%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM291+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:33:08 AM UTC 2026
% Result : Theorem 1.21s 0.58s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 149 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 859 ( 270 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1588 ( 369 ~; 231 |; 21 &; 949 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 273 ( 270 usr; 258 con; 0-4 aty)
% Number of variables : 331 ( 0 ^; 331 !; 0 ?; 331 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n10,type,
n10: $i ).
thf(tp_n100,type,
n100: $i ).
thf(tp_n101,type,
n101: $i ).
thf(tp_n102,type,
n102: $i ).
thf(tp_n103,type,
n103: $i ).
thf(tp_n104,type,
n104: $i ).
thf(tp_n105,type,
n105: $i ).
thf(tp_n106,type,
n106: $i ).
thf(tp_n107,type,
n107: $i ).
thf(tp_n108,type,
n108: $i ).
thf(tp_n109,type,
n109: $i ).
thf(tp_n11,type,
n11: $i ).
thf(tp_n110,type,
n110: $i ).
thf(tp_n111,type,
n111: $i ).
thf(tp_n112,type,
n112: $i ).
thf(tp_n113,type,
n113: $i ).
thf(tp_n114,type,
n114: $i ).
thf(tp_n115,type,
n115: $i ).
thf(tp_n116,type,
n116: $i ).
thf(tp_n117,type,
n117: $i ).
thf(tp_n118,type,
n118: $i ).
thf(tp_n119,type,
n119: $i ).
thf(tp_n12,type,
n12: $i ).
thf(tp_n120,type,
n120: $i ).
thf(tp_n121,type,
n121: $i ).
thf(tp_n122,type,
n122: $i ).
thf(tp_n123,type,
n123: $i ).
thf(tp_n124,type,
n124: $i ).
thf(tp_n125,type,
n125: $i ).
thf(tp_n126,type,
n126: $i ).
thf(tp_n127,type,
n127: $i ).
thf(tp_n13,type,
n13: $i ).
thf(tp_n14,type,
n14: $i ).
thf(tp_n15,type,
n15: $i ).
thf(tp_n16,type,
n16: $i ).
thf(tp_n17,type,
n17: $i ).
thf(tp_n18,type,
n18: $i ).
thf(tp_n19,type,
n19: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n20,type,
n20: $i ).
thf(tp_n21,type,
n21: $i ).
thf(tp_n22,type,
n22: $i ).
thf(tp_n23,type,
n23: $i ).
thf(tp_n24,type,
n24: $i ).
thf(tp_n25,type,
n25: $i ).
thf(tp_n26,type,
n26: $i ).
thf(tp_n27,type,
n27: $i ).
thf(tp_n28,type,
n28: $i ).
thf(tp_n29,type,
n29: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_n30,type,
n30: $i ).
thf(tp_n31,type,
n31: $i ).
thf(tp_n32,type,
n32: $i ).
thf(tp_n33,type,
n33: $i ).
thf(tp_n34,type,
n34: $i ).
thf(tp_n35,type,
n35: $i ).
thf(tp_n36,type,
n36: $i ).
thf(tp_n37,type,
n37: $i ).
thf(tp_n38,type,
n38: $i ).
thf(tp_n39,type,
n39: $i ).
thf(tp_n4,type,
n4: $i ).
thf(tp_n40,type,
n40: $i ).
thf(tp_n41,type,
n41: $i ).
thf(tp_n42,type,
n42: $i ).
thf(tp_n43,type,
n43: $i ).
thf(tp_n44,type,
n44: $i ).
thf(tp_n45,type,
n45: $i ).
thf(tp_n46,type,
n46: $i ).
thf(tp_n47,type,
n47: $i ).
thf(tp_n48,type,
n48: $i ).
thf(tp_n49,type,
n49: $i ).
thf(tp_n5,type,
n5: $i ).
thf(tp_n50,type,
n50: $i ).
thf(tp_n51,type,
n51: $i ).
thf(tp_n52,type,
n52: $i ).
