TSTP Solution File: HWV001-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 19:14:27 EDT 2022
% Result : Unsatisfiable 1.81s 2.01s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 41
% Syntax : Number of clauses : 312 ( 312 unt; 0 nHn; 312 RR)
% Number of literals : 312 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 22 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(and__dfg(u,v),and__dfg(v,u)),
file('HWV001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('HWV001-1.p',unknown),
[] ).
cnf(3,axiom,
equal(and__dfg(and__dfg(u,v),w),and__dfg(u,and__dfg(v,w))),
file('HWV001-1.p',unknown),
[] ).
cnf(4,axiom,
equal(or__dfg(or__dfg(u,v),w),or__dfg(u,or__dfg(v,w))),
file('HWV001-1.p',unknown),
[] ).
cnf(6,axiom,
equal(and__dfg(and__dfg(u,v),w),and__dfg(and__dfg(u,w),v)),
file('HWV001-1.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),not__dfg(v)),not__dfg(and__dfg(u,v))),
file('HWV001-1.p',unknown),
[] ).
cnf(8,axiom,
equal(and__dfg(not__dfg(u),not__dfg(v)),not__dfg(or__dfg(u,v))),
file('HWV001-1.p',unknown),
[] ).
cnf(9,axiom,
equal(or__dfg(and__dfg(u,v),and__dfg(w,v)),and__dfg(or__dfg(u,w),v)),
file('HWV001-1.p',unknown),
[] ).
cnf(10,axiom,
equal(and__dfg(u,u),u),
file('HWV001-1.p',unknown),
[] ).
cnf(11,axiom,
equal(and__dfg(and__dfg(u,v),v),and__dfg(u,v)),
file('HWV001-1.p',unknown),
[] ).
cnf(12,axiom,
equal(and__dfg(and__dfg(u,v),u),and__dfg(u,v)),
file('HWV001-1.p',unknown),
[] ).
cnf(15,axiom,
equal(or__dfg(or__dfg(u,v),u),or__dfg(u,v)),
file('HWV001-1.p',unknown),
[] ).
cnf(16,axiom,
equal(and__dfg(u,not__dfg(u)),n0),
file('HWV001-1.p',unknown),
[] ).
cnf(18,axiom,
equal(and__dfg(and__dfg(u,v),not__dfg(u)),n0),
file('HWV001-1.p',unknown),
[] ).
cnf(19,axiom,
equal(or__dfg(u,not__dfg(u)),n1),
file('HWV001-1.p',unknown),
[] ).
cnf(21,axiom,
equal(or__dfg(or__dfg(u,v),not__dfg(u)),n1),
file('HWV001-1.p',unknown),
[] ).
cnf(22,axiom,
equal(not__dfg(not__dfg(u)),u),
file('HWV001-1.p',unknown),
[] ).
cnf(23,axiom,
equal(or__dfg(and__dfg(u,v),and__dfg(u,not__dfg(v))),u),
file('HWV001-1.p',unknown),
[] ).
cnf(24,axiom,
equal(or__dfg(and__dfg(u,v),and__dfg(v,not__dfg(u))),v),
file('HWV001-1.p',unknown),
[] ).
cnf(25,axiom,
equal(and__dfg(b1,b3),a1),
file('HWV001-1.p',unknown),
[] ).
cnf(26,axiom,
equal(and__dfg(b2,b3),a2),
file('HWV001-1.p',unknown),
[] ).
cnf(27,axiom,
equal(not__dfg(d1),b1),
file('HWV001-1.p',unknown),
[] ).
cnf(28,axiom,
equal(not__dfg(d2),b2),
file('HWV001-1.p',unknown),
[] ).
cnf(29,axiom,
equal(or__dfg(c1,c2),b3),
file('HWV001-1.p',unknown),
[] ).
cnf(30,axiom,
equal(or__dfg(d1,d3),c1),
file('HWV001-1.p',unknown),
[] ).
cnf(31,axiom,
equal(or__dfg(d2,d3),c2),
file('HWV001-1.p',unknown),
[] ).
cnf(32,axiom,
equal(f3,d3),
file('HWV001-1.p',unknown),
[] ).
cnf(33,axiom,
equal(not__dfg(e1),d1),
file('HWV001-1.p',unknown),
[] ).
cnf(34,axiom,
equal(not__dfg(e2),d2),
file('HWV001-1.p',unknown),
[] ).
cnf(35,axiom,
equal(or__dfg(f1,f3),e1),
file('HWV001-1.p',unknown),
[] ).
cnf(36,axiom,
equal(or__dfg(f2,f3),e2),
file('HWV001-1.p',unknown),
[] ).
cnf(37,axiom,
equal(not__dfg(i1),f1),
file('HWV001-1.p',unknown),
[] ).
cnf(38,axiom,
equal(not__dfg(i2),f2),
file('HWV001-1.p',unknown),
[] ).
cnf(39,axiom,
equal(and__dfg(i1,i2),f3),
file('HWV001-1.p',unknown),
[] ).
cnf(40,axiom,
circuit(input(i1,i2),output(a1,a2)),
file('HWV001-1.p',unknown),
[] ).
cnf(41,axiom,
~ circuit(input(i1,i2),output(i2,i1)),
file('HWV001-1.p',unknown),
[] ).
cnf(42,axiom,
equal(and__dfg(u,n0),n0),
file('HWV001-1.p',unknown),
[] ).
cnf(43,axiom,
equal(and__dfg(u,n1),u),
file('HWV001-1.p',unknown),
[] ).
cnf(44,axiom,
equal(or__dfg(u,n0),u),
file('HWV001-1.p',unknown),
[] ).
cnf(45,axiom,
equal(or__dfg(u,n1),n1),
file('HWV001-1.p',unknown),
[] ).
cnf(47,axiom,
equal(not__dfg(n1),n0),
file('HWV001-1.p',unknown),
[] ).
cnf(48,plain,
equal(and__dfg(i1,i2),d3),
inference(rew,[status(thm),theory(equality)],[32,39]),
[iquote('0:Rew:32.0,39.0')] ).
cnf(49,plain,
equal(or__dfg(f2,d3),e2),
inference(rew,[status(thm),theory(equality)],[32,36]),
[iquote('0:Rew:32.0,36.0')] ).
cnf(50,plain,
equal(or__dfg(f1,d3),e1),
inference(rew,[status(thm),theory(equality)],[32,35]),
[iquote('0:Rew:32.0,35.0')] ).
cnf(51,plain,
equal(or__dfg(d3,f1),e1),
inference(rew,[status(thm),theory(equality)],[2,50]),
[iquote('0:Rew:2.0,50.0')] ).
cnf(52,plain,
equal(or__dfg(d3,f2),e2),
inference(rew,[status(thm),theory(equality)],[2,49]),
[iquote('0:Rew:2.0,49.0')] ).
cnf(53,plain,
equal(and__dfg(b3,b2),a2),
inference(rew,[status(thm),theory(equality)],[1,26]),
[iquote('0:Rew:1.0,26.0')] ).
cnf(54,plain,
equal(or__dfg(not__dfg(u),or__dfg(u,v)),n1),
inference(rew,[status(thm),theory(equality)],[2,21]),
[iquote('0:Rew:2.0,21.0')] ).
cnf(56,plain,
equal(and__dfg(not__dfg(u),and__dfg(u,v)),n0),
inference(rew,[status(thm),theory(equality)],[1,18]),
[iquote('0:Rew:1.0,18.0')] ).
cnf(58,plain,
equal(or__dfg(u,or__dfg(u,v)),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[2,15]),
[iquote('0:Rew:2.0,15.0')] ).
cnf(60,plain,
equal(and__dfg(u,and__dfg(u,v)),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[1,12]),
[iquote('0:Rew:1.0,12.0')] ).
cnf(61,plain,
equal(and__dfg(u,and__dfg(v,u)),and__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[1,11]),
[iquote('0:Rew:1.0,11.0')] ).
cnf(63,plain,
equal(and__dfg(and__dfg(u,v),w),and__dfg(u,and__dfg(w,v))),
inference(rew,[status(thm),theory(equality)],[3,6]),
[iquote('0:Rew:3.0,6.0')] ).
cnf(65,plain,
equal(and__dfg(u,and__dfg(v,w)),and__dfg(u,and__dfg(w,v))),
inference(rew,[status(thm),theory(equality)],[3,63]),
[iquote('0:Rew:3.0,63.0')] ).
