/0.45 = ( s @ zero ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 11:19:41 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a8iTFgKtnd/DTF2DTF3053.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(n6,type,
% 1.46/1.29 zero: $i ).
% 1.46/1.29
% 1.46/1.29 thf(n7,type,
% 1.46/1.29 s: $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(n8,type,
% 1.46/1.29 ite: $o > $i > $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(n9,type,
% 1.46/1.29 h: $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(n10,conjecture,
% 1.46/1.29 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.46/1.29 ( X100
% 1.46/1.29 => ( ( ite @ X100 @ U @ V )
% 1.46/1.29 = U ) )
% 1.46/1.29 & ! [X100: $o,U: $i,V: $i] :
% 1.46/1.29 ( ~ X100
% 1.46/1.29 => ( ( ite @ X100 @ U @ V )
% 1.46/1.29 = V ) )
% 1.46/1.29 & ! [X: $i] :
% 1.46/1.29 ( ( s @ X )
% 1.46/1.29 != X )
% 1.46/1.29 & ! [X: $i] :
% 1.46/1.29 ( ( h @ X )
% 1.46/1.29 = ( ite
% 1.46/1.29 @ ( X
% 1.46/1.29 = ( s @ zero ) )
% 1.46/1.29 @ zero
% 1.46/1.29 @ ( s @ zero ) ) ) )
% 1.46/1.29 => ? [H: $i > $i] :
% 1.46/1.29 ( ( ( H @ zero )
% 1.46/1.29 = ( s @ zero ) )
% 1.46/1.29 & ( ( H @ ( s @ zero ) )
% 1.46/1.29 = zero )
% 1.46/1.29 & ( ( H @ ( s @ ( s @ zero ) ) )
% 1.46/1.29 = ( s @ zero ) ) ) ) ).
% 1.46/1.29 ------------------------
% 1.65/1.30 % (3334)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_3053 for (2999ds/275Mi)
% 1.65/1.31 % (3334)Refutation not found, incomplete strategy
% 1.65/1.31 % (3334)------------------------------
% 1.65/1.31 % (3334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (3334)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.31
% 1.65/1.31
% 1.65/1.31 % (3334)Memory used [KB]: 5500
% 1.65/1.31 % (3334)Time elapsed: 0.004 s
% 1.65/1.31 % (3334)Instructions burned: 5 (million)
% 1.65/1.31 % (3334)------------------------------
% 1.65/1.31 % (3334)------------------------------
% 1.65/1.31 % (3329)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3053 for (2999ds/183Mi)
% 1.65/1.31 % (3330)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_3053 for (2999ds/4Mi)
% 1.65/1.31 % (3331)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_3053 for (2999ds/27Mi)
% 1.65/1.31 % (3332)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3053 for (2999ds/2Mi)
% 1.65/1.31 % (3333)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_3053 for (2999ds/2Mi)
% 1.65/1.31 % (3335)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3053 for (2999ds/18Mi)
% 1.65/1.31 % (3333)Instruction limit reached!
% 1.65/1.31 % (3333)------------------------------
% 1.65/1.31 % (3333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (3333)Termination reason: Unknown
% 1.65/1.31 % (3333)Termination phase: shuffling
% 1.65/1.31
% 1.65/1.31 % (3333)Memory used [KB]: 895
% 1.65/1.31 % (3333)Time elapsed: 0.003 s
% 1.65/1.31 % (3333)Instructions burned: 2 (million)
% 1.65/1.31 % (3333)------------------------------
% 1.65/1.31 % (3333)------------------------------
% 1.65/1.31 % (3332)Instruction limit reached!
% 1.65/1.31 % (3332)------------------------------
% 1.65/1.31 % (3332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (3332)Termination reason: Unknown
% 1.65/1.31 % (3332)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (3332)Memory used [KB]: 5500
% 1.65/1.31 % (3332)Time elapsed: 0.004 s
% 1.65/1.31 % (3332)Instructions burned: 2 (million)
% 1.65/1.31 % (3332)------------------------------
% 1.65/1.31 % (3332)------------------------------
% 1.65/1.31 % (3330)Instruction limit reached!