thf(tp_n53,type,
n53: $i ).
thf(tp_n54,type,
n54: $i ).
thf(tp_n55,type,
n55: $i ).
thf(tp_n56,type,
n56: $i ).
thf(tp_n57,type,
n57: $i ).
thf(tp_n58,type,
n58: $i ).
thf(tp_n59,type,
n59: $i ).
thf(tp_n6,type,
n6: $i ).
thf(tp_n60,type,
n60: $i ).
thf(tp_n61,type,
n61: $i ).
thf(tp_n62,type,
n62: $i ).
thf(tp_n63,type,
n63: $i ).
thf(tp_n64,type,
n64: $i ).
thf(tp_n65,type,
n65: $i ).
thf(tp_n66,type,
n66: $i ).
thf(tp_n67,type,
n67: $i ).
thf(tp_n68,type,
n68: $i ).
thf(tp_n69,type,
n69: $i ).
thf(tp_n7,type,
n7: $i ).
thf(tp_n70,type,
n70: $i ).
thf(tp_n71,type,
n71: $i ).
thf(tp_n72,type,
n72: $i ).
thf(tp_n73,type,
n73: $i ).
thf(tp_n74,type,
n74: $i ).
thf(tp_n75,type,
n75: $i ).
thf(tp_n76,type,
n76: $i ).
thf(tp_n77,type,
n77: $i ).
thf(tp_n78,type,
n78: $i ).
thf(tp_n79,type,
n79: $i ).
thf(tp_n8,type,
n8: $i ).
thf(tp_n80,type,
n80: $i ).
thf(tp_n81,type,
n81: $i ).
thf(tp_n82,type,
n82: $i ).
thf(tp_n83,type,
n83: $i ).
thf(tp_n84,type,
n84: $i ).
thf(tp_n85,type,
n85: $i ).
thf(tp_n86,type,
n86: $i ).
thf(tp_n87,type,
n87: $i ).
thf(tp_n88,type,
n88: $i ).
thf(tp_n89,type,
n89: $i ).
thf(tp_n9,type,
n9: $i ).
thf(tp_n90,type,
n90: $i ).
thf(tp_n91,type,
n91: $i ).
thf(tp_n92,type,
n92: $i ).
thf(tp_n93,type,
n93: $i ).
thf(tp_n94,type,
n94: $i ).
thf(tp_n95,type,
n95: $i ).
thf(tp_n96,type,
n96: $i ).
thf(tp_n97,type,
n97: $i ).
thf(tp_n98,type,
n98: $i ).
thf(tp_n99,type,
n99: $i ).
thf(tp_nn1,type,
nn1: $i ).
thf(tp_nn10,type,
nn10: $i ).
thf(tp_nn100,type,
nn100: $i ).
thf(tp_nn101,type,
nn101: $i ).
thf(tp_nn102,type,
nn102: $i ).
thf(tp_nn103,type,
nn103: $i ).
thf(tp_nn104,type,
nn104: $i ).
thf(tp_nn105,type,
nn105: $i ).
thf(tp_nn106,type,
nn106: $i ).
thf(tp_nn107,type,
nn107: $i ).
thf(tp_nn108,type,
nn108: $i ).
thf(tp_nn109,type,
nn109: $i ).
thf(tp_nn11,type,
nn11: $i ).
thf(tp_nn110,type,
nn110: $i ).
thf(tp_nn111,type,
nn111: $i ).
thf(tp_nn112,type,
nn112: $i ).
thf(tp_nn113,type,
nn113: $i ).
thf(tp_nn114,type,
nn114: $i ).
thf(tp_nn115,type,
nn115: $i ).
thf(tp_nn116,type,
nn116: $i ).
thf(tp_nn117,type,
nn117: $i ).
thf(tp_nn118,type,
nn118: $i ).
thf(tp_nn119,type,
nn119: $i ).
thf(tp_nn12,type,
nn12: $i ).
thf(tp_nn120,type,
nn120: $i ).
