TSTP Solution File: GRP039-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.49s 0.71s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 56 ( 23 unt; 6 nHn; 56 RR)
% Number of literals : 106 ( 0 equ; 45 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(u,v)) ),
file('GRP039-4.p',unknown),
[] ).
cnf(3,axiom,
( subgroup_member(u)
| subgroup_member(v)
| product(u,element_in_O2(u,v),v) ),
file('GRP039-4.p',unknown),
[] ).
cnf(4,axiom,
subgroup_member(b),
file('GRP039-4.p',unknown),
[] ).
cnf(5,axiom,
product(b,inverse(a),c),
file('GRP039-4.p',unknown),
[] ).
cnf(6,axiom,
product(a,c,d),
file('GRP039-4.p',unknown),
[] ).
cnf(7,axiom,
~ subgroup_member(d),
file('GRP039-4.p',unknown),
[] ).
cnf(8,axiom,
product(identity,u,u),
file('GRP039-4.p',unknown),
[] ).
cnf(9,axiom,
product(u,identity,u),
file('GRP039-4.p',unknown),
[] ).
cnf(10,axiom,
product(inverse(u),u,identity),
file('GRP039-4.p',unknown),
[] ).
cnf(11,axiom,
product(u,inverse(u),identity),
file('GRP039-4.p',unknown),
[] ).
cnf(12,axiom,
product(u,v,multiply(u,v)),
file('GRP039-4.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP039-4.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP039-4.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP039-4.p',unknown),
[] ).
cnf(16,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-4.p',unknown),
[] ).
cnf(17,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,u,w)
| subgroup_member(w) ),
file('GRP039-4.p',unknown),
[] ).
cnf(18,plain,
( ~ subgroup_member(u)
| ~ product(b,u,v)
| subgroup_member(v) ),
inference(res,[status(thm),theory(equality)],[4,17]),
[iquote('0:Res:4.0,17.0')] ).
cnf(21,plain,
( subgroup_member(u)
| product(d,element_in_O2(d,u),u) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.2,7.0')] ).
cnf(22,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(d,u)) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.2,7.0')] ).
cnf(29,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[6,17]),
[iquote('0:Res:6.0,17.2')] ).
cnf(32,plain,
( ~ product(u,c,v)
| ~ product(w,a,u)
| product(w,d,v) ),
inference(res,[status(thm),theory(equality)],[6,14]),
[iquote('0:Res:6.0,14.1')] ).
cnf(35,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[29,7]),
[iquote('0:MRR:29.2,7.0')] ).
cnf(41,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[5,18]),
[iquote('0:Res:5.0,18.1')] ).
cnf(45,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[41,16]),
[iquote('0:SoR:41.0,16.1')] ).
cnf(46,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[45,35]),
[iquote('0:MRR:45.1,35.0')] ).
cnf(73,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[9,13]),
[iquote('0:Res:9.0,13.0')] ).
cnf(78,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[12,13]),
[iquote('0:Res:12.0,13.0')] ).
cnf(93,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[9,15]),
[iquote('0:Res:9.0,15.0')] ).
cnf(96,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[10,15]),
[iquote('0:Res:10.0,15.0')] ).
cnf(117,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[8,14]),
[iquote('0:Res:8.0,14.0')] ).
cnf(122,plain,
( ~ product(u,inverse(v),w)
| ~ product(x,u,v)
| product(x,w,identity) ),
inference(res,[status(thm),theory(equality)],[11,14]),
[iquote('0:Res:11.0,14.0')] ).
cnf(237,plain,
( ~ product(u,a,identity)
| product(u,d,c) ),
inference(res,[status(thm),theory(equality)],[8,32]),
[iquote('0:Res:8.0,32.0')] ).
cnf(269,plain,
( ~ product(u,a,identity)
| equal(multiply(u,d),c) ),
inference(res,[status(thm),theory(equality)],[237,78]),
[iquote('0:Res:237.1,78.0')] ).
cnf(382,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[10,93]),
[iquote('0:Res:10.0,93.0')] ).
cnf(412,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[10,117]),
[iquote('0:Res:10.0,117.0')] ).
cnf(413,plain,
( ~ product(u,v,identity)
| product(u,identity,inverse(v)) ),
inference(res,[status(thm),theory(equality)],[11,117]),
[iquote('0:Res:11.0,117.0')] ).
cnf(480,plain,
equal(multiply(inverse(a),d),c),
inference(res,[status(thm),theory(equality)],[10,269]),
[iquote('0:Res:10.0,269.0')] ).
