%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN025^3 : 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 : n027.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 1.62s 1.38s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 427 ( 165 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 547 ( 77 ~; 65 |; 45 &; 341 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 102 ( 0 ^; 97 !; 5 ?; 102 :)
% 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(f119,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f73,f78,f105,f112,f118]) ).
thf(f118,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( zero != zero )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f10,f60]) ).
thf(f60,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_1
<=> ( zero
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f10,plain,
! [X9: $i] :
( zero
!= ( s @ X9 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( s @ X0 )
!= X0 )
& ! [X1: $i,X2: $i,X3: $o] :
( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
| ( $true = X3 ) )
& ! [X4: $i > $i] :
( ( zero
!= ( X4 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X4 @ zero ) )
| ( ( s @ zero )
!= ( X4 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X5: $i] :
( ( h @ X5 )
= ( ite @ ( zero = X5 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X5 )
@ zero
@ ( s @ zero ) ) ) )
& ! [X6: $i,X7: $o,X8: $i] :
( ( ( ite @ X7 @ X6 @ X8 )
= X6 )
| ( $true != X7 ) )
& ! [X9: $i] :
( zero
!= ( s @ X9 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X8: $i] :
( ( s @ X8 )
!= X8 )
& ! [X0: $i,X1: $i,X2: $o] :
( ( ( ite @ X2 @ X0 @ X1 )
= X1 )
| ( $true = X2 ) )
& ! [X9: $i > $i] :
( ( zero
!= ( X9 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X9 @ zero ) )
| ( ( s @ zero )
!= ( X9 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X4: $i] :
( ( ite @ ( zero = X4 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X4 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X4 ) )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X5 @ X7 )
= X5 )
| ( $true != X6 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X9: $i > $i] :
( ( zero
!= ( X9 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X9 @ zero ) )
| ( ( s @ zero )
!= ( X9 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X4: $i] :
( ( ite @ ( zero = X4 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X4 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X4 ) )
& ! [X0: $i,X1: $i,X2: $o] :
( ( ( ite @ X2 @ X0 @ X1 )
= X1 )
| ( $true = X2 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 )
& ! [X5: $i,X6: $o,X7: $i] :
( ( ( ite @ X6 @ X5 @ X7 )
= X5 )
| ( $true != X6 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X4: $i] :
( ( ite @ ( zero = X4 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X4 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X4 ) )
& ! [X0: $i,X1: $i,X2: $o] :
( ( $true != X2 )
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 )
& ! [X5: $i,X6: $o,X7: $i] :
( ( $true = X6 )
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero ) )
=> ? [X9: $i > $i] :
( ( ( s @ zero )
= ( X9 @ zero ) )
& ( zero
= ( X9 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $o] :
( ( $true != X2 )
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X4: $i] :
( ( ite @ ( zero = X4 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X4 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X4 ) )
& ! [X5: $i,X6: $o,X7: $i] :
( ( $true = X6 )
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 ) )
=> ? [X9: $i > $i] :
( ( ( s @ zero )
= ( X9 @ zero ) )
& ( zero
= ( X9 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $o] :
( ~ X2
=> ( ( ite @ X2 @ X0 @ X1 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X4: $i] :
( ( ite @ ( zero = X4 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X4 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X4 ) )
& ! [X5: $i,X6: $o,X7: $i] :
( X6
=> ( ( ite @ X6 @ X5 @ X7 )
= X5 ) )
& ! [X8: $i] :
( ( s @ X8 )
!= X8 ) )
=> ? [X9: $i > $i] :
( ( zero
= ( X9 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X9 @ zero ) )
& ( ( s @ zero )
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X3: $i] :
( ( ite @ ( zero = X3 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X3 ) )
& ! [X1: $i,X0: $o,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) )
& ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X3: $i] :
( ( ite @ ( zero = X3 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X3 )
@ zero
@ ( s @ zero ) ) )
= ( h @ X3 ) )
& ! [X1: $i,X0: $o,X2: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 ) )
=> ? [X4: $i > $i] :
( ( zero
= ( X4 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X4 @ zero ) )
& ( ( s @ zero )
= ( X4 @ ( s @ ( s @ zero ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g3rs5Z6rbb/DTF2THF_20826.p',n10) ).
thf(f112,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f111]) ).
thf(f111,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ( s @ zero )
!= ( s @ zero ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f15,f64]) ).
thf(f64,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl0_2
<=> ( ( s @ zero )
= ( s @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f15,plain,
! [X0: $i] :
( ( s @ X0 )
!= X0 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f105,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
| ~ spl0_3
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( zero != zero )
| ~ spl0_3
| spl0_4 ),
inference(superposition,[status(thm)],[f97,f96]) ).
thf(f96,plain,
( ( zero
= ( h @ zero ) )
| ~ spl0_3
| spl0_4 ),
inference(backward_demodulation,[status(thm)],[f67,f85]) ).
thf(f85,plain,
( ( zero
= ( s @ zero ) )
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( zero != zero )
| ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
= ( s @ zero ) )
| spl0_4 ),
inference(superposition,[status(thm)],[f72,f47]) ).
thf(f47,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( ( s @ zero )
!= X0 )
| ( zero = X0 ) ),
inference(forward_demodulation,[status(thm)],[f44,f16]) ).
