TSTP Solution File: HWV003-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 19:14:39 EDT 2022
% Result : Unsatisfiable 145.18s 145.38s
% Output : Refutation 147.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 34
% Syntax : Number of clauses : 763 ( 761 unt; 0 nHn; 763 RR)
% Number of literals : 765 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 20 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('HWV003-2.p',unknown),
[] ).
cnf(2,axiom,
equal(and__dfg(u,v),and__dfg(v,u)),
file('HWV003-2.p',unknown),
[] ).
cnf(3,axiom,
equal(or__dfg(or__dfg(u,v),w),or__dfg(u,or__dfg(v,w))),
file('HWV003-2.p',unknown),
[] ).
cnf(4,axiom,
equal(and__dfg(and__dfg(u,v),w),and__dfg(u,and__dfg(v,w))),
file('HWV003-2.p',unknown),
[] ).
cnf(5,axiom,
equal(or__dfg(u,ll0),u),
file('HWV003-2.p',unknown),
[] ).
cnf(6,axiom,
equal(and__dfg(u,ll1),u),
file('HWV003-2.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(and__dfg(u,v),and__dfg(u,w)),and__dfg(u,or__dfg(v,w))),
file('HWV003-2.p',unknown),
[] ).
cnf(8,axiom,
equal(and__dfg(or__dfg(u,v),or__dfg(u,w)),or__dfg(u,and__dfg(v,w))),
file('HWV003-2.p',unknown),
[] ).
cnf(9,axiom,
equal(or__dfg(u,not__dfg(u)),ll1),
file('HWV003-2.p',unknown),
[] ).
cnf(10,axiom,
equal(and__dfg(u,not__dfg(u)),ll0),
file('HWV003-2.p',unknown),
[] ).
cnf(12,axiom,
equal(and__dfg(u,u),u),
file('HWV003-2.p',unknown),
[] ).
cnf(13,axiom,
equal(not__dfg(not__dfg(u)),u),
file('HWV003-2.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(ll0),ll1),
file('HWV003-2.p',unknown),
[] ).
cnf(15,axiom,
equal(not__dfg(ll1),ll0),
file('HWV003-2.p',unknown),
[] ).
cnf(17,axiom,
equal(and__dfg(u,ll0),ll0),
file('HWV003-2.p',unknown),
[] ).
cnf(18,axiom,
equal(or__dfg(u,and__dfg(u,v)),u),
file('HWV003-2.p',unknown),
[] ).
cnf(19,axiom,
equal(and__dfg(u,or__dfg(u,v)),u),
file('HWV003-2.p',unknown),
[] ).
cnf(20,axiom,
equal(and__dfg(not__dfg(u),not__dfg(v)),not__dfg(or__dfg(u,v))),
file('HWV003-2.p',unknown),
[] ).
cnf(21,axiom,
equal(or__dfg(not__dfg(u),not__dfg(v)),not__dfg(and__dfg(u,v))),
file('HWV003-2.p',unknown),
[] ).
cnf(22,axiom,
equal(or__dfg(and__dfg(not__dfg(u),v),and__dfg(u,not__dfg(v))),xor__dfg(u,v)),
file('HWV003-2.p',unknown),
[] ).
cnf(23,axiom,
equal(xor__dfg(u,v),xor__dfg(v,u)),
file('HWV003-2.p',unknown),
[] ).
cnf(24,axiom,
equal(xor__dfg(xor__dfg(u,v),w),xor__dfg(u,xor__dfg(v,w))),
file('HWV003-2.p',unknown),
[] ).
cnf(25,axiom,
equal(xor__dfg(xor__dfg(a,b),cin),sum_def),
file('HWV003-2.p',unknown),
[] ).
cnf(26,axiom,
equal(or__dfg(and__dfg(cin,or__dfg(a,b)),and__dfg(not__dfg(cin),and__dfg(a,b))),carry_def),
file('HWV003-2.p',unknown),
[] ).
cnf(27,axiom,
equal(not__dfg(and__dfg(a,b)),t1),
file('HWV003-2.p',unknown),
[] ).
cnf(28,axiom,
equal(not__dfg(and__dfg(a,t1)),t2),
file('HWV003-2.p',unknown),
[] ).
cnf(29,axiom,
equal(not__dfg(and__dfg(b,t1)),t3),
file('HWV003-2.p',unknown),
[] ).
cnf(30,axiom,
equal(not__dfg(and__dfg(t2,t3)),t4),
file('HWV003-2.p',unknown),
[] ).
cnf(31,axiom,
equal(not__dfg(and__dfg(t4,cin)),t5),
file('HWV003-2.p',unknown),
[] ).
cnf(32,axiom,
equal(not__dfg(and__dfg(t4,t5)),t6),
file('HWV003-2.p',unknown),
[] ).
cnf(33,axiom,
equal(not__dfg(and__dfg(t5,cin)),t7),
file('HWV003-2.p',unknown),
[] ).
cnf(34,axiom,
equal(not__dfg(and__dfg(t6,t7)),sum__dfg),
file('HWV003-2.p',unknown),
[] ).
cnf(35,axiom,
equal(not__dfg(and__dfg(t1,t5)),carry),
file('HWV003-2.p',unknown),
[] ).
cnf(36,axiom,
( ~ equal(carry,carry_def)
| ~ equal(sum__dfg,sum_def) ),
file('HWV003-2.p',unknown),
[] ).
cnf(37,plain,
equal(xor__dfg(cin,xor__dfg(a,b)),sum_def),
inference(rew,[status(thm),theory(equality)],[23,25]),
[iquote('0:Rew:23.0,25.0')] ).
cnf(38,plain,
equal(not__dfg(and__dfg(cin,t4)),t5),
inference(rew,[status(thm),theory(equality)],[2,31]),
[iquote('0:Rew:2.0,31.0')] ).
cnf(39,plain,
equal(not__dfg(and__dfg(cin,t5)),t7),
inference(rew,[status(thm),theory(equality)],[2,33]),
[iquote('0:Rew:2.0,33.0')] ).
cnf(40,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(not__dfg(u),v)),xor__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[1,22]),
[iquote('0:Rew:1.0,22.0')] ).
cnf(57,plain,
equal(and__dfg(t1,t5),not__dfg(carry)),
inference(spr,[status(thm),theory(equality)],[35,13]),
[iquote('0:SpR:35.0,13.0')] ).
cnf(60,plain,
equal(and__dfg(t6,t7),not__dfg(sum__dfg)),
inference(spr,[status(thm),theory(equality)],[34,13]),
[iquote('0:SpR:34.0,13.0')] ).
cnf(63,plain,
equal(and__dfg(t4,t5),not__dfg(t6)),
inference(spr,[status(thm),theory(equality)],[32,13]),
[iquote('0:SpR:32.0,13.0')] ).
cnf(66,plain,
equal(and__dfg(t2,t3),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[30,13]),
[iquote('0:SpR:30.0,13.0')] ).
cnf(69,plain,
equal(and__dfg(b,t1),not__dfg(t3)),
inference(spr,[status(thm),theory(equality)],[29,13]),
[iquote('0:SpR:29.0,13.0')] ).
cnf(72,plain,
equal(and__dfg(a,t1),not__dfg(t2)),
inference(spr,[status(thm),theory(equality)],[28,13]),
[iquote('0:SpR:28.0,13.0')] ).
cnf(75,plain,
equal(and__dfg(a,b),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[27,13]),
[iquote('0:SpR:27.0,13.0')] ).
cnf(78,plain,
equal(or__dfg(and__dfg(cin,or__dfg(a,b)),and__dfg(not__dfg(cin),not__dfg(t1))),carry_def),
inference(rew,[status(thm),theory(equality)],[75,26]),
[iquote('0:Rew:75.0,26.0')] ).
cnf(79,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,or__dfg(a,b))),carry_def),
inference(rew,[status(thm),theory(equality)],[1,78,20]),
[iquote('0:Rew:1.0,78.0,20.0,78.0')] ).
cnf(80,plain,
equal(and__dfg(cin,t4),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[38,13]),
[iquote('0:SpR:38.0,13.0')] ).
cnf(83,plain,
equal(and__dfg(cin,t5),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[39,13]),
[iquote('0:SpR:39.0,13.0')] ).
cnf(120,plain,
equal(or__dfg(cin,not__dfg(t7)),cin),
inference(spr,[status(thm),theory(equality)],[83,18]),
[iquote('0:SpR:83.0,18.0')] ).
cnf(121,plain,
equal(or__dfg(t6,not__dfg(sum__dfg)),t6),
inference(spr,[status(thm),theory(equality)],[60,18]),
[iquote('0:SpR:60.0,18.0')] ).
cnf(122,plain,
equal(or__dfg(t2,not__dfg(t4)),t2),
inference(spr,[status(thm),theory(equality)],[66,18]),
[iquote('0:SpR:66.0,18.0')] ).
cnf(123,plain,
equal(or__dfg(b,not__dfg(t3)),b),
inference(spr,[status(thm),theory(equality)],[69,18]),
[iquote('0:SpR:69.0,18.0')] ).
cnf(124,plain,
equal(or__dfg(a,not__dfg(t2)),a),
inference(spr,[status(thm),theory(equality)],[72,18]),
[iquote('0:SpR:72.0,18.0')] ).
cnf(125,plain,
equal(or__dfg(a,not__dfg(t1)),a),
inference(spr,[status(thm),theory(equality)],[75,18]),
[iquote('0:SpR:75.0,18.0')] ).
cnf(126,plain,
equal(or__dfg(cin,not__dfg(t5)),cin),
inference(spr,[status(thm),theory(equality)],[80,18]),
[iquote('0:SpR:80.0,18.0')] ).
cnf(143,plain,
equal(and__dfg(ll0,u),ll0),
inference(spr,[status(thm),theory(equality)],[2,17]),
[iquote('0:SpR:2.0,17.0')] ).
cnf(144,plain,
equal(and__dfg(ll1,u),u),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(146,plain,
equal(or__dfg(u,and__dfg(v,u)),u),
inference(spr,[status(thm),theory(equality)],[2,18]),
[iquote('0:SpR:2.0,18.0')] ).
cnf(168,plain,
equal(or__dfg(ll1,u),ll1),
inference(spr,[status(thm),theory(equality)],[144,19]),
[iquote('0:SpR:144.0,19.0')] ).
cnf(183,plain,
equal(or__dfg(ll0,u),u),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(185,plain,
equal(and__dfg(u,or__dfg(v,u)),u),
inference(spr,[status(thm),theory(equality)],[1,19]),
[iquote('0:SpR:1.0,19.0')] ).
cnf(220,plain,
equal(or__dfg(t5,not__dfg(carry)),t5),
inference(spr,[status(thm),theory(equality)],[57,146]),
[iquote('0:SpR:57.0,146.0')] ).
cnf(221,plain,
equal(or__dfg(t5,not__dfg(t6)),t5),
inference(spr,[status(thm),theory(equality)],[63,146]),
[iquote('0:SpR:63.0,146.0')] ).
cnf(222,plain,
equal(or__dfg(t5,not__dfg(t7)),t5),
inference(spr,[status(thm),theory(equality)],[83,146]),
[iquote('0:SpR:83.0,146.0')] ).
cnf(223,plain,
equal(or__dfg(t7,not__dfg(sum__dfg)),t7),
inference(spr,[status(thm),theory(equality)],[60,146]),
[iquote('0:SpR:60.0,146.0')] ).
cnf(224,plain,
equal(or__dfg(t3,not__dfg(t4)),t3),
inference(spr,[status(thm),theory(equality)],[66,146]),
[iquote('0:SpR:66.0,146.0')] ).
cnf(225,plain,
equal(or__dfg(t1,not__dfg(t3)),t1),
inference(spr,[status(thm),theory(equality)],[69,146]),
[iquote('0:SpR:69.0,146.0')] ).
cnf(226,plain,
equal(or__dfg(t1,not__dfg(t2)),t1),
inference(spr,[status(thm),theory(equality)],[72,146]),
[iquote('0:SpR:72.0,146.0')] ).
cnf(227,plain,
equal(or__dfg(b,not__dfg(t1)),b),
inference(spr,[status(thm),theory(equality)],[75,146]),
[iquote('0:SpR:75.0,146.0')] ).
cnf(228,plain,
equal(or__dfg(t4,not__dfg(t5)),t4),
inference(spr,[status(thm),theory(equality)],[80,146]),
[iquote('0:SpR:80.0,146.0')] ).
cnf(249,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[13,21]),
[iquote('0:SpR:13.0,21.0')] ).
cnf(252,plain,
equal(not__dfg(and__dfg(not__dfg(u),v)),or__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[13,21]),
[iquote('0:SpR:13.0,21.0')] ).
cnf(274,plain,
equal(and__dfg(not__dfg(u),not__dfg(v)),not__dfg(or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[20,2]),
[iquote('0:SpR:20.0,2.0')] ).
cnf(280,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[13,20]),
[iquote('0:SpR:13.0,20.0')] ).
cnf(283,plain,
equal(not__dfg(or__dfg(not__dfg(u),v)),and__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[13,20]),
[iquote('0:SpR:13.0,20.0')] ).
cnf(291,plain,
equal(not__dfg(or__dfg(u,v)),not__dfg(or__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[20,274]),
[iquote('0:Rew:20.0,274.0')] ).
cnf(309,plain,
equal(and__dfg(and__dfg(u,v),v),and__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[146,185]),
[iquote('0:SpR:146.0,185.0')] ).
cnf(311,plain,
equal(and__dfg(not__dfg(carry),t5),not__dfg(carry)),
inference(spr,[status(thm),theory(equality)],[220,185]),
[iquote('0:SpR:220.0,185.0')] ).
cnf(313,plain,
equal(and__dfg(not__dfg(t6),t5),not__dfg(t6)),
inference(spr,[status(thm),theory(equality)],[221,185]),
[iquote('0:SpR:221.0,185.0')] ).
cnf(314,plain,
equal(and__dfg(not__dfg(t7),cin),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[120,185]),
[iquote('0:SpR:120.0,185.0')] ).
cnf(315,plain,
equal(and__dfg(not__dfg(t5),cin),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[126,185]),
[iquote('0:SpR:126.0,185.0')] ).
cnf(316,plain,
equal(and__dfg(not__dfg(sum__dfg),t6),not__dfg(sum__dfg)),
inference(spr,[status(thm),theory(equality)],[121,185]),
[iquote('0:SpR:121.0,185.0')] ).
cnf(317,plain,
equal(and__dfg(not__dfg(sum__dfg),t7),not__dfg(sum__dfg)),
inference(spr,[status(thm),theory(equality)],[223,185]),
[iquote('0:SpR:223.0,185.0')] ).
cnf(318,plain,
equal(and__dfg(not__dfg(t4),t2),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[122,185]),
[iquote('0:SpR:122.0,185.0')] ).
cnf(319,plain,
equal(and__dfg(not__dfg(t4),t3),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[224,185]),
[iquote('0:SpR:224.0,185.0')] ).
cnf(320,plain,
equal(and__dfg(not__dfg(t3),b),not__dfg(t3)),
inference(spr,[status(thm),theory(equality)],[123,185]),
[iquote('0:SpR:123.0,185.0')] ).
cnf(321,plain,
equal(and__dfg(not__dfg(t3),t1),not__dfg(t3)),
inference(spr,[status(thm),theory(equality)],[225,185]),
[iquote('0:SpR:225.0,185.0')] ).
cnf(322,plain,
equal(and__dfg(not__dfg(t2),a),not__dfg(t2)),
inference(spr,[status(thm),theory(equality)],[124,185]),
[iquote('0:SpR:124.0,185.0')] ).
cnf(323,plain,
equal(and__dfg(not__dfg(t1),a),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[125,185]),
[iquote('0:SpR:125.0,185.0')] ).
cnf(324,plain,
equal(and__dfg(not__dfg(t7),t5),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[222,185]),
[iquote('0:SpR:222.0,185.0')] ).
cnf(326,plain,
equal(and__dfg(not__dfg(t2),t1),not__dfg(t2)),
inference(spr,[status(thm),theory(equality)],[226,185]),
[iquote('0:SpR:226.0,185.0')] ).
cnf(327,plain,
equal(and__dfg(not__dfg(t1),b),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[227,185]),
[iquote('0:SpR:227.0,185.0')] ).
cnf(328,plain,
equal(and__dfg(not__dfg(t5),t4),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[228,185]),
[iquote('0:SpR:228.0,185.0')] ).
cnf(333,plain,
equal(and__dfg(t5,not__dfg(carry)),not__dfg(carry)),
inference(rew,[status(thm),theory(equality)],[2,311]),
[iquote('0:Rew:2.0,311.0')] ).
cnf(335,plain,
equal(and__dfg(t5,not__dfg(t6)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[2,313]),
[iquote('0:Rew:2.0,313.0')] ).
cnf(336,plain,
equal(and__dfg(cin,not__dfg(t7)),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[2,314]),
[iquote('0:Rew:2.0,314.0')] ).
cnf(337,plain,
equal(and__dfg(cin,not__dfg(t5)),not__dfg(t5)),
inference(rew,[status(thm),theory(equality)],[2,315]),
[iquote('0:Rew:2.0,315.0')] ).
cnf(338,plain,
equal(and__dfg(t6,not__dfg(sum__dfg)),not__dfg(sum__dfg)),
inference(rew,[status(thm),theory(equality)],[2,316]),
[iquote('0:Rew:2.0,316.0')] ).
cnf(339,plain,
equal(and__dfg(t7,not__dfg(sum__dfg)),not__dfg(sum__dfg)),
inference(rew,[status(thm),theory(equality)],[2,317]),
[iquote('0:Rew:2.0,317.0')] ).
cnf(340,plain,
equal(and__dfg(t2,not__dfg(t4)),not__dfg(t4)),
inference(rew,[status(thm),theory(equality)],[2,318]),
[iquote('0:Rew:2.0,318.0')] ).
cnf(341,plain,
equal(and__dfg(t3,not__dfg(t4)),not__dfg(t4)),
inference(rew,[status(thm),theory(equality)],[2,319]),
[iquote('0:Rew:2.0,319.0')] ).
cnf(342,plain,
equal(and__dfg(b,not__dfg(t3)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[2,320]),
[iquote('0:Rew:2.0,320.0')] ).
cnf(343,plain,
equal(and__dfg(t1,not__dfg(t3)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[2,321]),
[iquote('0:Rew:2.0,321.0')] ).
cnf(344,plain,
equal(and__dfg(a,not__dfg(t2)),not__dfg(t2)),
inference(rew,[status(thm),theory(equality)],[2,322]),
[iquote('0:Rew:2.0,322.0')] ).
cnf(345,plain,
equal(and__dfg(a,not__dfg(t1)),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[2,323]),
[iquote('0:Rew:2.0,323.0')] ).
cnf(346,plain,
equal(and__dfg(t5,not__dfg(t7)),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[2,324]),
[iquote('0:Rew:2.0,324.0')] ).
cnf(347,plain,
equal(and__dfg(t1,not__dfg(t2)),not__dfg(t2)),
inference(rew,[status(thm),theory(equality)],[2,326]),
[iquote('0:Rew:2.0,326.0')] ).
cnf(348,plain,
equal(and__dfg(b,not__dfg(t1)),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[2,327]),
[iquote('0:Rew:2.0,327.0')] ).
cnf(349,plain,
equal(and__dfg(t4,not__dfg(t5)),not__dfg(t5)),
inference(rew,[status(thm),theory(equality)],[2,328]),
[iquote('0:Rew:2.0,328.0')] ).
cnf(352,plain,
equal(and__dfg(u,and__dfg(v,u)),and__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[2,309]),
[iquote('0:Rew:2.0,309.0')] ).
cnf(360,plain,
equal(xor__dfg(u,xor__dfg(v,w)),xor__dfg(v,xor__dfg(w,u))),
inference(spr,[status(thm),theory(equality)],[24,23]),
[iquote('0:SpR:24.0,23.0')] ).
cnf(365,plain,
equal(xor__dfg(xor__dfg(u,v),w),xor__dfg(v,xor__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[23,24]),
[iquote('0:SpR:23.0,24.0')] ).
cnf(367,plain,
equal(xor__dfg(a,xor__dfg(b,cin)),sum_def),
inference(rew,[status(thm),theory(equality)],[360,37]),
[iquote('0:Rew:360.0,37.0')] ).
cnf(371,plain,
equal(xor__dfg(u,xor__dfg(v,w)),xor__dfg(v,xor__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[24,365]),
[iquote('0:Rew:24.0,365.0')] ).
cnf(404,plain,
equal(and__dfg(u,and__dfg(v,not__dfg(and__dfg(u,v)))),ll0),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.0,10.0')] ).
cnf(405,plain,
equal(and__dfg(u,and__dfg(v,or__dfg(and__dfg(u,v),w))),and__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[4,19]),
[iquote('0:SpR:4.0,19.0')] ).
cnf(408,plain,
equal(and__dfg(u,and__dfg(v,w)),and__dfg(w,and__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(416,plain,
equal(and__dfg(u,and__dfg(not__dfg(u),v)),and__dfg(ll0,v)),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(417,plain,
equal(and__dfg(u,and__dfg(or__dfg(u,v),w)),and__dfg(u,w)),
inference(spr,[status(thm),theory(equality)],[19,4]),
[iquote('0:SpR:19.0,4.0')] ).
cnf(419,plain,
equal(and__dfg(and__dfg(u,v),w),and__dfg(v,and__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(420,plain,
equal(and__dfg(t1,and__dfg(t5,u)),and__dfg(not__dfg(carry),u)),
inference(spr,[status(thm),theory(equality)],[57,4]),
[iquote('0:SpR:57.0,4.0')] ).
cnf(421,plain,
equal(and__dfg(t4,and__dfg(t5,u)),and__dfg(not__dfg(t6),u)),
inference(spr,[status(thm),theory(equality)],[63,4]),
[iquote('0:SpR:63.0,4.0')] ).
cnf(422,plain,
equal(and__dfg(cin,and__dfg(t5,u)),and__dfg(not__dfg(t7),u)),
inference(spr,[status(thm),theory(equality)],[83,4]),
[iquote('0:SpR:83.0,4.0')] ).
cnf(424,plain,
equal(and__dfg(t2,and__dfg(t3,u)),and__dfg(not__dfg(t4),u)),
inference(spr,[status(thm),theory(equality)],[66,4]),
[iquote('0:SpR:66.0,4.0')] ).
cnf(425,plain,
equal(and__dfg(b,and__dfg(t1,u)),and__dfg(not__dfg(t3),u)),
inference(spr,[status(thm),theory(equality)],[69,4]),
[iquote('0:SpR:69.0,4.0')] ).
