%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM318+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 10:33:13 AM UTC 2026
% Result : Theorem 1.20s 0.43s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of formulae : 207 ( 149 unt; 0 typ; 0 def)
% Number of atoms : 954 ( 291 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2299 ( 300 ~; 201 |; 24 &;1750 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 464 ( 0 ^; 464 !; 0 ?; 464 :)
% 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(10,axiom,
rdn_digit_add @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n9_n0_n9_n0) ).
thf(20,axiom,
rdn_digit_add @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n8_n0_n8_n0) ).
thf(30,axiom,
rdn_digit_add @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n7_n0_n7_n0) ).
thf(40,axiom,
rdn_digit_add @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n6_n0_n6_n0) ).
thf(45,axiom,
rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n5_n0_n1) ).
thf(50,axiom,
rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).
thf(60,axiom,
rdn_digit_add @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n4_n0_n4_n0) ).
thf(70,axiom,
rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n0_n2_n0) ).
thf(90,axiom,
rdn_digit_add @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n1_n0_n1_n0) ).
thf(91,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n9_n9_n0) ).
thf(92,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n8_n8_n0) ).
thf(93,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n7_n7_n0) ).
thf(94,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n6_n6_n0) ).
thf(95,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n5_n5_n0) ).
thf(96,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n4_n4_n0) ).
thf(97,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n2_n2_n0) ).
thf(99,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n1_n1_n0) ).
thf(100,axiom,
rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n0_n0_n0) ).
thf(105,axiom,
! [C: $i,D1: $i,D2: $i,RD: $i,ID: $i] :
( ( ( rdn_digit_add @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ ID ) @ ( rdnn @ n0 ) )
& ( rdn_digit_add @ ( rdnn @ ID ) @ ( rdnn @ C ) @ ( rdnn @ RD ) @ ( rdnn @ n0 ) ) )
=> ( rdn_add_with_carry @ ( rdnn @ C ) @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ RD ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
thf(106,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( sum @ Y @ Z @ X )
<=> ( difference @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus_entry_point) ).
thf(107,axiom,
! [X: $i,Y1: $i,Y2: $i,Z: $i] :
( ( ( sum @ X @ Y1 @ Z )
& ( sum @ X @ Y2 @ Z ) )
=> ( Y1 = Y2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_RHS) ).
thf(108,axiom,
! [X1: $i,X2: $i,Y: $i,Z: $i] :
( ( ( sum @ X1 @ Y @ Z )
& ( sum @ X2 @ Y @ Z ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_LHS) ).
thf(109,axiom,
! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ( ( sum @ X @ Y @ Z1 )
& ( sum @ X @ Y @ Z2 ) )
=> ( Z1 = Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_sum) ).
thf(110,axiom,
! [X: $i,Y: $i,Z: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( sum @ Y @ X @ Z ) )
=> ( sum @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_neg_pos) ).
thf(111,axiom,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ( ( rdn_translate @ POS_X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ NEG_X @ ( rdn_neg @ RDN_X ) ) )
=> ( sum @ POS_X @ NEG_X @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_posx_negx) ).
thf(116,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( sum @ X @ n1 @ Y )
& ( less @ Z @ Y ) )
=> ( less_or_equal @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_successor) ).
thf(131,axiom,
rdn_positive_less @ ( rdnn @ n5 ) @ ( rdnn @ n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less56) ).
thf(132,axiom,
rdn_positive_less @ ( rdnn @ n4 ) @ ( rdnn @ n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less45) ).
thf(136,axiom,
rdn_positive_less @ ( rdnn @ n0 ) @ ( rdnn @ n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less01) ).
thf(141,axiom,
rdn_non_zero_digit @ ( rdnn @ n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit5) ).
thf(269,axiom,
rdn_translate @ nn5 @ ( rdn_neg @ ( rdnn @ n5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn5) ).
thf(396,axiom,
rdn_translate @ n5 @ ( rdn_pos @ ( rdnn @ n5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).
thf(401,axiom,
rdn_translate @ n0 @ ( rdn_pos @ ( rdnn @ n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn0) ).
thf(402,conjecture,
sum @ n5 @ nn5 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn5_n0) ).
