TSTP Solution File: GRP777+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP777+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:49:22 EDT 2022
% Result : Theorem 1.49s 1.66s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 10
% Syntax : Number of clauses : 146 ( 146 unt; 0 nHn; 146 RR)
% Number of literals : 146 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,u),u),
file('GRP777+1.p',unknown),
[] ).
cnf(2,axiom,
equal(difference(u,product(u,v)),v),
file('GRP777+1.p',unknown),
[] ).
cnf(3,axiom,
equal(product(u,difference(u,v)),v),
file('GRP777+1.p',unknown),
[] ).
cnf(4,axiom,
equal(quotient(product(u,v),v),u),
file('GRP777+1.p',unknown),
[] ).
cnf(5,axiom,
equal(product(quotient(u,v),v),u),
file('GRP777+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(bigC(c,c,skc1),bigC(a,b,skc1)),
file('GRP777+1.p',unknown),
[] ).
cnf(7,axiom,
equal(product(product(a,c),product(c,b)),product(a,b)),
file('GRP777+1.p',unknown),
[] ).
cnf(8,axiom,
equal(product(product(u,v),product(w,u)),bigC(u,v,w)),
file('GRP777+1.p',unknown),
[] ).
cnf(9,axiom,
equal(product(product(product(u,v),v),product(v,product(v,u))),v),
file('GRP777+1.p',unknown),
[] ).
cnf(10,axiom,
equal(product(product(u,v),product(w,x)),product(product(u,w),product(v,x))),
file('GRP777+1.p',unknown),
[] ).
cnf(20,plain,
equal(quotient(u,difference(v,u)),v),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(25,plain,
equal(difference(quotient(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(38,plain,
equal(quotient(product(a,b),product(c,b)),product(a,c)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(48,plain,
equal(quotient(bigC(u,v,w),product(w,u)),product(u,v)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(49,plain,
equal(difference(product(u,v),bigC(u,v,w)),product(w,u)),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(53,plain,
equal(product(product(u,v),u),bigC(u,v,u)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(54,plain,
equal(product(product(difference(u,v),w),v),bigC(difference(u,v),w,u)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(55,plain,
equal(bigC(u,v,quotient(w,u)),product(product(u,v),w)),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(57,plain,
equal(product(u,product(v,u)),bigC(u,u,v)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(58,plain,
equal(bigC(u,difference(u,v),w),product(v,product(w,u))),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(63,plain,
equal(difference(product(product(u,v),v),v),product(v,product(v,u))),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(79,plain,
equal(product(product(product(a,b),product(c,b)),product(product(c,b),product(product(c,b),product(a,c)))),product(c,b)),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(87,plain,
equal(product(product(product(a,b),product(c,b)),product(product(c,b),bigC(c,b,a))),product(c,b)),
inference(rew,[status(thm),theory(equality)],[8,79]),
[iquote('0:Rew:8.0,79.0')] ).
cnf(88,plain,
equal(product(product(product(a,c),product(c,b)),product(product(b,b),bigC(c,b,a))),product(c,b)),
inference(rew,[status(thm),theory(equality)],[10,87]),
[iquote('0:Rew:10.0,87.0,10.0,87.0')] ).
cnf(89,plain,
equal(product(product(a,b),product(b,bigC(c,b,a))),product(c,b)),
inference(rew,[status(thm),theory(equality)],[7,88,1]),
[iquote('0:Rew:7.0,88.0,1.0,88.0')] ).
cnf(97,plain,
equal(quotient(bigC(u,v,u),u),product(u,v)),
inference(spr,[status(thm),theory(equality)],[53,4]),
[iquote('0:SpR:53.0,4.0')] ).
cnf(108,plain,
equal(bigC(quotient(u,v),v,quotient(u,v)),product(u,quotient(u,v))),
inference(spr,[status(thm),theory(equality)],[5,53]),
[iquote('0:SpR:5.0,53.0')] ).
cnf(126,plain,
equal(difference(u,bigC(u,u,v)),product(v,u)),
inference(spr,[status(thm),theory(equality)],[57,2]),
[iquote('0:SpR:57.0,2.0')] ).
cnf(171,plain,
equal(product(product(u,v),product(w,u)),bigC(u,w,v)),
inference(spr,[status(thm),theory(equality)],[10,8]),
[iquote('0:SpR:10.0,8.0')] ).