cnf(426,plain,
equal(and__dfg(a,and__dfg(t1,u)),and__dfg(not__dfg(t2),u)),
inference(spr,[status(thm),theory(equality)],[72,4]),
[iquote('0:SpR:72.0,4.0')] ).
cnf(428,plain,
equal(and__dfg(cin,and__dfg(t4,u)),and__dfg(not__dfg(t5),u)),
inference(spr,[status(thm),theory(equality)],[80,4]),
[iquote('0:SpR:80.0,4.0')] ).
cnf(448,plain,
equal(and__dfg(u,and__dfg(not__dfg(u),v)),ll0),
inference(rew,[status(thm),theory(equality)],[143,416]),
[iquote('0:Rew:143.0,416.0')] ).
cnf(450,plain,
equal(and__dfg(u,and__dfg(v,w)),and__dfg(v,and__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[4,419]),
[iquote('0:Rew:4.0,419.0')] ).
cnf(476,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(w,or__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(486,plain,
equal(or__dfg(u,or__dfg(not__dfg(u),v)),or__dfg(ll1,v)),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(488,plain,
equal(or__dfg(u,or__dfg(and__dfg(u,v),w)),or__dfg(u,w)),
inference(spr,[status(thm),theory(equality)],[18,3]),
[iquote('0:SpR:18.0,3.0')] ).
cnf(489,plain,
equal(or__dfg(u,or__dfg(and__dfg(v,u),w)),or__dfg(u,w)),
inference(spr,[status(thm),theory(equality)],[146,3]),
[iquote('0:SpR:146.0,3.0')] ).
cnf(517,plain,
equal(or__dfg(u,or__dfg(not__dfg(u),v)),ll1),
inference(rew,[status(thm),theory(equality)],[168,486]),
[iquote('0:Rew:168.0,486.0')] ).
cnf(540,plain,
equal(and__dfg(not__dfg(or__dfg(cin,t1)),carry_def),not__dfg(or__dfg(cin,t1))),
inference(spr,[status(thm),theory(equality)],[79,19]),
[iquote('0:SpR:79.0,19.0')] ).
cnf(541,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),or__dfg(and__dfg(cin,or__dfg(a,b)),u)),or__dfg(carry_def,u)),
inference(spr,[status(thm),theory(equality)],[79,3]),
[iquote('0:SpR:79.0,3.0')] ).
cnf(544,plain,
equal(and__dfg(carry_def,not__dfg(or__dfg(cin,t1))),not__dfg(or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[2,540]),
[iquote('0:Rew:2.0,540.0')] ).
cnf(563,plain,
equal(and__dfg(u,and__dfg(v,not__dfg(u))),ll0),
inference(spr,[status(thm),theory(equality)],[2,448]),
[iquote('0:SpR:2.0,448.0')] ).
cnf(565,plain,
equal(and__dfg(u,not__dfg(or__dfg(u,v))),ll0),
inference(spr,[status(thm),theory(equality)],[20,448]),
[iquote('0:SpR:20.0,448.0')] ).
cnf(588,plain,
equal(or__dfg(u,not__dfg(and__dfg(u,v))),ll1),
inference(spr,[status(thm),theory(equality)],[21,517]),
[iquote('0:SpR:21.0,517.0')] ).
cnf(590,plain,
equal(or__dfg(or__dfg(cin,t1),carry_def),ll1),
inference(spr,[status(thm),theory(equality)],[79,517]),
[iquote('0:SpR:79.0,517.0')] ).
cnf(593,plain,
equal(or__dfg(cin,or__dfg(carry_def,t1)),ll1),
inference(rew,[status(thm),theory(equality)],[1,590,3]),
[iquote('0:Rew:1.0,590.0,3.0,590.0')] ).
cnf(619,plain,
equal(and__dfg(u,not__dfg(or__dfg(v,u))),ll0),
inference(spr,[status(thm),theory(equality)],[20,563]),
[iquote('0:SpR:20.0,563.0')] ).
cnf(649,plain,
equal(or__dfg(and__dfg(not__dfg(u),not__dfg(v)),and__dfg(u,v)),xor__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[13,40]),
[iquote('0:SpR:13.0,40.0')] ).
cnf(651,plain,
equal(or__dfg(and__dfg(u,not__dfg(ll1)),not__dfg(u)),xor__dfg(u,ll1)),
inference(spr,[status(thm),theory(equality)],[6,40]),
[iquote('0:SpR:6.0,40.0')] ).
cnf(655,plain,
equal(or__dfg(and__dfg(u,not__dfg(or__dfg(v,not__dfg(u)))),not__dfg(u)),xor__dfg(u,or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[185,40]),
[iquote('0:SpR:185.0,40.0')] ).
cnf(656,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(v,not__dfg(u))),xor__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[2,40]),
[iquote('0:SpR:2.0,40.0')] ).
cnf(657,plain,
equal(or__dfg(and__dfg(u,not__dfg(and__dfg(v,not__dfg(not__dfg(u))))),ll0),xor__dfg(u,and__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[563,40]),
[iquote('0:SpR:563.0,40.0')] ).
cnf(658,plain,
equal(or__dfg(and__dfg(u,not__dfg(and__dfg(not__dfg(not__dfg(u)),v))),ll0),xor__dfg(u,and__dfg(not__dfg(not__dfg(u)),v))),
inference(spr,[status(thm),theory(equality)],[448,40]),
[iquote('0:SpR:448.0,40.0')] ).
cnf(663,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[13,40]),
[iquote('0:SpR:13.0,40.0')] ).
cnf(665,plain,
equal(or__dfg(ll0,and__dfg(not__dfg(u),u)),xor__dfg(u,u)),
inference(spr,[status(thm),theory(equality)],[10,40]),
[iquote('0:SpR:10.0,40.0')] ).
cnf(668,plain,
equal(or__dfg(ll0,and__dfg(not__dfg(ll0),u)),xor__dfg(ll0,u)),
inference(spr,[status(thm),theory(equality)],[143,40]),
[iquote('0:SpR:143.0,40.0')] ).
cnf(691,plain,
equal(xor__dfg(u,u),ll0),
inference(rew,[status(thm),theory(equality)],[183,665,10,2]),
[iquote('0:Rew:183.0,665.0,10.0,665.0,2.0,665.0')] ).
cnf(692,plain,
equal(xor__dfg(ll0,u),u),
inference(rew,[status(thm),theory(equality)],[183,668,144,14]),
[iquote('0:Rew:183.0,668.0,144.0,668.0,14.0,668.0')] ).
cnf(693,plain,
equal(xor__dfg(u,ll1),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[183,651,17,15]),
[iquote('0:Rew:183.0,651.0,17.0,651.0,15.0,651.0')] ).
cnf(721,plain,
equal(or__dfg(and__dfg(u,v),not__dfg(or__dfg(u,v))),xor__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[1,649,20]),
[iquote('0:Rew:1.0,649.0,20.0,649.0')] ).
cnf(723,plain,
equal(or__dfg(and__dfg(u,v),not__dfg(or__dfg(u,v))),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[20,663]),
[iquote('0:Rew:20.0,663.0')] ).
cnf(724,plain,
equal(xor__dfg(not__dfg(u),v),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[721,723]),
[iquote('0:Rew:721.0,723.0')] ).
cnf(725,plain,
equal(or__dfg(and__dfg(u,v),not__dfg(or__dfg(u,v))),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[724,721]),
[iquote('0:Rew:724.0,721.0')] ).
cnf(767,plain,
equal(or__dfg(not__dfg(u),and__dfg(u,not__dfg(or__dfg(v,not__dfg(u))))),xor__dfg(u,or__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[1,655]),
[iquote('0:Rew:1.0,655.0')] ).
cnf(768,plain,
equal(or__dfg(not__dfg(u),and__dfg(not__dfg(v),u)),xor__dfg(u,or__dfg(v,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[352,767,280]),
[iquote('0:Rew:352.0,767.0,280.0,767.0')] ).
cnf(769,plain,
equal(and__dfg(u,not__dfg(and__dfg(v,u))),xor__dfg(u,and__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[183,657,1,13]),
[iquote('0:Rew:183.0,657.0,1.0,657.0,13.0,657.0')] ).
cnf(770,plain,
equal(and__dfg(u,xor__dfg(v,and__dfg(u,v))),ll0),
inference(rew,[status(thm),theory(equality)],[769,404]),
[iquote('0:Rew:769.0,404.0')] ).
cnf(771,plain,
equal(and__dfg(u,not__dfg(and__dfg(u,v))),xor__dfg(u,and__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[183,658,1,13]),
[iquote('0:Rew:183.0,658.0,1.0,658.0,13.0,658.0')] ).
cnf(781,plain,
equal(xor__dfg(u,xor__dfg(u,v)),xor__dfg(ll0,v)),
inference(spr,[status(thm),theory(equality)],[691,24]),
[iquote('0:SpR:691.0,24.0')] ).
cnf(785,plain,
equal(xor__dfg(u,xor__dfg(u,v)),v),
inference(rew,[status(thm),theory(equality)],[692,781]),
[iquote('0:Rew:692.0,781.0')] ).
cnf(797,plain,
equal(xor__dfg(u,xor__dfg(v,ll1)),not__dfg(xor__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[693,24]),
[iquote('0:SpR:693.0,24.0')] ).
cnf(800,plain,
equal(not__dfg(xor__dfg(u,v)),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[693,797]),
[iquote('0:Rew:693.0,797.0')] ).
cnf(804,plain,
equal(and__dfg(or__dfg(u,v),or__dfg(u,w)),or__dfg(u,and__dfg(w,v))),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(812,plain,
equal(or__dfg(u,and__dfg(v,not__dfg(u))),and__dfg(or__dfg(u,v),ll1)),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(813,plain,
equal(and__dfg(or__dfg(u,v),or__dfg(w,u)),or__dfg(u,and__dfg(v,w))),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(814,plain,
equal(or__dfg(u,and__dfg(v,and__dfg(u,w))),and__dfg(or__dfg(u,v),u)),
inference(spr,[status(thm),theory(equality)],[18,8]),
[iquote('0:SpR:18.0,8.0')] ).
cnf(821,plain,
equal(or__dfg(cin,and__dfg(u,not__dfg(t7))),and__dfg(or__dfg(cin,u),cin)),
inference(spr,[status(thm),theory(equality)],[120,8]),
[iquote('0:SpR:120.0,8.0')] ).
cnf(846,plain,
equal(or__dfg(u,and__dfg(not__dfg(u),v)),and__dfg(ll1,or__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(847,plain,
equal(and__dfg(or__dfg(u,v),or__dfg(v,w)),or__dfg(v,and__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(874,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(and__dfg(cin,or__dfg(a,b)),u)),and__dfg(carry_def,or__dfg(not__dfg(or__dfg(cin,t1)),u))),
inference(spr,[status(thm),theory(equality)],[79,8]),
[iquote('0:SpR:79.0,8.0')] ).
cnf(876,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(and__dfg(not__dfg(u),v),w)),and__dfg(xor__dfg(u,v),or__dfg(and__dfg(u,not__dfg(v)),w))),
inference(spr,[status(thm),theory(equality)],[40,8]),
[iquote('0:SpR:40.0,8.0')] ).
cnf(889,plain,
equal(or__dfg(u,and__dfg(v,not__dfg(u))),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[144,812,2]),
[iquote('0:Rew:144.0,812.0,2.0,812.0')] ).
cnf(894,plain,
equal(or__dfg(cin,and__dfg(u,not__dfg(t7))),cin),
inference(rew,[status(thm),theory(equality)],[19,821,2]),
[iquote('0:Rew:19.0,821.0,2.0,821.0')] ).
cnf(908,plain,
equal(or__dfg(u,and__dfg(not__dfg(u),v)),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[144,846]),
[iquote('0:Rew:144.0,846.0')] ).
cnf(928,plain,
equal(or__dfg(u,and__dfg(v,w)),or__dfg(u,and__dfg(w,v))),
inference(rew,[status(thm),theory(equality)],[8,804]),
[iquote('0:Rew:8.0,804.0')] ).
cnf(931,plain,
equal(or__dfg(u,and__dfg(v,and__dfg(u,w))),u),
inference(rew,[status(thm),theory(equality)],[19,814,2]),
[iquote('0:Rew:19.0,814.0,2.0,814.0')] ).
cnf(941,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,and__dfg(or__dfg(a,b),u))),and__dfg(carry_def,or__dfg(not__dfg(or__dfg(cin,t1)),u))),
inference(rew,[status(thm),theory(equality)],[4,874]),
[iquote('0:Rew:4.0,874.0')] ).
cnf(943,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(not__dfg(u),and__dfg(v,w))),and__dfg(xor__dfg(u,v),or__dfg(and__dfg(u,not__dfg(v)),w))),
inference(rew,[status(thm),theory(equality)],[4,876]),
[iquote('0:Rew:4.0,876.0')] ).
cnf(972,plain,
equal(xor__dfg(u,xor__dfg(v,u)),v),
inference(spr,[status(thm),theory(equality)],[23,785]),
[iquote('0:SpR:23.0,785.0')] ).
cnf(979,plain,
equal(xor__dfg(b,cin),xor__dfg(a,sum_def)),
inference(spr,[status(thm),theory(equality)],[367,785]),
[iquote('0:SpR:367.0,785.0')] ).
cnf(990,plain,
equal(xor__dfg(b,xor__dfg(a,sum_def)),cin),
inference(spr,[status(thm),theory(equality)],[979,785]),
[iquote('0:SpR:979.0,785.0')] ).
cnf(992,plain,
equal(xor__dfg(a,xor__dfg(b,sum_def)),cin),
inference(rew,[status(thm),theory(equality)],[371,990]),
[iquote('0:Rew:371.0,990.0')] ).
cnf(1008,plain,
equal(and__dfg(u,or__dfg(v,not__dfg(u))),or__dfg(and__dfg(u,v),ll0)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(1011,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(w,u)),and__dfg(u,or__dfg(v,w))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(1022,plain,
equal(or__dfg(and__dfg(cin,u),not__dfg(t5)),and__dfg(cin,or__dfg(u,t4))),
inference(spr,[status(thm),theory(equality)],[80,7]),
[iquote('0:SpR:80.0,7.0')] ).
cnf(1050,plain,
equal(and__dfg(u,or__dfg(not__dfg(u),v)),or__dfg(ll0,and__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(1053,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(v,w)),and__dfg(v,or__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(1101,plain,
equal(and__dfg(u,or__dfg(v,not__dfg(u))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[183,1008,1]),
[iquote('0:Rew:183.0,1008.0,1.0,1008.0')] ).
cnf(1110,plain,
equal(or__dfg(not__dfg(t5),and__dfg(cin,u)),and__dfg(cin,or__dfg(u,t4))),
inference(rew,[status(thm),theory(equality)],[1,1022]),
[iquote('0:Rew:1.0,1022.0')] ).
cnf(1111,plain,
equal(and__dfg(u,or__dfg(not__dfg(u),v)),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[183,1050]),
[iquote('0:Rew:183.0,1050.0')] ).
cnf(1176,plain,
equal(xor__dfg(b,sum_def),xor__dfg(a,cin)),
inference(spr,[status(thm),theory(equality)],[992,785]),
[iquote('0:SpR:992.0,785.0')] ).
cnf(1205,plain,
equal(xor__dfg(sum_def,xor__dfg(a,cin)),b),
inference(spr,[status(thm),theory(equality)],[1176,972]),
[iquote('0:SpR:1176.0,972.0')] ).
cnf(1212,plain,
equal(xor__dfg(a,xor__dfg(sum_def,cin)),b),
inference(rew,[status(thm),theory(equality)],[371,1205]),
[iquote('0:Rew:371.0,1205.0')] ).
cnf(1213,plain,
equal(xor__dfg(a,xor__dfg(cin,sum_def)),b),
inference(rew,[status(thm),theory(equality)],[23,1212]),
[iquote('0:Rew:23.0,1212.0')] ).
cnf(1221,plain,
equal(xor__dfg(cin,sum_def),xor__dfg(a,b)),
inference(spr,[status(thm),theory(equality)],[1213,785]),
[iquote('0:SpR:1213.0,785.0')] ).
cnf(1390,plain,
equal(or__dfg(not__dfg(u),not__dfg(or__dfg(v,w))),not__dfg(and__dfg(u,or__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[291,21]),
[iquote('0:SpR:291.0,21.0')] ).
cnf(1450,plain,
equal(not__dfg(and__dfg(u,or__dfg(v,w))),not__dfg(and__dfg(u,or__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[21,1390]),
[iquote('0:Rew:21.0,1390.0')] ).
cnf(1491,plain,
equal(or__dfg(cin,not__dfg(or__dfg(u,t7))),cin),
inference(spr,[status(thm),theory(equality)],[20,894]),
[iquote('0:SpR:20.0,894.0')] ).
cnf(1538,plain,
equal(xor__dfg(u,not__dfg(v)),xor__dfg(v,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[724,23]),
[iquote('0:SpR:724.0,23.0')] ).
cnf(1682,plain,
equal(and__dfg(t6,xor__dfg(t7,not__dfg(sum__dfg))),ll0),
inference(spr,[status(thm),theory(equality)],[60,770]),
[iquote('0:SpR:60.0,770.0')] ).
cnf(1683,plain,
equal(and__dfg(t2,xor__dfg(t3,not__dfg(t4))),ll0),
inference(spr,[status(thm),theory(equality)],[66,770]),
[iquote('0:SpR:66.0,770.0')] ).
cnf(1686,plain,
equal(and__dfg(a,xor__dfg(b,not__dfg(t1))),ll0),
inference(spr,[status(thm),theory(equality)],[75,770]),
[iquote('0:SpR:75.0,770.0')] ).
cnf(1687,plain,
equal(and__dfg(cin,xor__dfg(t4,not__dfg(t5))),ll0),
inference(spr,[status(thm),theory(equality)],[80,770]),
[iquote('0:SpR:80.0,770.0')] ).
cnf(1805,plain,
equal(and__dfg(and__dfg(u,and__dfg(v,w)),v),and__dfg(u,and__dfg(v,w))),
inference(spr,[status(thm),theory(equality)],[931,185]),
[iquote('0:SpR:931.0,185.0')] ).
cnf(1879,plain,
equal(and__dfg(u,and__dfg(v,and__dfg(w,v))),and__dfg(u,and__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[4,1805]),
[iquote('0:Rew:4.0,1805.0,4.0,1805.0')] ).
cnf(1880,plain,
equal(and__dfg(u,and__dfg(v,w)),and__dfg(u,and__dfg(w,v))),
inference(rew,[status(thm),theory(equality)],[352,1879]),
[iquote('0:Rew:352.0,1879.0')] ).
cnf(2135,plain,
equal(or__dfg(not__dfg(t5),t6),not__dfg(not__dfg(t6))),
inference(spr,[status(thm),theory(equality)],[335,249]),
[iquote('0:SpR:335.0,249.0')] ).
cnf(2136,plain,
equal(or__dfg(not__dfg(cin),t7),not__dfg(not__dfg(t7))),
inference(spr,[status(thm),theory(equality)],[336,249]),
[iquote('0:SpR:336.0,249.0')] ).
cnf(2137,plain,
equal(or__dfg(not__dfg(cin),t5),not__dfg(not__dfg(t5))),
inference(spr,[status(thm),theory(equality)],[337,249]),
[iquote('0:SpR:337.0,249.0')] ).
cnf(2138,plain,
equal(or__dfg(not__dfg(t6),sum__dfg),not__dfg(not__dfg(sum__dfg))),
inference(spr,[status(thm),theory(equality)],[338,249]),
[iquote('0:SpR:338.0,249.0')] ).
cnf(2139,plain,
equal(or__dfg(not__dfg(t7),sum__dfg),not__dfg(not__dfg(sum__dfg))),
inference(spr,[status(thm),theory(equality)],[339,249]),
[iquote('0:SpR:339.0,249.0')] ).
cnf(2143,plain,
equal(or__dfg(not__dfg(t1),t3),not__dfg(not__dfg(t3))),
inference(spr,[status(thm),theory(equality)],[343,249]),
[iquote('0:SpR:343.0,249.0')] ).
cnf(2144,plain,
equal(or__dfg(not__dfg(a),t2),not__dfg(not__dfg(t2))),
inference(spr,[status(thm),theory(equality)],[344,249]),
[iquote('0:SpR:344.0,249.0')] ).
cnf(2157,plain,
equal(or__dfg(t6,not__dfg(t5)),t6),
inference(rew,[status(thm),theory(equality)],[1,2135,13]),
[iquote('0:Rew:1.0,2135.0,13.0,2135.0')] ).
cnf(2158,plain,
equal(or__dfg(t7,not__dfg(cin)),t7),
inference(rew,[status(thm),theory(equality)],[1,2136,13]),
[iquote('0:Rew:1.0,2136.0,13.0,2136.0')] ).
cnf(2159,plain,
equal(or__dfg(t5,not__dfg(cin)),t5),
inference(rew,[status(thm),theory(equality)],[1,2137,13]),
[iquote('0:Rew:1.0,2137.0,13.0,2137.0')] ).
cnf(2160,plain,
equal(or__dfg(sum__dfg,not__dfg(t6)),sum__dfg),
inference(rew,[status(thm),theory(equality)],[1,2138,13]),
[iquote('0:Rew:1.0,2138.0,13.0,2138.0')] ).
cnf(2161,plain,
equal(or__dfg(sum__dfg,not__dfg(t7)),sum__dfg),
inference(rew,[status(thm),theory(equality)],[1,2139,13]),
[iquote('0:Rew:1.0,2139.0,13.0,2139.0')] ).
cnf(2165,plain,
equal(or__dfg(t3,not__dfg(t1)),t3),
inference(rew,[status(thm),theory(equality)],[1,2143,13]),
[iquote('0:Rew:1.0,2143.0,13.0,2143.0')] ).
cnf(2166,plain,
equal(or__dfg(t2,not__dfg(a)),t2),
inference(rew,[status(thm),theory(equality)],[1,2144,13]),
[iquote('0:Rew:1.0,2144.0,13.0,2144.0')] ).
cnf(2229,plain,
equal(and__dfg(not__dfg(t5),t6),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[2157,185]),
[iquote('0:SpR:2157.0,185.0')] ).
cnf(2232,plain,
equal(and__dfg(t6,not__dfg(t5)),not__dfg(t5)),
inference(rew,[status(thm),theory(equality)],[2,2229]),
[iquote('0:Rew:2.0,2229.0')] ).
cnf(2318,plain,
equal(and__dfg(not__dfg(cin),t7),not__dfg(cin)),
inference(spr,[status(thm),theory(equality)],[2158,185]),
[iquote('0:SpR:2158.0,185.0')] ).
cnf(2321,plain,
equal(and__dfg(t7,not__dfg(cin)),not__dfg(cin)),
inference(rew,[status(thm),theory(equality)],[2,2318]),
[iquote('0:Rew:2.0,2318.0')] ).
