TSTP Solution File: GRP200-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:46:18 EDT 2022
% Result : Unsatisfiable 2.47s 2.71s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 65 RR)
% Number of literals : 65 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(identity,u),u),
file('GRP200-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(u,identity),u),
file('GRP200-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,left_division(u,v)),v),
file('GRP200-1.p',unknown),
[] ).
cnf(4,axiom,
equal(left_division(u,multiply(u,v)),v),
file('GRP200-1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(right_division(u,v),v),u),
file('GRP200-1.p',unknown),
[] ).
cnf(6,axiom,
equal(right_division(multiply(u,v),v),u),
file('GRP200-1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,right_inverse(u)),identity),
file('GRP200-1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(multiply(u,multiply(v,w)),u),multiply(multiply(u,v),multiply(w,u))),
file('GRP200-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(multiply(multiply(multiply(a,b),c),b),multiply(a,multiply(b,multiply(c,b)))),
file('GRP200-1.p',unknown),
[] ).
cnf(50,plain,
equal(left_division(right_division(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(55,plain,
equal(right_division(u,left_division(v,u)),v),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(87,plain,
equal(multiply(multiply(u,identity),multiply(v,u)),multiply(multiply(u,v),u)),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(97,plain,
equal(multiply(multiply(u,v),u),multiply(u,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[2,87]),
[iquote('0:Rew:2.0,87.0')] ).
cnf(98,plain,
equal(multiply(multiply(u,v),multiply(w,u)),multiply(u,multiply(multiply(v,w),u))),
inference(rew,[status(thm),theory(equality)],[97,9]),
[iquote('0:Rew:97.0,9.0')] ).
cnf(133,plain,
equal(right_division(multiply(u,multiply(v,u)),u),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[97,6]),
[iquote('0:SpR:97.0,6.0')] ).
cnf(134,plain,
equal(left_division(multiply(u,v),multiply(u,multiply(v,u))),u),
inference(spr,[status(thm),theory(equality)],[97,4]),
[iquote('0:SpR:97.0,4.0')] ).
cnf(140,plain,
equal(multiply(u,multiply(left_division(u,v),u)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[3,97]),
[iquote('0:SpR:3.0,97.0')] ).
cnf(179,plain,
equal(multiply(multiply(multiply(u,v),w),multiply(v,multiply(multiply(x,u),v))),multiply(multiply(u,v),multiply(multiply(w,multiply(v,x)),multiply(u,v)))),
inference(spr,[status(thm),theory(equality)],[98]),
[iquote('0:SpR:98.0,98.0')] ).
cnf(189,plain,
equal(multiply(right_inverse(u),multiply(multiply(v,u),right_inverse(u))),multiply(multiply(right_inverse(u),v),identity)),
inference(spr,[status(thm),theory(equality)],[7,98]),
[iquote('0:SpR:7.0,98.0')] ).
cnf(191,plain,
equal(multiply(u,multiply(multiply(v,right_division(w,u)),u)),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[5,98]),
[iquote('0:SpR:5.0,98.0')] ).
cnf(196,plain,
equal(multiply(u,multiply(multiply(right_inverse(u),v),u)),multiply(identity,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[7,98]),
[iquote('0:SpR:7.0,98.0')] ).
cnf(197,plain,
equal(multiply(u,multiply(multiply(left_division(u,v),w),u)),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[3,98]),
[iquote('0:SpR:3.0,98.0')] ).
cnf(198,plain,
equal(multiply(right_division(u,v),multiply(multiply(v,w),right_division(u,v))),multiply(u,multiply(w,right_division(u,v)))),
inference(spr,[status(thm),theory(equality)],[5,98]),
[iquote('0:SpR:5.0,98.0')] ).
cnf(204,plain,
equal(multiply(u,multiply(multiply(right_inverse(u),v),u)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[1,196]),
[iquote('0:Rew:1.0,196.0')] ).
