TSTP Solution File: GRP431-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 11:47:26 EDT 2022
% Result : Unsatisfiable 3.07s 3.27s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 65 RR)
% Number of literals : 65 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),u)))),x),
file('GRP431-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP431-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,z)))))),inverse(multiply(z,w))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(x)),u)))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,x))),multiply(y,inverse(y))),multiply(w,u)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(15,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(w)),multiply(x,inverse(x))),multiply(y,u)))),inverse(multiply(z,multiply(multiply(multiply(x1,inverse(x1)),inverse(multiply(w,z))),y)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(16,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(x,u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,x))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(29,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,multiply(w,inverse(multiply(multiply(x,multiply(y,inverse(y))),multiply(v,w))))))),x),
inference(spr,[status(thm),theory(equality)],[16,1]),
[iquote('0:SpR:16.0,1.0')] ).
cnf(30,plain,
equal(multiply(u,inverse(multiply(multiply(v,inverse(multiply(multiply(w,multiply(x,inverse(x))),multiply(y,v)))),multiply(w,u)))),y),
inference(spr,[status(thm),theory(equality)],[16,5]),
[iquote('0:SpR:16.0,5.0')] ).
cnf(107,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,multiply(w,multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[1,30]),
[iquote('0:SpR:1.0,30.0')] ).
cnf(111,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(multiply(w,multiply(x,inverse(x))),multiply(u,v)))))),inverse(multiply(inverse(y),w))),y),
inference(spr,[status(thm),theory(equality)],[29,1]),
[iquote('0:SpR:29.0,1.0')] ).
cnf(113,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(multiply(w,multiply(x,inverse(x))),multiply(u,v)))))),inverse(multiply(inverse(multiply(y,multiply(multiply(multiply(z,inverse(z)),inverse(multiply(multiply(x1,inverse(x1)),y))),x2))),w))),x2),
inference(spr,[status(thm),theory(equality)],[29,4]),
[iquote('0:SpR:29.0,4.0')] ).
cnf(139,plain,
equal(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(multiply(w,inverse(w)),u))),x)),x),
inference(rew,[status(thm),theory(equality)],[111,113]),
[iquote('0:Rew:111.0,113.0')] ).
cnf(141,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(multiply(x1,inverse(x1)),multiply(multiply(x2,inverse(x2)),inverse(multiply(y,v)))))),w)),
inference(spr,[status(thm),theory(equality)],[139,4]),
[iquote('0:SpR:139.0,4.0')] ).
cnf(154,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[139,1]),
[iquote('0:SpR:139.0,1.0')] ).
cnf(162,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(w)),multiply(x,inverse(x))),multiply(y,u)))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(multiply(x1,inverse(x1)),y))),w)),
inference(spr,[status(thm),theory(equality)],[139,5]),
[iquote('0:SpR:139.0,5.0')] ).
cnf(177,plain,
equal(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(multiply(y,inverse(y)),z)))))),multiply(z,w)),
inference(spr,[status(thm),theory(equality)],[1,139]),
[iquote('0:SpR:1.0,139.0')] ).
cnf(197,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(multiply(w,inverse(w)),u)))),v),
inference(spr,[status(thm),theory(equality)],[154,1]),
[iquote('0:SpR:154.0,1.0')] ).
cnf(199,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(x,u)))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[154,5]),
[iquote('0:SpR:154.0,5.0')] ).
cnf(201,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),w),
inference(spr,[status(thm),theory(equality)],[154,139]),
[iquote('0:SpR:154.0,139.0')] ).
cnf(227,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(x,inverse(x))))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,u))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[154,16]),
[iquote('0:SpR:154.0,16.0')] ).
cnf(328,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),multiply(multiply(z,inverse(z)),multiply(multiply(x1,inverse(x1)),inverse(multiply(y,v))))))),
inference(spr,[status(thm),theory(equality)],[197,4]),
[iquote('0:SpR:197.0,4.0')] ).
cnf(364,plain,
equal(multiply(inverse(multiply(u,inverse(u))),inverse(multiply(inverse(v),multiply(w,inverse(w))))),v),
inference(spr,[status(thm),theory(equality)],[154,197]),
[iquote('0:SpR:154.0,197.0')] ).
cnf(400,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(v,inverse(v))),inverse(multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[154,201]),
[iquote('0:SpR:154.0,201.0')] ).
cnf(428,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[400,201]),
[iquote('0:SpR:400.0,201.0')] ).
cnf(663,plain,
equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[428,154]),
[iquote('0:SpR:428.0,154.0')] ).