cnf(91,plain,
equal(not__dfg(f2),i2),
inference(spr,[status(thm),theory(equality)],[38,22]),
[iquote('0:SpR:38.0,22.0')] ).
cnf(92,plain,
equal(not__dfg(f1),i1),
inference(spr,[status(thm),theory(equality)],[37,22]),
[iquote('0:SpR:37.0,22.0')] ).
cnf(93,plain,
equal(not__dfg(d2),e2),
inference(spr,[status(thm),theory(equality)],[34,22]),
[iquote('0:SpR:34.0,22.0')] ).
cnf(94,plain,
equal(not__dfg(d1),e1),
inference(spr,[status(thm),theory(equality)],[33,22]),
[iquote('0:SpR:33.0,22.0')] ).
cnf(95,plain,
equal(not__dfg(b2),d2),
inference(spr,[status(thm),theory(equality)],[28,22]),
[iquote('0:SpR:28.0,22.0')] ).
cnf(96,plain,
equal(not__dfg(b1),d1),
inference(spr,[status(thm),theory(equality)],[27,22]),
[iquote('0:SpR:27.0,22.0')] ).
cnf(97,plain,
equal(e2,b2),
inference(rew,[status(thm),theory(equality)],[28,93]),
[iquote('0:Rew:28.0,93.0')] ).
cnf(99,plain,
equal(or__dfg(d3,f2),b2),
inference(rew,[status(thm),theory(equality)],[97,52]),
[iquote('0:Rew:97.0,52.0')] ).
cnf(100,plain,
equal(e1,b1),
inference(rew,[status(thm),theory(equality)],[27,94]),
[iquote('0:Rew:27.0,94.0')] ).
cnf(102,plain,
equal(or__dfg(d3,f1),b1),
inference(rew,[status(thm),theory(equality)],[100,51]),
[iquote('0:Rew:100.0,51.0')] ).
cnf(126,plain,
equal(or__dfg(d2,b2),n1),
inference(spr,[status(thm),theory(equality)],[28,19]),
[iquote('0:SpR:28.0,19.0')] ).
cnf(135,plain,
equal(or__dfg(b2,d2),n1),
inference(rew,[status(thm),theory(equality)],[2,126]),
[iquote('0:Rew:2.0,126.0')] ).
cnf(142,plain,
equal(and__dfg(i2,f2),n0),
inference(spr,[status(thm),theory(equality)],[38,16]),
[iquote('0:SpR:38.0,16.0')] ).
cnf(145,plain,
equal(and__dfg(d1,b1),n0),
inference(spr,[status(thm),theory(equality)],[27,16]),
[iquote('0:SpR:27.0,16.0')] ).
cnf(151,plain,
equal(and__dfg(f2,i2),n0),
inference(rew,[status(thm),theory(equality)],[1,142]),
[iquote('0:Rew:1.0,142.0')] ).
cnf(154,plain,
equal(and__dfg(b1,d1),n0),
inference(rew,[status(thm),theory(equality)],[1,145]),
[iquote('0:Rew:1.0,145.0')] ).
cnf(163,plain,
equal(or__dfg(n1,u),n1),
inference(spr,[status(thm),theory(equality)],[2,45]),
[iquote('0:SpR:2.0,45.0')] ).
cnf(164,plain,
equal(or__dfg(n0,u),u),
inference(spr,[status(thm),theory(equality)],[2,44]),
[iquote('0:SpR:2.0,44.0')] ).
cnf(173,plain,
equal(and__dfg(n0,u),n0),
inference(spr,[status(thm),theory(equality)],[1,42]),
[iquote('0:SpR:1.0,42.0')] ).
cnf(174,plain,
equal(and__dfg(n1,u),u),
inference(spr,[status(thm),theory(equality)],[1,43]),
[iquote('0:SpR:1.0,43.0')] ).
cnf(214,plain,
equal(or__dfg(not__dfg(d1),c1),n1),
inference(spr,[status(thm),theory(equality)],[30,54]),
[iquote('0:SpR:30.0,54.0')] ).
cnf(221,plain,
equal(or__dfg(not__dfg(d3),b2),n1),
inference(spr,[status(thm),theory(equality)],[99,54]),
[iquote('0:SpR:99.0,54.0')] ).
cnf(222,plain,
equal(or__dfg(not__dfg(d3),b1),n1),
inference(spr,[status(thm),theory(equality)],[102,54]),
[iquote('0:SpR:102.0,54.0')] ).
cnf(242,plain,
equal(or__dfg(b1,c1),n1),
inference(rew,[status(thm),theory(equality)],[27,214]),
[iquote('0:Rew:27.0,214.0')] ).
cnf(246,plain,
equal(or__dfg(b2,not__dfg(d3)),n1),
inference(rew,[status(thm),theory(equality)],[2,221]),
[iquote('0:Rew:2.0,221.0')] ).
cnf(247,plain,
equal(or__dfg(b1,not__dfg(d3)),n1),
inference(rew,[status(thm),theory(equality)],[2,222]),
[iquote('0:Rew:2.0,222.0')] ).
cnf(419,plain,
equal(or__dfg(c1,b3),b3),
inference(spr,[status(thm),theory(equality)],[29,58]),
[iquote('0:SpR:29.0,58.0')] ).
cnf(446,plain,
equal(or__dfg(b3,c1),b3),
inference(rew,[status(thm),theory(equality)],[2,419]),
[iquote('0:Rew:2.0,419.0')] ).
cnf(565,plain,
equal(and__dfg(i1,d3),d3),
inference(spr,[status(thm),theory(equality)],[48,60]),
[iquote('0:SpR:48.0,60.0')] ).
cnf(587,plain,
equal(and__dfg(d3,i1),d3),
inference(rew,[status(thm),theory(equality)],[1,565]),
[iquote('0:Rew:1.0,565.0')] ).
cnf(628,plain,
equal(and__dfg(i2,d3),d3),
inference(spr,[status(thm),theory(equality)],[48,61]),
[iquote('0:SpR:48.0,61.0')] ).
cnf(653,plain,
equal(and__dfg(d3,i2),d3),
inference(rew,[status(thm),theory(equality)],[1,628]),
[iquote('0:Rew:1.0,628.0')] ).
cnf(693,plain,
equal(and__dfg(not__dfg(not__dfg(u)),not__dfg(or__dfg(u,v))),n0),
inference(spr,[status(thm),theory(equality)],[8,56]),
[iquote('0:SpR:8.0,56.0')] ).
cnf(702,plain,
equal(not__dfg(or__dfg(u,i1)),and__dfg(not__dfg(u),f1)),
inference(spr,[status(thm),theory(equality)],[37,8]),
[iquote('0:SpR:37.0,8.0')] ).
cnf(704,plain,
equal(not__dfg(or__dfg(u,d1)),and__dfg(not__dfg(u),b1)),
inference(spr,[status(thm),theory(equality)],[27,8]),
[iquote('0:SpR:27.0,8.0')] ).
cnf(705,plain,
equal(not__dfg(or__dfg(u,not__dfg(v))),and__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[22,8]),
[iquote('0:SpR:22.0,8.0')] ).
cnf(714,plain,
equal(not__dfg(or__dfg(d2,u)),and__dfg(b2,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[28,8]),
[iquote('0:SpR:28.0,8.0')] ).
cnf(715,plain,
equal(not__dfg(or__dfg(d1,u)),and__dfg(b1,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[27,8]),
[iquote('0:SpR:27.0,8.0')] ).
cnf(726,plain,
equal(not__dfg(or__dfg(u,i1)),and__dfg(f1,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[1,702]),
[iquote('0:Rew:1.0,702.0')] ).
cnf(728,plain,
equal(not__dfg(or__dfg(u,d1)),and__dfg(b1,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[1,704]),
[iquote('0:Rew:1.0,704.0')] ).
cnf(736,plain,
equal(and__dfg(u,not__dfg(or__dfg(u,v))),n0),
inference(rew,[status(thm),theory(equality)],[22,693]),
[iquote('0:Rew:22.0,693.0')] ).
cnf(804,plain,
equal(or__dfg(not__dfg(u),f2),not__dfg(and__dfg(u,i2))),
inference(spr,[status(thm),theory(equality)],[38,7]),
[iquote('0:SpR:38.0,7.0')] ).