thf(tp_nn121,type,
nn121: $i ).
thf(tp_nn122,type,
nn122: $i ).
thf(tp_nn123,type,
nn123: $i ).
thf(tp_nn124,type,
nn124: $i ).
thf(tp_nn125,type,
nn125: $i ).
thf(tp_nn126,type,
nn126: $i ).
thf(tp_nn127,type,
nn127: $i ).
thf(tp_nn128,type,
nn128: $i ).
thf(tp_nn13,type,
nn13: $i ).
thf(tp_nn14,type,
nn14: $i ).
thf(tp_nn15,type,
nn15: $i ).
thf(tp_nn16,type,
nn16: $i ).
thf(tp_nn17,type,
nn17: $i ).
thf(tp_nn18,type,
nn18: $i ).
thf(tp_nn19,type,
nn19: $i ).
thf(tp_nn2,type,
nn2: $i ).
thf(tp_nn20,type,
nn20: $i ).
thf(tp_nn21,type,
nn21: $i ).
thf(tp_nn22,type,
nn22: $i ).
thf(tp_nn23,type,
nn23: $i ).
thf(tp_nn24,type,
nn24: $i ).
thf(tp_nn25,type,
nn25: $i ).
thf(tp_nn26,type,
nn26: $i ).
thf(tp_nn27,type,
nn27: $i ).
thf(tp_nn28,type,
nn28: $i ).
thf(tp_nn29,type,
nn29: $i ).
thf(tp_nn3,type,
nn3: $i ).
thf(tp_nn30,type,
nn30: $i ).
thf(tp_nn31,type,
nn31: $i ).
thf(tp_nn32,type,
nn32: $i ).
thf(tp_nn33,type,
nn33: $i ).
thf(tp_nn34,type,
nn34: $i ).
thf(tp_nn35,type,
nn35: $i ).
thf(tp_nn36,type,
nn36: $i ).
thf(tp_nn37,type,
nn37: $i ).
thf(tp_nn38,type,
nn38: $i ).
thf(tp_nn39,type,
nn39: $i ).
thf(tp_nn4,type,
nn4: $i ).
thf(tp_nn40,type,
nn40: $i ).
thf(tp_nn41,type,
nn41: $i ).
thf(tp_nn42,type,
nn42: $i ).
thf(tp_nn43,type,
nn43: $i ).
thf(tp_nn44,type,
nn44: $i ).
thf(tp_nn45,type,
nn45: $i ).
thf(tp_nn46,type,
nn46: $i ).
thf(tp_nn47,type,
nn47: $i ).
thf(tp_nn48,type,
nn48: $i ).
thf(tp_nn49,type,
nn49: $i ).
thf(tp_nn5,type,
nn5: $i ).
thf(tp_nn50,type,
nn50: $i ).
thf(tp_nn51,type,
nn51: $i ).
thf(tp_nn52,type,
nn52: $i ).
thf(tp_nn53,type,
nn53: $i ).
thf(tp_nn54,type,
nn54: $i ).
thf(tp_nn55,type,
nn55: $i ).
thf(tp_nn56,type,
nn56: $i ).
thf(tp_nn57,type,
nn57: $i ).
thf(tp_nn58,type,
nn58: $i ).
thf(tp_nn59,type,
nn59: $i ).
thf(tp_nn6,type,
nn6: $i ).
thf(tp_nn60,type,
nn60: $i ).
thf(tp_nn61,type,
nn61: $i ).
thf(tp_nn62,type,
nn62: $i ).
thf(tp_nn63,type,
nn63: $i ).
thf(tp_nn64,type,
nn64: $i ).
thf(tp_nn65,type,
nn65: $i ).
thf(tp_nn66,type,
nn66: $i ).
thf(tp_nn67,type,
nn67: $i ).
thf(tp_nn68,type,
nn68: $i ).
thf(tp_nn69,type,
nn69: $i ).
thf(tp_nn7,type,
nn7: $i ).
thf(tp_nn70,type,
nn70: $i ).
