TSTP Solution File: GRP035-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:44:54 EDT 2022
% Result : Unsatisfiable 0.55s 0.76s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of clauses : 58 ( 32 unt; 0 nHn; 58 RR)
% Number of literals : 100 ( 0 equ; 47 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subgroup_member(a),
file('GRP035-3.p',unknown),
[] ).
cnf(2,axiom,
subgroup_member(b),
file('GRP035-3.p',unknown),
[] ).
cnf(3,axiom,
product(a,b,c),
file('GRP035-3.p',unknown),
[] ).
cnf(4,axiom,
~ subgroup_member(c),
file('GRP035-3.p',unknown),
[] ).
cnf(5,axiom,
product(identity,u,u),
file('GRP035-3.p',unknown),
[] ).
cnf(6,axiom,
product(u,identity,u),
file('GRP035-3.p',unknown),
[] ).
cnf(7,axiom,
product(inverse(u),u,identity),
file('GRP035-3.p',unknown),
[] ).
cnf(8,axiom,
product(u,inverse(u),identity),
file('GRP035-3.p',unknown),
[] ).
cnf(9,axiom,
product(u,v,multiply(u,v)),
file('GRP035-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP035-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP035-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP035-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),w)
| subgroup_member(w) ),
file('GRP035-3.p',unknown),
[] ).
cnf(14,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,inverse(u),c) ),
inference(res,[status(thm),theory(equality)],[13,4]),
[iquote('0:Res:13.3,4.0')] ).
cnf(15,plain,
( ~ product(a,b,u)
| equal(u,c) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.0')] ).
cnf(16,plain,
( ~ product(identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(17,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.0')] ).
cnf(20,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(22,plain,
equal(multiply(a,b),c),
inference(res,[status(thm),theory(equality)],[9,15]),
[iquote('0:Res:9.0,15.0')] ).
cnf(27,plain,
equal(inverse(identity),identity),
inference(res,[status(thm),theory(equality)],[8,16]),
[iquote('0:Res:8.0,16.0')] ).
cnf(28,plain,
equal(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[9,16]),
[iquote('0:Res:9.0,16.0')] ).
cnf(33,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(identity)
| subgroup_member(inverse(u)) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.2')] ).
cnf(35,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.0,13.2')] ).
cnf(37,plain,
( ~ subgroup_member(u)
| subgroup_member(identity) ),
inference(obv,[status(thm),theory(equality)],[35]),
[iquote('0:Obv:35.0')] ).
cnf(38,plain,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
inference(mrr,[status(thm)],[33,37]),
[iquote('0:MRR:33.1,37.1')] ).
cnf(40,plain,
subgroup_member(identity),
inference(ems,[status(thm)],[37,1]),
[iquote('0:EmS:37.0,1.0')] ).
cnf(47,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[6,12]),
[iquote('0:Res:6.0,12.0')] ).
cnf(67,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.0')] ).
cnf(69,plain,
( ~ product(u,v,w)
| ~ product(x,u,inverse(v))
| product(x,w,identity) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.0,11.0')] ).
cnf(70,plain,
( ~ product(u,inverse(v),w)
| ~ product(x,u,v)
| product(x,w,identity) ),
inference(res,[status(thm),theory(equality)],[8,11]),
[iquote('0:Res:8.0,11.0')] ).
cnf(97,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(u)
| ~ product(u,identity,c) ),
inference(spl,[status(thm),theory(equality)],[27,14]),
[iquote('0:SpL:27.0,14.2')] ).
cnf(98,plain,
( ~ subgroup_member(u)
| ~ product(u,identity,c) ),
inference(ssi,[status(thm)],[97,40]),
[iquote('0:SSi:97.0,40.0')] ).
cnf(99,plain,
~ subgroup_member(c),
inference(res,[status(thm),theory(equality)],[6,98]),
[iquote('0:Res:6.0,98.1')] ).
cnf(142,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[7,47]),
[iquote('0:Res:7.0,47.0')] ).
cnf(153,plain,
product(identity,u,inverse(inverse(u))),
inference(res,[status(thm),theory(equality)],[7,142]),
[iquote('0:Res:7.0,142.0')] ).
cnf(155,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[9,142]),
[iquote('0:Res:9.0,142.0')] ).
cnf(160,plain,
( ~ product(u,v,identity)
| product(u,identity,inverse(v)) ),
inference(res,[status(thm),theory(equality)],[8,67]),
[iquote('0:Res:8.0,67.0')] ).
cnf(173,plain,
equal(inverse(inverse(u)),u),
inference(res,[status(thm),theory(equality)],[153,16]),
[iquote('0:Res:153.0,16.0')] ).
cnf(200,plain,
( ~ subgroup_member(inverse(u))
| subgroup_member(u) ),
inference(spr,[status(thm),theory(equality)],[173,38]),
[iquote('0:SpR:173.0,38.1')] ).
