%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO038^1.003.003 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 09:53:12 AM UTC 2026
% Result : Theorem 1.59s 1.38s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 40 unt; 0 typ; 4 def)
% Number of atoms : 490 ( 103 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 700 ( 58 ~; 51 |; 0 &; 584 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
f: $i > $i > $i ).
thf(func_def_3,type,
d: $i > $o ).
thf(f342,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f45,f74,f91,f116,f341]) ).
thf(f341,plain,
~ spl0_4,
inference(avatar_split_clause,[status(thm)],[f338,f88]) ).
thf(f88,definition,
( spl0_4
<=> ( $true
= ( d @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f338,plain,
( $true
!= ( d @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f337]) ).
thf(f337,plain,
( ( $true
!= ( d @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f333,f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( $true
= ( d @ ( s @ X0 ) ) )
| ( $true
!= ( d @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( $true
= ( d @ ( s @ X0 ) ) )
| ( $true
!= ( d @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( $true
= ( d @ X0 ) )
=> ( $true
= ( d @ ( s @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i] :
( ( d @ X0 )
=> ( d @ ( s @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: $i] :
( ( d @ X1 )
=> ( d @ ( s @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax5) ).
thf(f333,plain,
( $true
!= ( d @ ( s @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f332]) ).
thf(f332,plain,
( ( $true != $true )
| ( $true
!= ( d @ ( s @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f318,f34]) ).
thf(f34,plain,
! [X0: $i] :
( ( $true
= ( d @ ( f @ one @ ( s @ X0 ) ) ) )
| ( $true
!= ( d @ ( s @ ( f @ one @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f25,f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( s @ ( s @ ( f @ one @ X0 ) ) )
= ( f @ one @ ( s @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( s @ ( s @ ( f @ one @ X0 ) ) )
= ( f @ one @ ( s @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i] :
( ( f @ one @ ( s @ X1 ) )
= ( s @ ( s @ ( f @ one @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax2) ).
thf(f318,plain,
( $true
!= ( d @ ( f @ one @ ( s @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f311,f166]) ).
thf(f166,plain,
( ( d @ ( f @ ( s @ one ) @ ( s @ ( s @ ( s @ one ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f29,f165]) ).
thf(f165,plain,
( ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) )
= ( f @ ( s @ one ) @ ( s @ ( s @ ( s @ one ) ) ) ) ),
inference(superposition,[status(thm)],[f21,f158]) ).
thf(f158,plain,
( ( f @ ( s @ ( s @ one ) ) @ ( s @ one ) )
= ( s @ ( s @ ( s @ one ) ) ) ),
inference(superposition,[status(thm)],[f149,f122]) ).
thf(f122,plain,
! [X0: $i] :
( ( f @ X0 @ ( s @ one ) )
= ( f @ ( s @ X0 ) @ ( s @ one ) ) ),
inference(superposition,[status(thm)],[f21,f24]) ).
thf(f24,plain,
! [X0: $i] :
( ( f @ X0 @ one )
= ( s @ one ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( f @ X0 @ one )
= ( s @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax1) ).
thf(f149,plain,
( ( f @ ( s @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( s @ ( s @ ( s @ one ) ) ) ),
inference(forward_demodulation,[status(thm)],[f147,f33]) ).
thf(f33,plain,
( ( s @ ( s @ ( s @ one ) ) )
= ( f @ one @ ( s @ one ) ) ),
inference(superposition,[status(thm)],[f23,f24]) ).
thf(f147,plain,
( ( f @ ( f @ one @ ( s @ one ) ) @ ( s @ one ) )
= ( s @ ( s @ ( s @ one ) ) ) ),
inference(superposition,[status(thm)],[f133,f128]) ).
thf(f128,plain,
! [X0: $i] :
( ( f @ ( f @ one @ ( s @ X0 ) ) @ ( s @ one ) )
= ( f @ ( f @ one @ X0 ) @ ( s @ one ) ) ),
inference(forward_demodulation,[status(thm)],[f125,f122]) ).
thf(f125,plain,
! [X0: $i] :
( ( f @ ( f @ one @ ( s @ X0 ) ) @ ( s @ one ) )
= ( f @ ( s @ ( f @ one @ X0 ) ) @ ( s @ one ) ) ),
inference(superposition,[status(thm)],[f122,f23]) ).
thf(f133,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( s @ ( s @ ( s @ one ) ) ) ),
inference(forward_demodulation,[status(thm)],[f132,f33]) ).
thf(f132,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( f @ one @ ( s @ one ) ) ),
inference(forward_demodulation,[status(thm)],[f131,f122]) ).
thf(f131,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( f @ ( s @ one ) @ ( s @ one ) ) ),
inference(forward_demodulation,[status(thm)],[f130,f122]) ).
thf(f130,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( f @ ( s @ ( s @ one ) ) @ ( s @ one ) ) ),
inference(forward_demodulation,[status(thm)],[f129,f122]) ).
thf(f129,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( f @ ( s @ ( s @ ( s @ one ) ) ) @ ( s @ one ) ) ),
inference(forward_demodulation,[status(thm)],[f126,f122]) ).
thf(f126,plain,
( ( f @ ( f @ one @ ( s @ ( s @ one ) ) ) @ ( s @ one ) )
= ( f @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) @ ( s @ one ) ) ),
inference(superposition,[status(thm)],[f122,f35]) ).
thf(f35,plain,
( ( s @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) )
= ( f @ one @ ( s @ ( s @ one ) ) ) ),
inference(superposition,[status(thm)],[f23,f33]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( f @ ( s @ X0 ) @ ( s @ X1 ) )
= ( f @ X0 @ ( f @ ( s @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( f @ ( s @ X0 ) @ ( s @ X1 ) )
= ( f @ X0 @ ( f @ ( s @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i,X0: $i] :
( ( f @ ( s @ X1 ) @ ( s @ X0 ) )
= ( f @ X1 @ ( f @ ( s @ X1 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( f @ ( s @ X0 ) @ ( s @ X1 ) )
= ( f @ X0 @ ( f @ ( s @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax3) ).