cnf(203,plain,
equal(product(product(u,v),product(w,v)),product(product(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(211,plain,
equal(product(product(u,v),product(u,w)),product(u,product(v,w))),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(212,plain,
equal(product(product(u,v),product(difference(u,w),x)),product(w,product(v,x))),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(223,plain,
equal(product(product(u,product(v,w)),product(x,product(y,v))),product(product(u,x),bigC(v,w,y))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(237,plain,
equal(bigC(u,v,w),bigC(u,w,v)),
inference(rew,[status(thm),theory(equality)],[8,171]),
[iquote('0:Rew:8.0,171.0')] ).
cnf(238,plain,
equal(product(product(a,b),product(b,bigC(c,a,b))),product(c,b)),
inference(rew,[status(thm),theory(equality)],[237,89]),
[iquote('0:Rew:237.0,89.0')] ).
cnf(284,plain,
equal(quotient(bigC(u,u,v),u),product(u,v)),
inference(spr,[status(thm),theory(equality)],[237,97]),
[iquote('0:SpR:237.0,97.0')] ).
cnf(293,plain,
equal(difference(u,bigC(u,v,u)),product(v,u)),
inference(spr,[status(thm),theory(equality)],[237,126]),
[iquote('0:SpR:237.0,126.0')] ).
cnf(299,plain,
equal(difference(product(u,v),bigC(u,u,v)),u),
inference(spr,[status(thm),theory(equality)],[284,25]),
[iquote('0:SpR:284.0,25.0')] ).
cnf(320,plain,
equal(quotient(bigC(difference(u,v),w,u),v),product(difference(u,v),w)),
inference(spr,[status(thm),theory(equality)],[3,48]),
[iquote('0:SpR:3.0,48.0')] ).
cnf(329,plain,
equal(quotient(bigC(u,v,w),product(v,u)),product(u,w)),
inference(spr,[status(thm),theory(equality)],[237,48]),
[iquote('0:SpR:237.0,48.0')] ).
cnf(343,plain,
equal(difference(u,bigC(v,v,difference(v,u))),v),
inference(spr,[status(thm),theory(equality)],[3,299]),
[iquote('0:SpR:3.0,299.0')] ).
cnf(371,plain,
equal(bigC(u,u,difference(u,v)),product(v,u)),
inference(spr,[status(thm),theory(equality)],[343,3]),
[iquote('0:SpR:343.0,3.0')] ).
cnf(398,plain,
equal(difference(u,product(v,u)),product(difference(u,v),u)),
inference(spr,[status(thm),theory(equality)],[371,126]),
[iquote('0:SpR:371.0,126.0')] ).
cnf(427,plain,
equal(product(difference(difference(u,v),u),difference(u,v)),difference(difference(u,v),v)),
inference(spr,[status(thm),theory(equality)],[3,398]),
[iquote('0:SpR:3.0,398.0')] ).
cnf(428,plain,
equal(product(difference(u,quotient(v,u)),u),difference(u,v)),
inference(spr,[status(thm),theory(equality)],[5,398]),
[iquote('0:SpR:5.0,398.0')] ).
cnf(430,plain,
equal(product(difference(product(u,v),product(v,w)),product(u,v)),difference(product(u,v),bigC(v,w,u))),
inference(spr,[status(thm),theory(equality)],[8,398]),
[iquote('0:SpR:8.0,398.0')] ).
cnf(447,plain,
equal(difference(product(u,v),bigC(u,w,v)),product(w,u)),
inference(spr,[status(thm),theory(equality)],[237,49]),
[iquote('0:SpR:237.0,49.0')] ).
cnf(504,plain,
equal(quotient(difference(u,v),u),difference(u,quotient(v,u))),
inference(spr,[status(thm),theory(equality)],[428,4]),
[iquote('0:SpR:428.0,4.0')] ).
cnf(507,plain,
equal(product(product(difference(u,v),u),product(u,product(u,difference(u,quotient(v,u))))),u),
inference(spr,[status(thm),theory(equality)],[428,9]),
[iquote('0:SpR:428.0,9.0')] ).
cnf(536,plain,
equal(product(product(difference(u,v),u),product(u,quotient(v,u))),u),
inference(rew,[status(thm),theory(equality)],[3,507]),
[iquote('0:Rew:3.0,507.0')] ).