cnf(806,plain,
equal(or__dfg(not__dfg(u),b2),not__dfg(and__dfg(u,d2))),
inference(spr,[status(thm),theory(equality)],[28,7]),
[iquote('0:SpR:28.0,7.0')] ).
cnf(807,plain,
equal(or__dfg(not__dfg(u),b1),not__dfg(and__dfg(u,d1))),
inference(spr,[status(thm),theory(equality)],[27,7]),
[iquote('0:SpR:27.0,7.0')] ).
cnf(828,plain,
equal(or__dfg(f2,not__dfg(u)),not__dfg(and__dfg(u,i2))),
inference(rew,[status(thm),theory(equality)],[2,804]),
[iquote('0:Rew:2.0,804.0')] ).
cnf(830,plain,
equal(or__dfg(b2,not__dfg(u)),not__dfg(and__dfg(u,d2))),
inference(rew,[status(thm),theory(equality)],[2,806]),
[iquote('0:Rew:2.0,806.0')] ).
cnf(831,plain,
equal(not__dfg(and__dfg(d3,d2)),n1),
inference(rew,[status(thm),theory(equality)],[830,246]),
[iquote('0:Rew:830.0,246.0')] ).
cnf(832,plain,
equal(not__dfg(and__dfg(d2,d3)),n1),
inference(rew,[status(thm),theory(equality)],[1,831]),
[iquote('0:Rew:1.0,831.0')] ).
cnf(833,plain,
equal(or__dfg(b1,not__dfg(u)),not__dfg(and__dfg(u,d1))),
inference(rew,[status(thm),theory(equality)],[2,807]),
[iquote('0:Rew:2.0,807.0')] ).
cnf(834,plain,
equal(not__dfg(and__dfg(d3,d1)),n1),
inference(rew,[status(thm),theory(equality)],[833,247]),
[iquote('0:Rew:833.0,247.0')] ).
cnf(835,plain,
equal(not__dfg(and__dfg(d1,d3)),n1),
inference(rew,[status(thm),theory(equality)],[1,834]),
[iquote('0:Rew:1.0,834.0')] ).
cnf(856,plain,
equal(and__dfg(d2,d3),not__dfg(n1)),
inference(spr,[status(thm),theory(equality)],[832,22]),
[iquote('0:SpR:832.0,22.0')] ).
cnf(868,plain,
equal(and__dfg(d2,d3),n0),
inference(rew,[status(thm),theory(equality)],[47,856]),
[iquote('0:Rew:47.0,856.0')] ).
cnf(892,plain,
equal(and__dfg(d1,d3),not__dfg(n1)),
inference(spr,[status(thm),theory(equality)],[835,22]),
[iquote('0:SpR:835.0,22.0')] ).
cnf(904,plain,
equal(and__dfg(d1,d3),n0),
inference(rew,[status(thm),theory(equality)],[47,892]),
[iquote('0:Rew:47.0,892.0')] ).
cnf(929,plain,
equal(or__dfg(and__dfg(u,v),v),v),
inference(spr,[status(thm),theory(equality)],[24,58]),
[iquote('0:SpR:24.0,58.0')] ).
cnf(953,plain,
equal(or__dfg(d3,and__dfg(i2,not__dfg(i1))),i2),
inference(spr,[status(thm),theory(equality)],[48,24]),
[iquote('0:SpR:48.0,24.0')] ).
cnf(985,plain,
equal(or__dfg(n0,and__dfg(d3,not__dfg(d2))),d3),
inference(spr,[status(thm),theory(equality)],[868,24]),
[iquote('0:SpR:868.0,24.0')] ).
cnf(986,plain,
equal(or__dfg(n0,and__dfg(d3,not__dfg(d1))),d3),
inference(spr,[status(thm),theory(equality)],[904,24]),
[iquote('0:SpR:904.0,24.0')] ).
cnf(987,plain,
equal(or__dfg(u,and__dfg(v,u)),u),
inference(rew,[status(thm),theory(equality)],[2,929]),
[iquote('0:Rew:2.0,929.0')] ).
cnf(995,plain,
equal(or__dfg(d3,and__dfg(f1,i2)),i2),
inference(rew,[status(thm),theory(equality)],[1,953,37]),
[iquote('0:Rew:1.0,953.0,37.0,953.0')] ).
cnf(1007,plain,
equal(and__dfg(b2,d3),d3),
inference(rew,[status(thm),theory(equality)],[164,985,1,28]),
[iquote('0:Rew:164.0,985.0,1.0,985.0,28.0,985.0')] ).
cnf(1008,plain,
equal(and__dfg(b1,d3),d3),
inference(rew,[status(thm),theory(equality)],[164,986,1,27]),
[iquote('0:Rew:164.0,986.0,1.0,986.0,27.0,986.0')] ).
cnf(1065,plain,
equal(or__dfg(and__dfg(u,v),u),u),
inference(spr,[status(thm),theory(equality)],[23,58]),
[iquote('0:SpR:23.0,58.0')] ).
cnf(1092,plain,
equal(or__dfg(d3,and__dfg(i1,not__dfg(i2))),i1),
inference(spr,[status(thm),theory(equality)],[48,23]),
[iquote('0:SpR:48.0,23.0')] ).
cnf(1126,plain,
equal(or__dfg(d3,and__dfg(b2,not__dfg(d3))),b2),
inference(spr,[status(thm),theory(equality)],[1007,23]),
[iquote('0:SpR:1007.0,23.0')] ).
cnf(1127,plain,
equal(or__dfg(d3,and__dfg(b1,not__dfg(d3))),b1),
inference(spr,[status(thm),theory(equality)],[1008,23]),
[iquote('0:SpR:1008.0,23.0')] ).
cnf(1130,plain,
equal(or__dfg(u,and__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[2,1065]),
[iquote('0:Rew:2.0,1065.0')] ).
cnf(1140,plain,
equal(or__dfg(d3,and__dfg(f2,i1)),i1),
inference(rew,[status(thm),theory(equality)],[1,1092,38]),
[iquote('0:Rew:1.0,1092.0,38.0,1092.0')] ).
cnf(1245,plain,
equal(or__dfg(d2,or__dfg(d3,u)),or__dfg(c2,u)),
inference(spr,[status(thm),theory(equality)],[31,4]),
[iquote('0:SpR:31.0,4.0')] ).
cnf(1246,plain,
equal(or__dfg(d1,or__dfg(d3,u)),or__dfg(c1,u)),
inference(spr,[status(thm),theory(equality)],[30,4]),
[iquote('0:SpR:30.0,4.0')] ).
cnf(1249,plain,
equal(or__dfg(c1,or__dfg(c2,u)),or__dfg(b3,u)),
inference(spr,[status(thm),theory(equality)],[29,4]),
[iquote('0:SpR:29.0,4.0')] ).
cnf(1256,plain,
equal(or__dfg(or__dfg(u,v),w),or__dfg(v,or__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(1260,plain,
equal(or__dfg(d3,or__dfg(f1,u)),or__dfg(b1,u)),
inference(spr,[status(thm),theory(equality)],[102,4]),
[iquote('0:SpR:102.0,4.0')] ).
cnf(1319,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[4,1256]),
[iquote('0:Rew:4.0,1256.0')] ).
cnf(1336,plain,
equal(or__dfg(d3,i2),i2),
inference(spr,[status(thm),theory(equality)],[995,58]),
[iquote('0:SpR:995.0,58.0')] ).
cnf(1358,plain,
equal(and__dfg(u,and__dfg(v,not__dfg(and__dfg(u,v)))),n0),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(1375,plain,
equal(and__dfg(b1,and__dfg(b3,u)),and__dfg(a1,u)),
inference(spr,[status(thm),theory(equality)],[25,3]),
[iquote('0:SpR:25.0,3.0')] ).
cnf(1377,plain,
equal(and__dfg(b3,and__dfg(b2,u)),and__dfg(a2,u)),
inference(spr,[status(thm),theory(equality)],[53,3]),
[iquote('0:SpR:53.0,3.0')] ).
cnf(1495,plain,
equal(or__dfg(d3,i1),i1),
inference(spr,[status(thm),theory(equality)],[1140,58]),
[iquote('0:SpR:1140.0,58.0')] ).
cnf(1843,plain,
equal(or__dfg(and__dfg(u,i2),d3),and__dfg(or__dfg(u,i1),i2)),
inference(spr,[status(thm),theory(equality)],[48,9]),
[iquote('0:SpR:48.0,9.0')] ).
