TSTP Solution File: KRS052+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KRS052+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 03:30:24 EDT 2022
% Result : Satisfiable 2.23s 2.42s
% Output : Saturation 2.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1356)
% Comments :
%------------------------------------------------------------------------------
cnf(1357,plain,
( ~ ccardinality_N_times_M(u)
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(skf39(skf35(u)),u)
| equal(skf40(skf35(u)),u) ),
inference(mrr,[status(thm)],[1356,7]),
[iquote('0:MRR:1356.1,7.1')] ).
cnf(821,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,skf38(skf35(u)))
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v) ),
inference(res,[status(thm),theory(equality)],[148,740]),
[iquote('0:Res:148.1,740.0')] ).
cnf(815,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,skf38(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v) ),
inference(res,[status(thm),theory(equality)],[148,705]),
[iquote('0:Res:148.1,705.0')] ).
cnf(809,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v) ),
inference(res,[status(thm),theory(equality)],[148,692]),
[iquote('0:Res:148.1,692.0')] ).
cnf(787,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(v,skf38(skf35(u)))
| equal(v,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v) ),
inference(res,[status(thm),theory(equality)],[148,685]),
[iquote('0:Res:148.1,685.0')] ).
cnf(780,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(v,u)
| equal(v,skf37(skf35(u)))
| equal(v,skf38(skf35(u)))
| equal(v,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v) ),
inference(res,[status(thm),theory(equality)],[148,684]),
[iquote('0:Res:148.1,684.0')] ).
cnf(774,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(v,skf37(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf38(skf35(u)),v)
| equal(skf38(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,665]),
[iquote('0:Res:148.1,665.0')] ).
cnf(768,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(v,skf37(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,652]),
[iquote('0:Res:148.1,652.0')] ).
cnf(746,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(v,skf38(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,645]),
[iquote('0:Res:148.1,645.0')] ).
cnf(739,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(v,skf38(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf37(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,644]),
[iquote('0:Res:148.1,644.0')] ).
cnf(733,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf37(skf35(u)),u)
| equal(v,skf37(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,631]),
[iquote('0:Res:148.1,631.0')] ).
cnf(727,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(v,skf38(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,624]),
[iquote('0:Res:148.1,624.0')] ).
cnf(704,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),u)
| equal(skf38(skf35(u)),u)
| equal(v,skf38(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf37(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,623]),
[iquote('0:Res:148.1,623.0')] ).
cnf(698,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf36(skf35(u)),u)
| equal(skf39(skf35(u)),u)
| equal(v,skf39(skf35(u)))
| equal(v,skf36(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf36(skf35(u)))
| equal(w,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,616]),
[iquote('0:Res:148.1,616.0')] ).
cnf(691,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf37(skf35(u)),u)
| equal(skf39(skf35(u)),u)
| equal(v,skf39(skf35(u)))
| equal(v,skf37(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf37(skf35(u)))
| equal(w,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,615]),
[iquote('0:Res:148.1,615.0')] ).
cnf(683,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf39(skf35(u)),u)
| equal(v,skf39(skf35(u)))
| equal(v,skf38(skf35(u)))
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(w,skf38(skf35(u)))
| equal(w,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w) ),
inference(res,[status(thm),theory(equality)],[148,614]),
[iquote('0:Res:148.1,614.0')] ).
cnf(677,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(w,skf36(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf36(skf35(u)))
| equal(skf37(skf35(u)),skf36(skf35(u)))
| equal(skf37(skf35(u)),u)
| equal(skf37(skf35(u)),v)
| equal(skf37(skf35(u)),w)
| equal(skf37(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,601]),
[iquote('0:Res:148.1,601.0')] ).
cnf(671,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(w,skf36(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf36(skf35(u)))
| equal(skf38(skf35(u)),skf36(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf38(skf35(u)),v)
| equal(skf38(skf35(u)),w)
| equal(skf38(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,549]),
[iquote('0:Res:148.1,549.0')] ).
cnf(664,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf37(skf35(u)),u)
| equal(v,u)
| equal(v,skf37(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf37(skf35(u)))
| equal(skf38(skf35(u)),skf37(skf35(u)))
| equal(skf38(skf35(u)),u)
| equal(skf38(skf35(u)),v)
| equal(skf38(skf35(u)),w)
| equal(skf38(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,548]),
[iquote('0:Res:148.1,548.0')] ).
cnf(658,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(w,skf36(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf36(skf35(u)))
| equal(skf39(skf35(u)),skf36(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w)
| equal(skf39(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,501]),
[iquote('0:Res:148.1,501.0')] ).
cnf(651,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf37(skf35(u)),u)
| equal(v,u)
| equal(v,skf37(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf37(skf35(u)))
| equal(skf39(skf35(u)),skf37(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w)
| equal(skf39(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,500]),
[iquote('0:Res:148.1,500.0')] ).
cnf(643,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf38(skf35(u)),u)
| equal(v,u)
| equal(v,skf38(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf38(skf35(u)))
| equal(skf39(skf35(u)),skf38(skf35(u)))
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w)
| equal(skf39(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,499]),
[iquote('0:Res:148.1,499.0')] ).
cnf(637,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf36(skf35(u)),u)
| equal(v,u)
| equal(v,skf36(skf35(u)))
| equal(w,skf36(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf36(skf35(u)))
| equal(skf40(skf35(u)),skf36(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w)
| equal(skf40(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,458]),
[iquote('0:Res:148.1,458.0')] ).
cnf(630,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf37(skf35(u)),u)
| equal(v,u)
| equal(v,skf37(skf35(u)))
| equal(w,skf37(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf37(skf35(u)))
| equal(skf40(skf35(u)),skf37(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w)
| equal(skf40(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,457]),
[iquote('0:Res:148.1,457.0')] ).
cnf(622,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf38(skf35(u)),u)
| equal(v,u)
| equal(v,skf38(skf35(u)))
| equal(w,skf38(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf38(skf35(u)))
| equal(skf40(skf35(u)),skf38(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w)
| equal(skf40(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,456]),
[iquote('0:Res:148.1,456.0')] ).