thf(f29,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
= $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',conj) ).
thf(f311,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ) )
| ( $true
= ( d @ ( f @ ( s @ one ) @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f249,f142]) ).
thf(f142,plain,
( ( f @ ( s @ one ) @ ( s @ ( s @ ( s @ one ) ) ) )
= ( f @ one @ ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) ) ) ),
inference(superposition,[status(thm)],[f21,f134]) ).
thf(f134,plain,
( ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) )
= ( f @ ( s @ one ) @ ( s @ ( s @ one ) ) ) ),
inference(superposition,[status(thm)],[f127,f33]) ).
thf(f127,plain,
! [X0: $i] :
( ( f @ X0 @ ( f @ X0 @ ( s @ one ) ) )
= ( f @ ( s @ X0 ) @ ( s @ ( s @ one ) ) ) ),
inference(superposition,[status(thm)],[f21,f122]) ).
thf(f249,plain,
! [X0: $i] :
( ( $true
= ( d @ ( f @ one @ ( f @ one @ ( s @ X0 ) ) ) ) )
| ( $true
!= ( d @ ( f @ one @ ( s @ ( f @ one @ X0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f248]) ).
thf(f248,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( d @ ( f @ one @ ( s @ ( f @ one @ X0 ) ) ) ) )
| ( $true
= ( d @ ( f @ one @ ( f @ one @ ( s @ X0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f79,f25]) ).
thf(f79,plain,
! [X0: $i] :
( ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( f @ one @ X0 ) ) ) ) ) )
| ( $true
= ( d @ ( f @ one @ ( f @ one @ ( s @ X0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f34,f23]) ).
thf(f116,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f115,f84,f42]) ).
thf(f42,definition,
( spl0_2
<=> ( $true
= ( d @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f84,definition,
( spl0_3
<=> ( $true
= ( d @ ( s @ ( f @ one @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f115,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ one ) ) ) ) )
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ one ) ) ) ) )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[status(thm)],[f109,f25]) ).
thf(f109,plain,
( ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) )
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[status(thm)],[f105,f34]) ).
thf(f105,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[status(thm)],[f99,f25]) ).
thf(f99,plain,
( ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) )
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true != $true )
| ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) )
| spl0_3 ),
inference(superposition,[status(thm)],[f95,f34]) ).
thf(f95,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) )
| spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true
!= ( d @ ( f @ one @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[status(thm)],[f86,f25]) ).
thf(f86,plain,
( ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f91,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f80,f88,f84]) ).
thf(f80,plain,
( ( $true
= ( d @ ( f @ one @ ( f @ one @ ( s @ ( s @ one ) ) ) ) ) )
| ( $true
!= ( d @ ( s @ ( f @ one @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f34,f35]) ).
thf(f74,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true = $false )
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f22,f68]) ).
thf(f68,plain,
( ( ( d @ one )
= $false )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ( ( d @ one )
= $false )
| spl0_1 ),
inference(fool_paramodulation,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( d @ one )
!= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( ( d @ one )
!= $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f58,f25]) ).
thf(f58,plain,
( ( $true
!= ( d @ ( s @ one ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
!= ( d @ ( s @ one ) ) )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f54,f25]) ).
thf(f54,plain,
( ( $true
!= ( d @ ( s @ ( s @ one ) ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
!= ( d @ ( s @ ( s @ one ) ) ) )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f48,f25]) ).
thf(f48,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ one ) ) ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true != $true )
| ( $true
!= ( d @ ( s @ ( s @ ( s @ one ) ) ) ) )
| spl0_1 ),
inference(superposition,[status(thm)],[f40,f25]) ).
thf(f40,plain,
( ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl0_1
<=> ( $true
= ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f22,plain,
( ( d @ one )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( d @ one )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
d @ one,
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
d @ one,
file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax4) ).
thf(f45,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f42,f38]) ).
thf(f36,plain,
( ( $true
= ( d @ ( f @ one @ ( s @ ( s @ one ) ) ) ) )
| ( $true
!= ( d @ ( s @ ( s @ ( s @ ( s @ one ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f25,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO038^1.003.003 : TPTP v9.2.1. Released v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:22:01 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO038^1.003.003 : TPTP v9.2.1. Released v5.3.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : Boolos' Curious Inference, size f(3,3)
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Boo87] Boolos (1987), A Curious Inference
% 0.28/0.46 % : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.28/0.46 % : [BB07] Benzmueller & Brown (2007), The Curious Inference of B
% 0.28/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Ben09]
% 0.28/0.46 % Names : Example 35 [BB05]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0
% 0.28/0.46 % Syntax : Number of formulae : 10 ( 5 unt; 4 typ; 0 def)
% 0.28/0.46 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.28/0.46 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 30 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 6 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : The first order proof is infeasibly long - f(5,5) is huge. It is
% 0.28/0.46 % a number that makes googolplex look tiny. Practically impossible
% 0.28/0.46 % to solve using only first-order means. However, there exists a
% 0.28/0.46 % proof in higher-order logic that is very short but hard to find.
% 0.28/0.46 % : f(3,3) is 16. Relatively easy.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(one,type,
% 0.28/0.46 one: $i ).
% 0.28/0.46
% 0.28/0.46 thf(s,type,
% 0.28/0.46 s: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(f,type,
% 0.28/0.46 f: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(d,type,
% 0.28/0.46 d: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(ax1,axiom,
% 0.28/0.46 ! [N: $i] :
% 0.28/0.46 ( ( f @ N @ one )
% 0.28/0.46 = ( s @ one ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax2,axiom,
% 0.28/0.46 ! [X: $i] :
% 0.28/0.46 ( ( f @ one @ ( s @ X ) )
% 0.28/0.46 = ( s @ ( s @ ( f @ one @ X ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax3,axiom,
% 0.28/0.46 ! [N: $i,X: $i] :
% 0.28/0.46 ( ( f @ ( s @ N ) @ ( s @ X ) )
% 0.28/0.46 = ( f @ N @ ( f @ ( s @ N ) @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax4,axiom,
% 0.28/0.46 d @ one ).