thf(f16,plain,
! [X8: $i,X6: $i] :
( ( ite @ $true @ X6 @ X8 )
= X6 ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X8: $i,X6: $i,X7: $o] :
( ( ( ite @ X7 @ X6 @ X8 )
= X6 )
| ( $true != X7 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f44,plain,
! [X0: $i] :
( ( zero = X0 )
| ( ( s @ zero )
!= X0 )
| ( ( h @ X0 )
= ( ite @ $true @ zero @ ( s @ zero ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i] :
( ( zero = X0 )
| ( ( h @ X0 )
= ( ite @ $true @ zero @ ( s @ zero ) ) )
| ( ( ( s @ zero )
= X0 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
| ( zero = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( ( zero = X0 )
= $true )
| ( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( ite @ X3 @ X1 @ X2 )
= X2 )
| ( $true = X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f12,plain,
! [X5: $i] :
( ( h @ X5 )
= ( ite @ ( zero = X5 ) @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X5 )
@ zero
@ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f72,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_4
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f67,plain,
( ( ( s @ zero )
= ( h @ zero ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl0_3
<=> ( ( s @ zero )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f97,plain,
( ( zero
!= ( h @ zero ) )
| spl0_4 ),
inference(backward_demodulation,[status(thm)],[f72,f85]) ).
thf(f78,plain,
spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( zero != zero )
| ( ( s @ zero )
!= ( s @ zero ) )
| spl0_3 ),
inference(superposition,[status(thm)],[f68,f37]) ).
thf(f37,plain,
! [X5: $i] :
( ( ( s @ zero )
= ( h @ X5 ) )
| ( zero != X5 ) ),
inference(forward_demodulation,[status(thm)],[f31,f16]) ).
thf(f31,plain,
! [X5: $i] :
( ( ( h @ X5 )
= ( ite @ $true @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X5 )
@ zero
@ ( s @ zero ) ) ) )
| ( zero != X5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X5: $i] :
( ( ( zero = X5 )
= $false )
| ( ( h @ X5 )
= ( ite @ $true @ ( s @ zero )
@ ( ite
@ ( ( s @ zero )
= X5 )
@ zero
@ ( s @ zero ) ) ) ) ),
inference(fool_paramodulation,[status(thm)],[f12]) ).
thf(f68,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f73,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f55,f70,f66,f62,f58]) ).
thf(f55,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( zero
= ( s @ ( s @ zero ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
= ( s @ ( s @ zero ) ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
= ( s @ ( s @ zero ) ) ) ),
inference(superposition,[status(thm)],[f13,f46]) ).
thf(f46,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( zero = X0 )
| ( ( s @ zero )
= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( ( ( s @ zero )
= X0 )
= $true )
| ( zero = X0 ) ),
inference(superposition,[status(thm)],[f14,f33]) ).
thf(f13,plain,
! [X4: $i > $i] :
( ( ( s @ zero )
!= ( X4 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X4 @ zero ) )
| ( zero
!= ( X4 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN025^3 : 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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:20:07 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : NUN025^3 : TPTP v9.2.1. Released v6.4.0.
% 0.28/0.45 % Domain : Number Theory
% 0.28/0.45 % Problem : Function h s.t. h(0) = 1, h(1) = 0, h(2) = 1, with witness
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English : Using an axiomatiztion of if-then-else, find the if-then-else
% 0.28/0.45 % term that expresses the function H.
% 0.28/0.45
% 0.28/0.45 % Refs : [Rie16] Riener (2016), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [TPTP]
% 0.28/0.45 % Names : ntape6-2-with-witness2.tptp [Rie16]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 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
% 0.28/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.28/0.45 % Number of atoms : 10 ( 10 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 8 ( 10 avg)
% 0.28/0.45 % Number of connectives : 38 ( 3 ~; 0 |; 6 &; 26 @)
% 0.28/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.28/0.45 % Number of types : 2 ( 0 usr)
% 0.28/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 5 ( 4 usr; 1 con; 0-3 aty)
% 0.28/0.45 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments :
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(n6,type,
% 0.28/0.45 zero: $i ).
% 0.28/0.45
% 0.28/0.45 thf(n7,type,
% 0.28/0.45 s: $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(n8,type,
% 0.28/0.45 ite: $o > $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(n9,type,
% 0.28/0.45 h: $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(n10,conjecture,
% 0.28/0.45 ( ( ! [X100: $o,U: $i,V: $i] :
% 0.28/0.45 ( X100
% 0.28/0.45 => ( ( ite @ X100 @ U @ V )
% 0.28/0.45 = U ) )
% 0.28/0.45 & ! [X100: $o,U: $i,V: $i] :
% 0.28/0.45 ( ~ X100
% 0.28/0.45 => ( ( ite @ X100 @ U @ V )
% 0.28/0.45 = V ) )
% 0.28/0.45 & ! [X: $i] :
% 0.28/0.45 ( ( s @ X )
% 0.28/0.45 != zero )
% 0.28/0.45 & ! [X: $i] :
% 0.28/0.45 ( ( s @ X )
% 0.28/0.45 != X )
% 0.28/0.45 & ! [X: $i] :
% 0.28/0.45 ( ( h @ X )
% 0.28/0.45 = ( ite @ ( X = zero ) @ ( s @ zero )
% 0.28/0.45 @ ( ite
% 0.28/0.45 @ ( X
% 0.28/0.45 = ( s @ zero ) )
% 0.28/0.45 @ zero
% 0.28/0.45 @ ( s @ zero ) ) ) ) )
% 0.28/0.45 => ? [H: $i > $i] :
% 0.28/0.45 ( ( ( H @ zero )
% 0.28/0.45 = ( s @ zero ) )
% 0.28/0.45 & ( ( H @ ( s @ zero ) )
% 0.28/0.45 = zero )
% 0.28/0.45 & ( ( H @ ( s @ ( s @ zero ) ) )
% 0.28/0.45 = ( s @ zero ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 11:20:08 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g3rs5Z6rbb/DTF2DTF20826.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(n6,type,
% 1.46/1.28 zero: $i ).