cnf(613,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| equal(skf39(skf35(u)),u)
| equal(v,u)
| equal(v,skf39(skf35(u)))
| equal(w,skf39(skf35(u)))
| equal(w,u)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,u)
| equal(x,skf39(skf35(u)))
| equal(skf40(skf35(u)),skf39(skf35(u)))
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w)
| equal(skf40(skf35(u)),x) ),
inference(res,[status(thm),theory(equality)],[148,455]),
[iquote('0:Res:148.1,455.0')] ).
cnf(607,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(x,u)
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,u)
| equal(skf36(skf35(u)),u)
| equal(skf36(skf35(u)),v)
| equal(skf36(skf35(u)),w)
| equal(skf36(skf35(u)),x)
| equal(skf36(skf35(u)),y) ),
inference(res,[status(thm),theory(equality)],[148,272]),
[iquote('0:Res:148.1,272.0')] ).
cnf(600,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(x,u)
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,u)
| equal(skf37(skf35(u)),u)
| equal(skf37(skf35(u)),v)
| equal(skf37(skf35(u)),w)
| equal(skf37(skf35(u)),x)
| equal(skf37(skf35(u)),y) ),
inference(res,[status(thm),theory(equality)],[148,271]),
[iquote('0:Res:148.1,271.0')] ).
cnf(547,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(x,u)
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,u)
| equal(skf38(skf35(u)),u)
| equal(skf38(skf35(u)),v)
| equal(skf38(skf35(u)),w)
| equal(skf38(skf35(u)),x)
| equal(skf38(skf35(u)),y) ),
inference(res,[status(thm),theory(equality)],[148,270]),
[iquote('0:Res:148.1,270.0')] ).
cnf(781,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| equal(skf39(u),skf38(u))
| equal(skf38(u),skf37(u))
| equal(skf39(u),skf37(u))
| equal(skf39(u),skf36(u))
| equal(skf38(u),skf36(u))
| equal(skf37(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf37(u))
| equal(v,skf38(u))
| equal(v,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v) ),
inference(mrr,[status(thm)],[775,114]),
[iquote('0:MRR:775.0,114.1')] ).
cnf(740,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| equal(skf38(u),skf37(u))
| equal(skf37(u),skf36(u))
| equal(skf38(u),skf36(u))
| equal(v,skf38(u))
| equal(v,skf37(u))
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(w,skf37(u))
| equal(w,skf38(u))
| equal(skf39(u),skf38(u))
| equal(skf39(u),skf37(u))
| equal(skf39(u),skf36(u))
| equal(skf39(u),v)
| equal(skf39(u),w) ),
inference(mrr,[status(thm)],[734,114]),
[iquote('0:MRR:734.0,114.1')] ).
cnf(705,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| equal(skf38(u),skf37(u))
| equal(skf37(u),skf36(u))
| equal(skf38(u),skf36(u))
| equal(v,skf38(u))
| equal(v,skf37(u))
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(w,skf37(u))
| equal(w,skf38(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w) ),
inference(mrr,[status(thm)],[699,114]),
[iquote('0:MRR:699.0,114.1')] ).
cnf(692,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| equal(skf39(u),skf37(u))
| equal(skf37(u),skf36(u))
| equal(skf39(u),skf36(u))
| equal(v,skf39(u))
| equal(v,skf37(u))
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(w,skf37(u))
| equal(w,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w) ),
inference(mrr,[status(thm)],[686,114]),
[iquote('0:MRR:686.0,114.1')] ).
cnf(498,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(x,u)
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,u)
| equal(skf39(skf35(u)),u)
| equal(skf39(skf35(u)),v)
| equal(skf39(skf35(u)),w)
| equal(skf39(skf35(u)),x)
| equal(skf39(skf35(u)),y) ),
inference(res,[status(thm),theory(equality)],[148,269]),
[iquote('0:Res:148.1,269.0')] ).
cnf(685,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| equal(skf39(u),skf38(u))
| equal(skf38(u),skf36(u))
| equal(skf39(u),skf36(u))
| equal(v,skf39(u))
| equal(v,skf38(u))
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(w,skf38(u))
| equal(w,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w) ),
inference(mrr,[status(thm)],[678,114]),
[iquote('0:MRR:678.0,114.1')] ).
cnf(684,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| equal(skf39(u),skf38(u))
| equal(skf38(u),skf37(u))
| equal(skf39(u),skf37(u))
| equal(v,skf39(u))
| equal(v,skf38(u))
| equal(v,skf37(u))
| equal(w,v)
| equal(w,skf37(u))
| equal(w,skf38(u))
| equal(w,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),v)
| equal(skf40(u),w) ),
inference(mrr,[status(thm)],[679,114]),
[iquote('0:MRR:679.0,114.1')] ).
cnf(665,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf37(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf37(u))
| equal(w,skf37(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf37(u))
| equal(skf38(u),skf37(u))
| equal(skf38(u),skf36(u))
| equal(skf38(u),v)
| equal(skf38(u),w)
| equal(skf38(u),x) ),
inference(mrr,[status(thm)],[659,114]),
[iquote('0:MRR:659.0,114.1')] ).
cnf(652,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf37(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf37(u))
| equal(w,skf37(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf37(u))
| equal(skf39(u),skf37(u))
| equal(skf39(u),skf36(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x) ),
inference(mrr,[status(thm)],[646,114]),
[iquote('0:MRR:646.0,114.1')] ).
cnf(454,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(x,u)
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,u)
| equal(skf40(skf35(u)),u)
| equal(skf40(skf35(u)),v)
| equal(skf40(skf35(u)),w)
| equal(skf40(skf35(u)),x)
| equal(skf40(skf35(u)),y) ),
inference(res,[status(thm),theory(equality)],[148,268]),
[iquote('0:Res:148.1,268.0')] ).
cnf(645,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf38(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf38(u))
| equal(w,skf38(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf38(u))
| equal(skf39(u),skf38(u))
| equal(skf39(u),skf36(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x) ),
inference(mrr,[status(thm)],[638,114]),
[iquote('0:MRR:638.0,114.1')] ).
cnf(644,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf38(u),skf37(u))
| equal(v,skf37(u))
| equal(v,skf38(u))
| equal(w,skf38(u))
| equal(w,skf37(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf37(u))
| equal(x,skf38(u))
| equal(skf39(u),skf38(u))
| equal(skf39(u),skf37(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x) ),
inference(mrr,[status(thm)],[639,114]),
[iquote('0:MRR:639.0,114.1')] ).