% 0.28/0.46
% 0.28/0.46 thf(ax5,axiom,
% 0.28/0.46 ! [X: $i] :
% 0.28/0.46 ( ( d @ X )
% 0.28/0.46 => ( d @ ( s @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(conj,conjecture,
% 0.28/0.46 d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 14:22:02 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2DTF7457.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(one,type,
% 1.47/1.26 one: $i ).
% 1.47/1.26
% 1.47/1.26 thf(s,type,
% 1.47/1.26 s: $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(f,type,
% 1.47/1.26 f: $i > $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(d,type,
% 1.47/1.26 d: $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(ax1,axiom,
% 1.47/1.26 ! [N: $i] :
% 1.47/1.26 ( ( f @ N @ one )
% 1.47/1.26 = ( s @ one ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(ax2,axiom,
% 1.47/1.26 ! [X: $i] :
% 1.47/1.26 ( ( f @ one @ ( s @ X ) )
% 1.47/1.26 = ( s @ ( s @ ( f @ one @ X ) ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(ax3,axiom,
% 1.47/1.26 ! [N: $i,X: $i] :
% 1.47/1.26 ( ( f @ ( s @ N ) @ ( s @ X ) )
% 1.47/1.26 = ( f @ N @ ( f @ ( s @ N ) @ X ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(ax4,axiom,
% 1.47/1.26 d @ one ).
% 1.47/1.26
% 1.47/1.26 thf(ax5,axiom,
% 1.47/1.26 ! [X: $i] :
% 1.47/1.26 ( ( d @ X )
% 1.47/1.26 => ( d @ ( s @ X ) ) ) ).
% 1.47/1.26
% 1.47/1.26 thf(conj,conjecture,
% 1.47/1.26 d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (7668)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/183Mi)
% 1.47/1.28 % (7674)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/18Mi)
% 1.47/1.28 % (7674)Instruction limit reached!
% 1.47/1.28 % (7674)------------------------------
% 1.47/1.28 % (7674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7674)Termination reason: Unknown
% 1.47/1.28 % (7674)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (7674)Memory used [KB]: 5628
% 1.47/1.28 % (7674)Time elapsed: 0.008 s
% 1.47/1.28 % (7674)Instructions burned: 19 (million)
% 1.47/1.28 % (7674)------------------------------
% 1.47/1.28 % (7674)------------------------------
% 1.47/1.28 % (7669)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_7457 for (2999ds/4Mi)
% 1.47/1.28 % (7670)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_7457 for (2999ds/27Mi)
% 1.47/1.28 % (7671)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/2Mi)
% 1.47/1.28 % (7672)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_7457 for (2999ds/2Mi)
% 1.47/1.28 % (7673)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_7457 for (2999ds/275Mi)
% 1.47/1.28 % (7672)Instruction limit reached!
% 1.47/1.28 % (7672)------------------------------
% 1.47/1.28 % (7672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7672)Termination reason: Unknown
% 1.47/1.28 % (7672)Termination phase: Property scanning
% 1.47/1.28
% 1.47/1.28 % (7672)Memory used [KB]: 895
% 1.47/1.28 % (7672)Time elapsed: 0.003 s
% 1.47/1.28 % (7672)Instructions burned: 2 (million)
% 1.47/1.28 % (7672)------------------------------
% 1.47/1.28 % (7672)------------------------------
% 1.47/1.28 % (7671)Instruction limit reached!
% 1.47/1.28 % (7671)------------------------------
% 1.47/1.28 % (7671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7671)Termination reason: Unknown
% 1.47/1.28 % (7671)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (7671)Memory used [KB]: 5500
% 1.47/1.28 % (7671)Time elapsed: 0.004 s
% 1.47/1.28 % (7671)Instructions burned: 2 (million)
% 1.47/1.28 % (7671)------------------------------
% 1.47/1.28 % (7671)------------------------------
% 1.47/1.28 % (7673)Refutation not found, incomplete strategy
% 1.47/1.28 % (7673)------------------------------
% 1.47/1.28 % (7673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7673)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.28
% 1.47/1.28
% 1.47/1.28 % (7673)Memory used [KB]: 5500
% 1.47/1.28 % (7673)Time elapsed: 0.004 s
% 1.47/1.28 % (7673)Instructions burned: 2 (million)
% 1.47/1.28 % (7673)------------------------------
% 1.47/1.28 % (7673)------------------------------
% 1.47/1.28 % (7669)Instruction limit reached!
% 1.47/1.28 % (7669)------------------------------
% 1.47/1.28 % (7669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (7669)Termination reason: Unknown
% 1.47/1.28 % (7669)Termination phase: Saturation
% 1.47/1.28
% 1.47/1.28 % (7669)Memory used [KB]: 5500
% 1.47/1.28 % (7669)Time elapsed: 0.005 s
% 1.47/1.28 % (7669)Instructions burned: 4 (million)
% 1.47/1.28 % (7669)------------------------------
% 1.47/1.28 % (7669)------------------------------
% 1.47/1.29 % (7675)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/3Mi)
% 1.47/1.29 % (7675)Instruction limit reached!
% 1.47/1.29 % (7675)------------------------------
% 1.47/1.29 % (7675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (7675)Termination reason: Unknown
% 1.47/1.29 % (7675)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (7675)Memory used [KB]: 5500
% 1.47/1.29 % (7675)Time elapsed: 0.003 s
% 1.47/1.29 % (7675)Instructions burned: 3 (million)
% 1.47/1.29 % (7675)------------------------------
% 1.47/1.29 % (7675)------------------------------
% 1.59/1.30 % (7670)Instruction limit reached!