cnf(552,plain,
equal(difference(product(u,v),quotient(bigC(u,v,w),product(u,v))),quotient(product(w,u),product(u,v))),
inference(spr,[status(thm),theory(equality)],[49,504]),
[iquote('0:SpR:49.0,504.0')] ).
cnf(597,plain,
equal(bigC(u,quotient(v,u),w),product(product(u,w),v)),
inference(spr,[status(thm),theory(equality)],[55,237]),
[iquote('0:SpR:55.0,237.0')] ).
cnf(602,plain,
equal(quotient(product(product(u,u),v),u),product(u,quotient(v,u))),
inference(spr,[status(thm),theory(equality)],[55,284]),
[iquote('0:SpR:55.0,284.0')] ).
cnf(610,plain,
equal(product(product(u,v),bigC(u,u,w)),bigC(u,v,product(u,w))),
inference(spr,[status(thm),theory(equality)],[284,55]),
[iquote('0:SpR:284.0,55.0')] ).
cnf(614,plain,
equal(quotient(product(u,v),u),product(u,quotient(v,u))),
inference(rew,[status(thm),theory(equality)],[1,602]),
[iquote('0:Rew:1.0,602.0')] ).
cnf(630,plain,
equal(product(product(u,v),quotient(product(w,u),product(u,v))),quotient(bigC(u,v,w),product(u,v))),
inference(spr,[status(thm),theory(equality)],[8,614]),
[iquote('0:SpR:8.0,614.0')] ).
cnf(707,plain,
equal(product(bigC(u,v,u),product(w,u)),bigC(u,product(v,u),w)),
inference(spr,[status(thm),theory(equality)],[293,58]),
[iquote('0:SpR:293.0,58.0')] ).
cnf(727,plain,
equal(product(difference(product(u,v),product(v,w)),product(u,v)),difference(product(u,v),bigC(v,u,w))),
inference(spr,[status(thm),theory(equality)],[329,428]),
[iquote('0:SpR:329.0,428.0')] ).
cnf(751,plain,
equal(difference(product(u,v),bigC(v,w,u)),difference(product(u,v),bigC(v,u,w))),
inference(rew,[status(thm),theory(equality)],[430,727]),
[iquote('0:Rew:430.0,727.0')] ).
cnf(915,plain,
equal(product(u,product(u,quotient(v,u))),difference(product(v,u),u)),
inference(spr,[status(thm),theory(equality)],[5,63]),
[iquote('0:SpR:5.0,63.0')] ).
cnf(1015,plain,
equal(product(bigC(u,v,u),product(w,u)),product(product(product(u,v),w),u)),
inference(spr,[status(thm),theory(equality)],[53,203]),
[iquote('0:SpR:53.0,203.0')] ).
cnf(1025,plain,
equal(product(product(product(u,v),w),u),bigC(u,product(v,u),w)),
inference(rew,[status(thm),theory(equality)],[707,1015]),
[iquote('0:Rew:707.0,1015.0')] ).
cnf(1075,plain,
equal(product(product(u,product(v,w)),product(x,product(u,v))),bigC(product(u,v),product(u,w),x)),
inference(spr,[status(thm),theory(equality)],[211,8]),
[iquote('0:SpR:211.0,8.0')] ).
cnf(1104,plain,
equal(product(product(u,product(v,w)),product(x,product(v,y))),product(product(u,x),product(v,product(w,y)))),
inference(spr,[status(thm),theory(equality)],[211,10]),
[iquote('0:SpR:211.0,10.0')] ).
cnf(1114,plain,
equal(product(product(u,v),bigC(u,u,w)),product(u,product(v,product(w,u)))),
inference(spr,[status(thm),theory(equality)],[57,211]),
[iquote('0:SpR:57.0,211.0')] ).
cnf(1139,plain,
equal(product(u,product(v,product(w,u))),bigC(u,v,product(u,w))),
inference(rew,[status(thm),theory(equality)],[610,1114]),
[iquote('0:Rew:610.0,1114.0')] ).
cnf(1161,plain,
equal(bigC(product(u,v),product(u,w),x),product(product(u,x),bigC(v,w,u))),
inference(rew,[status(thm),theory(equality)],[223,1075]),
[iquote('0:Rew:223.0,1075.0')] ).