cnf(631,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf37(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf37(u))
| equal(w,skf37(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf37(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[625,114]),
[iquote('0:MRR:625.0,114.1')] ).
cnf(624,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf38(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf38(u))
| equal(w,skf38(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf38(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[617,114]),
[iquote('0:MRR:617.0,114.1')] ).
cnf(267,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvR_N_times_M_to_1(skf35(u),v)
| ~ rinvR_N_times_M_to_1(skf35(u),w)
| ~ rinvR_N_times_M_to_1(skf35(u),x)
| ~ rinvR_N_times_M_to_1(skf35(u),y)
| ~ rinvR_N_times_M_to_1(skf35(u),z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(u,v)
| equal(u,w)
| equal(u,x)
| equal(u,y)
| equal(u,z) ),
inference(res,[status(thm),theory(equality)],[148,116]),
[iquote('0:Res:148.1,116.0')] ).
cnf(623,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf38(u),skf37(u))
| equal(v,skf37(u))
| equal(v,skf38(u))
| equal(w,skf38(u))
| equal(w,skf37(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf37(u))
| equal(x,skf38(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[618,114]),
[iquote('0:MRR:618.0,114.1')] ).
cnf(616,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf39(u),skf36(u))
| equal(v,skf36(u))
| equal(v,skf39(u))
| equal(w,skf39(u))
| equal(w,skf36(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf36(u))
| equal(x,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[608,114]),
[iquote('0:MRR:608.0,114.1')] ).
cnf(615,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf39(u),skf37(u))
| equal(v,skf37(u))
| equal(v,skf39(u))
| equal(w,skf39(u))
| equal(w,skf37(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf37(u))
| equal(x,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[609,114]),
[iquote('0:MRR:609.0,114.1')] ).
cnf(614,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| equal(skf39(u),skf38(u))
| equal(v,skf38(u))
| equal(v,skf39(u))
| equal(w,skf39(u))
| equal(w,skf38(u))
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(x,skf38(u))
| equal(x,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x) ),
inference(mrr,[status(thm)],[610,114]),
[iquote('0:MRR:610.0,114.1')] ).
cnf(601,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(x,skf36(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf36(u))
| equal(skf37(u),skf36(u))
| equal(skf37(u),v)
| equal(skf37(u),w)
| equal(skf37(u),x)
| equal(skf37(u),y) ),
inference(mrr,[status(thm)],[595,114]),
[iquote('0:MRR:595.0,114.1')] ).
cnf(549,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(x,skf36(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf36(u))
| equal(skf38(u),skf36(u))
| equal(skf38(u),v)
| equal(skf38(u),w)
| equal(skf38(u),x)
| equal(skf38(u),y) ),
inference(mrr,[status(thm)],[542,114]),
[iquote('0:MRR:542.0,114.1')] ).
cnf(548,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf37(u))
| equal(w,v)
| equal(w,skf37(u))
| equal(x,skf37(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf37(u))
| equal(skf38(u),skf37(u))
| equal(skf38(u),v)
| equal(skf38(u),w)
| equal(skf38(u),x)
| equal(skf38(u),y) ),
inference(mrr,[status(thm)],[543,114]),
[iquote('0:MRR:543.0,114.1')] ).
cnf(501,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(x,skf36(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf36(u))
| equal(skf39(u),skf36(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x)
| equal(skf39(u),y) ),
inference(mrr,[status(thm)],[493,114]),
[iquote('0:MRR:493.0,114.1')] ).
cnf(500,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf37(u))
| equal(w,v)
| equal(w,skf37(u))
| equal(x,skf37(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf37(u))
| equal(skf39(u),skf37(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x)
| equal(skf39(u),y) ),
inference(mrr,[status(thm)],[494,114]),
[iquote('0:MRR:494.0,114.1')] ).
cnf(499,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf38(u))
| equal(w,v)
| equal(w,skf38(u))
| equal(x,skf38(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf38(u))
| equal(skf39(u),skf38(u))
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x)
| equal(skf39(u),y) ),
inference(mrr,[status(thm)],[495,114]),
[iquote('0:MRR:495.0,114.1')] ).
cnf(458,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf36(u))
| equal(w,v)
| equal(w,skf36(u))
| equal(x,skf36(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf36(u))
| equal(skf40(u),skf36(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x)
| equal(skf40(u),y) ),
inference(mrr,[status(thm)],[449,114]),
[iquote('0:MRR:449.0,114.1')] ).
cnf(457,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf37(u))
| equal(w,v)
| equal(w,skf37(u))
| equal(x,skf37(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf37(u))
| equal(skf40(u),skf37(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x)
| equal(skf40(u),y) ),
inference(mrr,[status(thm)],[450,114]),
[iquote('0:MRR:450.0,114.1')] ).
cnf(456,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf38(u))
| equal(w,v)
| equal(w,skf38(u))
| equal(x,skf38(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf38(u))
| equal(skf40(u),skf38(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x)
| equal(skf40(u),y) ),
inference(mrr,[status(thm)],[451,114]),
[iquote('0:MRR:451.0,114.1')] ).
cnf(455,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| equal(v,skf39(u))
| equal(w,v)
| equal(w,skf39(u))
| equal(x,skf39(u))
| equal(x,v)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(y,v)
| equal(y,skf39(u))
| equal(skf40(u),skf39(u))
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x)
| equal(skf40(u),y) ),
inference(mrr,[status(thm)],[452,114]),
[iquote('0:MRR:452.0,114.1')] ).
cnf(272,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(skf36(u),v)
| equal(skf36(u),w)
| equal(skf36(u),x)
| equal(skf36(u),y)
| equal(skf36(u),z) ),
inference(mrr,[status(thm)],[262,114]),
[iquote('0:MRR:262.0,114.1')] ).
cnf(271,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(skf37(u),v)
| equal(skf37(u),w)
| equal(skf37(u),x)
| equal(skf37(u),y)
| equal(skf37(u),z) ),
inference(mrr,[status(thm)],[263,114]),
[iquote('0:MRR:263.0,114.1')] ).
