TSTP Solution File: LAT394-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT394-1 : TPTP v8.1.0. Released v5.4.0.
% 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 : Sun Jul 17 06:51:52 EDT 2022
% Result : Unsatisfiable 48.05s 48.24s
% Output : Refutation 48.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of clauses : 153 ( 153 unt; 0 nHn; 153 RR)
% Number of literals : 153 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(f(f(u,v),f(v,w)),x),f(v,f(f(v,f(f(u,u),u)),w))),v),
file('LAT394-1.p',unknown),
[] ).
cnf(2,axiom,
equal(f(f(u,u),f(v,v)),or__dfg(u,v)),
file('LAT394-1.p',unknown),
[] ).
cnf(3,axiom,
equal(f(f(u,v),f(u,v)),and__dfg(u,v)),
file('LAT394-1.p',unknown),
[] ).
cnf(4,axiom,
equal(f(u,u),neg(u)),
file('LAT394-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(f(x1__dfg,f(x1__dfg,x1__dfg)),f(x0__dfg,f(x0__dfg,x0__dfg))),
file('LAT394-1.p',unknown),
[] ).
cnf(6,plain,
equal(neg(f(u,v)),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(f(neg(u),neg(v)),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[4,2]),
[iquote('0:Rew:4.0,2.0,4.0,2.0')] ).
cnf(8,plain,
~ equal(f(x1__dfg,neg(x1__dfg)),f(x0__dfg,neg(x0__dfg))),
inference(rew,[status(thm),theory(equality)],[4,5]),
[iquote('0:Rew:4.0,5.0,4.0,5.0')] ).
cnf(9,plain,
equal(f(f(f(f(u,v),f(v,w)),x),f(v,f(f(v,f(neg(u),u)),w))),v),
inference(rew,[status(thm),theory(equality)],[4,1]),
[iquote('0:Rew:4.0,1.0')] ).
cnf(12,plain,
equal(and__dfg(u,u),neg(neg(u))),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(14,plain,
equal(or__dfg(u,u),neg(neg(u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(15,plain,
equal(and__dfg(neg(u),neg(v)),neg(or__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(17,plain,
equal(f(neg(u),and__dfg(v,w)),or__dfg(u,f(v,w))),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(18,plain,
equal(f(and__dfg(u,v),neg(w)),or__dfg(f(u,v),w)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(29,plain,
equal(f(and__dfg(u,v),and__dfg(w,x)),or__dfg(f(u,v),f(w,x))),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(43,plain,
equal(f(u,f(f(u,v),f(f(f(u,v),f(neg(f(w,u)),f(w,u))),x))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(44,plain,
equal(f(f(u,v),f(u,f(f(u,f(neg(f(f(w,u),f(u,x))),f(f(w,u),f(u,x)))),f(f(u,f(neg(w),w)),x)))),u),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(49,plain,
equal(f(f(f(f(u,f(neg(u),u)),f(f(neg(u),u),v)),w),f(f(neg(u),u),f(neg(f(neg(u),u)),v))),f(neg(u),u)),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(50,plain,
equal(f(f(f(f(u,v),f(v,f(v,f(neg(u),u)))),w),f(v,neg(f(v,f(neg(u),u))))),v),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(55,plain,
equal(f(f(f(neg(u),f(u,v)),w),f(u,f(f(u,f(neg(u),u)),v))),u),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(59,plain,
equal(f(f(neg(f(u,u)),v),f(u,f(f(u,f(neg(u),u)),u))),u),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(60,plain,
equal(f(neg(f(f(u,v),f(v,w))),f(v,f(f(v,f(neg(u),u)),w))),v),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(61,plain,
equal(f(f(neg(neg(u)),v),f(u,f(f(u,f(neg(u),u)),u))),u),
inference(rew,[status(thm),theory(equality)],[4,59]),
[iquote('0:Rew:4.0,59.0')] ).
cnf(62,plain,
equal(f(and__dfg(f(u,v),f(v,w)),f(v,f(f(v,f(neg(u),u)),w))),v),
inference(rew,[status(thm),theory(equality)],[6,60]),
[iquote('0:Rew:6.0,60.0')] ).
cnf(63,plain,
equal(f(u,f(f(u,v),f(f(f(u,v),f(and__dfg(w,u),f(w,u))),x))),f(u,v)),
inference(rew,[status(thm),theory(equality)],[6,43]),
[iquote('0:Rew:6.0,43.0')] ).
cnf(64,plain,
equal(f(f(f(f(u,v),f(v,f(v,f(neg(u),u)))),w),f(v,and__dfg(v,f(neg(u),u)))),v),
inference(rew,[status(thm),theory(equality)],[6,50]),
[iquote('0:Rew:6.0,50.0')] ).
cnf(67,plain,
equal(f(f(f(f(u,f(neg(u),u)),f(f(neg(u),u),v)),w),f(f(neg(u),u),f(and__dfg(neg(u),u),v))),f(neg(u),u)),
inference(rew,[status(thm),theory(equality)],[6,49]),
[iquote('0:Rew:6.0,49.0')] ).