thf(403,negated_conjecture,
( ( sum @ n5 @ nn5 @ n0 )
= $false ),
inference(negate_conjecture,[status(cth)],[402]) ).
thf(404,plain,
( ( sum @ n5 @ nn5 @ n0 )
= $false ),
inference(unfold_def,[status(thm)],[403]) ).
thf(405,plain,
( ( rdn_digit_add @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(406,plain,
( ( rdn_digit_add @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(407,plain,
( ( rdn_digit_add @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(408,plain,
( ( rdn_digit_add @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(409,plain,
( ( rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(410,plain,
( ( rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(411,plain,
( ( rdn_digit_add @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(412,plain,
( ( rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(413,plain,
( ( rdn_digit_add @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(414,plain,
( ( rdn_digit_add @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(415,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(416,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(417,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(418,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(419,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(420,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(421,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(422,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(423,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(424,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(425,plain,
( ( ! [C: $i,D1: $i,D2: $i,RD: $i,ID: $i] :
( ( ( rdn_digit_add @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ ID ) @ ( rdnn @ n0 ) )
& ( rdn_digit_add @ ( rdnn @ ID ) @ ( rdnn @ C ) @ ( rdnn @ RD ) @ ( rdnn @ n0 ) ) )
=> ( rdn_add_with_carry @ ( rdnn @ C ) @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ RD ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(426,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( sum @ Y @ Z @ X )
<=> ( difference @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(427,plain,
( ( ! [X: $i,Y1: $i,Y2: $i,Z: $i] :
( ( ( sum @ X @ Y1 @ Z )
& ( sum @ X @ Y2 @ Z ) )
=> ( Y1 = Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(428,plain,
( ( ! [X1: $i,X2: $i,Y: $i,Z: $i] :
( ( ( sum @ X1 @ Y @ Z )
& ( sum @ X2 @ Y @ Z ) )
=> ( X1 = X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(429,plain,
( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ( ( sum @ X @ Y @ Z1 )
& ( sum @ X @ Y @ Z2 ) )
=> ( Z1 = Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(430,plain,
( ( ! [X: $i,Y: $i,Z: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( sum @ Y @ X @ Z ) )
=> ( sum @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(431,plain,
( ( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ( ( rdn_translate @ POS_X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ NEG_X @ ( rdn_neg @ RDN_X ) ) )
=> ( sum @ POS_X @ NEG_X @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(432,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(433,plain,
( ( rdn_positive_less @ ( rdnn @ n5 ) @ ( rdnn @ n6 ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(434,plain,
( ( rdn_positive_less @ ( rdnn @ n4 ) @ ( rdnn @ n5 ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(435,plain,
( ( rdn_positive_less @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(436,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n5 ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(437,plain,
( ( rdn_translate @ nn5 @ ( rdn_neg @ ( rdnn @ n5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(438,plain,
( ( rdn_translate @ n5 @ ( rdn_pos @ ( rdnn @ n5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(439,plain,
( ( rdn_translate @ n0 @ ( rdn_pos @ ( rdnn @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(440,plain,
( ( ~ ( sum @ n5 @ nn5 @ n0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[404]) ).