cnf(580,plain,
( ~ ccardinality_N_times_M(u)
| equal(skf27(skf34(u)),skf26(skf34(u)))
| equal(skf26(skf34(u)),u)
| equal(skf27(skf34(u)),u)
| equal(skf28(skf34(u)),u) ),
inference(mrr,[status(thm)],[579,6]),
[iquote('0:MRR:579.1,6.1')] ).
cnf(270,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(skf38(u),v)
| equal(skf38(u),w)
| equal(skf38(u),x)
| equal(skf38(u),y)
| equal(skf38(u),z) ),
inference(mrr,[status(thm)],[264,114]),
[iquote('0:MRR:264.0,114.1')] ).
cnf(462,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| equal(skf26(skf34(u)),u)
| equal(v,u)
| equal(v,skf26(skf34(u)))
| equal(skf27(skf34(u)),skf26(skf34(u)))
| equal(skf27(skf34(u)),u)
| equal(skf27(skf34(u)),v) ),
inference(res,[status(thm),theory(equality)],[132,386]),
[iquote('0:Res:132.1,386.0')] ).
cnf(448,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| equal(skf26(skf34(u)),u)
| equal(v,u)
| equal(v,skf26(skf34(u)))
| equal(skf28(skf34(u)),skf26(skf34(u)))
| equal(skf28(skf34(u)),u)
| equal(skf28(skf34(u)),v) ),
inference(res,[status(thm),theory(equality)],[132,372]),
[iquote('0:Res:132.1,372.0')] ).
cnf(439,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| equal(skf27(skf34(u)),u)
| equal(v,u)
| equal(v,skf27(skf34(u)))
| equal(skf28(skf34(u)),skf27(skf34(u)))
| equal(skf28(skf34(u)),u)
| equal(skf28(skf34(u)),v) ),
inference(res,[status(thm),theory(equality)],[132,371]),
[iquote('0:Res:132.1,371.0')] ).
cnf(428,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| ~ rinvQ_1_to_M(skf34(u),w)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(skf26(skf34(u)),u)
| equal(skf26(skf34(u)),v)
| equal(skf26(skf34(u)),w) ),
inference(res,[status(thm),theory(equality)],[132,243]),
[iquote('0:Res:132.1,243.0')] ).
cnf(269,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(skf39(u),v)
| equal(skf39(u),w)
| equal(skf39(u),x)
| equal(skf39(u),y)
| equal(skf39(u),z) ),
inference(mrr,[status(thm)],[265,114]),
[iquote('0:MRR:265.0,114.1')] ).
cnf(385,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| ~ rinvQ_1_to_M(skf34(u),w)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(skf27(skf34(u)),u)
| equal(skf27(skf34(u)),v)
| equal(skf27(skf34(u)),w) ),
inference(res,[status(thm),theory(equality)],[132,242]),
[iquote('0:Res:132.1,242.0')] ).
cnf(370,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| ~ rinvQ_1_to_M(skf34(u),w)
| equal(v,u)
| equal(w,v)
| equal(w,u)
| equal(skf28(skf34(u)),u)
| equal(skf28(skf34(u)),v)
| equal(skf28(skf34(u)),w) ),
inference(res,[status(thm),theory(equality)],[132,241]),
[iquote('0:Res:132.1,241.0')] ).
cnf(240,plain,
( ~ ccardinality_N_times_M(u)
| ~ rinvQ_1_to_M(skf34(u),v)
| ~ rinvQ_1_to_M(skf34(u),w)
| ~ rinvQ_1_to_M(skf34(u),x)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(u,v)
| equal(u,w)
| equal(u,x) ),
inference(res,[status(thm),theory(equality)],[132,108]),
[iquote('0:Res:132.1,108.0')] ).
cnf(386,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| equal(v,skf26(u))
| equal(w,v)
| equal(w,skf26(u))
| equal(skf27(u),skf26(u))
| equal(skf27(u),v)
| equal(skf27(u),w) ),
inference(mrr,[status(thm)],[382,106]),
[iquote('0:MRR:382.0,106.1')] ).
cnf(268,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(y,v)
| equal(y,w)
| equal(y,x)
| equal(z,y)
| equal(z,x)
| equal(z,w)
| equal(z,v)
| equal(skf40(u),v)
| equal(skf40(u),w)
| equal(skf40(u),x)
| equal(skf40(u),y)
| equal(skf40(u),z) ),
inference(mrr,[status(thm)],[266,114]),
[iquote('0:MRR:266.0,114.1')] ).
cnf(372,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| equal(v,skf26(u))
| equal(w,v)
| equal(w,skf26(u))
| equal(skf28(u),skf26(u))
| equal(skf28(u),v)
| equal(skf28(u),w) ),
inference(mrr,[status(thm)],[367,106]),
[iquote('0:MRR:367.0,106.1')] ).
cnf(440,plain,
( ~ rinvQ_1_to_M(u,v)
| equal(skf27(u),skf26(u))
| equal(v,skf26(u))
| equal(v,skf27(u))
| equal(skf28(u),skf27(u))
| equal(skf28(u),skf26(u))
| equal(skf28(u),v) ),
inference(mrr,[status(thm)],[436,106]),
[iquote('0:MRR:436.0,106.1')] ).
cnf(371,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| equal(v,skf27(u))
| equal(w,v)
| equal(w,skf27(u))
| equal(skf28(u),skf27(u))
| equal(skf28(u),v)
| equal(skf28(u),w) ),
inference(mrr,[status(thm)],[368,106]),
[iquote('0:MRR:368.0,106.1')] ).
cnf(221,plain,
( ~ ccardinality_N(u)
| ~ rinvP_1_to_N(skf33(u),v)
| ~ rinvP_1_to_N(skf33(u),w)
| equal(w,v)
| equal(u,v)
| equal(u,w) ),
inference(res,[status(thm),theory(equality)],[126,101]),
[iquote('0:Res:126.1,101.0')] ).
cnf(243,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| ~ rinvQ_1_to_M(u,x)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(skf26(u),v)
| equal(skf26(u),w)
| equal(skf26(u),x) ),
inference(mrr,[status(thm)],[237,106]),
[iquote('0:MRR:237.0,106.1')] ).