% 1.65/1.31 % (3330)------------------------------
% 1.65/1.31 % (3330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (3330)Termination reason: Unknown
% 1.65/1.31 % (3330)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (3330)Memory used [KB]: 5500
% 1.65/1.31 % (3330)Time elapsed: 0.005 s
% 1.65/1.31 % (3330)Instructions burned: 4 (million)
% 1.65/1.31 % (3330)------------------------------
% 1.65/1.31 % (3330)------------------------------
% 1.65/1.32 % (3331)Refutation not found, incomplete strategy
% 1.65/1.32 % (3331)------------------------------
% 1.65/1.32 % (3331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (3331)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.32
% 1.65/1.32
% 1.65/1.32 % (3331)Memory used [KB]: 5500
% 1.65/1.32 % (3331)Time elapsed: 0.006 s
% 1.65/1.32 % (3331)Instructions burned: 5 (million)
% 1.65/1.32 % (3331)------------------------------
% 1.65/1.32 % (3331)------------------------------
% 1.65/1.32 % (3336)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3053 for (2999ds/3Mi)
% 1.65/1.32 % (3336)Instruction limit reached!
% 1.65/1.32 % (3336)------------------------------
% 1.65/1.32 % (3336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (3336)Termination reason: Unknown
% 1.65/1.32 % (3336)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (3336)Memory used [KB]: 5500
% 1.65/1.32 % (3336)Time elapsed: 0.003 s
% 1.65/1.32 % (3336)Instructions burned: 5 (million)
% 1.65/1.32 % (3336)------------------------------
% 1.65/1.32 % (3336)------------------------------
% 1.65/1.32 % (3335)Instruction limit reached!
% 1.65/1.32 % (3335)------------------------------
% 1.65/1.32 % (3335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (3335)Termination reason: Unknown
% 1.65/1.32 % (3335)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (3335)Memory used [KB]: 5628
% 1.65/1.32 % (3335)Time elapsed: 0.013 s
% 1.65/1.32 % (3335)Instructions burned: 18 (million)
% 1.65/1.32 % (3335)------------------------------
% 1.65/1.32 % (3335)------------------------------
% 1.65/1.33 % (3341)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3053 for (2999ds/7Mi)
% 1.65/1.33 % (3337)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_3053 for (2999ds/37Mi)
% 1.65/1.33 % (3338)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_3053 for (2999ds/15Mi)
% 1.65/1.33 % (3341)Instruction limit reached!
% 1.65/1.33 % (3341)------------------------------
% 1.65/1.33 % (3341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (3341)Termination reason: Unknown
% 1.65/1.33 % (3341)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (3341)Memory used [KB]: 1023
% 1.65/1.33 % (3341)Time elapsed: 0.004 s
% 1.65/1.33 % (3341)Instructions burned: 8 (million)
% 1.65/1.33 % (3341)------------------------------
% 1.65/1.33 % (3341)------------------------------
% 1.65/1.33 % (3340)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_3053 for (2999ds/1041Mi)
% 1.65/1.33 % (3339)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_3053 for (2999ds/3Mi)
% 1.65/1.33 % (3339)Instruction limit reached!
% 1.65/1.33 % (3339)------------------------------
% 1.65/1.33 % (3339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (3339)Termination reason: Unknown
% 1.65/1.33 % (3339)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (3339)Memory used [KB]: 5500
% 1.65/1.33 % (3339)Time elapsed: 0.004 s
% 1.65/1.33 % (3339)Instructions burned: 3 (million)
% 1.65/1.33 % (3339)------------------------------
% 1.65/1.33 % (3339)------------------------------
% 1.65/1.33 % (3338)First to succeed.
% 1.65/1.34 % (3338)Refutation found. Thanks to Tanya!
% 1.65/1.34 % SZS status Theorem for DTF2THF_3053
% 1.65/1.34 % SZS output start Proof for DTF2THF_3053
% 1.65/1.34 thf(func_def_1, type, s: $i > $i).