% 1.59/1.30 % (7670)------------------------------
% 1.59/1.30 % (7670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (7670)Termination reason: Unknown
% 1.59/1.30 % (7670)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (7670)Memory used [KB]: 5628
% 1.59/1.30 % (7670)Time elapsed: 0.019 s
% 1.59/1.30 % (7670)Instructions burned: 27 (million)
% 1.59/1.30 % (7670)------------------------------
% 1.59/1.30 % (7670)------------------------------
% 1.59/1.30 % (7676)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_7457 for (2999ds/37Mi)
% 1.59/1.30 % (7677)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_7457 for (2999ds/15Mi)
% 1.59/1.30 % (7678)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_7457 for (2999ds/3Mi)
% 1.59/1.30 % (7679)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_7457 for (2999ds/1041Mi)
% 1.59/1.30 % (7680)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/7Mi)
% 1.59/1.30 % (7677)Refutation not found, incomplete strategy
% 1.59/1.30 % (7677)------------------------------
% 1.59/1.30 % (7677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (7677)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.30
% 1.59/1.30
% 1.59/1.30 % (7677)Memory used [KB]: 5500
% 1.59/1.30 % (7677)Time elapsed: 0.004 s
% 1.59/1.30 % (7677)Instructions burned: 3 (million)
% 1.59/1.30 % (7677)------------------------------
% 1.59/1.30 % (7677)------------------------------
% 1.59/1.30 % (7678)Instruction limit reached!
% 1.59/1.30 % (7678)------------------------------
% 1.59/1.30 % (7678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (7678)Termination reason: Unknown
% 1.59/1.30 % (7678)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (7678)Memory used [KB]: 5500
% 1.59/1.30 % (7678)Time elapsed: 0.004 s
% 1.59/1.30 % (7678)Instructions burned: 3 (million)
% 1.59/1.30 % (7678)------------------------------
% 1.59/1.30 % (7678)------------------------------
% 1.59/1.31 % (7680)Instruction limit reached!
% 1.59/1.31 % (7680)------------------------------
% 1.59/1.31 % (7680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (7680)Termination reason: Unknown
% 1.59/1.31 % (7680)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (7680)Memory used [KB]: 1023
% 1.59/1.31 % (7680)Time elapsed: 0.005 s
% 1.59/1.31 % (7680)Instructions burned: 8 (million)
% 1.59/1.31 % (7680)------------------------------
% 1.59/1.31 % (7680)------------------------------
% 1.59/1.32 % (7681)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/16Mi)
% 1.59/1.32 % (7684)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/7Mi)
% 1.59/1.32 % (7684)Refutation not found, incomplete strategy
% 1.59/1.32 % (7684)------------------------------
% 1.59/1.32 % (7684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (7684)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.32
% 1.59/1.32
% 1.59/1.32 % (7684)Memory used [KB]: 5500
% 1.59/1.32 % (7684)Time elapsed: 0.002 s
% 1.59/1.32 % (7684)Instructions burned: 1 (million)
% 1.59/1.32 % (7684)------------------------------
% 1.59/1.32 % (7684)------------------------------
% 1.59/1.32 % (7682)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_7457 for (2999ds/3Mi)
% 1.59/1.32 % (7683)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_7457 for (2999ds/3Mi)
% 1.59/1.32 % (7676)Instruction limit reached!
% 1.59/1.32 % (7676)------------------------------
% 1.59/1.32 % (7676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (7676)Termination reason: Unknown
% 1.59/1.32 % (7676)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (7676)Memory used [KB]: 5756
% 1.59/1.32 % (7676)Time elapsed: 0.025 s
% 1.59/1.32 % (7676)Instructions burned: 38 (million)
% 1.59/1.32 % (7676)------------------------------
% 1.59/1.32 % (7676)------------------------------
% 1.59/1.32 % (7682)Instruction limit reached!
% 1.59/1.32 % (7682)------------------------------
% 1.59/1.32 % (7682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (7682)Termination reason: Unknown
% 1.59/1.32 % (7682)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (7682)Memory used [KB]: 5500
% 1.59/1.32 % (7682)Time elapsed: 0.004 s
% 1.59/1.32 % (7682)Instructions burned: 3 (million)
% 1.59/1.32 % (7682)------------------------------
% 1.59/1.32 % (7682)------------------------------
% 1.59/1.32 % (7683)Instruction limit reached!
% 1.59/1.32 % (7683)------------------------------
% 1.59/1.32 % (7683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (7683)Termination reason: Unknown
% 1.59/1.32 % (7683)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (7683)Memory used [KB]: 1023
% 1.59/1.32 % (7683)Time elapsed: 0.004 s
% 1.59/1.32 % (7683)Instructions burned: 4 (million)
% 1.59/1.32 % (7683)------------------------------
% 1.59/1.32 % (7683)------------------------------
% 1.59/1.33 % (7681)Instruction limit reached!
% 1.59/1.33 % (7681)------------------------------
% 1.59/1.33 % (7681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (7681)Termination reason: Unknown
% 1.59/1.33 % (7681)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (7681)Memory used [KB]: 5628
% 1.59/1.33 % (7681)Time elapsed: 0.013 s
% 1.59/1.33 % (7681)Instructions burned: 17 (million)
% 1.59/1.33 % (7681)------------------------------
% 1.59/1.33 % (7681)------------------------------
% 1.59/1.33 % (7685)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/3Mi)
% 1.59/1.33 % (7685)Instruction limit reached!
% 1.59/1.33 % (7685)------------------------------
% 1.59/1.33 % (7685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (7685)Termination reason: Unknown
% 1.59/1.33 % (7685)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (7685)Memory used [KB]: 5500
% 1.59/1.33 % (7685)Time elapsed: 0.003 s
% 1.59/1.33 % (7685)Instructions burned: 3 (million)
% 1.59/1.33 % (7685)------------------------------
% 1.59/1.33 % (7685)------------------------------
% 1.59/1.33 % (7668)Instruction limit reached!
% 1.59/1.33 % (7668)------------------------------
% 1.59/1.33 % (7668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (7668)Termination reason: Unknown
% 1.59/1.33 % (7668)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (7668)Memory used [KB]: 6524
% 1.59/1.33 % (7668)Time elapsed: 0.059 s
% 1.59/1.33 % (7668)Instructions burned: 184 (million)
% 1.59/1.33 % (7668)------------------------------
% 1.59/1.33 % (7668)------------------------------
% 1.59/1.34 % (7686)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/4Mi)
% 1.59/1.34 % (7686)Instruction limit reached!