cnf(358,plain,
( ~ ccardinality_N(u)
| ~ rinvP_1_to_N(skf33(u),v)
| equal(v,u)
| equal(skf47(skf33(u)),u)
| equal(skf47(skf33(u)),v) ),
inference(res,[status(thm),theory(equality)],[126,223]),
[iquote('0:Res:126.1,223.0')] ).
cnf(345,plain,
( ~ ccardinality_N(u)
| ~ rinvP_1_to_N(skf33(u),v)
| equal(v,u)
| equal(skf48(skf33(u)),u)
| equal(skf48(skf33(u)),v) ),
inference(res,[status(thm),theory(equality)],[126,222]),
[iquote('0:Res:126.1,222.0')] ).
cnf(399,plain,
( ~ ccardinality_N(u)
| equal(skf47(skf33(u)),u)
| equal(skf48(skf33(u)),u) ),
inference(mrr,[status(thm)],[398,5]),
[iquote('0:MRR:398.1,5.1')] ).
cnf(242,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| ~ rinvQ_1_to_M(u,x)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(skf27(u),v)
| equal(skf27(u),w)
| equal(skf27(u),x) ),
inference(mrr,[status(thm)],[238,106]),
[iquote('0:MRR:238.0,106.1')] ).
cnf(346,plain,
( ~ rinvP_1_to_N(u,v)
| equal(v,skf47(u))
| equal(skf48(u),skf47(u))
| equal(skf48(u),v) ),
inference(mrr,[status(thm)],[343,99]),
[iquote('0:MRR:343.0,99.1')] ).
cnf(348,plain,
( ~ cinfinite(u)
| ~ rinvP_1_to_N(v,skf48(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[28,305]),
[iquote('0:Res:28.1,305.1')] ).
cnf(341,plain,
( ~ cinfinite(u)
| ~ rinvP_1_to_N(v,skf47(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[28,296]),
[iquote('0:Res:28.1,296.1')] ).
cnf(338,plain,
( ~ ccardinality_N(u)
| ~ rinvQ_1_to_M(v,skf28(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[30,278]),
[iquote('0:Res:30.1,278.1')] ).
cnf(241,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| ~ rinvQ_1_to_M(u,x)
| equal(w,v)
| equal(x,w)
| equal(x,v)
| equal(skf28(u),v)
| equal(skf28(u),w)
| equal(skf28(u),x) ),
inference(mrr,[status(thm)],[239,106]),
[iquote('0:MRR:239.0,106.1')] ).
cnf(335,plain,
( ~ ccardinality_N(u)
| ~ rinvQ_1_to_M(v,skf27(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[30,258]),
[iquote('0:Res:30.1,258.1')] ).
cnf(332,plain,
( ~ ccardinality_N(u)
| ~ rinvQ_1_to_M(v,skf26(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[30,249]),
[iquote('0:Res:30.1,249.1')] ).
cnf(326,plain,
( ~ cinfinite(u)
| ~ rinvR_N_times_M_to_1(v,skf40(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[32,225]),
[iquote('0:Res:32.1,225.1')] ).
cnf(323,plain,
( ~ cinfinite(u)
| ~ rinvR_N_times_M_to_1(v,skf39(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[32,211]),
[iquote('0:Res:32.1,211.1')] ).
cnf(223,plain,
( ~ rinvP_1_to_N(u,v)
| ~ rinvP_1_to_N(u,w)
| equal(w,v)
| equal(skf47(u),v)
| equal(skf47(u),w) ),
inference(mrr,[status(thm)],[219,99]),
[iquote('0:MRR:219.0,99.1')] ).
cnf(320,plain,
( ~ cinfinite(u)
| ~ rinvR_N_times_M_to_1(v,skf38(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[32,202]),
[iquote('0:Res:32.1,202.1')] ).
cnf(317,plain,
( ~ cinfinite(u)
| ~ rinvR_N_times_M_to_1(v,skf37(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[32,190]),
[iquote('0:Res:32.1,190.1')] ).
cnf(310,plain,
( ~ cinfinite(u)
| ~ rinvR_N_times_M_to_1(v,skf36(u))
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[32,181]),
[iquote('0:Res:32.1,181.1')] ).
cnf(305,plain,
( ~ cinfinite(u)
| ~ rp_N_to_1(skf48(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[303,50]),
[iquote('0:Res:303.1,50.0')] ).
cnf(222,plain,
( ~ rinvP_1_to_N(u,v)
| ~ rinvP_1_to_N(u,w)
| equal(w,v)
| equal(skf48(u),v)
| equal(skf48(u),w) ),
inference(mrr,[status(thm)],[220,99]),
[iquote('0:MRR:220.0,99.1')] ).
cnf(296,plain,
( ~ cinfinite(u)
| ~ rp_N_to_1(skf47(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[288,50]),
[iquote('0:Res:288.1,50.0')] ).
cnf(278,plain,
( ~ ccardinality_N(u)
| ~ rq_M_to_1(skf28(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[276,51]),
[iquote('0:Res:276.1,51.0')] ).
cnf(258,plain,
( ~ ccardinality_N(u)
| ~ rq_M_to_1(skf27(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[256,51]),
[iquote('0:Res:256.1,51.0')] ).
cnf(249,plain,
( ~ ccardinality_N(u)
| ~ rq_M_to_1(skf26(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[247,51]),
[iquote('0:Res:247.1,51.0')] ).
cnf(199,plain,
( ~ rinvP_1_to_N(u,v)
| ~ rp_N_to_1(v,w)
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[28,50]),
[iquote('0:Res:28.1,50.0')] ).
cnf(225,plain,
( ~ cinfinite(u)
| ~ rr_N_times_M_to_1(skf40(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[218,52]),
[iquote('0:Res:218.1,52.0')] ).
cnf(211,plain,
( ~ cinfinite(u)
| ~ rr_N_times_M_to_1(skf39(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[209,52]),
[iquote('0:Res:209.1,52.0')] ).
cnf(202,plain,
( ~ cinfinite(u)
| ~ rr_N_times_M_to_1(skf38(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[197,52]),
[iquote('0:Res:197.1,52.0')] ).
