TSTP Solution File: LCL159-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 : Sun Jul 17 14:34:59 EDT 2022
% Result : Unsatisfiable 0.34s 0.53s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of clauses : 108 ( 108 unt; 0 nHn; 108 RR)
% Number of literals : 108 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(xor__dfg(xor__dfg(x__dfg,truth),y__dfg),xor__dfg(x__dfg,xor__dfg(truth,y__dfg))),
file('LCL159-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL159-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL159-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL159-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL159-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
file('LCL159-1.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(or__dfg(u,v),w),or__dfg(u,or__dfg(v,w))),
file('LCL159-1.p',unknown),
[] ).
cnf(8,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('LCL159-1.p',unknown),
[] ).
cnf(9,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL159-1.p',unknown),
[] ).
cnf(11,axiom,
equal(and__dfg(u,v),and__dfg(v,u)),
file('LCL159-1.p',unknown),
[] ).
cnf(12,axiom,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(not__dfg(u),v)),xor__dfg(u,v)),
file('LCL159-1.p',unknown),
[] ).
cnf(13,axiom,
equal(xor__dfg(u,v),xor__dfg(v,u)),
file('LCL159-1.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and_star(u,v)),
file('LCL159-1.p',unknown),
[] ).
cnf(15,axiom,
equal(and_star(and_star(u,v),w),and_star(u,and_star(v,w))),
file('LCL159-1.p',unknown),
[] ).
cnf(17,axiom,
equal(not__dfg(truth),falsehood),
file('LCL159-1.p',unknown),
[] ).
cnf(18,plain,
equal(and_star(u,v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[14,9]),
[iquote('0:Rew:14.0,9.0')] ).
cnf(20,plain,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[18,14]),
[iquote('0:Rew:18.0,14.0')] ).
cnf(22,plain,
equal(and__dfg(and__dfg(u,v),w),and__dfg(u,and__dfg(v,w))),
inference(rew,[status(thm),theory(equality)],[18,15]),
[iquote('0:Rew:18.0,15.0,18.0,15.0,18.0,15.0,18.0,15.0')] ).
cnf(23,plain,
equal(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(24,plain,
~ equal(xor__dfg(y__dfg,xor__dfg(x__dfg,truth)),xor__dfg(x__dfg,xor__dfg(truth,y__dfg))),
inference(rew,[status(thm),theory(equality)],[13,1]),
[iquote('0:Rew:13.0,1.0')] ).
cnf(41,plain,
equal(implies__dfg(falsehood,u),or__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[17,6]),
[iquote('0:SpR:17.0,6.0')] ).
cnf(45,plain,
equal(implies__dfg(or__dfg(u,not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(46,plain,
equal(implies__dfg(or__dfg(u,not__dfg(falsehood)),or__dfg(truth,u)),truth),
inference(spr,[status(thm),theory(equality)],[41,23]),
[iquote('0:SpR:41.0,23.0')] ).
cnf(51,plain,
equal(implies__dfg(or__dfg(u,falsehood),u),truth),
inference(rew,[status(thm),theory(equality)],[17,45]),
[iquote('0:Rew:17.0,45.0')] ).
cnf(58,plain,
equal(not__dfg(or__dfg(not__dfg(u),falsehood)),and__dfg(u,truth)),
inference(spr,[status(thm),theory(equality)],[17,20]),
[iquote('0:SpR:17.0,20.0')] ).
cnf(62,plain,
equal(not__dfg(or__dfg(falsehood,not__dfg(u))),and__dfg(u,truth)),
inference(rew,[status(thm),theory(equality)],[8,58]),
[iquote('0:Rew:8.0,58.0')] ).
cnf(69,plain,
equal(implies__dfg(or__dfg(falsehood,u),u),truth),
inference(spr,[status(thm),theory(equality)],[8,51]),
[iquote('0:SpR:8.0,51.0')] ).
cnf(71,plain,
equal(implies__dfg(or__dfg(u,not__dfg(or__dfg(falsehood,u))),truth),truth),
inference(spr,[status(thm),theory(equality)],[69,23]),
[iquote('0:SpR:69.0,23.0')] ).