% 1.46/1.28
% 1.46/1.28 thf(n7,type,
% 1.46/1.28 s: $i > $i ).
% 1.46/1.28
% 1.46/1.28 thf(n8,type,
% 1.46/1.28 ite: $o > $i > $i > $i ).
% 1.46/1.28
% 1.46/1.28 thf(n9,type,
% 1.46/1.28 h: $i > $i ).
% 1.46/1.28
% 1.46/1.28 thf(n10,conjecture,
% 1.46/1.28 ( ( ! [X100: $o,U: $i,V: $i] :
% 1.46/1.28 ( X100
% 1.46/1.28 => ( ( ite @ X100 @ U @ V )
% 1.46/1.28 = U ) )
% 1.46/1.28 & ! [X100: $o,U: $i,V: $i] :
% 1.46/1.28 ( ~ X100
% 1.46/1.28 => ( ( ite @ X100 @ U @ V )
% 1.46/1.28 = V ) )
% 1.46/1.28 & ! [X: $i] :
% 1.46/1.28 ( ( s @ X )
% 1.46/1.28 != zero )
% 1.46/1.28 & ! [X: $i] :
% 1.46/1.28 ( ( s @ X )
% 1.46/1.28 != X )
% 1.46/1.28 & ! [X: $i] :
% 1.46/1.28 ( ( h @ X )
% 1.46/1.28 = ( ite @ ( X = zero ) @ ( s @ zero )
% 1.46/1.28 @ ( ite
% 1.46/1.28 @ ( X
% 1.46/1.28 = ( s @ zero ) )
% 1.46/1.28 @ zero
% 1.46/1.28 @ ( s @ zero ) ) ) ) )
% 1.46/1.28 => ? [H: $i > $i] :
% 1.46/1.28 ( ( ( H @ zero )
% 1.46/1.28 = ( s @ zero ) )
% 1.46/1.28 & ( ( H @ ( s @ zero ) )
% 1.46/1.28 = zero )
% 1.46/1.28 & ( ( H @ ( s @ ( s @ zero ) ) )
% 1.46/1.28 = ( s @ zero ) ) ) ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (21110)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20826 for (3000ds/18Mi)
% 1.46/1.29 % (21104)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20826 for (3000ds/183Mi)
% 1.46/1.30 % (21110)Instruction limit reached!
% 1.46/1.30 % (21110)------------------------------
% 1.46/1.30 % (21110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (21110)Termination reason: Unknown
% 1.46/1.30 % (21110)Termination phase: Saturation
% 1.46/1.30
% 1.46/1.30 % (21110)Memory used [KB]: 5628
% 1.46/1.30 % (21110)Time elapsed: 0.008 s
% 1.46/1.30 % (21110)Instructions burned: 19 (million)
% 1.46/1.30 % (21110)------------------------------
% 1.46/1.30 % (21110)------------------------------
% 1.46/1.30 % (21105)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_20826 for (3000ds/4Mi)
% 1.46/1.30 % (21106)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_20826 for (3000ds/27Mi)
% 1.46/1.30 % (21107)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20826 for (3000ds/2Mi)
% 1.46/1.30 % (21108)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_20826 for (3000ds/2Mi)
% 1.62/1.30 % (21109)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_20826 for (3000ds/275Mi)
% 1.62/1.30 % (21107)Instruction limit reached!
% 1.62/1.30 % (21107)------------------------------
% 1.62/1.30 % (21107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (21107)Termination reason: Unknown
% 1.62/1.30 % (21107)Termination phase: Property scanning
% 1.62/1.30
% 1.62/1.30 % (21107)Memory used [KB]: 895
% 1.62/1.30 % (21107)Time elapsed: 0.003 s
% 1.62/1.30 % (21107)Instructions burned: 2 (million)
% 1.62/1.30 % (21107)------------------------------
% 1.62/1.30 % (21107)------------------------------
% 1.62/1.30 % (21108)Instruction limit reached!
% 1.62/1.30 % (21108)------------------------------
% 1.62/1.30 % (21108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (21108)Termination reason: Unknown
% 1.62/1.30 % (21108)Termination phase: Property scanning
% 1.62/1.30
% 1.62/1.30 % (21108)Memory used [KB]: 895
% 1.62/1.30 % (21108)Time elapsed: 0.003 s
% 1.62/1.30 % (21108)Instructions burned: 2 (million)
% 1.62/1.30 % (21108)------------------------------
% 1.62/1.30 % (21108)------------------------------
% 1.62/1.30 % (21105)Instruction limit reached!
