TSTP Solution File: GRP039-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.52s
% Output : Refutation 0.20s
% 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('GRP039-5.p',unknown),
[] ).
cnf(3,axiom,
subgroup_member(identity),
file('GRP039-5.p',unknown),
[] ).
cnf(4,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(v,u)) ),
file('GRP039-5.p',unknown),
[] ).
cnf(5,axiom,
( subgroup_member(u)
| subgroup_member(v)
| equal(multiply(v,element_in_O2(v,u)),u) ),
file('GRP039-5.p',unknown),
[] ).
cnf(6,axiom,
subgroup_member(b),
file('GRP039-5.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(b,inverse(a)),c),
file('GRP039-5.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(a,c),d),
file('GRP039-5.p',unknown),
[] ).
cnf(9,axiom,
~ subgroup_member(d),
file('GRP039-5.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(identity,u),u),
file('GRP039-5.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP039-5.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP039-5.p',unknown),
[] ).
cnf(13,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-5.p',unknown),
[] ).
cnf(14,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ equal(multiply(v,u),w)
| subgroup_member(w) ),
file('GRP039-5.p',unknown),
[] ).
cnf(20,plain,
( subgroup_member(u)
| equal(multiply(u,element_in_O2(u,d)),d) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.1,9.0')] ).
cnf(21,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(u,d)) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.1,9.0')] ).
cnf(23,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[8,14]),
[iquote('0:Res:8.0,14.2')] ).
cnf(24,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.0,14.2')] ).
cnf(25,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[23,9]),
[iquote('0:MRR:23.2,9.0')] ).
cnf(26,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(mrr,[status(thm)],[24,6]),
[iquote('0:MRR:24.0,6.0')] ).
cnf(43,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[26,13]),
[iquote('0:SoR:26.0,13.1')] ).
cnf(45,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[43,25]),
[iquote('0:MRR:43.1,25.0')] ).
cnf(64,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(66,plain,
equal(multiply(b,multiply(inverse(a),u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(71,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[10,64]),
[iquote('0:Rew:10.0,64.0')] ).
cnf(79,plain,
equal(multiply(inverse(a),d),c),
inference(spr,[status(thm),theory(equality)],[8,71]),
[iquote('0:SpR:8.0,71.0')] ).
cnf(98,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(identity)
| ~ equal(u,v)
| subgroup_member(v) ),
inference(spl,[status(thm),theory(equality)],[10,14]),
[iquote('0:SpL:10.0,14.2')] ).
cnf(106,plain,
( ~ subgroup_member(u)
| ~ equal(u,v)
| subgroup_member(v) ),
inference(ssi,[status(thm)],[98,3]),
[iquote('0:SSi:98.1,3.0')] ).
cnf(231,plain,
( ~ subgroup_member(u)
| ~ equal(u,a) ),
inference(sor,[status(thm)],[45,106]),
[iquote('0:SoR:45.0,106.2')] ).
cnf(257,plain,
equal(multiply(c,a),multiply(b,identity)),
inference(spr,[status(thm),theory(equality)],[11,66]),
[iquote('0:SpR:11.0,66.0')] ).
cnf(263,plain,
equal(multiply(c,multiply(a,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[71,66]),
[iquote('0:SpR:71.0,66.0')] ).
cnf(264,plain,
equal(multiply(c,d),multiply(b,c)),
inference(spr,[status(thm),theory(equality)],[79,66]),
[iquote('0:SpR:79.0,66.0')] ).
cnf(267,plain,
equal(multiply(c,a),b),
inference(rew,[status(thm),theory(equality)],[1,257]),
[iquote('0:Rew:1.0,257.0')] ).
cnf(277,plain,
equal(multiply(inverse(c),b),a),
inference(spr,[status(thm),theory(equality)],[267,71]),
[iquote('0:SpR:267.0,71.0')] ).
cnf(285,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| ~ equal(a,u)
| subgroup_member(u) ),
inference(spl,[status(thm),theory(equality)],[277,14]),
[iquote('0:SpL:277.0,14.2')] ).
cnf(287,plain,
( ~ subgroup_member(inverse(c))
| ~ equal(a,u)
| subgroup_member(u) ),
inference(ssi,[status(thm)],[285,6]),
[iquote('0:SSi:285.0,6.0')] ).
cnf(288,plain,
( ~ subgroup_member(inverse(c))
| ~ equal(a,u) ),
inference(mrr,[status(thm)],[287,231]),
[iquote('0:MRR:287.2,231.0')] ).
cnf(313,plain,
( ~ subgroup_member(c)
| ~ equal(a,u) ),
inference(sor,[status(thm)],[288,13]),
[iquote('0:SoR:288.0,13.1')] ).
cnf(316,plain,
~ subgroup_member(c),
inference(aed,[status(thm),theory(equality)],[313]),
[iquote('0:AED:313.1')] ).
cnf(775,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(c,d)) ),
inference(spr,[status(thm),theory(equality)],[20,263]),
[iquote('0:SpR:20.1,263.0')] ).
cnf(783,plain,
( subgroup_member(a)
| equal(multiply(b,element_in_O2(a,d)),multiply(b,c)) ),
inference(rew,[status(thm),theory(equality)],[264,775]),
[iquote('0:Rew:264.0,775.1')] ).
cnf(784,plain,
equal(multiply(b,element_in_O2(a,d)),multiply(b,c)),
inference(mrr,[status(thm)],[783,45]),
[iquote('0:MRR:783.0,45.0')] ).
cnf(1002,plain,
equal(multiply(inverse(b),multiply(b,c)),element_in_O2(a,d)),
inference(spr,[status(thm),theory(equality)],[784,71]),
[iquote('0:SpR:784.0,71.0')] ).
cnf(1010,plain,
equal(element_in_O2(a,d),c),
inference(rew,[status(thm),theory(equality)],[71,1002]),
[iquote('0:Rew:71.0,1002.0')] ).
cnf(1018,plain,
( subgroup_member(a)
| subgroup_member(c) ),
inference(spr,[status(thm),theory(equality)],[1010,21]),
[iquote('0:SpR:1010.0,21.1')] ).
cnf(1024,plain,
$false,
inference(mrr,[status(thm)],[1018,45,316]),
[iquote('0:MRR:1018.0,1018.1,45.0,316.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : GRP039-5 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n025.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 : Mon Jun 13 22:43:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 764 clauses, backtracked 0 clauses, performed 0 splits and kept 324 clauses.
% 0.20/0.52 SPASS allocated 76502 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.52 0:00:00.04 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.08 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 5, length 45 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 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
% 0.20/0.52
%------------------------------------------------------------------------------