cnf(76,plain,
equal(or__dfg(or__dfg(falsehood,not__dfg(u)),v),implies__dfg(and__dfg(u,truth),v)),
inference(spr,[status(thm),theory(equality)],[62,6]),
[iquote('0:SpR:62.0,6.0')] ).
cnf(78,plain,
equal(not__dfg(or__dfg(falsehood,and__dfg(u,truth))),and__dfg(or__dfg(falsehood,not__dfg(u)),truth)),
inference(spr,[status(thm),theory(equality)],[62]),
[iquote('0:SpR:62.0,62.0')] ).
cnf(84,plain,
equal(or__dfg(falsehood,or__dfg(not__dfg(u),v)),implies__dfg(and__dfg(u,truth),v)),
inference(rew,[status(thm),theory(equality)],[7,76]),
[iquote('0:Rew:7.0,76.0')] ).
cnf(85,plain,
equal(not__dfg(or__dfg(falsehood,and__dfg(u,truth))),and__dfg(truth,or__dfg(falsehood,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[11,78]),
[iquote('0:Rew:11.0,78.0')] ).
cnf(113,plain,
equal(implies__dfg(u,u),implies__dfg(implies__dfg(u,truth),truth)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(114,plain,
equal(implies__dfg(or__dfg(truth,u),u),implies__dfg(implies__dfg(u,falsehood),falsehood)),
inference(spr,[status(thm),theory(equality)],[41,4]),
[iquote('0:SpR:41.0,4.0')] ).
cnf(122,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),truth),or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[113,6]),
[iquote('0:SpR:113.0,6.0')] ).
cnf(139,plain,
equal(implies__dfg(or__dfg(u,truth),truth),or__dfg(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[6,122]),
[iquote('0:Rew:6.0,122.0')] ).
cnf(187,plain,
equal(implies__dfg(or__dfg(not__dfg(u),and__dfg(u,truth)),truth),truth),
inference(spr,[status(thm),theory(equality)],[62,71]),
[iquote('0:SpR:62.0,71.0')] ).
cnf(264,plain,
equal(or__dfg(falsehood,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[139,69]),
[iquote('0:SpR:139.0,69.0')] ).
cnf(285,plain,
equal(implies__dfg(truth,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[264,69]),
[iquote('0:SpR:264.0,69.0')] ).
cnf(293,plain,
equal(not__dfg(falsehood),truth),
inference(rew,[status(thm),theory(equality)],[2,285]),
[iquote('0:Rew:2.0,285.0')] ).
cnf(294,plain,
equal(implies__dfg(or__dfg(u,truth),or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[293,46]),
[iquote('0:Rew:293.0,46.0')] ).
cnf(325,plain,
equal(implies__dfg(truth,u),or__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[293,6]),
[iquote('0:SpR:293.0,6.0')] ).
cnf(326,plain,
equal(not__dfg(or__dfg(truth,not__dfg(u))),and__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[293,20]),
[iquote('0:SpR:293.0,20.0')] ).
cnf(333,plain,
equal(or__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[2,325]),
[iquote('0:Rew:2.0,325.0')] ).
cnf(336,plain,
equal(not__dfg(not__dfg(u)),and__dfg(u,truth)),
inference(rew,[status(thm),theory(equality)],[333,62]),
[iquote('0:Rew:333.0,62.0')] ).
cnf(337,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[333,69]),
[iquote('0:Rew:333.0,69.0')] ).
cnf(344,plain,
equal(and__dfg(truth,or__dfg(falsehood,not__dfg(u))),not__dfg(and__dfg(u,truth))),
inference(rew,[status(thm),theory(equality)],[333,85]),
[iquote('0:Rew:333.0,85.0')] ).
cnf(350,plain,
equal(implies__dfg(and__dfg(u,truth),v),or__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[333,84]),
[iquote('0:Rew:333.0,84.0')] ).