thf(441,plain,
( ( rdn_translate @ n0 @ ( rdn_pos @ ( rdnn @ n0 ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(442,plain,
( ( rdn_translate @ n5 @ ( rdn_pos @ ( rdnn @ n5 ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(443,plain,
( ( rdn_translate @ nn5 @ ( rdn_neg @ ( rdnn @ n5 ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(444,plain,
( ( rdn_non_zero_digit @ ( rdnn @ n5 ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(445,plain,
( ( rdn_positive_less @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(446,plain,
( ( rdn_positive_less @ ( rdnn @ n4 ) @ ( rdnn @ n5 ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(447,plain,
( ( rdn_positive_less @ ( rdnn @ n5 ) @ ( rdnn @ n6 ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(448,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( sum @ X @ n1 @ Y )
& ( less @ Z @ Y ) )
=> ( less_or_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(449,plain,
( ( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ( ( rdn_translate @ POS_X @ ( rdn_pos @ RDN_X ) )
& ( rdn_translate @ NEG_X @ ( rdn_neg @ RDN_X ) ) )
=> ( sum @ POS_X @ NEG_X @ n0 ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(450,plain,
( ( ! [X: $i,Y: $i,Z: $i,RDN_X: $i,RDN_Y: $i] :
( ( ( rdn_translate @ X @ ( rdn_neg @ RDN_X ) )
& ( rdn_translate @ Y @ ( rdn_pos @ RDN_Y ) )
& ( sum @ Y @ X @ Z ) )
=> ( sum @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(451,plain,
( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
( ( ( sum @ X @ Y @ Z1 )
& ( sum @ X @ Y @ Z2 ) )
=> ( Z1 = Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(452,plain,
( ( ! [X1: $i,X2: $i,Y: $i,Z: $i] :
( ( ( sum @ X1 @ Y @ Z )
& ( sum @ X2 @ Y @ Z ) )
=> ( X1 = X2 ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(453,plain,
( ( ! [X: $i,Y1: $i,Y2: $i,Z: $i] :
( ( ( sum @ X @ Y1 @ Z )
& ( sum @ X @ Y2 @ Z ) )
=> ( Y1 = Y2 ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(454,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( sum @ Y @ Z @ X )
<=> ( difference @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(455,plain,
( ( ! [C: $i,D1: $i,D2: $i,RD: $i,ID: $i] :
( ( ( rdn_digit_add @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ ID ) @ ( rdnn @ n0 ) )
& ( rdn_digit_add @ ( rdnn @ ID ) @ ( rdnn @ C ) @ ( rdnn @ RD ) @ ( rdnn @ n0 ) ) )
=> ( rdn_add_with_carry @ ( rdnn @ C ) @ ( rdnn @ D1 ) @ ( rdnn @ D2 ) @ ( rdnn @ RD ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(456,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(457,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(458,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(459,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(460,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(461,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(462,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(463,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(464,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(465,plain,
( ( rdn_digit_add @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(466,plain,
( ( rdn_digit_add @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(467,plain,
( ( rdn_digit_add @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) @ ( rdnn @ n2 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(468,plain,
( ( rdn_digit_add @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) @ ( rdnn @ n3 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(469,plain,
( ( rdn_digit_add @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) @ ( rdnn @ n4 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(470,plain,
( ( rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(471,plain,
( ( rdn_digit_add @ ( rdnn @ n5 ) @ ( rdnn @ n5 ) @ ( rdnn @ n0 ) @ ( rdnn @ n1 ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(472,plain,
( ( rdn_digit_add @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) @ ( rdnn @ n6 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(473,plain,
( ( rdn_digit_add @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) @ ( rdnn @ n7 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(474,plain,
( ( rdn_digit_add @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) @ ( rdnn @ n8 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(475,plain,
( ( rdn_digit_add @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) @ ( rdnn @ n9 ) @ ( rdnn @ n0 ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(476,plain,
( ( ~ ( sum @ n5 @ nn5 @ n0 ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(477,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( sum @ SX0 @ SX1 @ SX2 )
| ~ ( sum @ SX0 @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SX1 ) @ ( rdnn @ SX2 ) @ ( rdnn @ SX4 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SX4 ) @ ( rdnn @ SX0 ) @ ( rdnn @ SX3 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SX0 ) @ ( rdnn @ SX1 ) @ ( rdnn @ SX2 ) @ ( rdnn @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(479,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SX0 @ ( rdn_neg @ SX3 ) )
| ~ ( rdn_translate @ SX1 @ ( rdn_pos @ SX4 ) ) )
| ~ ( sum @ SX1 @ SX0 @ SX2 ) )
| ( sum @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( sum @ SX1 @ SX2 @ SX0 )
| ( difference @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( difference @ SX0 @ SX1 @ SX2 )
| ( sum @ SX1 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(481,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)],[448]) ).
