TSTP Solution File: FLD027-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD027-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 02:28:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 14 unt; 1 nHn; 26 RR)
% Number of literals : 44 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD027-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD027-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD027-3.p',unknown),
[] ).
cnf(4,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD027-3.p',unknown),
[] ).
cnf(5,axiom,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('FLD027-3.p',unknown),
[] ).
cnf(6,axiom,
~ product(multiplicative_identity,a,b),
file('FLD027-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD027-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD027-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD027-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD027-3.p',unknown),
[] ).
cnf(23,axiom,
defined(multiplicative_identity),
file('FLD027-3.p',unknown),
[] ).
cnf(35,plain,
( ~ product(u,v,b)
| ~ product(u,w,multiplicative_identity)
| ~ product(w,a,v) ),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.3,6.0')] ).
cnf(37,plain,
( ~ defined(b)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[15,4]),
[iquote('0:Res:15.2,4.0')] ).
cnf(44,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[15,3]),
[iquote('0:Res:15.2,3.0')] ).
cnf(53,plain,
( ~ product(multiplicative_identity,u,v)
| ~ product(multiplicative_inverse(a),w,u)
| product(multiplicative_inverse(b),w,v) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.0')] ).
cnf(66,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(mrr,[status(thm)],[37,2]),
[iquote('0:MRR:37.0,2.0')] ).
cnf(67,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[44,1]),
[iquote('0:MRR:44.0,1.0')] ).
cnf(83,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[66,16]),
[iquote('0:Res:66.0,16.0')] ).
cnf(86,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[14,16]),
[iquote('0:Res:14.1,16.0')] ).
cnf(316,plain,
( ~ defined(b)
| ~ product(b,u,multiplicative_identity)
| ~ product(u,a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[86,35]),
[iquote('0:Res:86.1,35.0')] ).
cnf(318,plain,
( ~ product(b,u,multiplicative_identity)
| ~ product(u,a,multiplicative_identity) ),
inference(ssi,[status(thm)],[316,2]),
[iquote('0:SSi:316.0,2.0')] ).
cnf(323,plain,
( ~ product(multiplicative_identity,multiplicative_identity,u)
| product(multiplicative_inverse(b),a,u) ),
inference(res,[status(thm),theory(equality)],[67,53]),
[iquote('0:Res:67.0,53.1')] ).
cnf(334,plain,
~ product(multiplicative_inverse(b),a,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[83,318]),
[iquote('0:Res:83.0,318.0')] ).
cnf(336,plain,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[323,334]),
[iquote('0:Res:323.1,334.0')] ).
cnf(344,plain,
~ defined(multiplicative_identity),
inference(res,[status(thm),theory(equality)],[14,336]),
[iquote('0:Res:14.1,336.0')] ).
cnf(346,plain,
$false,
inference(ssi,[status(thm)],[344,23]),
[iquote('0:SSi:344.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : FLD027-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 6 21:43:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 259 clauses, backtracked 0 clauses, performed 0 splits and kept 218 clauses.
% 0.19/0.47 SPASS allocated 75949 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.05 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 5, length 26 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 not_sum_4 product_5 not_product_6 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication well_definedness_of_multiplicative_identity
% 0.19/0.47
%------------------------------------------------------------------------------