TSTP Solution File: GRP039-7 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:44:57 EDT 2022
% Result : Unsatisfiable 0.34s 0.53s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 45 ( 24 unt; 7 nHn; 45 RR)
% Number of literals : 78 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,identity),u),
file('GRP039-7.p',unknown),
[] ).
cnf(5,axiom,
subgroup_member(identity),
file('GRP039-7.p',unknown),
[] ).
cnf(6,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(v,u)) ),
file('GRP039-7.p',unknown),
[] ).
cnf(7,axiom,
( subgroup_member(u)
| subgroup_member(v)
| equal(multiply(v,element_in_O2(v,u)),u) ),
file('GRP039-7.p',unknown),
[] ).
cnf(8,axiom,
subgroup_member(b),
file('GRP039-7.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(b,inverse(a)),c),
file('GRP039-7.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(a,c),d),
file('GRP039-7.p',unknown),
[] ).
cnf(11,axiom,
~ subgroup_member(d),
file('GRP039-7.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(identity,u),u),
file('GRP039-7.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP039-7.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP039-7.p',unknown),
[] ).
cnf(15,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-7.p',unknown),
[] ).
cnf(16,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ equal(multiply(v,u),w)
| subgroup_member(w) ),
file('GRP039-7.p',unknown),
[] ).
cnf(22,plain,
( subgroup_member(u)
| equal(multiply(u,element_in_O2(u,d)),d) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.1,11.0')] ).
cnf(23,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(u,d)) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.1,11.0')] ).
cnf(25,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[10,16]),
[iquote('0:Res:10.0,16.2')] ).
cnf(26,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[9,16]),
[iquote('0:Res:9.0,16.2')] ).
cnf(27,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[25,11]),
[iquote('0:MRR:25.2,11.0')] ).
cnf(28,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(mrr,[status(thm)],[26,8]),
[iquote('0:MRR:26.0,8.0')] ).
cnf(56,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[28,15]),
[iquote('0:SoR:28.0,15.1')] ).
cnf(59,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[56,27]),
[iquote('0:MRR:56.1,27.0')] ).
cnf(83,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[13,14]),
[iquote('0:SpR:13.0,14.0')] ).
cnf(85,plain,
equal(multiply(b,multiply(inverse(a),u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[9,14]),
[iquote('0:SpR:9.0,14.0')] ).
cnf(91,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[12,83]),
[iquote('0:Rew:12.0,83.0')] ).
cnf(99,plain,
equal(multiply(inverse(a),d),c),
inference(spr,[status(thm),theory(equality)],[10,91]),
[iquote('0:SpR:10.0,91.0')] ).
cnf(133,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(identity)
| ~ equal(u,v)
| subgroup_member(v) ),
inference(spl,[status(thm),theory(equality)],[12,16]),
[iquote('0:SpL:12.0,16.2')] ).
cnf(141,plain,
( ~ subgroup_member(u)
| ~ equal(u,v)
| subgroup_member(v) ),
inference(ssi,[status(thm)],[133,5]),
[iquote('0:SSi:133.1,5.0')] ).
cnf(254,plain,
( ~ subgroup_member(u)
| ~ equal(u,a) ),
inference(sor,[status(thm)],[59,141]),
[iquote('0:SoR:59.0,141.2')] ).
cnf(276,plain,
equal(multiply(c,a),multiply(b,identity)),
inference(spr,[status(thm),theory(equality)],[13,85]),
[iquote('0:SpR:13.0,85.0')] ).
cnf(282,plain,
equal(multiply(c,multiply(a,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[91,85]),
[iquote('0:SpR:91.0,85.0')] ).
cnf(283,plain,
equal(multiply(c,d),multiply(b,c)),
inference(spr,[status(thm),theory(equality)],[99,85]),
[iquote('0:SpR:99.0,85.0')] ).
cnf(286,plain,
equal(multiply(c,a),b),
inference(rew,[status(thm),theory(equality)],[1,276]),
[iquote('0:Rew:1.0,276.0')] ).
cnf(296,plain,
equal(multiply(inverse(c),b),a),
inference(spr,[status(thm),theory(equality)],[286,91]),
[iquote('0:SpR:286.0,91.0')] ).
cnf(303,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| ~ equal(a,u)
| subgroup_member(u) ),
inference(spl,[status(thm),theory(equality)],[296,16]),
[iquote('0:SpL:296.0,16.2')] ).
cnf(306,plain,
( ~ subgroup_member(inverse(c))
| ~ equal(a,u)
| subgroup_member(u) ),
inference(ssi,[status(thm)],[303,8]),
[iquote('0:SSi:303.0,8.0')] ).
cnf(307,plain,
( ~ subgroup_member(inverse(c))
| ~ equal(a,u) ),
inference(mrr,[status(thm)],[306,254]),
[iquote('0:MRR:306.2,254.0')] ).
cnf(422,plain,
( ~ subgroup_member(c)
| ~ equal(a,u) ),
inference(sor,[status(thm)],[307,15]),
[iquote('0:SoR:307.0,15.1')] ).
cnf(425,plain,
~ subgroup_member(c),
inference(aed,[status(thm),theory(equality)],[422]),
[iquote('0:AED:422.1')] ).
cnf(805,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(c,d)) ),
inference(spr,[status(thm),theory(equality)],[22,282]),
[iquote('0:SpR:22.1,282.0')] ).
cnf(813,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(b,c)) ),
inference(rew,[status(thm),theory(equality)],[283,805]),
[iquote('0:Rew:283.0,805.1')] ).
cnf(814,plain,
equal(multiply(b,element_in_O2(a,d)),multiply(b,c)),
inference(mrr,[status(thm)],[813,59]),
[iquote('0:MRR:813.0,59.0')] ).
cnf(1048,plain,
equal(multiply(inverse(b),multiply(b,c)),element_in_O2(a,d)),
inference(spr,[status(thm),theory(equality)],[814,91]),
[iquote('0:SpR:814.0,91.0')] ).
cnf(1055,plain,
equal(element_in_O2(a,d),c),
inference(rew,[status(thm),theory(equality)],[91,1048]),
[iquote('0:Rew:91.0,1048.0')] ).
cnf(1060,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(spr,[status(thm),theory(equality)],[1055,23]),
[iquote('0:SpR:1055.0,23.1')] ).
cnf(1069,plain,
$false,
inference(mrr,[status(thm)],[1060,59,425]),
[iquote('0:MRR:1060.0,1060.1,59.0,425.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:39:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.34/0.53
% 0.34/0.53 SPASS V 3.9
% 0.34/0.53 SPASS beiseite: Proof found.
% 0.34/0.53 % SZS status Theorem
% 0.34/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/0.53 SPASS derived 801 clauses, backtracked 0 clauses, performed 0 splits and kept 332 clauses.
% 0.34/0.53 SPASS allocated 76521 KBytes.
% 0.34/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.34/0.53 0:00:00.04 for the input.
% 0.34/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.34/0.53 0:00:00.02 for inferences.
% 0.34/0.53 0:00:00.00 for the backtracking.
% 0.34/0.53 0:00:00.08 for the reduction.
% 0.34/0.53
% 0.34/0.53
% 0.34/0.53 Here is a proof with depth 5, length 45 :
% 0.34/0.53 % SZS output start Refutation
% See solution above
% 0.34/0.53 Formulae used in the proof : right_identity identity_in_O2 an_element_in_O2 property_of_O2 b_in_O2 b_times_a_inverse_is_c a_times_c_is_d prove_d_in_O2 left_identity left_inverse associativity closure_of_inverse closure_of_multiply
% 0.34/0.53
%------------------------------------------------------------------------------