thf(tp_nn71,type,
nn71: $i ).
thf(tp_nn72,type,
nn72: $i ).
thf(tp_nn73,type,
nn73: $i ).
thf(tp_nn74,type,
nn74: $i ).
thf(tp_nn75,type,
nn75: $i ).
thf(tp_nn76,type,
nn76: $i ).
thf(tp_nn77,type,
nn77: $i ).
thf(tp_nn78,type,
nn78: $i ).
thf(tp_nn79,type,
nn79: $i ).
thf(tp_nn8,type,
nn8: $i ).
thf(tp_nn80,type,
nn80: $i ).
thf(tp_nn81,type,
nn81: $i ).
thf(tp_nn82,type,
nn82: $i ).
thf(tp_nn83,type,
nn83: $i ).
thf(tp_nn84,type,
nn84: $i ).
thf(tp_nn85,type,
nn85: $i ).
thf(tp_nn86,type,
nn86: $i ).
thf(tp_nn87,type,
nn87: $i ).
thf(tp_nn88,type,
nn88: $i ).
thf(tp_nn89,type,
nn89: $i ).
thf(tp_nn9,type,
nn9: $i ).
thf(tp_nn90,type,
nn90: $i ).
thf(tp_nn91,type,
nn91: $i ).
thf(tp_nn92,type,
nn92: $i ).
thf(tp_nn93,type,
nn93: $i ).
thf(tp_nn94,type,
nn94: $i ).
thf(tp_nn95,type,
nn95: $i ).
thf(tp_nn96,type,
nn96: $i ).
thf(tp_nn97,type,
nn97: $i ).
thf(tp_nn98,type,
nn98: $i ).
thf(tp_nn99,type,
nn99: $i ).
thf(tp_rdn,type,
rdn: $i > $i > $i ).
thf(tp_rdn_add_with_carry,type,
rdn_add_with_carry: $i > $i > $i > $i > $o ).
thf(tp_rdn_digit_add,type,
rdn_digit_add: $i > $i > $i > $i > $o ).
thf(tp_rdn_neg,type,
rdn_neg: $i > $i ).
thf(tp_rdn_non_zero,type,
rdn_non_zero: $i > $o ).
thf(tp_rdn_non_zero_digit,type,
rdn_non_zero_digit: $i > $o ).
thf(tp_rdn_pos,type,
rdn_pos: $i > $i ).
thf(tp_rdn_positive_less,type,
rdn_positive_less: $i > $i > $o ).
thf(tp_rdn_translate,type,
rdn_translate: $i > $i > $o ).
thf(tp_rdnn,type,
rdnn: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(70,axiom,
rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n3_n0_n3_n0) ).
thf(80,axiom,
rdn_digit_add @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n2_n0_n2_n0) ).
thf(97,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n0_n3_n3_n0) ).
thf(98,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n0_n2_n2_n0) ).
thf(116,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( sum @ X @ n1 @ Y )
& ( less @ Z @ Y ) )
=> ( less_or_equal @ Z @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_successor) ).
thf(117,axiom,
! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal) ).
thf(118,axiom,
! [X: $i,Y: $i] :
( ( less @ X @ Y )
<=> ( ~ ( less @ Y @ X )
& ( Y != X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
thf(119,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_neg @ RDN_Y ) )
& ( rdn_positive_less @ RDN_Y @ RDN_X ) )
=> ( less @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_neg_neg) ).
thf(120,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) ) )
=> ( less @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
thf(121,axiom,
! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( rdn_positive_less @ RDN_X @ RDN_Y ) )
=> ( less @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
thf(133,axiom,
rdn_positive_less @ ( rdnn @ n3 ) @ ( rdnn @ n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less34) ).
thf(134,axiom,
rdn_positive_less @ ( rdnn @ n2 ) @ ( rdnn @ n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less23) ).
thf(135,axiom,
rdn_positive_less @ ( rdnn @ n1 ) @ ( rdnn @ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less12) ).