% 1.65/1.34 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.65/1.34 thf(func_def_3, type, h: $i > $i).
% 1.65/1.34 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.34 thf(f59,plain,(
% 1.65/1.34 $false),
% 1.65/1.34 inference(avatar_sat_refutation,[status(thm)],[f43,f50,f58])).
% 1.65/1.34 thf(f58,plain,(
% 1.65/1.34 spl0_2),
% 1.65/1.34 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.65/1.34 thf(f57,plain,(
% 1.65/1.34 $false | spl0_2),
% 1.65/1.34 inference(subsumption_resolution,[status(thm)],[f56,f13])).
% 1.65/1.34 thf(f13,plain,(
% 1.65/1.34 ( ! [X1 : $i] : (((s @ X1) != X1)) )),
% 1.65/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.34 thf(f9,plain,(
% 1.65/1.34 ! [X0 : $i] : ((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))) & ! [X1 : $i] : ((s @ X1) != X1) & ! [X2 : $i,X3 : $o,X4 : $i] : (((ite @ X3 @ X2 @ X4) = X2) | ($true != X3)) & ! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X7 @ X5) = X5) | ($true = X6)) & ! [X8 : $i > $i] : ((zero != (X8 @ (s @ zero))) | ((s @ zero) != (X8 @ zero)) | ((s @ zero) != (X8 @ (s @ (s @ zero)))))),
% 1.65/1.34 inference(rectify,[status(thm)],[f8])).
% 1.65/1.34 thf(f8,plain,(
% 1.65/1.34 ! [X3 : $i] : ((h @ X3) = (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) & ! [X4 : $i] : ((s @ X4) != X4) & ! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X5 @ X7) = X5) | ($true != X6)) & ! [X0 : $i,X1 : $o,X2 : $i] : (((ite @ X1 @ X2 @ X0) = X0) | ($true = X1)) & ! [X8 : $i > $i] : ((zero != (X8 @ (s @ zero))) | ((s @ zero) != (X8 @ zero)) | ((s @ zero) != (X8 @ (s @ (s @ zero)))))),
% 1.65/1.34 inference(flattening,[status(thm)],[f7])).
% 1.65/1.34 thf(f7,plain,(
% 1.65/1.34 ! [X8 : $i > $i] : ((zero != (X8 @ (s @ zero))) | ((s @ zero) != (X8 @ zero)) | ((s @ zero) != (X8 @ (s @ (s @ zero))))) & (! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X5 @ X7) = X5) | ($true != X6)) & ! [X0 : $i,X1 : $o,X2 : $i] : (((ite @ X1 @ X2 @ X0) = X0) | ($true = X1)) & ! [X4 : $i] : ((s @ X4) != X4) & ! [X3 : $i] : ((h @ X3) = (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))))),
% 1.65/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.34 thf(f6,plain,(
% 1.65/1.34 ~((! [X5 : $i,X6 : $o,X7 : $i] : (($true = X6) => ((ite @ X6 @ X5 @ X7) = X5)) & ! [X0 : $i,X1 : $o,X2 : $i] : (($true != X1) => ((ite @ X1 @ X2 @ X0) = X0)) & ! [X4 : $i] : ((s @ X4) != X4) & ! [X3 : $i] : ((h @ X3) = (ite @ ((s @ zero) = X3) @ zero @ (s @ zero)))) => ? [X8 : $i > $i] : ((zero = (X8 @ (s @ zero))) & ((s @ zero) = (X8 @ zero)) & ((s @ zero) = (X8 @ (s @ (s @ zero))))))),
% 1.65/1.34 inference(flattening,[status(thm)],[f5])).