cnf(926,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(multiply(y,inverse(y)),inverse(multiply(z,inverse(z))))))))),inverse(multiply(inverse(x1),w))),x1),
inference(spr,[status(thm),theory(equality)],[663,3]),
[iquote('0:SpR:663.0,3.0')] ).
cnf(1023,plain,
equal(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(multiply(inverse(w),v))),w),
inference(rew,[status(thm),theory(equality)],[177,926]),
[iquote('0:Rew:177.0,926.0')] ).
cnf(1040,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,u)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[1023,1]),
[iquote('0:SpR:1023.0,1.0')] ).
cnf(1099,plain,
equal(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(multiply(v,w))),inverse(x)),multiply(y,multiply(multiply(multiply(z,inverse(z)),inverse(multiply(w,y))),multiply(multiply(x1,inverse(x1)),inverse(multiply(x,v)))))),
inference(spr,[status(thm),theory(equality)],[3,1023]),
[iquote('0:SpR:3.0,1023.0')] ).
cnf(1101,plain,
equal(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v))),inverse(multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[154,1023]),
[iquote('0:SpR:154.0,1023.0')] ).
cnf(1130,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(u),multiply(w,inverse(w))))))),v),
inference(spr,[status(thm),theory(equality)],[364,1023]),
[iquote('0:SpR:364.0,1023.0')] ).
cnf(1179,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(multiply(w,multiply(multiply(multiply(x,inverse(x)),inverse(multiply(y,w))),v)))))),multiply(multiply(z,inverse(z)),inverse(y))),
inference(spr,[status(thm),theory(equality)],[15,29]),
[iquote('0:SpR:15.0,29.0')] ).
cnf(1386,plain,
equal(multiply(multiply(u,inverse(u)),inverse(v)),multiply(multiply(w,inverse(w)),inverse(v))),
inference(rew,[status(thm),theory(equality)],[1,1179]),
[iquote('0:Rew:1.0,1179.0')] ).
cnf(1569,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(x),u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(multiply(z,inverse(z)),inverse(x)))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[1386,16]),
[iquote('0:SpR:1386.0,16.0')] ).
cnf(1619,plain,
equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(multiply(v,inverse(v)),inverse(w)))),multiply(x,inverse(x))),inverse(inverse(w))),
inference(rew,[status(thm),theory(equality)],[199,1569]),
[iquote('0:Rew:199.0,1569.0')] ).
cnf(1637,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(inverse(inverse(multiply(w,inverse(w)))),multiply(u,inverse(multiply(x,inverse(x))))))))),v),
inference(spr,[status(thm),theory(equality)],[1040,1023]),
[iquote('0:SpR:1040.0,1023.0')] ).
cnf(1795,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(w)))),multiply(w,inverse(v))),
inference(spr,[status(thm),theory(equality)],[1,1130]),
[iquote('0:SpR:1.0,1130.0')] ).
cnf(1798,plain,
equal(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v))),v),
inference(spr,[status(thm),theory(equality)],[1040,1130]),
[iquote('0:SpR:1040.0,1130.0')] ).
cnf(1801,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[1798,1101]),
[iquote('0:Rew:1798.0,1101.0')] ).
cnf(1904,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(inverse(inverse(multiply(w,inverse(w)))),u))))),v),
inference(rew,[status(thm),theory(equality)],[1801,1637]),
[iquote('0:Rew:1801.0,1637.0')] ).
cnf(1957,plain,
equal(multiply(multiply(u,inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[1795,1619]),
[iquote('0:Rew:1795.0,1619.0')] ).
cnf(1989,plain,
equal(multiply(u,multiply(v,inverse(v))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[1801,1957]),
[iquote('0:Rew:1801.0,1957.0')] ).
cnf(1999,plain,
equal(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(inverse(inverse(v))))),v),
inference(rew,[status(thm),theory(equality)],[1989,364]),
[iquote('0:Rew:1989.0,364.0')] ).
cnf(2177,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(inverse(v)),multiply(w,inverse(w))))),multiply(multiply(multiply(x,inverse(x)),inverse(multiply(v,u))),multiply(y,inverse(y)))),
inference(rew,[status(thm),theory(equality)],[1989,227]),
[iquote('0:Rew:1989.0,227.0')] ).
cnf(2319,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,inverse(inverse(w)))))),
inference(rew,[status(thm),theory(equality)],[1989,107]),
[iquote('0:Rew:1989.0,107.0')] ).
cnf(2470,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(multiply(v,inverse(v)),inverse(w)))),multiply(x,u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(multiply(z,inverse(z)),x))),w)),
inference(rew,[status(thm),theory(equality)],[1989,162]),
[iquote('0:Rew:1989.0,162.0')] ).
cnf(2505,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1798,1999]),
[iquote('0:Rew:1798.0,1999.0')] ).