cnf(1851,plain,
equal(or__dfg(and__dfg(u,v),v),and__dfg(or__dfg(u,v),v)),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.0')] ).
cnf(1852,plain,
equal(or__dfg(and__dfg(u,not__dfg(v)),n0),and__dfg(or__dfg(u,v),not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[16,9]),
[iquote('0:SpR:16.0,9.0')] ).
cnf(1867,plain,
equal(or__dfg(and__dfg(u,i1),d3),and__dfg(or__dfg(u,d3),i1)),
inference(spr,[status(thm),theory(equality)],[587,9]),
[iquote('0:SpR:587.0,9.0')] ).
cnf(1868,plain,
equal(or__dfg(and__dfg(u,i2),d3),and__dfg(or__dfg(u,d3),i2)),
inference(spr,[status(thm),theory(equality)],[653,9]),
[iquote('0:SpR:653.0,9.0')] ).
cnf(1896,plain,
equal(or__dfg(u,and__dfg(v,u)),and__dfg(or__dfg(u,v),u)),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.0')] ).
cnf(1935,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,i1))),
inference(rew,[status(thm),theory(equality)],[2,1843,1]),
[iquote('0:Rew:2.0,1843.0,1.0,1843.0')] ).
cnf(1946,plain,
equal(or__dfg(u,and__dfg(v,u)),and__dfg(u,or__dfg(v,u))),
inference(rew,[status(thm),theory(equality)],[2,1851,1]),
[iquote('0:Rew:2.0,1851.0,1.0,1851.0')] ).
cnf(1947,plain,
equal(and__dfg(u,or__dfg(v,u)),u),
inference(rew,[status(thm),theory(equality)],[987,1946]),
[iquote('0:Rew:987.0,1946.0')] ).
cnf(1955,plain,
equal(or__dfg(d3,and__dfg(u,i1)),and__dfg(i1,or__dfg(u,d3))),
inference(rew,[status(thm),theory(equality)],[2,1867,1]),
[iquote('0:Rew:2.0,1867.0,1.0,1867.0')] ).
cnf(1956,plain,
equal(and__dfg(i1,or__dfg(f2,d3)),i1),
inference(rew,[status(thm),theory(equality)],[1955,1140]),
[iquote('0:Rew:1955.0,1140.0')] ).
cnf(1957,plain,
equal(and__dfg(b2,i1),i1),
inference(rew,[status(thm),theory(equality)],[1,1956,99,2]),
[iquote('0:Rew:1.0,1956.0,99.0,1956.0,2.0,1956.0')] ).
cnf(1958,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,d3))),
inference(rew,[status(thm),theory(equality)],[2,1868,1]),
[iquote('0:Rew:2.0,1868.0,1.0,1868.0')] ).
cnf(1959,plain,
equal(and__dfg(i2,or__dfg(u,i1)),and__dfg(i2,or__dfg(u,d3))),
inference(rew,[status(thm),theory(equality)],[1935,1958]),
[iquote('0:Rew:1935.0,1958.0')] ).
cnf(1960,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,d3))),
inference(rew,[status(thm),theory(equality)],[1959,1935]),
[iquote('0:Rew:1959.0,1935.0')] ).
cnf(1984,plain,
equal(or__dfg(u,and__dfg(v,u)),and__dfg(u,or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[1,1896]),
[iquote('0:Rew:1.0,1896.0')] ).
cnf(1985,plain,
equal(and__dfg(u,or__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[987,1984]),
[iquote('0:Rew:987.0,1984.0')] ).
cnf(2016,plain,
equal(and__dfg(not__dfg(u),or__dfg(v,u)),and__dfg(v,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[164,1852,2,1]),
[iquote('0:Rew:164.0,1852.0,2.0,1852.0,1.0,1852.0')] ).
cnf(2096,plain,
equal(or__dfg(i1,and__dfg(b2,not__dfg(i1))),b2),
inference(spr,[status(thm),theory(equality)],[1957,23]),
[iquote('0:SpR:1957.0,23.0')] ).
cnf(2102,plain,
equal(or__dfg(i1,and__dfg(b2,f1)),b2),
inference(rew,[status(thm),theory(equality)],[37,2096]),
[iquote('0:Rew:37.0,2096.0')] ).
cnf(2717,plain,
equal(and__dfg(d3,c2),d3),
inference(spr,[status(thm),theory(equality)],[31,1947]),
[iquote('0:SpR:31.0,1947.0')] ).
cnf(2721,plain,
equal(and__dfg(c2,b3),c2),
inference(spr,[status(thm),theory(equality)],[29,1947]),
[iquote('0:SpR:29.0,1947.0')] ).
cnf(2731,plain,
equal(and__dfg(f2,b2),f2),
inference(spr,[status(thm),theory(equality)],[99,1947]),
[iquote('0:SpR:99.0,1947.0')] ).
cnf(2732,plain,
equal(and__dfg(f1,b1),f1),
inference(spr,[status(thm),theory(equality)],[102,1947]),
[iquote('0:SpR:102.0,1947.0')] ).
cnf(2774,plain,
equal(and__dfg(c1,b3),c1),
inference(spr,[status(thm),theory(equality)],[446,1947]),
[iquote('0:SpR:446.0,1947.0')] ).
cnf(2787,plain,
equal(and__dfg(c2,d3),d3),
inference(rew,[status(thm),theory(equality)],[1,2717]),
[iquote('0:Rew:1.0,2717.0')] ).
cnf(2791,plain,
equal(and__dfg(b3,c2),c2),
inference(rew,[status(thm),theory(equality)],[1,2721]),
[iquote('0:Rew:1.0,2721.0')] ).
cnf(2793,plain,
equal(and__dfg(b2,f2),f2),
inference(rew,[status(thm),theory(equality)],[1,2731]),
[iquote('0:Rew:1.0,2731.0')] ).
cnf(2794,plain,
equal(and__dfg(b1,f1),f1),
inference(rew,[status(thm),theory(equality)],[1,2732]),
[iquote('0:Rew:1.0,2732.0')] ).
cnf(2800,plain,
equal(and__dfg(b3,c1),c1),
inference(rew,[status(thm),theory(equality)],[1,2774]),
[iquote('0:Rew:1.0,2774.0')] ).
cnf(2823,plain,
equal(or__dfg(and__dfg(u,d3),d3),and__dfg(or__dfg(u,c2),d3)),
inference(spr,[status(thm),theory(equality)],[2787,9]),
[iquote('0:SpR:2787.0,9.0')] ).
cnf(2825,plain,
equal(and__dfg(d3,or__dfg(u,c2)),d3),
inference(rew,[status(thm),theory(equality)],[987,2823,2,1]),
[iquote('0:Rew:987.0,2823.0,2.0,2823.0,1.0,2823.0')] ).
cnf(2849,plain,
equal(or__dfg(f2,and__dfg(b2,not__dfg(f2))),b2),
inference(spr,[status(thm),theory(equality)],[2793,23]),
[iquote('0:SpR:2793.0,23.0')] ).
cnf(2857,plain,
equal(or__dfg(f2,and__dfg(b2,i2)),b2),
inference(rew,[status(thm),theory(equality)],[91,2849]),
[iquote('0:Rew:91.0,2849.0')] ).
cnf(2881,plain,
equal(and__dfg(d2,c2),d2),
inference(spr,[status(thm),theory(equality)],[31,1985]),
[iquote('0:SpR:31.0,1985.0')] ).
cnf(2967,plain,
equal(or__dfg(f1,and__dfg(b1,not__dfg(f1))),b1),
inference(spr,[status(thm),theory(equality)],[2794,23]),
[iquote('0:SpR:2794.0,23.0')] ).
cnf(2974,plain,
equal(or__dfg(f1,and__dfg(b1,i1)),b1),
inference(rew,[status(thm),theory(equality)],[92,2967]),
[iquote('0:Rew:92.0,2967.0')] ).
cnf(2991,plain,
equal(or__dfg(d2,and__dfg(u,c2)),and__dfg(or__dfg(d2,u),c2)),
inference(spr,[status(thm),theory(equality)],[2881,9]),
[iquote('0:SpR:2881.0,9.0')] ).
cnf(3001,plain,
equal(or__dfg(d2,and__dfg(u,c2)),and__dfg(c2,or__dfg(d2,u))),
inference(rew,[status(thm),theory(equality)],[1,2991]),
[iquote('0:Rew:1.0,2991.0')] ).