cnf(1197,plain,
equal(bigC(product(difference(u,v),u),product(u,quotient(v,u)),w),product(u,product(w,product(difference(u,v),u)))),
inference(spr,[status(thm),theory(equality)],[536,8]),
[iquote('0:SpR:536.0,8.0')] ).
cnf(1202,plain,
equal(difference(u,bigC(product(difference(u,v),u),product(u,quotient(v,u)),w)),product(w,product(difference(u,v),u))),
inference(spr,[status(thm),theory(equality)],[536,49]),
[iquote('0:SpR:536.0,49.0')] ).
cnf(1214,plain,
equal(bigC(product(u,quotient(v,u)),w,product(difference(u,v),u)),product(product(product(u,quotient(v,u)),w),u)),
inference(spr,[status(thm),theory(equality)],[536,8]),
[iquote('0:SpR:536.0,8.0')] ).
cnf(1215,plain,
equal(quotient(bigC(product(u,quotient(v,u)),w,product(difference(u,v),u)),u),product(product(u,quotient(v,u)),w)),
inference(spr,[status(thm),theory(equality)],[536,48]),
[iquote('0:SpR:536.0,48.0')] ).
cnf(1217,plain,
equal(bigC(product(u,quotient(v,u)),product(u,quotient(v,u)),product(difference(u,v),u)),product(product(u,quotient(v,u)),u)),
inference(spr,[status(thm),theory(equality)],[536,57]),
[iquote('0:SpR:536.0,57.0')] ).
cnf(1264,plain,
equal(bigC(product(u,quotient(v,u)),w,product(difference(u,v),u)),bigC(u,product(quotient(v,u),u),w)),
inference(rew,[status(thm),theory(equality)],[1025,1214]),
[iquote('0:Rew:1025.0,1214.0')] ).
cnf(1265,plain,
equal(bigC(product(u,quotient(v,u)),w,product(difference(u,v),u)),bigC(u,v,w)),
inference(rew,[status(thm),theory(equality)],[5,1264]),
[iquote('0:Rew:5.0,1264.0')] ).
cnf(1266,plain,
equal(product(product(u,quotient(v,u)),w),quotient(bigC(u,v,w),u)),
inference(rew,[status(thm),theory(equality)],[1265,1215]),
[iquote('0:Rew:1265.0,1215.0')] ).
cnf(1276,plain,
equal(bigC(product(difference(u,v),u),product(u,quotient(v,u)),w),bigC(u,w,product(u,difference(u,v)))),
inference(rew,[status(thm),theory(equality)],[1139,1197]),
[iquote('0:Rew:1139.0,1197.0')] ).
cnf(1277,plain,
equal(bigC(product(difference(u,v),u),product(u,quotient(v,u)),w),bigC(u,w,v)),
inference(rew,[status(thm),theory(equality)],[3,1276]),
[iquote('0:Rew:3.0,1276.0')] ).
cnf(1278,plain,
equal(product(u,product(difference(v,w),v)),difference(v,bigC(v,u,w))),
inference(rew,[status(thm),theory(equality)],[1277,1202]),
[iquote('0:Rew:1277.0,1202.0')] ).
cnf(1295,plain,
equal(bigC(product(u,quotient(v,u)),product(u,quotient(v,u)),product(difference(u,v),u)),product(u,v)),
inference(rew,[status(thm),theory(equality)],[1,1217,597,53]),
[iquote('0:Rew:1.0,1217.0,597.0,1217.0,53.0,1217.0')] ).
cnf(1296,plain,
equal(product(difference(u,bigC(u,u,v)),bigC(quotient(v,u),quotient(v,u),u)),product(u,v)),
inference(rew,[status(thm),theory(equality)],[1278,1295,1161]),
[iquote('0:Rew:1278.0,1295.0,1161.0,1295.0')] ).
cnf(1297,plain,
equal(product(product(u,v),bigC(quotient(u,v),v,quotient(u,v))),product(v,u)),
inference(rew,[status(thm),theory(equality)],[126,1296,237]),
[iquote('0:Rew:126.0,1296.0,237.0,1296.0')] ).
cnf(1298,plain,
equal(product(product(u,v),product(u,quotient(u,v))),product(v,u)),
inference(rew,[status(thm),theory(equality)],[108,1297]),
[iquote('0:Rew:108.0,1297.0')] ).