cnf(353,plain,
equal(implies__dfg(implies__dfg(u,truth),truth),truth),
inference(rew,[status(thm),theory(equality)],[337,113]),
[iquote('0:Rew:337.0,113.0')] ).
cnf(382,plain,
equal(not__dfg(and__dfg(u,truth)),and__dfg(truth,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[333,344]),
[iquote('0:Rew:333.0,344.0')] ).
cnf(398,plain,
equal(or__dfg(and__dfg(truth,not__dfg(u)),and__dfg(falsehood,u)),xor__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[17,12]),
[iquote('0:SpR:17.0,12.0')] ).
cnf(400,plain,
equal(or__dfg(and__dfg(falsehood,not__dfg(u)),and__dfg(truth,u)),xor__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[293,12]),
[iquote('0:SpR:293.0,12.0')] ).
cnf(405,plain,
equal(or__dfg(and__dfg(u,truth),and__dfg(not__dfg(u),falsehood)),xor__dfg(u,falsehood)),
inference(spr,[status(thm),theory(equality)],[293,12]),
[iquote('0:SpR:293.0,12.0')] ).
cnf(409,plain,
equal(or__dfg(and__dfg(falsehood,u),and__dfg(truth,not__dfg(u))),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[8,398]),
[iquote('0:Rew:8.0,398.0')] ).
cnf(410,plain,
equal(or__dfg(and__dfg(truth,u),and__dfg(falsehood,not__dfg(u))),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[8,400]),
[iquote('0:Rew:8.0,400.0')] ).
cnf(412,plain,
equal(or__dfg(and__dfg(u,truth),and__dfg(falsehood,not__dfg(u))),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[11,405]),
[iquote('0:Rew:11.0,405.0')] ).
cnf(422,plain,
equal(or__dfg(u,falsehood),u),
inference(spr,[status(thm),theory(equality)],[333,8]),
[iquote('0:SpR:333.0,8.0')] ).
cnf(444,plain,
equal(or__dfg(u,not__dfg(u)),truth),
inference(spr,[status(thm),theory(equality)],[337,6]),
[iquote('0:SpR:337.0,6.0')] ).
cnf(477,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and__dfg(u,truth)),v),implies__dfg(implies__dfg(v,truth),truth)),truth),
inference(spr,[status(thm),theory(equality)],[187,3]),
[iquote('0:SpR:187.0,3.0')] ).
cnf(508,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and__dfg(u,truth)),v),truth),truth),
inference(rew,[status(thm),theory(equality)],[353,477]),
[iquote('0:Rew:353.0,477.0')] ).
cnf(580,plain,
equal(or__dfg(and__dfg(not__dfg(u),not__dfg(v)),and__dfg(and__dfg(u,truth),v)),xor__dfg(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[336,12]),
[iquote('0:SpR:336.0,12.0')] ).
cnf(582,plain,
equal(or__dfg(not__dfg(u),and__dfg(u,truth)),truth),
inference(spr,[status(thm),theory(equality)],[336,444]),
[iquote('0:SpR:336.0,444.0')] ).
cnf(586,plain,
equal(or__dfg(and__dfg(u,and__dfg(v,truth)),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(u,not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[336,12]),
[iquote('0:SpR:336.0,12.0')] ).
cnf(598,plain,
equal(implies__dfg(implies__dfg(truth,u),truth),truth),
inference(rew,[status(thm),theory(equality)],[582,508]),
[iquote('0:Rew:582.0,508.0')] ).
cnf(600,plain,
equal(implies__dfg(u,truth),truth),
inference(rew,[status(thm),theory(equality)],[2,598]),
[iquote('0:Rew:2.0,598.0')] ).
cnf(617,plain,
equal(or__dfg(and__dfg(u,and__dfg(truth,v)),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[8,580,22]),
[iquote('0:Rew:8.0,580.0,22.0,580.0')] ).
cnf(624,plain,
equal(or__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[600,6]),
[iquote('0:SpR:600.0,6.0')] ).
cnf(631,plain,
equal(implies__dfg(truth,or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[624,294]),
[iquote('0:Rew:624.0,294.0')] ).
