TSTP Solution File: GRP002-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 11:44:41 EDT 2022
% Result : Unsatisfiable 0.38s 0.55s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 72 RR)
% Number of literals : 72 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,identity),u),
file('GRP002-2.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(u,inverse(u)),identity),
file('GRP002-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,multiply(u,u)),identity),
file('GRP002-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(a,b),c),
file('GRP002-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(c,inverse(a)),d),
file('GRP002-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(d,inverse(b)),h),
file('GRP002-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(h,b),j),
file('GRP002-2.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(j,inverse(h)),k),
file('GRP002-2.p',unknown),
[] ).
cnf(9,axiom,
~ equal(multiply(k,inverse(b)),identity),
file('GRP002-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(identity,u),u),
file('GRP002-2.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP002-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP002-2.p',unknown),
[] ).
cnf(36,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,v)))),identity),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(41,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[11,12]),
[iquote('0:SpR:11.0,12.0')] ).
cnf(44,plain,
equal(multiply(j,multiply(inverse(h),u)),multiply(k,u)),
inference(spr,[status(thm),theory(equality)],[8,12]),
[iquote('0:SpR:8.0,12.0')] ).
cnf(45,plain,
equal(multiply(d,multiply(inverse(b),u)),multiply(h,u)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(46,plain,
equal(multiply(c,multiply(inverse(a),u)),multiply(d,u)),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(50,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[10,41]),
[iquote('0:Rew:10.0,41.0')] ).
cnf(59,plain,
equal(multiply(inverse(h),j),b),
inference(spr,[status(thm),theory(equality)],[7,50]),
[iquote('0:SpR:7.0,50.0')] ).
cnf(60,plain,
equal(multiply(inverse(a),c),b),
inference(spr,[status(thm),theory(equality)],[4,50]),
[iquote('0:SpR:4.0,50.0')] ).
cnf(62,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[11,50]),
[iquote('0:SpR:11.0,50.0')] ).
cnf(64,plain,
equal(multiply(inverse(u),identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[3,50]),
[iquote('0:SpR:3.0,50.0')] ).
cnf(66,plain,
equal(multiply(inverse(d),h),inverse(b)),
inference(spr,[status(thm),theory(equality)],[6,50]),
[iquote('0:SpR:6.0,50.0')] ).
cnf(72,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1,62]),
[iquote('0:Rew:1.0,62.0')] ).
cnf(74,plain,
equal(multiply(u,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1,64]),
[iquote('0:Rew:1.0,64.0')] ).
cnf(101,plain,
equal(multiply(inverse(h),multiply(j,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[59,12]),
[iquote('0:SpR:59.0,12.0')] ).
cnf(113,plain,
equal(multiply(u,multiply(u,v)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[74,12]),
[iquote('0:SpR:74.0,12.0')] ).
cnf(187,plain,
equal(multiply(k,j),multiply(j,b)),
inference(spr,[status(thm),theory(equality)],[59,44]),
[iquote('0:SpR:59.0,44.0')] ).
cnf(215,plain,
equal(multiply(h,b),multiply(d,identity)),
inference(spr,[status(thm),theory(equality)],[11,45]),
[iquote('0:SpR:11.0,45.0')] ).
cnf(220,plain,
equal(multiply(h,multiply(b,u)),multiply(d,u)),
inference(spr,[status(thm),theory(equality)],[50,45]),
[iquote('0:SpR:50.0,45.0')] ).
cnf(221,plain,
equal(j,d),
inference(rew,[status(thm),theory(equality)],[7,215,1]),
[iquote('0:Rew:7.0,215.0,1.0,215.0')] ).
cnf(233,plain,
equal(multiply(k,d),multiply(d,b)),
inference(rew,[status(thm),theory(equality)],[221,187]),
[iquote('0:Rew:221.0,187.0')] ).
cnf(234,plain,
equal(multiply(inverse(h),multiply(d,u)),multiply(b,u)),
inference(rew,[status(thm),theory(equality)],[221,101]),
[iquote('0:Rew:221.0,101.0')] ).
cnf(267,plain,
equal(multiply(d,c),multiply(c,b)),
inference(spr,[status(thm),theory(equality)],[60,46]),
[iquote('0:SpR:60.0,46.0')] ).
cnf(318,plain,
equal(multiply(multiply(c,b),u),multiply(d,multiply(c,u))),
inference(spr,[status(thm),theory(equality)],[267,12]),
[iquote('0:SpR:267.0,12.0')] ).