% 1.59/1.34 % (7686)------------------------------
% 1.59/1.34 % (7686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7686)Termination reason: Unknown
% 1.59/1.34 % (7686)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7686)Memory used [KB]: 5500
% 1.59/1.34 % (7686)Time elapsed: 0.004 s
% 1.59/1.34 % (7686)Instructions burned: 6 (million)
% 1.59/1.34 % (7686)------------------------------
% 1.59/1.34 % (7686)------------------------------
% 1.59/1.34 % (7690)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_7457 for (2999ds/902Mi)
% 1.59/1.34 % (7690)Refutation not found, incomplete strategy
% 1.59/1.34 % (7690)------------------------------
% 1.59/1.34 % (7690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7690)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 % (7690)Memory used [KB]: 5500
% 1.59/1.34 % (7690)Time elapsed: 0.002 s
% 1.59/1.34 % (7690)Instructions burned: 1 (million)
% 1.59/1.34 % (7690)------------------------------
% 1.59/1.34 % (7690)------------------------------
% 1.59/1.34 % (7691)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_7457 for (2999ds/21Mi)
% 1.59/1.34 % (7687)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/18Mi)
% 1.59/1.34 % (7688)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/710Mi)
% 1.59/1.34 % (7689)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/6Mi)
% 1.59/1.34 % (7689)Instruction limit reached!
% 1.59/1.34 % (7689)------------------------------
% 1.59/1.34 % (7689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (7689)Termination reason: Unknown
% 1.59/1.34 % (7689)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (7689)Memory used [KB]: 5500
% 1.59/1.34 % (7689)Time elapsed: 0.005 s
% 1.59/1.34 % (7689)Instructions burned: 7 (million)
% 1.59/1.34 % (7689)------------------------------
% 1.59/1.34 % (7689)------------------------------
% 1.59/1.35 % (7692)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/5Mi)
% 1.59/1.35 % (7691)Instruction limit reached!
% 1.59/1.35 % (7691)------------------------------
% 1.59/1.35 % (7691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (7691)Termination reason: Unknown
% 1.59/1.35 % (7691)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (7691)Memory used [KB]: 5628
% 1.59/1.35 % (7691)Time elapsed: 0.009 s
% 1.59/1.35 % (7691)Instructions burned: 22 (million)
% 1.59/1.35 % (7691)------------------------------
% 1.59/1.35 % (7691)------------------------------
% 1.59/1.35 % (7692)Instruction limit reached!
% 1.59/1.35 % (7692)------------------------------
% 1.59/1.35 % (7692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (7692)Termination reason: Unknown
% 1.59/1.35 % (7692)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (7692)Memory used [KB]: 5500
% 1.59/1.35 % (7692)Time elapsed: 0.004 s
% 1.59/1.35 % (7692)Instructions burned: 6 (million)
% 1.59/1.35 % (7692)------------------------------
% 1.59/1.35 % (7692)------------------------------
% 1.59/1.35 % (7693)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_7457 for (2999ds/6Mi)
% 1.59/1.35 % (7693)Refutation not found, incomplete strategy
% 1.59/1.35 % (7693)------------------------------
% 1.59/1.35 % (7693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (7693)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.35
% 1.59/1.35
% 1.59/1.35 % (7693)Memory used [KB]: 5500
% 1.59/1.35 % (7693)Time elapsed: 0.002 s
% 1.59/1.35 % (7693)Instructions burned: 1 (million)
% 1.59/1.35 % (7693)------------------------------
% 1.59/1.35 % (7693)------------------------------
% 1.59/1.35 % (7687)Instruction limit reached!
% 1.59/1.35 % (7687)------------------------------
% 1.59/1.35 % (7687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (7687)Termination reason: Unknown
% 1.59/1.35 % (7687)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (7687)Memory used [KB]: 5628
% 1.59/1.35 % (7687)Time elapsed: 0.013 s
% 1.59/1.35 % (7687)Instructions burned: 18 (million)
% 1.59/1.35 % (7687)------------------------------
% 1.59/1.35 % (7687)------------------------------
% 1.59/1.35 % (7694)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/377Mi)
% 1.59/1.36 % (7695)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/779Mi)
% 1.59/1.36 % (7696)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_7457 for (2999ds/19Mi)
% 1.59/1.36 % (7696)Refutation not found, incomplete strategy
% 1.59/1.36 % (7696)------------------------------
% 1.59/1.36 % (7696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (7696)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.36
% 1.59/1.36
% 1.59/1.36 % (7696)Memory used [KB]: 5500
% 1.59/1.36 % (7696)Time elapsed: 0.002 s
% 1.59/1.36 % (7696)Instructions burned: 1 (million)
% 1.59/1.36 % (7696)------------------------------
% 1.59/1.36 % (7696)------------------------------
% 1.59/1.36 % (7697)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/879Mi)
% 1.59/1.37 % (7698)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/17Mi)
% 1.59/1.37 % (7699)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7457 for (2999ds/3Mi)
% 1.59/1.37 % (7699)Instruction limit reached!
% 1.59/1.37 % (7699)------------------------------
% 1.59/1.37 % (7699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.37 % (7699)Termination reason: Unknown
% 1.59/1.37 % (7699)Termination phase: Saturation
% 1.59/1.37
% 1.59/1.37 % (7699)Memory used [KB]: 1023
% 1.59/1.37 % (7699)Time elapsed: 0.003 s
% 1.59/1.37 % (7699)Instructions burned: 4 (million)
% 1.59/1.37 % (7699)------------------------------
% 1.59/1.37 % (7699)------------------------------
% 1.59/1.38 % (7694)First to succeed.
% 1.59/1.38 % (7698)Instruction limit reached!
% 1.59/1.38 % (7698)------------------------------
% 1.59/1.38 % (7698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (7698)Termination reason: Unknown
% 1.59/1.38 % (7698)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (7698)Memory used [KB]: 5628
% 1.59/1.38 % (7698)Time elapsed: 0.013 s
% 1.59/1.38 % (7698)Instructions burned: 17 (million)
% 1.59/1.38 % (7698)------------------------------
% 1.59/1.38 % (7698)------------------------------
% 1.59/1.38 % (7694)Refutation found. Thanks to Tanya!
