TSTP Solution File: GRP096-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 52 unt; 0 nHn; 60 RR)
% Number of literals : 76 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 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(u,inverse(divide(v,divide(u,w)))),w),v),
file('GRP096-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP096-1.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('GRP096-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(multiply(u,divide(v,divide(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,divide(v,divide(u,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(divide(multiply(multiply(u,divide(v,divide(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(multiply(u,divide(v,divide(u,divide(w,x)))),divide(multiply(w,v),x)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(11,plain,
equal(multiply(multiply(u,divide(v,multiply(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,6]),
[iquote('0:Rew:2.0,6.0')] ).
cnf(13,plain,
equal(multiply(multiply(multiply(u,divide(v,multiply(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[11]),
[iquote('0:SpR:11.0,11.0')] ).
cnf(15,plain,
equal(multiply(u,divide(v,divide(u,multiply(w,x)))),multiply(multiply(w,v),x)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(25,plain,
equal(divide(multiply(multiply(u,divide(v,divide(u,w))),x),w),multiply(y,divide(x,divide(y,v)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(35,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(64,plain,
equal(divide(divide(multiply(u,v),inverse(w)),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[2,35]),
[iquote('0:SpR:2.0,35.0')] ).
cnf(72,plain,
equal(divide(multiply(multiply(u,v),w),multiply(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,64]),
[iquote('0:Rew:2.0,64.0')] ).
cnf(81,plain,
equal(divide(u,divide(v,multiply(v,divide(w,u)))),w),
inference(spr,[status(thm),theory(equality)],[72,7]),
[iquote('0:SpR:72.0,7.0')] ).
cnf(96,plain,
equal(divide(divide(multiply(u,v),divide(w,multiply(w,divide(x,u)))),x),v),
inference(spr,[status(thm),theory(equality)],[81,35]),
[iquote('0:SpR:81.0,35.0')] ).
cnf(97,plain,
equal(divide(multiply(u,v),multiply(u,divide(w,x))),multiply(x,divide(v,w))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(99,plain,
equal(divide(multiply(u,v),multiply(u,divide(v,w))),w),
inference(spr,[status(thm),theory(equality)],[81,4]),
[iquote('0:SpR:81.0,4.0')] ).
cnf(103,plain,
equal(multiply(u,divide(v,divide(u,w))),divide(multiply(x,v),divide(y,multiply(y,divide(w,x))))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(105,plain,
equal(divide(inverse(u),divide(v,multiply(v,multiply(w,u)))),w),
inference(spr,[status(thm),theory(equality)],[2,81]),
[iquote('0:SpR:2.0,81.0')] ).
cnf(106,plain,
equal(divide(u,divide(v,multiply(v,w))),multiply(x,divide(w,divide(x,u)))),
inference(spr,[status(thm),theory(equality)],[4,81]),
[iquote('0:SpR:4.0,81.0')] ).
cnf(108,plain,
equal(divide(multiply(u,v),divide(w,multiply(w,x))),multiply(multiply(u,x),v)),
inference(spr,[status(thm),theory(equality)],[72,81]),
[iquote('0:SpR:72.0,81.0')] ).
cnf(112,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[97,99]),
[iquote('0:Rew:97.0,99.0')] ).
cnf(113,plain,
equal(divide(multiply(multiply(u,divide(v,u)),w),v),w),
inference(rew,[status(thm),theory(equality)],[108,96]),
[iquote('0:Rew:108.0,96.0')] ).
cnf(119,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(multiply(x,divide(w,x)),v)),
inference(rew,[status(thm),theory(equality)],[108,103]),
[iquote('0:Rew:108.0,103.0')] ).
cnf(139,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[11,13]),
[iquote('0:SpR:11.0,13.0')] ).
cnf(140,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[139,113]),
[iquote('0:Rew:139.0,113.0')] ).
cnf(142,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[139,119]),
[iquote('0:Rew:139.0,119.0')] ).
cnf(143,plain,
equal(multiply(divide(u,v),w),divide(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[142,8]),
[iquote('0:Rew:142.0,8.0')] ).
cnf(146,plain,
equal(divide(u,divide(v,multiply(v,w))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[142,106]),
[iquote('0:Rew:142.0,106.0')] ).
cnf(152,plain,
equal(divide(multiply(multiply(u,divide(v,divide(u,w))),x),w),multiply(v,x)),
inference(rew,[status(thm),theory(equality)],[142,25]),
[iquote('0:Rew:142.0,25.0')] ).