cnf(2326,plain,
equal(or__dfg(t5,and__dfg(not__dfg(cin),u)),and__dfg(t5,or__dfg(t5,u))),
inference(spr,[status(thm),theory(equality)],[2159,8]),
[iquote('0:SpR:2159.0,8.0')] ).
cnf(2328,plain,
equal(and__dfg(not__dfg(cin),t5),not__dfg(cin)),
inference(spr,[status(thm),theory(equality)],[2159,185]),
[iquote('0:SpR:2159.0,185.0')] ).
cnf(2329,plain,
equal(or__dfg(t5,and__dfg(u,not__dfg(cin))),and__dfg(or__dfg(t5,u),t5)),
inference(spr,[status(thm),theory(equality)],[2159,8]),
[iquote('0:SpR:2159.0,8.0')] ).
cnf(2331,plain,
equal(and__dfg(t5,not__dfg(cin)),not__dfg(cin)),
inference(rew,[status(thm),theory(equality)],[2,2328]),
[iquote('0:Rew:2.0,2328.0')] ).
cnf(2332,plain,
equal(or__dfg(t5,and__dfg(not__dfg(cin),u)),t5),
inference(rew,[status(thm),theory(equality)],[19,2326]),
[iquote('0:Rew:19.0,2326.0')] ).
cnf(2333,plain,
equal(or__dfg(t5,and__dfg(u,not__dfg(cin))),t5),
inference(rew,[status(thm),theory(equality)],[19,2329,2]),
[iquote('0:Rew:19.0,2329.0,2.0,2329.0')] ).
cnf(2338,plain,
equal(and__dfg(not__dfg(t6),sum__dfg),not__dfg(t6)),
inference(spr,[status(thm),theory(equality)],[2160,185]),
[iquote('0:SpR:2160.0,185.0')] ).
cnf(2341,plain,
equal(and__dfg(sum__dfg,not__dfg(t6)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[2,2338]),
[iquote('0:Rew:2.0,2338.0')] ).
cnf(2348,plain,
equal(and__dfg(not__dfg(t7),sum__dfg),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[2161,185]),
[iquote('0:SpR:2161.0,185.0')] ).
cnf(2351,plain,
equal(and__dfg(sum__dfg,not__dfg(t7)),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[2,2348]),
[iquote('0:Rew:2.0,2348.0')] ).
cnf(2396,plain,
equal(and__dfg(not__dfg(t3),t4),not__dfg(t3)),
inference(spr,[status(thm),theory(equality)],[224,280]),
[iquote('0:SpR:224.0,280.0')] ).
cnf(2398,plain,
equal(and__dfg(not__dfg(b),t3),not__dfg(b)),
inference(spr,[status(thm),theory(equality)],[123,280]),
[iquote('0:SpR:123.0,280.0')] ).
cnf(2399,plain,
equal(and__dfg(not__dfg(t1),t3),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[225,280]),
[iquote('0:SpR:225.0,280.0')] ).
cnf(2401,plain,
equal(and__dfg(not__dfg(a),t1),not__dfg(a)),
inference(spr,[status(thm),theory(equality)],[125,280]),
[iquote('0:SpR:125.0,280.0')] ).
cnf(2402,plain,
equal(and__dfg(not__dfg(t5),t7),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[222,280]),
[iquote('0:SpR:222.0,280.0')] ).
cnf(2405,plain,
equal(and__dfg(not__dfg(t1),t2),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[226,280]),
[iquote('0:SpR:226.0,280.0')] ).
cnf(2406,plain,
equal(and__dfg(not__dfg(b),t1),not__dfg(b)),
inference(spr,[status(thm),theory(equality)],[227,280]),
[iquote('0:SpR:227.0,280.0')] ).
cnf(2408,plain,
equal(and__dfg(not__dfg(t4),t5),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[228,280]),
[iquote('0:SpR:228.0,280.0')] ).
cnf(2428,plain,
equal(and__dfg(t4,not__dfg(t3)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[2,2396]),
[iquote('0:Rew:2.0,2396.0')] ).
cnf(2430,plain,
equal(and__dfg(t3,not__dfg(b)),not__dfg(b)),
inference(rew,[status(thm),theory(equality)],[2,2398]),
[iquote('0:Rew:2.0,2398.0')] ).
cnf(2431,plain,
equal(and__dfg(t3,not__dfg(t1)),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[2,2399]),
[iquote('0:Rew:2.0,2399.0')] ).
cnf(2433,plain,
equal(and__dfg(t1,not__dfg(a)),not__dfg(a)),
inference(rew,[status(thm),theory(equality)],[2,2401]),
[iquote('0:Rew:2.0,2401.0')] ).
cnf(2434,plain,
equal(and__dfg(t7,not__dfg(t5)),not__dfg(t5)),
inference(rew,[status(thm),theory(equality)],[2,2402]),
[iquote('0:Rew:2.0,2402.0')] ).
cnf(2436,plain,
equal(and__dfg(t2,not__dfg(t1)),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[2,2405]),
[iquote('0:Rew:2.0,2405.0')] ).
cnf(2437,plain,
equal(and__dfg(t1,not__dfg(b)),not__dfg(b)),
inference(rew,[status(thm),theory(equality)],[2,2406]),
[iquote('0:Rew:2.0,2406.0')] ).
cnf(2439,plain,
equal(and__dfg(t5,not__dfg(t4)),not__dfg(t4)),
inference(rew,[status(thm),theory(equality)],[2,2408]),
[iquote('0:Rew:2.0,2408.0')] ).
cnf(2512,plain,
equal(or__dfg(t3,and__dfg(u,not__dfg(t1))),and__dfg(or__dfg(t3,u),t3)),
inference(spr,[status(thm),theory(equality)],[2165,8]),
[iquote('0:SpR:2165.0,8.0')] ).
cnf(2517,plain,
equal(or__dfg(t3,and__dfg(u,not__dfg(t1))),t3),
inference(rew,[status(thm),theory(equality)],[19,2512,2]),
[iquote('0:Rew:19.0,2512.0,2.0,2512.0')] ).
cnf(2601,plain,
equal(or__dfg(t2,and__dfg(u,not__dfg(a))),and__dfg(or__dfg(t2,u),t2)),
inference(spr,[status(thm),theory(equality)],[2166,8]),
[iquote('0:SpR:2166.0,8.0')] ).
cnf(2606,plain,
equal(or__dfg(t2,and__dfg(u,not__dfg(a))),t2),
inference(rew,[status(thm),theory(equality)],[19,2601,2]),
[iquote('0:Rew:19.0,2601.0,2.0,2601.0')] ).
cnf(2834,plain,
equal(or__dfg(not__dfg(u),and__dfg(v,u)),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[13,889]),
[iquote('0:SpR:13.0,889.0')] ).
cnf(2849,plain,
equal(or__dfg(u,not__dfg(or__dfg(v,u))),or__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[20,889]),
[iquote('0:SpR:20.0,889.0')] ).
cnf(2851,plain,
equal(or__dfg(carry,not__dfg(carry)),or__dfg(carry,t5)),
inference(spr,[status(thm),theory(equality)],[333,889]),
[iquote('0:SpR:333.0,889.0')] ).
cnf(2856,plain,
equal(or__dfg(sum__dfg,not__dfg(sum__dfg)),or__dfg(sum__dfg,t6)),
inference(spr,[status(thm),theory(equality)],[338,889]),
[iquote('0:SpR:338.0,889.0')] ).
cnf(2857,plain,
equal(or__dfg(sum__dfg,not__dfg(sum__dfg)),or__dfg(sum__dfg,t7)),
inference(spr,[status(thm),theory(equality)],[339,889]),
[iquote('0:SpR:339.0,889.0')] ).
cnf(2858,plain,
equal(or__dfg(t4,not__dfg(t4)),or__dfg(t4,t2)),
inference(spr,[status(thm),theory(equality)],[340,889]),
[iquote('0:SpR:340.0,889.0')] ).
cnf(2859,plain,
equal(or__dfg(t4,not__dfg(t4)),or__dfg(t4,t3)),
inference(spr,[status(thm),theory(equality)],[341,889]),
[iquote('0:SpR:341.0,889.0')] ).
cnf(2863,plain,
equal(or__dfg(t1,not__dfg(t1)),or__dfg(t1,a)),
inference(spr,[status(thm),theory(equality)],[345,889]),
[iquote('0:SpR:345.0,889.0')] ).
cnf(2866,plain,
equal(or__dfg(t1,not__dfg(t1)),or__dfg(t1,b)),
inference(spr,[status(thm),theory(equality)],[348,889]),
[iquote('0:SpR:348.0,889.0')] ).
cnf(2868,plain,
equal(or__dfg(t5,not__dfg(t5)),or__dfg(t5,t4)),
inference(spr,[status(thm),theory(equality)],[349,889]),
[iquote('0:SpR:349.0,889.0')] ).
cnf(2875,plain,
equal(or__dfg(t5,carry),ll1),
inference(rew,[status(thm),theory(equality)],[9,2851,1]),
[iquote('0:Rew:9.0,2851.0,1.0,2851.0')] ).
cnf(2880,plain,
equal(or__dfg(t6,sum__dfg),ll1),
inference(rew,[status(thm),theory(equality)],[9,2856,1]),
[iquote('0:Rew:9.0,2856.0,1.0,2856.0')] ).
cnf(2881,plain,
equal(or__dfg(t7,sum__dfg),ll1),
inference(rew,[status(thm),theory(equality)],[9,2857,1]),
[iquote('0:Rew:9.0,2857.0,1.0,2857.0')] ).
cnf(2882,plain,
equal(or__dfg(t2,t4),ll1),
inference(rew,[status(thm),theory(equality)],[9,2858,1]),
[iquote('0:Rew:9.0,2858.0,1.0,2858.0')] ).
cnf(2883,plain,
equal(or__dfg(t3,t4),ll1),
inference(rew,[status(thm),theory(equality)],[9,2859,1]),
[iquote('0:Rew:9.0,2859.0,1.0,2859.0')] ).
cnf(2887,plain,
equal(or__dfg(a,t1),ll1),
inference(rew,[status(thm),theory(equality)],[9,2863,1]),
[iquote('0:Rew:9.0,2863.0,1.0,2863.0')] ).
cnf(2890,plain,
equal(or__dfg(b,t1),ll1),
inference(rew,[status(thm),theory(equality)],[9,2866,1]),
[iquote('0:Rew:9.0,2866.0,1.0,2866.0')] ).
cnf(2892,plain,
equal(or__dfg(t4,t5),ll1),
inference(rew,[status(thm),theory(equality)],[9,2868,1]),
[iquote('0:Rew:9.0,2868.0,1.0,2868.0')] ).
cnf(2896,plain,
equal(xor__dfg(u,or__dfg(v,not__dfg(u))),or__dfg(not__dfg(u),not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[2834,768]),
[iquote('0:Rew:2834.0,768.0')] ).
cnf(2900,plain,
equal(xor__dfg(u,or__dfg(v,not__dfg(u))),not__dfg(and__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[21,2896]),
[iquote('0:Rew:21.0,2896.0')] ).
cnf(2983,plain,
equal(and__dfg(u,not__dfg(and__dfg(not__dfg(not__dfg(u)),v))),not__dfg(or__dfg(not__dfg(u),v))),
inference(spr,[status(thm),theory(equality)],[908,283]),
[iquote('0:SpR:908.0,283.0')] ).
cnf(3003,plain,
equal(or__dfg(not__dfg(u),and__dfg(u,v)),or__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[13,908]),
[iquote('0:SpR:13.0,908.0')] ).
cnf(3023,plain,
equal(or__dfg(u,not__dfg(or__dfg(u,v))),or__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[20,908]),
[iquote('0:SpR:20.0,908.0')] ).
cnf(3040,plain,
equal(and__dfg(u,not__dfg(and__dfg(u,v))),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[13,2983,283]),
[iquote('0:Rew:13.0,2983.0,283.0,2983.0')] ).
cnf(3041,plain,
equal(xor__dfg(u,and__dfg(u,v)),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[771,3040]),
[iquote('0:Rew:771.0,3040.0')] ).
cnf(3043,plain,
equal(and__dfg(u,not__dfg(and__dfg(u,v))),and__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[3041,771]),
[iquote('0:Rew:3041.0,771.0')] ).
cnf(3078,plain,
equal(and__dfg(or__dfg(t6,u),ll1),or__dfg(t6,and__dfg(u,sum__dfg))),
inference(spr,[status(thm),theory(equality)],[2880,8]),
[iquote('0:SpR:2880.0,8.0')] ).
cnf(3084,plain,
equal(or__dfg(t6,and__dfg(u,sum__dfg)),or__dfg(t6,u)),
inference(rew,[status(thm),theory(equality)],[144,3078,2]),
[iquote('0:Rew:144.0,3078.0,2.0,3078.0')] ).
cnf(3087,plain,
equal(and__dfg(ll1,or__dfg(t7,u)),or__dfg(t7,and__dfg(sum__dfg,u))),
inference(spr,[status(thm),theory(equality)],[2881,8]),
[iquote('0:SpR:2881.0,8.0')] ).
cnf(3094,plain,
equal(or__dfg(t7,and__dfg(sum__dfg,u)),or__dfg(t7,u)),
inference(rew,[status(thm),theory(equality)],[144,3087]),
[iquote('0:Rew:144.0,3087.0')] ).
cnf(3108,plain,
equal(or__dfg(and__dfg(u,not__dfg(or__dfg(v,not__dfg(not__dfg(u))))),and__dfg(not__dfg(u),v)),xor__dfg(u,or__dfg(v,not__dfg(not__dfg(u))))),
inference(spr,[status(thm),theory(equality)],[1101,40]),
[iquote('0:SpR:1101.0,40.0')] ).
cnf(3192,plain,
equal(or__dfg(and__dfg(not__dfg(u),v),and__dfg(u,not__dfg(or__dfg(v,u)))),xor__dfg(u,or__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[1,3108,13]),
[iquote('0:Rew:1.0,3108.0,13.0,3108.0')] ).
cnf(3193,plain,
equal(or__dfg(and__dfg(not__dfg(u),v),ll0),xor__dfg(u,or__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[619,3192]),
[iquote('0:Rew:619.0,3192.0')] ).
cnf(3194,plain,
equal(xor__dfg(u,or__dfg(v,u)),and__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[183,3193,1]),
[iquote('0:Rew:183.0,3193.0,1.0,3193.0')] ).
cnf(3204,plain,
equal(and__dfg(or__dfg(t2,u),ll1),or__dfg(t2,and__dfg(u,t4))),
inference(spr,[status(thm),theory(equality)],[2882,8]),
[iquote('0:SpR:2882.0,8.0')] ).
cnf(3210,plain,
equal(or__dfg(t2,and__dfg(u,t4)),or__dfg(t2,u)),
inference(rew,[status(thm),theory(equality)],[144,3204,2]),
[iquote('0:Rew:144.0,3204.0,2.0,3204.0')] ).
cnf(3212,plain,
equal(or__dfg(t3,or__dfg(t4,u)),or__dfg(ll1,u)),
inference(spr,[status(thm),theory(equality)],[2883,3]),
[iquote('0:SpR:2883.0,3.0')] ).
cnf(3219,plain,
equal(or__dfg(t3,or__dfg(t4,u)),ll1),
inference(rew,[status(thm),theory(equality)],[168,3212]),
[iquote('0:Rew:168.0,3212.0')] ).
cnf(3258,plain,
equal(or__dfg(and__dfg(u,not__dfg(or__dfg(not__dfg(not__dfg(u)),v))),and__dfg(not__dfg(u),v)),xor__dfg(u,or__dfg(not__dfg(not__dfg(u)),v))),
inference(spr,[status(thm),theory(equality)],[1111,40]),
[iquote('0:SpR:1111.0,40.0')] ).
cnf(3282,plain,
equal(and__dfg(or__dfg(cin,t1),and__dfg(cin,or__dfg(a,b))),and__dfg(or__dfg(cin,t1),carry_def)),
inference(spr,[status(thm),theory(equality)],[79,1111]),
[iquote('0:SpR:79.0,1111.0')] ).
cnf(3304,plain,
equal(and__dfg(or__dfg(cin,t1),and__dfg(cin,or__dfg(a,b))),and__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[2,3282]),
[iquote('0:Rew:2.0,3282.0')] ).
cnf(3305,plain,
equal(and__dfg(cin,and__dfg(or__dfg(a,b),or__dfg(cin,t1))),and__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[1880,3304,450]),
[iquote('0:Rew:1880.0,3304.0,450.0,3304.0')] ).
cnf(3314,plain,
equal(or__dfg(and__dfg(not__dfg(u),v),and__dfg(u,not__dfg(or__dfg(u,v)))),xor__dfg(u,or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[1,3258,13]),
[iquote('0:Rew:1.0,3258.0,13.0,3258.0')] ).
cnf(3315,plain,
equal(or__dfg(and__dfg(not__dfg(u),v),ll0),xor__dfg(u,or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[565,3314]),
[iquote('0:Rew:565.0,3314.0')] ).
cnf(3316,plain,
equal(xor__dfg(u,or__dfg(u,v)),and__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[183,3315,1]),
[iquote('0:Rew:183.0,3315.0,1.0,3315.0')] ).
cnf(3330,plain,
equal(or__dfg(a,or__dfg(t1,u)),or__dfg(ll1,u)),
inference(spr,[status(thm),theory(equality)],[2887,3]),
[iquote('0:SpR:2887.0,3.0')] ).
cnf(3337,plain,
equal(or__dfg(a,or__dfg(t1,u)),ll1),
inference(rew,[status(thm),theory(equality)],[168,3330]),
[iquote('0:Rew:168.0,3330.0')] ).
cnf(3364,plain,
equal(and__dfg(carry_def,or__dfg(not__dfg(or__dfg(cin,t1)),u)),or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,u))),
inference(spr,[status(thm),theory(equality)],[544,7]),
[iquote('0:SpR:544.0,7.0')] ).
cnf(3366,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(not__dfg(carry_def),or__dfg(cin,t1))),xor__dfg(carry_def,or__dfg(cin,t1))),
inference(spr,[status(thm),theory(equality)],[544,40]),
[iquote('0:SpR:544.0,40.0')] ).
cnf(3377,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,and__dfg(or__dfg(a,b),u))),or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,u))),
inference(rew,[status(thm),theory(equality)],[3364,941]),
[iquote('0:Rew:3364.0,941.0')] ).
cnf(3379,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),not__dfg(carry_def)),xor__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[2834,3366]),
[iquote('0:Rew:2834.0,3366.0')] ).
cnf(3380,plain,
equal(not__dfg(and__dfg(carry_def,or__dfg(cin,t1))),xor__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[21,3379,1]),
[iquote('0:Rew:21.0,3379.0,1.0,3379.0')] ).
cnf(3426,plain,
equal(or__dfg(not__dfg(t5),and__dfg(not__dfg(t6),t5)),xor__dfg(t6,t5)),
inference(spr,[status(thm),theory(equality)],[2232,40]),
[iquote('0:SpR:2232.0,40.0')] ).
cnf(3436,plain,
equal(not__dfg(and__dfg(t5,t6)),xor__dfg(t5,t6)),
inference(rew,[status(thm),theory(equality)],[21,3426,335,2,23]),
[iquote('0:Rew:21.0,3426.0,335.0,3426.0,2.0,3426.0,23.0,3426.0')] ).
cnf(3469,plain,
equal(or__dfg(not__dfg(cin),and__dfg(not__dfg(t7),cin)),xor__dfg(t7,cin)),
inference(spr,[status(thm),theory(equality)],[2321,40]),
[iquote('0:SpR:2321.0,40.0')] ).
cnf(3478,plain,
equal(not__dfg(and__dfg(cin,t7)),xor__dfg(cin,t7)),
inference(rew,[status(thm),theory(equality)],[21,3469,336,2,23]),
[iquote('0:Rew:21.0,3469.0,336.0,3469.0,2.0,3469.0,23.0,3469.0')] ).
cnf(3481,plain,
equal(and__dfg(t5,and__dfg(not__dfg(cin),u)),and__dfg(not__dfg(cin),u)),
inference(spr,[status(thm),theory(equality)],[2331,4]),
[iquote('0:SpR:2331.0,4.0')] ).
cnf(3484,plain,
equal(or__dfg(not__dfg(cin),and__dfg(not__dfg(t5),cin)),xor__dfg(t5,cin)),
inference(spr,[status(thm),theory(equality)],[2331,40]),
[iquote('0:SpR:2331.0,40.0')] ).
cnf(3493,plain,
equal(xor__dfg(cin,t5),t7),
inference(rew,[status(thm),theory(equality)],[13,3484,83,21,337,2,23]),
[iquote('0:Rew:13.0,3484.0,83.0,3484.0,21.0,3484.0,337.0,3484.0,2.0,3484.0,23.0,3484.0')] ).
cnf(3495,plain,
equal(xor__dfg(t5,t7),cin),
inference(spr,[status(thm),theory(equality)],[3493,972]),
[iquote('0:SpR:3493.0,972.0')] ).
cnf(3497,plain,
equal(xor__dfg(cin,t7),t5),
inference(spr,[status(thm),theory(equality)],[3493,785]),
[iquote('0:SpR:3493.0,785.0')] ).
cnf(3499,plain,
equal(not__dfg(and__dfg(cin,t7)),t5),
inference(rew,[status(thm),theory(equality)],[3497,3478]),
[iquote('0:Rew:3497.0,3478.0')] ).
cnf(3577,plain,
equal(and__dfg(cin,t7),not__dfg(t5)),
inference(spr,[status(thm),theory(equality)],[3499,13]),
[iquote('0:SpR:3499.0,13.0')] ).
cnf(3644,plain,
equal(or__dfg(and__dfg(cin,u),not__dfg(t5)),and__dfg(cin,or__dfg(u,t7))),
inference(spr,[status(thm),theory(equality)],[3577,7]),
[iquote('0:SpR:3577.0,7.0')] ).
cnf(3651,plain,
equal(or__dfg(not__dfg(t5),and__dfg(cin,u)),and__dfg(cin,or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[1,3644]),
[iquote('0:Rew:1.0,3644.0')] ).
cnf(3652,plain,
equal(and__dfg(cin,or__dfg(u,t7)),and__dfg(cin,or__dfg(u,t4))),
inference(rew,[status(thm),theory(equality)],[1110,3651]),
[iquote('0:Rew:1110.0,3651.0')] ).
cnf(3659,plain,
equal(or__dfg(not__dfg(t6),and__dfg(not__dfg(sum__dfg),t6)),xor__dfg(sum__dfg,t6)),
inference(spr,[status(thm),theory(equality)],[2341,40]),
[iquote('0:SpR:2341.0,40.0')] ).