% 1.59/1.38 % SZS status Theorem for DTF2THF_7457
% 1.59/1.38 % SZS output start Proof for DTF2THF_7457
% 1.59/1.38 thf(func_def_1, type, s: $i > $i).
% 1.59/1.38 thf(func_def_2, type, f: $i > $i > $i).
% 1.59/1.38 thf(func_def_3, type, d: $i > $o).
% 1.59/1.38 thf(f342,plain,(
% 1.59/1.38 $false),
% 1.59/1.38 inference(avatar_sat_refutation,[status(thm)],[f45,f74,f91,f116,f341])).
% 1.59/1.38 thf(f341,plain,(
% 1.59/1.38 ~spl0_4),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f338,f88])).
% 1.59/1.38 thf(f88,definition,(
% 1.59/1.38 spl0_4 <=> ($true = (d @ (f @ one @ (f @ one @ (s @ (s @ one))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.59/1.38 thf(f338,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (f @ one @ (s @ (s @ one))))))),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f337])).
% 1.59/1.38 thf(f337,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (f @ one @ (s @ (s @ one)))))) | ($true != $true)),
% 1.59/1.38 inference(superposition,[status(thm)],[f333,f25])).
% 1.59/1.38 thf(f25,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (($true = (d @ (s @ X0))) | ($true != (d @ X0))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f18])).
% 1.59/1.38 thf(f18,plain,(
% 1.59/1.38 ! [X0 : $i] : (($true = (d @ (s @ X0))) | ($true != (d @ X0)))),
% 1.59/1.38 inference(ennf_transformation,[status(thm)],[f12])).
% 1.59/1.38 thf(f12,plain,(
% 1.59/1.38 ! [X0 : $i] : (($true = (d @ X0)) => ($true = (d @ (s @ X0))))),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f11])).
% 1.59/1.38 thf(f11,plain,(
% 1.59/1.38 ! [X0 : $i] : ((d @ X0) => (d @ (s @ X0)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f5])).
% 1.59/1.38 thf(f5,axiom,(
% 1.59/1.38 ! [X1 : $i] : ((d @ X1) => (d @ (s @ X1)))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax5)).
% 1.59/1.38 thf(f333,plain,(
% 1.59/1.38 ($true != (d @ (s @ (f @ one @ (f @ one @ (s @ (s @ one)))))))),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f332])).
% 1.59/1.38 thf(f332,plain,(
% 1.59/1.38 ($true != $true) | ($true != (d @ (s @ (f @ one @ (f @ one @ (s @ (s @ one)))))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f318,f34])).
% 1.59/1.38 thf(f34,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (($true = (d @ (f @ one @ (s @ X0)))) | ($true != (d @ (s @ (f @ one @ X0))))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f25,f23])).
% 1.59/1.38 thf(f23,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((s @ (s @ (f @ one @ X0))) = (f @ one @ (s @ X0)))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f16])).
% 1.59/1.38 thf(f16,plain,(
% 1.59/1.38 ! [X0 : $i] : ((s @ (s @ (f @ one @ X0))) = (f @ one @ (s @ X0)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f2])).
% 1.59/1.38 thf(f2,axiom,(
% 1.59/1.38 ! [X1 : $i] : ((f @ one @ (s @ X1)) = (s @ (s @ (f @ one @ X1))))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax2)).
% 1.59/1.38 thf(f318,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (f @ one @ (s @ (s @ one)))))))),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.59/1.38 thf(f317,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (f @ one @ (s @ (s @ one))))))) | ($true = $false)),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f311,f166])).
% 1.59/1.38 thf(f166,plain,(
% 1.59/1.38 ((d @ (f @ (s @ one) @ (s @ (s @ (s @ one))))) = $false)),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f29,f165])).
% 1.59/1.38 thf(f165,plain,(
% 1.59/1.38 ((f @ (s @ (s @ one)) @ (s @ (s @ one))) = (f @ (s @ one) @ (s @ (s @ (s @ one)))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f21,f158])).
% 1.59/1.38 thf(f158,plain,(
% 1.59/1.38 ((f @ (s @ (s @ one)) @ (s @ one)) = (s @ (s @ (s @ one))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f149,f122])).
% 1.59/1.38 thf(f122,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((f @ X0 @ (s @ one)) = (f @ (s @ X0) @ (s @ one)))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f21,f24])).
% 1.59/1.38 thf(f24,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((f @ X0 @ one) = (s @ one))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f1])).
% 1.59/1.38 thf(f1,axiom,(
% 1.59/1.38 ! [X0 : $i] : ((f @ X0 @ one) = (s @ one))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax1)).
% 1.59/1.38 thf(f149,plain,(
% 1.59/1.38 ((f @ (s @ (s @ (s @ one))) @ (s @ one)) = (s @ (s @ (s @ one))))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f147,f33])).
% 1.59/1.38 thf(f33,plain,(
% 1.59/1.38 ((s @ (s @ (s @ one))) = (f @ one @ (s @ one)))),
% 1.59/1.38 inference(superposition,[status(thm)],[f23,f24])).
% 1.59/1.38 thf(f147,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ one)) @ (s @ one)) = (s @ (s @ (s @ one))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f133,f128])).
% 1.59/1.38 thf(f128,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((f @ (f @ one @ (s @ X0)) @ (s @ one)) = (f @ (f @ one @ X0) @ (s @ one)))) )),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f125,f122])).
% 1.59/1.38 thf(f125,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((f @ (f @ one @ (s @ X0)) @ (s @ one)) = (f @ (s @ (f @ one @ X0)) @ (s @ one)))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f122,f23])).
% 1.59/1.38 thf(f133,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (s @ (s @ (s @ one))))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f132,f33])).
% 1.59/1.38 thf(f132,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (f @ one @ (s @ one)))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f131,f122])).
% 1.59/1.38 thf(f131,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (f @ (s @ one) @ (s @ one)))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f130,f122])).
% 1.59/1.38 thf(f130,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (f @ (s @ (s @ one)) @ (s @ one)))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f129,f122])).
