TSTP Solution File: GRP039-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:44:55 EDT 2022
% Result : Unsatisfiable 0.60s 0.84s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 82 ( 37 unt; 9 nHn; 82 RR)
% Number of literals : 152 ( 0 equ; 69 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( subgroup_member(u)
| subgroup_member(v)
| subgroup_member(element_in_O2(u,v)) ),
file('GRP039-1.p',unknown),
[] ).
cnf(2,axiom,
( subgroup_member(u)
| subgroup_member(v)
| product(u,element_in_O2(u,v),v) ),
file('GRP039-1.p',unknown),
[] ).
cnf(3,axiom,
subgroup_member(b),
file('GRP039-1.p',unknown),
[] ).
cnf(4,axiom,
product(b,inverse(a),c),
file('GRP039-1.p',unknown),
[] ).
cnf(5,axiom,
product(a,c,d),
file('GRP039-1.p',unknown),
[] ).
cnf(6,axiom,
~ subgroup_member(d),
file('GRP039-1.p',unknown),
[] ).
cnf(7,axiom,
product(identity,u,u),
file('GRP039-1.p',unknown),
[] ).
cnf(8,axiom,
product(u,identity,u),
file('GRP039-1.p',unknown),
[] ).
cnf(9,axiom,
product(inverse(u),u,identity),
file('GRP039-1.p',unknown),
[] ).
cnf(10,axiom,
product(u,inverse(u),identity),
file('GRP039-1.p',unknown),
[] ).
cnf(11,axiom,
product(u,v,multiply(u,v)),
file('GRP039-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP039-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP039-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP039-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ subgroup_member(u)
| subgroup_member(inverse(u)) ),
file('GRP039-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,u,w)
| subgroup_member(w) ),
file('GRP039-1.p',unknown),
[] ).
cnf(17,plain,
( ~ subgroup_member(u)
| ~ product(b,u,v)
| subgroup_member(v) ),
inference(res,[status(thm),theory(equality)],[3,16]),
[iquote('0:Res:3.0,16.0')] ).
cnf(18,plain,
subgroup_member(inverse(b)),
inference(res,[status(thm),theory(equality)],[3,15]),
[iquote('0:Res:3.0,15.0')] ).
cnf(20,plain,
( subgroup_member(u)
| product(d,element_in_O2(d,u),u) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.2,6.0')] ).
cnf(21,plain,
( subgroup_member(u)
| subgroup_member(element_in_O2(d,u)) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.2,6.0')] ).
cnf(24,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| ~ product(v,u,d) ),
inference(res,[status(thm),theory(equality)],[16,6]),
[iquote('0:Res:16.3,6.0')] ).
cnf(26,plain,
( ~ product(a,u,v)
| ~ product(c,w,u)
| product(d,w,v) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.0,14.0')] ).
cnf(28,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| subgroup_member(d) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.2')] ).
cnf(32,plain,
( ~ product(u,d,v)
| ~ product(u,a,w)
| product(w,c,v) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.0,14.1')] ).
cnf(33,plain,
( ~ product(u,v,a)
| ~ product(v,c,w)
| product(u,w,d) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.2')] ).
cnf(34,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(mrr,[status(thm)],[28,6]),
[iquote('0:MRR:28.2,6.0')] ).
cnf(40,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(res,[status(thm),theory(equality)],[4,17]),
[iquote('0:Res:4.0,17.1')] ).
cnf(41,plain,
( ~ subgroup_member(inverse(b))
| subgroup_member(identity) ),
inference(res,[status(thm),theory(equality)],[10,17]),
[iquote('0:Res:10.0,17.1')] ).
cnf(45,plain,
subgroup_member(identity),
inference(ssi,[status(thm)],[41,18]),
[iquote('0:SSi:41.0,18.0')] ).
cnf(47,plain,
( ~ subgroup_member(a)
| subgroup_member(c) ),
inference(sor,[status(thm)],[40,15]),
[iquote('0:SoR:40.0,15.1')] ).
cnf(48,plain,
~ subgroup_member(a),
inference(mrr,[status(thm)],[47,34]),
[iquote('0:MRR:47.1,34.0')] ).
cnf(56,plain,
( ~ subgroup_member(u)
| ~ subgroup_member(v)
| subgroup_member(multiply(v,u)) ),
inference(res,[status(thm),theory(equality)],[11,16]),
[iquote('0:Res:11.0,16.2')] ).
cnf(65,plain,
( ~ product(identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[7,12]),
[iquote('0:Res:7.0,12.0')] ).
cnf(66,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[8,12]),
[iquote('0:Res:8.0,12.0')] ).
cnf(71,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[11,12]),
[iquote('0:Res:11.0,12.0')] ).
cnf(93,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[8,14]),
[iquote('0:Res:8.0,14.0')] ).
cnf(96,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[9,14]),
[iquote('0:Res:9.0,14.0')] ).
cnf(115,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[7,13]),
[iquote('0:Res:7.0,13.0')] ).