cnf(190,plain,
( ~ cinfinite(u)
| ~ rr_N_times_M_to_1(skf37(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[188,52]),
[iquote('0:Res:188.1,52.0')] ).
cnf(178,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rq_M_to_1(v,w)
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[30,51]),
[iquote('0:Res:30.1,51.0')] ).
cnf(181,plain,
( ~ cinfinite(u)
| ~ rr_N_times_M_to_1(skf36(u),v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[176,52]),
[iquote('0:Res:176.1,52.0')] ).
cnf(303,plain,
( ~ cinfinite(u)
| rp_N_to_1(skf48(u),u) ),
inference(ssi,[status(thm)],[300,105]),
[iquote('0:SSi:300.1,105.1')] ).
cnf(283,plain,
( ~ cinfinite(u)
| equal(skf33(skf48(u)),u) ),
inference(res,[status(thm),theory(equality)],[25,232]),
[iquote('0:Res:25.1,232.0')] ).
cnf(288,plain,
( ~ cinfinite(u)
| rp_N_to_1(skf47(u),u) ),
inference(ssi,[status(thm)],[285,104]),
[iquote('0:SSi:285.1,104.1')] ).
cnf(163,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rr_N_times_M_to_1(v,w)
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[32,52]),
[iquote('0:Res:32.1,52.0')] ).
cnf(282,plain,
( ~ cinfinite(u)
| equal(skf33(skf47(u)),u) ),
inference(res,[status(thm),theory(equality)],[26,232]),
[iquote('0:Res:26.1,232.0')] ).
cnf(232,plain,
( ~ rinvP_1_to_N(u,v)
| equal(u,skf33(v)) ),
inference(res,[status(thm),theory(equality)],[28,200]),
[iquote('0:Res:28.1,200.0')] ).
cnf(276,plain,
( ~ ccardinality_N(u)
| rq_M_to_1(skf28(u),u) ),
inference(ssi,[status(thm)],[273,119]),
[iquote('0:SSi:273.1,119.1')] ).
cnf(235,plain,
( ~ ccardinality_N(u)
| equal(skf34(skf28(u)),u) ),
inference(res,[status(thm),theory(equality)],[14,230]),
[iquote('0:Res:14.1,230.0')] ).
cnf(116,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ~ rinvR_N_times_M_to_1(u,w)
| ~ rinvR_N_times_M_to_1(u,x)
| ~ rinvR_N_times_M_to_1(u,y)
| ~ rinvR_N_times_M_to_1(u,z)
| ~ rinvR_N_times_M_to_1(u,x1)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(z,w)
| equal(z,x)
| equal(z,y)
| equal(x1,z)
| equal(x1,y)
| equal(x1,x)
| equal(x1,w)
| equal(v,w)
| equal(v,x)
| equal(v,y)
| equal(v,z)
| equal(v,x1) ),
inference(mrr,[status(thm)],[92,114]),
[iquote('0:MRR:92.0,114.1')] ).
cnf(256,plain,
( ~ ccardinality_N(u)
| rq_M_to_1(skf27(u),u) ),
inference(ssi,[status(thm)],[253,118]),
[iquote('0:SSi:253.1,118.1')] ).
cnf(234,plain,
( ~ ccardinality_N(u)
| equal(skf34(skf27(u)),u) ),
inference(res,[status(thm),theory(equality)],[15,230]),
[iquote('0:Res:15.1,230.0')] ).
cnf(247,plain,
( ~ ccardinality_N(u)
| rq_M_to_1(skf26(u),u) ),
inference(ssi,[status(thm)],[244,117]),
[iquote('0:SSi:244.1,117.1')] ).
cnf(233,plain,
( ~ ccardinality_N(u)
| equal(skf34(skf26(u)),u) ),
inference(res,[status(thm),theory(equality)],[16,230]),
[iquote('0:Res:16.1,230.0')] ).
cnf(108,plain,
( ~ rinvQ_1_to_M(u,v)
| ~ rinvQ_1_to_M(u,w)
| ~ rinvQ_1_to_M(u,x)
| ~ rinvQ_1_to_M(u,y)
| equal(x,w)
| equal(y,x)
| equal(y,w)
| equal(v,w)
| equal(v,x)
| equal(v,y) ),
inference(mrr,[status(thm)],[70,106]),
[iquote('0:MRR:70.0,106.1')] ).
cnf(230,plain,
( ~ rinvQ_1_to_M(u,v)
| equal(u,skf34(v)) ),
inference(res,[status(thm),theory(equality)],[30,179]),
[iquote('0:Res:30.1,179.0')] ).
cnf(200,plain,
( ~ rp_N_to_1(u,v)
| equal(v,skf33(u)) ),
inference(mrr,[status(thm)],[198,8]),
[iquote('0:MRR:198.0,8.1')] ).
cnf(179,plain,
( ~ rq_M_to_1(u,v)
| equal(v,skf34(u)) ),
inference(mrr,[status(thm)],[177,10]),
[iquote('0:MRR:177.0,10.1')] ).
cnf(218,plain,
( ~ cinfinite(u)
| rr_N_times_M_to_1(skf40(u),u) ),
inference(ssi,[status(thm)],[215,143]),
[iquote('0:SSi:215.1,143.1')] ).
cnf(101,plain,
( ~ rinvP_1_to_N(u,v)
| ~ rinvP_1_to_N(u,w)
| ~ rinvP_1_to_N(u,x)
| equal(x,w)
| equal(v,w)
| equal(v,x) ),
inference(mrr,[status(thm)],[59,99]),
[iquote('0:MRR:59.0,99.1')] ).
cnf(171,plain,
( ~ cinfinite(u)
| equal(skf35(skf40(u)),u) ),
inference(res,[status(thm),theory(equality)],[20,166]),
[iquote('0:Res:20.1,166.0')] ).
cnf(209,plain,
( ~ cinfinite(u)
| rr_N_times_M_to_1(skf39(u),u) ),
inference(ssi,[status(thm)],[206,142]),
[iquote('0:SSi:206.1,142.1')] ).
cnf(170,plain,
( ~ cinfinite(u)
| equal(skf35(skf39(u)),u) ),
inference(res,[status(thm),theory(equality)],[21,166]),
[iquote('0:Res:21.1,166.0')] ).
