TSTP Solution File: FLD032-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD032-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 02:28:24 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 9 unt; 2 nHn; 22 RR)
% Number of literals : 41 ( 0 equ; 22 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 : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD032-3.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD032-3.p',unknown),
[] ).
cnf(3,axiom,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
file('FLD032-3.p',unknown),
[] ).
cnf(4,axiom,
~ product(multiplicative_identity,a,multiplicative_identity),
file('FLD032-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD032-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD032-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD032-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD032-3.p',unknown),
[] ).
cnf(22,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD032-3.p',unknown),
[] ).
cnf(33,plain,
( ~ product(u,v,multiplicative_identity)
| ~ product(u,w,multiplicative_identity)
| ~ product(w,a,v) ),
inference(res,[status(thm),theory(equality)],[11,4]),
[iquote('0:Res:11.3,4.0')] ).
cnf(39,plain,
( ~ product(u,v,multiplicative_inverse(a))
| ~ product(multiplicative_identity,u,w)
| product(w,v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.2')] ).
cnf(48,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[13,2]),
[iquote('0:Res:13.2,2.0')] ).
cnf(49,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[22,2]),
[iquote('0:Res:22.2,2.0')] ).
cnf(55,plain,
defined(multiplicative_inverse(a)),
inference(mrr,[status(thm)],[49,1]),
[iquote('0:MRR:49.0,1.0')] ).
cnf(56,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[48,1]),
[iquote('0:MRR:48.0,1.0')] ).
cnf(57,plain,
( ~ product(multiplicative_inverse(a),u,multiplicative_inverse(a))
| product(multiplicative_identity,u,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[3,39]),
[iquote('0:Res:3.0,39.0')] ).
cnf(72,plain,
( ~ product(multiplicative_identity,u,multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,u) ),
inference(res,[status(thm),theory(equality)],[3,33]),
[iquote('0:Res:3.0,33.0')] ).
cnf(90,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[12,14]),
[iquote('0:Res:12.1,14.0')] ).
cnf(97,plain,
( ~ defined(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[90,57]),
[iquote('0:Res:90.1,57.0')] ).
cnf(98,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(ssi,[status(thm)],[97,55]),
[iquote('0:SSi:97.0,55.0')] ).
cnf(101,plain,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[56,72]),
[iquote('0:Res:56.0,72.1')] ).
cnf(103,plain,
$false,
inference(mrr,[status(thm)],[101,98]),
[iquote('0:MRR:101.0,98.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD032-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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 : Tue Jun 7 01:56:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 61 clauses, backtracked 0 clauses, performed 0 splits and kept 71 clauses.
% 0.18/0.42 SPASS allocated 75693 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.04 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 3, length 22 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : a_is_defined not_sum_2 product_3 not_product_4 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication well_definedness_of_multiplicative_inverse
% 0.18/0.42
%------------------------------------------------------------------------------