cnf(2511,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[2505,1989]),
[iquote('0:Rew:2505.0,1989.0')] ).
cnf(2517,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),v),
inference(rew,[status(thm),theory(equality)],[2505,1798]),
[iquote('0:Rew:2505.0,1798.0')] ).
cnf(2541,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[2517,201]),
[iquote('0:Rew:2517.0,201.0')] ).
cnf(2544,plain,
equal(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,z))))),multiply(inverse(multiply(z,w)),inverse(y))),
inference(rew,[status(thm),theory(equality)],[2517,1099]),
[iquote('0:Rew:2517.0,1099.0')] ).
cnf(2563,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(multiply(x1,inverse(x1)),inverse(multiply(y,v))))),w)),
inference(rew,[status(thm),theory(equality)],[2541,141]),
[iquote('0:Rew:2541.0,141.0')] ).
cnf(2572,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),multiply(multiply(z,inverse(z)),inverse(multiply(y,v)))))),
inference(rew,[status(thm),theory(equality)],[2541,328]),
[iquote('0:Rew:2541.0,328.0')] ).
cnf(2587,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[2541,1795]),
[iquote('0:Rew:2541.0,1795.0')] ).
cnf(2633,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[2505,1904,2587,2541]),
[iquote('0:Rew:2505.0,1904.0,2587.0,1904.0,2541.0,1904.0,2587.0,1904.0,2587.0,1904.0')] ).
cnf(2667,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),inverse(multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2541,2319,2505]),
[iquote('0:Rew:2541.0,2319.0,2505.0,2319.0')] ).
cnf(2814,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[2511,2177,2505,2541]),
[iquote('0:Rew:2511.0,2177.0,2505.0,2177.0,2511.0,2177.0,2541.0,2177.0')] ).
cnf(2885,plain,
equal(inverse(multiply(multiply(u,v),w)),inverse(multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[2667,2544,2814,2541]),
[iquote('0:Rew:2667.0,2544.0,2814.0,2544.0,2541.0,2544.0,2541.0,2544.0,2814.0,2544.0')] ).
cnf(2939,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[2667,2470,2505,2541]),
[iquote('0:Rew:2667.0,2470.0,2505.0,2470.0,2541.0,2470.0,2541.0,2470.0,2541.0,2470.0')] ).
cnf(2961,plain,
equal(multiply(u,multiply(multiply(inverse(u),v),multiply(w,x))),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[2939,2572,2541,2505,2885,2814]),
[iquote('0:Rew:2939.0,2572.0,2939.0,2572.0,2541.0,2572.0,2505.0,2572.0,2885.0,2572.0,2814.0,2572.0,2541.0,2572.0')] ).
cnf(3074,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2961,2563,2939,2541,2505]),
[iquote('0:Rew:2961.0,2563.0,2939.0,2563.0,2939.0,2563.0,2541.0,2563.0,2541.0,2563.0,2505.0,2563.0,2541.0,2563.0')] ).
cnf(3075,plain,
~ equal(multiply(inverse(b2),multiply(b2,a2)),a2),
inference(rew,[status(thm),theory(equality)],[3074,2]),
[iquote('0:Rew:3074.0,2.0')] ).
cnf(3092,plain,
~ equal(a2,a2),
inference(rew,[status(thm),theory(equality)],[2633,3075]),
[iquote('0:Rew:2633.0,3075.0')] ).
cnf(3093,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3092]),
[iquote('0:Obv:3092.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% 0.09/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 19:43:09 EDT 2022
% 0.15/0.37 % CPUTime :
% 3.07/3.27
% 3.07/3.27 SPASS V 3.9
% 3.07/3.27 SPASS beiseite: Proof found.
% 3.07/3.27 % SZS status Theorem
% 3.07/3.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.07/3.27 SPASS derived 2553 clauses, backtracked 0 clauses, performed 0 splits and kept 888 clauses.
% 3.07/3.27 SPASS allocated 73859 KBytes.
% 3.07/3.27 SPASS spent 0:00:02.89 on the problem.
% 3.07/3.27 0:00:00.04 for the input.
% 3.07/3.27 0:00:00.00 for the FLOTTER CNF translation.
% 3.07/3.27 0:00:00.03 for inferences.
% 3.07/3.27 0:00:00.00 for the backtracking.
% 3.07/3.27 0:00:02.81 for the reduction.
% 3.07/3.27
% 3.07/3.27
% 3.07/3.27 Here is a proof with depth 12, length 65 :
% 3.07/3.27 % SZS output start Refutation
% See solution above
% 3.15/3.34 Formulae used in the proof : single_axiom prove_these_axioms_2
% 3.15/3.34
%------------------------------------------------------------------------------