cnf(69,plain,
equal(f(f(u,v),f(u,f(f(u,f(and__dfg(f(w,u),f(u,x)),f(f(w,u),f(u,x)))),f(f(u,f(neg(w),w)),x)))),u),
inference(rew,[status(thm),theory(equality)],[6,44]),
[iquote('0:Rew:6.0,44.0')] ).
cnf(162,plain,
equal(and__dfg(f(neg(neg(u)),v),f(u,f(f(u,f(neg(u),u)),u))),neg(u)),
inference(spr,[status(thm),theory(equality)],[61,6]),
[iquote('0:SpR:61.0,6.0')] ).
cnf(176,plain,
equal(f(neg(neg(neg(u))),f(u,f(f(u,f(neg(u),u)),u))),u),
inference(spr,[status(thm),theory(equality)],[4,61]),
[iquote('0:SpR:4.0,61.0')] ).
cnf(177,plain,
equal(f(or__dfg(neg(u),v),f(u,f(f(u,f(neg(u),u)),u))),u),
inference(spr,[status(thm),theory(equality)],[7,61]),
[iquote('0:SpR:7.0,61.0')] ).
cnf(183,plain,
equal(and__dfg(neg(neg(neg(u))),f(u,f(f(u,f(neg(u),u)),u))),neg(u)),
inference(spr,[status(thm),theory(equality)],[176,6]),
[iquote('0:SpR:176.0,6.0')] ).
cnf(200,plain,
equal(and__dfg(or__dfg(neg(u),v),f(u,f(f(u,f(neg(u),u)),u))),neg(u)),
inference(spr,[status(thm),theory(equality)],[177,6]),
[iquote('0:SpR:177.0,6.0')] ).
cnf(272,plain,
equal(f(and__dfg(f(u,v),neg(v)),f(v,f(f(v,f(neg(u),u)),v))),v),
inference(spr,[status(thm),theory(equality)],[4,62]),
[iquote('0:SpR:4.0,62.0')] ).
cnf(376,plain,
equal(and__dfg(and__dfg(f(u,v),neg(v)),f(v,f(f(v,f(neg(u),u)),v))),neg(v)),
inference(spr,[status(thm),theory(equality)],[272,6]),
[iquote('0:SpR:272.0,6.0')] ).
cnf(459,plain,
equal(f(u,f(neg(u),f(f(neg(u),f(neg(neg(u)),neg(u))),v))),neg(u)),
inference(spr,[status(thm),theory(equality)],[61,55]),
[iquote('0:SpR:61.0,55.0')] ).
cnf(460,plain,
equal(f(u,f(neg(u),f(f(neg(u),or__dfg(neg(u),u)),v))),neg(u)),
inference(rew,[status(thm),theory(equality)],[7,459]),
[iquote('0:Rew:7.0,459.0')] ).
cnf(486,plain,
equal(and__dfg(u,f(neg(u),f(f(neg(u),or__dfg(neg(u),u)),v))),neg(neg(u))),
inference(spr,[status(thm),theory(equality)],[460,6]),
[iquote('0:SpR:460.0,6.0')] ).
cnf(509,plain,
equal(f(neg(u),f(neg(neg(u)),u)),neg(neg(u))),
inference(spr,[status(thm),theory(equality)],[61,460]),
[iquote('0:SpR:61.0,460.0')] ).
cnf(523,plain,
equal(and__dfg(neg(u),f(neg(neg(u)),u)),neg(neg(neg(u)))),
inference(spr,[status(thm),theory(equality)],[509,6]),
[iquote('0:SpR:509.0,6.0')] ).
cnf(537,plain,
equal(f(neg(neg(u)),or__dfg(neg(neg(u)),u)),neg(neg(neg(u)))),
inference(spr,[status(thm),theory(equality)],[7,509]),
[iquote('0:SpR:7.0,509.0')] ).
cnf(556,plain,
equal(and__dfg(neg(neg(u)),or__dfg(neg(neg(u)),u)),neg(neg(neg(neg(u))))),
inference(spr,[status(thm),theory(equality)],[7,523]),
[iquote('0:SpR:7.0,523.0')] ).
cnf(1835,plain,
equal(f(u,f(f(u,v),f(and__dfg(w,u),f(w,u)))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[63]),
[iquote('0:SpR:63.0,63.0')] ).
cnf(1901,plain,
equal(f(neg(u),f(f(neg(u),f(u,v)),u)),f(neg(u),f(u,v))),
inference(spr,[status(thm),theory(equality)],[55,63]),
[iquote('0:SpR:55.0,63.0')] ).
cnf(2768,plain,
equal(f(u,f(f(u,v),f(and__dfg(u,u),neg(u)))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[4,1835]),
[iquote('0:SpR:4.0,1835.0')] ).
cnf(2841,plain,
equal(f(u,f(f(u,v),or__dfg(neg(u),u))),f(u,v)),
inference(rew,[status(thm),theory(equality)],[7,2768,12]),
[iquote('0:Rew:7.0,2768.0,12.0,2768.0')] ).