cnf(637,plain,
equal(or__dfg(truth,u),truth),
inference(rew,[status(thm),theory(equality)],[2,631]),
[iquote('0:Rew:2.0,631.0')] ).
cnf(641,plain,
equal(and__dfg(falsehood,u),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[637,326]),
[iquote('0:Rew:637.0,326.0')] ).
cnf(642,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),implies__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[637,114]),
[iquote('0:Rew:637.0,114.0')] ).
cnf(643,plain,
equal(and__dfg(falsehood,u),falsehood),
inference(rew,[status(thm),theory(equality)],[17,641]),
[iquote('0:Rew:17.0,641.0')] ).
cnf(645,plain,
equal(or__dfg(and__dfg(truth,u),falsehood),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[643,410]),
[iquote('0:Rew:643.0,410.0')] ).
cnf(646,plain,
equal(or__dfg(and__dfg(u,truth),falsehood),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[643,412]),
[iquote('0:Rew:643.0,412.0')] ).
cnf(648,plain,
equal(or__dfg(falsehood,and__dfg(truth,not__dfg(u))),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[643,409]),
[iquote('0:Rew:643.0,409.0')] ).
cnf(651,plain,
equal(implies__dfg(implies__dfg(u,falsehood),falsehood),u),
inference(rew,[status(thm),theory(equality)],[2,642]),
[iquote('0:Rew:2.0,642.0')] ).
cnf(652,plain,
equal(and__dfg(truth,u),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[422,645]),
[iquote('0:Rew:422.0,645.0')] ).
cnf(655,plain,
equal(or__dfg(and__dfg(u,xor__dfg(falsehood,v)),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[652,617]),
[iquote('0:Rew:652.0,617.0')] ).
cnf(658,plain,
equal(not__dfg(and__dfg(u,truth)),xor__dfg(falsehood,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[652,382]),
[iquote('0:Rew:652.0,382.0')] ).
cnf(662,plain,
equal(and__dfg(u,truth),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[422,646]),
[iquote('0:Rew:422.0,646.0')] ).
cnf(663,plain,
equal(not__dfg(not__dfg(u)),xor__dfg(u,falsehood)),
inference(rew,[status(thm),theory(equality)],[662,336]),
[iquote('0:Rew:662.0,336.0')] ).
cnf(664,plain,
equal(implies__dfg(xor__dfg(u,falsehood),v),or__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[662,350]),
[iquote('0:Rew:662.0,350.0')] ).
cnf(668,plain,
equal(or__dfg(and__dfg(u,xor__dfg(v,falsehood)),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[662,586]),
[iquote('0:Rew:662.0,586.0')] ).
cnf(670,plain,
equal(not__dfg(xor__dfg(u,falsehood)),xor__dfg(falsehood,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[662,658]),
[iquote('0:Rew:662.0,658.0')] ).
cnf(671,plain,
equal(and__dfg(truth,not__dfg(u)),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[333,648]),
[iquote('0:Rew:333.0,648.0')] ).
cnf(672,plain,
equal(xor__dfg(falsehood,not__dfg(u)),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[652,671]),
[iquote('0:Rew:652.0,671.0')] ).
cnf(674,plain,
equal(not__dfg(xor__dfg(u,falsehood)),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[672,670]),
[iquote('0:Rew:672.0,670.0')] ).
cnf(715,plain,
equal(and__dfg(u,falsehood),falsehood),
inference(spr,[status(thm),theory(equality)],[643,11]),
[iquote('0:SpR:643.0,11.0')] ).
cnf(763,plain,
equal(implies__dfg(or__dfg(u,falsehood),falsehood),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[6,651]),
[iquote('0:SpR:6.0,651.0')] ).
cnf(768,plain,
equal(implies__dfg(u,falsehood),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[422,763]),
[iquote('0:Rew:422.0,763.0')] ).
cnf(769,plain,
equal(not__dfg(implies__dfg(u,falsehood)),u),
inference(rew,[status(thm),theory(equality)],[768,651]),
[iquote('0:Rew:768.0,651.0')] ).