% 1.59/1.38 thf(f129,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (f @ (s @ (s @ (s @ one))) @ (s @ one)))),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f126,f122])).
% 1.59/1.38 thf(f126,plain,(
% 1.59/1.38 ((f @ (f @ one @ (s @ (s @ one))) @ (s @ one)) = (f @ (s @ (s @ (s @ (s @ one)))) @ (s @ one)))),
% 1.59/1.38 inference(superposition,[status(thm)],[f122,f35])).
% 1.59/1.38 thf(f35,plain,(
% 1.59/1.38 ((s @ (s @ (s @ (s @ (s @ one))))) = (f @ one @ (s @ (s @ one))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f23,f33])).
% 1.59/1.38 thf(f21,plain,(
% 1.59/1.38 ( ! [X0 : $i,X1 : $i] : (((f @ (s @ X0) @ (s @ X1)) = (f @ X0 @ (f @ (s @ X0) @ X1)))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.59/1.38 thf(f19,plain,(
% 1.59/1.38 ! [X0 : $i,X1 : $i] : ((f @ (s @ X0) @ (s @ X1)) = (f @ X0 @ (f @ (s @ X0) @ X1)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f15])).
% 1.59/1.38 thf(f15,plain,(
% 1.59/1.38 ! [X1 : $i,X0 : $i] : ((f @ (s @ X1) @ (s @ X0)) = (f @ X1 @ (f @ (s @ X1) @ X0)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f3])).
% 1.59/1.38 thf(f3,axiom,(
% 1.59/1.38 ! [X1 : $i,X0 : $i] : ((f @ (s @ X0) @ (s @ X1)) = (f @ X0 @ (f @ (s @ X0) @ X1)))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax3)).
% 1.59/1.38 thf(f29,plain,(
% 1.59/1.38 ((d @ (f @ (s @ (s @ one)) @ (s @ (s @ one)))) = $false)),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.59/1.38 thf(f28,plain,(
% 1.59/1.38 ((d @ (f @ (s @ (s @ one)) @ (s @ (s @ one)))) = $false) | ($true != $true)),
% 1.59/1.38 inference(fool_paramodulation,[status(thm)],[f20])).
% 1.59/1.38 thf(f20,plain,(
% 1.59/1.38 ((d @ (f @ (s @ (s @ one)) @ (s @ (s @ one)))) != $true)),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f17])).
% 1.59/1.38 thf(f17,plain,(
% 1.59/1.38 ((d @ (f @ (s @ (s @ one)) @ (s @ (s @ one)))) != $true)),
% 1.59/1.38 inference(flattening,[status(thm)],[f10])).
% 1.59/1.38 thf(f10,plain,(
% 1.59/1.38 ~((d @ (f @ (s @ (s @ one)) @ (s @ (s @ one)))) = $true)),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f9])).
% 1.59/1.38 thf(f9,plain,(
% 1.59/1.38 ~(d @ (f @ (s @ (s @ one)) @ (s @ (s @ one))))),
% 1.59/1.38 inference(rectify,[status(thm)],[f7])).
% 1.59/1.38 thf(f7,negated_conjecture,(
% 1.59/1.38 ~(d @ (f @ (s @ (s @ one)) @ (s @ (s @ one))))),
% 1.59/1.38 inference(negated_conjecture,[status(cth)],[f6])).
% 1.59/1.38 thf(f6,conjecture,(
% 1.59/1.38 (d @ (f @ (s @ (s @ one)) @ (s @ (s @ one))))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',conj)).
% 1.59/1.38 thf(f311,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (f @ one @ (s @ (s @ one))))))) | ($true = (d @ (f @ (s @ one) @ (s @ (s @ (s @ one))))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f249,f142])).
% 1.59/1.38 thf(f142,plain,(
% 1.59/1.38 ((f @ (s @ one) @ (s @ (s @ (s @ one)))) = (f @ one @ (f @ one @ (s @ (s @ (s @ one))))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f21,f134])).
% 1.59/1.38 thf(f134,plain,(
% 1.59/1.38 ((f @ one @ (s @ (s @ (s @ one)))) = (f @ (s @ one) @ (s @ (s @ one))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f127,f33])).
% 1.59/1.38 thf(f127,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (((f @ X0 @ (f @ X0 @ (s @ one))) = (f @ (s @ X0) @ (s @ (s @ one))))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f21,f122])).
% 1.59/1.38 thf(f249,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (($true = (d @ (f @ one @ (f @ one @ (s @ X0))))) | ($true != (d @ (f @ one @ (s @ (f @ one @ X0)))))) )),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f248])).
% 1.59/1.38 thf(f248,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (($true != $true) | ($true != (d @ (f @ one @ (s @ (f @ one @ X0))))) | ($true = (d @ (f @ one @ (f @ one @ (s @ X0)))))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f79,f25])).
% 1.59/1.38 thf(f79,plain,(
% 1.59/1.38 ( ! [X0 : $i] : (($true != (d @ (s @ (f @ one @ (s @ (f @ one @ X0)))))) | ($true = (d @ (f @ one @ (f @ one @ (s @ X0)))))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f34,f23])).
% 1.59/1.38 thf(f116,plain,(
% 1.59/1.38 ~spl0_2 | spl0_3),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f115,f84,f42])).
% 1.59/1.38 thf(f42,definition,(
% 1.59/1.38 spl0_2 <=> ($true = (d @ (f @ one @ (s @ (s @ one)))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.59/1.38 thf(f84,definition,(
% 1.59/1.38 spl0_3 <=> ($true = (d @ (s @ (f @ one @ (s @ (s @ (s @ (s @ one))))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.59/1.38 thf(f115,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ one))))) | spl0_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.59/1.38 thf(f113,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ one))))) | ($true != $true) | spl0_3),
% 1.59/1.38 inference(superposition,[status(thm)],[f109,f25])).