cnf(4137,plain,
equal(and__dfg(i1,not__dfg(b2)),n0),
inference(spr,[status(thm),theory(equality)],[2102,736]),
[iquote('0:SpR:2102.0,736.0')] ).
cnf(4139,plain,
equal(and__dfg(f2,not__dfg(b2)),n0),
inference(spr,[status(thm),theory(equality)],[2857,736]),
[iquote('0:SpR:2857.0,736.0')] ).
cnf(4142,plain,
equal(and__dfg(f1,not__dfg(b1)),n0),
inference(spr,[status(thm),theory(equality)],[2974,736]),
[iquote('0:SpR:2974.0,736.0')] ).
cnf(4193,plain,
equal(and__dfg(d2,i1),n0),
inference(rew,[status(thm),theory(equality)],[1,4137,95]),
[iquote('0:Rew:1.0,4137.0,95.0,4137.0')] ).
cnf(4195,plain,
equal(and__dfg(d2,f2),n0),
inference(rew,[status(thm),theory(equality)],[1,4139,95]),
[iquote('0:Rew:1.0,4139.0,95.0,4139.0')] ).
cnf(4196,plain,
equal(and__dfg(d1,f1),n0),
inference(rew,[status(thm),theory(equality)],[1,4142,96]),
[iquote('0:Rew:1.0,4142.0,96.0,4142.0')] ).
cnf(4213,plain,
equal(or__dfg(n0,and__dfg(d2,not__dfg(i1))),d2),
inference(spr,[status(thm),theory(equality)],[4193,23]),
[iquote('0:SpR:4193.0,23.0')] ).
cnf(4214,plain,
equal(and__dfg(d2,and__dfg(i1,u)),and__dfg(n0,u)),
inference(spr,[status(thm),theory(equality)],[4193,3]),
[iquote('0:SpR:4193.0,3.0')] ).
cnf(4224,plain,
equal(and__dfg(d2,f1),d2),
inference(rew,[status(thm),theory(equality)],[164,4213,37]),
[iquote('0:Rew:164.0,4213.0,37.0,4213.0')] ).
cnf(4225,plain,
equal(and__dfg(d2,and__dfg(i1,u)),n0),
inference(rew,[status(thm),theory(equality)],[173,4214]),
[iquote('0:Rew:173.0,4214.0')] ).
cnf(4229,plain,
equal(or__dfg(n0,and__dfg(d2,not__dfg(f2))),d2),
inference(spr,[status(thm),theory(equality)],[4195,23]),
[iquote('0:SpR:4195.0,23.0')] ).
cnf(4240,plain,
equal(and__dfg(d2,i2),d2),
inference(rew,[status(thm),theory(equality)],[164,4229,91]),
[iquote('0:Rew:164.0,4229.0,91.0,4229.0')] ).
cnf(4245,plain,
equal(or__dfg(n0,and__dfg(d1,not__dfg(f1))),d1),
inference(spr,[status(thm),theory(equality)],[4196,23]),
[iquote('0:SpR:4196.0,23.0')] ).
cnf(4256,plain,
equal(and__dfg(d1,i1),d1),
inference(rew,[status(thm),theory(equality)],[164,4245,92]),
[iquote('0:Rew:164.0,4245.0,92.0,4245.0')] ).
cnf(4262,plain,
equal(and__dfg(d2,and__dfg(f1,u)),and__dfg(d2,u)),
inference(spr,[status(thm),theory(equality)],[4224,3]),
[iquote('0:SpR:4224.0,3.0')] ).
cnf(4462,plain,
equal(or__dfg(i2,d2),i2),
inference(spr,[status(thm),theory(equality)],[4240,987]),
[iquote('0:SpR:4240.0,987.0')] ).
cnf(4469,plain,
equal(or__dfg(d2,i2),i2),
inference(rew,[status(thm),theory(equality)],[2,4462]),
[iquote('0:Rew:2.0,4462.0')] ).
cnf(4480,plain,
equal(or__dfg(i1,d1),i1),
inference(spr,[status(thm),theory(equality)],[4256,987]),
[iquote('0:SpR:4256.0,987.0')] ).
cnf(4487,plain,
equal(or__dfg(d1,i1),i1),
inference(rew,[status(thm),theory(equality)],[2,4480]),
[iquote('0:Rew:2.0,4480.0')] ).
cnf(5178,plain,
equal(and__dfg(d3,b3),d3),
inference(spr,[status(thm),theory(equality)],[29,2825]),
[iquote('0:SpR:29.0,2825.0')] ).
cnf(5188,plain,
equal(and__dfg(b3,d3),d3),
inference(rew,[status(thm),theory(equality)],[1,5178]),
[iquote('0:Rew:1.0,5178.0')] ).
cnf(6160,plain,
equal(and__dfg(d2,and__dfg(u,i1)),n0),
inference(spr,[status(thm),theory(equality)],[4225,65]),
[iquote('0:SpR:4225.0,65.0')] ).
cnf(6219,plain,
equal(and__dfg(b2,not__dfg(d3)),not__dfg(c2)),
inference(spr,[status(thm),theory(equality)],[31,714]),
[iquote('0:SpR:31.0,714.0')] ).
cnf(6239,plain,
equal(or__dfg(d3,not__dfg(c2)),b2),
inference(rew,[status(thm),theory(equality)],[6219,1126]),
[iquote('0:Rew:6219.0,1126.0')] ).
cnf(6403,plain,
equal(and__dfg(b1,not__dfg(d3)),not__dfg(c1)),
inference(spr,[status(thm),theory(equality)],[30,715]),
[iquote('0:SpR:30.0,715.0')] ).
cnf(6422,plain,
equal(or__dfg(d3,not__dfg(c1)),b1),
inference(rew,[status(thm),theory(equality)],[6403,1127]),
[iquote('0:Rew:6403.0,1127.0')] ).
cnf(6581,plain,
equal(not__dfg(and__dfg(i1,i2)),or__dfg(f2,f1)),
inference(spr,[status(thm),theory(equality)],[37,828]),
[iquote('0:SpR:37.0,828.0')] ).
cnf(6583,plain,
equal(not__dfg(and__dfg(d1,i2)),or__dfg(f2,b1)),
inference(spr,[status(thm),theory(equality)],[27,828]),
[iquote('0:SpR:27.0,828.0')] ).
cnf(6603,plain,
equal(or__dfg(f1,f2),not__dfg(d3)),
inference(rew,[status(thm),theory(equality)],[48,6581,2]),
[iquote('0:Rew:48.0,6581.0,2.0,6581.0')] ).
cnf(6605,plain,
equal(not__dfg(and__dfg(d1,i2)),or__dfg(b1,f2)),
inference(rew,[status(thm),theory(equality)],[2,6583]),
[iquote('0:Rew:2.0,6583.0')] ).
cnf(6867,plain,
equal(and__dfg(d2,d1),n0),
inference(spr,[status(thm),theory(equality)],[4256,6160]),
[iquote('0:SpR:4256.0,6160.0')] ).
cnf(6868,plain,
equal(and__dfg(d1,d2),n0),
inference(rew,[status(thm),theory(equality)],[1,6867]),
[iquote('0:Rew:1.0,6867.0')] ).
cnf(6879,plain,
equal(or__dfg(n0,and__dfg(d1,not__dfg(d2))),d1),
inference(spr,[status(thm),theory(equality)],[6868,23]),
[iquote('0:SpR:6868.0,23.0')] ).
cnf(6894,plain,
equal(and__dfg(b2,d1),d1),
inference(rew,[status(thm),theory(equality)],[164,6879,1,28]),
[iquote('0:Rew:164.0,6879.0,1.0,6879.0,28.0,6879.0')] ).
cnf(6903,plain,
equal(or__dfg(b2,d1),b2),
inference(spr,[status(thm),theory(equality)],[6894,1130]),
[iquote('0:SpR:6894.0,1130.0')] ).
cnf(6920,plain,
equal(and__dfg(b1,not__dfg(b2)),not__dfg(b2)),
inference(spr,[status(thm),theory(equality)],[6903,728]),
[iquote('0:SpR:6903.0,728.0')] ).
cnf(6936,plain,
equal(and__dfg(b1,d2),d2),
inference(rew,[status(thm),theory(equality)],[95,6920]),
[iquote('0:Rew:95.0,6920.0')] ).
cnf(7015,plain,
equal(or__dfg(b1,d2),b1),
inference(spr,[status(thm),theory(equality)],[6936,1130]),
[iquote('0:SpR:6936.0,1130.0')] ).