thf(482,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( sum @ SX0 @ SX1 @ SX3 )
| ~ ( sum @ SX0 @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( sum @ SX0 @ SX2 @ SX3 )
| ~ ( sum @ SX1 @ SX2 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(484,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rdn_translate @ SX0 @ ( rdn_pos @ SX2 ) )
| ~ ( rdn_translate @ SX1 @ ( rdn_neg @ SX2 ) ) )
| ( sum @ SX0 @ SX1 @ n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(485,plain,
( ( sum @ n5 @ nn5 @ n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(486,plain,
! [SV1: $i] :
( ( ! [SY31: $i,SY32: $i,SY33: $i] :
( ~ ~ ( ~ ( sum @ SV1 @ SY31 @ SY32 )
| ~ ( sum @ SV1 @ SY31 @ SY33 ) )
| ( SY32 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(487,plain,
! [SV2: $i] :
( ( ! [SY34: $i,SY35: $i,SY36: $i,SY37: $i] :
( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SY34 ) @ ( rdnn @ SY35 ) @ ( rdnn @ SY37 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SY37 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SY36 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SY34 ) @ ( rdnn @ SY35 ) @ ( rdnn @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(488,plain,
! [SV3: $i] :
( ( ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SY40 ) )
| ~ ( rdn_translate @ SY38 @ ( rdn_pos @ SY41 ) ) )
| ~ ( sum @ SY38 @ SV3 @ SY39 ) )
| ( sum @ SV3 @ SY38 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(489,plain,
! [SV4: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ~ ( sum @ SY42 @ SY43 @ SV4 )
| ( difference @ SV4 @ SY42 @ SY43 ) )
| ~ ( ~ ( difference @ SV4 @ SY42 @ SY43 )
| ( sum @ SY42 @ SY43 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(490,plain,
! [SV5: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( sum @ SV5 @ n1 @ SY44 )
| ~ ( less @ SY45 @ SY44 ) )
| ( less_or_equal @ SY45 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(491,plain,
! [SV6: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ~ ( ~ ( sum @ SV6 @ SY46 @ SY48 )
| ~ ( sum @ SV6 @ SY47 @ SY48 ) )
| ( SY46 = SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(492,plain,
! [SV7: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ~ ( ~ ( sum @ SV7 @ SY50 @ SY51 )
| ~ ( sum @ SY49 @ SY50 @ SY51 ) )
| ( SV7 = SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(493,plain,
! [SV8: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SY53 ) )
| ~ ( rdn_translate @ SY52 @ ( rdn_neg @ SY53 ) ) )
| ( sum @ SV8 @ SY52 @ n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(494,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ~ ( ~ ( sum @ SV1 @ SV9 @ SY54 )
| ~ ( sum @ SV1 @ SV9 @ SY55 ) )
| ( SY54 = SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(495,plain,
! [SV2: $i,SV10: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SY56 ) @ ( rdnn @ SY58 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SY58 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SY57 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SY56 ) @ ( rdnn @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(496,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY59: $i,SY60: $i,SY61: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SY60 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SY61 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SY59 ) )
| ( sum @ SV3 @ SV11 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(497,plain,
! [SV4: $i,SV12: $i] :
( ( ! [SY62: $i] :
~ ( ~ ( ~ ( sum @ SV12 @ SY62 @ SV4 )
| ( difference @ SV4 @ SV12 @ SY62 ) )
| ~ ( ~ ( difference @ SV4 @ SV12 @ SY62 )
| ( sum @ SV12 @ SY62 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(498,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY63: $i] :
( ~ ~ ( ~ ( sum @ SV5 @ n1 @ SV13 )
| ~ ( less @ SY63 @ SV13 ) )
| ( less_or_equal @ SY63 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(499,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ~ ( ~ ( sum @ SV6 @ SV14 @ SY65 )
| ~ ( sum @ SV6 @ SY64 @ SY65 ) )
| ( SV14 = SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(500,plain,
! [SV15: $i,SV7: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ~ ( ~ ( sum @ SV7 @ SY66 @ SY67 )
| ~ ( sum @ SV15 @ SY66 @ SY67 ) )
| ( SV7 = SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(501,plain,
! [SV16: $i,SV8: $i] :
( ( ! [SY68: $i] :
( ~ ~ ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SY68 ) )
| ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SY68 ) ) )
| ( sum @ SV8 @ SV16 @ n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(502,plain,
! [SV17: $i,SV9: $i,SV1: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( sum @ SV1 @ SV9 @ SV17 )
| ~ ( sum @ SV1 @ SV9 @ SY69 ) )
| ( SV17 = SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(503,plain,