cnf(491,plain,
product(inverse(a),d,c),
inference(spr,[status(thm),theory(equality)],[480,12]),
[iquote('0:SpR:480.0,12.0')] ).
cnf(535,plain,
( ~ product(d,u,a)
| product(c,u,identity) ),
inference(res,[status(thm),theory(equality)],[491,96]),
[iquote('0:Res:491.0,96.1')] ).
cnf(541,plain,
( subgroup_member(a)
| product(c,element_in_O2(d,a),identity) ),
inference(res,[status(thm),theory(equality)],[21,535]),
[iquote('0:Res:21.1,535.0')] ).
cnf(545,plain,
product(c,element_in_O2(d,a),identity),
inference(mrr,[status(thm)],[541,46]),
[iquote('0:MRR:541.0,46.0')] ).
cnf(659,plain,
( ~ product(u,b,a)
| product(u,c,identity) ),
inference(res,[status(thm),theory(equality)],[5,122]),
[iquote('0:Res:5.0,122.0')] ).
cnf(1145,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[10,412]),
[iquote('0:Res:10.0,412.0')] ).
cnf(1162,plain,
equal(inverse(inverse(u)),u),
inference(res,[status(thm),theory(equality)],[1145,73]),
[iquote('0:Res:1145.0,73.0')] ).
cnf(1234,plain,
( ~ product(u,v,identity)
| equal(inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[413,73]),
[iquote('0:Res:413.1,73.0')] ).
cnf(1374,plain,
equal(inverse(element_in_O2(d,a)),c),
inference(res,[status(thm),theory(equality)],[545,1234]),
[iquote('0:Res:545.0,1234.0')] ).
cnf(1379,plain,
( ~ product(u,b,a)
| equal(inverse(c),u) ),
inference(res,[status(thm),theory(equality)],[659,1234]),
[iquote('0:Res:659.1,1234.0')] ).
cnf(1397,plain,
equal(element_in_O2(d,a),inverse(c)),
inference(spr,[status(thm),theory(equality)],[1374,1162]),
[iquote('0:SpR:1374.0,1162.0')] ).
cnf(1444,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(spr,[status(thm),theory(equality)],[1397,22]),
[iquote('0:SpR:1397.0,22.1')] ).
cnf(1454,plain,
subgroup_member(inverse(c)),
inference(mrr,[status(thm)],[1444,46]),
[iquote('0:MRR:1444.0,46.0')] ).
cnf(1686,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[12,382]),
[iquote('0:Res:12.0,382.0')] ).
cnf(1762,plain,
equal(multiply(a,inverse(b)),inverse(c)),
inference(res,[status(thm),theory(equality)],[1686,1379]),
[iquote('0:Res:1686.0,1379.0')] ).
cnf(1785,plain,
product(inverse(c),b,a),
inference(spr,[status(thm),theory(equality)],[1762,1686]),
[iquote('0:SpR:1762.0,1686.0')] ).
cnf(1855,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(res,[status(thm),theory(equality)],[1785,17]),
[iquote('0:Res:1785.0,17.2')] ).
cnf(1867,plain,
subgroup_member(a),
inference(ssi,[status(thm)],[1855,1454,4]),
[iquote('0:SSi:1855.1,1855.0,1454.0,4.0')] ).
cnf(1868,plain,
$false,
inference(mrr,[status(thm)],[1867,46]),
[iquote('0:MRR:1867.0,46.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 19:16:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.71
% 0.49/0.71 SPASS V 3.9
% 0.49/0.71 SPASS beiseite: Proof found.
% 0.49/0.71 % SZS status Theorem
% 0.49/0.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.71 SPASS derived 1502 clauses, backtracked 25 clauses, performed 1 splits and kept 742 clauses.
% 0.49/0.71 SPASS allocated 76871 KBytes.
% 0.49/0.71 SPASS spent 0:00:00.35 on the problem.
% 0.49/0.71 0:00:00.03 for the input.
% 0.49/0.71 0:00:00.00 for the FLOTTER CNF translation.
% 0.49/0.71 0:00:00.02 for inferences.
% 0.49/0.71 0:00:00.00 for the backtracking.
% 0.49/0.71 0:00:00.27 for the reduction.
% 0.49/0.71
% 0.49/0.71
% 0.49/0.71 Here is a proof with depth 10, length 56 :
% 0.49/0.71 % SZS output start Refutation
% See solution above
% 0.49/0.71 Formulae used in the proof : 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 left_identity right_identity left_inverse right_inverse total_function1 total_function2 associativity1 associativity2 closure_of_inverse closure_of_product
% 0.49/0.71
%------------------------------------------------------------------------------