% 1.62/1.30 % (21105)------------------------------
% 1.62/1.30 % (21105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (21105)Termination reason: Unknown
% 1.62/1.30 % (21105)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (21105)Memory used [KB]: 5500
% 1.62/1.30 % (21105)Time elapsed: 0.005 s
% 1.62/1.30 % (21105)Instructions burned: 4 (million)
% 1.62/1.30 % (21105)------------------------------
% 1.62/1.30 % (21105)------------------------------
% 1.62/1.30 % (21109)Refutation not found, incomplete strategy
% 1.62/1.30 % (21109)------------------------------
% 1.62/1.30 % (21109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (21109)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (21109)Memory used [KB]: 5500
% 1.62/1.30 % (21109)Time elapsed: 0.009 s
% 1.62/1.30 % (21109)Instructions burned: 10 (million)
% 1.62/1.30 % (21109)------------------------------
% 1.62/1.30 % (21109)------------------------------
% 1.62/1.30 % (21106)Refutation not found, incomplete strategy
% 1.62/1.30 % (21106)------------------------------
% 1.62/1.30 % (21106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (21106)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (21106)Memory used [KB]: 5500
% 1.62/1.30 % (21106)Time elapsed: 0.009 s
% 1.62/1.30 % (21106)Instructions burned: 10 (million)
% 1.62/1.30 % (21106)------------------------------
% 1.62/1.30 % (21106)------------------------------
% 1.62/1.31 % (21111)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/3Mi)
% 1.62/1.31 % (21111)Instruction limit reached!
% 1.62/1.31 % (21111)------------------------------
% 1.62/1.31 % (21111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (21111)Termination reason: Unknown
% 1.62/1.31 % (21111)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (21111)Memory used [KB]: 5500
% 1.62/1.31 % (21111)Time elapsed: 0.003 s
% 1.62/1.31 % (21111)Instructions burned: 3 (million)
% 1.62/1.31 % (21111)------------------------------
% 1.62/1.31 % (21111)------------------------------
% 1.62/1.31 % (21113)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_20826 for (2999ds/15Mi)
% 1.62/1.31 % (21112)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_20826 for (2999ds/37Mi)
% 1.62/1.32 % (21114)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_20826 for (2999ds/3Mi)
% 1.62/1.32 % (21117)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/16Mi)
% 1.62/1.32 % (21114)Instruction limit reached!
% 1.62/1.32 % (21114)------------------------------
% 1.62/1.32 % (21114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (21114)Termination reason: Unknown
% 1.62/1.32 % (21114)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (21114)Memory used [KB]: 5500
% 1.62/1.32 % (21114)Time elapsed: 0.004 s
% 1.62/1.32 % (21114)Instructions burned: 3 (million)
% 1.62/1.32 % (21114)------------------------------
% 1.62/1.32 % (21114)------------------------------
% 1.62/1.32 % (21115)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_20826 for (2999ds/1041Mi)
% 1.62/1.32 % (21116)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/7Mi)
% 1.62/1.32 % (21117)Instruction limit reached!
% 1.62/1.32 % (21117)------------------------------
% 1.62/1.32 % (21117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (21117)Termination reason: Unknown
% 1.62/1.32 % (21117)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (21117)Memory used [KB]: 5628
% 1.62/1.32 % (21117)Time elapsed: 0.008 s
% 1.62/1.32 % (21117)Instructions burned: 16 (million)
% 1.62/1.32 % (21117)------------------------------
% 1.62/1.32 % (21117)------------------------------
% 1.62/1.32 % (21113)Instruction limit reached!
% 1.62/1.32 % (21113)------------------------------
% 1.62/1.32 % (21113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (21113)Termination reason: Unknown
% 1.62/1.32 % (21113)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (21113)Memory used [KB]: 5628
% 1.62/1.32 % (21113)Time elapsed: 0.012 s
% 1.62/1.32 % (21113)Instructions burned: 15 (million)
% 1.62/1.32 % (21113)------------------------------
% 1.62/1.32 % (21113)------------------------------
% 1.62/1.33 % (21116)Instruction limit reached!
% 1.62/1.33 % (21116)------------------------------
% 1.62/1.33 % (21116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (21116)Termination reason: Unknown
% 1.62/1.33 % (21116)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (21116)Memory used [KB]: 1023
% 1.62/1.33 % (21116)Time elapsed: 0.007 s
% 1.62/1.33 % (21116)Instructions burned: 8 (million)
% 1.62/1.33 % (21116)------------------------------
% 1.62/1.33 % (21116)------------------------------
% 1.62/1.33 % (21119)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/3Mi)
% 1.62/1.33 % (21119)Instruction limit reached!
% 1.62/1.33 % (21119)------------------------------
% 1.62/1.33 % (21119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (21119)Termination reason: Unknown
% 1.62/1.33 % (21119)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (21119)Memory used [KB]: 5500
% 1.62/1.33 % (21119)Time elapsed: 0.003 s
% 1.62/1.33 % (21119)Instructions burned: 4 (million)
% 1.62/1.33 % (21119)------------------------------
% 1.62/1.33 % (21119)------------------------------
% 1.62/1.34 % (21118)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_20826 for (2999ds/3Mi)
% 1.62/1.34 % (21112)Instruction limit reached!
% 1.62/1.34 % (21112)------------------------------
% 1.62/1.34 % (21112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (21112)Termination reason: Unknown
% 1.62/1.34 % (21112)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (21112)Memory used [KB]: 5756
% 1.62/1.34 % (21112)Time elapsed: 0.024 s
% 1.62/1.34 % (21112)Instructions burned: 38 (million)
% 1.62/1.34 % (21112)------------------------------
% 1.62/1.34 % (21112)------------------------------
% 1.62/1.34 % (21118)Instruction limit reached!