cnf(1299,plain,
equal(product(u,product(v,quotient(u,v))),product(v,u)),
inference(rew,[status(thm),theory(equality)],[211,1298]),
[iquote('0:Rew:211.0,1298.0')] ).
cnf(1320,plain,
equal(quotient(product(c,b),product(b,bigC(c,a,b))),product(a,b)),
inference(spr,[status(thm),theory(equality)],[238,4]),
[iquote('0:SpR:238.0,4.0')] ).
cnf(1321,plain,
equal(difference(product(a,b),product(c,b)),product(b,bigC(c,a,b))),
inference(spr,[status(thm),theory(equality)],[238,2]),
[iquote('0:SpR:238.0,2.0')] ).
cnf(1364,plain,
equal(difference(u,product(v,u)),product(v,quotient(u,v))),
inference(spr,[status(thm),theory(equality)],[1299,2]),
[iquote('0:SpR:1299.0,2.0')] ).
cnf(1395,plain,
equal(product(u,product(difference(v,u),v)),product(difference(v,u),u)),
inference(spr,[status(thm),theory(equality)],[20,1299]),
[iquote('0:SpR:20.0,1299.0')] ).
cnf(1403,plain,
equal(product(difference(u,v),product(u,difference(u,quotient(v,u)))),product(u,difference(u,v))),
inference(spr,[status(thm),theory(equality)],[504,1299]),
[iquote('0:SpR:504.0,1299.0')] ).
cnf(1407,plain,
equal(product(difference(u,v),u),product(v,quotient(u,v))),
inference(rew,[status(thm),theory(equality)],[398,1364]),
[iquote('0:Rew:398.0,1364.0')] ).
cnf(1409,plain,
equal(product(u,quotient(difference(u,v),u)),difference(difference(u,v),v)),
inference(rew,[status(thm),theory(equality)],[1407,427]),
[iquote('0:Rew:1407.0,427.0')] ).
cnf(1425,plain,
equal(difference(u,bigC(u,v,v)),product(difference(u,v),v)),
inference(rew,[status(thm),theory(equality)],[1278,1395]),
[iquote('0:Rew:1278.0,1395.0')] ).
cnf(1429,plain,
equal(difference(difference(u,v),v),quotient(v,u)),
inference(rew,[status(thm),theory(equality)],[3,1409,504]),
[iquote('0:Rew:3.0,1409.0,504.0,1409.0')] ).
cnf(1452,plain,
equal(product(difference(u,v),quotient(v,u)),v),
inference(rew,[status(thm),theory(equality)],[3,1403]),
[iquote('0:Rew:3.0,1403.0,3.0,1403.0')] ).
cnf(1520,plain,
equal(difference(product(u,v),bigC(v,w,u)),quotient(bigC(v,w,u),product(v,w))),
inference(spr,[status(thm),theory(equality)],[49,1429]),
[iquote('0:SpR:49.0,1429.0')] ).
cnf(1521,plain,
equal(difference(product(u,v),bigC(v,u,w)),quotient(bigC(v,u,w),product(v,w))),
inference(spr,[status(thm),theory(equality)],[447,1429]),
[iquote('0:SpR:447.0,1429.0')] ).
cnf(1601,plain,
equal(product(difference(u,product(v,u)),v),product(v,u)),
inference(spr,[status(thm),theory(equality)],[4,1452]),
[iquote('0:SpR:4.0,1452.0')] ).
cnf(1608,plain,
equal(product(difference(u,bigC(u,v,u)),product(u,v)),bigC(u,v,u)),
inference(spr,[status(thm),theory(equality)],[97,1452]),
[iquote('0:SpR:97.0,1452.0')] ).
cnf(1611,plain,
equal(product(difference(product(u,v),bigC(v,u,w)),product(v,w)),bigC(v,u,w)),
inference(spr,[status(thm),theory(equality)],[329,1452]),
[iquote('0:SpR:329.0,1452.0')] ).
cnf(1621,plain,
equal(product(product(u,v),quotient(bigC(v,w,u),product(v,w))),bigC(v,w,u)),
inference(spr,[status(thm),theory(equality)],[49,1452]),
[iquote('0:SpR:49.0,1452.0')] ).