cnf(2909,plain,
equal(and__dfg(u,f(f(u,v),or__dfg(neg(u),u))),neg(f(u,v))),
inference(spr,[status(thm),theory(equality)],[2841,6]),
[iquote('0:SpR:2841.0,6.0')] ).
cnf(2975,plain,
equal(f(neg(u),f(or__dfg(u,v),or__dfg(neg(neg(u)),neg(u)))),or__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[7,2841]),
[iquote('0:SpR:7.0,2841.0')] ).
cnf(3000,plain,
equal(and__dfg(u,f(f(u,v),or__dfg(neg(u),u))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2909]),
[iquote('0:Rew:6.0,2909.0')] ).
cnf(3059,plain,
equal(and__dfg(neg(u),f(or__dfg(u,v),or__dfg(neg(neg(u)),neg(u)))),and__dfg(neg(u),neg(v))),
inference(spr,[status(thm),theory(equality)],[7,3000]),
[iquote('0:SpR:7.0,3000.0')] ).
cnf(3088,plain,
equal(and__dfg(neg(u),f(or__dfg(u,v),or__dfg(neg(neg(u)),neg(u)))),neg(or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[15,3059]),
[iquote('0:Rew:15.0,3059.0')] ).
cnf(3585,plain,
equal(and__dfg(neg(u),f(f(neg(u),f(u,v)),u)),neg(f(neg(u),f(u,v)))),
inference(spr,[status(thm),theory(equality)],[1901,6]),
[iquote('0:SpR:1901.0,6.0')] ).
cnf(3657,plain,
equal(f(neg(neg(u)),f(f(neg(neg(u)),or__dfg(u,v)),neg(u))),f(neg(neg(u)),or__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[2975,1901]),
[iquote('0:SpR:2975.0,1901.0')] ).
cnf(3670,plain,
equal(and__dfg(neg(u),f(f(neg(u),f(u,v)),u)),and__dfg(neg(u),f(u,v))),
inference(rew,[status(thm),theory(equality)],[6,3585]),
[iquote('0:Rew:6.0,3585.0')] ).
cnf(4124,plain,
equal(and__dfg(neg(neg(u)),f(f(neg(neg(u)),or__dfg(u,v)),neg(u))),and__dfg(neg(neg(u)),or__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[2975,3670]),
[iquote('0:SpR:2975.0,3670.0')] ).
cnf(6196,plain,
equal(f(u,f(f(u,v),f(u,v))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[69,63]),
[iquote('0:SpR:69.0,63.0')] ).
cnf(6205,plain,
equal(and__dfg(u,f(neg(u),neg(u))),neg(neg(u))),
inference(spr,[status(thm),theory(equality)],[69,486]),
[iquote('0:SpR:69.0,486.0')] ).
cnf(6212,plain,
equal(f(f(u,v),f(v,and__dfg(v,f(neg(u),u)))),v),
inference(spr,[status(thm),theory(equality)],[69,64]),
[iquote('0:SpR:69.0,64.0')] ).
cnf(6215,plain,
equal(f(f(f(f(u,f(neg(u),u)),neg(u)),v),f(f(neg(u),u),f(and__dfg(neg(u),u),f(neg(u),f(f(neg(u),f(and__dfg(f(w,neg(u)),f(neg(u),x)),f(f(w,neg(u)),f(neg(u),x)))),f(f(neg(u),f(neg(w),w)),x)))))),f(neg(u),u)),
inference(spr,[status(thm),theory(equality)],[69,67]),
[iquote('0:SpR:69.0,67.0')] ).
cnf(6487,plain,
equal(and__dfg(u,neg(neg(u))),neg(neg(u))),
inference(rew,[status(thm),theory(equality)],[14,6205,7]),
[iquote('0:Rew:14.0,6205.0,7.0,6205.0')] ).
cnf(6488,plain,
equal(f(u,and__dfg(u,v)),f(u,v)),
inference(rew,[status(thm),theory(equality)],[6,6196,4]),
[iquote('0:Rew:6.0,6196.0,4.0,6196.0')] ).
cnf(6723,plain,
equal(f(f(u,v),f(v,f(neg(u),u))),v),
inference(rew,[status(thm),theory(equality)],[6488,6212]),
[iquote('0:Rew:6488.0,6212.0')] ).
cnf(7226,plain,
equal(f(neg(u),neg(or__dfg(u,v))),f(neg(u),neg(v))),
inference(spr,[status(thm),theory(equality)],[15,6488]),
[iquote('0:SpR:15.0,6488.0')] ).
cnf(7228,plain,
equal(f(neg(neg(neg(u))),f(u,f(f(u,f(neg(u),u)),u))),f(neg(neg(neg(u))),neg(u))),
inference(spr,[status(thm),theory(equality)],[183,6488]),
[iquote('0:SpR:183.0,6488.0')] ).