% 1.62/1.34 % (21118)------------------------------
% 1.62/1.34 % (21118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (21118)Termination reason: Unknown
% 1.62/1.34 % (21118)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (21118)Memory used [KB]: 5500
% 1.62/1.34 % (21118)Time elapsed: 0.004 s
% 1.62/1.34 % (21118)Instructions burned: 4 (million)
% 1.62/1.34 % (21118)------------------------------
% 1.62/1.34 % (21118)------------------------------
% 1.62/1.34 % (21120)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/7Mi)
% 1.62/1.34 % (21121)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/3Mi)
% 1.62/1.34 % (21122)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/4Mi)
% 1.62/1.35 % (21121)Instruction limit reached!
% 1.62/1.35 % (21121)------------------------------
% 1.62/1.35 % (21121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (21121)Termination reason: Unknown
% 1.62/1.35 % (21121)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (21121)Memory used [KB]: 895
% 1.62/1.35 % (21121)Time elapsed: 0.003 s
% 1.62/1.35 % (21121)Instructions burned: 3 (million)
% 1.62/1.35 % (21121)------------------------------
% 1.62/1.35 % (21121)------------------------------
% 1.62/1.35 % (21120)Instruction limit reached!
% 1.62/1.35 % (21120)------------------------------
% 1.62/1.35 % (21120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (21120)Termination reason: Unknown
% 1.62/1.35 % (21120)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (21120)Memory used [KB]: 5500
% 1.62/1.35 % (21120)Time elapsed: 0.006 s
% 1.62/1.35 % (21120)Instructions burned: 7 (million)
% 1.62/1.35 % (21120)------------------------------
% 1.62/1.35 % (21120)------------------------------
% 1.62/1.35 % (21122)Instruction limit reached!
% 1.62/1.35 % (21122)------------------------------
% 1.62/1.35 % (21122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (21122)Termination reason: Unknown
% 1.62/1.35 % (21122)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (21122)Memory used [KB]: 5500
% 1.62/1.35 % (21122)Time elapsed: 0.003 s
% 1.62/1.35 % (21122)Instructions burned: 4 (million)
% 1.62/1.35 % (21122)------------------------------
% 1.62/1.35 % (21122)------------------------------
% 1.62/1.35 % (21123)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/18Mi)
% 1.62/1.35 % (21124)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/710Mi)
% 1.62/1.36 % (21126)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/902Mi)
% 1.62/1.36 % (21127)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/21Mi)
% 1.62/1.36 % (21104)Instruction limit reached!
% 1.62/1.36 % (21104)------------------------------
% 1.62/1.36 % (21104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (21104)Termination reason: Unknown
% 1.62/1.36 % (21104)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (21104)Memory used [KB]: 6012
% 1.62/1.36 % (21104)Time elapsed: 0.067 s
% 1.62/1.36 % (21104)Instructions burned: 184 (million)
% 1.62/1.36 % (21104)------------------------------
% 1.62/1.36 % (21104)------------------------------
% 1.62/1.36 % (21123)Refutation not found, incomplete strategy
% 1.62/1.36 % (21123)------------------------------
% 1.62/1.36 % (21123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (21123)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.36
% 1.62/1.36
% 1.62/1.36 % (21123)Memory used [KB]: 5500
% 1.62/1.36 % (21123)Time elapsed: 0.009 s
% 1.62/1.36 % (21123)Instructions burned: 11 (million)
% 1.62/1.36 % (21123)------------------------------
% 1.62/1.36 % (21123)------------------------------
% 1.62/1.36 % (21125)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/6Mi)
% 1.62/1.36 % (21127)Instruction limit reached!
% 1.62/1.36 % (21127)------------------------------
% 1.62/1.36 % (21127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (21127)Termination reason: Unknown
% 1.62/1.36 % (21127)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (21127)Memory used [KB]: 5628
% 1.62/1.36 % (21127)Time elapsed: 0.010 s
% 1.62/1.36 % (21127)Instructions burned: 21 (million)
% 1.62/1.36 % (21127)------------------------------
% 1.62/1.36 % (21127)------------------------------
% 1.62/1.37 % (21125)Instruction limit reached!
% 1.62/1.37 % (21125)------------------------------
% 1.62/1.37 % (21125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (21125)Termination reason: Unknown
% 1.62/1.37 % (21125)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (21125)Memory used [KB]: 5500
% 1.62/1.37 % (21125)Time elapsed: 0.006 s
% 1.62/1.37 % (21125)Instructions burned: 6 (million)
% 1.62/1.37 % (21125)------------------------------
% 1.62/1.37 % (21125)------------------------------
% 1.62/1.37 % (21128)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/5Mi)
% 1.62/1.37 % (21128)Instruction limit reached!
% 1.62/1.37 % (21128)------------------------------
% 1.62/1.37 % (21128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (21128)Termination reason: Unknown
% 1.62/1.37 % (21128)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (21128)Memory used [KB]: 5500
% 1.62/1.37 % (21128)Time elapsed: 0.004 s
% 1.62/1.37 % (21128)Instructions burned: 7 (million)
% 1.62/1.37 % (21128)------------------------------
% 1.62/1.37 % (21128)------------------------------
% 1.62/1.37 % (21130)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/377Mi)
% 1.62/1.38 % (21129)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/6Mi)
% 1.62/1.38 % (21130)First to succeed.