cnf(7364,plain,
equal(or__dfg(c2,f2),or__dfg(d2,b2)),
inference(spr,[status(thm),theory(equality)],[99,1245]),
[iquote('0:SpR:99.0,1245.0')] ).
cnf(7365,plain,
equal(or__dfg(c2,f1),or__dfg(d2,b1)),
inference(spr,[status(thm),theory(equality)],[102,1245]),
[iquote('0:SpR:102.0,1245.0')] ).
cnf(7366,plain,
equal(or__dfg(c2,i2),or__dfg(d2,i2)),
inference(spr,[status(thm),theory(equality)],[1336,1245]),
[iquote('0:SpR:1336.0,1245.0')] ).
cnf(7367,plain,
equal(or__dfg(c2,i1),or__dfg(d2,i1)),
inference(spr,[status(thm),theory(equality)],[1495,1245]),
[iquote('0:SpR:1495.0,1245.0')] ).
cnf(7384,plain,
equal(or__dfg(c2,f2),n1),
inference(rew,[status(thm),theory(equality)],[135,7364,2]),
[iquote('0:Rew:135.0,7364.0,2.0,7364.0')] ).
cnf(7385,plain,
equal(or__dfg(c2,f1),b1),
inference(rew,[status(thm),theory(equality)],[7015,7365,2]),
[iquote('0:Rew:7015.0,7365.0,2.0,7365.0')] ).
cnf(7386,plain,
equal(or__dfg(c2,i2),i2),
inference(rew,[status(thm),theory(equality)],[4469,7366]),
[iquote('0:Rew:4469.0,7366.0')] ).
cnf(7421,plain,
equal(and__dfg(c2,b1),c2),
inference(spr,[status(thm),theory(equality)],[7385,1985]),
[iquote('0:SpR:7385.0,1985.0')] ).
cnf(7430,plain,
equal(and__dfg(b1,c2),c2),
inference(rew,[status(thm),theory(equality)],[1,7421]),
[iquote('0:Rew:1.0,7421.0')] ).
cnf(7441,plain,
equal(and__dfg(c2,i2),c2),
inference(spr,[status(thm),theory(equality)],[7386,1985]),
[iquote('0:SpR:7386.0,1985.0')] ).
cnf(7493,plain,
equal(or__dfg(c1,f2),or__dfg(d1,b2)),
inference(spr,[status(thm),theory(equality)],[99,1246]),
[iquote('0:SpR:99.0,1246.0')] ).
cnf(7496,plain,
equal(or__dfg(c1,i1),or__dfg(d1,i1)),
inference(spr,[status(thm),theory(equality)],[1495,1246]),
[iquote('0:SpR:1495.0,1246.0')] ).
cnf(7504,plain,
equal(or__dfg(c1,not__dfg(c2)),or__dfg(d1,b2)),
inference(spr,[status(thm),theory(equality)],[6239,1246]),
[iquote('0:SpR:6239.0,1246.0')] ).
cnf(7513,plain,
equal(or__dfg(c1,f2),b2),
inference(rew,[status(thm),theory(equality)],[6903,7493,2]),
[iquote('0:Rew:6903.0,7493.0,2.0,7493.0')] ).
cnf(7515,plain,
equal(or__dfg(c1,i1),i1),
inference(rew,[status(thm),theory(equality)],[4487,7496]),
[iquote('0:Rew:4487.0,7496.0')] ).
cnf(7517,plain,
equal(or__dfg(c1,not__dfg(c2)),b2),
inference(rew,[status(thm),theory(equality)],[6903,7504,2]),
[iquote('0:Rew:6903.0,7504.0,2.0,7504.0')] ).
cnf(7638,plain,
equal(or__dfg(c1,n1),or__dfg(b3,f2)),
inference(spr,[status(thm),theory(equality)],[7384,1249]),
[iquote('0:SpR:7384.0,1249.0')] ).
cnf(7639,plain,
equal(or__dfg(c1,b1),or__dfg(b3,f1)),
inference(spr,[status(thm),theory(equality)],[7385,1249]),
[iquote('0:SpR:7385.0,1249.0')] ).
cnf(7646,plain,
equal(or__dfg(b3,f2),n1),
inference(rew,[status(thm),theory(equality)],[163,7638,2]),
[iquote('0:Rew:163.0,7638.0,2.0,7638.0')] ).
cnf(7647,plain,
equal(or__dfg(b3,f1),n1),
inference(rew,[status(thm),theory(equality)],[242,7639,2]),
[iquote('0:Rew:242.0,7639.0,2.0,7639.0')] ).
cnf(7671,plain,
equal(and__dfg(c1,b2),c1),
inference(spr,[status(thm),theory(equality)],[7513,1985]),
[iquote('0:SpR:7513.0,1985.0')] ).
cnf(7679,plain,
equal(and__dfg(b2,c1),c1),
inference(rew,[status(thm),theory(equality)],[1,7671]),
[iquote('0:Rew:1.0,7671.0')] ).
cnf(7702,plain,
equal(and__dfg(c1,i1),c1),
inference(spr,[status(thm),theory(equality)],[7515,1985]),
[iquote('0:SpR:7515.0,1985.0')] ).
cnf(7841,plain,
equal(or__dfg(c1,and__dfg(b2,not__dfg(c1))),b2),
inference(spr,[status(thm),theory(equality)],[7679,23]),
[iquote('0:SpR:7679.0,23.0')] ).
cnf(7909,plain,
equal(or__dfg(d3,not__dfg(d3)),or__dfg(b1,f2)),
inference(spr,[status(thm),theory(equality)],[6603,1260]),
[iquote('0:SpR:6603.0,1260.0')] ).
cnf(7918,plain,
equal(or__dfg(b1,f2),n1),
inference(rew,[status(thm),theory(equality)],[19,7909]),
[iquote('0:Rew:19.0,7909.0')] ).
cnf(7919,plain,
equal(not__dfg(and__dfg(d1,i2)),n1),
inference(rew,[status(thm),theory(equality)],[7918,6605]),
[iquote('0:Rew:7918.0,6605.0')] ).
cnf(8191,plain,
equal(and__dfg(b1,c2),and__dfg(a1,c2)),
inference(spr,[status(thm),theory(equality)],[2791,1375]),
[iquote('0:SpR:2791.0,1375.0')] ).
cnf(8205,plain,
equal(and__dfg(b1,d3),and__dfg(a1,d3)),
inference(spr,[status(thm),theory(equality)],[5188,1375]),
[iquote('0:SpR:5188.0,1375.0')] ).
cnf(8214,plain,
equal(and__dfg(a1,c2),c2),
inference(rew,[status(thm),theory(equality)],[7430,8191]),
[iquote('0:Rew:7430.0,8191.0')] ).
cnf(8219,plain,
equal(and__dfg(a1,d3),d3),
inference(rew,[status(thm),theory(equality)],[1008,8205]),
[iquote('0:Rew:1008.0,8205.0')] ).
cnf(8244,plain,
equal(or__dfg(c2,and__dfg(a1,not__dfg(c2))),a1),
inference(spr,[status(thm),theory(equality)],[8214,23]),
[iquote('0:SpR:8214.0,23.0')] ).
cnf(8260,plain,
equal(or__dfg(a1,d3),a1),
inference(spr,[status(thm),theory(equality)],[8219,1130]),
[iquote('0:SpR:8219.0,1130.0')] ).
cnf(8321,plain,
equal(and__dfg(a2,i1),and__dfg(b3,i1)),
inference(spr,[status(thm),theory(equality)],[1957,1377]),
[iquote('0:SpR:1957.0,1377.0')] ).
cnf(8332,plain,
equal(and__dfg(a2,not__dfg(d3)),and__dfg(b3,not__dfg(c2))),
inference(spr,[status(thm),theory(equality)],[6219,1377]),
[iquote('0:SpR:6219.0,1377.0')] ).
cnf(8335,plain,
equal(and__dfg(a2,c1),and__dfg(b3,c1)),
inference(spr,[status(thm),theory(equality)],[7679,1377]),
[iquote('0:SpR:7679.0,1377.0')] ).
cnf(8342,plain,
equal(and__dfg(a2,c1),c1),
inference(rew,[status(thm),theory(equality)],[2800,8335]),
[iquote('0:Rew:2800.0,8335.0')] ).
