TSTP Solution File: FLD011-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 02:28:16 EDT 2022
% Result : Unsatisfiable 2.42s 2.60s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of clauses : 62 ( 20 unt; 4 nHn; 62 RR)
% Number of literals : 144 ( 0 equ; 82 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD011-3.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD011-3.p',unknown),
[] ).
cnf(3,axiom,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('FLD011-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD011-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD011-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD011-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD011-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD011-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD011-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD011-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD011-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD011-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD011-3.p',unknown),
[] ).
cnf(17,axiom,
defined(additive_identity),
file('FLD011-3.p',unknown),
[] ).
cnf(20,axiom,
defined(multiplicative_identity),
file('FLD011-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD011-3.p',unknown),
[] ).
cnf(29,axiom,
~ sum__dfg(additive_identity,additive_identity,multiplicative_identity),
file('FLD011-3.p',unknown),
[] ).
cnf(30,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.2,2.0')] ).
cnf(31,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[21,2]),
[iquote('0:Res:21.2,2.0')] ).
cnf(37,plain,
~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[13,3]),
[iquote('0:Res:13.1,3.0')] ).
cnf(41,plain,
defined(multiplicative_inverse(a)),
inference(mrr,[status(thm)],[31,1]),
[iquote('0:MRR:31.0,1.0')] ).
cnf(42,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[30,1]),
[iquote('0:MRR:30.0,1.0')] ).
cnf(51,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[42,13]),
[iquote('0:Res:42.0,13.0')] ).
cnf(55,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.1,8.0')] ).
cnf(91,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_identity)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.1,9.0')] ).
cnf(108,plain,
( ~ defined(u)
| ~ sum__dfg(v,w,u)
| ~ sum__dfg(additive_identity,v,x)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[6,5]),
[iquote('0:Res:6.1,5.0')] ).
cnf(109,plain,
( ~ defined(u)
| ~ sum__dfg(v,w,u)
| ~ sum__dfg(additive_inverse(u),v,x)
| sum__dfg(x,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.1,5.0')] ).
cnf(125,plain,
( ~ defined(u)
| ~ sum__dfg(v,u,w)
| ~ sum__dfg(x,v,additive_identity)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.1,4.0')] ).
cnf(237,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,u,y)
| ~ sum__dfg(v,multiplicative_identity,x)
| sum__dfg(w,u,y) ),
inference(res,[status(thm),theory(equality)],[11,14]),
[iquote('0:Res:11.1,14.0')] ).
cnf(475,plain,
( ~ defined(a)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[42,91]),
[iquote('0:Res:42.0,91.1')] ).
cnf(505,plain,
( ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(ssi,[status(thm)],[475,1]),
[iquote('0:SSi:475.0,1.0')] ).
cnf(527,plain,
( ~ defined(multiplicative_inverse(a))
| sum__dfg(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[12,505]),
[iquote('0:Res:12.2,505.0')] ).
cnf(530,plain,
product(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[51,505]),
[iquote('0:Res:51.0,505.0')] ).
cnf(537,plain,
( sum__dfg(additive_identity,multiplicative_inverse(a),additive_identity)
| product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity,a) ),
inference(ssi,[status(thm)],[527,41]),
[iquote('0:SSi:527.0,41.0')] ).
cnf(538,plain,
sum__dfg(additive_identity,multiplicative_inverse(a),additive_identity),
inference(mrr,[status(thm)],[537,37]),
[iquote('0:MRR:537.1,37.0')] ).
cnf(544,plain,
product(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[530,13]),
[iquote('0:Res:530.0,13.0')] ).
cnf(562,plain,
sum__dfg(multiplicative_inverse(a),additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[538,8]),
[iquote('0:Res:538.0,8.0')] ).
cnf(563,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[6,108]),
[iquote('0:Res:6.1,108.1')] ).
cnf(570,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[55,108]),
[iquote('0:Res:55.1,108.1')] ).
cnf(574,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(obv,[status(thm),theory(equality)],[563]),
[iquote('0:Obv:563.0')] ).
cnf(575,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(obv,[status(thm),theory(equality)],[570]),
[iquote('0:Obv:570.0')] ).
cnf(588,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(additive_identity,multiplicative_inverse(a),u)
| sum__dfg(u,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[562,108]),
[iquote('0:Res:562.0,108.1')] ).
cnf(589,plain,
( ~ sum__dfg(additive_identity,multiplicative_inverse(a),u)
| sum__dfg(u,additive_identity,additive_identity) ),
inference(ssi,[status(thm)],[588,17]),
[iquote('0:SSi:588.0,17.0')] ).
