TSTP Solution File: GRP098-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP098-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:45:17 EDT 2022
% Result : Unsatisfiable 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 63 ( 55 unt; 0 nHn; 63 RR)
% Number of literals : 78 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,inverse(v)),w),divide(u,w)),v),
file('GRP098-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP098-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP098-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(divide(divide(multiply(divide(multiply(u,v),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(divide(divide(multiply(u,v),inverse(w)),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(10,plain,
equal(divide(multiply(multiply(u,v),w),multiply(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,8]),
[iquote('0:Rew:2.0,8.0')] ).
cnf(13,plain,
equal(divide(u,divide(multiply(v,u),multiply(v,w))),w),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(15,plain,
equal(divide(divide(multiply(u,v),divide(multiply(w,u),multiply(w,x))),x),v),
inference(spr,[status(thm),theory(equality)],[13,4]),
[iquote('0:SpR:13.0,4.0')] ).
cnf(18,plain,
equal(multiply(divide(multiply(divide(multiply(u,inverse(v)),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(56,plain,
equal(divide(divide(u,divide(divide(multiply(v,inverse(w)),x),divide(v,x))),u),w),
inference(spr,[status(thm),theory(equality)],[18,6]),
[iquote('0:SpR:18.0,6.0')] ).
cnf(57,plain,
equal(multiply(divide(inverse(u),divide(divide(multiply(v,inverse(w)),x),divide(v,x))),u),w),
inference(spr,[status(thm),theory(equality)],[18]),
[iquote('0:SpR:18.0,18.0')] ).
cnf(71,plain,
equal(multiply(divide(multiply(u,v),divide(w,divide(multiply(x,multiply(w,inverse(y))),multiply(x,u)))),y),v),
inference(spr,[status(thm),theory(equality)],[13,18]),
[iquote('0:SpR:13.0,18.0')] ).
cnf(74,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[2,56,4]),
[iquote('0:Rew:2.0,56.0,4.0,56.0')] ).
cnf(75,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[2,57,4]),
[iquote('0:Rew:2.0,57.0,4.0,57.0')] ).
cnf(82,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[74,4]),
[iquote('0:SpR:74.0,4.0')] ).
cnf(98,plain,
equal(multiply(divide(u,u),v),v),
inference(spr,[status(thm),theory(equality)],[82,74]),
[iquote('0:SpR:82.0,74.0')] ).
cnf(119,plain,
equal(divide(multiply(u,v),multiply(divide(w,w),v)),u),
inference(spr,[status(thm),theory(equality)],[98,10]),
[iquote('0:SpR:98.0,10.0')] ).
cnf(126,plain,
equal(divide(u,divide(multiply(divide(v,v),u),w)),w),
inference(spr,[status(thm),theory(equality)],[98,13]),
[iquote('0:SpR:98.0,13.0')] ).
cnf(136,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[2,98]),
[iquote('0:SpR:2.0,98.0')] ).
cnf(138,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[136,3]),
[iquote('0:Rew:136.0,3.3')] ).
cnf(139,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[98,119]),
[iquote('0:Rew:98.0,119.0')] ).
cnf(141,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[98,126]),
[iquote('0:Rew:98.0,126.0')] ).
cnf(149,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[138]),
[iquote('0:Obv:138.3')] ).
cnf(157,plain,
equal(multiply(divide(multiply(u,v),divide(u,inverse(w))),w),v),
inference(spr,[status(thm),theory(equality)],[139,18]),
[iquote('0:SpR:139.0,18.0')] ).
cnf(166,plain,
equal(divide(multiply(u,v),multiply(u,w)),divide(v,w)),
inference(spr,[status(thm),theory(equality)],[139,15]),
[iquote('0:SpR:139.0,15.0')] ).
cnf(167,plain,
equal(divide(multiply(divide(multiply(u,inverse(v)),w),x),divide(u,w)),divide(x,v)),
inference(spr,[status(thm),theory(equality)],[18,139]),
[iquote('0:SpR:18.0,139.0')] ).
cnf(168,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[98,139]),
[iquote('0:SpR:98.0,139.0')] ).
cnf(183,plain,
equal(multiply(divide(multiply(u,v),divide(w,divide(multiply(w,inverse(x)),u))),x),v),
inference(rew,[status(thm),theory(equality)],[166,71]),
[iquote('0:Rew:166.0,71.0')] ).
cnf(193,plain,
equal(multiply(divide(multiply(u,v),multiply(u,w)),w),v),
inference(rew,[status(thm),theory(equality)],[2,157]),
[iquote('0:Rew:2.0,157.0')] ).
cnf(194,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[166,193]),
[iquote('0:Rew:166.0,193.0')] ).
cnf(224,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[2,141]),
[iquote('0:SpR:2.0,141.0')] ).
cnf(312,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[2,194]),
[iquote('0:SpR:2.0,194.0')] ).
cnf(316,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[74,194]),
[iquote('0:SpR:74.0,194.0')] ).
cnf(318,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[10,194]),
[iquote('0:SpR:10.0,194.0')] ).
cnf(319,plain,
equal(multiply(u,divide(v,w)),divide(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[4,194]),
[iquote('0:SpR:4.0,194.0')] ).