% 1.62/1.38 % (21129)Instruction limit reached!
% 1.62/1.38 % (21129)------------------------------
% 1.62/1.38 % (21129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (21129)Termination reason: Unknown
% 1.62/1.38 % (21129)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (21129)Memory used [KB]: 5500
% 1.62/1.38 % (21129)Time elapsed: 0.005 s
% 1.62/1.38 % (21129)Instructions burned: 6 (million)
% 1.62/1.38 % (21129)------------------------------
% 1.62/1.38 % (21129)------------------------------
% 1.62/1.38 % (21132)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_20826 for (2999ds/19Mi)
% 1.62/1.38 % (21130)Refutation found. Thanks to Tanya!
% 1.62/1.38 % SZS status Theorem for DTF2THF_20826
% 1.62/1.38 % SZS output start Proof for DTF2THF_20826
% 1.62/1.38 thf(func_def_1, type, s: $i > $i).
% 1.62/1.38 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 1.62/1.38 thf(func_def_3, type, h: $i > $i).
% 1.62/1.38 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.38 thf(f119,plain,(
% 1.62/1.38 $false),
% 1.62/1.38 inference(avatar_sat_refutation,[status(thm)],[f73,f78,f105,f112,f118])).
% 1.62/1.38 thf(f118,plain,(
% 1.62/1.38 ~spl0_1),
% 1.62/1.38 inference(avatar_contradiction_clause,[status(thm)],[f117])).
% 1.62/1.38 thf(f117,plain,(
% 1.62/1.38 $false | ~spl0_1),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.62/1.38 thf(f116,plain,(
% 1.62/1.38 (zero != zero) | ~spl0_1),
% 1.62/1.38 inference(superposition,[status(thm)],[f10,f60])).
% 1.62/1.38 thf(f60,plain,(
% 1.62/1.38 (zero = (s @ (s @ zero))) | ~spl0_1),
% 1.62/1.38 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.62/1.38 thf(f58,definition,(
% 1.62/1.38 spl0_1 <=> (zero = (s @ (s @ zero)))),
% 1.62/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.62/1.38 thf(f10,plain,(
% 1.62/1.38 ( ! [X9 : $i] : ((zero != (s @ X9))) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 thf(f9,plain,(
% 1.62/1.38 ! [X0 : $i] : ((s @ X0) != X0) & ! [X1 : $i,X2 : $i,X3 : $o] : (((ite @ X3 @ X1 @ X2) = X2) | ($true = X3)) & ! [X4 : $i > $i] : ((zero != (X4 @ (s @ zero))) | ((s @ zero) != (X4 @ zero)) | ((s @ zero) != (X4 @ (s @ (s @ zero))))) & ! [X5 : $i] : ((h @ X5) = (ite @ (zero = X5) @ (s @ zero) @ (ite @ ((s @ zero) = X5) @ zero @ (s @ zero)))) & ! [X6 : $i,X7 : $o,X8 : $i] : (((ite @ X7 @ X6 @ X8) = X6) | ($true != X7)) & ! [X9 : $i] : (zero != (s @ X9))),
% 1.62/1.38 inference(rectify,[status(thm)],[f8])).
% 1.62/1.38 thf(f8,plain,(
% 1.62/1.38 ! [X8 : $i] : ((s @ X8) != X8) & ! [X0 : $i,X1 : $i,X2 : $o] : (((ite @ X2 @ X0 @ X1) = X1) | ($true = X2)) & ! [X9 : $i > $i] : ((zero != (X9 @ (s @ zero))) | ((s @ zero) != (X9 @ zero)) | ((s @ zero) != (X9 @ (s @ (s @ zero))))) & ! [X4 : $i] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X5 @ X7) = X5) | ($true != X6)) & ! [X3 : $i] : ((s @ X3) != zero)),
% 1.62/1.38 inference(flattening,[status(thm)],[f7])).
% 1.62/1.38 thf(f7,plain,(
% 1.62/1.38 ! [X9 : $i > $i] : ((zero != (X9 @ (s @ zero))) | ((s @ zero) != (X9 @ zero)) | ((s @ zero) != (X9 @ (s @ (s @ zero))))) & (! [X4 : $i] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X0 : $i,X1 : $i,X2 : $o] : (((ite @ X2 @ X0 @ X1) = X1) | ($true = X2)) & ! [X8 : $i] : ((s @ X8) != X8) & ! [X5 : $i,X6 : $o,X7 : $i] : (((ite @ X6 @ X5 @ X7) = X5) | ($true != X6)) & ! [X3 : $i] : ((s @ X3) != zero))),
% 1.62/1.38 inference(ennf_transformation,[status(thm)],[f6])).
% 1.62/1.38 thf(f6,plain,(
% 1.62/1.38 ~((! [X4 : $i] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X0 : $i,X1 : $i,X2 : $o] : (($true != X2) => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X8 : $i] : ((s @ X8) != X8) & ! [X5 : $i,X6 : $o,X7 : $i] : (($true = X6) => ((ite @ X6 @ X5 @ X7) = X5)) & ! [X3 : $i] : ((s @ X3) != zero)) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 1.62/1.38 inference(flattening,[status(thm)],[f5])).