% 1.59/1.38 thf(f109,plain,(
% 1.59/1.38 ($true != (d @ (s @ (f @ one @ (s @ (s @ one)))))) | spl0_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.59/1.38 thf(f108,plain,(
% 1.59/1.38 ($true != (d @ (s @ (f @ one @ (s @ (s @ one)))))) | ($true != $true) | spl0_3),
% 1.59/1.38 inference(superposition,[status(thm)],[f105,f34])).
% 1.59/1.38 thf(f105,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ (s @ one)))))) | spl0_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.59/1.38 thf(f103,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ (s @ one)))))) | ($true != $true) | spl0_3),
% 1.59/1.38 inference(superposition,[status(thm)],[f99,f25])).
% 1.59/1.38 thf(f99,plain,(
% 1.59/1.38 ($true != (d @ (s @ (f @ one @ (s @ (s @ (s @ one))))))) | spl0_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.59/1.38 thf(f98,plain,(
% 1.59/1.38 ($true != $true) | ($true != (d @ (s @ (f @ one @ (s @ (s @ (s @ one))))))) | spl0_3),
% 1.59/1.38 inference(superposition,[status(thm)],[f95,f34])).
% 1.59/1.38 thf(f95,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ (s @ (s @ one))))))) | spl0_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.59/1.38 thf(f93,plain,(
% 1.59/1.38 ($true != (d @ (f @ one @ (s @ (s @ (s @ (s @ one))))))) | ($true != $true) | spl0_3),
% 1.59/1.38 inference(superposition,[status(thm)],[f86,f25])).
% 1.59/1.38 thf(f86,plain,(
% 1.59/1.38 ($true != (d @ (s @ (f @ one @ (s @ (s @ (s @ (s @ one)))))))) | spl0_3),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.59/1.38 thf(f91,plain,(
% 1.59/1.38 ~spl0_3 | spl0_4),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f80,f88,f84])).
% 1.59/1.38 thf(f80,plain,(
% 1.59/1.38 ($true = (d @ (f @ one @ (f @ one @ (s @ (s @ one)))))) | ($true != (d @ (s @ (f @ one @ (s @ (s @ (s @ (s @ one))))))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f34,f35])).
% 1.59/1.38 thf(f74,plain,(
% 1.59/1.38 spl0_1),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.59/1.38 thf(f73,plain,(
% 1.59/1.38 $false | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.59/1.38 thf(f72,plain,(
% 1.59/1.38 ($true = $false) | spl0_1),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f22,f68])).
% 1.59/1.38 thf(f68,plain,(
% 1.59/1.38 ((d @ one) = $false) | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.59/1.38 thf(f66,plain,(
% 1.59/1.38 ($true != $true) | ((d @ one) = $false) | spl0_1),
% 1.59/1.38 inference(fool_paramodulation,[status(thm)],[f64])).
% 1.59/1.38 thf(f64,plain,(
% 1.59/1.38 ((d @ one) != $true) | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.59/1.38 thf(f62,plain,(
% 1.59/1.38 ($true != $true) | ((d @ one) != $true) | spl0_1),
% 1.59/1.38 inference(superposition,[status(thm)],[f58,f25])).
% 1.59/1.38 thf(f58,plain,(
% 1.59/1.38 ($true != (d @ (s @ one))) | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.59/1.38 thf(f57,plain,(
% 1.59/1.38 ($true != (d @ (s @ one))) | ($true != $true) | spl0_1),
% 1.59/1.38 inference(superposition,[status(thm)],[f54,f25])).
% 1.59/1.38 thf(f54,plain,(
% 1.59/1.38 ($true != (d @ (s @ (s @ one)))) | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.59/1.38 thf(f52,plain,(
% 1.59/1.38 ($true != (d @ (s @ (s @ one)))) | ($true != $true) | spl0_1),
% 1.59/1.38 inference(superposition,[status(thm)],[f48,f25])).
% 1.59/1.38 thf(f48,plain,(
% 1.59/1.38 ($true != (d @ (s @ (s @ (s @ one))))) | spl0_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.59/1.38 thf(f47,plain,(
% 1.59/1.38 ($true != $true) | ($true != (d @ (s @ (s @ (s @ one))))) | spl0_1),
% 1.59/1.38 inference(superposition,[status(thm)],[f40,f25])).
% 1.59/1.38 thf(f40,plain,(
% 1.59/1.38 ($true != (d @ (s @ (s @ (s @ (s @ one)))))) | spl0_1),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.59/1.38 thf(f38,definition,(
% 1.59/1.38 spl0_1 <=> ($true = (d @ (s @ (s @ (s @ (s @ one))))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.59/1.38 thf(f22,plain,(
% 1.59/1.38 ((d @ one) = $true)),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f14])).
% 1.59/1.38 thf(f14,plain,(
% 1.59/1.38 ((d @ one) = $true)),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f13])).
% 1.59/1.38 thf(f13,plain,(
% 1.59/1.38 (d @ one)),
% 1.59/1.38 inference(rectify,[status(thm)],[f4])).
% 1.59/1.38 thf(f4,axiom,(
% 1.59/1.38 (d @ one)),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.JEQebMKw9K/DTF2THF_7457.p',ax4)).
% 1.59/1.38 thf(f45,plain,(
% 1.59/1.38 ~spl0_1 | spl0_2),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f36,f42,f38])).
% 1.59/1.38 thf(f36,plain,(
% 1.59/1.38 ($true = (d @ (f @ one @ (s @ (s @ one))))) | ($true != (d @ (s @ (s @ (s @ (s @ one))))))),
% 1.59/1.38 inference(superposition,[status(thm)],[f25,f35])).
% 1.59/1.38 % SZS output end Proof for DTF2THF_7457
% 1.59/1.38 % (7694)------------------------------
% 1.59/1.38 % (7694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (7694)Termination reason: Refutation
% 1.59/1.38
% 1.59/1.38 % (7694)Memory used [KB]: 5756
% 1.59/1.38 % (7694)Time elapsed: 0.027 s
% 1.59/1.38 % (7694)Instructions burned: 71 (million)
% 1.59/1.38 % (7694)------------------------------
% 1.59/1.38 % (7694)------------------------------
% 1.59/1.38 % (7667)Success in time 0.105 s
%------------------------------------------------------------------------------