! [SV2: $i,SV18: $i,SV10: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SY71 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SY71 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SY70 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(504,plain,
! [SV19: $i,SV11: $i,SV3: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SY72 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SY73 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) )
| ( sum @ SV3 @ SV11 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(505,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( sum @ SV12 @ SV20 @ SV4 )
| ( difference @ SV4 @ SV12 @ SV20 ) )
| ~ ( ~ ( difference @ SV4 @ SV12 @ SV20 )
| ( sum @ SV12 @ SV20 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(506,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ~ ~ ( ~ ( sum @ SV5 @ n1 @ SV13 )
| ~ ( less @ SV21 @ SV13 ) )
| ( less_or_equal @ SV21 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(507,plain,
! [SV22: $i,SV14: $i,SV6: $i] :
( ( ! [SY74: $i] :
( ~ ~ ( ~ ( sum @ SV6 @ SV14 @ SY74 )
| ~ ( sum @ SV6 @ SV22 @ SY74 ) )
| ( SV14 = SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(508,plain,
! [SV15: $i,SV23: $i,SV7: $i] :
( ( ! [SY75: $i] :
( ~ ~ ( ~ ( sum @ SV7 @ SV23 @ SY75 )
| ~ ( sum @ SV15 @ SV23 @ SY75 ) )
| ( SV7 = SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(509,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ~ ~ ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
| ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) )
| ( sum @ SV8 @ SV16 @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(510,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ~ ~ ( ~ ( sum @ SV1 @ SV9 @ SV17 )
| ~ ( sum @ SV1 @ SV9 @ SV25 ) )
| ( SV17 = SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(511,plain,
! [SV26: $i,SV2: $i,SV18: $i,SV10: $i] :
( ( ! [SY76: $i] :
( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SY76 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SY76 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(512,plain,
! [SV19: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ! [SY77: $i] :
( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SY77 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) )
| ( sum @ SV3 @ SV11 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(513,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ~ ( ~ ( sum @ SV12 @ SV20 @ SV4 )
| ( difference @ SV4 @ SV12 @ SV20 ) )
| ~ ( ~ ( difference @ SV4 @ SV12 @ SV20 )
| ( sum @ SV12 @ SV20 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(514,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( sum @ SV5 @ n1 @ SV13 )
| ~ ( less @ SV21 @ SV13 ) ) )
= $true )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(515,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ~ ~ ( ~ ( sum @ SV6 @ SV14 @ SV28 )
| ~ ( sum @ SV6 @ SV22 @ SV28 ) )
| ( SV14 = SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(516,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ~ ~ ( ~ ( sum @ SV7 @ SV23 @ SV29 )
| ~ ( sum @ SV15 @ SV23 @ SV29 ) )
| ( SV7 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(517,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
| ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) ) )
= $true )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(518,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( sum @ SV1 @ SV9 @ SV17 )
| ~ ( sum @ SV1 @ SV9 @ SV25 ) ) )
= $true )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(519,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) )
| ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(520,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) )
| ( sum @ SV3 @ SV11 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(521,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ~ ( ~ ( sum @ SV12 @ SV20 @ SV4 )
| ( difference @ SV4 @ SV12 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(522,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( ~ ( ~ ( difference @ SV4 @ SV12 @ SV20 )
| ( sum @ SV12 @ SV20 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(523,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( ~ ( sum @ SV5 @ n1 @ SV13 )
| ~ ( less @ SV21 @ SV13 ) ) )
= $false )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(524,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( sum @ SV6 @ SV14 @ SV28 )
| ~ ( sum @ SV6 @ SV22 @ SV28 ) ) )
= $true )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(525,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( sum @ SV7 @ SV23 @ SV29 )
| ~ ( sum @ SV15 @ SV23 @ SV29 ) ) )
= $true )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(526,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
| ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) ) )
= $false )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(527,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( ~ ( sum @ SV1 @ SV9 @ SV17 )
| ~ ( sum @ SV1 @ SV9 @ SV25 ) ) )