cnf(320,plain,
equal(divide(multiply(divide(multiply(u,v),w),x),divide(u,w)),multiply(x,v)),
inference(spr,[status(thm),theory(equality)],[6,194]),
[iquote('0:SpR:6.0,194.0')] ).
cnf(323,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[316,149]),
[iquote('0:Rew:316.0,149.2')] ).
cnf(331,plain,
equal(multiply(u,divide(multiply(v,w),divide(x,divide(multiply(x,inverse(u)),v)))),w),
inference(rew,[status(thm),theory(equality)],[316,183]),
[iquote('0:Rew:316.0,183.0')] ).
cnf(347,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[316,75]),
[iquote('0:Rew:316.0,75.0')] ).
cnf(348,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[316,312]),
[iquote('0:Rew:316.0,312.0')] ).
cnf(369,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[320,167]),
[iquote('0:Rew:320.0,167.0')] ).
cnf(387,plain,
equal(divide(multiply(u,multiply(v,w)),divide(x,divide(divide(x,w),v))),u),
inference(rew,[status(thm),theory(equality)],[318,331,319,369]),
[iquote('0:Rew:318.0,331.0,319.0,331.0,369.0,331.0')] ).
cnf(408,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[369,323,316]),
[iquote('0:Rew:369.0,323.1,316.0,323.1,369.0,323.1,316.0,323.1,316.0,323.0')] ).
cnf(409,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[408]),
[iquote('0:Obv:408.0')] ).
cnf(429,plain,
equal(divide(divide(u,u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[98,224]),
[iquote('0:SpR:98.0,224.0')] ).
cnf(445,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[348,224]),
[iquote('0:SpR:348.0,224.0')] ).
cnf(511,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[347,74]),
[iquote('0:SpR:347.0,74.0')] ).
cnf(513,plain,
equal(inverse(multiply(inverse(u),v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[347,224]),
[iquote('0:SpR:347.0,224.0')] ).
cnf(538,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[511,513]),
[iquote('0:Rew:511.0,513.0')] ).
cnf(694,plain,
equal(multiply(u,divide(v,w)),divide(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[538,2]),
[iquote('0:SpR:538.0,2.0')] ).
cnf(715,plain,
equal(divide(multiply(u,v),w),divide(v,divide(w,u))),
inference(rew,[status(thm),theory(equality)],[319,694]),
[iquote('0:Rew:319.0,694.0')] ).
cnf(730,plain,
equal(divide(multiply(u,v),divide(divide(w,divide(divide(w,v),u)),x)),x),
inference(rew,[status(thm),theory(equality)],[715,387]),
[iquote('0:Rew:715.0,387.0')] ).
cnf(793,plain,
equal(divide(u,divide(divide(divide(v,divide(divide(v,u),w)),x),w)),x),
inference(rew,[status(thm),theory(equality)],[715,730]),
[iquote('0:Rew:715.0,730.0')] ).
cnf(973,plain,
equal(multiply(divide(u,divide(divide(u,v),w)),x),divide(v,divide(inverse(x),w))),
inference(spr,[status(thm),theory(equality)],[224,793]),
[iquote('0:SpR:224.0,793.0')] ).
cnf(979,plain,
equal(divide(u,divide(divide(u,v),w)),divide(v,inverse(w))),
inference(spr,[status(thm),theory(equality)],[429,793]),
[iquote('0:SpR:429.0,793.0')] ).
cnf(986,plain,
equal(divide(u,divide(divide(u,v),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[2,979]),
[iquote('0:Rew:2.0,979.0')] ).
cnf(1055,plain,
equal(multiply(divide(u,divide(divide(u,v),w)),x),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[2,973,445]),
[iquote('0:Rew:2.0,973.0,445.0,973.0')] ).
cnf(1056,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[318,1055,986]),
[iquote('0:Rew:318.0,1055.0,986.0,1055.0')] ).
cnf(1057,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1056,409]),
[iquote('0:Rew:1056.0,409.1')] ).
cnf(1069,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[316,1057]),
[iquote('0:Rew:316.0,1057.1')] ).
cnf(1070,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(obv,[status(thm),theory(equality)],[1069]),
[iquote('0:Obv:1069.1')] ).
cnf(1071,plain,
$false,
inference(unc,[status(thm)],[1070,168]),
[iquote('0:UnC:1070.0,168.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP098-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 04:40:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.56
% 0.21/0.56 SPASS V 3.9
% 0.21/0.56 SPASS beiseite: Proof found.
% 0.21/0.56 % SZS status Theorem
% 0.21/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.56 SPASS derived 610 clauses, backtracked 0 clauses, performed 0 splits and kept 204 clauses.
% 0.21/0.56 SPASS allocated 64537 KBytes.
% 0.21/0.56 SPASS spent 0:00:00.18 on the problem.
% 0.21/0.56 0:00:00.03 for the input.
% 0.21/0.56 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.56 0:00:00.01 for inferences.
% 0.21/0.56 0:00:00.00 for the backtracking.
% 0.21/0.56 0:00:00.12 for the reduction.
% 0.21/0.56
% 0.21/0.56
% 0.21/0.56 Here is a proof with depth 9, length 63 :
% 0.21/0.56 % SZS output start Refutation
% See solution above
% 0.21/0.56 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.21/0.56
%------------------------------------------------------------------------------