cnf(3670,plain,
equal(not__dfg(and__dfg(t6,sum__dfg)),xor__dfg(t6,sum__dfg)),
inference(rew,[status(thm),theory(equality)],[21,3659,338,2,23]),
[iquote('0:Rew:21.0,3659.0,338.0,3659.0,2.0,3659.0,23.0,3659.0')] ).
cnf(3704,plain,
equal(xor__dfg(u,xor__dfg(v,w)),xor__dfg(w,xor__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[23,360]),
[iquote('0:SpR:23.0,360.0')] ).
cnf(3814,plain,
equal(or__dfg(not__dfg(t7),and__dfg(not__dfg(sum__dfg),t7)),xor__dfg(sum__dfg,t7)),
inference(spr,[status(thm),theory(equality)],[2351,40]),
[iquote('0:SpR:2351.0,40.0')] ).
cnf(3824,plain,
equal(not__dfg(and__dfg(t7,sum__dfg)),xor__dfg(t7,sum__dfg)),
inference(rew,[status(thm),theory(equality)],[21,3814,339,2,23]),
[iquote('0:Rew:21.0,3814.0,339.0,3814.0,2.0,3814.0,23.0,3814.0')] ).
cnf(3846,plain,
equal(or__dfg(not__dfg(t3),and__dfg(not__dfg(t4),t3)),xor__dfg(t4,t3)),
inference(spr,[status(thm),theory(equality)],[2428,40]),
[iquote('0:SpR:2428.0,40.0')] ).
cnf(3857,plain,
equal(not__dfg(and__dfg(t3,t4)),xor__dfg(t3,t4)),
inference(rew,[status(thm),theory(equality)],[21,3846,341,2,23]),
[iquote('0:Rew:21.0,3846.0,341.0,3846.0,2.0,3846.0,23.0,3846.0')] ).
cnf(3863,plain,
equal(or__dfg(not__dfg(b),and__dfg(not__dfg(t3),b)),xor__dfg(t3,b)),
inference(spr,[status(thm),theory(equality)],[2430,40]),
[iquote('0:SpR:2430.0,40.0')] ).
cnf(3872,plain,
equal(not__dfg(and__dfg(b,t3)),xor__dfg(b,t3)),
inference(rew,[status(thm),theory(equality)],[21,3863,342,2,23]),
[iquote('0:Rew:21.0,3863.0,342.0,3863.0,2.0,3863.0,23.0,3863.0')] ).
cnf(4006,plain,
equal(or__dfg(not__dfg(t1),and__dfg(not__dfg(t3),t1)),xor__dfg(t3,t1)),
inference(spr,[status(thm),theory(equality)],[2431,40]),
[iquote('0:SpR:2431.0,40.0')] ).
cnf(4016,plain,
equal(not__dfg(and__dfg(t1,t3)),xor__dfg(t1,t3)),
inference(rew,[status(thm),theory(equality)],[21,4006,343,2,23]),
[iquote('0:Rew:21.0,4006.0,343.0,4006.0,2.0,4006.0,23.0,4006.0')] ).
cnf(4037,plain,
equal(or__dfg(not__dfg(a),and__dfg(not__dfg(t1),a)),xor__dfg(t1,a)),
inference(spr,[status(thm),theory(equality)],[2433,40]),
[iquote('0:SpR:2433.0,40.0')] ).
cnf(4046,plain,
equal(xor__dfg(a,t1),t2),
inference(rew,[status(thm),theory(equality)],[13,4037,72,21,345,2,23]),
[iquote('0:Rew:13.0,4037.0,72.0,4037.0,21.0,4037.0,345.0,4037.0,2.0,4037.0,23.0,4037.0')] ).
cnf(4048,plain,
equal(xor__dfg(t1,t2),a),
inference(spr,[status(thm),theory(equality)],[4046,972]),
[iquote('0:SpR:4046.0,972.0')] ).
cnf(4186,plain,
equal(and__dfg(u,and__dfg(v,w)),and__dfg(w,and__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[2,408]),
[iquote('0:SpR:2.0,408.0')] ).
cnf(4596,plain,
equal(or__dfg(or__dfg(u,v),and__dfg(u,w)),or__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[417,931]),
[iquote('0:SpR:417.0,931.0')] ).
cnf(4694,plain,
equal(and__dfg(u,and__dfg(v,or__dfg(u,w))),and__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[2,417]),
[iquote('0:SpR:2.0,417.0')] ).
cnf(4728,plain,
equal(or__dfg(u,or__dfg(v,and__dfg(u,w))),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[3,4596]),
[iquote('0:Rew:3.0,4596.0')] ).
cnf(4732,plain,
equal(and__dfg(carry_def,or__dfg(cin,t1)),and__dfg(cin,or__dfg(a,b))),
inference(rew,[status(thm),theory(equality)],[4694,3305]),
[iquote('0:Rew:4694.0,3305.0')] ).
cnf(4734,plain,
equal(not__dfg(and__dfg(cin,or__dfg(a,b))),xor__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[4732,3380]),
[iquote('0:Rew:4732.0,3380.0')] ).
cnf(4770,plain,
equal(and__dfg(t7,or__dfg(not__dfg(t5),u)),or__dfg(not__dfg(t5),and__dfg(t7,u))),
inference(spr,[status(thm),theory(equality)],[2434,7]),
[iquote('0:SpR:2434.0,7.0')] ).
cnf(4773,plain,
equal(or__dfg(not__dfg(t5),and__dfg(not__dfg(t7),t5)),xor__dfg(t7,t5)),
inference(spr,[status(thm),theory(equality)],[2434,40]),
[iquote('0:SpR:2434.0,40.0')] ).
cnf(4785,plain,
equal(not__dfg(and__dfg(t5,t7)),cin),
inference(rew,[status(thm),theory(equality)],[21,4773,346,2,3495,23]),
[iquote('0:Rew:21.0,4773.0,346.0,4773.0,2.0,4773.0,3495.0,4773.0,23.0,4773.0')] ).
cnf(4789,plain,
equal(and__dfg(t5,t7),not__dfg(cin)),
inference(spr,[status(thm),theory(equality)],[4785,13]),
[iquote('0:SpR:4785.0,13.0')] ).
cnf(4877,plain,
equal(or__dfg(not__dfg(t1),and__dfg(not__dfg(t2),t1)),xor__dfg(t2,t1)),
inference(spr,[status(thm),theory(equality)],[2436,40]),
[iquote('0:SpR:2436.0,40.0')] ).
cnf(4889,plain,
equal(not__dfg(and__dfg(t1,t2)),a),
inference(rew,[status(thm),theory(equality)],[21,4877,347,2,4048,23]),
[iquote('0:Rew:21.0,4877.0,347.0,4877.0,2.0,4877.0,4048.0,4877.0,23.0,4877.0')] ).
cnf(4957,plain,
equal(and__dfg(u,and__dfg(v,or__dfg(w,u))),and__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[185,450]),
[iquote('0:SpR:185.0,450.0')] ).
cnf(4970,plain,
equal(and__dfg(t2,and__dfg(u,t3)),and__dfg(u,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[66,450]),
[iquote('0:SpR:66.0,450.0')] ).
cnf(4975,plain,
equal(and__dfg(cin,and__dfg(u,t4)),and__dfg(u,not__dfg(t5))),
inference(spr,[status(thm),theory(equality)],[80,450]),
[iquote('0:SpR:80.0,450.0')] ).
cnf(5012,plain,
equal(and__dfg(t5,and__dfg(u,not__dfg(cin))),and__dfg(u,not__dfg(cin))),
inference(spr,[status(thm),theory(equality)],[2331,450]),
[iquote('0:SpR:2331.0,450.0')] ).
cnf(5186,plain,
equal(and__dfg(t1,t2),not__dfg(a)),
inference(spr,[status(thm),theory(equality)],[4889,13]),
[iquote('0:SpR:4889.0,13.0')] ).
cnf(5277,plain,
equal(or__dfg(not__dfg(b),and__dfg(not__dfg(t1),b)),xor__dfg(t1,b)),
inference(spr,[status(thm),theory(equality)],[2437,40]),
[iquote('0:SpR:2437.0,40.0')] ).
cnf(5290,plain,
equal(xor__dfg(b,t1),t3),
inference(rew,[status(thm),theory(equality)],[13,5277,69,21,348,2,23]),
[iquote('0:Rew:13.0,5277.0,69.0,5277.0,21.0,5277.0,348.0,5277.0,2.0,5277.0,23.0,5277.0')] ).
cnf(5294,plain,
equal(xor__dfg(t1,t3),b),
inference(spr,[status(thm),theory(equality)],[5290,972]),
[iquote('0:SpR:5290.0,972.0')] ).
cnf(5298,plain,
equal(xor__dfg(b,t3),t1),
inference(spr,[status(thm),theory(equality)],[5290,785]),
[iquote('0:SpR:5290.0,785.0')] ).
cnf(5302,plain,
equal(not__dfg(and__dfg(t1,t3)),b),
inference(rew,[status(thm),theory(equality)],[5294,4016]),
[iquote('0:Rew:5294.0,4016.0')] ).
cnf(5303,plain,
equal(not__dfg(and__dfg(b,t3)),t1),
inference(rew,[status(thm),theory(equality)],[5298,3872]),
[iquote('0:Rew:5298.0,3872.0')] ).
cnf(5447,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(w,or__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[1,476]),
[iquote('0:SpR:1.0,476.0')] ).
cnf(5810,plain,
equal(and__dfg(t1,t3),not__dfg(b)),
inference(spr,[status(thm),theory(equality)],[5302,13]),
[iquote('0:SpR:5302.0,13.0')] ).
cnf(5874,plain,
equal(and__dfg(b,t3),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[5303,13]),
[iquote('0:SpR:5303.0,13.0')] ).
cnf(6289,plain,
equal(or__dfg(not__dfg(t1),and__dfg(b,u)),and__dfg(b,or__dfg(t3,u))),
inference(spr,[status(thm),theory(equality)],[5874,7]),
[iquote('0:SpR:5874.0,7.0')] ).
cnf(6316,plain,
equal(or__dfg(not__dfg(t4),and__dfg(not__dfg(t5),t4)),xor__dfg(t5,t4)),
inference(spr,[status(thm),theory(equality)],[2439,40]),
[iquote('0:SpR:2439.0,40.0')] ).
cnf(6331,plain,
equal(xor__dfg(t4,t5),t6),
inference(rew,[status(thm),theory(equality)],[13,6316,63,21,349,2,23]),
[iquote('0:Rew:13.0,6316.0,63.0,6316.0,21.0,6316.0,349.0,6316.0,2.0,6316.0,23.0,6316.0')] ).
cnf(6335,plain,
equal(xor__dfg(t5,t6),t4),
inference(spr,[status(thm),theory(equality)],[6331,972]),
[iquote('0:SpR:6331.0,972.0')] ).
cnf(6343,plain,
equal(not__dfg(and__dfg(t5,t6)),t4),
inference(rew,[status(thm),theory(equality)],[6335,3436]),
[iquote('0:Rew:6335.0,3436.0')] ).
cnf(6466,plain,
equal(or__dfg(u,and__dfg(not__dfg(u),v)),or__dfg(u,xor__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[40,488]),
[iquote('0:SpR:40.0,488.0')] ).
cnf(6491,plain,
equal(or__dfg(u,xor__dfg(u,v)),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[908,6466]),
[iquote('0:Rew:908.0,6466.0')] ).
cnf(6545,plain,
equal(and__dfg(t5,t6),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[6343,13]),
[iquote('0:SpR:6343.0,13.0')] ).
cnf(6675,plain,
equal(or__dfg(u,and__dfg(v,w)),or__dfg(and__dfg(w,v),u)),
inference(spr,[status(thm),theory(equality)],[928,1]),
[iquote('0:SpR:928.0,1.0')] ).
cnf(8152,plain,
equal(or__dfg(and__dfg(and__dfg(u,v),not__dfg(or__dfg(u,v))),not__dfg(xor__dfg(u,not__dfg(v)))),xor__dfg(and__dfg(u,v),not__dfg(not__dfg(or__dfg(u,v))))),
inference(spr,[status(thm),theory(equality)],[725]),
[iquote('0:SpR:725.0,725.0')] ).
cnf(8221,plain,
equal(or__dfg(and__dfg(b,t1),not__dfg(ll1)),xor__dfg(b,not__dfg(t1))),
inference(spr,[status(thm),theory(equality)],[2890,725]),
[iquote('0:SpR:2890.0,725.0')] ).
cnf(8261,plain,
equal(or__dfg(and__dfg(t5,carry),not__dfg(ll1)),xor__dfg(t5,not__dfg(carry))),
inference(spr,[status(thm),theory(equality)],[2875,725]),
[iquote('0:SpR:2875.0,725.0')] ).
cnf(8269,plain,
equal(or__dfg(and__dfg(t7,sum__dfg),not__dfg(ll1)),xor__dfg(t7,not__dfg(sum__dfg))),
inference(spr,[status(thm),theory(equality)],[2881,725]),
[iquote('0:SpR:2881.0,725.0')] ).
cnf(8271,plain,
equal(or__dfg(and__dfg(t3,t4),not__dfg(ll1)),xor__dfg(t3,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[2883,725]),
[iquote('0:SpR:2883.0,725.0')] ).
cnf(8276,plain,
equal(or__dfg(and__dfg(t4,t5),not__dfg(ll1)),xor__dfg(t4,not__dfg(t5))),
inference(spr,[status(thm),theory(equality)],[2892,725]),
[iquote('0:SpR:2892.0,725.0')] ).
cnf(8298,plain,
equal(or__dfg(not__dfg(carry),not__dfg(or__dfg(t1,t5))),xor__dfg(t1,not__dfg(t5))),
inference(spr,[status(thm),theory(equality)],[57,725]),
[iquote('0:SpR:57.0,725.0')] ).
cnf(8307,plain,
equal(or__dfg(not__dfg(t1),not__dfg(or__dfg(a,b))),xor__dfg(a,not__dfg(b))),
inference(spr,[status(thm),theory(equality)],[75,725]),
[iquote('0:SpR:75.0,725.0')] ).
cnf(8309,plain,
equal(or__dfg(not__dfg(t5),not__dfg(or__dfg(cin,t4))),xor__dfg(cin,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[80,725]),
[iquote('0:SpR:80.0,725.0')] ).
cnf(8357,plain,
equal(or__dfg(ll0,not__dfg(or__dfg(t6,xor__dfg(t7,not__dfg(sum__dfg))))),xor__dfg(t6,not__dfg(xor__dfg(t7,not__dfg(sum__dfg))))),
inference(spr,[status(thm),theory(equality)],[1682,725]),
[iquote('0:SpR:1682.0,725.0')] ).
cnf(8358,plain,
equal(or__dfg(ll0,not__dfg(or__dfg(t2,xor__dfg(t3,not__dfg(t4))))),xor__dfg(t2,not__dfg(xor__dfg(t3,not__dfg(t4))))),
inference(spr,[status(thm),theory(equality)],[1683,725]),
[iquote('0:SpR:1683.0,725.0')] ).
cnf(8361,plain,
equal(or__dfg(ll0,not__dfg(or__dfg(a,xor__dfg(b,not__dfg(t1))))),xor__dfg(a,not__dfg(xor__dfg(b,not__dfg(t1))))),
inference(spr,[status(thm),theory(equality)],[1686,725]),
[iquote('0:SpR:1686.0,725.0')] ).
cnf(8376,plain,
equal(xor__dfg(b,not__dfg(t1)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[183,8221,1,69,15]),
[iquote('0:Rew:183.0,8221.0,1.0,8221.0,69.0,8221.0,15.0,8221.0')] ).
cnf(8377,plain,
equal(and__dfg(a,not__dfg(t3)),ll0),
inference(rew,[status(thm),theory(equality)],[8376,1686]),
[iquote('0:Rew:8376.0,1686.0')] ).
cnf(8383,plain,
equal(xor__dfg(t5,not__dfg(carry)),and__dfg(t5,carry)),
inference(rew,[status(thm),theory(equality)],[183,8261,1,15]),
[iquote('0:Rew:183.0,8261.0,1.0,8261.0,15.0,8261.0')] ).
cnf(8404,plain,
equal(xor__dfg(t7,not__dfg(sum__dfg)),and__dfg(t7,sum__dfg)),
inference(rew,[status(thm),theory(equality)],[183,8269,1,15]),
[iquote('0:Rew:183.0,8269.0,1.0,8269.0,15.0,8269.0')] ).
cnf(8416,plain,
equal(xor__dfg(t3,not__dfg(t4)),and__dfg(t3,t4)),
inference(rew,[status(thm),theory(equality)],[183,8271,1,15]),
[iquote('0:Rew:183.0,8271.0,1.0,8271.0,15.0,8271.0')] ).
cnf(8446,plain,
equal(xor__dfg(t4,not__dfg(t5)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[183,8276,1,63,15]),
[iquote('0:Rew:183.0,8276.0,1.0,8276.0,63.0,8276.0,15.0,8276.0')] ).
cnf(8447,plain,
equal(and__dfg(cin,not__dfg(t6)),ll0),
inference(rew,[status(thm),theory(equality)],[8446,1687]),
[iquote('0:Rew:8446.0,1687.0')] ).
cnf(8459,plain,
equal(not__dfg(and__dfg(carry,or__dfg(t1,t5))),xor__dfg(t1,not__dfg(t5))),
inference(rew,[status(thm),theory(equality)],[21,8298]),
[iquote('0:Rew:21.0,8298.0')] ).
cnf(8468,plain,
equal(not__dfg(and__dfg(t1,or__dfg(a,b))),xor__dfg(a,not__dfg(b))),
inference(rew,[status(thm),theory(equality)],[21,8307]),
[iquote('0:Rew:21.0,8307.0')] ).
cnf(8470,plain,
equal(not__dfg(and__dfg(t5,or__dfg(cin,t4))),xor__dfg(cin,not__dfg(t4))),
inference(rew,[status(thm),theory(equality)],[21,8309]),
[iquote('0:Rew:21.0,8309.0')] ).
cnf(8631,plain,
equal(not__dfg(or__dfg(t6,xor__dfg(t7,not__dfg(sum__dfg)))),xor__dfg(t6,not__dfg(xor__dfg(t7,not__dfg(sum__dfg))))),
inference(rew,[status(thm),theory(equality)],[183,8357]),
[iquote('0:Rew:183.0,8357.0')] ).
cnf(8632,plain,
equal(xor__dfg(t6,xor__dfg(t7,sum__dfg)),not__dfg(or__dfg(t6,t7))),
inference(rew,[status(thm),theory(equality)],[3084,8631,3824,8404]),
[iquote('0:Rew:3084.0,8631.0,3824.0,8631.0,8404.0,8631.0')] ).
cnf(8633,plain,
equal(not__dfg(or__dfg(t2,xor__dfg(t3,not__dfg(t4)))),xor__dfg(t2,not__dfg(xor__dfg(t3,not__dfg(t4))))),
inference(rew,[status(thm),theory(equality)],[183,8358]),
[iquote('0:Rew:183.0,8358.0')] ).
cnf(8634,plain,
equal(xor__dfg(t2,xor__dfg(t3,t4)),not__dfg(or__dfg(t2,t3))),
inference(rew,[status(thm),theory(equality)],[3210,8633,3857,8416]),
[iquote('0:Rew:3210.0,8633.0,3857.0,8633.0,8416.0,8633.0')] ).
cnf(8641,plain,
equal(not__dfg(or__dfg(a,xor__dfg(b,not__dfg(t1)))),xor__dfg(a,not__dfg(xor__dfg(b,not__dfg(t1))))),
inference(rew,[status(thm),theory(equality)],[183,8361]),
[iquote('0:Rew:183.0,8361.0')] ).
cnf(8642,plain,
equal(not__dfg(or__dfg(a,not__dfg(t3))),xor__dfg(a,not__dfg(not__dfg(t3)))),
inference(rew,[status(thm),theory(equality)],[8376,8641]),
[iquote('0:Rew:8376.0,8641.0')] ).
cnf(8643,plain,
equal(and__dfg(t3,not__dfg(a)),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[2,8642,280,13]),
[iquote('0:Rew:2.0,8642.0,280.0,8642.0,13.0,8642.0')] ).
cnf(8671,plain,
equal(or__dfg(not__dfg(xor__dfg(u,not__dfg(v))),and__dfg(u,and__dfg(v,not__dfg(or__dfg(u,v))))),xor__dfg(or__dfg(u,v),and__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[1,8152,4,23,13]),
[iquote('0:Rew:1.0,8152.0,4.0,8152.0,23.0,8152.0,13.0,8152.0')] ).
cnf(8672,plain,
equal(or__dfg(and__dfg(ll0,u),xor__dfg(u,not__dfg(not__dfg(v)))),xor__dfg(or__dfg(u,v),and__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[6675,8671,800,619]),
[iquote('0:Rew:6675.0,8671.0,800.0,8671.0,619.0,8671.0')] ).
cnf(8673,plain,
equal(xor__dfg(or__dfg(u,v),and__dfg(u,v)),xor__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[183,8672,143,13]),
[iquote('0:Rew:183.0,8672.0,143.0,8672.0,13.0,8672.0')] ).
cnf(8696,plain,
equal(or__dfg(t3,a),or__dfg(t3,ll0)),
inference(spr,[status(thm),theory(equality)],[8377,889]),
[iquote('0:SpR:8377.0,889.0')] ).
cnf(8704,plain,
equal(or__dfg(a,t3),t3),
inference(rew,[status(thm),theory(equality)],[1,8696,183]),
[iquote('0:Rew:1.0,8696.0,183.0,8696.0,1.0,8696.0')] ).
cnf(8718,plain,
equal(and__dfg(a,t3),a),
inference(spr,[status(thm),theory(equality)],[8704,19]),
[iquote('0:SpR:8704.0,19.0')] ).
cnf(8719,plain,
equal(or__dfg(and__dfg(a,t3),not__dfg(t3)),xor__dfg(a,not__dfg(t3))),
inference(spr,[status(thm),theory(equality)],[8704,725]),
[iquote('0:SpR:8704.0,725.0')] ).
cnf(8722,plain,
equal(and__dfg(a,and__dfg(t3,u)),and__dfg(a,u)),
inference(spr,[status(thm),theory(equality)],[8704,417]),
[iquote('0:SpR:8704.0,417.0')] ).
cnf(8734,plain,
equal(or__dfg(not__dfg(t3),and__dfg(a,t3)),xor__dfg(a,not__dfg(t3))),
inference(rew,[status(thm),theory(equality)],[1,8719]),
[iquote('0:Rew:1.0,8719.0')] ).
cnf(8735,plain,
equal(or__dfg(not__dfg(t3),a),xor__dfg(a,not__dfg(t3))),
inference(rew,[status(thm),theory(equality)],[8718,8734]),
[iquote('0:Rew:8718.0,8734.0')] ).