cnf(322,plain,
equal(multiply(d,multiply(c,u)),multiply(c,multiply(b,u))),
inference(rew,[status(thm),theory(equality)],[12,318]),
[iquote('0:Rew:12.0,318.0')] ).
cnf(333,plain,
equal(multiply(u,inverse(multiply(v,u))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[36,50]),
[iquote('0:SpR:36.0,50.0')] ).
cnf(410,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1,333]),
[iquote('0:Rew:1.0,333.0')] ).
cnf(499,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[410]),
[iquote('0:SpR:410.0,410.0')] ).
cnf(501,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[410,50]),
[iquote('0:SpR:410.0,50.0')] ).
cnf(578,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[72,499]),
[iquote('0:Rew:72.0,499.0')] ).
cnf(895,plain,
equal(multiply(inverse(h),inverse(d)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[74,234]),
[iquote('0:SpR:74.0,234.0')] ).
cnf(907,plain,
equal(inverse(multiply(d,h)),multiply(b,d)),
inference(rew,[status(thm),theory(equality)],[501,895]),
[iquote('0:Rew:501.0,895.0')] ).
cnf(940,plain,
equal(inverse(multiply(b,d)),multiply(d,h)),
inference(spr,[status(thm),theory(equality)],[907,72]),
[iquote('0:SpR:907.0,72.0')] ).
cnf(1239,plain,
equal(multiply(inverse(a),b),multiply(a,c)),
inference(spr,[status(thm),theory(equality)],[4,113]),
[iquote('0:SpR:4.0,113.0')] ).
cnf(1250,plain,
equal(multiply(inverse(c),inverse(a)),multiply(c,d)),
inference(spr,[status(thm),theory(equality)],[5,113]),
[iquote('0:SpR:5.0,113.0')] ).
cnf(1274,plain,
equal(multiply(inverse(multiply(u,v)),inverse(v)),multiply(inverse(inverse(multiply(u,v))),u)),
inference(spr,[status(thm),theory(equality)],[578,113]),
[iquote('0:SpR:578.0,113.0')] ).
cnf(1305,plain,
equal(inverse(multiply(a,c)),multiply(c,d)),
inference(rew,[status(thm),theory(equality)],[501,1250]),
[iquote('0:Rew:501.0,1250.0')] ).
cnf(1379,plain,
equal(inverse(multiply(u,multiply(v,u))),multiply(v,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[501,1274,12,72]),
[iquote('0:Rew:501.0,1274.0,12.0,1274.0,72.0,1274.0')] ).
cnf(1402,plain,
equal(multiply(b,inverse(multiply(a,c))),inverse(inverse(a))),
inference(spr,[status(thm),theory(equality)],[1239,410]),
[iquote('0:SpR:1239.0,410.0')] ).
cnf(1408,plain,
equal(multiply(c,multiply(a,c)),multiply(d,b)),
inference(spr,[status(thm),theory(equality)],[1239,46]),
[iquote('0:SpR:1239.0,46.0')] ).
cnf(1412,plain,
equal(multiply(b,inverse(multiply(a,c))),a),
inference(rew,[status(thm),theory(equality)],[72,1402]),
[iquote('0:Rew:72.0,1402.0')] ).
cnf(1413,plain,
equal(multiply(b,multiply(c,d)),a),
inference(rew,[status(thm),theory(equality)],[1305,1412]),
[iquote('0:Rew:1305.0,1412.0')] ).
cnf(1419,plain,
equal(multiply(d,multiply(c,d)),multiply(h,a)),
inference(spr,[status(thm),theory(equality)],[1413,220]),
[iquote('0:SpR:1413.0,220.0')] ).
cnf(1423,plain,
equal(multiply(inverse(a),b),inverse(multiply(c,d))),
inference(spr,[status(thm),theory(equality)],[1413,578]),
[iquote('0:SpR:1413.0,578.0')] ).
cnf(1427,plain,
equal(multiply(c,multiply(b,d)),multiply(h,a)),
inference(rew,[status(thm),theory(equality)],[322,1419]),
[iquote('0:Rew:322.0,1419.0')] ).
cnf(1429,plain,
equal(inverse(multiply(c,d)),multiply(a,c)),
inference(rew,[status(thm),theory(equality)],[1239,1423]),
[iquote('0:Rew:1239.0,1423.0')] ).