cnf(160,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[142,15]),
[iquote('0:Rew:142.0,15.0')] ).
cnf(168,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[146,105]),
[iquote('0:Rew:146.0,105.0')] ).
cnf(174,plain,
equal(divide(multiply(multiply(u,v),w),u),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[142,152]),
[iquote('0:Rew:142.0,152.0')] ).
cnf(198,plain,
equal(divide(divide(u,v),divide(u,v)),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[112,35]),
[iquote('0:SpR:112.0,35.0')] ).
cnf(203,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[2,112]),
[iquote('0:SpR:2.0,112.0')] ).
cnf(206,plain,
equal(divide(divide(u,v),divide(w,v)),divide(u,w)),
inference(spr,[status(thm),theory(equality)],[139,35]),
[iquote('0:SpR:139.0,35.0')] ).
cnf(220,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[206,198]),
[iquote('0:Rew:206.0,198.0')] ).
cnf(226,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[140,2]),
[iquote('0:SpR:140.0,2.0')] ).
cnf(231,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[220,2]),
[iquote('0:SpR:220.0,2.0')] ).
cnf(259,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(spr,[status(thm),theory(equality)],[139,168]),
[iquote('0:SpR:139.0,168.0')] ).
cnf(276,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[203,226]),
[iquote('0:SpR:203.0,226.0')] ).
cnf(284,plain,
equal(multiply(multiply(inverse(u),u),v),divide(multiply(w,v),w)),
inference(spr,[status(thm),theory(equality)],[231,143]),
[iquote('0:SpR:231.0,143.0')] ).
cnf(295,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[140,284]),
[iquote('0:Rew:140.0,284.0')] ).
cnf(296,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)],[295,3]),
[iquote('0:Rew:295.0,3.3')] ).
cnf(297,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)],[296]),
[iquote('0:Obv:296.3')] ).
cnf(319,plain,
equal(multiply(inverse(u),v),inverse(divide(u,v))),
inference(spr,[status(thm),theory(equality)],[259,168]),
[iquote('0:SpR:259.0,168.0')] ).
cnf(328,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),inverse(divide(b1,b1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[319,297]),
[iquote('0:Rew:319.0,297.1')] ).
cnf(337,plain,
equal(inverse(divide(u,u)),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[319,276]),
[iquote('0:Rew:319.0,276.0')] ).
cnf(351,plain,
equal(inverse(divide(u,u)),inverse(divide(v,v))),
inference(rew,[status(thm),theory(equality)],[319,337]),
[iquote('0:Rew:319.0,337.0')] ).
cnf(353,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(divide(b1,b1)),inverse(divide(a1,a1)))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[319,328]),
[iquote('0:Rew:319.0,328.1')] ).
cnf(579,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[174,139]),
[iquote('0:SpR:174.0,139.0')] ).
cnf(595,plain,
equal(divide(multiply(multiply(u,v),w),u),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[160,174]),
[iquote('0:SpR:160.0,174.0')] ).
cnf(600,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(divide(b1,b1)),inverse(divide(a1,a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[579,353]),
[iquote('0:Rew:579.0,353.2')] ).
cnf(621,plain,
equal(divide(multiply(u,multiply(v,w)),u),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[579,595]),
[iquote('0:Rew:579.0,595.0')] ).
cnf(622,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[140,621]),
[iquote('0:Rew:140.0,621.0')] ).
cnf(666,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(divide(b1,b1)),inverse(divide(a1,a1))) ),
inference(obv,[status(thm),theory(equality)],[600]),
[iquote('0:Obv:600.2')] ).
cnf(667,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(inverse(divide(b1,b1)),inverse(divide(a1,a1))) ),
inference(rew,[status(thm),theory(equality)],[622,666]),
[iquote('0:Rew:622.0,666.0')] ).
cnf(668,plain,
~ equal(inverse(divide(b1,b1)),inverse(divide(a1,a1))),
inference(obv,[status(thm),theory(equality)],[667]),
[iquote('0:Obv:667.0')] ).
cnf(669,plain,
$false,
inference(unc,[status(thm)],[668,351]),
[iquote('0:UnC:668.0,351.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 22:20:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 492 clauses, backtracked 0 clauses, performed 0 splits and kept 154 clauses.
% 0.21/0.50 SPASS allocated 63841 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.50 0:00:00.03 for the input.
% 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.06 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 8, length 60 :
% 0.21/0.50 % SZS output start Refutation
% See solution above
% 0.21/0.50 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.21/0.50
%------------------------------------------------------------------------------