cnf(7233,plain,
equal(f(and__dfg(f(u,v),neg(v)),f(v,f(f(v,f(neg(u),u)),v))),f(and__dfg(f(u,v),neg(v)),neg(v))),
inference(spr,[status(thm),theory(equality)],[376,6488]),
[iquote('0:SpR:376.0,6488.0')] ).
cnf(7234,plain,
equal(f(or__dfg(neg(u),v),f(u,f(f(u,f(neg(u),u)),u))),f(or__dfg(neg(u),v),neg(u))),
inference(spr,[status(thm),theory(equality)],[200,6488]),
[iquote('0:SpR:200.0,6488.0')] ).
cnf(7235,plain,
equal(f(f(neg(neg(u)),v),f(u,f(f(u,f(neg(u),u)),u))),f(f(neg(neg(u)),v),neg(u))),
inference(spr,[status(thm),theory(equality)],[162,6488]),
[iquote('0:SpR:162.0,6488.0')] ).
cnf(7444,plain,
equal(or__dfg(u,or__dfg(u,v)),or__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[7,7226]),
[iquote('0:Rew:7.0,7226.0,7.0,7226.0')] ).
cnf(7551,plain,
equal(f(or__dfg(neg(u),v),neg(u)),u),
inference(rew,[status(thm),theory(equality)],[177,7234]),
[iquote('0:Rew:177.0,7234.0')] ).
cnf(7552,plain,
equal(or__dfg(neg(neg(u)),u),u),
inference(rew,[status(thm),theory(equality)],[176,7228,7]),
[iquote('0:Rew:176.0,7228.0,7.0,7228.0')] ).
cnf(7553,plain,
equal(f(neg(neg(u)),u),neg(neg(neg(u)))),
inference(rew,[status(thm),theory(equality)],[7552,537]),
[iquote('0:Rew:7552.0,537.0')] ).
cnf(7554,plain,
equal(and__dfg(neg(neg(u)),u),neg(neg(neg(neg(u))))),
inference(rew,[status(thm),theory(equality)],[7552,556]),
[iquote('0:Rew:7552.0,556.0')] ).
cnf(7613,plain,
equal(f(f(neg(neg(u)),v),neg(u)),u),
inference(rew,[status(thm),theory(equality)],[61,7235]),
[iquote('0:Rew:61.0,7235.0')] ).
cnf(7616,plain,
equal(f(neg(neg(u)),or__dfg(u,v)),f(neg(neg(u)),u)),
inference(rew,[status(thm),theory(equality)],[7613,3657]),
[iquote('0:Rew:7613.0,3657.0')] ).
cnf(7617,plain,
equal(and__dfg(neg(neg(u)),or__dfg(u,v)),and__dfg(neg(neg(u)),u)),
inference(rew,[status(thm),theory(equality)],[7613,4124]),
[iquote('0:Rew:7613.0,4124.0')] ).
cnf(7618,plain,
equal(f(neg(neg(u)),or__dfg(u,v)),neg(neg(neg(u)))),
inference(rew,[status(thm),theory(equality)],[7553,7616]),
[iquote('0:Rew:7553.0,7616.0')] ).
cnf(7627,plain,
equal(and__dfg(neg(neg(u)),or__dfg(u,v)),neg(neg(neg(neg(u))))),
inference(rew,[status(thm),theory(equality)],[7554,7617]),
[iquote('0:Rew:7554.0,7617.0')] ).
cnf(7651,plain,
equal(or__dfg(f(f(u,v),neg(v)),v),v),
inference(rew,[status(thm),theory(equality)],[272,7233,18]),
[iquote('0:Rew:272.0,7233.0,18.0,7233.0')] ).
cnf(8035,plain,
equal(or__dfg(neg(and__dfg(u,v)),f(u,v)),f(u,v)),
inference(spr,[status(thm),theory(equality)],[6,7552]),
[iquote('0:SpR:6.0,7552.0')] ).
cnf(8123,plain,
equal(f(and__dfg(u,neg(neg(u))),f(neg(u),f(f(neg(u),f(neg(or__dfg(neg(u),v)),or__dfg(neg(u),v))),neg(u)))),neg(u)),
inference(spr,[status(thm),theory(equality)],[7551,272]),
[iquote('0:SpR:7551.0,272.0')] ).
cnf(8180,plain,
equal(f(neg(neg(u)),f(neg(u),f(f(neg(u),f(neg(or__dfg(neg(u),v)),or__dfg(neg(u),v))),neg(u)))),neg(u)),
inference(rew,[status(thm),theory(equality)],[6487,8123]),
[iquote('0:Rew:6487.0,8123.0')] ).
cnf(8865,plain,
equal(or__dfg(neg(neg(u)),u),neg(neg(neg(neg(u))))),
inference(spr,[status(thm),theory(equality)],[7553,7]),
[iquote('0:SpR:7553.0,7.0')] ).
cnf(8885,plain,
equal(or__dfg(neg(and__dfg(u,v)),f(u,v)),neg(neg(neg(and__dfg(u,v))))),
inference(spr,[status(thm),theory(equality)],[7553,17]),
[iquote('0:SpR:7553.0,17.0')] ).