thf(143,axiom,
rdn_non_zero_digit @ ( rdnn @ n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit3) ).
thf(144,axiom,
rdn_non_zero_digit @ ( rdnn @ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit2) ).
thf(398,axiom,
rdn_translate @ n3 @ ( rdn_pos @ ( rdnn @ n3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn3) ).
thf(399,axiom,
rdn_translate @ n2 @ ( rdn_pos @ ( rdnn @ n2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn2) ).
thf(402,conjecture,
~ ( less @ n3 @ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n3_not_less_n2) ).
thf(403,negated_conjecture,
( ( ~ ( less @ n3 @ n2 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[402]) ).
thf(404,plain,
( ( ~ ( less @ n3 @ n2 ) )
= $false ),
inference(unfold_def,[status(thm)],[403]) ).
thf(405,plain,
( ( rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(406,plain,
( ( rdn_digit_add @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(407,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(408,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(409,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( sum @ X @ n1 @ Y )
& ( less @ Z @ Y ) )
=> ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(410,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(411,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
<=> ( ~ ( less @ Y @ X )
& ( Y != X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(412,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_neg @ RDN_Y ) )
& ( rdn_positive_less @ RDN_Y @ RDN_X ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(413,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(414,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( rdn_positive_less @ RDN_X @ RDN_Y ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(415,plain,
( ( rdn_positive_less @ ( rdnn @ n3 ) @ ( rdnn @ n4 ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(416,plain,
( ( rdn_positive_less @ ( rdnn @ n2 ) @ ( rdnn @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(417,plain,
( ( rdn_positive_less @ ( rdnn @ n1 ) @ ( rdnn @ n2 ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(418,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(419,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n2 ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(420,plain,
( ( rdn_translate @ n3 @ ( rdn_pos @ ( rdnn @ n3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(421,plain,
( ( rdn_translate @ n2 @ ( rdn_pos @ ( rdnn @ n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(422,plain,
( ( less @ n3 @ n2 )
= $true ),
inference(polarity_switch,[status(thm)],[404]) ).
thf(423,plain,
( ( rdn_translate @ n2 @ ( rdn_pos @ ( rdnn @ n2 ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(424,plain,
( ( rdn_translate @ n3 @ ( rdn_pos @ ( rdnn @ n3 ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(425,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n2 ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(426,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n3 ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(427,plain,
( ( rdn_positive_less @ ( rdnn @ n1 ) @ ( rdnn @ n2 ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(428,plain,
( ( rdn_positive_less @ ( rdnn @ n2 ) @ ( rdnn @ n3 ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(429,plain,
( ( rdn_positive_less @ ( rdnn @ n3 ) @ ( rdnn @ n4 ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(430,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( rdn_positive_less @ RDN_X @ RDN_Y ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(431,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(432,plain,
( ( ! [X: $i,Y: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_neg @ RDN_Y ) )
& ( rdn_positive_less @ RDN_Y @ RDN_X ) )
=> ( less @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(433,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
<=> ( ~ ( less @ Y @ X )
& ( Y != X ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(434,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(435,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( sum @ X @ n1 @ Y )
& ( less @ Z @ Y ) )
=> ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(436,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(437,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(438,plain,
( ( rdn_digit_add @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(439,plain,
( ( rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(440,plain,
( ( less @ n3 @ n2 )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(441,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( sum @ SX0 @ n1 @ SX1 )
| ~ ( less @ SX2 @ SX1 ) )
| ( less_or_equal @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( rdn_translate @ SX0 @ ( rdn_neg @ SX2 ) )
| ~ ( rdn_translate @ SX1 @ ( rdn_pos @ SX3 ) ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(443,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SX0 @ ( rdn_neg @ SX2 ) )
| ~ ( rdn_translate @ SX1 @ ( rdn_neg @ SX3 ) ) )
| ~ ( rdn_positive_less @ SX3 @ SX2 ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(444,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( less_or_equal @ SX0 @ SX1 )
| ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ~ ( ~ ( ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( less_or_equal @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SX0 @ ( rdn_pos @ SX2 ) )
