TSTP Solution File: GRP601-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 11:48:14 EDT 2022
% Result : Unsatisfiable 0.57s 0.73s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 85 RR)
% Number of literals : 85 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(double_divide(inverse(double_divide(u,inverse(double_divide(v,double_divide(u,w))))),w)),v),
file('GRP601-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP601-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP601-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,w)),x),u),multiply(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),multiply(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(15,plain,
equal(multiply(double_divide(multiply(u,v),double_divide(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(18,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),w),u),x),multiply(x,w)),v),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(33,plain,
equal(double_divide(u,multiply(double_divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.0,15.0')] ).
cnf(58,plain,
equal(multiply(multiply(double_divide(multiply(u,v),w),u),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[33,2]),
[iquote('0:SpR:33.0,2.0')] ).
cnf(65,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),u),double_divide(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[33]),
[iquote('0:SpR:33.0,33.0')] ).
cnf(72,plain,
equal(double_divide(multiply(u,v),double_divide(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[12,33]),
[iquote('0:SpR:12.0,33.0')] ).
cnf(74,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[72,2]),
[iquote('0:SpR:72.0,2.0')] ).
cnf(76,plain,
equal(multiply(multiply(u,v),multiply(w,x)),multiply(multiply(u,w),multiply(v,x))),
inference(spr,[status(thm),theory(equality)],[72,6]),
[iquote('0:SpR:72.0,6.0')] ).
cnf(113,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),w),u),double_divide(multiply(w,x),double_divide(x,y))),y),v),
inference(spr,[status(thm),theory(equality)],[15,18]),
[iquote('0:SpR:15.0,18.0')] ).
cnf(141,plain,
equal(multiply(multiply(double_divide(inverse(u),v),multiply(double_divide(multiply(w,x),u),w)),x),inverse(v)),
inference(spr,[status(thm),theory(equality)],[58]),
[iquote('0:SpR:58.0,58.0')] ).
cnf(142,plain,
equal(multiply(double_divide(u,multiply(double_divide(multiply(v,multiply(w,u)),x),v)),inverse(x)),w),
inference(spr,[status(thm),theory(equality)],[58,9]),
[iquote('0:SpR:58.0,9.0')] ).
cnf(157,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[65,142]),
[iquote('0:Rew:65.0,142.0')] ).
cnf(167,plain,
equal(multiply(multiply(u,v),multiply(inverse(u),w)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[74,4]),
[iquote('0:SpR:74.0,4.0')] ).
cnf(171,plain,
equal(multiply(multiply(double_divide(inverse(u),v),double_divide(w,multiply(u,x))),multiply(x,w)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[74,58]),
[iquote('0:SpR:74.0,58.0')] ).
cnf(176,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(multiply(w,x),u)),inverse(double_divide(x,multiply(v,w)))),
inference(spr,[status(thm),theory(equality)],[74]),
[iquote('0:SpR:74.0,74.0')] ).
cnf(192,plain,
equal(multiply(double_divide(u,v),multiply(multiply(w,x),u)),inverse(double_divide(multiply(multiply(double_divide(y,v),x),y),w))),
inference(spr,[status(thm),theory(equality)],[18,74]),
[iquote('0:SpR:18.0,74.0')] ).
cnf(196,plain,
equal(multiply(multiply(double_divide(inverse(u),v),w),multiply(double_divide(x,multiply(u,w)),x)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[76,171]),
[iquote('0:Rew:76.0,171.0')] ).
cnf(197,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(multiply(w,x),u)),multiply(multiply(v,w),x)),
inference(rew,[status(thm),theory(equality)],[2,176]),
[iquote('0:Rew:2.0,176.0')] ).
cnf(198,plain,
equal(multiply(double_divide(u,v),multiply(multiply(w,x),u)),multiply(w,multiply(multiply(double_divide(y,v),x),y))),
inference(rew,[status(thm),theory(equality)],[2,192]),
[iquote('0:Rew:2.0,192.0')] ).
cnf(201,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,w),double_divide(x,double_divide(x,multiply(u,v))))),w),
inference(spr,[status(thm),theory(equality)],[157,33]),
[iquote('0:SpR:157.0,33.0')] ).
cnf(213,plain,
equal(double_divide(multiply(inverse(u),v),multiply(u,w)),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[157,33]),
[iquote('0:SpR:157.0,33.0')] ).
cnf(222,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),inverse(multiply(double_divide(multiply(w,x),v),w))),x),
inference(spr,[status(thm),theory(equality)],[58,157]),
[iquote('0:SpR:58.0,157.0')] ).
cnf(223,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(w)),multiply(multiply(double_divide(x,w),v),x)),
inference(spr,[status(thm),theory(equality)],[4,157]),
[iquote('0:SpR:4.0,157.0')] ).
cnf(225,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(double_divide(w,x))),multiply(x,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[9,157]),
[iquote('0:SpR:9.0,157.0')] ).