cnf(1631,plain,
equal(product(product(difference(u,v),u),v),product(v,u)),
inference(rew,[status(thm),theory(equality)],[398,1601]),
[iquote('0:Rew:398.0,1601.0')] ).
cnf(1636,plain,
equal(bigC(u,v,v),bigC(v,u,v)),
inference(rew,[status(thm),theory(equality)],[8,1608,293]),
[iquote('0:Rew:8.0,1608.0,293.0,1608.0')] ).
cnf(2167,plain,
equal(quotient(product(u,quotient(v,u)),v),difference(v,u)),
inference(spr,[status(thm),theory(equality)],[1407,4]),
[iquote('0:SpR:1407.0,4.0')] ).
cnf(2168,plain,
equal(difference(difference(u,v),product(v,quotient(u,v))),u),
inference(spr,[status(thm),theory(equality)],[1407,2]),
[iquote('0:SpR:1407.0,2.0')] ).
cnf(2172,plain,
equal(product(product(u,quotient(v,u)),difference(v,u)),bigC(difference(v,u),v,difference(v,u))),
inference(spr,[status(thm),theory(equality)],[1407,53]),
[iquote('0:SpR:1407.0,53.0')] ).
cnf(2273,plain,
equal(product(product(u,quotient(v,u)),difference(v,u)),product(u,product(difference(v,u),v))),
inference(rew,[status(thm),theory(equality)],[58,2172,1636]),
[iquote('0:Rew:58.0,2172.0,1636.0,2172.0')] ).
cnf(2274,plain,
equal(quotient(bigC(u,v,difference(v,u)),u),product(difference(v,u),u)),
inference(rew,[status(thm),theory(equality)],[1266,2273,1425,1278]),
[iquote('0:Rew:1266.0,2273.0,1425.0,2273.0,1278.0,2273.0')] ).
cnf(2863,plain,
equal(quotient(product(product(c,b),product(a,c)),product(a,b)),difference(product(a,b),product(c,b))),
inference(spr,[status(thm),theory(equality)],[38,2167]),
[iquote('0:SpR:38.0,2167.0')] ).
cnf(2894,plain,
equal(quotient(bigC(c,a,b),product(a,b)),difference(product(a,b),product(c,b))),
inference(rew,[status(thm),theory(equality)],[8,2863,10]),
[iquote('0:Rew:8.0,2863.0,10.0,2863.0')] ).
cnf(2895,plain,
equal(quotient(bigC(c,a,b),product(a,b)),product(b,bigC(c,a,b))),
inference(rew,[status(thm),theory(equality)],[1321,2894]),
[iquote('0:Rew:1321.0,2894.0')] ).
cnf(2903,plain,
equal(product(product(u,difference(u,v)),product(v,quotient(u,v))),product(product(v,quotient(u,v)),difference(u,v))),
inference(spr,[status(thm),theory(equality)],[2168,1631]),
[iquote('0:SpR:2168.0,1631.0')] ).
cnf(2986,plain,
equal(product(product(u,quotient(v,u)),difference(v,u)),product(u,product(u,quotient(v,u)))),
inference(rew,[status(thm),theory(equality)],[3,2903]),
[iquote('0:Rew:3.0,2903.0')] ).
cnf(2987,plain,
equal(difference(product(u,v),v),product(difference(u,v),v)),
inference(rew,[status(thm),theory(equality)],[2274,2986,1266,915]),
[iquote('0:Rew:2274.0,2986.0,1266.0,2986.0,915.0,2986.0')] ).
cnf(2988,plain,
equal(product(difference(product(u,v),v),v),product(v,product(v,u))),
inference(rew,[status(thm),theory(equality)],[2987,63]),
[iquote('0:Rew:2987.0,63.0')] ).
cnf(3014,plain,
equal(product(product(difference(u,v),v),v),product(v,product(v,u))),
inference(rew,[status(thm),theory(equality)],[2987,2988]),
[iquote('0:Rew:2987.0,2988.0')] ).
cnf(3066,plain,
equal(product(product(product(difference(u,v),v),w),product(v,product(v,u))),product(product(difference(u,v),v),product(w,v))),
inference(spr,[status(thm),theory(equality)],[3014,211]),
[iquote('0:SpR:3014.0,211.0')] ).