cnf(205,plain,
equal(multiply(right_inverse(u),multiply(multiply(v,u),right_inverse(u))),multiply(right_inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[2,189]),
[iquote('0:Rew:2.0,189.0')] ).
cnf(231,plain,
equal(right_division(multiply(u,v),u),multiply(u,right_division(v,u))),
inference(spr,[status(thm),theory(equality)],[5,133]),
[iquote('0:SpR:5.0,133.0')] ).
cnf(255,plain,
equal(left_division(multiply(u,right_division(v,u)),multiply(u,v)),u),
inference(spr,[status(thm),theory(equality)],[5,134]),
[iquote('0:SpR:5.0,134.0')] ).
cnf(282,plain,
equal(left_division(u,multiply(v,u)),multiply(left_division(u,v),u)),
inference(spr,[status(thm),theory(equality)],[140,4]),
[iquote('0:SpR:140.0,4.0')] ).
cnf(355,plain,
equal(multiply(u,right_division(multiply(multiply(right_inverse(u),v),u),u)),right_division(multiply(v,u),u)),
inference(spr,[status(thm),theory(equality)],[204,231]),
[iquote('0:SpR:204.0,231.0')] ).
cnf(379,plain,
equal(multiply(u,multiply(right_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,355]),
[iquote('0:Rew:6.0,355.0,6.0,355.0')] ).
cnf(391,plain,
equal(multiply(right_inverse(u),v),left_division(u,v)),
inference(spr,[status(thm),theory(equality)],[379,4]),
[iquote('0:SpR:379.0,4.0')] ).
cnf(405,plain,
equal(left_division(right_inverse(u),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[3,379]),
[iquote('0:SpR:3.0,379.0')] ).
cnf(413,plain,
equal(multiply(right_inverse(u),multiply(multiply(v,u),right_inverse(u))),left_division(u,v)),
inference(rew,[status(thm),theory(equality)],[391,205]),
[iquote('0:Rew:391.0,205.0')] ).
cnf(427,plain,
equal(left_division(u,multiply(multiply(v,u),right_inverse(u))),left_division(u,v)),
inference(rew,[status(thm),theory(equality)],[391,413]),
[iquote('0:Rew:391.0,413.0')] ).
cnf(440,plain,
equal(right_division(left_division(u,v),v),right_inverse(u)),
inference(spr,[status(thm),theory(equality)],[391,6]),
[iquote('0:SpR:391.0,6.0')] ).
cnf(442,plain,
equal(multiply(right_inverse(u),multiply(v,right_inverse(u))),multiply(left_division(u,v),right_inverse(u))),
inference(spr,[status(thm),theory(equality)],[391,97]),
[iquote('0:SpR:391.0,97.0')] ).
cnf(456,plain,
equal(left_division(u,multiply(v,right_inverse(u))),multiply(left_division(u,v),right_inverse(u))),
inference(rew,[status(thm),theory(equality)],[391,442]),
[iquote('0:Rew:391.0,442.0')] ).
cnf(457,plain,
equal(multiply(left_division(u,multiply(v,u)),right_inverse(u)),left_division(u,v)),
inference(rew,[status(thm),theory(equality)],[456,427]),
[iquote('0:Rew:456.0,427.0')] ).
cnf(458,plain,
equal(multiply(multiply(left_division(u,v),u),right_inverse(u)),left_division(u,v)),
inference(rew,[status(thm),theory(equality)],[282,457]),
[iquote('0:Rew:282.0,457.0')] ).
cnf(475,plain,
equal(right_division(u,multiply(v,u)),right_inverse(v)),
inference(spr,[status(thm),theory(equality)],[405,55]),
[iquote('0:SpR:405.0,55.0')] ).
cnf(515,plain,
equal(multiply(multiply(u,v),right_inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[4,458]),
[iquote('0:SpR:4.0,458.0')] ).