| ~ ( rdn_translate @ SX1 @ ( rdn_pos @ SX3 ) ) )
| ~ ( rdn_positive_less @ SX2 @ SX3 ) )
| ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( less @ SX0 @ SX1 )
| ~ ( ~ ~ ( less @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( less @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) ) )
| ( less @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(447,plain,
! [SV1: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ~ ( ~ ( sum @ SV1 @ n1 @ SY19 )
| ~ ( less @ SY20 @ SY19 ) )
| ( less_or_equal @ SY20 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(448,plain,
! [SV2: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ~ ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SY22 ) )
| ~ ( rdn_translate @ SY21 @ ( rdn_pos @ SY23 ) ) )
| ( less @ SV2 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(449,plain,
! [SV3: $i] :
( ( ! [SY24: $i,SY25: $i,SY26: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SY25 ) )
| ~ ( rdn_translate @ SY24 @ ( rdn_neg @ SY26 ) ) )
| ~ ( rdn_positive_less @ SY26 @ SY25 ) )
| ( less @ SV3 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(450,plain,
! [SV4: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( less_or_equal @ SV4 @ SY27 )
| ( less @ SV4 @ SY27 )
| ( SV4 = SY27 ) )
| ~ ( ~ ( ( less @ SV4 @ SY27 )
| ( SV4 = SY27 ) )
| ( less_or_equal @ SV4 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(451,plain,
! [SV5: $i] :
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SY29 ) )
| ~ ( rdn_translate @ SY28 @ ( rdn_pos @ SY30 ) ) )
| ~ ( rdn_positive_less @ SY29 @ SY30 ) )
| ( less @ SV5 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(452,plain,
! [SV6: $i] :
( ( ! [SY31: $i] :
~ ( ~ ( ~ ( less @ SV6 @ SY31 )
| ~ ( ~ ~ ( less @ SY31 @ SV6 )
| ~ ( ( SY31 != SV6 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( less @ SY31 @ SV6 )
| ~ ( ( SY31 != SV6 ) ) )
| ( less @ SV6 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(453,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY32: $i] :
( ~ ~ ( ~ ( sum @ SV1 @ n1 @ SV7 )
| ~ ( less @ SY32 @ SV7 ) )
| ( less_or_equal @ SY32 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(454,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SY33 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SY34 ) ) )
| ( less @ SV2 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(455,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SY35 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SY36 ) ) )
| ~ ( rdn_positive_less @ SY36 @ SY35 ) )
| ( less @ SV3 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(456,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( less_or_equal @ SV4 @ SV10 )
| ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ~ ( ~ ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ( less_or_equal @ SV4 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SY37 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SY38 ) ) )
| ~ ( rdn_positive_less @ SY37 @ SY38 ) )
| ( less @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( less @ SV6 @ SV12 )
| ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
| ( less @ SV6 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(459,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ~ ~ ( ~ ( sum @ SV1 @ n1 @ SV7 )
| ~ ( less @ SV13 @ SV7 ) )
| ( less_or_equal @ SV13 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(460,plain,
! [SV8: $i,SV14: $i,SV2: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SY39 ) ) )
| ( less @ SV2 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(461,plain,
! [SV9: $i,SV15: $i,SV3: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SY40 ) ) )
| ~ ( rdn_positive_less @ SY40 @ SV15 ) )
| ( less @ SV3 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(462,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( less_or_equal @ SV4 @ SV10 )
| ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ~ ( ~ ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ( less_or_equal @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(463,plain,
! [SV11: $i,SV16: $i,SV5: $i] :
( ( ! [SY41: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SY41 ) ) )
| ~ ( rdn_positive_less @ SV16 @ SY41 ) )
| ( less @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(464,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( less @ SV6 @ SV12 )
| ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
| ( less @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(465,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( sum @ SV1 @ n1 @ SV7 )
| ~ ( less @ SV13 @ SV7 ) ) )
= $true )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(466,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ~ ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) )
| ( less @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(467,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
| ~ ( rdn_positive_less @ SV18 @ SV15 ) )
| ( less @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(468,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( less_or_equal @ SV4 @ SV10 )
| ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(469,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ( less_or_equal @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(470,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
| ~ ( rdn_positive_less @ SV16 @ SV19 ) )