% 1.62/1.38 thf(f5,plain,(
% 1.62/1.38 ~((! [X0 : $i,X1 : $i,X2 : $o] : (~($true = X2) => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X4 : $i] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5 : $i,X6 : $o,X7 : $i] : (($true = X6) => ((ite @ X6 @ X5 @ X7) = X5)) & ! [X8 : $i] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 1.62/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.38 thf(f4,plain,(
% 1.62/1.38 ~((! [X0 : $i,X1 : $i,X2 : $o] : (~X2 => ((ite @ X2 @ X0 @ X1) = X1)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X4 : $i] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5 : $i,X6 : $o,X7 : $i] : (X6 => ((ite @ X6 @ X5 @ X7) = X5)) & ! [X8 : $i] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : ((zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ zero)) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 1.62/1.38 inference(rectify,[status(thm)],[f2])).
% 1.62/1.38 thf(f2,negated_conjecture,(
% 1.62/1.38 ~((! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X3 : $i] : ((ite @ (zero = X3) @ (s @ zero) @ (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) = (h @ X3)) & ! [X1 : $i,X0 : $o,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero))))))),
% 1.62/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.38 thf(f1,conjecture,(
% 1.62/1.38 (! [X1 : $i,X2 : $i,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3 : $i] : ((s @ X3) != zero) & ! [X3 : $i] : ((ite @ (zero = X3) @ (s @ zero) @ (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) = (h @ X3)) & ! [X1 : $i,X0 : $o,X2 : $i] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3 : $i] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero)))))),
% 1.62/1.38 file('/export/starexec/sandbox/tmp/tmp.g3rs5Z6rbb/DTF2THF_20826.p',n10)).
% 1.62/1.38 thf(f112,plain,(
% 1.62/1.38 ~spl0_2),
% 1.62/1.38 inference(avatar_contradiction_clause,[status(thm)],[f111])).
% 1.62/1.38 thf(f111,plain,(
% 1.62/1.38 $false | ~spl0_2),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.62/1.38 thf(f109,plain,(
% 1.62/1.38 ((s @ zero) != (s @ zero)) | ~spl0_2),
% 1.62/1.38 inference(superposition,[status(thm)],[f15,f64])).
% 1.62/1.38 thf(f64,plain,(
% 1.62/1.38 ((s @ zero) = (s @ (s @ zero))) | ~spl0_2),
% 1.62/1.38 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.62/1.38 thf(f62,definition,(
% 1.62/1.38 spl0_2 <=> ((s @ zero) = (s @ (s @ zero)))),
% 1.62/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.62/1.38 thf(f15,plain,(
% 1.62/1.38 ( ! [X0 : $i] : (((s @ X0) != X0)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 thf(f105,plain,(
% 1.62/1.38 ~spl0_3 | spl0_4),
% 1.62/1.38 inference(avatar_contradiction_clause,[status(thm)],[f104])).
% 1.62/1.38 thf(f104,plain,(
% 1.62/1.38 $false | (~spl0_3 | spl0_4)),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.62/1.38 thf(f103,plain,(
% 1.62/1.38 (zero != zero) | (~spl0_3 | spl0_4)),
% 1.62/1.38 inference(superposition,[status(thm)],[f97,f96])).
% 1.62/1.38 thf(f96,plain,(
% 1.62/1.38 (zero = (h @ zero)) | (~spl0_3 | spl0_4)),
% 1.62/1.38 inference(backward_demodulation,[status(thm)],[f67,f85])).
% 1.62/1.38 thf(f85,plain,(
% 1.62/1.38 (zero = (s @ zero)) | spl0_4),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.62/1.38 thf(f82,plain,(
% 1.62/1.38 (zero != zero) | ((s @ zero) != (s @ zero)) | (zero = (s @ zero)) | spl0_4),
% 1.62/1.38 inference(superposition,[status(thm)],[f72,f47])).
% 1.62/1.38 thf(f47,plain,(
% 1.62/1.38 ( ! [X0 : $i] : ((zero = (h @ X0)) | ((s @ zero) != X0) | (zero = X0)) )),
% 1.62/1.38 inference(forward_demodulation,[status(thm)],[f44,f16])).
% 1.62/1.38 thf(f16,plain,(
% 1.62/1.38 ( ! [X8 : $i,X6 : $i] : (((ite @ $true @ X6 @ X8) = X6)) )),
% 1.62/1.38 inference(equality_resolution,[status(thm)],[f11])).
% 1.62/1.38 thf(f11,plain,(
% 1.62/1.38 ( ! [X8 : $i,X6 : $i,X7 : $o] : (((ite @ X7 @ X6 @ X8) = X6) | ($true != X7)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 thf(f44,plain,(
% 1.62/1.38 ( ! [X0 : $i] : ((zero = X0) | ((s @ zero) != X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero)))) )),
% 1.62/1.38 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.38 thf(f40,plain,(
% 1.62/1.38 ( ! [X0 : $i] : ((zero = X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero))) | (((s @ zero) = X0) = $false)) )),
% 1.62/1.38 inference(fool_paramodulation,[status(thm)],[f33])).
% 1.62/1.38 thf(f33,plain,(
% 1.62/1.38 ( ! [X0 : $i] : (((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))) | (zero = X0)) )),
% 1.62/1.38 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.62/1.38 thf(f29,plain,(
% 1.62/1.38 ( ! [X0 : $i] : (((zero = X0) = $true) | ((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero)))) )),
% 1.62/1.38 inference(superposition,[status(thm)],[f12,f14])).