cnf(550,plain,
equal(right_inverse(right_division(u,v)),right_division(v,u)),
inference(spr,[status(thm),theory(equality)],[50,440]),
[iquote('0:SpR:50.0,440.0')] ).
cnf(586,plain,
equal(right_division(u,right_inverse(v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[515,6]),
[iquote('0:SpR:515.0,6.0')] ).
cnf(601,plain,
equal(multiply(u,right_inverse(v)),right_division(u,v)),
inference(spr,[status(thm),theory(equality)],[5,515]),
[iquote('0:SpR:5.0,515.0')] ).
cnf(694,plain,
equal(left_division(right_division(u,v),w),multiply(right_division(v,u),w)),
inference(spr,[status(thm),theory(equality)],[550,391]),
[iquote('0:SpR:550.0,391.0')] ).
cnf(721,plain,
equal(right_division(u,right_division(v,w)),multiply(u,right_division(w,v))),
inference(spr,[status(thm),theory(equality)],[550,586]),
[iquote('0:SpR:550.0,586.0')] ).
cnf(963,plain,
equal(multiply(multiply(u,v),multiply(multiply(w,right_inverse(u)),multiply(u,v))),multiply(multiply(multiply(u,v),w),v)),
inference(spr,[status(thm),theory(equality)],[475,191]),
[iquote('0:SpR:475.0,191.0')] ).
cnf(969,plain,
equal(multiply(multiply(u,right_division(v,right_division(w,u))),w),multiply(u,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,191]),
[iquote('0:SpR:5.0,191.0')] ).
cnf(981,plain,
equal(multiply(multiply(u,multiply(v,right_division(u,w))),w),multiply(u,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[721,969]),
[iquote('0:Rew:721.0,969.0')] ).
cnf(997,plain,
equal(multiply(multiply(u,v),multiply(right_division(w,u),multiply(u,v))),multiply(multiply(multiply(u,v),w),v)),
inference(rew,[status(thm),theory(equality)],[601,963]),
[iquote('0:Rew:601.0,963.0')] ).
cnf(1216,plain,
equal(multiply(multiply(u,right_division(v,u)),multiply(multiply(u,w),multiply(u,right_division(v,u)))),multiply(multiply(u,v),multiply(w,multiply(u,right_division(v,u))))),
inference(spr,[status(thm),theory(equality)],[255,197]),
[iquote('0:SpR:255.0,197.0')] ).
cnf(1360,plain,
equal(multiply(right_division(u,v),multiply(right_division(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[694,4]),
[iquote('0:SpR:694.0,4.0')] ).
cnf(1666,plain,
equal(multiply(multiply(u,right_division(v,w)),right_division(w,v)),u),
inference(spr,[status(thm),theory(equality)],[721,6]),
[iquote('0:SpR:721.0,6.0')] ).
cnf(1866,plain,
equal(multiply(right_division(u,v),multiply(w,right_division(u,v))),multiply(u,multiply(left_division(v,w),right_division(u,v)))),
inference(spr,[status(thm),theory(equality)],[3,198]),
[iquote('0:SpR:3.0,198.0')] ).
cnf(3218,plain,
equal(multiply(multiply(u,right_division(v,w)),multiply(multiply(right_division(w,v),multiply(right_division(v,w),x)),multiply(u,right_division(v,w)))),multiply(u,multiply(right_division(v,w),multiply(multiply(x,u),right_division(v,w))))),
inference(spr,[status(thm),theory(equality)],[1666,179]),
[iquote('0:SpR:1666.0,179.0')] ).
cnf(3310,plain,
equal(multiply(multiply(u,right_division(v,w)),multiply(x,multiply(u,right_division(v,w)))),multiply(u,multiply(right_division(v,w),multiply(multiply(x,u),right_division(v,w))))),
inference(rew,[status(thm),theory(equality)],[1360,3218]),
[iquote('0:Rew:1360.0,3218.0')] ).