cnf(774,plain,
equal(xor__dfg(u,falsehood),u),
inference(rew,[status(thm),theory(equality)],[663,769,768]),
[iquote('0:Rew:663.0,769.0,768.0,769.0')] ).
cnf(776,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[774,668]),
[iquote('0:Rew:774.0,668.0')] ).
cnf(777,plain,
equal(and__dfg(u,truth),u),
inference(rew,[status(thm),theory(equality)],[774,662]),
[iquote('0:Rew:774.0,662.0')] ).
cnf(778,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[774,663]),
[iquote('0:Rew:774.0,663.0')] ).
cnf(781,plain,
equal(xor__dfg(truth,u),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[774,674]),
[iquote('0:Rew:774.0,674.0')] ).
cnf(782,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[774,664]),
[iquote('0:Rew:774.0,664.0')] ).
cnf(784,plain,
~ equal(xor__dfg(y__dfg,xor__dfg(x__dfg,truth)),xor__dfg(x__dfg,not__dfg(y__dfg))),
inference(rew,[status(thm),theory(equality)],[781,24]),
[iquote('0:Rew:781.0,24.0')] ).
cnf(788,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[782,20]),
[iquote('0:Rew:782.0,20.0')] ).
cnf(820,plain,
equal(not__dfg(not__dfg(u)),and__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[2,788]),
[iquote('0:SpR:2.0,788.0')] ).
cnf(827,plain,
equal(xor__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[778,820,652]),
[iquote('0:Rew:778.0,820.0,652.0,820.0')] ).
cnf(829,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(not__dfg(u),not__dfg(v))),xor__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[827,655]),
[iquote('0:Rew:827.0,655.0')] ).
cnf(843,plain,
equal(xor__dfg(not__dfg(u),v),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[776,829]),
[iquote('0:Rew:776.0,829.0')] ).
cnf(854,plain,
equal(or__dfg(and__dfg(u,not__dfg(truth)),not__dfg(u)),xor__dfg(u,truth)),
inference(spr,[status(thm),theory(equality)],[777,12]),
[iquote('0:SpR:777.0,12.0')] ).
cnf(858,plain,
equal(xor__dfg(u,truth),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[333,854,715,17]),
[iquote('0:Rew:333.0,854.0,715.0,854.0,17.0,854.0')] ).
cnf(859,plain,
~ equal(xor__dfg(y__dfg,not__dfg(x__dfg)),xor__dfg(x__dfg,not__dfg(y__dfg))),
inference(rew,[status(thm),theory(equality)],[858,784]),
[iquote('0:Rew:858.0,784.0')] ).
cnf(1415,plain,
equal(xor__dfg(u,not__dfg(v)),xor__dfg(v,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[843,13]),
[iquote('0:SpR:843.0,13.0')] ).
cnf(1430,plain,
$false,
inference(unc,[status(thm)],[1415,859]),
[iquote('0:UnC:1415.0,859.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 10:12:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.34/0.53
% 0.34/0.53 SPASS V 3.9
% 0.34/0.53 SPASS beiseite: Proof found.
% 0.34/0.53 % SZS status Theorem
% 0.34/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/0.53 SPASS derived 972 clauses, backtracked 0 clauses, performed 0 splits and kept 338 clauses.
% 0.34/0.53 SPASS allocated 64429 KBytes.
% 0.34/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.34/0.53 0:00:00.04 for the input.
% 0.34/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.34/0.53 0:00:00.01 for inferences.
% 0.34/0.53 0:00:00.00 for the backtracking.
% 0.34/0.53 0:00:00.11 for the reduction.
% 0.34/0.53
% 0.34/0.53
% 0.34/0.53 Here is a proof with depth 6, length 108 :
% 0.34/0.53 % SZS output start Refutation
% See solution above
% 0.36/0.55 Formulae used in the proof : prove_alternative_wajsberg_axiom wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4 or_definition or_associativity or_commutativity and_definition and_commutativity xor_definition xor_commutativity and_star_definition and_star_associativity false_definition
% 0.36/0.55
%------------------------------------------------------------------------------