| ( less @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(471,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( less @ SV6 @ SV12 )
| ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(472,plain,
! [SV6: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
| ( less @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(473,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ( sum @ SV1 @ n1 @ SV7 )
| ~ ( less @ SV13 @ SV7 ) ) )
= $false )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(474,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) ) )
= $true )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(475,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
| ~ ( rdn_positive_less @ SV18 @ SV15 ) ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(476,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( less_or_equal @ SV4 @ SV10 )
| ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(477,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
| ( less_or_equal @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(478,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
| ~ ( rdn_positive_less @ SV16 @ SV19 ) ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(479,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( less @ SV6 @ SV12 )
| ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(480,plain,
! [SV6: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
| ( less @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(481,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ n1 @ SV7 )
| ~ ( less @ SV13 @ SV7 ) )
= $true )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(482,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) ) )
= $false )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(483,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
| ~ ( rdn_positive_less @ SV18 @ SV15 ) ) )
= $false )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(484,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( less_or_equal @ SV4 @ SV10 ) )
= $true )
| ( ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(485,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) ) )
= $true )
| ( ( less_or_equal @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(486,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
| ~ ( rdn_positive_less @ SV16 @ SV19 ) ) )
= $false )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(487,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( less @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(488,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(489,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ n1 @ SV7 ) )
= $true )
| ( ( ~ ( less @ SV13 @ SV7 ) )
= $true )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(490,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
| ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) )
= $true )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(491,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
| ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(492,plain,
! [SV10: $i,SV4: $i] :
( ( ( less_or_equal @ SV4 @ SV10 )
= $false )
| ( ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(493,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( less @ SV4 @ SV10 )
| ( SV4 = SV10 ) )
= $false )
| ( ( less_or_equal @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(494,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
| ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(495,plain,
! [SV12: $i,SV6: $i] :
( ( ( less @ SV6 @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(496,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) ) )
= $false )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(497,plain,
! [SV13: $i,SV7: $i,SV1: $i] :
( ( ( sum @ SV1 @ n1 @ SV7 )
= $false )
| ( ( ~ ( less @ SV13 @ SV7 ) )
= $true )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(498,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) ) )
= $true )
| ( ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) )
= $true )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(499,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(500,plain,
! [SV10: $i,SV4: $i] :
( ( ( less @ SV4 @ SV10 )
= $true )
| ( ( SV4 = SV10 )
= $true )
| ( ( less_or_equal @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(501,plain,
! [SV10: $i,SV4: $i] :
( ( ( less @ SV4 @ SV10 )
= $false )
| ( ( less_or_equal @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(502,plain,
! [SV10: $i,SV4: $i] :
( ( ( SV4 = SV10 )
= $false )
| ( ( less_or_equal @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(503,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(504,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
= $false )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(505,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ~ ( less @ SV12 @ SV6 )
| ~ ( ( SV12 != SV6 ) ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(506,plain,
! [SV1: $i,SV7: $i,SV13: $i] :
( ( ( less @ SV13 @ SV7 )
= $false )
| ( ( sum @ SV1 @ n1 @ SV7 )
= $false )
| ( ( less_or_equal @ SV13 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(507,plain,
! [SV17: $i,SV8: $i,SV14: $i,SV2: $i] :
( ( ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
= $false )
| ( ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) ) )
= $true )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(508,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) ) )