cnf(3311,plain,
equal(multiply(multiply(u,right_division(v,w)),multiply(x,multiply(u,right_division(v,w)))),multiply(u,multiply(v,multiply(left_division(w,multiply(x,u)),right_division(v,w))))),
inference(rew,[status(thm),theory(equality)],[1866,3310]),
[iquote('0:Rew:1866.0,3310.0')] ).
cnf(3324,plain,
equal(multiply(u,multiply(v,multiply(left_division(u,multiply(multiply(u,w),u)),right_division(v,u)))),multiply(multiply(u,v),multiply(w,multiply(u,right_division(v,u))))),
inference(rew,[status(thm),theory(equality)],[3311,1216]),
[iquote('0:Rew:3311.0,1216.0')] ).
cnf(3330,plain,
equal(multiply(multiply(u,v),multiply(w,multiply(u,right_division(v,u)))),multiply(u,multiply(v,multiply(multiply(w,u),right_division(v,u))))),
inference(rew,[status(thm),theory(equality)],[4,3324,97]),
[iquote('0:Rew:4.0,3324.0,97.0,3324.0')] ).
cnf(6214,plain,
equal(multiply(multiply(multiply(u,v),multiply(w,multiply(u,right_division(v,u)))),u),multiply(multiply(u,v),multiply(w,multiply(u,v)))),
inference(spr,[status(thm),theory(equality)],[231,981]),
[iquote('0:SpR:231.0,981.0')] ).
cnf(6305,plain,
equal(multiply(multiply(u,multiply(v,multiply(multiply(w,u),right_division(v,u)))),u),multiply(multiply(u,v),multiply(w,multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[3330,6214]),
[iquote('0:Rew:3330.0,6214.0')] ).
cnf(6306,plain,
equal(multiply(multiply(u,v),multiply(w,multiply(u,v))),multiply(u,multiply(v,multiply(multiply(w,u),v)))),
inference(rew,[status(thm),theory(equality)],[981,6305,97]),
[iquote('0:Rew:981.0,6305.0,97.0,6305.0')] ).
cnf(6432,plain,
equal(multiply(u,multiply(v,multiply(multiply(right_division(w,u),u),v))),multiply(multiply(multiply(u,v),w),v)),
inference(rew,[status(thm),theory(equality)],[6306,997]),
[iquote('0:Rew:6306.0,997.0')] ).
cnf(6442,plain,
equal(multiply(multiply(multiply(u,v),w),v),multiply(u,multiply(v,multiply(w,v)))),
inference(rew,[status(thm),theory(equality)],[5,6432]),
[iquote('0:Rew:5.0,6432.0')] ).
cnf(6443,plain,
$false,
inference(unc,[status(thm)],[6442,10]),
[iquote('0:UnC:6442.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Tue Jun 14 06:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.47/2.71
% 2.47/2.71 SPASS V 3.9
% 2.47/2.71 SPASS beiseite: Proof found.
% 2.47/2.71 % SZS status Theorem
% 2.47/2.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.47/2.71 SPASS derived 3444 clauses, backtracked 0 clauses, performed 0 splits and kept 1254 clauses.
% 2.47/2.71 SPASS allocated 75841 KBytes.
% 2.47/2.71 SPASS spent 0:00:02.37 on the problem.
% 2.47/2.71 0:00:00.03 for the input.
% 2.47/2.71 0:00:00.00 for the FLOTTER CNF translation.
% 2.47/2.71 0:00:00.03 for inferences.
% 2.47/2.71 0:00:00.00 for the backtracking.
% 2.47/2.71 0:00:02.29 for the reduction.
% 2.47/2.71
% 2.47/2.71
% 2.47/2.71 Here is a proof with depth 10, length 65 :
% 2.47/2.71 % SZS output start Refutation
% See solution above
% 2.55/2.77 Formulae used in the proof : left_identity right_identity multiply_left_division left_division_multiply multiply_right_division right_division_multiply right_inverse moufang1 prove_moufang2
% 2.55/2.77
%------------------------------------------------------------------------------