cnf(8400,plain,
equal(or__dfg(c1,and__dfg(a2,not__dfg(c1))),a2),
inference(spr,[status(thm),theory(equality)],[8342,23]),
[iquote('0:SpR:8342.0,23.0')] ).
cnf(8532,plain,
equal(and__dfg(d1,i2),not__dfg(n1)),
inference(spr,[status(thm),theory(equality)],[7919,22]),
[iquote('0:SpR:7919.0,22.0')] ).
cnf(8551,plain,
equal(and__dfg(d1,i2),n0),
inference(rew,[status(thm),theory(equality)],[47,8532]),
[iquote('0:Rew:47.0,8532.0')] ).
cnf(9103,plain,
equal(or__dfg(c1,or__dfg(d2,i1)),or__dfg(b3,i1)),
inference(spr,[status(thm),theory(equality)],[7367,1249]),
[iquote('0:SpR:7367.0,1249.0')] ).
cnf(9111,plain,
equal(or__dfg(d2,or__dfg(c1,i1)),or__dfg(b3,i1)),
inference(rew,[status(thm),theory(equality)],[1319,9103]),
[iquote('0:Rew:1319.0,9103.0')] ).
cnf(9112,plain,
equal(or__dfg(d2,i1),or__dfg(b3,i1)),
inference(rew,[status(thm),theory(equality)],[7515,9111]),
[iquote('0:Rew:7515.0,9111.0')] ).
cnf(9496,plain,
equal(and__dfg(not__dfg(d3),c1),not__dfg(b1)),
inference(spr,[status(thm),theory(equality)],[6422,705]),
[iquote('0:SpR:6422.0,705.0')] ).
cnf(9497,plain,
equal(and__dfg(not__dfg(c1),c2),not__dfg(b2)),
inference(spr,[status(thm),theory(equality)],[7517,705]),
[iquote('0:SpR:7517.0,705.0')] ).
cnf(9517,plain,
equal(and__dfg(c1,not__dfg(d3)),d1),
inference(rew,[status(thm),theory(equality)],[1,9496,96]),
[iquote('0:Rew:1.0,9496.0,96.0,9496.0')] ).
cnf(9520,plain,
equal(and__dfg(c2,not__dfg(c1)),d2),
inference(rew,[status(thm),theory(equality)],[1,9497,95]),
[iquote('0:Rew:1.0,9497.0,95.0,9497.0')] ).
cnf(9652,plain,
equal(or__dfg(and__dfg(c2,c1),d2),c2),
inference(spr,[status(thm),theory(equality)],[9520,23]),
[iquote('0:SpR:9520.0,23.0')] ).
cnf(9665,plain,
equal(or__dfg(d2,and__dfg(c1,c2)),c2),
inference(rew,[status(thm),theory(equality)],[2,9652,1]),
[iquote('0:Rew:2.0,9652.0,1.0,9652.0')] ).
cnf(9666,plain,
equal(and__dfg(c2,or__dfg(d2,c1)),c2),
inference(rew,[status(thm),theory(equality)],[3001,9665]),
[iquote('0:Rew:3001.0,9665.0')] ).
cnf(10195,plain,
equal(and__dfg(d2,not__dfg(or__dfg(b3,i1))),n0),
inference(spr,[status(thm),theory(equality)],[9112,736]),
[iquote('0:SpR:9112.0,736.0')] ).
cnf(10209,plain,
equal(and__dfg(d2,and__dfg(f1,not__dfg(b3))),n0),
inference(rew,[status(thm),theory(equality)],[726,10195]),
[iquote('0:Rew:726.0,10195.0')] ).
cnf(10210,plain,
equal(and__dfg(d2,not__dfg(b3)),n0),
inference(rew,[status(thm),theory(equality)],[4262,10209]),
[iquote('0:Rew:4262.0,10209.0')] ).
cnf(10366,plain,
equal(or__dfg(and__dfg(d2,b3),n0),d2),
inference(spr,[status(thm),theory(equality)],[10210,23]),
[iquote('0:SpR:10210.0,23.0')] ).
cnf(10373,plain,
equal(and__dfg(b3,d2),d2),
inference(rew,[status(thm),theory(equality)],[164,10366,2,1]),
[iquote('0:Rew:164.0,10366.0,2.0,10366.0,1.0,10366.0')] ).
cnf(10386,plain,
equal(or__dfg(b3,d2),b3),
inference(spr,[status(thm),theory(equality)],[10373,1130]),
[iquote('0:SpR:10373.0,1130.0')] ).
cnf(12400,plain,
equal(or__dfg(or__dfg(d2,c1),c2),or__dfg(d2,c1)),
inference(spr,[status(thm),theory(equality)],[9666,987]),
[iquote('0:SpR:9666.0,987.0')] ).
cnf(12406,plain,
equal(or__dfg(d2,c1),b3),
inference(rew,[status(thm),theory(equality)],[10386,12400,2,29,4]),
[iquote('0:Rew:10386.0,12400.0,2.0,12400.0,29.0,12400.0,4.0,12400.0')] ).
cnf(12424,plain,
equal(and__dfg(b2,not__dfg(c1)),not__dfg(b3)),
inference(spr,[status(thm),theory(equality)],[12406,714]),
[iquote('0:SpR:12406.0,714.0')] ).
cnf(12436,plain,
equal(or__dfg(c1,not__dfg(b3)),b2),
inference(rew,[status(thm),theory(equality)],[12424,7841]),
[iquote('0:Rew:12424.0,7841.0')] ).
cnf(12454,plain,
equal(and__dfg(not__dfg(c1),b3),not__dfg(b2)),
inference(spr,[status(thm),theory(equality)],[12436,705]),
[iquote('0:SpR:12436.0,705.0')] ).
cnf(12464,plain,
equal(and__dfg(b3,not__dfg(c1)),d2),
inference(rew,[status(thm),theory(equality)],[1,12454,95]),
[iquote('0:Rew:1.0,12454.0,95.0,12454.0')] ).
cnf(12973,plain,
equal(and__dfg(b3,and__dfg(not__dfg(c1),not__dfg(d2))),n0),
inference(spr,[status(thm),theory(equality)],[12464,1358]),
[iquote('0:SpR:12464.0,1358.0')] ).
cnf(12998,plain,
equal(and__dfg(a2,not__dfg(c1)),n0),
inference(rew,[status(thm),theory(equality)],[1377,12973,1,28]),
[iquote('0:Rew:1377.0,12973.0,1.0,12973.0,28.0,12973.0')] ).
cnf(12999,plain,
equal(or__dfg(c1,n0),a2),
inference(rew,[status(thm),theory(equality)],[12998,8400]),
[iquote('0:Rew:12998.0,8400.0')] ).
cnf(13000,plain,
equal(c1,a2),
inference(rew,[status(thm),theory(equality)],[164,12999,2]),
[iquote('0:Rew:164.0,12999.0,2.0,12999.0')] ).
cnf(13001,plain,
equal(or__dfg(d1,d3),a2),
inference(rew,[status(thm),theory(equality)],[13000,30]),
[iquote('0:Rew:13000.0,30.0')] ).
cnf(13002,plain,
equal(or__dfg(a2,c2),b3),
inference(rew,[status(thm),theory(equality)],[13000,29]),
[iquote('0:Rew:13000.0,29.0')] ).
cnf(13038,plain,
equal(and__dfg(a2,i1),a2),
inference(rew,[status(thm),theory(equality)],[13000,7702]),
[iquote('0:Rew:13000.0,7702.0')] ).
cnf(13045,plain,
equal(and__dfg(a2,not__dfg(d3)),d1),
inference(rew,[status(thm),theory(equality)],[13000,9517]),
[iquote('0:Rew:13000.0,9517.0')] ).
cnf(13173,plain,
equal(and__dfg(b3,i1),a2),
inference(rew,[status(thm),theory(equality)],[8321,13038]),
[iquote('0:Rew:8321.0,13038.0')] ).
cnf(13179,plain,
equal(and__dfg(b3,not__dfg(c2)),d1),
inference(rew,[status(thm),theory(equality)],[8332,13045]),
[iquote('0:Rew:8332.0,13045.0')] ).
cnf(14244,plain,
equal(and__dfg(a1,not__dfg(c2)),and__dfg(b1,d1)),
inference(spr,[status(thm),theory(equality)],[13179,1375]),
[iquote('0:SpR:13179.0,1375.0')] ).