cnf(8907,plain,
equal(neg(neg(neg(neg(u)))),u),
inference(rew,[status(thm),theory(equality)],[7552,8865]),
[iquote('0:Rew:7552.0,8865.0')] ).
cnf(8941,plain,
equal(and__dfg(neg(neg(u)),or__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[8907,7627]),
[iquote('0:Rew:8907.0,7627.0')] ).
cnf(8956,plain,
equal(neg(neg(neg(and__dfg(u,v)))),f(u,v)),
inference(rew,[status(thm),theory(equality)],[8035,8885]),
[iquote('0:Rew:8035.0,8885.0')] ).
cnf(9034,plain,
equal(or__dfg(neg(neg(neg(u))),v),f(u,neg(v))),
inference(spr,[status(thm),theory(equality)],[8907,7]),
[iquote('0:SpR:8907.0,7.0')] ).
cnf(9053,plain,
equal(and__dfg(neg(neg(neg(u))),f(f(neg(neg(neg(u))),v),or__dfg(u,neg(neg(neg(u)))))),and__dfg(neg(neg(neg(u))),v)),
inference(spr,[status(thm),theory(equality)],[8907,3000]),
[iquote('0:SpR:8907.0,3000.0')] ).
cnf(9056,plain,
equal(and__dfg(or__dfg(u,v),f(neg(neg(neg(u))),f(f(neg(neg(neg(u))),f(u,neg(neg(neg(u))))),neg(neg(neg(u)))))),u),
inference(spr,[status(thm),theory(equality)],[8907,200]),
[iquote('0:SpR:8907.0,200.0')] ).
cnf(9095,plain,
equal(or__dfg(u,neg(neg(neg(v)))),f(neg(u),v)),
inference(spr,[status(thm),theory(equality)],[8907,7]),
[iquote('0:SpR:8907.0,7.0')] ).
cnf(9205,plain,
equal(and__dfg(neg(neg(neg(u))),f(f(neg(neg(neg(u))),v),f(neg(u),u))),and__dfg(neg(neg(neg(u))),v)),
inference(rew,[status(thm),theory(equality)],[9095,9053]),
[iquote('0:Rew:9095.0,9053.0')] ).
cnf(10154,plain,
equal(f(neg(neg(u)),f(neg(u),v)),f(neg(neg(u)),u)),
inference(spr,[status(thm),theory(equality)],[7613,1901]),
[iquote('0:SpR:7613.0,1901.0')] ).
cnf(10177,plain,
equal(f(f(neg(u),v),u),neg(neg(neg(u)))),
inference(spr,[status(thm),theory(equality)],[8907,7613]),
[iquote('0:SpR:8907.0,7613.0')] ).
cnf(10211,plain,
equal(f(neg(u),neg(neg(neg(u)))),f(neg(u),f(u,v))),
inference(rew,[status(thm),theory(equality)],[10177,1901]),
[iquote('0:Rew:10177.0,1901.0')] ).
cnf(10264,plain,
equal(f(neg(neg(u)),f(neg(u),v)),neg(neg(neg(u)))),
inference(rew,[status(thm),theory(equality)],[7553,10154]),
[iquote('0:Rew:7553.0,10154.0')] ).
cnf(10265,plain,
equal(neg(neg(neg(u))),neg(u)),
inference(rew,[status(thm),theory(equality)],[10264,8180]),
[iquote('0:Rew:10264.0,8180.0')] ).
cnf(10289,plain,
equal(neg(neg(u)),u),
inference(rew,[status(thm),theory(equality)],[10265,8907]),
[iquote('0:Rew:10265.0,8907.0')] ).
cnf(10293,plain,
equal(neg(and__dfg(u,v)),f(u,v)),
inference(rew,[status(thm),theory(equality)],[10265,8956]),
[iquote('0:Rew:10265.0,8956.0')] ).
cnf(10316,plain,
equal(f(neg(u),v),or__dfg(u,neg(v))),
inference(rew,[status(thm),theory(equality)],[10265,9095]),
[iquote('0:Rew:10265.0,9095.0')] ).
cnf(10344,plain,
equal(f(neg(neg(u)),or__dfg(u,v)),neg(u)),
inference(rew,[status(thm),theory(equality)],[10265,7618]),
[iquote('0:Rew:10265.0,7618.0')] ).
cnf(10356,plain,
equal(f(u,neg(v)),or__dfg(neg(u),v)),
inference(rew,[status(thm),theory(equality)],[10265,9034]),
[iquote('0:Rew:10265.0,9034.0')] ).
cnf(10413,plain,
equal(and__dfg(neg(u),f(f(neg(u),v),f(neg(u),u))),and__dfg(neg(u),v)),
inference(rew,[status(thm),theory(equality)],[10265,9205]),
[iquote('0:Rew:10265.0,9205.0')] ).
cnf(10415,plain,
equal(and__dfg(or__dfg(u,v),f(neg(u),f(f(neg(u),f(u,neg(u))),neg(u)))),u),
inference(rew,[status(thm),theory(equality)],[10265,9056]),
[iquote('0:Rew:10265.0,9056.0')] ).