% 1.65/1.34 thf(f5,plain,(
% 1.65/1.34 ~((! [X0 : $i,X1 : $o,X2 : $i] : (~($true = X1) => ((ite @ X1 @ X2 @ X0) = X0)) & ! [X3 : $i] : ((h @ X3) = (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) & ! [X4 : $i] : ((s @ X4) != X4) & ! [X5 : $i,X6 : $o,X7 : $i] : (($true = X6) => ((ite @ X6 @ X5 @ X7) = X5))) => ? [X8 : $i > $i] : ((zero = (X8 @ (s @ zero))) & ((s @ zero) = (X8 @ zero)) & ((s @ zero) = (X8 @ (s @ (s @ zero))))))),
% 1.65/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.34 thf(f4,plain,(
% 1.65/1.34 ~((! [X0 : $i,X1 : $o,X2 : $i] : (~X1 => ((ite @ X1 @ X2 @ X0) = X0)) & ! [X3 : $i] : ((ite @ ((s @ zero) = X3) @ zero @ (s @ zero)) = (h @ X3)) & ! [X4 : $i] : ((s @ X4) != X4) & ! [X5 : $i,X6 : $o,X7 : $i] : (X6 => ((ite @ X6 @ X5 @ X7) = X5))) => ? [X8 : $i > $i] : (((s @ zero) = (X8 @ (s @ (s @ zero)))) & (zero = (X8 @ (s @ zero))) & ((s @ zero) = (X8 @ zero))))),
% 1.65/1.34 inference(rectify,[status(thm)],[f2])).
% 1.65/1.34 thf(f2,negated_conjecture,(
% 1.65/1.34 ~((! [X2 : $i,X0 : $o,X1 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((ite @ ((s @ zero) = X3) @ zero @ (s @ zero)) = (h @ X3)) & ! [X3 : $i] : ((s @ X3) != X3) & ! [X1 : $i,X0 : $o,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X4 : $i > $i] : (((s @ zero) = (X4 @ (s @ (s @ zero)))) & (zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero))))),
% 1.65/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.34 thf(f1,conjecture,(
% 1.65/1.34 (! [X2 : $i,X0 : $o,X1 : $i] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((ite @ ((s @ zero) = X3) @ zero @ (s @ zero)) = (h @ X3)) & ! [X3 : $i] : ((s @ X3) != X3) & ! [X1 : $i,X0 : $o,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X4 : $i > $i] : (((s @ zero) = (X4 @ (s @ (s @ zero)))) & (zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)))),
% 1.65/1.34 file('/export/starexec/sandbox/tmp/tmp.a8iTFgKtnd/DTF2THF_3053.p',n10)).
% 1.65/1.34 thf(f56,plain,(
% 1.65/1.34 (zero = (s @ zero)) | spl0_2),
% 1.65/1.34 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.65/1.34 thf(f53,plain,(
% 1.65/1.34 ((s @ zero) != (s @ zero)) | (zero = (s @ zero)) | spl0_2),
% 1.65/1.34 inference(superposition,[status(thm)],[f42,f26])).
% 1.65/1.34 thf(f26,plain,(
% 1.65/1.34 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | ((s @ zero) = X0)) )),
% 1.65/1.34 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.65/1.34 thf(f24,plain,(
% 1.65/1.34 ( ! [X0 : $i] : ((((s @ zero) = X0) = $true) | ((s @ zero) = (h @ X0))) )),
% 1.65/1.34 inference(superposition,[status(thm)],[f11,f14])).
% 1.65/1.34 thf(f14,plain,(
% 1.65/1.34 ( ! [X0 : $i] : (((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero)))) )),
% 1.65/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.34 thf(f11,plain,(
% 1.65/1.34 ( ! [X6 : $o,X7 : $i,X5 : $i] : (((ite @ X6 @ X7 @ X5) = X5) | ($true = X6)) )),
% 1.65/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.34 thf(f42,plain,(
% 1.65/1.34 ((s @ zero) != (h @ zero)) | spl0_2),
% 1.65/1.34 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.65/1.34 thf(f40,definition,(
% 1.65/1.34 spl0_2 <=> ((s @ zero) = (h @ zero))),
% 1.65/1.34 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.34 thf(f50,plain,(
% 1.65/1.34 spl0_1),
% 1.65/1.34 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.65/1.34 thf(f49,plain,(
% 1.65/1.34 $false | spl0_1),
% 1.65/1.34 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.65/1.34 thf(f48,plain,(
% 1.65/1.34 ((s @ zero) != (s @ zero)) | (zero != zero) | spl0_1),
% 1.65/1.34 inference(superposition,[status(thm)],[f38,f28])).