= $false )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(528,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) ) )
= $true )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(529,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(530,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ~ ( sum @ SV12 @ SV20 @ SV4 )
| ( difference @ SV4 @ SV12 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(531,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( ~ ( difference @ SV4 @ SV12 @ SV20 )
| ( sum @ SV12 @ SV20 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(532,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( sum @ SV5 @ n1 @ SV13 )
| ~ ( less @ SV21 @ SV13 ) )
= $true )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(533,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( ~ ( sum @ SV6 @ SV14 @ SV28 )
| ~ ( sum @ SV6 @ SV22 @ SV28 ) ) )
= $false )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(534,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( ~ ( sum @ SV7 @ SV23 @ SV29 )
| ~ ( sum @ SV15 @ SV23 @ SV29 ) ) )
= $false )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(535,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
| ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) )
= $true )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(536,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ SV9 @ SV17 )
| ~ ( sum @ SV1 @ SV9 @ SV25 ) )
= $true )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(537,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) ) )
= $false )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(538,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) ) )
= $false )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(539,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( sum @ SV12 @ SV20 @ SV4 ) )
= $true )
| ( ( difference @ SV4 @ SV12 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(540,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( difference @ SV4 @ SV12 @ SV20 ) )
= $true )
| ( ( sum @ SV12 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(541,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( sum @ SV5 @ n1 @ SV13 ) )
= $true )
| ( ( ~ ( less @ SV21 @ SV13 ) )
= $true )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(542,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( sum @ SV6 @ SV14 @ SV28 )
| ~ ( sum @ SV6 @ SV22 @ SV28 ) )
= $true )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(543,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( sum @ SV7 @ SV23 @ SV29 )
| ~ ( sum @ SV15 @ SV23 @ SV29 ) )
= $true )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(544,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) ) )
= $true )
| ( ( ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) )
= $true )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(545,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ SV9 @ SV17 ) )
= $true )
| ( ( ~ ( sum @ SV1 @ SV9 @ SV25 ) )
= $true )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(546,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
| ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) )
= $true )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(547,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
| ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(548,plain,
! [SV4: $i,SV20: $i,SV12: $i] :
( ( ( sum @ SV12 @ SV20 @ SV4 )
= $false )
| ( ( difference @ SV4 @ SV12 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(549,plain,
! [SV20: $i,SV12: $i,SV4: $i] :
( ( ( difference @ SV4 @ SV12 @ SV20 )
= $false )
| ( ( sum @ SV12 @ SV20 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(550,plain,
! [SV21: $i,SV13: $i,SV5: $i] :
( ( ( sum @ SV5 @ n1 @ SV13 )
= $false )
| ( ( ~ ( less @ SV21 @ SV13 ) )
= $true )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(551,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( sum @ SV6 @ SV14 @ SV28 ) )
= $true )
| ( ( ~ ( sum @ SV6 @ SV22 @ SV28 ) )
= $true )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(552,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( sum @ SV7 @ SV23 @ SV29 ) )
= $true )
| ( ( ~ ( sum @ SV15 @ SV23 @ SV29 ) )
= $true )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(553,plain,
! [SV16: $i,SV24: $i,SV8: $i] :
( ( ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
= $false )
| ( ( ~ ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) ) )
= $true )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(554,plain,
! [SV25: $i,SV17: $i,SV9: $i,SV1: $i] :
( ( ( sum @ SV1 @ SV9 @ SV17 )
= $false )
| ( ( ~ ( sum @ SV1 @ SV9 @ SV25 ) )
= $true )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(555,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) ) )
= $true )
| ( ( ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) )