cnf(8736,plain,
equal(or__dfg(a,not__dfg(t3)),xor__dfg(a,not__dfg(t3))),
inference(rew,[status(thm),theory(equality)],[1,8735]),
[iquote('0:Rew:1.0,8735.0')] ).
cnf(8773,plain,
equal(or__dfg(t6,cin),or__dfg(t6,ll0)),
inference(spr,[status(thm),theory(equality)],[8447,889]),
[iquote('0:SpR:8447.0,889.0')] ).
cnf(8781,plain,
equal(or__dfg(cin,t6),t6),
inference(rew,[status(thm),theory(equality)],[1,8773,183]),
[iquote('0:Rew:1.0,8773.0,183.0,8773.0,1.0,8773.0')] ).
cnf(8806,plain,
equal(or__dfg(and__dfg(u,or__dfg(and__dfg(v,u),w)),and__dfg(v,u)),and__dfg(u,or__dfg(and__dfg(v,u),w))),
inference(spr,[status(thm),theory(equality)],[405,146]),
[iquote('0:SpR:405.0,146.0')] ).
cnf(9044,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(v,or__dfg(and__dfg(u,v),w))),and__dfg(v,or__dfg(and__dfg(u,v),w))),
inference(rew,[status(thm),theory(equality)],[1,8806]),
[iquote('0:Rew:1.0,8806.0')] ).
cnf(9045,plain,
equal(and__dfg(u,or__dfg(v,or__dfg(and__dfg(v,u),w))),and__dfg(u,or__dfg(and__dfg(v,u),w))),
inference(rew,[status(thm),theory(equality)],[1053,9044]),
[iquote('0:Rew:1053.0,9044.0')] ).
cnf(9046,plain,
equal(and__dfg(u,or__dfg(and__dfg(v,u),w)),and__dfg(u,or__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[488,9045]),
[iquote('0:Rew:488.0,9045.0')] ).
cnf(9609,plain,
equal(and__dfg(or__dfg(and__dfg(u,v),w),v),or__dfg(and__dfg(u,v),and__dfg(w,v))),
inference(spr,[status(thm),theory(equality)],[146,813]),
[iquote('0:SpR:146.0,813.0')] ).
cnf(9829,plain,
equal(and__dfg(t3,or__dfg(u,a)),or__dfg(a,and__dfg(t3,u))),
inference(spr,[status(thm),theory(equality)],[8704,813]),
[iquote('0:SpR:8704.0,813.0')] ).
cnf(10087,plain,
equal(and__dfg(u,or__dfg(and__dfg(v,u),w)),or__dfg(and__dfg(v,u),and__dfg(w,u))),
inference(rew,[status(thm),theory(equality)],[2,9609]),
[iquote('0:Rew:2.0,9609.0')] ).
cnf(10088,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(w,v)),and__dfg(v,or__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[9046,10087]),
[iquote('0:Rew:9046.0,10087.0')] ).
cnf(10473,plain,
equal(and__dfg(t6,or__dfg(t6,u)),or__dfg(t6,and__dfg(cin,u))),
inference(spr,[status(thm),theory(equality)],[8781,847]),
[iquote('0:SpR:8781.0,847.0')] ).
cnf(10480,plain,
equal(and__dfg(t3,or__dfg(t3,u)),or__dfg(t3,and__dfg(a,u))),
inference(spr,[status(thm),theory(equality)],[8704,847]),
[iquote('0:SpR:8704.0,847.0')] ).
cnf(10546,plain,
equal(or__dfg(t6,and__dfg(cin,u)),t6),
inference(rew,[status(thm),theory(equality)],[19,10473]),
[iquote('0:Rew:19.0,10473.0')] ).
cnf(10553,plain,
equal(or__dfg(t3,and__dfg(a,u)),t3),
inference(rew,[status(thm),theory(equality)],[19,10480]),
[iquote('0:Rew:19.0,10480.0')] ).
cnf(10890,plain,
equal(or__dfg(and__dfg(t7,u),not__dfg(t5)),and__dfg(t7,or__dfg(u,cin))),
inference(spr,[status(thm),theory(equality)],[3577,1011]),
[iquote('0:SpR:3577.0,1011.0')] ).
cnf(11081,plain,
equal(or__dfg(not__dfg(t5),and__dfg(t7,u)),and__dfg(t7,or__dfg(u,cin))),
inference(rew,[status(thm),theory(equality)],[1,10890]),
[iquote('0:Rew:1.0,10890.0')] ).
cnf(11082,plain,
equal(and__dfg(t7,or__dfg(not__dfg(t5),u)),and__dfg(t7,or__dfg(u,cin))),
inference(rew,[status(thm),theory(equality)],[11081,4770]),
[iquote('0:Rew:11081.0,4770.0')] ).
cnf(11682,plain,
equal(or__dfg(not__dfg(t1),and__dfg(b,u)),and__dfg(b,or__dfg(a,u))),
inference(spr,[status(thm),theory(equality)],[75,1053]),
[iquote('0:SpR:75.0,1053.0')] ).
cnf(11796,plain,
equal(and__dfg(b,or__dfg(t3,u)),and__dfg(b,or__dfg(a,u))),
inference(rew,[status(thm),theory(equality)],[6289,11682]),
[iquote('0:Rew:6289.0,11682.0')] ).
cnf(13025,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,or__dfg(a,b))),or__dfg(carry_def,and__dfg(and__dfg(cin,or__dfg(a,b)),u))),
inference(spr,[status(thm),theory(equality)],[18,541]),
[iquote('0:SpR:18.0,541.0')] ).
cnf(13067,plain,
equal(or__dfg(carry_def,and__dfg(cin,and__dfg(or__dfg(a,b),u))),carry_def),
inference(rew,[status(thm),theory(equality)],[79,13025,4]),
[iquote('0:Rew:79.0,13025.0,4.0,13025.0')] ).
cnf(14941,plain,
equal(or__dfg(t6,not__dfg(t7)),t6),
inference(spr,[status(thm),theory(equality)],[83,10546]),
[iquote('0:SpR:83.0,10546.0')] ).
cnf(14977,plain,
equal(or__dfg(and__dfg(t6,not__dfg(t7)),not__dfg(t6)),xor__dfg(t6,not__dfg(not__dfg(t7)))),
inference(spr,[status(thm),theory(equality)],[14941,725]),
[iquote('0:SpR:14941.0,725.0')] ).
cnf(14985,plain,
equal(and__dfg(not__dfg(t6),t7),not__dfg(t6)),
inference(spr,[status(thm),theory(equality)],[14941,280]),
[iquote('0:SpR:14941.0,280.0')] ).
cnf(14987,plain,
equal(and__dfg(not__dfg(t7),t6),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[14941,185]),
[iquote('0:SpR:14941.0,185.0')] ).
cnf(14999,plain,
equal(and__dfg(t7,not__dfg(t6)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[2,14985]),
[iquote('0:Rew:2.0,14985.0')] ).
cnf(15000,plain,
equal(and__dfg(t6,not__dfg(t7)),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[2,14987]),
[iquote('0:Rew:2.0,14987.0')] ).
cnf(15008,plain,
equal(or__dfg(not__dfg(t6),and__dfg(t6,not__dfg(t7))),xor__dfg(t6,t7)),
inference(rew,[status(thm),theory(equality)],[1,14977,13]),
[iquote('0:Rew:1.0,14977.0,13.0,14977.0')] ).
cnf(15009,plain,
equal(or__dfg(not__dfg(t6),not__dfg(t7)),xor__dfg(t6,t7)),
inference(rew,[status(thm),theory(equality)],[15000,15008]),
[iquote('0:Rew:15000.0,15008.0')] ).
cnf(15010,plain,
equal(xor__dfg(t6,t7),sum__dfg),
inference(rew,[status(thm),theory(equality)],[13,15009,60,21]),
[iquote('0:Rew:13.0,15009.0,60.0,15009.0,21.0,15009.0')] ).
cnf(15014,plain,
equal(xor__dfg(t7,sum__dfg),t6),
inference(spr,[status(thm),theory(equality)],[15010,972]),
[iquote('0:SpR:15010.0,972.0')] ).
cnf(15018,plain,
equal(xor__dfg(t6,sum__dfg),t7),
inference(spr,[status(thm),theory(equality)],[15010,785]),
[iquote('0:SpR:15010.0,785.0')] ).
cnf(15023,plain,
equal(not__dfg(or__dfg(t6,t7)),xor__dfg(t6,t6)),
inference(rew,[status(thm),theory(equality)],[15014,8632]),
[iquote('0:Rew:15014.0,8632.0')] ).
cnf(15024,plain,
equal(not__dfg(and__dfg(t6,sum__dfg)),t7),
inference(rew,[status(thm),theory(equality)],[15018,3670]),
[iquote('0:Rew:15018.0,3670.0')] ).
cnf(15025,plain,
equal(not__dfg(or__dfg(t6,t7)),ll0),
inference(rew,[status(thm),theory(equality)],[691,15023]),
[iquote('0:Rew:691.0,15023.0')] ).
cnf(15606,plain,
equal(and__dfg(t6,sum__dfg),not__dfg(t7)),
inference(spr,[status(thm),theory(equality)],[15024,13]),
[iquote('0:SpR:15024.0,13.0')] ).
cnf(15709,plain,
equal(or__dfg(t6,t7),not__dfg(ll0)),
inference(spr,[status(thm),theory(equality)],[15025,13]),
[iquote('0:SpR:15025.0,13.0')] ).
cnf(15746,plain,
equal(or__dfg(t6,t7),ll1),
inference(rew,[status(thm),theory(equality)],[14,15709]),
[iquote('0:Rew:14.0,15709.0')] ).
cnf(18018,plain,
equal(or__dfg(t3,not__dfg(t2)),t3),
inference(spr,[status(thm),theory(equality)],[72,10553]),
[iquote('0:SpR:72.0,10553.0')] ).
cnf(18058,plain,
equal(or__dfg(and__dfg(t3,not__dfg(t2)),not__dfg(t3)),xor__dfg(t3,not__dfg(not__dfg(t2)))),
inference(spr,[status(thm),theory(equality)],[18018,725]),
[iquote('0:SpR:18018.0,725.0')] ).
cnf(18067,plain,
equal(and__dfg(not__dfg(t3),t2),not__dfg(t3)),
inference(spr,[status(thm),theory(equality)],[18018,280]),
[iquote('0:SpR:18018.0,280.0')] ).
cnf(18070,plain,
equal(and__dfg(not__dfg(t2),t3),not__dfg(t2)),
inference(spr,[status(thm),theory(equality)],[18018,185]),
[iquote('0:SpR:18018.0,185.0')] ).
cnf(18083,plain,
equal(and__dfg(t2,not__dfg(t3)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[2,18067]),
[iquote('0:Rew:2.0,18067.0')] ).
cnf(18084,plain,
equal(and__dfg(t3,not__dfg(t2)),not__dfg(t2)),
inference(rew,[status(thm),theory(equality)],[2,18070]),
[iquote('0:Rew:2.0,18070.0')] ).
cnf(18092,plain,
equal(or__dfg(not__dfg(t3),and__dfg(t3,not__dfg(t2))),xor__dfg(t2,t3)),
inference(rew,[status(thm),theory(equality)],[1,18058,23,13]),
[iquote('0:Rew:1.0,18058.0,23.0,18058.0,13.0,18058.0')] ).
cnf(18093,plain,
equal(or__dfg(not__dfg(t3),not__dfg(t2)),xor__dfg(t2,t3)),
inference(rew,[status(thm),theory(equality)],[18084,18092]),
[iquote('0:Rew:18084.0,18092.0')] ).
cnf(18094,plain,
equal(xor__dfg(t2,t3),t4),
inference(rew,[status(thm),theory(equality)],[13,18093,66,21,1]),
[iquote('0:Rew:13.0,18093.0,66.0,18093.0,21.0,18093.0,1.0,18093.0')] ).
cnf(18103,plain,
equal(xor__dfg(t3,t4),t2),
inference(spr,[status(thm),theory(equality)],[18094,972]),
[iquote('0:SpR:18094.0,972.0')] ).
cnf(18112,plain,
equal(not__dfg(or__dfg(t2,t3)),xor__dfg(t2,t2)),
inference(rew,[status(thm),theory(equality)],[18103,8634]),
[iquote('0:Rew:18103.0,8634.0')] ).
cnf(18114,plain,
equal(not__dfg(or__dfg(t2,t3)),ll0),
inference(rew,[status(thm),theory(equality)],[691,18112]),
[iquote('0:Rew:691.0,18112.0')] ).
cnf(19672,plain,
equal(or__dfg(t2,t3),not__dfg(ll0)),
inference(spr,[status(thm),theory(equality)],[18114,13]),
[iquote('0:SpR:18114.0,13.0')] ).
cnf(19712,plain,
equal(or__dfg(t2,t3),ll1),
inference(rew,[status(thm),theory(equality)],[14,19672]),
[iquote('0:Rew:14.0,19672.0')] ).
cnf(23164,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,or__dfg(a,b))),or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,or__dfg(a,b)))),
inference(spr,[status(thm),theory(equality)],[12,3377]),
[iquote('0:SpR:12.0,3377.0')] ).
cnf(23166,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,or__dfg(or__dfg(a,b),u))),or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(cin,or__dfg(a,b)))),
inference(spr,[status(thm),theory(equality)],[19,3377]),
[iquote('0:SpR:19.0,3377.0')] ).
cnf(23197,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,or__dfg(a,b))),carry_def),
inference(rew,[status(thm),theory(equality)],[79,23164]),
[iquote('0:Rew:79.0,23164.0')] ).
cnf(23203,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,or__dfg(a,or__dfg(b,u)))),carry_def),
inference(rew,[status(thm),theory(equality)],[3,23166,79]),
[iquote('0:Rew:3.0,23166.0,79.0,23166.0')] ).
cnf(23920,plain,
equal(or__dfg(not__dfg(t5),and__dfg(not__dfg(cin),and__dfg(t5,u))),and__dfg(xor__dfg(cin,t5),or__dfg(not__dfg(t5),u))),
inference(spr,[status(thm),theory(equality)],[337,943]),
[iquote('0:SpR:337.0,943.0')] ).
cnf(23982,plain,
equal(or__dfg(not__dfg(t5),and__dfg(t5,and__dfg(u,not__dfg(cin)))),and__dfg(t7,or__dfg(not__dfg(t5),u))),
inference(rew,[status(thm),theory(equality)],[408,23920,3493]),
[iquote('0:Rew:408.0,23920.0,3493.0,23920.0')] ).
cnf(23983,plain,
equal(or__dfg(not__dfg(t5),and__dfg(u,not__dfg(cin))),and__dfg(t7,or__dfg(u,cin))),
inference(rew,[status(thm),theory(equality)],[5012,23982,11082]),
[iquote('0:Rew:5012.0,23982.0,11082.0,23982.0')] ).
cnf(28852,plain,
equal(or__dfg(and__dfg(cin,not__dfg(or__dfg(u,t7))),not__dfg(cin)),xor__dfg(cin,not__dfg(not__dfg(or__dfg(u,t7))))),
inference(spr,[status(thm),theory(equality)],[1491,725]),
[iquote('0:SpR:1491.0,725.0')] ).
cnf(28867,plain,
equal(and__dfg(not__dfg(or__dfg(u,t7)),cin),not__dfg(or__dfg(u,t7))),
inference(spr,[status(thm),theory(equality)],[1491,185]),
[iquote('0:SpR:1491.0,185.0')] ).
cnf(28897,plain,
equal(and__dfg(cin,not__dfg(or__dfg(u,t7))),not__dfg(or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[2,28867]),
[iquote('0:Rew:2.0,28867.0')] ).
cnf(28905,plain,
equal(or__dfg(not__dfg(cin),and__dfg(cin,not__dfg(or__dfg(u,t7)))),xor__dfg(cin,or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[1,28852,13]),
[iquote('0:Rew:1.0,28852.0,13.0,28852.0')] ).
cnf(28906,plain,
equal(or__dfg(not__dfg(cin),not__dfg(or__dfg(u,t7))),xor__dfg(cin,or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[28897,28905]),
[iquote('0:Rew:28897.0,28905.0')] ).
cnf(28907,plain,
equal(not__dfg(and__dfg(cin,or__dfg(u,t7))),xor__dfg(cin,or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[21,28906]),
[iquote('0:Rew:21.0,28906.0')] ).
cnf(28908,plain,
equal(not__dfg(and__dfg(cin,or__dfg(u,t4))),xor__dfg(cin,or__dfg(u,t7))),
inference(rew,[status(thm),theory(equality)],[3652,28907]),
[iquote('0:Rew:3652.0,28907.0')] ).
cnf(31758,plain,
equal(or__dfg(and__dfg(t5,and__dfg(not__dfg(cin),u)),not__dfg(t5)),xor__dfg(t5,not__dfg(and__dfg(not__dfg(cin),u)))),
inference(spr,[status(thm),theory(equality)],[2332,725]),
[iquote('0:SpR:2332.0,725.0')] ).
cnf(31829,plain,
equal(or__dfg(not__dfg(t5),and__dfg(t5,and__dfg(not__dfg(cin),u))),xor__dfg(t5,or__dfg(cin,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[1,31758,252]),
[iquote('0:Rew:1.0,31758.0,252.0,31758.0')] ).
cnf(31830,plain,
equal(or__dfg(not__dfg(t5),and__dfg(not__dfg(cin),u)),xor__dfg(t5,or__dfg(cin,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[3481,31829]),
[iquote('0:Rew:3481.0,31829.0')] ).
cnf(31846,plain,
equal(or__dfg(and__dfg(t5,and__dfg(u,not__dfg(cin))),not__dfg(t5)),xor__dfg(t5,not__dfg(and__dfg(u,not__dfg(cin))))),
inference(spr,[status(thm),theory(equality)],[2333,725]),
[iquote('0:SpR:2333.0,725.0')] ).
cnf(31903,plain,
equal(or__dfg(not__dfg(t5),and__dfg(t5,and__dfg(u,not__dfg(cin)))),xor__dfg(t5,or__dfg(cin,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[1,31846,249]),
[iquote('0:Rew:1.0,31846.0,1.0,31846.0,249.0,31846.0')] ).
cnf(31904,plain,
equal(xor__dfg(t5,or__dfg(cin,not__dfg(u))),and__dfg(t7,or__dfg(u,cin))),
inference(rew,[status(thm),theory(equality)],[23983,31903,5012]),
[iquote('0:Rew:23983.0,31903.0,5012.0,31903.0')] ).
cnf(31905,plain,
equal(or__dfg(not__dfg(t5),and__dfg(not__dfg(cin),u)),and__dfg(t7,or__dfg(u,cin))),
inference(rew,[status(thm),theory(equality)],[31904,31830]),
[iquote('0:Rew:31904.0,31830.0')] ).
cnf(32621,plain,
equal(and__dfg(u,or__dfg(v,and__dfg(w,u))),or__dfg(and__dfg(v,u),and__dfg(w,u))),
inference(spr,[status(thm),theory(equality)],[352,1053]),
[iquote('0:SpR:352.0,1053.0')] ).
cnf(32799,plain,
equal(and__dfg(u,or__dfg(v,and__dfg(w,u))),and__dfg(u,or__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[10088,32621]),
[iquote('0:Rew:10088.0,32621.0')] ).
cnf(34730,plain,
equal(or__dfg(t2,xor__dfg(a,t3)),t2),
inference(spr,[status(thm),theory(equality)],[8643,2606]),
[iquote('0:SpR:8643.0,2606.0')] ).
cnf(34776,plain,
equal(and__dfg(xor__dfg(a,t3),t2),xor__dfg(a,t3)),
inference(spr,[status(thm),theory(equality)],[34730,185]),
[iquote('0:SpR:34730.0,185.0')] ).
cnf(34794,plain,
equal(and__dfg(t2,xor__dfg(a,t3)),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[2,34776]),
[iquote('0:Rew:2.0,34776.0')] ).
cnf(36419,plain,
equal(and__dfg(not__dfg(carry),t7),and__dfg(t1,not__dfg(cin))),
inference(spr,[status(thm),theory(equality)],[4789,420]),
[iquote('0:SpR:4789.0,420.0')] ).
cnf(36422,plain,
equal(and__dfg(not__dfg(carry),not__dfg(t6)),and__dfg(t1,not__dfg(t6))),
inference(spr,[status(thm),theory(equality)],[335,420]),
[iquote('0:SpR:335.0,420.0')] ).
cnf(36434,plain,
equal(and__dfg(not__dfg(carry),t6),and__dfg(t1,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[6545,420]),
[iquote('0:SpR:6545.0,420.0')] ).
cnf(36442,plain,
equal(and__dfg(t7,not__dfg(carry)),and__dfg(t1,not__dfg(cin))),
inference(rew,[status(thm),theory(equality)],[2,36419]),
[iquote('0:Rew:2.0,36419.0')] ).
cnf(36443,plain,
equal(and__dfg(t6,not__dfg(carry)),and__dfg(t1,not__dfg(t4))),
inference(rew,[status(thm),theory(equality)],[2,36434]),
[iquote('0:Rew:2.0,36434.0')] ).
cnf(36450,plain,
equal(not__dfg(or__dfg(t6,carry)),and__dfg(t1,not__dfg(t6))),
inference(rew,[status(thm),theory(equality)],[1,36422,20]),
[iquote('0:Rew:1.0,36422.0,20.0,36422.0')] ).
cnf(36972,plain,
equal(and__dfg(not__dfg(t6),t7),and__dfg(t4,not__dfg(cin))),
inference(spr,[status(thm),theory(equality)],[4789,421]),
[iquote('0:SpR:4789.0,421.0')] ).
cnf(36974,plain,
equal(and__dfg(not__dfg(t6),not__dfg(carry)),and__dfg(t4,not__dfg(carry))),
inference(spr,[status(thm),theory(equality)],[333,421]),
[iquote('0:SpR:333.0,421.0')] ).
cnf(36977,plain,
equal(and__dfg(not__dfg(t6),not__dfg(t7)),and__dfg(t4,not__dfg(t7))),
inference(spr,[status(thm),theory(equality)],[346,421]),
[iquote('0:SpR:346.0,421.0')] ).
cnf(36995,plain,
equal(and__dfg(t4,not__dfg(cin)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[14999,36972,2]),
[iquote('0:Rew:14999.0,36972.0,2.0,36972.0')] ).
cnf(37002,plain,
equal(not__dfg(or__dfg(t6,carry)),and__dfg(t4,not__dfg(carry))),
inference(rew,[status(thm),theory(equality)],[20,36974]),
[iquote('0:Rew:20.0,36974.0')] ).