cnf(173,plain,
( ~ product(c,u,inverse(a))
| product(d,u,identity) ),
inference(res,[status(thm),theory(equality)],[10,26]),
[iquote('0:Res:10.0,26.0')] ).
cnf(207,plain,
( subgroup_member(c)
| subgroup_member(inverse(a))
| product(d,element_in_O2(c,inverse(a)),identity) ),
inference(res,[status(thm),theory(equality)],[2,173]),
[iquote('0:Res:2.2,173.0')] ).
cnf(208,plain,
( subgroup_member(c)
| product(d,element_in_O2(c,inverse(a)),identity) ),
inference(mrr,[status(thm)],[207,40]),
[iquote('0:MRR:207.1,40.0')] ).
cnf(209,plain,
( subgroup_member(c)
| equal(multiply(d,element_in_O2(c,inverse(a))),identity) ),
inference(res,[status(thm),theory(equality)],[208,71]),
[iquote('0:Res:208.1,71.0')] ).
cnf(216,plain,
( ~ product(inverse(d),a,u)
| product(u,c,identity) ),
inference(res,[status(thm),theory(equality)],[9,32]),
[iquote('0:Res:9.0,32.0')] ).
cnf(223,plain,
subgroup_member(c),
inference(spt,[spt(split,[position(s1)])],[209]),
[iquote('1:Spt:209.0')] ).
cnf(280,plain,
( ~ product(element_in_O2(d,a),c,u)
| subgroup_member(a)
| product(d,u,d) ),
inference(res,[status(thm),theory(equality)],[20,33]),
[iquote('0:Res:20.1,33.0')] ).
cnf(284,plain,
( ~ product(element_in_O2(d,a),c,u)
| product(d,u,d) ),
inference(mrr,[status(thm)],[280,48]),
[iquote('0:MRR:280.1,48.0')] ).
cnf(388,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[9,93]),
[iquote('0:Res:9.0,93.0')] ).
cnf(423,plain,
( ~ product(u,b,identity)
| product(u,c,inverse(a)) ),
inference(res,[status(thm),theory(equality)],[4,115]),
[iquote('0:Res:4.0,115.0')] ).
cnf(424,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[9,115]),
[iquote('0:Res:9.0,115.0')] ).
cnf(485,plain,
product(multiply(inverse(d),a),c,identity),
inference(res,[status(thm),theory(equality)],[11,216]),
[iquote('0:Res:11.0,216.0')] ).
cnf(488,plain,
equal(multiply(multiply(inverse(d),a),c),identity),
inference(res,[status(thm),theory(equality)],[485,71]),
[iquote('0:Res:485.0,71.0')] ).
cnf(554,plain,
( ~ product(u,v,u)
| product(identity,v,identity) ),
inference(res,[status(thm),theory(equality)],[9,96]),
[iquote('0:Res:9.0,96.1')] ).
cnf(1104,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(u)
| ~ product(u,b,identity)
| subgroup_member(inverse(a)) ),
inference(res,[status(thm),theory(equality)],[423,16]),
[iquote('0:Res:423.1,16.2')] ).
cnf(1121,plain,
( ~ subgroup_member(u)
| ~ product(u,b,identity)
| subgroup_member(inverse(a)) ),
inference(ssi,[status(thm)],[1104,223]),
[iquote('1:SSi:1104.0,223.0')] ).
cnf(1252,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[9,424]),
[iquote('0:Res:9.0,424.0')] ).
cnf(1266,plain,
equal(inverse(inverse(u)),u),
inference(res,[status(thm),theory(equality)],[1252,66]),
[iquote('0:Res:1252.0,66.0')] ).
cnf(1269,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(inverse(inverse(d))) ),
inference(res,[status(thm),theory(equality)],[1252,24]),
[iquote('0:Res:1252.0,24.2')] ).
cnf(1290,plain,
~ subgroup_member(inverse(inverse(d))),
inference(ssi,[status(thm)],[1269,45]),
[iquote('0:SSi:1269.0,45.0')] ).
cnf(1308,plain,
~ subgroup_member(inverse(d)),
inference(sor,[status(thm)],[1290,15]),
[iquote('0:SoR:1290.0,15.1')] ).
cnf(1312,plain,
( ~ subgroup_member(inverse(u))
| subgroup_member(u) ),
inference(spr,[status(thm),theory(equality)],[1266,15]),
[iquote('0:SpR:1266.0,15.1')] ).
cnf(1672,plain,
product(multiply(u,inverse(v)),v,u),
inference(res,[status(thm),theory(equality)],[11,388]),
[iquote('0:Res:11.0,388.0')] ).
cnf(1723,plain,
product(multiply(u,v),inverse(v),u),
inference(spr,[status(thm),theory(equality)],[1266,1672]),
[iquote('0:SpR:1266.0,1672.0')] ).
cnf(1856,plain,
product(identity,inverse(c),multiply(inverse(d),a)),
inference(spr,[status(thm),theory(equality)],[488,1723]),
[iquote('0:SpR:488.0,1723.0')] ).
