TSTP Solution File: GRP039-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 0.49s 0.70s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of clauses : 68 ( 26 unt; 6 nHn; 68 RR)
% Number of literals : 133 ( 0 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subgroup_member(u)
| ~ equalish(u,v)
| subgroup_member(v) ),
file('GRP039-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ equalish(u,v)
| ~ product(w,x,u)
| product(w,x,v) ),
file('GRP039-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,u,w)
| subgroup_member(w) ),
file('GRP039-6.p',unknown),
[] ).
cnf(7,axiom,
product(identity,u,u),
file('GRP039-6.p',unknown),
[] ).
cnf(8,axiom,
product(u,identity,u),
file('GRP039-6.p',unknown),
[] ).
cnf(9,axiom,
product(inverse(u),u,identity),
file('GRP039-6.p',unknown),
[] ).
cnf(10,axiom,
product(u,inverse(u),identity),
file('GRP039-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP039-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP039-6.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP039-6.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(u,x,w)
| equalish(v,x) ),
file('GRP039-6.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ product(x,v,w)
| equalish(u,x) ),
file('GRP039-6.p',unknown),
[] ).
cnf(17,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(u,v)) ),
file('GRP039-6.p',unknown),
[] ).
cnf(18,axiom,
( subgroup_member(u)
| subgroup_member(v)
| product(u,element_in_O2(u,v),v) ),
file('GRP039-6.p',unknown),
[] ).
cnf(19,axiom,
subgroup_member(b),
file('GRP039-6.p',unknown),
[] ).
cnf(20,axiom,
product(b,inverse(a),c),
file('GRP039-6.p',unknown),
[] ).
cnf(21,axiom,
product(a,c,d),
file('GRP039-6.p',unknown),
[] ).
cnf(22,axiom,
~ subgroup_member(d),
file('GRP039-6.p',unknown),
[] ).
cnf(23,plain,
( ~ subgroup_member(u)
| ~ product(b,u,v)
| subgroup_member(v) ),
inference(res,[status(thm),theory(equality)],[19,6]),
[iquote('0:Res:19.0,6.0')] ).
cnf(25,plain,
subgroup_member(inverse(b)),
inference(res,[status(thm),theory(equality)],[19,5]),
[iquote('0:Res:19.0,5.0')] ).
cnf(30,plain,
( ~ subgroup_member(u)
| ~ equalish(u,d) ),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.2,22.0')] ).
cnf(31,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(u,d)) ),
inference(res,[status(thm),theory(equality)],[17,22]),
[iquote('0:Res:17.1,22.0')] ).
cnf(32,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,u,d) ),
inference(res,[status(thm),theory(equality)],[6,22]),
[iquote('0:Res:6.3,22.0')] ).
cnf(36,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[21,6]),
[iquote('0:Res:21.0,6.2')] ).
cnf(37,plain,
( ~ product(a,c,u)
| equalish(d,u) ),
inference(res,[status(thm),theory(equality)],[21,13]),
[iquote('0:Res:21.0,13.0')] ).
cnf(38,plain,
( ~ product(a,u,d)
| equalish(u,c) ),
inference(res,[status(thm),theory(equality)],[21,15]),
[iquote('0:Res:21.0,15.0')] ).
cnf(46,plain,
( ~ product(u,d,v)
| ~ product(u,a,w)
| product(w,c,v) ),
inference(res,[status(thm),theory(equality)],[21,12]),
[iquote('0:Res:21.0,12.1')] ).
cnf(47,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[36,22]),
[iquote('0:MRR:36.2,22.0')] ).
cnf(68,plain,
equalish(d,d),
inference(res,[status(thm),theory(equality)],[21,37]),
[iquote('0:Res:21.0,37.0')] ).
cnf(70,plain,
~ subgroup_member(d),
inference(res,[status(thm),theory(equality)],[68,30]),
[iquote('0:Res:68.0,30.1')] ).
cnf(87,plain,
( subgroup_member(a)
| subgroup_member(d)
| equalish(element_in_O2(a,d),c) ),
inference(res,[status(thm),theory(equality)],[18,38]),
[iquote('0:Res:18.2,38.0')] ).
cnf(88,plain,
( subgroup_member(a)
| equalish(element_in_O2(a,d),c) ),
inference(mrr,[status(thm)],[87,70]),
[iquote('0:MRR:87.1,70.0')] ).
cnf(89,plain,
subgroup_member(a),
inference(spt,[spt(split,[position(s1)])],[88]),
[iquote('1:Spt:88.0')] ).
cnf(90,plain,
~ subgroup_member(c),
inference(mrr,[status(thm)],[47,89]),
[iquote('1:MRR:47.1,89.0')] ).
cnf(97,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[20,23]),
[iquote('0:Res:20.0,23.1')] ).
cnf(101,plain,
subgroup_member(c),
inference(ssi,[status(thm)],[97,5,89]),
[iquote('1:SSi:97.0,5.0,89.1')] ).
cnf(102,plain,
$false,
inference(mrr,[status(thm)],[101,90]),
[iquote('1:MRR:101.0,90.0')] ).
cnf(104,plain,
~ subgroup_member(a),
inference(spt,[spt(split,[position(sa)])],[102,89]),
[iquote('1:Spt:102.0,88.0,89.0')] ).
cnf(105,plain,
equalish(element_in_O2(a,d),c),
inference(spt,[spt(split,[position(s2)])],[88]),
[iquote('1:Spt:102.0,88.1')] ).
cnf(107,plain,
( ~ subgroup_member(element_in_O2(a,d))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[105,1]),
[iquote('1:Res:105.0,1.1')] ).
cnf(109,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[97,5]),
[iquote('0:SoR:97.0,5.1')] ).
cnf(110,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[109,47]),
[iquote('0:MRR:109.1,47.0')] ).