= $false )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(509,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) ) )
= $false )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(510,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ~ ( less @ SV12 @ SV6 ) )
= $false )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(511,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV6 ) ) )
= $false )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(512,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ~ ( less @ SV12 @ SV6 ) )
= $true )
| ( ( ~ ( ( SV12 != SV6 ) ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(513,plain,
! [SV14: $i,SV2: $i,SV17: $i,SV8: $i] :
( ( ( rdn_translate @ SV8 @ ( rdn_pos @ SV17 ) )
= $false )
| ( ( rdn_translate @ SV2 @ ( rdn_neg @ SV14 ) )
= $false )
| ( ( less @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(514,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
| ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(515,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(516,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( less @ SV12 @ SV6 ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(517,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12 != SV6 )
= $true )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(518,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( less @ SV12 @ SV6 ) )
= $false )
| ( ( ~ ( ( SV12 != SV6 ) ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(519,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) ) )
= $true )
| ( ( ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(520,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) ) )
= $true )
| ( ( ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(521,plain,
! [SV6: $i,SV12: $i] :
( ( ( less @ SV12 @ SV6 )
= $false )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(522,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12 = SV6 )
= $false )
| ( ( less @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(523,plain,
! [SV6: $i,SV12: $i] :
( ( ( less @ SV12 @ SV6 )
= $true )
| ( ( ~ ( ( SV12 != SV6 ) ) )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(524,plain,
! [SV18: $i,SV9: $i,SV15: $i,SV3: $i] :
( ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
= $false )
| ( ( ~ ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(525,plain,
! [SV19: $i,SV11: $i,SV16: $i,SV5: $i] :
( ( ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
= $false )
| ( ( ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) ) )
= $true )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(526,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12 != SV6 )
= $false )
| ( ( less @ SV12 @ SV6 )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(527,plain,
! [SV15: $i,SV3: $i,SV18: $i,SV9: $i] :
( ( ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) )
= $false )
| ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
= $false )
| ( ( ~ ( rdn_positive_less @ SV18 @ SV15 ) )
= $true )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(528,plain,
! [SV16: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) )
= $false )
| ( ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
= $false )
| ( ( ~ ( rdn_positive_less @ SV16 @ SV19 ) )
= $true )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(529,plain,
! [SV6: $i,SV12: $i] :
( ( ( SV12 = SV6 )
= $true )
| ( ( less @ SV12 @ SV6 )
= $true )
| ( ( less @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(530,plain,
! [SV9: $i,SV3: $i,SV15: $i,SV18: $i] :
( ( ( rdn_positive_less @ SV18 @ SV15 )
= $false )
| ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV15 ) )
= $false )
| ( ( rdn_translate @ SV9 @ ( rdn_neg @ SV18 ) )
= $false )
| ( ( less @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(531,plain,
! [SV11: $i,SV5: $i,SV19: $i,SV16: $i] :
( ( ( rdn_positive_less @ SV16 @ SV19 )
= $false )
| ( ( rdn_translate @ SV5 @ ( rdn_pos @ SV16 ) )
= $false )
| ( ( rdn_translate @ SV11 @ ( rdn_pos @ SV19 ) )
= $false )
| ( ( less @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(532,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[423,531,530,529,522,521,513,506,502,501,500,440,439,438,437,436,429,428,427,426,425,424]) ).
thf(533,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM291+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.22 % Computer : n016.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Oct 6 13:13:14 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/0.58 .
% 1.21/0.58
% 1.21/0.58 No.of.Axioms: 17
% 1.21/0.58
% 1.21/0.58 Length.of.Defs: 0
% 1.21/0.58
% 1.21/0.58 Contains.Choice.Funs: false
% 1.21/0.58 .....
% 1.21/0.58
% 1.21/0.58 ********************************
% 1.21/0.58 * All subproblems solved! *
% 1.21/0.58 ********************************
% 1.21/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:532,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.21/0.58
% 1.21/0.58 %**** Beginning of derivation protocol ****
% 1.21/0.58 % SZS output start CNFRefutation
% See solution above
% 1.21/0.58
% 1.21/0.58 %**** End of derivation protocol ****
% 1.21/0.58 %**** no. of clauses in derivation: 149 ****
% 1.21/0.58 %**** clause counter: 532 ****
% 1.21/0.58
% 1.21/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:532,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------