cnf(214,plain,
product(multiply(u,v),inverse(v),u),
inference(spr,[status(thm),theory(equality)],[173,155]),
[iquote('0:SpR:173.0,155.0')] ).
cnf(259,plain,
product(c,inverse(b),a),
inference(spr,[status(thm),theory(equality)],[22,214]),
[iquote('0:SpR:22.0,214.0')] ).
cnf(265,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(res,[status(thm),theory(equality)],[214,20]),
[iquote('0:Res:214.0,20.0')] ).
cnf(409,plain,
( ~ product(u,c,b)
| product(u,a,identity) ),
inference(res,[status(thm),theory(equality)],[259,70]),
[iquote('0:Res:259.0,70.0')] ).
cnf(442,plain,
product(multiply(b,inverse(c)),a,identity),
inference(res,[status(thm),theory(equality)],[155,409]),
[iquote('0:Res:155.0,409.0')] ).
cnf(461,plain,
equal(multiply(multiply(b,inverse(c)),a),identity),
inference(res,[status(thm),theory(equality)],[442,20]),
[iquote('0:Res:442.0,20.0')] ).
cnf(469,plain,
equal(multiply(identity,inverse(a)),multiply(b,inverse(c))),
inference(spr,[status(thm),theory(equality)],[461,265]),
[iquote('0:SpR:461.0,265.0')] ).
cnf(471,plain,
equal(multiply(b,inverse(c)),inverse(a)),
inference(rew,[status(thm),theory(equality)],[28,469]),
[iquote('0:Rew:28.0,469.0')] ).
cnf(480,plain,
product(b,inverse(c),inverse(a)),
inference(spr,[status(thm),theory(equality)],[471,9]),
[iquote('0:SpR:471.0,9.0')] ).
cnf(525,plain,
( ~ product(inverse(c),a,u)
| product(b,u,identity) ),
inference(res,[status(thm),theory(equality)],[480,69]),
[iquote('0:Res:480.0,69.1')] ).
cnf(615,plain,
( ~ product(u,v,identity)
| equal(inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[160,17]),
[iquote('0:Res:160.1,17.0')] ).
cnf(1836,plain,
product(b,multiply(inverse(c),a),identity),
inference(res,[status(thm),theory(equality)],[9,525]),
[iquote('0:Res:9.0,525.0')] ).
cnf(1851,plain,
equal(inverse(multiply(inverse(c),a)),b),
inference(res,[status(thm),theory(equality)],[1836,615]),
[iquote('0:Res:1836.0,615.0')] ).
cnf(1860,plain,
equal(multiply(inverse(c),a),inverse(b)),
inference(spr,[status(thm),theory(equality)],[1851,173]),
[iquote('0:SpR:1851.0,173.0')] ).
cnf(1962,plain,
product(inverse(b),inverse(a),inverse(c)),
inference(spr,[status(thm),theory(equality)],[1860,214]),
[iquote('0:SpR:1860.0,214.0')] ).
cnf(1993,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(inverse(b))
| subgroup_member(inverse(c)) ),
inference(res,[status(thm),theory(equality)],[1962,13]),
[iquote('0:Res:1962.0,13.2')] ).
cnf(1998,plain,
subgroup_member(inverse(c)),
inference(ssi,[status(thm)],[1993,38,2,1]),
[iquote('0:SSi:1993.1,1993.0,38.0,2.0,1.1')] ).
cnf(2000,plain,
subgroup_member(c),
inference(sor,[status(thm)],[200,1998]),
[iquote('0:SoR:200.0,1998.0')] ).
cnf(2001,plain,
$false,
inference(mrr,[status(thm)],[2000,99]),
[iquote('0:MRR:2000.0,99.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 01:10:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.55/0.76
% 0.55/0.76 SPASS V 3.9
% 0.55/0.76 SPASS beiseite: Proof found.
% 0.55/0.76 % SZS status Theorem
% 0.55/0.76 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.76 SPASS derived 1629 clauses, backtracked 0 clauses, performed 0 splits and kept 762 clauses.
% 0.55/0.76 SPASS allocated 76877 KBytes.
% 0.55/0.76 SPASS spent 0:00:00.39 on the problem.
% 0.55/0.76 0:00:00.04 for the input.
% 0.55/0.76 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.76 0:00:00.02 for inferences.
% 0.55/0.76 0:00:00.00 for the backtracking.
% 0.55/0.76 0:00:00.31 for the reduction.
% 0.55/0.76
% 0.55/0.76
% 0.55/0.76 Here is a proof with depth 18, length 58 :
% 0.55/0.76 % SZS output start Refutation
% See solution above
% 0.55/0.76 Formulae used in the proof : a_is_in_subgroup b_is_in_subgroup a_times_b_is_c prove_c_is_in_subgroup left_identity right_identity left_inverse right_inverse total_function1 total_function2 associativity1 associativity2 closure_of_product_and_inverse
% 0.55/0.76
%------------------------------------------------------------------------------