cnf(197,plain,
( ~ cinfinite(u)
| rr_N_times_M_to_1(skf38(u),u) ),
inference(ssi,[status(thm)],[194,141]),
[iquote('0:SSi:194.1,141.1')] ).
cnf(50,axiom,
( ~ rp_N_to_1(u,v)
| ~ rp_N_to_1(u,w)
| equal(w,v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(169,plain,
( ~ cinfinite(u)
| equal(skf35(skf38(u)),u) ),
inference(res,[status(thm),theory(equality)],[22,166]),
[iquote('0:Res:22.1,166.0')] ).
cnf(188,plain,
( ~ cinfinite(u)
| rr_N_times_M_to_1(skf37(u),u) ),
inference(ssi,[status(thm)],[185,140]),
[iquote('0:SSi:185.1,140.1')] ).
cnf(168,plain,
( ~ cinfinite(u)
| equal(skf35(skf37(u)),u) ),
inference(res,[status(thm),theory(equality)],[23,166]),
[iquote('0:Res:23.1,166.0')] ).
cnf(176,plain,
( ~ cinfinite(u)
| rr_N_times_M_to_1(skf36(u),u) ),
inference(ssi,[status(thm)],[173,139]),
[iquote('0:SSi:173.1,139.1')] ).
cnf(51,axiom,
( ~ rq_M_to_1(u,v)
| ~ rq_M_to_1(u,w)
| equal(w,v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(167,plain,
( ~ cinfinite(u)
| equal(skf35(skf36(u)),u) ),
inference(res,[status(thm),theory(equality)],[24,166]),
[iquote('0:Res:24.1,166.0')] ).
cnf(166,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| equal(u,skf35(v)) ),
inference(res,[status(thm),theory(equality)],[32,164]),
[iquote('0:Res:32.1,164.0')] ).
cnf(164,plain,
( ~ rr_N_times_M_to_1(u,v)
| equal(v,skf35(u)) ),
inference(mrr,[status(thm)],[162,12]),
[iquote('0:MRR:162.0,12.1')] ).
cnf(52,axiom,
( ~ rr_N_times_M_to_1(u,v)
| ~ rr_N_times_M_to_1(u,w)
| equal(w,v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ cinfinite(u)
| ~ equal(skf40(u),skf39(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ cinfinite(u)
| ~ equal(skf40(u),skf38(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ cinfinite(u)
| ~ equal(skf40(u),skf37(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ cinfinite(u)
| ~ equal(skf40(u),skf36(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ cinfinite(u)
| ~ equal(skf39(u),skf36(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ cinfinite(u)
| ~ equal(skf39(u),skf37(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ cinfinite(u)
| ~ equal(skf39(u),skf38(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ cinfinite(u)
| ~ equal(skf38(u),skf37(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ cinfinite(u)
| ~ equal(skf38(u),skf36(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ cinfinite(u)
| ~ equal(skf37(u),skf36(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ cinfinite(u)
| ~ equal(skf48(u),skf47(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ ccardinality_N(u)
| ~ equal(skf28(u),skf27(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ ccardinality_N(u)
| ~ equal(skf28(u),skf26(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(148,plain,
( ~ ccardinality_N_times_M(u)
| rinvR_N_times_M_to_1(skf35(u),u) ),
inference(res,[status(thm),theory(equality)],[19,31]),
[iquote('0:Res:19.1,31.0')] ).
cnf(132,plain,
( ~ ccardinality_N_times_M(u)
| rinvQ_1_to_M(skf34(u),u) ),
inference(res,[status(thm),theory(equality)],[18,29]),
[iquote('0:Res:18.1,29.0')] ).
cnf(35,axiom,
( ~ ccardinality_N(u)
| ~ equal(skf27(u),skf26(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(126,plain,
( ~ ccardinality_N(u)
| rinvP_1_to_N(skf33(u),u) ),
inference(res,[status(thm),theory(equality)],[17,27]),
[iquote('0:Res:17.1,27.0')] ).
cnf(143,plain,
( ~ cinfinite(u)
| ccardinality_N_times_M(skf40(u)) ),
inference(res,[status(thm),theory(equality)],[20,115]),
[iquote('0:Res:20.1,115.0')] ).
cnf(142,plain,
( ~ cinfinite(u)
| ccardinality_N_times_M(skf39(u)) ),
inference(res,[status(thm),theory(equality)],[21,115]),
[iquote('0:Res:21.1,115.0')] ).
cnf(141,plain,
( ~ cinfinite(u)
| ccardinality_N_times_M(skf38(u)) ),
inference(res,[status(thm),theory(equality)],[22,115]),
[iquote('0:Res:22.1,115.0')] ).
cnf(31,axiom,
( ~ rr_N_times_M_to_1(u,v)
| rinvR_N_times_M_to_1(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(140,plain,
( ~ cinfinite(u)
| ccardinality_N_times_M(skf37(u)) ),
inference(res,[status(thm),theory(equality)],[23,115]),
[iquote('0:Res:23.1,115.0')] ).
cnf(139,plain,
( ~ cinfinite(u)
| ccardinality_N_times_M(skf36(u)) ),
inference(res,[status(thm),theory(equality)],[24,115]),
[iquote('0:Res:24.1,115.0')] ).
cnf(115,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| ccardinality_N_times_M(v) ),
inference(res,[status(thm),theory(equality)],[32,12]),
[iquote('0:Res:32.1,12.0')] ).
cnf(114,plain,
( ~ rinvR_N_times_M_to_1(u,v)
| cinfinite(u) ),
inference(res,[status(thm),theory(equality)],[32,13]),
[iquote('0:Res:32.1,13.0')] ).
cnf(29,axiom,
( ~ rq_M_to_1(u,v)
| rinvQ_1_to_M(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(130,plain,
( ~ cinfinite(u)
| ccardinality_N(skf34(v)) ),
inference(ems,[status(thm)],[121,105]),
[iquote('0:EmS:121.0,105.1')] ).
cnf(128,plain,
( ~ cinfinite(u)
| cinfinite(skf35(v)) ),
inference(ems,[status(thm)],[120,105]),
[iquote('0:EmS:120.0,105.1')] ).