% 1.62/1.38 thf(f14,plain,(
% 1.62/1.38 ( ! [X2 : $i,X3 : $o,X1 : $i] : (((ite @ X3 @ X1 @ X2) = X2) | ($true = X3)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 thf(f12,plain,(
% 1.62/1.38 ( ! [X5 : $i] : (((h @ X5) = (ite @ (zero = X5) @ (s @ zero) @ (ite @ ((s @ zero) = X5) @ zero @ (s @ zero))))) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 thf(f72,plain,(
% 1.62/1.38 (zero != (h @ (s @ zero))) | spl0_4),
% 1.62/1.38 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.62/1.38 thf(f70,definition,(
% 1.62/1.38 spl0_4 <=> (zero = (h @ (s @ zero)))),
% 1.62/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.62/1.38 thf(f67,plain,(
% 1.62/1.38 ((s @ zero) = (h @ zero)) | ~spl0_3),
% 1.62/1.38 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.62/1.38 thf(f66,definition,(
% 1.62/1.38 spl0_3 <=> ((s @ zero) = (h @ zero))),
% 1.62/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.62/1.38 thf(f97,plain,(
% 1.62/1.38 (zero != (h @ zero)) | spl0_4),
% 1.62/1.38 inference(backward_demodulation,[status(thm)],[f72,f85])).
% 1.62/1.38 thf(f78,plain,(
% 1.62/1.38 spl0_3),
% 1.62/1.38 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.62/1.38 thf(f77,plain,(
% 1.62/1.38 $false | spl0_3),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.62/1.38 thf(f76,plain,(
% 1.62/1.38 (zero != zero) | ((s @ zero) != (s @ zero)) | spl0_3),
% 1.62/1.38 inference(superposition,[status(thm)],[f68,f37])).
% 1.62/1.38 thf(f37,plain,(
% 1.62/1.38 ( ! [X5 : $i] : (((s @ zero) = (h @ X5)) | (zero != X5)) )),
% 1.62/1.38 inference(forward_demodulation,[status(thm)],[f31,f16])).
% 1.62/1.38 thf(f31,plain,(
% 1.62/1.38 ( ! [X5 : $i] : (((h @ X5) = (ite @ $true @ (s @ zero) @ (ite @ ((s @ zero) = X5) @ zero @ (s @ zero)))) | (zero != X5)) )),
% 1.62/1.38 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.62/1.38 thf(f26,plain,(
% 1.62/1.38 ( ! [X5 : $i] : (((zero = X5) = $false) | ((h @ X5) = (ite @ $true @ (s @ zero) @ (ite @ ((s @ zero) = X5) @ zero @ (s @ zero))))) )),
% 1.62/1.38 inference(fool_paramodulation,[status(thm)],[f12])).
% 1.62/1.38 thf(f68,plain,(
% 1.62/1.38 ((s @ zero) != (h @ zero)) | spl0_3),
% 1.62/1.38 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.62/1.38 thf(f73,plain,(
% 1.62/1.38 spl0_1 | spl0_2 | ~spl0_3 | ~spl0_4),
% 1.62/1.38 inference(avatar_split_clause,[status(thm)],[f55,f70,f66,f62,f58])).
% 1.62/1.38 thf(f55,plain,(
% 1.62/1.38 ((s @ zero) = (s @ (s @ zero))) | ((s @ zero) != (h @ zero)) | (zero != (h @ (s @ zero))) | (zero = (s @ (s @ zero)))),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.62/1.38 thf(f53,plain,(
% 1.62/1.38 ((s @ zero) != (h @ zero)) | ((s @ zero) != (s @ zero)) | (zero = (s @ (s @ zero))) | (zero != (h @ (s @ zero))) | ((s @ zero) = (s @ (s @ zero)))),
% 1.62/1.38 inference(superposition,[status(thm)],[f13,f46])).
% 1.62/1.38 thf(f46,plain,(
% 1.62/1.38 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | (zero = X0) | ((s @ zero) = X0)) )),
% 1.62/1.38 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 1.62/1.38 thf(f43,plain,(
% 1.62/1.38 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | (((s @ zero) = X0) = $true) | (zero = X0)) )),
% 1.62/1.38 inference(superposition,[status(thm)],[f14,f33])).
% 1.62/1.38 thf(f13,plain,(
% 1.62/1.38 ( ! [X4 : $i > $i] : (((s @ zero) != (X4 @ (s @ (s @ zero)))) | ((s @ zero) != (X4 @ zero)) | (zero != (X4 @ (s @ zero)))) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.38 % SZS output end Proof for DTF2THF_20826
% 1.62/1.38 % (21130)------------------------------
% 1.62/1.38 % (21130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (21130)Termination reason: Refutation
% 1.62/1.38
% 1.62/1.38 % (21130)Memory used [KB]: 5628
% 1.62/1.38 % (21130)Time elapsed: 0.009 s
% 1.62/1.38 % (21130)Instructions burned: 17 (million)
% 1.62/1.38 % (21130)------------------------------
% 1.62/1.38 % (21130)------------------------------
% 1.62/1.38 % (21103)Success in time 0.092 s
%------------------------------------------------------------------------------