cnf(37003,plain,
equal(and__dfg(t4,not__dfg(carry)),and__dfg(t1,not__dfg(t6))),
inference(rew,[status(thm),theory(equality)],[36450,37002]),
[iquote('0:Rew:36450.0,37002.0')] ).
cnf(37006,plain,
equal(and__dfg(t4,not__dfg(t7)),ll0),
inference(rew,[status(thm),theory(equality)],[15,36977,15746,20]),
[iquote('0:Rew:15.0,36977.0,15746.0,36977.0,20.0,36977.0')] ).
cnf(37081,plain,
equal(or__dfg(t7,t4),or__dfg(t7,ll0)),
inference(spr,[status(thm),theory(equality)],[37006,889]),
[iquote('0:SpR:37006.0,889.0')] ).
cnf(37097,plain,
equal(or__dfg(t4,t7),t7),
inference(rew,[status(thm),theory(equality)],[1,37081,183]),
[iquote('0:Rew:1.0,37081.0,183.0,37081.0,1.0,37081.0')] ).
cnf(37162,plain,
equal(or__dfg(t3,t7),ll1),
inference(spr,[status(thm),theory(equality)],[37097,3219]),
[iquote('0:SpR:37097.0,3219.0')] ).
cnf(37393,plain,
equal(and__dfg(not__dfg(t7),t6),and__dfg(cin,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[6545,422]),
[iquote('0:SpR:6545.0,422.0')] ).
cnf(37403,plain,
equal(and__dfg(cin,not__dfg(t4)),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[15000,37393,2]),
[iquote('0:Rew:15000.0,37393.0,2.0,37393.0')] ).
cnf(37618,plain,
equal(or__dfg(not__dfg(t6),and__dfg(not__dfg(t4),cin)),xor__dfg(t4,cin)),
inference(spr,[status(thm),theory(equality)],[36995,40]),
[iquote('0:SpR:36995.0,40.0')] ).
cnf(37669,plain,
equal(or__dfg(not__dfg(t6),and__dfg(cin,not__dfg(t4))),xor__dfg(cin,t4)),
inference(rew,[status(thm),theory(equality)],[2,37618,23]),
[iquote('0:Rew:2.0,37618.0,23.0,37618.0')] ).
cnf(37670,plain,
equal(or__dfg(not__dfg(t6),not__dfg(t7)),xor__dfg(cin,t4)),
inference(rew,[status(thm),theory(equality)],[37403,37669]),
[iquote('0:Rew:37403.0,37669.0')] ).
cnf(37671,plain,
equal(xor__dfg(cin,t4),sum__dfg),
inference(rew,[status(thm),theory(equality)],[13,37670,60,21]),
[iquote('0:Rew:13.0,37670.0,60.0,37670.0,21.0,37670.0')] ).
cnf(37733,plain,
equal(xor__dfg(cin,not__dfg(t4)),not__dfg(sum__dfg)),
inference(spr,[status(thm),theory(equality)],[37671,800]),
[iquote('0:SpR:37671.0,800.0')] ).
cnf(37738,plain,
equal(not__dfg(and__dfg(t5,or__dfg(cin,t4))),not__dfg(sum__dfg)),
inference(rew,[status(thm),theory(equality)],[37733,8470]),
[iquote('0:Rew:37733.0,8470.0')] ).
cnf(37774,plain,
equal(or__dfg(t5,not__dfg(sum__dfg)),ll1),
inference(spr,[status(thm),theory(equality)],[37738,588]),
[iquote('0:SpR:37738.0,588.0')] ).
cnf(37976,plain,
equal(and__dfg(sum__dfg,t5),and__dfg(sum__dfg,ll1)),
inference(spr,[status(thm),theory(equality)],[37774,1101]),
[iquote('0:SpR:37774.0,1101.0')] ).
cnf(37996,plain,
equal(and__dfg(t5,sum__dfg),sum__dfg),
inference(rew,[status(thm),theory(equality)],[2,37976,144]),
[iquote('0:Rew:2.0,37976.0,144.0,37976.0,2.0,37976.0')] ).
cnf(38178,plain,
equal(and__dfg(not__dfg(carry),sum__dfg),and__dfg(t1,sum__dfg)),
inference(spr,[status(thm),theory(equality)],[37996,420]),
[iquote('0:SpR:37996.0,420.0')] ).
cnf(38194,plain,
equal(and__dfg(sum__dfg,not__dfg(carry)),and__dfg(t1,sum__dfg)),
inference(rew,[status(thm),theory(equality)],[2,38178]),
[iquote('0:Rew:2.0,38178.0')] ).
cnf(38507,plain,
equal(and__dfg(not__dfg(t4),not__dfg(t1)),and__dfg(t2,not__dfg(t1))),
inference(spr,[status(thm),theory(equality)],[2431,424]),
[iquote('0:SpR:2431.0,424.0')] ).
cnf(38509,plain,
equal(and__dfg(not__dfg(t4),not__dfg(b)),and__dfg(t2,not__dfg(b))),
inference(spr,[status(thm),theory(equality)],[2430,424]),
[iquote('0:SpR:2430.0,424.0')] ).
cnf(38510,plain,
equal(and__dfg(not__dfg(t4),not__dfg(a)),and__dfg(t2,xor__dfg(a,t3))),
inference(spr,[status(thm),theory(equality)],[8643,424]),
[iquote('0:SpR:8643.0,424.0')] ).
cnf(38534,plain,
equal(not__dfg(or__dfg(t1,t4)),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[1,38507,20,2436]),
[iquote('0:Rew:1.0,38507.0,20.0,38507.0,2436.0,38507.0')] ).
cnf(38535,plain,
equal(not__dfg(or__dfg(b,t4)),and__dfg(t2,not__dfg(b))),
inference(rew,[status(thm),theory(equality)],[1,38509,20]),
[iquote('0:Rew:1.0,38509.0,20.0,38509.0')] ).
cnf(38539,plain,
equal(and__dfg(t2,xor__dfg(a,t3)),not__dfg(or__dfg(a,t4))),
inference(rew,[status(thm),theory(equality)],[1,38510,20]),
[iquote('0:Rew:1.0,38510.0,20.0,38510.0')] ).
cnf(38540,plain,
equal(not__dfg(or__dfg(a,t4)),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[34794,38539]),
[iquote('0:Rew:34794.0,38539.0')] ).
cnf(38672,plain,
equal(or__dfg(not__dfg(cin),t4),not__dfg(not__dfg(t7))),
inference(spr,[status(thm),theory(equality)],[37403,249]),
[iquote('0:SpR:37403.0,249.0')] ).
cnf(38700,plain,
equal(or__dfg(t4,not__dfg(cin)),t7),
inference(rew,[status(thm),theory(equality)],[1,38672,13]),
[iquote('0:Rew:1.0,38672.0,13.0,38672.0')] ).
cnf(38928,plain,
equal(and__dfg(not__dfg(t3),not__dfg(t2)),and__dfg(b,not__dfg(t2))),
inference(spr,[status(thm),theory(equality)],[347,425]),
[iquote('0:SpR:347.0,425.0')] ).
cnf(38939,plain,
equal(and__dfg(not__dfg(t3),t2),and__dfg(b,not__dfg(a))),
inference(spr,[status(thm),theory(equality)],[5186,425]),
[iquote('0:SpR:5186.0,425.0')] ).
cnf(38950,plain,
equal(and__dfg(b,not__dfg(a)),not__dfg(t3)),
inference(rew,[status(thm),theory(equality)],[18083,38939,2]),
[iquote('0:Rew:18083.0,38939.0,2.0,38939.0')] ).
cnf(38959,plain,
equal(and__dfg(b,not__dfg(t2)),ll0),
inference(rew,[status(thm),theory(equality)],[15,38928,19712,1,20]),
[iquote('0:Rew:15.0,38928.0,19712.0,38928.0,1.0,38928.0,20.0,38928.0')] ).
cnf(39088,plain,
equal(or__dfg(ll0,and__dfg(not__dfg(b),t2)),xor__dfg(b,t2)),
inference(spr,[status(thm),theory(equality)],[38959,40]),
[iquote('0:SpR:38959.0,40.0')] ).
cnf(39121,plain,
equal(and__dfg(t2,not__dfg(b)),xor__dfg(b,t2)),
inference(rew,[status(thm),theory(equality)],[183,39088,2]),
[iquote('0:Rew:183.0,39088.0,2.0,39088.0')] ).
cnf(39122,plain,
equal(not__dfg(or__dfg(b,t4)),xor__dfg(b,t2)),
inference(rew,[status(thm),theory(equality)],[39121,38535]),
[iquote('0:Rew:39121.0,38535.0')] ).
cnf(39342,plain,
equal(and__dfg(not__dfg(t2),t3),and__dfg(a,not__dfg(b))),
inference(spr,[status(thm),theory(equality)],[5810,426]),
[iquote('0:SpR:5810.0,426.0')] ).
cnf(39354,plain,
equal(and__dfg(a,not__dfg(b)),not__dfg(t2)),
inference(rew,[status(thm),theory(equality)],[18084,39342,2]),
[iquote('0:Rew:18084.0,39342.0,2.0,39342.0')] ).
cnf(40151,plain,
equal(not__dfg(not__dfg(t1)),or__dfg(t1,t4)),
inference(spr,[status(thm),theory(equality)],[38534,13]),
[iquote('0:SpR:38534.0,13.0')] ).
cnf(40201,plain,
equal(or__dfg(t1,t4),t1),
inference(rew,[status(thm),theory(equality)],[13,40151]),
[iquote('0:Rew:13.0,40151.0')] ).
cnf(40288,plain,
equal(and__dfg(t4,t1),t4),
inference(spr,[status(thm),theory(equality)],[40201,185]),
[iquote('0:SpR:40201.0,185.0')] ).
cnf(40309,plain,
equal(and__dfg(t1,t4),t4),
inference(rew,[status(thm),theory(equality)],[2,40288]),
[iquote('0:Rew:2.0,40288.0')] ).
cnf(40340,plain,
equal(or__dfg(t1,not__dfg(t4)),ll1),
inference(spr,[status(thm),theory(equality)],[40309,588]),
[iquote('0:SpR:40309.0,588.0')] ).
cnf(40494,plain,
equal(or__dfg(and__dfg(t1,not__dfg(t4)),not__dfg(ll1)),xor__dfg(t1,not__dfg(not__dfg(t4)))),
inference(spr,[status(thm),theory(equality)],[40340,725]),
[iquote('0:SpR:40340.0,725.0')] ).
cnf(40508,plain,
equal(and__dfg(not__dfg(t1),t4),not__dfg(ll1)),
inference(spr,[status(thm),theory(equality)],[40340,280]),
[iquote('0:SpR:40340.0,280.0')] ).
cnf(40528,plain,
equal(and__dfg(t4,not__dfg(t1)),ll0),
inference(rew,[status(thm),theory(equality)],[2,40508,15]),
[iquote('0:Rew:2.0,40508.0,15.0,40508.0')] ).
cnf(40544,plain,
equal(and__dfg(t1,not__dfg(t4)),xor__dfg(t1,t4)),
inference(rew,[status(thm),theory(equality)],[183,40494,1,15,13]),
[iquote('0:Rew:183.0,40494.0,1.0,40494.0,15.0,40494.0,13.0,40494.0')] ).
cnf(40545,plain,
equal(and__dfg(t6,not__dfg(carry)),xor__dfg(t1,t4)),
inference(rew,[status(thm),theory(equality)],[40544,36443]),
[iquote('0:Rew:40544.0,36443.0')] ).
cnf(40718,plain,
equal(and__dfg(not__dfg(t5),not__dfg(t1)),and__dfg(cin,ll0)),
inference(spr,[status(thm),theory(equality)],[40528,428]),
[iquote('0:SpR:40528.0,428.0')] ).
cnf(40752,plain,
equal(not__dfg(or__dfg(t1,t5)),ll0),
inference(rew,[status(thm),theory(equality)],[1,40718,20,143,2]),
[iquote('0:Rew:1.0,40718.0,20.0,40718.0,143.0,40718.0,2.0,40718.0')] ).
cnf(40889,plain,
equal(or__dfg(t1,t5),not__dfg(ll0)),
inference(spr,[status(thm),theory(equality)],[40752,13]),
[iquote('0:SpR:40752.0,13.0')] ).
cnf(40938,plain,
equal(or__dfg(t1,t5),ll1),
inference(rew,[status(thm),theory(equality)],[14,40889]),
[iquote('0:Rew:14.0,40889.0')] ).
cnf(40940,plain,
equal(not__dfg(and__dfg(carry,ll1)),xor__dfg(t1,not__dfg(t5))),
inference(rew,[status(thm),theory(equality)],[40938,8459]),
[iquote('0:Rew:40938.0,8459.0')] ).
cnf(40947,plain,
equal(xor__dfg(t1,not__dfg(t5)),not__dfg(carry)),
inference(rew,[status(thm),theory(equality)],[144,40940,2]),
[iquote('0:Rew:144.0,40940.0,2.0,40940.0')] ).
cnf(41268,plain,
equal(xor__dfg(not__dfg(t5),not__dfg(carry)),t1),
inference(spr,[status(thm),theory(equality)],[40947,972]),
[iquote('0:SpR:40947.0,972.0')] ).
cnf(41273,plain,
equal(xor__dfg(t1,not__dfg(not__dfg(t5))),not__dfg(not__dfg(carry))),
inference(spr,[status(thm),theory(equality)],[40947,800]),
[iquote('0:SpR:40947.0,800.0')] ).
cnf(41278,plain,
equal(xor__dfg(t5,carry),t1),
inference(rew,[status(thm),theory(equality)],[23,41268,13,1538]),
[iquote('0:Rew:23.0,41268.0,13.0,41268.0,1538.0,41268.0')] ).
cnf(41360,plain,
equal(xor__dfg(t1,t5),carry),
inference(rew,[status(thm),theory(equality)],[13,41273]),
[iquote('0:Rew:13.0,41273.0,13.0,41273.0')] ).
cnf(41453,plain,
equal(xor__dfg(t5,not__dfg(carry)),not__dfg(t1)),
inference(spr,[status(thm),theory(equality)],[41278,800]),
[iquote('0:SpR:41278.0,800.0')] ).
cnf(41460,plain,
equal(and__dfg(t5,carry),not__dfg(t1)),
inference(rew,[status(thm),theory(equality)],[8383,41453]),
[iquote('0:Rew:8383.0,41453.0')] ).
cnf(41764,plain,
equal(and__dfg(not__dfg(t6),carry),and__dfg(t4,not__dfg(t1))),
inference(spr,[status(thm),theory(equality)],[41460,421]),
[iquote('0:SpR:41460.0,421.0')] ).
cnf(41765,plain,
equal(and__dfg(not__dfg(t7),carry),and__dfg(cin,not__dfg(t1))),
inference(spr,[status(thm),theory(equality)],[41460,422]),
[iquote('0:SpR:41460.0,422.0')] ).
cnf(41782,plain,
equal(and__dfg(carry,not__dfg(t6)),ll0),
inference(rew,[status(thm),theory(equality)],[2,41764,40528]),
[iquote('0:Rew:2.0,41764.0,40528.0,41764.0')] ).
cnf(41783,plain,
equal(and__dfg(carry,not__dfg(t7)),and__dfg(cin,not__dfg(t1))),
inference(rew,[status(thm),theory(equality)],[2,41765]),
[iquote('0:Rew:2.0,41765.0')] ).
cnf(41908,plain,
equal(or__dfg(ll0,and__dfg(not__dfg(carry),t6)),xor__dfg(carry,t6)),
inference(spr,[status(thm),theory(equality)],[41782,40]),
[iquote('0:SpR:41782.0,40.0')] ).
cnf(41920,plain,
equal(or__dfg(t6,carry),or__dfg(t6,ll0)),
inference(spr,[status(thm),theory(equality)],[41782,889]),
[iquote('0:SpR:41782.0,889.0')] ).
cnf(41936,plain,
equal(or__dfg(t6,carry),t6),
inference(rew,[status(thm),theory(equality)],[183,41920,1]),
[iquote('0:Rew:183.0,41920.0,1.0,41920.0')] ).
cnf(41937,plain,
equal(and__dfg(t1,not__dfg(t6)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[41936,36450]),
[iquote('0:Rew:41936.0,36450.0')] ).
cnf(41939,plain,
equal(and__dfg(t4,not__dfg(carry)),not__dfg(t6)),
inference(rew,[status(thm),theory(equality)],[41937,37003]),
[iquote('0:Rew:41937.0,37003.0')] ).
cnf(41944,plain,
equal(and__dfg(t6,not__dfg(carry)),xor__dfg(t6,carry)),
inference(rew,[status(thm),theory(equality)],[183,41908,2,23]),
[iquote('0:Rew:183.0,41908.0,2.0,41908.0,23.0,41908.0')] ).
cnf(41945,plain,
equal(xor__dfg(t6,carry),xor__dfg(t1,t4)),
inference(rew,[status(thm),theory(equality)],[40545,41944]),
[iquote('0:Rew:40545.0,41944.0')] ).
cnf(42087,plain,
equal(or__dfg(and__dfg(t6,carry),not__dfg(t6)),xor__dfg(t6,not__dfg(carry))),
inference(spr,[status(thm),theory(equality)],[41936,725]),
[iquote('0:SpR:41936.0,725.0')] ).
cnf(42100,plain,
equal(and__dfg(carry,t6),carry),
inference(spr,[status(thm),theory(equality)],[41936,185]),
[iquote('0:SpR:41936.0,185.0')] ).
cnf(42123,plain,
equal(and__dfg(t6,carry),carry),
inference(rew,[status(thm),theory(equality)],[2,42100]),
[iquote('0:Rew:2.0,42100.0')] ).
cnf(42130,plain,
equal(or__dfg(not__dfg(t6),and__dfg(t6,carry)),xor__dfg(t6,not__dfg(carry))),
inference(rew,[status(thm),theory(equality)],[1,42087]),
[iquote('0:Rew:1.0,42087.0')] ).
cnf(42131,plain,
equal(or__dfg(not__dfg(t6),carry),xor__dfg(t6,not__dfg(carry))),
inference(rew,[status(thm),theory(equality)],[42123,42130]),
[iquote('0:Rew:42123.0,42130.0')] ).
cnf(42132,plain,
equal(or__dfg(carry,not__dfg(t6)),xor__dfg(t6,not__dfg(carry))),
inference(rew,[status(thm),theory(equality)],[1,42131]),
[iquote('0:Rew:1.0,42131.0')] ).
cnf(42400,plain,
equal(and__dfg(t2,not__dfg(b)),and__dfg(t1,not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[5810,4970]),
[iquote('0:SpR:5810.0,4970.0')] ).
cnf(42409,plain,
equal(xor__dfg(t1,t4),xor__dfg(b,t2)),
inference(rew,[status(thm),theory(equality)],[39121,42400,40544]),
[iquote('0:Rew:39121.0,42400.0,40544.0,42400.0')] ).
cnf(42416,plain,
equal(xor__dfg(t6,carry),xor__dfg(b,t2)),
inference(rew,[status(thm),theory(equality)],[42409,41945]),
[iquote('0:Rew:42409.0,41945.0')] ).
cnf(42950,plain,
equal(or__dfg(not__dfg(t3),and__dfg(not__dfg(b),a)),xor__dfg(b,a)),
inference(spr,[status(thm),theory(equality)],[38950,40]),
[iquote('0:SpR:38950.0,40.0')] ).
cnf(42951,plain,
equal(or__dfg(not__dfg(b),a),not__dfg(not__dfg(t3))),
inference(spr,[status(thm),theory(equality)],[38950,249]),
[iquote('0:SpR:38950.0,249.0')] ).
cnf(42957,plain,
equal(or__dfg(a,not__dfg(t3)),or__dfg(a,b)),
inference(spr,[status(thm),theory(equality)],[38950,889]),
[iquote('0:SpR:38950.0,889.0')] ).
cnf(42977,plain,
equal(or__dfg(a,not__dfg(b)),t3),
inference(rew,[status(thm),theory(equality)],[1,42951,13]),
[iquote('0:Rew:1.0,42951.0,13.0,42951.0')] ).
cnf(42978,plain,
equal(xor__dfg(a,not__dfg(t3)),or__dfg(a,b)),
inference(rew,[status(thm),theory(equality)],[8736,42957]),
[iquote('0:Rew:8736.0,42957.0')] ).
cnf(43004,plain,
equal(or__dfg(not__dfg(t3),and__dfg(a,not__dfg(b))),xor__dfg(a,b)),
inference(rew,[status(thm),theory(equality)],[2,42950,23]),
[iquote('0:Rew:2.0,42950.0,23.0,42950.0')] ).
cnf(43005,plain,
equal(or__dfg(not__dfg(t3),not__dfg(t2)),xor__dfg(a,b)),
inference(rew,[status(thm),theory(equality)],[39354,43004]),
[iquote('0:Rew:39354.0,43004.0')] ).
cnf(43006,plain,
equal(xor__dfg(a,b),t4),
inference(rew,[status(thm),theory(equality)],[13,43005,66,21,1]),
[iquote('0:Rew:13.0,43005.0,66.0,43005.0,21.0,43005.0,1.0,43005.0')] ).
cnf(43007,plain,
equal(xor__dfg(cin,sum_def),t4),
inference(rew,[status(thm),theory(equality)],[43006,1221]),
[iquote('0:Rew:43006.0,1221.0')] ).
cnf(43103,plain,
equal(xor__dfg(b,t4),a),
inference(spr,[status(thm),theory(equality)],[43006,972]),
[iquote('0:SpR:43006.0,972.0')] ).
cnf(43108,plain,
equal(xor__dfg(a,not__dfg(b)),not__dfg(t4)),
inference(spr,[status(thm),theory(equality)],[43006,800]),
[iquote('0:SpR:43006.0,800.0')] ).
cnf(43109,plain,
equal(or__dfg(a,t4),or__dfg(a,b)),
inference(spr,[status(thm),theory(equality)],[43006,6491]),
[iquote('0:SpR:43006.0,6491.0')] ).
cnf(43113,plain,
equal(not__dfg(and__dfg(t1,or__dfg(a,b))),not__dfg(t4)),
inference(rew,[status(thm),theory(equality)],[43108,8468]),
[iquote('0:Rew:43108.0,8468.0')] ).
cnf(43116,plain,
equal(not__dfg(or__dfg(a,b)),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[43109,38540]),
[iquote('0:Rew:43109.0,38540.0')] ).
cnf(43144,plain,
equal(xor__dfg(cin,t4),sum_def),
inference(spr,[status(thm),theory(equality)],[43007,785]),
[iquote('0:SpR:43007.0,785.0')] ).
cnf(43150,plain,
equal(sum__dfg,sum_def),
inference(rew,[status(thm),theory(equality)],[37671,43144]),
[iquote('0:Rew:37671.0,43144.0')] ).