cnf(613,plain,
( ~ defined(multiplicative_inverse(a))
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[538,125]),
[iquote('0:Res:538.0,125.1')] ).
cnf(618,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,multiplicative_inverse(a)) ),
inference(ssi,[status(thm)],[613,41]),
[iquote('0:SSi:613.0,41.0')] ).
cnf(686,plain,
sum__dfg(additive_identity,additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[538,589]),
[iquote('0:Res:538.0,589.0')] ).
cnf(748,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,109]),
[iquote('0:Res:7.1,109.2')] ).
cnf(755,plain,
( ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[748]),
[iquote('0:Obv:748.0')] ).
cnf(863,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(additive_identity,u,multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[618,8]),
[iquote('0:Res:618.1,8.0')] ).
cnf(1781,plain,
( ~ defined(a)
| ~ product(u,a,v)
| ~ sum__dfg(multiplicative_inverse(a),multiplicative_identity,u)
| sum__dfg(multiplicative_identity,a,v) ),
inference(res,[status(thm),theory(equality)],[42,237]),
[iquote('0:Res:42.0,237.1')] ).
cnf(1841,plain,
( ~ product(u,a,v)
| ~ sum__dfg(multiplicative_inverse(a),multiplicative_identity,u)
| sum__dfg(multiplicative_identity,a,v) ),
inference(ssi,[status(thm)],[1781,1]),
[iquote('0:SSi:1781.0,1.0')] ).
cnf(3922,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,additive_identity)
| sum__dfg(multiplicative_inverse(a),u,u) ),
inference(res,[status(thm),theory(equality)],[863,574]),
[iquote('0:Res:863.1,574.1')] ).
cnf(3935,plain,
( ~ defined(u)
| sum__dfg(multiplicative_inverse(a),u,u) ),
inference(mrr,[status(thm)],[3922,686]),
[iquote('0:MRR:3922.1,686.0')] ).
cnf(5339,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(res,[status(thm),theory(equality)],[3935,1841]),
[iquote('0:Res:3935.1,1841.1')] ).
cnf(5340,plain,
( ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(ssi,[status(thm)],[5339,20]),
[iquote('0:SSi:5339.0,20.0')] ).
cnf(5391,plain,
sum__dfg(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[544,5340]),
[iquote('0:Res:544.0,5340.0')] ).
cnf(5409,plain,
sum__dfg(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[5391,8]),
[iquote('0:Res:5391.0,8.0')] ).
cnf(5430,plain,
( ~ defined(a)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5409,755]),
[iquote('0:Res:5409.0,755.1')] ).
cnf(5435,plain,
sum__dfg(additive_identity,multiplicative_identity,additive_identity),
inference(ssi,[status(thm)],[5430,1]),
[iquote('0:SSi:5430.0,1.0')] ).
cnf(5512,plain,
( ~ defined(multiplicative_identity)
| sum__dfg(additive_identity,additive_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[5435,575]),
[iquote('0:Res:5435.0,575.1')] ).
cnf(5519,plain,
sum__dfg(additive_identity,additive_identity,multiplicative_identity),
inference(ssi,[status(thm)],[5512,20]),
[iquote('0:SSi:5512.0,20.0')] ).
cnf(5520,plain,
$false,
inference(mrr,[status(thm)],[5519,29]),
[iquote('0:MRR:5519.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 16:59:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.42/2.60
% 2.42/2.60 SPASS V 3.9
% 2.42/2.60 SPASS beiseite: Proof found.
% 2.42/2.60 % SZS status Theorem
% 2.42/2.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.42/2.60 SPASS derived 3971 clauses, backtracked 0 clauses, performed 0 splits and kept 2647 clauses.
% 2.42/2.60 SPASS allocated 80255 KBytes.
% 2.42/2.60 SPASS spent 0:00:02.23 on the problem.
% 2.42/2.60 0:00:00.03 for the input.
% 2.42/2.60 0:00:00.00 for the FLOTTER CNF translation.
% 2.42/2.60 0:00:00.05 for inferences.
% 2.42/2.60 0:00:00.00 for the backtracking.
% 2.42/2.60 0:00:02.10 for the reduction.
% 2.42/2.60
% 2.42/2.60
% 2.42/2.60 Here is a proof with depth 11, length 62 :
% 2.42/2.60 % SZS output start Refutation
% See solution above
% 2.42/2.60 Formulae used in the proof : a_is_defined not_sum_2 not_product_3 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition associativity_multiplication_1 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1 well_definedness_of_additive_identity well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse different_identities
% 2.42/2.60
%------------------------------------------------------------------------------