= $true )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(556,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) ) )
= $true )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(557,plain,
! [SV5: $i,SV13: $i,SV21: $i] :
( ( ( less @ SV21 @ SV13 )
= $false )
| ( ( sum @ SV5 @ n1 @ SV13 )
= $false )
| ( ( less_or_equal @ SV21 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(558,plain,
! [SV22: $i,SV28: $i,SV14: $i,SV6: $i] :
( ( ( sum @ SV6 @ SV14 @ SV28 )
= $false )
| ( ( ~ ( sum @ SV6 @ SV22 @ SV28 ) )
= $true )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(559,plain,
! [SV15: $i,SV29: $i,SV23: $i,SV7: $i] :
( ( ( sum @ SV7 @ SV23 @ SV29 )
= $false )
| ( ( ~ ( sum @ SV15 @ SV23 @ SV29 ) )
= $true )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(560,plain,
! [SV8: $i,SV24: $i,SV16: $i] :
( ( ( rdn_translate @ SV16 @ ( rdn_neg @ SV24 ) )
= $false )
| ( ( rdn_translate @ SV8 @ ( rdn_pos @ SV24 ) )
= $false )
| ( ( sum @ SV8 @ SV16 @ n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(561,plain,
! [SV17: $i,SV25: $i,SV9: $i,SV1: $i] :
( ( ( sum @ SV1 @ SV9 @ SV25 )
= $false )
| ( ( sum @ SV1 @ SV9 @ SV17 )
= $false )
| ( ( SV17 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(562,plain,
! [SV26: $i,SV2: $i,SV30: $i,SV18: $i,SV10: $i] :
( ( ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
= $false )
| ( ( ~ ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) ) )
= $true )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(563,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) ) )
= $false )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(564,plain,
! [SV14: $i,SV28: $i,SV22: $i,SV6: $i] :
( ( ( sum @ SV6 @ SV22 @ SV28 )
= $false )
| ( ( sum @ SV6 @ SV14 @ SV28 )
= $false )
| ( ( SV14 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(565,plain,
! [SV7: $i,SV29: $i,SV23: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV23 @ SV29 )
= $false )
| ( ( sum @ SV7 @ SV23 @ SV29 )
= $false )
| ( ( SV7 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(566,plain,
! [SV18: $i,SV10: $i,SV26: $i,SV2: $i,SV30: $i] :
( ( ( rdn_digit_add @ ( rdnn @ SV30 ) @ ( rdnn @ SV2 ) @ ( rdnn @ SV26 ) @ ( rdnn @ n0 ) )
= $false )
| ( ( rdn_digit_add @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV30 ) @ ( rdnn @ n0 ) )
= $false )
| ( ( rdn_add_with_carry @ ( rdnn @ SV2 ) @ ( rdnn @ SV10 ) @ ( rdnn @ SV18 ) @ ( rdnn @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(567,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
| ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
= $true )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(568,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) ) )
= $true )
| ( ( ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
= $true )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(569,plain,
! [SV19: $i,SV31: $i,SV11: $i,SV27: $i,SV3: $i] :
( ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
= $false )
| ( ( ~ ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) ) )
= $true )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(570,plain,
! [SV19: $i,SV27: $i,SV3: $i,SV31: $i,SV11: $i] :
( ( ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) )
= $false )
| ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
= $false )
| ( ( ~ ( sum @ SV11 @ SV3 @ SV19 ) )
= $true )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(571,plain,
! [SV31: $i,SV27: $i,SV19: $i,SV3: $i,SV11: $i] :
( ( ( sum @ SV11 @ SV3 @ SV19 )
= $false )
| ( ( rdn_translate @ SV3 @ ( rdn_neg @ SV27 ) )
= $false )
| ( ( rdn_translate @ SV11 @ ( rdn_pos @ SV31 ) )
= $false )
| ( ( sum @ SV3 @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(572,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[441,571,566,565,564,561,560,557,549,548,485,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,447,446,445,444,443,442]) ).
thf(573,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n019.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 13:10:16 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.43 .
% 1.20/0.43
% 1.20/0.43 No.of.Axioms: 35
% 1.20/0.43
% 1.20/0.43 Length.of.Defs: 0
% 1.20/0.43
% 1.20/0.43 Contains.Choice.Funs: false
% 1.20/0.43 .......
% 1.20/0.43
% 1.20/0.43 ********************************
% 1.20/0.43 * All subproblems solved! *
% 1.20/0.43 ********************************
% 1.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:35,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.20/0.43
% 1.20/0.43 %**** Beginning of derivation protocol ****
% 1.20/0.43 % SZS output start CNFRefutation
% See solution above
% 1.20/0.43
% 1.20/0.43 %**** End of derivation protocol ****
% 1.20/0.43 %**** no. of clauses in derivation: 207 ****
% 1.20/0.43 %**** clause counter: 572 ****
% 1.20/0.43
% 1.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:35,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------