% 1.65/1.34 thf(f28,plain,(
% 1.65/1.34 ( ! [X0 : $i] : ((zero = (h @ X0)) | ((s @ zero) != X0)) )),
% 1.65/1.34 inference(forward_demodulation,[status(thm)],[f27,f15])).
% 1.65/1.34 thf(f15,plain,(
% 1.65/1.34 ( ! [X2 : $i,X4 : $i] : (((ite @ $true @ X2 @ X4) = X2)) )),
% 1.65/1.34 inference(equality_resolution,[status(thm)],[f12])).
% 1.65/1.34 thf(f12,plain,(
% 1.65/1.34 ( ! [X2 : $i,X3 : $o,X4 : $i] : (((ite @ X3 @ X2 @ X4) = X2) | ($true != X3)) )),
% 1.65/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.34 thf(f27,plain,(
% 1.65/1.34 ( ! [X0 : $i] : (((s @ zero) != X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero)))) )),
% 1.65/1.34 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.65/1.34 thf(f22,plain,(
% 1.65/1.34 ( ! [X0 : $i] : (((h @ X0) = (ite @ $true @ zero @ (s @ zero))) | ($false = ((s @ zero) = X0))) )),
% 1.65/1.34 inference(fool_paramodulation,[status(thm)],[f14])).
% 1.65/1.34 thf(f38,plain,(
% 1.65/1.34 (zero != (h @ (s @ zero))) | spl0_1),
% 1.65/1.34 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.65/1.34 thf(f36,definition,(
% 1.65/1.34 spl0_1 <=> (zero = (h @ (s @ zero)))),
% 1.65/1.34 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.34 thf(f43,plain,(
% 1.65/1.34 ~spl0_1 | ~spl0_2),
% 1.65/1.34 inference(avatar_split_clause,[status(thm)],[f34,f40,f36])).
% 1.65/1.34 thf(f34,plain,(
% 1.65/1.34 (zero != (h @ (s @ zero))) | ((s @ zero) != (h @ zero))),
% 1.65/1.34 inference(subsumption_resolution,[status(thm)],[f33,f13])).
% 1.65/1.34 thf(f33,plain,(
% 1.65/1.34 (zero != (h @ (s @ zero))) | ((s @ zero) = (s @ (s @ zero))) | ((s @ zero) != (h @ zero))),
% 1.65/1.34 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.65/1.34 thf(f32,plain,(
% 1.65/1.34 ((s @ zero) = (s @ (s @ zero))) | ((s @ zero) != (h @ zero)) | (zero != (h @ (s @ zero))) | ((s @ zero) != (s @ zero))),
% 1.65/1.34 inference(superposition,[status(thm)],[f10,f26])).
% 1.65/1.34 thf(f10,plain,(
% 1.65/1.34 ( ! [X8 : $i > $i] : (((s @ zero) != (X8 @ (s @ (s @ zero)))) | ((s @ zero) != (X8 @ zero)) | (zero != (X8 @ (s @ zero)))) )),
% 1.65/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.34 % SZS output end Proof for DTF2THF_3053
% 1.65/1.34 % (3338)------------------------------
% 1.65/1.34 % (3338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (3338)Termination reason: Refutation
% 1.65/1.34
% 1.65/1.34 % (3338)Memory used [KB]: 5500
% 1.65/1.34 % (3338)Time elapsed: 0.007 s
% 1.65/1.34 % (3338)Instructions burned: 6 (million)
% 1.65/1.34 % (3338)------------------------------
% 1.65/1.34 % (3338)------------------------------
% 1.65/1.34 % (3328)Success in time 0.04 s
%------------------------------------------------------------------------------