TSTP Solution File: FLD040-5 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD040-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 02:28:27 EDT 2022
% Result : Unsatisfiable 2.67s 2.89s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 52 ( 16 unt; 2 nHn; 52 RR)
% Number of literals : 122 ( 0 equ; 70 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 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('FLD040-5.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD040-5.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,multiplicative_inverse(a),additive_identity),
file('FLD040-5.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('FLD040-5.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD040-5.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD040-5.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD040-5.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD040-5.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD040-5.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD040-5.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD040-5.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('FLD040-5.p',unknown),
[] ).
cnf(20,axiom,
defined(multiplicative_identity),
file('FLD040-5.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD040-5.p',unknown),
[] ).
cnf(29,axiom,
~ sum__dfg(additive_identity,additive_identity,multiplicative_identity),
file('FLD040-5.p',unknown),
[] ).
cnf(33,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(multiplicative_inverse(a),w,u)
| sum__dfg(additive_identity,w,v) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.0,5.0')] ).
cnf(42,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(43,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[21,2]),
[iquote('0:Res:21.2,2.0')] ).
cnf(49,plain,
defined(multiplicative_inverse(a)),
inference(mrr,[status(thm)],[43,1]),
[iquote('0:MRR:43.0,1.0')] ).
cnf(50,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[42,1]),
[iquote('0:MRR:42.0,1.0')] ).
cnf(81,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[50,13]),
[iquote('0:Res:50.0,13.0')] ).
cnf(86,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(131,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(138,plain,
( ~ defined(multiplicative_inverse(a))
| ~ sum__dfg(additive_identity,multiplicative_inverse(a),u)
| sum__dfg(additive_identity,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[86,33]),
[iquote('0:Res:86.1,33.1')] ).
cnf(141,plain,
( ~ sum__dfg(additive_identity,multiplicative_inverse(a),u)
| sum__dfg(additive_identity,additive_identity,u) ),
inference(ssi,[status(thm)],[138,49]),
[iquote('0:SSi:138.0,49.0')] ).
cnf(146,plain,
( ~ defined(multiplicative_inverse(a))
| sum__dfg(additive_identity,additive_identity,multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[6,141]),
[iquote('0:Res:6.1,141.0')] ).
cnf(150,plain,
sum__dfg(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(ssi,[status(thm)],[146,49]),
[iquote('0:SSi:146.0,49.0')] ).
cnf(156,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(161,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(366,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(960,plain,
( ~ defined(a)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[50,131]),
[iquote('0:Res:50.0,131.1')] ).
cnf(968,plain,
( ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| product(u,multiplicative_identity,a) ),
inference(ssi,[status(thm)],[960,1]),
[iquote('0:SSi:960.0,1.0')] ).
cnf(1021,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(res,[status(thm),theory(equality)],[6,156]),
[iquote('0:Res:6.1,156.1')] ).
cnf(1063,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[86,156]),
[iquote('0:Res:86.1,156.1')] ).
cnf(1085,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,additive_identity,v)
| sum__dfg(v,u,u) ),
inference(obv,[status(thm),theory(equality)],[1021]),
[iquote('0:Obv:1021.0')] ).
cnf(1086,plain,
( ~ defined(u)
| ~ sum__dfg(additive_identity,u,v)
| sum__dfg(v,additive_identity,u) ),
inference(obv,[status(thm),theory(equality)],[1063]),
[iquote('0:Obv:1063.0')] ).
cnf(1293,plain,
( ~ defined(u)
| ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,161]),
[iquote('0:Res:7.1,161.2')] ).
cnf(1310,plain,
( ~ defined(u)
| ~ sum__dfg(u,v,u)
| sum__dfg(additive_identity,v,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[1293]),
[iquote('0:Obv:1293.0')] ).
cnf(1515,plain,
product(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[81,968]),
[iquote('0:Res:81.0,968.0')] ).
cnf(1522,plain,
product(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[1515,13]),
[iquote('0:Res:1515.0,13.0')] ).
cnf(2931,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)],[50,366]),
[iquote('0:Res:50.0,366.1')] ).
cnf(2959,plain,
( ~ product(u,a,v)
| ~ sum__dfg(multiplicative_inverse(a),multiplicative_identity,u)
| sum__dfg(multiplicative_identity,a,v) ),
inference(ssi,[status(thm)],[2931,1]),
[iquote('0:SSi:2931.0,1.0')] ).
cnf(5288,plain,
( ~ defined(u)
| sum__dfg(multiplicative_inverse(a),u,u) ),
inference(res,[status(thm),theory(equality)],[150,1085]),
[iquote('0:Res:150.0,1085.1')] ).
cnf(7591,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(res,[status(thm),theory(equality)],[5288,2959]),
[iquote('0:Res:5288.1,2959.1')] ).
cnf(7594,plain,
( ~ product(multiplicative_identity,a,u)
| sum__dfg(multiplicative_identity,a,u) ),
inference(ssi,[status(thm)],[7591,20]),
[iquote('0:SSi:7591.0,20.0')] ).
cnf(7601,plain,
sum__dfg(multiplicative_identity,a,a),
inference(res,[status(thm),theory(equality)],[1522,7594]),
[iquote('0:Res:1522.0,7594.0')] ).
cnf(7608,plain,
sum__dfg(a,multiplicative_identity,a),
inference(res,[status(thm),theory(equality)],[7601,8]),
[iquote('0:Res:7601.0,8.0')] ).
cnf(7630,plain,
( ~ defined(a)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7608,1310]),
[iquote('0:Res:7608.0,1310.1')] ).
cnf(7635,plain,
sum__dfg(additive_identity,multiplicative_identity,additive_identity),
inference(ssi,[status(thm)],[7630,1]),
[iquote('0:SSi:7630.0,1.0')] ).
cnf(7655,plain,
( ~ defined(multiplicative_identity)
| sum__dfg(additive_identity,additive_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[7635,1086]),
[iquote('0:Res:7635.0,1086.1')] ).
cnf(7666,plain,
sum__dfg(additive_identity,additive_identity,multiplicative_identity),
inference(ssi,[status(thm)],[7655,20]),
[iquote('0:SSi:7655.0,20.0')] ).
cnf(7667,plain,
$false,
inference(mrr,[status(thm)],[7666,29]),
[iquote('0:MRR:7666.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : FLD040-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 20:40:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.67/2.89
% 2.67/2.89 SPASS V 3.9
% 2.67/2.89 SPASS beiseite: Proof found.
% 2.67/2.89 % SZS status Theorem
% 2.67/2.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.67/2.89 SPASS derived 6001 clauses, backtracked 0 clauses, performed 0 splits and kept 3300 clauses.
% 2.67/2.89 SPASS allocated 81059 KBytes.
% 2.67/2.89 SPASS spent 0:00:02.50 on the problem.
% 2.67/2.89 0:00:00.03 for the input.
% 2.67/2.89 0:00:00.00 for the FLOTTER CNF translation.
% 2.67/2.89 0:00:00.06 for inferences.
% 2.67/2.89 0:00:00.00 for the backtracking.
% 2.67/2.89 0:00:02.35 for the reduction.
% 2.67/2.89
% 2.67/2.89
% 2.67/2.89 Here is a proof with depth 9, length 52 :
% 2.67/2.89 % SZS output start Refutation
% See solution above
% 2.67/2.89 Formulae used in the proof : a_is_defined not_sum_2 sum_3 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_multiplicative_identity well_definedness_of_multiplicative_inverse different_identities
% 2.67/2.89
%------------------------------------------------------------------------------