cnf(43168,plain,
( ~ equal(carry,carry_def)
| ~ equal(sum_def,sum_def) ),
inference(rew,[status(thm),theory(equality)],[43150,36]),
[iquote('0:Rew:43150.0,36.1')] ).
cnf(43185,plain,
equal(and__dfg(t6,sum_def),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[43150,15606]),
[iquote('0:Rew:43150.0,15606.0')] ).
cnf(43406,plain,
equal(or__dfg(t7,and__dfg(sum_def,u)),or__dfg(t7,u)),
inference(rew,[status(thm),theory(equality)],[43150,3094]),
[iquote('0:Rew:43150.0,3094.0')] ).
cnf(43544,plain,
equal(and__dfg(sum_def,not__dfg(carry)),and__dfg(t1,sum_def)),
inference(rew,[status(thm),theory(equality)],[43150,38194]),
[iquote('0:Rew:43150.0,38194.0')] ).
cnf(43611,plain,
equal(and__dfg(sum_def,t6),not__dfg(t7)),
inference(rew,[status(thm),theory(equality)],[2,43185]),
[iquote('0:Rew:2.0,43185.0')] ).
cnf(43619,plain,
~ equal(carry,carry_def),
inference(obv,[status(thm),theory(equality)],[43168]),
[iquote('0:Obv:43168.1')] ).
cnf(43620,plain,
equal(and__dfg(sum_def,not__dfg(carry)),and__dfg(sum_def,t1)),
inference(rew,[status(thm),theory(equality)],[2,43544]),
[iquote('0:Rew:2.0,43544.0')] ).
cnf(43699,plain,
equal(or__dfg(b,t4),or__dfg(b,a)),
inference(spr,[status(thm),theory(equality)],[43103,6491]),
[iquote('0:SpR:43103.0,6491.0')] ).
cnf(43706,plain,
equal(or__dfg(b,t4),or__dfg(a,b)),
inference(rew,[status(thm),theory(equality)],[1,43699]),
[iquote('0:Rew:1.0,43699.0')] ).
cnf(43707,plain,
equal(not__dfg(or__dfg(a,b)),xor__dfg(b,t2)),
inference(rew,[status(thm),theory(equality)],[43706,39122]),
[iquote('0:Rew:43706.0,39122.0')] ).
cnf(43709,plain,
equal(xor__dfg(b,t2),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[43116,43707]),
[iquote('0:Rew:43116.0,43707.0')] ).
cnf(43716,plain,
equal(xor__dfg(t6,carry),xor__dfg(a,t3)),
inference(rew,[status(thm),theory(equality)],[43709,42416]),
[iquote('0:Rew:43709.0,42416.0')] ).
cnf(44266,plain,
equal(or__dfg(a,and__dfg(u,not__dfg(b))),and__dfg(or__dfg(u,a),t3)),
inference(spr,[status(thm),theory(equality)],[42977,847]),
[iquote('0:SpR:42977.0,847.0')] ).
cnf(44284,plain,
equal(or__dfg(a,and__dfg(u,not__dfg(b))),and__dfg(t3,or__dfg(u,a))),
inference(rew,[status(thm),theory(equality)],[2,44266]),
[iquote('0:Rew:2.0,44266.0')] ).
cnf(44285,plain,
equal(or__dfg(a,and__dfg(u,not__dfg(b))),or__dfg(a,and__dfg(t3,u))),
inference(rew,[status(thm),theory(equality)],[9829,44284]),
[iquote('0:Rew:9829.0,44284.0')] ).
cnf(44772,plain,
equal(and__dfg(t1,or__dfg(a,b)),not__dfg(not__dfg(t4))),
inference(spr,[status(thm),theory(equality)],[43113,13]),
[iquote('0:SpR:43113.0,13.0')] ).
cnf(44820,plain,
equal(and__dfg(t1,or__dfg(a,b)),t4),
inference(rew,[status(thm),theory(equality)],[13,44772]),
[iquote('0:Rew:13.0,44772.0')] ).
cnf(45872,plain,
equal(or__dfg(carry,not__dfg(t6)),or__dfg(carry,t4)),
inference(spr,[status(thm),theory(equality)],[41939,889]),
[iquote('0:SpR:41939.0,889.0')] ).
cnf(45890,plain,
equal(or__dfg(carry,not__dfg(t6)),or__dfg(t4,carry)),
inference(rew,[status(thm),theory(equality)],[1,45872]),
[iquote('0:Rew:1.0,45872.0')] ).
cnf(45891,plain,
equal(xor__dfg(t6,not__dfg(carry)),or__dfg(t4,carry)),
inference(rew,[status(thm),theory(equality)],[42132,45890]),
[iquote('0:Rew:42132.0,45890.0')] ).
cnf(47008,plain,
equal(and__dfg(or__dfg(a,b),or__dfg(t4,u)),or__dfg(t4,and__dfg(a,u))),
inference(spr,[status(thm),theory(equality)],[43109,847]),
[iquote('0:SpR:43109.0,847.0')] ).
cnf(47012,plain,
equal(and__dfg(t4,or__dfg(a,b)),t4),
inference(spr,[status(thm),theory(equality)],[43109,185]),
[iquote('0:SpR:43109.0,185.0')] ).
cnf(52554,plain,
equal(xor__dfg(t6,xor__dfg(a,t3)),carry),
inference(spr,[status(thm),theory(equality)],[43716,785]),
[iquote('0:SpR:43716.0,785.0')] ).
cnf(52555,plain,
equal(not__dfg(xor__dfg(a,t3)),xor__dfg(t6,not__dfg(carry))),
inference(spr,[status(thm),theory(equality)],[43716,800]),
[iquote('0:SpR:43716.0,800.0')] ).
cnf(52556,plain,
equal(or__dfg(t6,xor__dfg(a,t3)),or__dfg(t6,carry)),
inference(spr,[status(thm),theory(equality)],[43716,6491]),
[iquote('0:SpR:43716.0,6491.0')] ).
cnf(52562,plain,
equal(xor__dfg(a,xor__dfg(t3,t6)),carry),
inference(rew,[status(thm),theory(equality)],[23,52554,371]),
[iquote('0:Rew:23.0,52554.0,371.0,52554.0')] ).
cnf(52563,plain,
equal(xor__dfg(t6,not__dfg(carry)),xor__dfg(a,not__dfg(t3))),
inference(rew,[status(thm),theory(equality)],[800,52555]),
[iquote('0:Rew:800.0,52555.0')] ).
cnf(52564,plain,
equal(or__dfg(t4,carry),or__dfg(a,b)),
inference(rew,[status(thm),theory(equality)],[45891,52563,42978]),
[iquote('0:Rew:45891.0,52563.0,42978.0,52563.0')] ).
cnf(52570,plain,
equal(or__dfg(t6,xor__dfg(a,t3)),t6),
inference(rew,[status(thm),theory(equality)],[41936,52556]),
[iquote('0:Rew:41936.0,52556.0')] ).
cnf(52620,plain,
equal(and__dfg(or__dfg(a,b),or__dfg(u,t1)),or__dfg(and__dfg(or__dfg(a,b),u),t4)),
inference(spr,[status(thm),theory(equality)],[44820,1011]),
[iquote('0:SpR:44820.0,1011.0')] ).
cnf(52663,plain,
equal(and__dfg(or__dfg(a,b),or__dfg(u,t1)),or__dfg(t4,and__dfg(or__dfg(a,b),u))),
inference(rew,[status(thm),theory(equality)],[1,52620]),
[iquote('0:Rew:1.0,52620.0')] ).
cnf(54191,plain,
equal(and__dfg(or__dfg(a,b),or__dfg(t4,u)),or__dfg(t4,and__dfg(or__dfg(a,b),u))),
inference(spr,[status(thm),theory(equality)],[47012,1053]),
[iquote('0:SpR:47012.0,1053.0')] ).
cnf(54204,plain,
equal(and__dfg(not__dfg(t5),or__dfg(a,b)),and__dfg(cin,t4)),
inference(spr,[status(thm),theory(equality)],[47012,428]),
[iquote('0:SpR:47012.0,428.0')] ).
cnf(54222,plain,
equal(and__dfg(not__dfg(t5),or__dfg(a,b)),not__dfg(t5)),
inference(rew,[status(thm),theory(equality)],[80,54204]),
[iquote('0:Rew:80.0,54204.0')] ).
cnf(54236,plain,
equal(or__dfg(t4,and__dfg(or__dfg(a,b),u)),or__dfg(t4,and__dfg(a,u))),
inference(rew,[status(thm),theory(equality)],[47008,54191]),
[iquote('0:Rew:47008.0,54191.0')] ).
cnf(54238,plain,
equal(and__dfg(or__dfg(a,b),or__dfg(u,t1)),or__dfg(t4,and__dfg(a,u))),
inference(rew,[status(thm),theory(equality)],[54236,52663]),
[iquote('0:Rew:54236.0,52663.0')] ).
cnf(55044,plain,
equal(xor__dfg(t3,t6),xor__dfg(a,carry)),
inference(spr,[status(thm),theory(equality)],[52562,785]),
[iquote('0:SpR:52562.0,785.0')] ).
cnf(56041,plain,
equal(and__dfg(carry,or__dfg(a,b)),carry),
inference(spr,[status(thm),theory(equality)],[52564,185]),
[iquote('0:SpR:52564.0,185.0')] ).
cnf(59887,plain,
equal(and__dfg(not__dfg(xor__dfg(a,t3)),t6),xor__dfg(xor__dfg(a,t3),t6)),
inference(spr,[status(thm),theory(equality)],[52570,3194]),
[iquote('0:SpR:52570.0,3194.0')] ).
cnf(60085,plain,
equal(and__dfg(t6,xor__dfg(a,not__dfg(t3))),carry),
inference(rew,[status(thm),theory(equality)],[2,59887,800,785,55044,24]),
[iquote('0:Rew:2.0,59887.0,800.0,59887.0,785.0,59887.0,55044.0,59887.0,24.0,59887.0')] ).
cnf(60086,plain,
equal(and__dfg(t6,or__dfg(a,b)),carry),
inference(rew,[status(thm),theory(equality)],[42978,60085]),
[iquote('0:Rew:42978.0,60085.0')] ).
cnf(64516,plain,
equal(or__dfg(carry_def,and__dfg(or__dfg(a,b),not__dfg(t5))),carry_def),
inference(spr,[status(thm),theory(equality)],[4975,13067]),
[iquote('0:SpR:4975.0,13067.0')] ).
cnf(64531,plain,
equal(or__dfg(carry_def,and__dfg(not__dfg(t5),or__dfg(a,b))),carry_def),
inference(rew,[status(thm),theory(equality)],[2,64516]),
[iquote('0:Rew:2.0,64516.0')] ).
cnf(64532,plain,
equal(or__dfg(carry_def,not__dfg(t5)),carry_def),
inference(rew,[status(thm),theory(equality)],[54222,64531]),
[iquote('0:Rew:54222.0,64531.0')] ).
cnf(64584,plain,
equal(and__dfg(not__dfg(carry_def),t5),not__dfg(carry_def)),
inference(spr,[status(thm),theory(equality)],[64532,280]),
[iquote('0:SpR:64532.0,280.0')] ).
cnf(64610,plain,
equal(and__dfg(t5,not__dfg(carry_def)),not__dfg(carry_def)),
inference(rew,[status(thm),theory(equality)],[2,64584]),
[iquote('0:Rew:2.0,64584.0')] ).
cnf(64757,plain,
equal(and__dfg(not__dfg(carry),not__dfg(carry_def)),and__dfg(t1,not__dfg(carry_def))),
inference(spr,[status(thm),theory(equality)],[64610,420]),
[iquote('0:SpR:64610.0,420.0')] ).
cnf(64792,plain,
equal(not__dfg(or__dfg(carry_def,carry)),and__dfg(t1,not__dfg(carry_def))),
inference(rew,[status(thm),theory(equality)],[1,64757,20]),
[iquote('0:Rew:1.0,64757.0,20.0,64757.0')] ).
cnf(65019,plain,
equal(and__dfg(b,or__dfg(a,t7)),and__dfg(b,ll1)),
inference(spr,[status(thm),theory(equality)],[37162,11796]),
[iquote('0:SpR:37162.0,11796.0')] ).
cnf(65026,plain,
equal(and__dfg(b,or__dfg(a,t7)),b),
inference(rew,[status(thm),theory(equality)],[144,65019,2]),
[iquote('0:Rew:144.0,65019.0,2.0,65019.0')] ).
cnf(65246,plain,
equal(or__dfg(or__dfg(a,t7),b),or__dfg(a,t7)),
inference(spr,[status(thm),theory(equality)],[65026,146]),
[iquote('0:SpR:65026.0,146.0')] ).
cnf(65270,plain,
equal(or__dfg(a,or__dfg(b,t7)),or__dfg(a,t7)),
inference(rew,[status(thm),theory(equality)],[1,65246,3]),
[iquote('0:Rew:1.0,65246.0,3.0,65246.0')] ).
cnf(68861,plain,
equal(or__dfg(or__dfg(carry_def,t1),not__dfg(cin)),or__dfg(or__dfg(carry_def,t1),not__dfg(ll1))),
inference(spr,[status(thm),theory(equality)],[593,2849]),
[iquote('0:SpR:593.0,2849.0')] ).
cnf(69168,plain,
equal(or__dfg(carry_def,or__dfg(t1,not__dfg(cin))),or__dfg(carry_def,t1)),
inference(rew,[status(thm),theory(equality)],[3,68861,183,1,15]),
[iquote('0:Rew:3.0,68861.0,183.0,68861.0,1.0,68861.0,3.0,68861.0,15.0,68861.0')] ).
cnf(70277,plain,
equal(not__dfg(and__dfg(u,or__dfg(a,b))),or__dfg(not__dfg(u),xor__dfg(a,t3))),
inference(spr,[status(thm),theory(equality)],[43116,21]),
[iquote('0:SpR:43116.0,21.0')] ).
cnf(70338,plain,
equal(or__dfg(not__dfg(cin),xor__dfg(a,t3)),xor__dfg(carry_def,or__dfg(cin,t1))),
inference(rew,[status(thm),theory(equality)],[70277,4734]),
[iquote('0:Rew:70277.0,4734.0')] ).
cnf(70661,plain,
equal(or__dfg(not__dfg(carry),or__dfg(a,b)),or__dfg(not__dfg(carry),carry)),
inference(spr,[status(thm),theory(equality)],[56041,3003]),
[iquote('0:SpR:56041.0,3003.0')] ).
cnf(70817,plain,
equal(or__dfg(a,or__dfg(b,not__dfg(carry))),ll1),
inference(rew,[status(thm),theory(equality)],[476,70661,9,1]),
[iquote('0:Rew:476.0,70661.0,9.0,70661.0,1.0,70661.0')] ).
cnf(71185,plain,
equal(and__dfg(sum_def,not__dfg(not__dfg(carry))),xor__dfg(sum_def,and__dfg(sum_def,t1))),
inference(spr,[status(thm),theory(equality)],[43620,3041]),
[iquote('0:SpR:43620.0,3041.0')] ).
cnf(71230,plain,
equal(and__dfg(sum_def,not__dfg(t1)),and__dfg(sum_def,carry)),
inference(rew,[status(thm),theory(equality)],[13,71185,3041]),
[iquote('0:Rew:13.0,71185.0,3041.0,71185.0')] ).
cnf(71515,plain,
equal(or__dfg(not__dfg(or__dfg(cin,t1)),not__dfg(and__dfg(cin,or__dfg(a,b)))),or__dfg(not__dfg(or__dfg(cin,t1)),not__dfg(carry_def))),
inference(spr,[status(thm),theory(equality)],[79,3023]),
[iquote('0:SpR:79.0,3023.0')] ).
cnf(72126,plain,
equal(not__dfg(and__dfg(cin,and__dfg(or__dfg(a,b),or__dfg(cin,t1)))),not__dfg(and__dfg(cin,or__dfg(a,b)))),
inference(rew,[status(thm),theory(equality)],[408,71515,21,4732,1]),
[iquote('0:Rew:408.0,71515.0,21.0,71515.0,4732.0,71515.0,21.0,71515.0,1.0,71515.0')] ).
cnf(72127,plain,
equal(xor__dfg(carry_def,or__dfg(cin,t1)),xor__dfg(cin,or__dfg(a,t7))),
inference(rew,[status(thm),theory(equality)],[28908,72126,1450,32799,54238,70338,70277]),
[iquote('0:Rew:28908.0,72126.0,1450.0,72126.0,32799.0,72126.0,54238.0,72126.0,70338.0,72126.0,70277.0,72126.0')] ).
cnf(72142,plain,
equal(or__dfg(not__dfg(cin),xor__dfg(a,t3)),xor__dfg(cin,or__dfg(a,t7))),
inference(rew,[status(thm),theory(equality)],[72127,70338]),
[iquote('0:Rew:72127.0,70338.0')] ).
cnf(80807,plain,
equal(or__dfg(a,not__dfg(or__dfg(b,not__dfg(carry)))),or__dfg(a,not__dfg(ll1))),
inference(spr,[status(thm),theory(equality)],[70817,3023]),
[iquote('0:SpR:70817.0,3023.0')] ).
cnf(80863,plain,
equal(or__dfg(a,and__dfg(carry,not__dfg(b))),a),
inference(rew,[status(thm),theory(equality)],[2,80807,280,183,1,15]),
[iquote('0:Rew:2.0,80807.0,280.0,80807.0,183.0,80807.0,1.0,80807.0,15.0,80807.0')] ).
cnf(80864,plain,
equal(or__dfg(a,and__dfg(t3,carry)),a),
inference(rew,[status(thm),theory(equality)],[44285,80863]),
[iquote('0:Rew:44285.0,80863.0')] ).
cnf(80929,plain,
equal(and__dfg(and__dfg(t3,carry),a),and__dfg(t3,carry)),
inference(spr,[status(thm),theory(equality)],[80864,185]),
[iquote('0:SpR:80864.0,185.0')] ).
cnf(80954,plain,
equal(and__dfg(a,and__dfg(t3,carry)),and__dfg(t3,carry)),
inference(rew,[status(thm),theory(equality)],[2,80929,408,4]),
[iquote('0:Rew:2.0,80929.0,408.0,80929.0,2.0,80929.0,4.0,80929.0')] ).
cnf(80955,plain,
equal(and__dfg(t3,carry),and__dfg(a,carry)),
inference(rew,[status(thm),theory(equality)],[8722,80954]),
[iquote('0:Rew:8722.0,80954.0')] ).
cnf(81826,plain,
equal(or__dfg(t3,and__dfg(sum_def,carry)),t3),
inference(spr,[status(thm),theory(equality)],[71230,2517]),
[iquote('0:SpR:71230.0,2517.0')] ).
cnf(89486,plain,
equal(and__dfg(and__dfg(u,and__dfg(v,w)),x),and__dfg(w,and__dfg(and__dfg(v,u),x))),
inference(spr,[status(thm),theory(equality)],[4186,4]),
[iquote('0:SpR:4186.0,4.0')] ).
cnf(90809,plain,
equal(and__dfg(u,and__dfg(v,and__dfg(w,x))),and__dfg(w,and__dfg(v,and__dfg(u,x)))),
inference(rew,[status(thm),theory(equality)],[4,89486]),
[iquote('0:Rew:4.0,89486.0,4.0,89486.0,4.0,89486.0')] ).
cnf(92076,plain,
equal(or__dfg(cin,not__dfg(or__dfg(cin,t1))),or__dfg(cin,carry_def)),
inference(spr,[status(thm),theory(equality)],[79,4728]),
[iquote('0:SpR:79.0,4728.0')] ).
cnf(92358,plain,
equal(or__dfg(cin,not__dfg(t1)),or__dfg(cin,carry_def)),
inference(rew,[status(thm),theory(equality)],[3023,92076]),
[iquote('0:Rew:3023.0,92076.0')] ).
cnf(92548,plain,
equal(or__dfg(cin,not__dfg(or__dfg(cin,carry_def))),or__dfg(cin,not__dfg(not__dfg(t1)))),
inference(spr,[status(thm),theory(equality)],[92358,3023]),
[iquote('0:SpR:92358.0,3023.0')] ).
cnf(92561,plain,
equal(and__dfg(not__dfg(cin),not__dfg(t1)),xor__dfg(cin,or__dfg(cin,carry_def))),
inference(spr,[status(thm),theory(equality)],[92358,3316]),
[iquote('0:SpR:92358.0,3316.0')] ).
cnf(92601,plain,
equal(not__dfg(or__dfg(cin,t1)),and__dfg(carry_def,not__dfg(cin))),
inference(rew,[status(thm),theory(equality)],[20,92561,2,3316]),
[iquote('0:Rew:20.0,92561.0,2.0,92561.0,3316.0,92561.0')] ).
cnf(92605,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(cin,and__dfg(or__dfg(a,b),u))),or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(carry_def,u))),
inference(rew,[status(thm),theory(equality)],[92601,3377]),
[iquote('0:Rew:92601.0,3377.0')] ).
cnf(92658,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(carry_def,or__dfg(a,b))),carry_def),
inference(rew,[status(thm),theory(equality)],[92601,23197]),
[iquote('0:Rew:92601.0,23197.0')] ).
cnf(92662,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(carry_def,or__dfg(a,or__dfg(b,u)))),carry_def),
inference(rew,[status(thm),theory(equality)],[92601,23203]),
[iquote('0:Rew:92601.0,23203.0')] ).
cnf(92712,plain,
equal(or__dfg(cin,not__dfg(carry_def)),or__dfg(cin,t1)),
inference(rew,[status(thm),theory(equality)],[3023,92548,13]),
[iquote('0:Rew:3023.0,92548.0,13.0,92548.0')] ).
cnf(92729,plain,
equal(and__dfg(carry_def,or__dfg(a,or__dfg(b,not__dfg(cin)))),carry_def),
inference(rew,[status(thm),theory(equality)],[476,92658,7]),
[iquote('0:Rew:476.0,92658.0,7.0,92658.0')] ).
cnf(92813,plain,
equal(and__dfg(carry_def,or__dfg(a,or__dfg(b,or__dfg(u,not__dfg(cin))))),carry_def),
inference(rew,[status(thm),theory(equality)],[3,92662,476,7]),
[iquote('0:Rew:3.0,92662.0,476.0,92662.0,7.0,92662.0')] ).
cnf(92911,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(cin,and__dfg(or__dfg(a,b),u))),and__dfg(carry_def,or__dfg(not__dfg(cin),u))),
inference(rew,[status(thm),theory(equality)],[7,92605]),
[iquote('0:Rew:7.0,92605.0')] ).