cnf(121,plain,
( ~ ccardinality_N(u)
| ccardinality_N(skf34(v)) ),
inference(ems,[status(thm)],[6,117]),
[iquote('0:EmS:6.0,117.1')] ).
cnf(120,plain,
( ~ ccardinality_N(u)
| cinfinite(skf35(v)) ),
inference(ems,[status(thm)],[7,117]),
[iquote('0:EmS:7.0,117.1')] ).
cnf(27,axiom,
( ~ rp_N_to_1(u,v)
| rinvP_1_to_N(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(119,plain,
( ~ ccardinality_N(u)
| ccardinality_N_times_M(skf28(u)) ),
inference(res,[status(thm),theory(equality)],[14,107]),
[iquote('0:Res:14.1,107.0')] ).
cnf(118,plain,
( ~ ccardinality_N(u)
| ccardinality_N_times_M(skf27(u)) ),
inference(res,[status(thm),theory(equality)],[15,107]),
[iquote('0:Res:15.1,107.0')] ).
cnf(117,plain,
( ~ ccardinality_N(u)
| ccardinality_N_times_M(skf26(u)) ),
inference(res,[status(thm),theory(equality)],[16,107]),
[iquote('0:Res:16.1,107.0')] ).
cnf(107,plain,
( ~ rinvQ_1_to_M(u,v)
| ccardinality_N_times_M(v) ),
inference(res,[status(thm),theory(equality)],[30,10]),
[iquote('0:Res:30.1,10.0')] ).
cnf(32,axiom,
( ~ rinvR_N_times_M_to_1(u,v)
| rr_N_times_M_to_1(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(106,plain,
( ~ rinvQ_1_to_M(u,v)
| ccardinality_N(u) ),
inference(res,[status(thm),theory(equality)],[30,11]),
[iquote('0:Res:30.1,11.0')] ).
cnf(109,plain,
( ~ cinfinite(u)
| cinfinite(skf33(v)) ),
inference(ems,[status(thm)],[5,104]),
[iquote('0:EmS:5.0,104.1')] ).
cnf(105,plain,
( ~ cinfinite(u)
| ccardinality_N(skf48(u)) ),
inference(res,[status(thm),theory(equality)],[25,100]),
[iquote('0:Res:25.1,100.0')] ).
cnf(104,plain,
( ~ cinfinite(u)
| ccardinality_N(skf47(u)) ),
inference(res,[status(thm),theory(equality)],[26,100]),
[iquote('0:Res:26.1,100.0')] ).
cnf(30,axiom,
( ~ rinvQ_1_to_M(u,v)
| rq_M_to_1(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(100,plain,
( ~ rinvP_1_to_N(u,v)
| ccardinality_N(v) ),
inference(res,[status(thm),theory(equality)],[28,8]),
[iquote('0:Res:28.1,8.0')] ).
cnf(99,plain,
( ~ rinvP_1_to_N(u,v)
| cinfinite(u) ),
inference(res,[status(thm),theory(equality)],[28,9]),
[iquote('0:Res:28.1,9.0')] ).
cnf(28,axiom,
( ~ rinvP_1_to_N(u,v)
| rp_N_to_1(v,u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cinfinite(u)
| rinvR_N_times_M_to_1(u,skf40(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ cinfinite(u)
| rinvR_N_times_M_to_1(u,skf39(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ cinfinite(u)
| rinvR_N_times_M_to_1(u,skf38(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ cinfinite(u)
| rinvR_N_times_M_to_1(u,skf37(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ cinfinite(u)
| rinvR_N_times_M_to_1(u,skf36(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ ccardinality_N(u)
| rinvQ_1_to_M(u,skf28(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ ccardinality_N(u)
| rinvQ_1_to_M(u,skf27(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ ccardinality_N(u)
| rinvQ_1_to_M(u,skf26(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ cinfinite(u)
| rinvP_1_to_N(u,skf48(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ cinfinite(u)
| rinvP_1_to_N(u,skf47(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ ccardinality_N(u)
| rp_N_to_1(u,skf33(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ ccardinality_N_times_M(u)
| rq_M_to_1(u,skf34(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ ccardinality_N_times_M(u)
| rr_N_times_M_to_1(u,skf35(u)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ rp_N_to_1(u,v)
| cinfinite(v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ rr_N_times_M_to_1(u,v)
| cinfinite(v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ rp_N_to_1(u,v)
| ccardinality_N(u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ rq_M_to_1(u,v)
| ccardinality_N(v) ),
file('KRS052+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ rq_M_to_1(u,v)
| ccardinality_N_times_M(u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ rr_N_times_M_to_1(u,v)
| ccardinality_N_times_M(u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ ccardinality_N(u)
| cinfinite(skf33(v)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ ccardinality_N_times_M(u)
| cinfinite(skf35(v)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ ccardinality_N_times_M(u)
| ccardinality_N(skf34(v)) ),
file('KRS052+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ xsd_integer(u)
| ~ xsd_string(u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(3,axiom,
( xsd_string(u)
| xsd_integer(u) ),
file('KRS052+1.p',unknown),
[] ).
cnf(2,axiom,
~ cowlNothing(u),
file('KRS052+1.p',unknown),
[] ).
cnf(1,axiom,
cowlThing(u),
file('KRS052+1.p',unknown),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS052+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.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 : Tue Jun 7 09:31:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.23/2.42
% 2.23/2.42 SPASS V 3.9
% 2.23/2.42 SPASS beiseite: Completion found.
% 2.23/2.42 % SZS status CounterSatisfiable
% 2.23/2.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.23/2.42 SPASS derived 1028 clauses, backtracked 0 clauses, performed 0 splits and kept 257 clauses.
% 2.23/2.42 SPASS allocated 101633 KBytes.
% 2.23/2.42 SPASS spent 0:00:02.09 on the problem.
% 2.23/2.42 0:00:00.03 for the input.
% 2.23/2.42 0:00:00.65 for the FLOTTER CNF translation.
% 2.23/2.42 0:00:00.04 for inferences.
% 2.23/2.42 0:00:00.00 for the backtracking.
% 2.23/2.42 0:00:01.33 for the reduction.
% 2.23/2.42
% 2.23/2.42
% 2.23/2.42 The saturated set of worked-off clauses is :
% 2.23/2.42 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------