TSTP Solution File: GRP604-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 0.46s 0.67s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 50 RR)
% Number of literals : 50 ( 0 equ; 1 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('GRP604-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP604-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP604-1.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(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(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(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(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(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(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(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(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(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(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(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,
$false,
inference(unc,[status(thm)],[745,3]),
[iquote('0:UnC:745.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 09:57:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.67
% 0.46/0.67 SPASS V 3.9
% 0.46/0.67 SPASS beiseite: Proof found.
% 0.46/0.67 % SZS status Theorem
% 0.46/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.67 SPASS derived 632 clauses, backtracked 0 clauses, performed 0 splits and kept 418 clauses.
% 0.46/0.67 SPASS allocated 65172 KBytes.
% 0.46/0.67 SPASS spent 0:00:00.31 on the problem.
% 0.46/0.67 0:00:00.04 for the input.
% 0.46/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.67 0:00:00.01 for inferences.
% 0.46/0.67 0:00:00.00 for the backtracking.
% 0.46/0.67 0:00:00.24 for the reduction.
% 0.46/0.67
% 0.46/0.67
% 0.46/0.67 Here is a proof with depth 8, length 50 :
% 0.46/0.67 % SZS output start Refutation
% See solution above
% 0.46/0.67 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.46/0.67
%------------------------------------------------------------------------------