cnf(93000,plain,
equal(xor__dfg(carry_def,or__dfg(cin,t1)),not__dfg(and__dfg(carry_def,cin))),
inference(spr,[status(thm),theory(equality)],[92712,2900]),
[iquote('0:SpR:92712.0,2900.0')] ).
cnf(93031,plain,
equal(xor__dfg(carry_def,or__dfg(cin,t1)),not__dfg(and__dfg(cin,carry_def))),
inference(rew,[status(thm),theory(equality)],[2,93000]),
[iquote('0:Rew:2.0,93000.0')] ).
cnf(93032,plain,
equal(xor__dfg(cin,or__dfg(a,t7)),not__dfg(and__dfg(cin,carry_def))),
inference(rew,[status(thm),theory(equality)],[72127,93031]),
[iquote('0:Rew:72127.0,93031.0')] ).
cnf(93035,plain,
equal(or__dfg(not__dfg(cin),xor__dfg(a,t3)),not__dfg(and__dfg(cin,carry_def))),
inference(rew,[status(thm),theory(equality)],[93032,72142]),
[iquote('0:Rew:93032.0,72142.0')] ).
cnf(93587,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(or__dfg(a,b),not__dfg(t5))),and__dfg(carry_def,or__dfg(not__dfg(cin),t4))),
inference(spr,[status(thm),theory(equality)],[4975,92911]),
[iquote('0:SpR:4975.0,92911.0')] ).
cnf(93621,plain,
equal(or__dfg(and__dfg(carry_def,not__dfg(cin)),and__dfg(not__dfg(t5),or__dfg(a,b))),and__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[2,93587,38700,1]),
[iquote('0:Rew:2.0,93587.0,38700.0,93587.0,1.0,93587.0')] ).
cnf(93622,plain,
equal(and__dfg(t7,or__dfg(carry_def,cin)),and__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[31905,93621,6675,54222]),
[iquote('0:Rew:31905.0,93621.0,6675.0,93621.0,54222.0,93621.0')] ).
cnf(93623,plain,
equal(and__dfg(t7,or__dfg(cin,carry_def)),and__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[1,93622]),
[iquote('0:Rew:1.0,93622.0')] ).
cnf(95430,plain,
equal(or__dfg(or__dfg(a,or__dfg(b,not__dfg(cin))),carry_def),or__dfg(a,or__dfg(b,not__dfg(cin)))),
inference(spr,[status(thm),theory(equality)],[92729,146]),
[iquote('0:SpR:92729.0,146.0')] ).
cnf(95476,plain,
equal(or__dfg(a,or__dfg(b,or__dfg(carry_def,not__dfg(cin)))),or__dfg(a,or__dfg(b,not__dfg(cin)))),
inference(rew,[status(thm),theory(equality)],[1,95430,3]),
[iquote('0:Rew:1.0,95430.0,3.0,95430.0,3.0,95430.0')] ).
cnf(98446,plain,
equal(or__dfg(not__dfg(cin),not__dfg(not__dfg(and__dfg(cin,carry_def)))),or__dfg(not__dfg(cin),not__dfg(xor__dfg(a,t3)))),
inference(spr,[status(thm),theory(equality)],[93035,3023]),
[iquote('0:SpR:93035.0,3023.0')] ).
cnf(98517,plain,
equal(or__dfg(a,or__dfg(b,not__dfg(cin))),or__dfg(carry_def,not__dfg(cin))),
inference(rew,[status(thm),theory(equality)],[1,98446,3003,13,476,42978,800]),
[iquote('0:Rew:1.0,98446.0,3003.0,98446.0,13.0,98446.0,476.0,98446.0,42978.0,98446.0,800.0,98446.0')] ).
cnf(98521,plain,
equal(or__dfg(a,or__dfg(b,or__dfg(carry_def,not__dfg(cin)))),or__dfg(carry_def,not__dfg(cin))),
inference(rew,[status(thm),theory(equality)],[98517,95476]),
[iquote('0:Rew:98517.0,95476.0')] ).
cnf(99794,plain,
equal(and__dfg(a,carry),and__dfg(a,t6)),
inference(spr,[status(thm),theory(equality)],[60086,4694]),
[iquote('0:SpR:60086.0,4694.0')] ).
cnf(99799,plain,
equal(and__dfg(t3,carry),and__dfg(a,t6)),
inference(rew,[status(thm),theory(equality)],[99794,80955]),
[iquote('0:Rew:99794.0,80955.0')] ).
cnf(101241,plain,
equal(and__dfg(and__dfg(sum_def,carry),and__dfg(u,t3)),and__dfg(u,and__dfg(sum_def,carry))),
inference(spr,[status(thm),theory(equality)],[81826,4957]),
[iquote('0:SpR:81826.0,4957.0')] ).
cnf(101604,plain,
equal(and__dfg(t3,and__dfg(u,and__dfg(sum_def,carry))),and__dfg(u,and__dfg(sum_def,carry))),
inference(rew,[status(thm),theory(equality)],[4186,101241]),
[iquote('0:Rew:4186.0,101241.0')] ).
cnf(101605,plain,
equal(and__dfg(sum_def,and__dfg(u,and__dfg(t3,carry))),and__dfg(u,and__dfg(sum_def,carry))),
inference(rew,[status(thm),theory(equality)],[90809,101604]),
[iquote('0:Rew:90809.0,101604.0')] ).
cnf(101606,plain,
equal(and__dfg(sum_def,and__dfg(u,and__dfg(a,t6))),and__dfg(u,and__dfg(sum_def,carry))),
inference(rew,[status(thm),theory(equality)],[99799,101605]),
[iquote('0:Rew:99799.0,101605.0')] ).
cnf(101607,plain,
equal(and__dfg(a,and__dfg(u,and__dfg(sum_def,t6))),and__dfg(u,and__dfg(sum_def,carry))),
inference(rew,[status(thm),theory(equality)],[90809,101606]),
[iquote('0:Rew:90809.0,101606.0')] ).
cnf(101608,plain,
equal(and__dfg(a,and__dfg(u,not__dfg(t7))),and__dfg(u,and__dfg(sum_def,carry))),
inference(rew,[status(thm),theory(equality)],[43611,101607]),
[iquote('0:Rew:43611.0,101607.0')] ).
cnf(104424,plain,
equal(or__dfg(or__dfg(u,or__dfg(v,w)),x),or__dfg(w,or__dfg(or__dfg(v,u),x))),
inference(spr,[status(thm),theory(equality)],[5447,3]),
[iquote('0:SpR:5447.0,3.0')] ).
cnf(106501,plain,
equal(or__dfg(u,or__dfg(v,or__dfg(w,x))),or__dfg(w,or__dfg(v,or__dfg(u,x)))),
inference(rew,[status(thm),theory(equality)],[3,104424]),
[iquote('0:Rew:3.0,104424.0,3.0,104424.0,3.0,104424.0')] ).
cnf(125907,plain,
equal(and__dfg(carry_def,or__dfg(a,or__dfg(b,t7))),carry_def),
inference(spr,[status(thm),theory(equality)],[2158,92813]),
[iquote('0:SpR:2158.0,92813.0')] ).
cnf(125938,plain,
equal(and__dfg(carry_def,or__dfg(a,t7)),carry_def),
inference(rew,[status(thm),theory(equality)],[65270,125907]),
[iquote('0:Rew:65270.0,125907.0')] ).
cnf(126040,plain,
equal(or__dfg(not__dfg(carry_def),or__dfg(a,t7)),or__dfg(not__dfg(carry_def),carry_def)),
inference(spr,[status(thm),theory(equality)],[125938,3003]),
[iquote('0:SpR:125938.0,3003.0')] ).
cnf(126048,plain,
equal(or__dfg(or__dfg(a,t7),or__dfg(carry_def,u)),or__dfg(or__dfg(a,t7),u)),
inference(spr,[status(thm),theory(equality)],[125938,489]),
[iquote('0:SpR:125938.0,489.0')] ).
cnf(126084,plain,
equal(or__dfg(a,or__dfg(t7,not__dfg(carry_def))),ll1),
inference(rew,[status(thm),theory(equality)],[1,126040,476,5447,9]),
[iquote('0:Rew:1.0,126040.0,476.0,126040.0,5447.0,126040.0,9.0,126040.0,1.0,126040.0')] ).
cnf(126097,plain,
equal(or__dfg(carry_def,or__dfg(u,or__dfg(a,t7))),or__dfg(a,or__dfg(t7,u))),
inference(rew,[status(thm),theory(equality)],[476,126048,3]),
[iquote('0:Rew:476.0,126048.0,3.0,126048.0')] ).
cnf(126098,plain,
equal(or__dfg(a,or__dfg(u,or__dfg(carry_def,t7))),or__dfg(a,or__dfg(t7,u))),
inference(rew,[status(thm),theory(equality)],[106501,126097]),
[iquote('0:Rew:106501.0,126097.0')] ).
cnf(126286,plain,
equal(and__dfg(not__dfg(or__dfg(t7,not__dfg(carry_def))),a),xor__dfg(or__dfg(t7,not__dfg(carry_def)),ll1)),
inference(spr,[status(thm),theory(equality)],[126084,3194]),
[iquote('0:SpR:126084.0,3194.0')] ).
cnf(126353,plain,
equal(and__dfg(a,and__dfg(carry_def,not__dfg(t7))),and__dfg(carry_def,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[2,126286,408,4,280,693]),
[iquote('0:Rew:2.0,126286.0,408.0,126286.0,2.0,126286.0,4.0,126286.0,2.0,126286.0,280.0,126286.0,693.0,126286.0')] ).
cnf(126354,plain,
equal(and__dfg(carry_def,and__dfg(sum_def,carry)),and__dfg(carry_def,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[101608,126353]),
[iquote('0:Rew:101608.0,126353.0')] ).
cnf(126355,plain,
equal(and__dfg(sum_def,and__dfg(carry_def,carry)),and__dfg(carry_def,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[2,126354,408]),
[iquote('0:Rew:2.0,126354.0,408.0,126354.0')] ).
cnf(153014,plain,
equal(and__dfg(t7,not__dfg(and__dfg(t1,not__dfg(cin)))),and__dfg(t7,not__dfg(not__dfg(carry)))),
inference(spr,[status(thm),theory(equality)],[36442,3043]),
[iquote('0:SpR:36442.0,3043.0')] ).
cnf(153050,plain,
equal(or__dfg(and__dfg(t1,not__dfg(cin)),and__dfg(not__dfg(t7),carry)),xor__dfg(t7,carry)),
inference(spr,[status(thm),theory(equality)],[36442,40]),
[iquote('0:SpR:36442.0,40.0')] ).
cnf(153051,plain,
equal(not__dfg(and__dfg(t1,not__dfg(cin))),or__dfg(not__dfg(t7),carry)),
inference(spr,[status(thm),theory(equality)],[36442,249]),
[iquote('0:SpR:36442.0,249.0')] ).
cnf(153086,plain,
equal(or__dfg(carry,not__dfg(t7)),or__dfg(cin,carry_def)),
inference(rew,[status(thm),theory(equality)],[92358,153051,1,249]),
[iquote('0:Rew:92358.0,153051.0,1.0,153051.0,249.0,153051.0,1.0,153051.0')] ).
cnf(153101,plain,
equal(and__dfg(t7,or__dfg(cin,carry_def)),and__dfg(t7,carry)),
inference(rew,[status(thm),theory(equality)],[92358,153014,1,249,13]),
[iquote('0:Rew:92358.0,153014.0,1.0,153014.0,249.0,153014.0,13.0,153014.0')] ).
cnf(153102,plain,
equal(and__dfg(t7,carry),and__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[93623,153101]),
[iquote('0:Rew:93623.0,153101.0')] ).
cnf(153114,plain,
equal(or__dfg(and__dfg(t1,not__dfg(cin)),and__dfg(carry,not__dfg(t7))),xor__dfg(t7,carry)),
inference(rew,[status(thm),theory(equality)],[2,153050]),
[iquote('0:Rew:2.0,153050.0')] ).
cnf(153115,plain,
equal(or__dfg(and__dfg(t1,not__dfg(cin)),and__dfg(cin,not__dfg(t1))),xor__dfg(t7,carry)),
inference(rew,[status(thm),theory(equality)],[41783,153114]),
[iquote('0:Rew:41783.0,153114.0')] ).
cnf(153116,plain,
equal(xor__dfg(t7,carry),xor__dfg(cin,t1)),
inference(rew,[status(thm),theory(equality)],[23,153115,656]),
[iquote('0:Rew:23.0,153115.0,656.0,153115.0')] ).
cnf(153178,plain,
equal(or__dfg(not__dfg(t7),and__dfg(carry_def,t7)),or__dfg(not__dfg(t7),carry)),
inference(spr,[status(thm),theory(equality)],[153102,3003]),
[iquote('0:SpR:153102.0,3003.0')] ).
cnf(153179,plain,
equal(xor__dfg(or__dfg(t7,carry),and__dfg(carry_def,t7)),xor__dfg(t7,carry)),
inference(spr,[status(thm),theory(equality)],[153102,8673]),
[iquote('0:SpR:153102.0,8673.0')] ).
cnf(153233,plain,
equal(or__dfg(carry,not__dfg(t7)),or__dfg(carry_def,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[1,153178,2834]),
[iquote('0:Rew:1.0,153178.0,2834.0,153178.0,1.0,153178.0')] ).
cnf(153234,plain,
equal(or__dfg(carry_def,not__dfg(t7)),or__dfg(cin,carry_def)),
inference(rew,[status(thm),theory(equality)],[153086,153233]),
[iquote('0:Rew:153086.0,153233.0')] ).
cnf(153235,plain,
equal(xor__dfg(or__dfg(t7,carry),and__dfg(carry_def,t7)),xor__dfg(cin,t1)),
inference(rew,[status(thm),theory(equality)],[153116,153179]),
[iquote('0:Rew:153116.0,153179.0')] ).
cnf(161012,plain,
equal(or__dfg(carry_def,not__dfg(or__dfg(cin,carry_def))),or__dfg(carry_def,not__dfg(not__dfg(t7)))),
inference(spr,[status(thm),theory(equality)],[153234,3023]),
[iquote('0:SpR:153234.0,3023.0')] ).
cnf(161088,plain,
equal(or__dfg(carry_def,not__dfg(cin)),or__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[2849,161012,13]),
[iquote('0:Rew:2849.0,161012.0,13.0,161012.0')] ).
cnf(161091,plain,
equal(or__dfg(a,or__dfg(b,or__dfg(carry_def,t7))),or__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[161088,98521]),
[iquote('0:Rew:161088.0,98521.0')] ).
cnf(161096,plain,
equal(or__dfg(a,or__dfg(t7,b)),or__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[126098,161091]),
[iquote('0:Rew:126098.0,161091.0')] ).
cnf(161097,plain,
equal(or__dfg(a,or__dfg(b,t7)),or__dfg(carry_def,t7)),
inference(rew,[status(thm),theory(equality)],[1,161096]),
[iquote('0:Rew:1.0,161096.0')] ).
cnf(161098,plain,
equal(or__dfg(carry_def,t7),or__dfg(a,t7)),
inference(rew,[status(thm),theory(equality)],[65270,161097]),
[iquote('0:Rew:65270.0,161097.0')] ).
cnf(161102,plain,
equal(or__dfg(carry_def,not__dfg(cin)),or__dfg(a,t7)),
inference(rew,[status(thm),theory(equality)],[161098,161088]),
[iquote('0:Rew:161098.0,161088.0')] ).
cnf(161211,plain,
equal(xor__dfg(or__dfg(a,t7),and__dfg(carry_def,t7)),xor__dfg(carry_def,t7)),
inference(spr,[status(thm),theory(equality)],[161098,8673]),
[iquote('0:SpR:161098.0,8673.0')] ).
cnf(161235,plain,
equal(xor__dfg(t7,or__dfg(a,t7)),and__dfg(not__dfg(t7),carry_def)),
inference(spr,[status(thm),theory(equality)],[161098,3194]),
[iquote('0:SpR:161098.0,3194.0')] ).
cnf(161276,plain,
equal(and__dfg(carry_def,not__dfg(t7)),and__dfg(a,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[2,161235,3194]),
[iquote('0:Rew:2.0,161235.0,3194.0,161235.0,2.0,161235.0')] ).
cnf(161278,plain,
equal(and__dfg(sum_def,and__dfg(carry_def,carry)),and__dfg(a,not__dfg(t7))),
inference(rew,[status(thm),theory(equality)],[161276,126355]),
[iquote('0:Rew:161276.0,126355.0')] ).
cnf(167356,plain,
equal(or__dfg(not__dfg(cin),or__dfg(carry_def,u)),or__dfg(u,or__dfg(a,t7))),
inference(spr,[status(thm),theory(equality)],[161102,5447]),
[iquote('0:SpR:161102.0,5447.0')] ).
cnf(167415,plain,
equal(or__dfg(carry_def,or__dfg(u,not__dfg(cin))),or__dfg(u,or__dfg(a,t7))),
inference(rew,[status(thm),theory(equality)],[476,167356]),
[iquote('0:Rew:476.0,167356.0')] ).
cnf(167418,plain,
equal(or__dfg(t1,or__dfg(a,t7)),or__dfg(carry_def,t1)),
inference(rew,[status(thm),theory(equality)],[167415,69168]),
[iquote('0:Rew:167415.0,69168.0')] ).
cnf(167419,plain,
equal(or__dfg(carry_def,t1),ll1),
inference(rew,[status(thm),theory(equality)],[3337,167418,1,476]),
[iquote('0:Rew:3337.0,167418.0,1.0,167418.0,476.0,167418.0')] ).
cnf(169530,plain,
equal(and__dfg(not__dfg(carry_def),t1),xor__dfg(carry_def,ll1)),
inference(spr,[status(thm),theory(equality)],[167419,3316]),
[iquote('0:SpR:167419.0,3316.0')] ).
cnf(169599,plain,
equal(and__dfg(t1,not__dfg(carry_def)),not__dfg(carry_def)),
inference(rew,[status(thm),theory(equality)],[2,169530,693]),
[iquote('0:Rew:2.0,169530.0,693.0,169530.0')] ).
cnf(169600,plain,
equal(not__dfg(or__dfg(carry_def,carry)),not__dfg(carry_def)),
inference(rew,[status(thm),theory(equality)],[169599,64792]),
[iquote('0:Rew:169599.0,64792.0')] ).
cnf(170705,plain,
equal(not__dfg(not__dfg(carry_def)),or__dfg(carry_def,carry)),
inference(spr,[status(thm),theory(equality)],[169600,13]),
[iquote('0:SpR:169600.0,13.0')] ).
cnf(170799,plain,
equal(or__dfg(carry_def,carry),carry_def),
inference(rew,[status(thm),theory(equality)],[13,170705]),
[iquote('0:Rew:13.0,170705.0')] ).
cnf(170947,plain,
equal(and__dfg(carry,carry_def),carry),
inference(spr,[status(thm),theory(equality)],[170799,185]),
[iquote('0:SpR:170799.0,185.0')] ).
cnf(170990,plain,
equal(and__dfg(carry_def,carry),carry),
inference(rew,[status(thm),theory(equality)],[2,170947]),
[iquote('0:Rew:2.0,170947.0')] ).
cnf(170991,plain,
equal(and__dfg(a,not__dfg(t7)),and__dfg(sum_def,carry)),
inference(rew,[status(thm),theory(equality)],[170990,161278]),
[iquote('0:Rew:170990.0,161278.0')] ).
cnf(188191,plain,
equal(or__dfg(t7,and__dfg(sum_def,carry)),or__dfg(t7,a)),
inference(spr,[status(thm),theory(equality)],[170991,889]),
[iquote('0:SpR:170991.0,889.0')] ).
cnf(188230,plain,
equal(or__dfg(t7,and__dfg(sum_def,carry)),or__dfg(a,t7)),
inference(rew,[status(thm),theory(equality)],[1,188191]),
[iquote('0:Rew:1.0,188191.0')] ).
cnf(188231,plain,
equal(or__dfg(t7,carry),or__dfg(a,t7)),
inference(rew,[status(thm),theory(equality)],[43406,188230]),
[iquote('0:Rew:43406.0,188230.0')] ).
cnf(188235,plain,
equal(xor__dfg(or__dfg(a,t7),and__dfg(carry_def,t7)),xor__dfg(cin,t1)),
inference(rew,[status(thm),theory(equality)],[188231,153235]),
[iquote('0:Rew:188231.0,153235.0')] ).
cnf(188292,plain,
equal(xor__dfg(carry_def,t7),xor__dfg(cin,t1)),
inference(rew,[status(thm),theory(equality)],[161211,188235]),
[iquote('0:Rew:161211.0,188235.0')] ).
cnf(189939,plain,
equal(xor__dfg(t7,xor__dfg(cin,t1)),carry_def),
inference(spr,[status(thm),theory(equality)],[188292,972]),
[iquote('0:SpR:188292.0,972.0')] ).
cnf(189954,plain,
equal(carry,carry_def),
inference(rew,[status(thm),theory(equality)],[41360,189939,3497,3704]),
[iquote('0:Rew:41360.0,189939.0,3497.0,189939.0,3704.0,189939.0')] ).
cnf(189955,plain,
$false,
inference(mrr,[status(thm)],[189954,43619]),
[iquote('0:MRR:189954.0,43619.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 06:11:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 145.18/145.38
% 145.18/145.38 SPASS V 3.9
% 145.18/145.38 SPASS beiseite: Proof found.
% 145.18/145.38 % SZS status Theorem
% 145.18/145.38 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 145.18/145.38 SPASS derived 107060 clauses, backtracked 0 clauses, performed 0 splits and kept 17679 clauses.
% 145.18/145.38 SPASS allocated 207810 KBytes.
% 145.18/145.38 SPASS spent 0:2:24.82 on the problem.
% 145.18/145.38 0:00:00.03 for the input.
% 145.18/145.38 0:00:00.00 for the FLOTTER CNF translation.
% 145.18/145.38 0:00:00.67 for inferences.
% 145.18/145.38 0:00:00.00 for the backtracking.
% 145.18/145.38 0:2:23.83 for the reduction.
% 145.18/145.38
% 145.18/145.38
% 145.18/145.38 Here is a proof with depth 12, length 763 :
% 145.18/145.38 % SZS output start Refutation
% See solution above
% 147.15/147.36 Formulae used in the proof : or_commutative and_commutative or_associative and_associative or_identity and_identity or_distributive and_distributive or_complement and_complement and_idempotent not_involution ll0_inverse ll1_inverse and_boundedness or_absorption and_absorption or_demorgan and_demorgan xor_definition xor_commutative xor_associative sum_def carry_def t1 t2 t3 t4 t5 t6 t7 sum__dfg carry prove_circuit
% 147.15/147.36
%------------------------------------------------------------------------------