cnf(232,plain,
equal(multiply(double_divide(u,double_divide(u,v)),multiply(w,x)),multiply(w,multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[2,225]),
[iquote('0:Rew:2.0,225.0')] ).
cnf(265,plain,
equal(multiply(u,multiply(multiply(double_divide(v,inverse(w)),x),v)),multiply(multiply(w,u),x)),
inference(spr,[status(thm),theory(equality)],[4,167]),
[iquote('0:SpR:4.0,167.0')] ).
cnf(272,plain,
equal(multiply(u,multiply(inverse(double_divide(v,w)),x)),multiply(multiply(w,multiply(u,v)),x)),
inference(spr,[status(thm),theory(equality)],[9,167]),
[iquote('0:SpR:9.0,167.0')] ).
cnf(279,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(v,multiply(multiply(u,w),x))),
inference(rew,[status(thm),theory(equality)],[2,272]),
[iquote('0:Rew:2.0,272.0')] ).
cnf(283,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(multiply(double_divide(inverse(w),x),u),v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[279,141]),
[iquote('0:Rew:279.0,141.0')] ).
cnf(416,plain,
equal(double_divide(multiply(inverse(double_divide(u,v)),w),x),double_divide(w,multiply(v,multiply(x,u)))),
inference(spr,[status(thm),theory(equality)],[9,213]),
[iquote('0:SpR:9.0,213.0')] ).
cnf(428,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(w,multiply(u,multiply(x,v)))),
inference(rew,[status(thm),theory(equality)],[2,416]),
[iquote('0:Rew:2.0,416.0')] ).
cnf(431,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),multiply(double_divide(multiply(w,x),double_divide(x,y)),w))),y),v),
inference(rew,[status(thm),theory(equality)],[428,113]),
[iquote('0:Rew:428.0,113.0')] ).
cnf(467,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),w)),w),v),
inference(rew,[status(thm),theory(equality)],[15,431]),
[iquote('0:Rew:15.0,431.0')] ).
cnf(502,plain,
equal(multiply(double_divide(multiply(u,v),w),u),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[467,33]),
[iquote('0:SpR:467.0,33.0')] ).
cnf(518,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[157,467]),
[iquote('0:SpR:157.0,467.0')] ).
cnf(521,plain,
equal(multiply(double_divide(u,v),multiply(w,multiply(v,u))),w),
inference(spr,[status(thm),theory(equality)],[9,467]),
[iquote('0:SpR:9.0,467.0')] ).
cnf(522,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[74,467]),
[iquote('0:SpR:74.0,467.0')] ).
cnf(524,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[502,33]),
[iquote('0:Rew:502.0,33.0')] ).
cnf(525,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[502,58]),
[iquote('0:Rew:502.0,58.0')] ).
cnf(540,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),inverse(double_divide(w,v))),w),
inference(rew,[status(thm),theory(equality)],[502,222]),
[iquote('0:Rew:502.0,222.0')] ).
cnf(541,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[502,65]),
[iquote('0:Rew:502.0,65.0')] ).
cnf(556,plain,
equal(multiply(multiply(double_divide(u,v),w),u),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[524,223]),
[iquote('0:Rew:524.0,223.0')] ).
cnf(557,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[524,232]),
[iquote('0:Rew:524.0,232.0')] ).
cnf(562,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,w),multiply(u,v))),w),
inference(rew,[status(thm),theory(equality)],[524,201]),
[iquote('0:Rew:524.0,201.0')] ).
cnf(566,plain,
equal(multiply(multiply(double_divide(inverse(u),v),w),inverse(multiply(u,w))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[525,196]),
[iquote('0:Rew:525.0,196.0')] ).
cnf(571,plain,
equal(multiply(double_divide(multiply(u,v),multiply(w,x)),multiply(w,u)),double_divide(v,x)),
inference(rew,[status(thm),theory(equality)],[541,12]),
[iquote('0:Rew:541.0,12.0')] ).
cnf(656,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(multiply(double_divide(inverse(v),x),w),u)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[541,283]),
[iquote('0:Rew:541.0,283.0')] ).
cnf(663,plain,
equal(multiply(u,multiply(double_divide(v,multiply(w,u)),v)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[557,74]),
[iquote('0:Rew:557.0,74.0')] ).
cnf(685,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[522,197]),
[iquote('0:Rew:522.0,197.0')] ).
cnf(691,plain,
equal(multiply(double_divide(u,v),multiply(multiply(w,x),u)),multiply(w,multiply(double_divide(y,v),multiply(x,y)))),
inference(rew,[status(thm),theory(equality)],[685,198]),
[iquote('0:Rew:685.0,198.0')] ).
cnf(695,plain,
equal(multiply(u,multiply(multiply(double_divide(v,inverse(w)),x),v)),multiply(w,multiply(u,x))),
inference(rew,[status(thm),theory(equality)],[685,265]),
[iquote('0:Rew:685.0,265.0')] ).