cnf(1949,plain,
product(d,multiply(element_in_O2(d,a),c),d),
inference(res,[status(thm),theory(equality)],[11,284]),
[iquote('0:Res:11.0,284.0')] ).
cnf(2103,plain,
equal(multiply(inverse(d),a),inverse(c)),
inference(res,[status(thm),theory(equality)],[1856,65]),
[iquote('0:Res:1856.0,65.0')] ).
cnf(2170,plain,
product(inverse(c),inverse(a),inverse(d)),
inference(spr,[status(thm),theory(equality)],[2103,1723]),
[iquote('0:SpR:2103.0,1723.0')] ).
cnf(2195,plain,
( ~ subgroup_member(inverse(a))
| ~ subgroup_member(inverse(c))
| subgroup_member(inverse(d)) ),
inference(res,[status(thm),theory(equality)],[2170,16]),
[iquote('0:Res:2170.0,16.2')] ).
cnf(2211,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(inverse(d)) ),
inference(ssi,[status(thm)],[2195,15,223]),
[iquote('1:SSi:2195.1,15.0,223.1')] ).
cnf(2212,plain,
~ subgroup_member(inverse(a)),
inference(mrr,[status(thm)],[2211,1308]),
[iquote('1:MRR:2211.1,1308.0')] ).
cnf(2216,plain,
( ~ subgroup_member(u)
| ~ product(u,b,identity) ),
inference(mrr,[status(thm)],[1121,2212]),
[iquote('1:MRR:1121.2,2212.0')] ).
cnf(2287,plain,
product(identity,multiply(element_in_O2(d,a),c),identity),
inference(res,[status(thm),theory(equality)],[1949,554]),
[iquote('0:Res:1949.0,554.0')] ).
cnf(2304,plain,
equal(multiply(element_in_O2(d,a),c),identity),
inference(res,[status(thm),theory(equality)],[2287,65]),
[iquote('0:Res:2287.0,65.0')] ).
cnf(2332,plain,
product(identity,inverse(c),element_in_O2(d,a)),
inference(spr,[status(thm),theory(equality)],[2304,1723]),
[iquote('0:SpR:2304.0,1723.0')] ).
cnf(2368,plain,
equal(element_in_O2(d,a),inverse(c)),
inference(res,[status(thm),theory(equality)],[2332,65]),
[iquote('0:Res:2332.0,65.0')] ).
cnf(2401,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference(spr,[status(thm),theory(equality)],[2368,21]),
[iquote('0:SpR:2368.0,21.1')] ).
cnf(2410,plain,
subgroup_member(inverse(c)),
inference(mrr,[status(thm)],[2401,48]),
[iquote('0:MRR:2401.0,48.0')] ).
cnf(2411,plain,
subgroup_member(c),
inference(sor,[status(thm)],[1312,2410]),
[iquote('0:SoR:1312.0,2410.0')] ).
cnf(2447,plain,
~ subgroup_member(multiply(identity,inverse(b))),
inference(res,[status(thm),theory(equality)],[1672,2216]),
[iquote('1:Res:1672.0,2216.1')] ).
cnf(2451,plain,
$false,
inference(ssi,[status(thm)],[2447,56,45,18]),
[iquote('1:SSi:2447.0,56.0,45.0,18.2')] ).
cnf(2452,plain,
~ subgroup_member(c),
inference(spt,[spt(split,[position(sa)])],[2451,223]),
[iquote('1:Spt:2451.0,209.0,223.0')] ).
cnf(2453,plain,
equal(multiply(d,element_in_O2(c,inverse(a))),identity),
inference(spt,[spt(split,[position(s2)])],[209]),
[iquote('1:Spt:2451.0,209.1')] ).
cnf(2454,plain,
$false,
inference(mrr,[status(thm)],[2452,2411]),
[iquote('1:MRR:2452.0,2411.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 12:36:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.84
% 0.60/0.84 SPASS V 3.9
% 0.60/0.84 SPASS beiseite: Proof found.
% 0.60/0.84 % SZS status Theorem
% 0.60/0.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.84 SPASS derived 1998 clauses, backtracked 59 clauses, performed 1 splits and kept 1050 clauses.
% 0.60/0.84 SPASS allocated 77256 KBytes.
% 0.60/0.84 SPASS spent 0:00:00.49 on the problem.
% 0.60/0.84 0:00:00.04 for the input.
% 0.60/0.84 0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.84 0:00:00.03 for inferences.
% 0.60/0.84 0:00:00.00 for the backtracking.
% 0.60/0.84 0:00:00.40 for the reduction.
% 0.60/0.84
% 0.60/0.84
% 0.60/0.84 Here is a proof with depth 9, length 82 :
% 0.60/0.84 % SZS output start Refutation
% See solution above
% 0.60/0.84 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
% 0.60/0.84
%------------------------------------------------------------------------------