cnf(14261,plain,
equal(and__dfg(a1,not__dfg(c2)),n0),
inference(rew,[status(thm),theory(equality)],[154,14244]),
[iquote('0:Rew:154.0,14244.0')] ).
cnf(14262,plain,
equal(or__dfg(c2,n0),a1),
inference(rew,[status(thm),theory(equality)],[14261,8244]),
[iquote('0:Rew:14261.0,8244.0')] ).
cnf(14263,plain,
equal(c2,a1),
inference(rew,[status(thm),theory(equality)],[164,14262,2]),
[iquote('0:Rew:164.0,14262.0,2.0,14262.0')] ).
cnf(14299,plain,
equal(and__dfg(a1,i2),a1),
inference(rew,[status(thm),theory(equality)],[14263,7441]),
[iquote('0:Rew:14263.0,7441.0')] ).
cnf(14307,plain,
equal(or__dfg(a2,a1),b3),
inference(rew,[status(thm),theory(equality)],[14263,13002]),
[iquote('0:Rew:14263.0,13002.0')] ).
cnf(14449,plain,
equal(or__dfg(a1,a2),b3),
inference(rew,[status(thm),theory(equality)],[2,14307]),
[iquote('0:Rew:2.0,14307.0')] ).
cnf(15254,plain,
equal(and__dfg(i2,or__dfg(f2,d3)),or__dfg(d3,n0)),
inference(spr,[status(thm),theory(equality)],[151,1960]),
[iquote('0:SpR:151.0,1960.0')] ).
cnf(15265,plain,
equal(and__dfg(i2,or__dfg(d1,d3)),or__dfg(d3,n0)),
inference(spr,[status(thm),theory(equality)],[8551,1960]),
[iquote('0:SpR:8551.0,1960.0')] ).
cnf(15270,plain,
equal(and__dfg(b2,i2),d3),
inference(rew,[status(thm),theory(equality)],[1,15254,99,2,164]),
[iquote('0:Rew:1.0,15254.0,99.0,15254.0,2.0,15254.0,164.0,15254.0,2.0,15254.0')] ).
cnf(15282,plain,
equal(and__dfg(a2,i2),d3),
inference(rew,[status(thm),theory(equality)],[1,15265,13001,164,2]),
[iquote('0:Rew:1.0,15265.0,13001.0,15265.0,164.0,15265.0,2.0,15265.0')] ).
cnf(15313,plain,
equal(or__dfg(and__dfg(u,i2),d3),and__dfg(or__dfg(u,b2),i2)),
inference(spr,[status(thm),theory(equality)],[15270,9]),
[iquote('0:SpR:15270.0,9.0')] ).
cnf(15331,plain,
equal(and__dfg(i2,or__dfg(u,d3)),and__dfg(i2,or__dfg(u,b2))),
inference(rew,[status(thm),theory(equality)],[1960,15313,2,1]),
[iquote('0:Rew:1960.0,15313.0,2.0,15313.0,1.0,15313.0')] ).
cnf(15332,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,b2))),
inference(rew,[status(thm),theory(equality)],[15331,1960]),
[iquote('0:Rew:15331.0,1960.0')] ).
cnf(15361,plain,
equal(or__dfg(and__dfg(u,i2),d3),and__dfg(or__dfg(u,a2),i2)),
inference(spr,[status(thm),theory(equality)],[15282,9]),
[iquote('0:SpR:15282.0,9.0')] ).
cnf(15375,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,a2))),
inference(rew,[status(thm),theory(equality)],[2,15361,1]),
[iquote('0:Rew:2.0,15361.0,1.0,15361.0')] ).
cnf(15376,plain,
equal(and__dfg(i2,or__dfg(u,b2)),and__dfg(i2,or__dfg(u,a2))),
inference(rew,[status(thm),theory(equality)],[15332,15375]),
[iquote('0:Rew:15332.0,15375.0')] ).
cnf(15383,plain,
equal(or__dfg(d3,and__dfg(u,i2)),and__dfg(i2,or__dfg(u,a2))),
inference(rew,[status(thm),theory(equality)],[15376,15332]),
[iquote('0:Rew:15376.0,15332.0')] ).
cnf(15770,plain,
equal(and__dfg(i2,or__dfg(a1,a2)),or__dfg(d3,a1)),
inference(spr,[status(thm),theory(equality)],[14299,15383]),
[iquote('0:SpR:14299.0,15383.0')] ).
cnf(15785,plain,
equal(and__dfg(b3,i2),a1),
inference(rew,[status(thm),theory(equality)],[1,15770,14449,8260,2]),
[iquote('0:Rew:1.0,15770.0,14449.0,15770.0,8260.0,15770.0,2.0,15770.0')] ).
cnf(16320,plain,
equal(and__dfg(not__dfg(f2),n1),and__dfg(b3,not__dfg(f2))),
inference(spr,[status(thm),theory(equality)],[7646,2016]),
[iquote('0:SpR:7646.0,2016.0')] ).
cnf(16325,plain,
equal(and__dfg(not__dfg(f1),n1),and__dfg(b3,not__dfg(f1))),
inference(spr,[status(thm),theory(equality)],[7647,2016]),
[iquote('0:SpR:7647.0,2016.0')] ).
cnf(16427,plain,
equal(i2,a1),
inference(rew,[status(thm),theory(equality)],[174,16320,1,15785,91]),
[iquote('0:Rew:174.0,16320.0,1.0,16320.0,15785.0,16320.0,91.0,16320.0')] ).
cnf(16433,plain,
circuit(input(i1,a1),output(a1,a2)),
inference(rew,[status(thm),theory(equality)],[16427,40]),
[iquote('0:Rew:16427.0,40.0')] ).
cnf(16434,plain,
~ circuit(input(i1,a1),output(a1,i1)),
inference(rew,[status(thm),theory(equality)],[16427,41]),
[iquote('0:Rew:16427.0,41.0')] ).
cnf(16693,plain,
equal(i1,a2),
inference(rew,[status(thm),theory(equality)],[174,16325,1,13173,92]),
[iquote('0:Rew:174.0,16325.0,1.0,16325.0,13173.0,16325.0,92.0,16325.0')] ).
cnf(16839,plain,
circuit(input(a2,a1),output(a1,a2)),
inference(rew,[status(thm),theory(equality)],[16693,16433]),
[iquote('0:Rew:16693.0,16433.0')] ).
cnf(16840,plain,
~ circuit(input(a2,a1),output(a1,a2)),
inference(rew,[status(thm),theory(equality)],[16693,16434]),
[iquote('0:Rew:16693.0,16434.0')] ).
cnf(16926,plain,
$false,
inference(mrr,[status(thm)],[16840,16839]),
[iquote('0:MRR:16840.0,16839.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 23:17:31 EDT 2022
% 0.19/0.34 % CPUTime :
% 1.81/2.01
% 1.81/2.01 SPASS V 3.9
% 1.81/2.01 SPASS beiseite: Proof found.
% 1.81/2.01 % SZS status Theorem
% 1.81/2.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.81/2.01 SPASS derived 11229 clauses, backtracked 0 clauses, performed 0 splits and kept 2317 clauses.
% 1.81/2.01 SPASS allocated 73971 KBytes.
% 1.81/2.01 SPASS spent 0:00:01.66 on the problem.
% 1.81/2.01 0:00:00.04 for the input.
% 1.81/2.01 0:00:00.00 for the FLOTTER CNF translation.
% 1.81/2.01 0:00:00.07 for inferences.
% 1.81/2.01 0:00:00.00 for the backtracking.
% 1.81/2.01 0:00:01.51 for the reduction.
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Here is a proof with depth 10, length 312 :
% 1.81/2.01 % SZS output start Refutation
% See solution above
% 1.90/2.08 Formulae used in the proof : and_commutativity or_commutativity and_associativity or_associativity and_sorting not_canonicalization1 not_canonicalization2 and_or_canonicalization and_simplification1 and_simplification2 and_simplification3 or_simplification3 and_not_simplification1 and_not_simplification3 or_not_simplification1 or_not_simplification3 not_simplification and_or_not_simplification1 and_or_not_simplification2 constructor1 constructor2 constructor3 constructor4 constructor5 constructor6 constructor7 constructor8 constructor9 constructor10 constructor11 constructor12 constructor13 constructor14 constructor15 circuit_description prove_interchange and_definition1 and_definition2 or_definition1 or_definition2 not_definition2
% 1.90/2.08
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