cnf(715,plain,
equal(multiply(double_divide(u,v),multiply(w,u)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[685,556]),
[iquote('0:Rew:685.0,556.0')] ).
cnf(716,plain,
equal(multiply(u,inverse(inverse(v))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[715,522]),
[iquote('0:Rew:715.0,522.0')] ).
cnf(722,plain,
equal(double_divide(inverse(u),multiply(u,inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[715,562]),
[iquote('0:Rew:715.0,562.0')] ).
cnf(729,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[525,663]),
[iquote('0:Rew:525.0,663.0')] ).
cnf(733,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),multiply(v,w)),w),
inference(rew,[status(thm),theory(equality)],[2,540]),
[iquote('0:Rew:2.0,540.0')] ).
cnf(734,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[557,733,524]),
[iquote('0:Rew:557.0,733.0,524.0,733.0')] ).
cnf(743,plain,
equal(double_divide(inverse(u),multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[518,566,729,685]),
[iquote('0:Rew:518.0,566.0,729.0,566.0,685.0,566.0')] ).
cnf(744,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[743,722]),
[iquote('0:Rew:743.0,722.0')] ).
cnf(745,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[744,716]),
[iquote('0:Rew:744.0,716.0')] ).
cnf(746,plain,
~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[745,3]),
[iquote('0:Rew:745.0,3.0')] ).
cnf(754,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[745,746]),
[iquote('0:Rew:745.0,746.0')] ).
cnf(764,plain,
equal(multiply(u,multiply(v,double_divide(w,multiply(u,multiply(x,v))))),double_divide(w,x)),
inference(rew,[status(thm),theory(equality)],[745,571,557,685,541]),
[iquote('0:Rew:745.0,571.0,557.0,571.0,685.0,571.0,541.0,571.0')] ).
cnf(815,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[744,695,715,685]),
[iquote('0:Rew:744.0,695.0,715.0,695.0,685.0,695.0')] ).
cnf(816,plain,
equal(multiply(u,multiply(double_divide(u,v),w)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[815,715]),
[iquote('0:Rew:815.0,715.0')] ).
cnf(830,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[743,656,685,518,816,815]),
[iquote('0:Rew:743.0,656.0,685.0,656.0,518.0,656.0,816.0,656.0,685.0,656.0,815.0,656.0,685.0,656.0')] ).
cnf(862,plain,
equal(multiply(double_divide(u,v),multiply(w,multiply(x,u))),multiply(w,multiply(x,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[685,691,816,815]),
[iquote('0:Rew:685.0,691.0,816.0,691.0,815.0,691.0')] ).
cnf(863,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[862,521]),
[iquote('0:Rew:862.0,521.0')] ).
cnf(944,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,744]),
[iquote('0:SpR:2.0,744.0')] ).
cnf(954,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[944,830]),
[iquote('0:Rew:944.0,830.0')] ).
cnf(1035,plain,
equal(multiply(u,multiply(v,double_divide(w,v))),double_divide(w,inverse(u))),
inference(spr,[status(thm),theory(equality)],[734,764]),
[iquote('0:SpR:734.0,764.0')] ).
cnf(1049,plain,
equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[954,1035]),
[iquote('0:Rew:954.0,1035.0')] ).
cnf(1051,plain,
~ equal(multiply(a1,inverse(a1)),double_divide(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[1049,754]),
[iquote('0:Rew:1049.0,754.0')] ).
cnf(1055,plain,
equal(multiply(u,double_divide(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[1049,863]),
[iquote('0:Rew:1049.0,863.0')] ).
cnf(1064,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[1049,1051]),
[iquote('0:Rew:1049.0,1051.0')] ).
cnf(1120,plain,
equal(multiply(double_divide(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[1055,745]),
[iquote('0:SpR:1055.0,745.0')] ).
cnf(1147,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[1120,1055]),
[iquote('0:SpR:1120.0,1055.0')] ).
cnf(1153,plain,
$false,
inference(unc,[status(thm)],[1147,1064]),
[iquote('0:UnC:1147.0,1064.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:15:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.73
% 0.57/0.73 SPASS V 3.9
% 0.57/0.73 SPASS beiseite: Proof found.
% 0.57/0.73 % SZS status Theorem
% 0.57/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.73 SPASS derived 776 clauses, backtracked 0 clauses, performed 0 splits and kept 450 clauses.
% 0.57/0.73 SPASS allocated 65347 KBytes.
% 0.57/0.73 SPASS spent 0:00:00.39 on the problem.
% 0.57/0.73 0:00:00.03 for the input.
% 0.57/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.57/0.73 0:00:00.01 for inferences.
% 0.57/0.73 0:00:00.00 for the backtracking.
% 0.57/0.73 0:00:00.33 for the reduction.
% 0.57/0.73
% 0.57/0.73
% 0.57/0.73 Here is a proof with depth 9, length 85 :
% 0.57/0.73 % SZS output start Refutation
% See solution above
% 0.57/0.74 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.57/0.74
%------------------------------------------------------------------------------