cnf(10433,plain,
equal(and__dfg(u,u),u),
inference(rew,[status(thm),theory(equality)],[10289,12]),
[iquote('0:Rew:10289.0,12.0')] ).
cnf(10434,plain,
equal(or__dfg(u,u),u),
inference(rew,[status(thm),theory(equality)],[10289,14]),
[iquote('0:Rew:10289.0,14.0')] ).
cnf(10441,plain,
equal(and__dfg(neg(u),f(or__dfg(u,v),or__dfg(u,neg(u)))),neg(or__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[10289,3088]),
[iquote('0:Rew:10289.0,3088.0')] ).
cnf(10448,plain,
equal(and__dfg(u,or__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[10289,8941]),
[iquote('0:Rew:10289.0,8941.0')] ).
cnf(10838,plain,
equal(f(f(f(f(u,or__dfg(u,neg(u))),f(or__dfg(u,neg(u)),v)),w),f(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),v))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[10316,67]),
[iquote('0:Rew:10316.0,67.0')] ).
cnf(10967,plain,
equal(f(f(f(f(u,f(neg(u),u)),neg(u)),v),f(f(neg(u),u),f(and__dfg(neg(u),u),or__dfg(u,neg(f(f(neg(u),f(and__dfg(f(w,neg(u)),f(neg(u),x)),f(f(w,neg(u)),f(neg(u),x)))),f(f(neg(u),f(neg(w),w)),x))))))),f(neg(u),u)),
inference(rew,[status(thm),theory(equality)],[10316,6215]),
[iquote('0:Rew:10316.0,6215.0')] ).
cnf(11684,plain,
equal(f(f(u,v),f(v,or__dfg(u,neg(u)))),v),
inference(rew,[status(thm),theory(equality)],[10316,6723]),
[iquote('0:Rew:10316.0,6723.0')] ).
cnf(11872,plain,
~ equal(f(x0__dfg,neg(x0__dfg)),or__dfg(neg(x1__dfg),x1__dfg)),
inference(rew,[status(thm),theory(equality)],[10356,8]),
[iquote('0:Rew:10356.0,8.0')] ).
cnf(11906,plain,
equal(or__dfg(or__dfg(neg(f(u,v)),v),v),v),
inference(rew,[status(thm),theory(equality)],[10356,7651]),
[iquote('0:Rew:10356.0,7651.0')] ).
cnf(11911,plain,
equal(f(u,or__dfg(u,v)),neg(u)),
inference(rew,[status(thm),theory(equality)],[10289,10344]),
[iquote('0:Rew:10289.0,10344.0')] ).
cnf(11924,plain,
~ equal(or__dfg(neg(x1__dfg),x1__dfg),or__dfg(neg(x0__dfg),x0__dfg)),
inference(rew,[status(thm),theory(equality)],[10356,11872]),
[iquote('0:Rew:10356.0,11872.0')] ).
cnf(11925,plain,
equal(or__dfg(or__dfg(and__dfg(u,v),v),v),v),
inference(rew,[status(thm),theory(equality)],[6,11906]),
[iquote('0:Rew:6.0,11906.0')] ).
cnf(11950,plain,
equal(or__dfg(u,neg(f(u,v))),u),
inference(rew,[status(thm),theory(equality)],[10434,10211,10289,10316]),
[iquote('0:Rew:10434.0,10211.0,10289.0,10211.0,10316.0,10211.0,10289.0,10211.0,10316.0,10211.0')] ).
cnf(11951,plain,
equal(or__dfg(u,and__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[6,11950]),
[iquote('0:Rew:6.0,11950.0')] ).
cnf(12006,plain,
equal(neg(or__dfg(u,neg(v))),and__dfg(neg(u),v)),
inference(rew,[status(thm),theory(equality)],[10441,10413,10316]),
[iquote('0:Rew:10441.0,10413.0,10316.0,10413.0,10316.0,10413.0')] ).
cnf(12042,plain,
equal(and__dfg(or__dfg(u,v),or__dfg(u,neg(or__dfg(neg(u),u)))),u),
inference(rew,[status(thm),theory(equality)],[10316,10415,10448,12006,10356]),
[iquote('0:Rew:10316.0,10415.0,10448.0,10415.0,12006.0,10415.0,10356.0,10415.0,10316.0,10415.0,10356.0,10415.0')] ).
cnf(12595,plain,
equal(f(f(or__dfg(u,neg(f(or__dfg(u,neg(u)),v))),w),f(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),v))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[10316,10838,11911]),
[iquote('0:Rew:10316.0,10838.0,11911.0,10838.0')] ).
cnf(12596,plain,
equal(f(f(or__dfg(u,and__dfg(or__dfg(u,neg(u)),v)),w),f(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),v))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[6,12595]),
[iquote('0:Rew:6.0,12595.0')] ).