cnf(123,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(sor,[status(thm)],[107,31]),
[iquote('1:SoR:107.0,31.1')] ).
cnf(124,plain,
subgroup_member(c),
inference(mrr,[status(thm)],[123,110]),
[iquote('1:MRR:123.1,110.0')] ).
cnf(129,plain,
( ~ equalish(u,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[7,2]),
[iquote('0:Res:7.0,2.1')] ).
cnf(130,plain,
( ~ equalish(u,v)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.0,2.1')] ).
cnf(134,plain,
( ~ equalish(identity,u)
| product(inverse(v),v,u) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.0,2.1')] ).
cnf(153,plain,
( ~ product(u,identity,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[8,16]),
[iquote('0:Res:8.0,16.0')] ).
cnf(157,plain,
( ~ product(u,v,identity)
| equalish(inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[9,16]),
[iquote('0:Res:9.0,16.0')] ).
cnf(201,plain,
equalish(u,u),
inference(res,[status(thm),theory(equality)],[8,153]),
[iquote('0:Res:8.0,153.0')] ).
cnf(204,plain,
( ~ equalish(u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[130,153]),
[iquote('0:Res:130.1,153.0')] ).
cnf(251,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.0,11.0')] ).
cnf(354,plain,
equalish(inverse(inverse(u)),u),
inference(res,[status(thm),theory(equality)],[10,157]),
[iquote('0:Res:10.0,157.0')] ).
cnf(359,plain,
equalish(u,inverse(inverse(u))),
inference(res,[status(thm),theory(equality)],[354,204]),
[iquote('0:Res:354.0,204.0')] ).
cnf(568,plain,
( ~ product(identity,a,u)
| product(u,c,d) ),
inference(res,[status(thm),theory(equality)],[7,46]),
[iquote('0:Res:7.0,46.0')] ).
cnf(658,plain,
( ~ equalish(a,u)
| product(u,c,d) ),
inference(res,[status(thm),theory(equality)],[129,568]),
[iquote('0:Res:129.1,568.0')] ).
cnf(661,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(u)
| ~ equalish(a,u) ),
inference(res,[status(thm),theory(equality)],[658,32]),
[iquote('0:Res:658.1,32.2')] ).
cnf(684,plain,
( ~ subgroup_member(u)
| ~ equalish(a,u) ),
inference(ssi,[status(thm)],[661,124]),
[iquote('1:SSi:661.0,124.0')] ).
cnf(716,plain,
~ subgroup_member(inverse(inverse(a))),
inference(res,[status(thm),theory(equality)],[359,684]),
[iquote('1:Res:359.0,684.1')] ).
cnf(738,plain,
~ subgroup_member(inverse(a)),
inference(sor,[status(thm)],[716,5]),
[iquote('1:SoR:716.0,5.1')] ).
cnf(875,plain,
( ~ product(u,b,identity)
| product(u,c,inverse(a)) ),
inference(res,[status(thm),theory(equality)],[20,251]),
[iquote('0:Res:20.0,251.0')] ).
cnf(2074,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(u)
| ~ product(u,b,identity)
| subgroup_member(inverse(a)) ),
inference(res,[status(thm),theory(equality)],[875,6]),
[iquote('0:Res:875.1,6.2')] ).
cnf(2090,plain,
( ~ subgroup_member(u)
| ~ product(u,b,identity)
| subgroup_member(inverse(a)) ),
inference(ssi,[status(thm)],[2074,124]),
[iquote('1:SSi:2074.0,124.0')] ).
cnf(2091,plain,
( ~ subgroup_member(u)
| ~ product(u,b,identity) ),
inference(mrr,[status(thm)],[2090,738]),
[iquote('1:MRR:2090.2,738.0')] ).
cnf(2148,plain,
( ~ subgroup_member(inverse(b))
| ~ equalish(identity,identity) ),
inference(res,[status(thm),theory(equality)],[134,2091]),
[iquote('1:Res:134.1,2091.1')] ).
cnf(2154,plain,
~ equalish(identity,identity),
inference(ssi,[status(thm)],[2148,25]),
[iquote('1:SSi:2148.0,25.0')] ).
cnf(2155,plain,
$false,
inference(mrr,[status(thm)],[2154,201]),
[iquote('1:MRR:2154.0,201.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 : Tue Jun 14 07:51:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.70
% 0.49/0.70 SPASS V 3.9
% 0.49/0.70 SPASS beiseite: Proof found.
% 0.49/0.70 % SZS status Theorem
% 0.49/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.70 SPASS derived 1965 clauses, backtracked 7 clauses, performed 1 splits and kept 971 clauses.
% 0.49/0.70 SPASS allocated 76964 KBytes.
% 0.49/0.70 SPASS spent 0:00:00.35 on the problem.
% 0.49/0.70 0:00:00.03 for the input.
% 0.49/0.70 0:00:00.00 for the FLOTTER CNF translation.
% 0.49/0.70 0:00:00.02 for inferences.
% 0.49/0.70 0:00:00.00 for the backtracking.
% 0.49/0.70 0:00:00.26 for the reduction.
% 0.49/0.70
% 0.49/0.70
% 0.49/0.70 Here is a proof with depth 6, length 68 :
% 0.49/0.70 % SZS output start Refutation
% See solution above
% 0.49/0.70 Formulae used in the proof : subgroup_member_substitution product_substitution3 closure_of_inverse closure_of_product left_identity right_identity left_inverse right_inverse associativity1 associativity2 well_defined product_right_cancellation product_left_cancellation an_element_in_O2 property_of_O2 b_is_in_subgroup b_times_a_inverse_is_c a_times_c_is_d prove_d_is_in_subgroup
% 0.49/0.70
%------------------------------------------------------------------------------