cnf(1641,plain,
equal(multiply(inverse(u),multiply(a,c)),inverse(multiply(multiply(c,d),u))),
inference(spr,[status(thm),theory(equality)],[1429,501]),
[iquote('0:SpR:1429.0,501.0')] ).
cnf(1653,plain,
equal(multiply(inverse(u),multiply(a,c)),inverse(multiply(c,multiply(d,u)))),
inference(rew,[status(thm),theory(equality)],[12,1641]),
[iquote('0:Rew:12.0,1641.0')] ).
cnf(1767,plain,
equal(multiply(inverse(c),multiply(a,c)),multiply(c,multiply(d,b))),
inference(spr,[status(thm),theory(equality)],[1408,113]),
[iquote('0:SpR:1408.0,113.0')] ).
cnf(1778,plain,
equal(multiply(c,multiply(d,b)),multiply(h,a)),
inference(rew,[status(thm),theory(equality)],[1427,1767,322,1379,1653]),
[iquote('0:Rew:1427.0,1767.0,322.0,1767.0,1379.0,1767.0,1653.0,1767.0')] ).
cnf(1783,plain,
equal(multiply(inverse(c),multiply(h,a)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[1427,50]),
[iquote('0:SpR:1427.0,50.0')] ).
cnf(1881,plain,
equal(multiply(inverse(c),multiply(h,a)),multiply(d,b)),
inference(spr,[status(thm),theory(equality)],[1778,50]),
[iquote('0:SpR:1778.0,50.0')] ).
cnf(1885,plain,
equal(multiply(d,b),multiply(b,d)),
inference(rew,[status(thm),theory(equality)],[1783,1881]),
[iquote('0:Rew:1783.0,1881.0')] ).
cnf(1886,plain,
equal(multiply(k,d),multiply(b,d)),
inference(rew,[status(thm),theory(equality)],[1885,233]),
[iquote('0:Rew:1885.0,233.0')] ).
cnf(1913,plain,
equal(multiply(d,inverse(multiply(b,d))),inverse(k)),
inference(spr,[status(thm),theory(equality)],[1886,410]),
[iquote('0:SpR:1886.0,410.0')] ).
cnf(1920,plain,
equal(inverse(k),inverse(b)),
inference(rew,[status(thm),theory(equality)],[66,1913,113,940]),
[iquote('0:Rew:66.0,1913.0,113.0,1913.0,940.0,1913.0')] ).
cnf(2010,plain,
equal(inverse(inverse(b)),k),
inference(spr,[status(thm),theory(equality)],[1920,72]),
[iquote('0:SpR:1920.0,72.0')] ).
cnf(2015,plain,
equal(k,b),
inference(rew,[status(thm),theory(equality)],[72,2010]),
[iquote('0:Rew:72.0,2010.0')] ).
cnf(2016,plain,
~ equal(multiply(b,inverse(b)),identity),
inference(rew,[status(thm),theory(equality)],[2015,9]),
[iquote('0:Rew:2015.0,9.0')] ).
cnf(2051,plain,
~ equal(identity,identity),
inference(rew,[status(thm),theory(equality)],[2,2016]),
[iquote('0:Rew:2.0,2016.0')] ).
cnf(2052,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2051]),
[iquote('0:Obv:2051.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 07:00:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.38/0.55
% 0.38/0.55 SPASS V 3.9
% 0.38/0.55 SPASS beiseite: Proof found.
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.55 SPASS derived 1157 clauses, backtracked 0 clauses, performed 0 splits and kept 323 clauses.
% 0.38/0.55 SPASS allocated 64698 KBytes.
% 0.38/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.38/0.55 0:00:00.03 for the input.
% 0.38/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.38/0.55 0:00:00.01 for inferences.
% 0.38/0.55 0:00:00.00 for the backtracking.
% 0.38/0.55 0:00:00.13 for the reduction.
% 0.38/0.55
% 0.38/0.55
% 0.38/0.55 Here is a proof with depth 7, length 72 :
% 0.38/0.55 % SZS output start Refutation
% See solution above
% 0.38/0.55 Formulae used in the proof : right_identity right_inverse x_cubed_is_identity a_times_b_is_c c_times_inverse_a_is_d d_times_inverse_b_is_h h_times_b_is_j j_times_inverse_h_is_k prove_k_times_inverse_b_is_e left_identity left_inverse associativity
% 0.38/0.55
%------------------------------------------------------------------------------