cnf(13592,plain,
equal(f(f(f(f(u,f(neg(u),u)),neg(u)),v),f(f(neg(u),u),f(and__dfg(neg(u),u),or__dfg(u,and__dfg(f(neg(u),f(and__dfg(f(w,neg(u)),f(neg(u),x)),f(f(w,neg(u)),f(neg(u),x)))),f(f(neg(u),f(neg(w),w)),x)))))),f(neg(u),u)),
inference(rew,[status(thm),theory(equality)],[6,10967]),
[iquote('0:Rew:6.0,10967.0')] ).
cnf(13593,plain,
equal(f(f(u,v),f(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),or__dfg(u,and__dfg(or__dfg(u,neg(f(and__dfg(or__dfg(neg(w),u),or__dfg(u,neg(x))),f(or__dfg(neg(w),u),or__dfg(u,neg(x)))))),f(or__dfg(u,and__dfg(neg(w),w)),x)))))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[10434,13592,10289,10316,11911,10356,12006]),
[iquote('0:Rew:10434.0,13592.0,10289.0,13592.0,10316.0,13592.0,11911.0,13592.0,10316.0,13592.0,10356.0,13592.0,10316.0,13592.0,12006.0,13592.0,10316.0,13592.0,10316.0,13592.0,10316.0,13592.0')] ).
cnf(13594,plain,
equal(f(f(u,v),f(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),or__dfg(u,and__dfg(or__dfg(u,and__dfg(and__dfg(or__dfg(neg(w),u),or__dfg(u,neg(x))),f(or__dfg(neg(w),u),or__dfg(u,neg(x))))),f(or__dfg(u,and__dfg(neg(w),w)),x)))))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[6,13593]),
[iquote('0:Rew:6.0,13593.0')] ).
cnf(14380,plain,
equal(neg(or__dfg(neg(u),v)),and__dfg(u,neg(v))),
inference(spr,[status(thm),theory(equality)],[10289,15]),
[iquote('0:SpR:10289.0,15.0')] ).
cnf(14493,plain,
equal(and__dfg(or__dfg(u,v),or__dfg(u,and__dfg(u,neg(u)))),u),
inference(rew,[status(thm),theory(equality)],[14380,12042]),
[iquote('0:Rew:14380.0,12042.0')] ).
cnf(14563,plain,
equal(and__dfg(or__dfg(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[11951,14493]),
[iquote('0:Rew:11951.0,14493.0')] ).
cnf(14645,plain,
equal(or__dfg(f(u,v),f(w,w)),f(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[10433,29]),
[iquote('0:SpR:10433.0,29.0')] ).
cnf(14656,plain,
equal(or__dfg(f(u,v),neg(w)),f(and__dfg(u,v),w)),
inference(rew,[status(thm),theory(equality)],[4,14645]),
[iquote('0:Rew:4.0,14645.0')] ).
cnf(15152,plain,
equal(or__dfg(neg(u),neg(v)),f(u,v)),
inference(spr,[status(thm),theory(equality)],[10289,10316]),
[iquote('0:SpR:10289.0,10316.0')] ).
cnf(15153,plain,
equal(or__dfg(and__dfg(u,v),neg(w)),f(f(u,v),w)),
inference(spr,[status(thm),theory(equality)],[10293,10316]),
[iquote('0:SpR:10293.0,10316.0')] ).
cnf(15406,plain,
equal(or__dfg(or__dfg(neg(or__dfg(u,v)),neg(v)),neg(v)),neg(v)),
inference(spr,[status(thm),theory(equality)],[15,11925]),
[iquote('0:SpR:15.0,11925.0')] ).
cnf(15416,plain,
equal(or__dfg(f(or__dfg(u,v),v),neg(v)),neg(v)),
inference(rew,[status(thm),theory(equality)],[15152,15406]),
[iquote('0:Rew:15152.0,15406.0')] ).
cnf(15417,plain,
equal(f(and__dfg(or__dfg(u,v),v),v),neg(v)),
inference(rew,[status(thm),theory(equality)],[14656,15416]),
[iquote('0:Rew:14656.0,15416.0')] ).
cnf(16031,plain,
equal(and__dfg(and__dfg(or__dfg(u,v),v),v),neg(neg(v))),
inference(spr,[status(thm),theory(equality)],[15417,6]),
[iquote('0:SpR:15417.0,6.0')] ).
cnf(16072,plain,
equal(and__dfg(and__dfg(or__dfg(u,v),v),v),v),
inference(rew,[status(thm),theory(equality)],[10289,16031]),
[iquote('0:Rew:10289.0,16031.0')] ).
cnf(16118,plain,
equal(or__dfg(and__dfg(or__dfg(u,v),v),v),and__dfg(or__dfg(u,v),v)),
inference(spr,[status(thm),theory(equality)],[16072,11951]),
[iquote('0:SpR:16072.0,11951.0')] ).
cnf(18030,plain,
equal(f(f(u,v),f(w,x)),or__dfg(and__dfg(u,v),and__dfg(w,x))),
inference(spr,[status(thm),theory(equality)],[6,15153]),
[iquote('0:SpR:6.0,15153.0')] ).