cnf(3072,plain,
equal(product(product(product(difference(u,v),v),w),product(v,x)),product(product(v,product(v,u)),product(w,x))),
inference(spr,[status(thm),theory(equality)],[3014,10]),
[iquote('0:SpR:3014.0,10.0')] ).
cnf(3161,plain,
equal(product(product(product(difference(u,v),v),w),product(v,product(v,u))),product(product(difference(u,v),w),v)),
inference(rew,[status(thm),theory(equality)],[203,3066]),
[iquote('0:Rew:203.0,3066.0')] ).
cnf(3162,plain,
equal(product(product(u,v),product(u,product(w,w))),product(product(difference(w,u),v),u)),
inference(rew,[status(thm),theory(equality)],[1104,3161,3072]),
[iquote('0:Rew:1104.0,3161.0,3072.0,3161.0')] ).
cnf(3163,plain,
equal(product(product(difference(u,v),w),v),product(v,product(w,u))),
inference(rew,[status(thm),theory(equality)],[211,3162,1]),
[iquote('0:Rew:211.0,3162.0,1.0,3162.0')] ).
cnf(3165,plain,
equal(bigC(difference(u,v),w,u),product(v,product(w,u))),
inference(rew,[status(thm),theory(equality)],[3163,54]),
[iquote('0:Rew:3163.0,54.0')] ).
cnf(3183,plain,
equal(quotient(product(u,product(v,w)),u),product(difference(w,u),v)),
inference(rew,[status(thm),theory(equality)],[3165,320]),
[iquote('0:Rew:3165.0,320.0')] ).
cnf(3201,plain,
equal(product(u,quotient(product(v,w),u)),product(difference(w,u),v)),
inference(rew,[status(thm),theory(equality)],[614,3183]),
[iquote('0:Rew:614.0,3183.0')] ).
cnf(3208,plain,
equal(quotient(bigC(u,v,w),product(u,v)),product(difference(u,product(u,v)),w)),
inference(rew,[status(thm),theory(equality)],[3201,630]),
[iquote('0:Rew:3201.0,630.0')] ).
cnf(3217,plain,
equal(quotient(bigC(u,v,w),product(u,v)),product(v,w)),
inference(rew,[status(thm),theory(equality)],[2,3208]),
[iquote('0:Rew:2.0,3208.0')] ).
cnf(3219,plain,
equal(difference(product(u,v),bigC(v,w,u)),product(w,u)),
inference(rew,[status(thm),theory(equality)],[3217,1520]),
[iquote('0:Rew:3217.0,1520.0')] ).
cnf(3220,plain,
equal(product(product(u,v),product(w,u)),bigC(v,w,u)),
inference(rew,[status(thm),theory(equality)],[3217,1621]),
[iquote('0:Rew:3217.0,1621.0')] ).
cnf(3221,plain,
equal(difference(product(u,v),product(v,w)),quotient(product(w,u),product(u,v))),
inference(rew,[status(thm),theory(equality)],[3217,552]),
[iquote('0:Rew:3217.0,552.0')] ).
cnf(3225,plain,
equal(difference(product(u,v),bigC(v,u,w)),product(w,u)),
inference(rew,[status(thm),theory(equality)],[3219,751]),
[iquote('0:Rew:3219.0,751.0')] ).
cnf(3228,plain,
equal(bigC(u,v,w),bigC(v,w,u)),
inference(rew,[status(thm),theory(equality)],[8,3220]),
[iquote('0:Rew:8.0,3220.0')] ).
cnf(3255,plain,
equal(quotient(product(c,b),product(b,bigC(a,b,c))),product(a,b)),
inference(rew,[status(thm),theory(equality)],[3228,1320]),
[iquote('0:Rew:3228.0,1320.0')] ).
cnf(3297,plain,
equal(quotient(bigC(a,b,c),product(a,b)),product(b,bigC(a,b,c))),
inference(rew,[status(thm),theory(equality)],[3228,2895]),
[iquote('0:Rew:3228.0,2895.0')] ).
cnf(3325,plain,
equal(quotient(bigC(u,v,w),product(u,w)),product(w,v)),
inference(rew,[status(thm),theory(equality)],[3225,1521]),
[iquote('0:Rew:3225.0,1521.0')] ).
cnf(3326,plain,
equal(product(product(u,v),product(w,u)),bigC(w,v,u)),
inference(rew,[status(thm),theory(equality)],[3225,1611]),
[iquote('0:Rew:3225.0,1611.0')] ).
