TSTP Solution File: GRP039-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:44:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 25 unt; 7 nHn; 42 RR)
% Number of literals : 67 ( 0 equ; 21 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('GRP039-2.p',unknown),
[] ).
cnf(3,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(v,u)) ),
file('GRP039-2.p',unknown),
[] ).
cnf(4,axiom,
( subgroup_member(u)
| subgroup_member(v)
| equal(multiply(v,element_in_O2(v,u)),u) ),
file('GRP039-2.p',unknown),
[] ).
cnf(5,axiom,
subgroup_member(b),
file('GRP039-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(b,inverse(a)),c),
file('GRP039-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(a,c),d),
file('GRP039-2.p',unknown),
[] ).
cnf(8,axiom,
~ subgroup_member(d),
file('GRP039-2.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(identity,u),u),
file('GRP039-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP039-2.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP039-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ equal(multiply(v,u),w)
| subgroup_member(w) ),
file('GRP039-2.p',unknown),
[] ).
cnf(19,plain,
( subgroup_member(u)
| equal(multiply(u,element_in_O2(u,d)),d) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.1,8.0')] ).
cnf(20,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(u,d)) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.1,8.0')] ).
cnf(22,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[7,13]),
[iquote('0:Res:7.0,13.2')] ).
cnf(23,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.0,13.2')] ).
cnf(24,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[22,8]),
[iquote('0:MRR:22.2,8.0')] ).
cnf(25,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(mrr,[status(thm)],[23,5]),
[iquote('0:MRR:23.0,5.0')] ).
cnf(42,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[25,12]),
[iquote('0:SoR:25.0,12.1')] ).
cnf(44,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[42,24]),
[iquote('0:MRR:42.1,24.0')] ).
cnf(62,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[10,11]),
[iquote('0:SpR:10.0,11.0')] ).
cnf(64,plain,
equal(multiply(b,multiply(inverse(a),u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[6,11]),
[iquote('0:SpR:6.0,11.0')] ).
cnf(69,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[9,62]),
[iquote('0:Rew:9.0,62.0')] ).
cnf(78,plain,
equal(multiply(inverse(a),d),c),
inference(spr,[status(thm),theory(equality)],[7,69]),
[iquote('0:SpR:7.0,69.0')] ).
cnf(103,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[13]),
[iquote('0:EqR:13.2')] ).
cnf(259,plain,
equal(multiply(c,a),multiply(b,identity)),
inference(spr,[status(thm),theory(equality)],[10,64]),
[iquote('0:SpR:10.0,64.0')] ).
cnf(265,plain,
equal(multiply(c,multiply(a,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[69,64]),
[iquote('0:SpR:69.0,64.0')] ).
cnf(266,plain,
equal(multiply(c,d),multiply(b,c)),
inference(spr,[status(thm),theory(equality)],[78,64]),
[iquote('0:SpR:78.0,64.0')] ).
cnf(269,plain,
equal(multiply(c,a),b),
inference(rew,[status(thm),theory(equality)],[1,259]),
[iquote('0:Rew:1.0,259.0')] ).
cnf(279,plain,
equal(multiply(inverse(c),b),a),
inference(spr,[status(thm),theory(equality)],[269,69]),
[iquote('0:SpR:269.0,69.0')] ).
cnf(459,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(spr,[status(thm),theory(equality)],[279,103]),
[iquote('0:SpR:279.0,103.2')] ).
cnf(464,plain,
( ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(ssi,[status(thm)],[459,5]),
[iquote('0:SSi:459.0,5.0')] ).
cnf(465,plain,
~ subgroup_member(inverse(c)),
inference(mrr,[status(thm)],[464,44]),
[iquote('0:MRR:464.1,44.0')] ).
cnf(472,plain,
~ subgroup_member(c),
inference(sor,[status(thm)],[465,12]),
[iquote('0:SoR:465.0,12.1')] ).
cnf(784,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(c,d)) ),
inference(spr,[status(thm),theory(equality)],[19,265]),
[iquote('0:SpR:19.1,265.0')] ).
cnf(792,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(b,c)) ),
inference(rew,[status(thm),theory(equality)],[266,784]),
[iquote('0:Rew:266.0,784.1')] ).
cnf(793,plain,
equal(multiply(b,element_in_O2(a,d)),multiply(b,c)),
inference(mrr,[status(thm)],[792,44]),
[iquote('0:MRR:792.0,44.0')] ).
cnf(1022,plain,
equal(multiply(inverse(b),multiply(b,c)),element_in_O2(a,d)),
inference(spr,[status(thm),theory(equality)],[793,69]),
[iquote('0:SpR:793.0,69.0')] ).
cnf(1031,plain,
equal(element_in_O2(a,d),c),
inference(rew,[status(thm),theory(equality)],[69,1022]),
[iquote('0:Rew:69.0,1022.0')] ).
cnf(1039,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(spr,[status(thm),theory(equality)],[1031,20]),
[iquote('0:SpR:1031.0,20.1')] ).
cnf(1053,plain,
subgroup_member(c),
inference(mrr,[status(thm)],[1039,44]),
[iquote('0:MRR:1039.0,44.0')] ).
cnf(1054,plain,
$false,
inference(mrr,[status(thm)],[1053,472]),
[iquote('0:MRR:1053.0,472.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n023.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 : Tue Jun 14 09:21:50 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 788 clauses, backtracked 86 clauses, performed 1 splits and kept 361 clauses.
% 0.20/0.53 SPASS allocated 76547 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.53 0:00:00.04 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.08 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 5, length 42 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : right_identity 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
% 0.20/0.53
%------------------------------------------------------------------------------