cnf(18073,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(v,or__dfg(u,neg(u)))),v),
inference(rew,[status(thm),theory(equality)],[18030,11684]),
[iquote('0:Rew:18030.0,11684.0')] ).
cnf(18202,plain,
equal(or__dfg(and__dfg(or__dfg(u,and__dfg(or__dfg(u,neg(u)),v)),w),and__dfg(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),v))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[18030,12596]),
[iquote('0:Rew:18030.0,12596.0')] ).
cnf(18659,plain,
equal(or__dfg(and__dfg(u,v),and__dfg(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),or__dfg(u,and__dfg(or__dfg(u,and__dfg(and__dfg(or__dfg(neg(w),u),or__dfg(u,neg(x))),f(or__dfg(neg(w),u),or__dfg(u,neg(x))))),f(or__dfg(u,and__dfg(neg(w),w)),x)))))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[18030,13594]),
[iquote('0:Rew:18030.0,13594.0')] ).
cnf(19545,plain,
equal(or__dfg(and__dfg(u,v),v),v),
inference(spr,[status(thm),theory(equality)],[18073,7444]),
[iquote('0:SpR:18073.0,7444.0')] ).
cnf(19649,plain,
equal(and__dfg(or__dfg(u,v),v),v),
inference(rew,[status(thm),theory(equality)],[19545,16118]),
[iquote('0:Rew:19545.0,16118.0')] ).
cnf(20496,plain,
equal(or__dfg(and__dfg(u,or__dfg(v,or__dfg(u,neg(u)))),or__dfg(u,neg(u))),or__dfg(v,or__dfg(u,neg(u)))),
inference(spr,[status(thm),theory(equality)],[19649,18073]),
[iquote('0:SpR:19649.0,18073.0')] ).
cnf(21293,plain,
equal(and__dfg(or__dfg(u,neg(u)),f(and__dfg(neg(u),u),v)),or__dfg(u,neg(u))),
inference(spr,[status(thm),theory(equality)],[18202,19545]),
[iquote('0:SpR:18202.0,19545.0')] ).
cnf(21360,plain,
equal(or__dfg(and__dfg(u,v),or__dfg(u,neg(u))),or__dfg(u,neg(u))),
inference(rew,[status(thm),theory(equality)],[21293,18659]),
[iquote('0:Rew:21293.0,18659.0')] ).
cnf(21375,plain,
equal(or__dfg(u,or__dfg(v,neg(v))),or__dfg(v,neg(v))),
inference(rew,[status(thm),theory(equality)],[21360,20496]),
[iquote('0:Rew:21360.0,20496.0')] ).
cnf(21508,plain,
equal(and__dfg(u,or__dfg(v,neg(v))),u),
inference(spr,[status(thm),theory(equality)],[21375,10448]),
[iquote('0:SpR:21375.0,10448.0')] ).
cnf(21509,plain,
equal(and__dfg(or__dfg(u,neg(u)),v),v),
inference(spr,[status(thm),theory(equality)],[21375,14563]),
[iquote('0:SpR:21375.0,14563.0')] ).
cnf(22447,plain,
equal(and__dfg(u,or__dfg(neg(v),v)),u),
inference(spr,[status(thm),theory(equality)],[10289,21508]),
[iquote('0:SpR:10289.0,21508.0')] ).
cnf(22800,plain,
equal(and__dfg(or__dfg(neg(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[10289,21509]),
[iquote('0:SpR:10289.0,21509.0')] ).
cnf(23351,plain,
equal(or__dfg(neg(u),u),or__dfg(neg(v),v)),
inference(spr,[status(thm),theory(equality)],[22800,22447]),
[iquote('0:SpR:22800.0,22447.0')] ).
cnf(23377,plain,
$false,
inference(unc,[status(thm)],[23351,11924]),
[iquote('0:UnC:23351.0,11924.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT394-1 : TPTP v8.1.0. Released v5.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 28 19:55:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 48.05/48.24
% 48.05/48.24 SPASS V 3.9
% 48.05/48.24 SPASS beiseite: Proof found.
% 48.05/48.24 % SZS status Theorem
% 48.05/48.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.05/48.24 SPASS derived 13391 clauses, backtracked 0 clauses, performed 0 splits and kept 6535 clauses.
% 48.05/48.24 SPASS allocated 179625 KBytes.
% 48.05/48.24 SPASS spent 0:0:47.90 on the problem.
% 48.05/48.24 0:00:00.04 for the input.
% 48.05/48.24 0:00:00.00 for the FLOTTER CNF translation.
% 48.05/48.24 0:00:00.11 for inferences.
% 48.05/48.24 0:00:00.00 for the backtracking.
% 48.05/48.24 0:0:47.72 for the reduction.
% 48.05/48.24
% 48.05/48.24
% 48.05/48.24 Here is a proof with depth 11, length 153 :
% 48.05/48.24 % SZS output start Refutation
% See solution above
% 48.59/48.80 Formulae used in the proof : sos sos_001 sos_002 sos_003 goals
% 48.59/48.80
%------------------------------------------------------------------------------