cnf(3332,plain,
equal(bigC(u,v,w),bigC(w,v,u)),
inference(rew,[status(thm),theory(equality)],[8,3326]),
[iquote('0:Rew:8.0,3326.0')] ).
cnf(3341,plain,
equal(quotient(product(c,b),product(b,bigC(a,c,b))),product(a,b)),
inference(rew,[status(thm),theory(equality)],[237,3255]),
[iquote('0:Rew:237.0,3255.0')] ).
cnf(3364,plain,
equal(quotient(bigC(a,c,b),product(a,b)),product(b,bigC(a,c,b))),
inference(rew,[status(thm),theory(equality)],[237,3297]),
[iquote('0:Rew:237.0,3297.0')] ).
cnf(3365,plain,
equal(product(b,bigC(a,c,b)),product(b,c)),
inference(rew,[status(thm),theory(equality)],[3325,3364]),
[iquote('0:Rew:3325.0,3364.0')] ).
cnf(3367,plain,
equal(quotient(product(c,b),product(b,c)),product(a,b)),
inference(rew,[status(thm),theory(equality)],[3365,3341]),
[iquote('0:Rew:3365.0,3341.0')] ).
cnf(3369,plain,
equal(difference(product(b,c),product(c,c)),product(a,b)),
inference(rew,[status(thm),theory(equality)],[3221,3367]),
[iquote('0:Rew:3221.0,3367.0')] ).
cnf(3370,plain,
equal(difference(product(b,c),c),product(a,b)),
inference(rew,[status(thm),theory(equality)],[1,3369]),
[iquote('0:Rew:1.0,3369.0')] ).
cnf(3371,plain,
equal(product(difference(b,c),c),product(a,b)),
inference(rew,[status(thm),theory(equality)],[2987,3370]),
[iquote('0:Rew:2987.0,3370.0')] ).
cnf(5617,plain,
equal(product(product(b,u),product(a,b)),product(c,product(u,c))),
inference(spr,[status(thm),theory(equality)],[3371,212]),
[iquote('0:SpR:3371.0,212.0')] ).
cnf(5651,plain,
equal(bigC(c,c,u),bigC(a,u,b)),
inference(rew,[status(thm),theory(equality)],[3332,5617,8,57]),
[iquote('0:Rew:3332.0,5617.0,8.0,5617.0,57.0,5617.0')] ).
cnf(5652,plain,
~ equal(bigC(a,skc1,b),bigC(a,b,skc1)),
inference(rew,[status(thm),theory(equality)],[5651,6]),
[iquote('0:Rew:5651.0,6.0')] ).
cnf(5657,plain,
~ equal(bigC(a,b,skc1),bigC(a,b,skc1)),
inference(rew,[status(thm),theory(equality)],[237,5652]),
[iquote('0:Rew:237.0,5652.0')] ).
cnf(5658,plain,
$false,
inference(obv,[status(thm),theory(equality)],[5657]),
[iquote('0:Obv:5657.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP777+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 07:49:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.49/1.66
% 1.49/1.66 SPASS V 3.9
% 1.49/1.66 SPASS beiseite: Proof found.
% 1.49/1.66 % SZS status Theorem
% 1.49/1.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.49/1.66 SPASS derived 3325 clauses, backtracked 0 clauses, performed 0 splits and kept 1557 clauses.
% 1.49/1.66 SPASS allocated 93057 KBytes.
% 1.49/1.66 SPASS spent 0:00:01.32 on the problem.
% 1.49/1.66 0:00:00.03 for the input.
% 1.49/1.66 0:00:00.03 for the FLOTTER CNF translation.
% 1.49/1.66 0:00:00.02 for inferences.
% 1.49/1.66 0:00:00.00 for the backtracking.
% 1.49/1.66 0:00:01.21 for the reduction.
% 1.49/1.66
% 1.49/1.66
% 1.49/1.66 Here is a proof with depth 13, length 146 :
% 1.49/1.66 % SZS output start Refutation
% See solution above
% 1.53/1.70 Formulae used in the proof : sos06 sos01 sos02 sos03 sos04 goals sos09 sos08 sos07 sos05
% 1.53/1.70
%------------------------------------------------------------------------------