TSTP Solution File: FLD010-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD010-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 02:28:15 EDT 2022
% Result : Unsatisfiable 0.87s 1.03s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 9 unt; 2 nHn; 27 RR)
% Number of literals : 64 ( 0 equ; 44 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 : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ sum__dfg(additive_identity,multiplicative_identity,additive_identity),
file('FLD010-5.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('FLD010-5.p',unknown),
[] ).
cnf(5,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD010-5.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD010-5.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD010-5.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD010-5.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD010-5.p',unknown),
[] ).
cnf(14,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ product(z,y,u)
| ~ sum__dfg(z,x,x1)
| product(x1,y,w) ),
file('FLD010-5.p',unknown),
[] ).
cnf(16,axiom,
defined(additive_identity),
file('FLD010-5.p',unknown),
[] ).
cnf(19,axiom,
defined(multiplicative_identity),
file('FLD010-5.p',unknown),
[] ).
cnf(20,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD010-5.p',unknown),
[] ).
cnf(29,plain,
( ~ defined(multiplicative_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.2,1.0')] ).
cnf(30,plain,
( ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.2,1.0')] ).
cnf(40,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,x,additive_identity)
| ~ product(w,x,multiplicative_identity)
| ~ product(v,x,multiplicative_inverse(multiplicative_identity)) ),
inference(res,[status(thm),theory(equality)],[13,2]),
[iquote('0:Res:13.4,2.0')] ).
cnf(41,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(mrr,[status(thm)],[30,19]),
[iquote('0:MRR:30.0,19.0')] ).
cnf(42,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(mrr,[status(thm)],[29,19]),
[iquote('0:MRR:29.0,19.0')] ).
cnf(51,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[10,12]),
[iquote('0:Res:10.1,12.0')] ).
cnf(211,plain,
( ~ defined(u)
| ~ product(v,w,u)
| ~ product(x,w,additive_identity)
| ~ sum__dfg(x,v,y)
| product(y,w,u) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.1,14.0')] ).
cnf(966,plain,
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ sum__dfg(u,multiplicative_inverse(multiplicative_identity),v)
| ~ product(u,multiplicative_identity,additive_identity)
| ~ product(v,multiplicative_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[51,40]),
[iquote('0:Res:51.1,40.3')] ).
cnf(970,plain,
( ~ sum__dfg(u,multiplicative_inverse(multiplicative_identity),v)
| ~ product(u,multiplicative_identity,additive_identity)
| ~ product(v,multiplicative_identity,multiplicative_identity) ),
inference(ssi,[status(thm)],[966,41]),
[iquote('0:SSi:966.0,41.0')] ).
cnf(1575,plain,
( ~ defined(multiplicative_identity)
| ~ product(u,multiplicative_identity,additive_identity)
| ~ sum__dfg(u,multiplicative_inverse(multiplicative_identity),v)
| product(v,multiplicative_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[42,211]),
[iquote('0:Res:42.0,211.1')] ).
cnf(1607,plain,
( ~ product(u,multiplicative_identity,additive_identity)
| ~ sum__dfg(u,multiplicative_inverse(multiplicative_identity),v)
| product(v,multiplicative_identity,multiplicative_identity) ),
inference(ssi,[status(thm)],[1575,19]),
[iquote('0:SSi:1575.0,19.0')] ).
cnf(1608,plain,
( ~ product(u,multiplicative_identity,additive_identity)
| ~ sum__dfg(u,multiplicative_inverse(multiplicative_identity),v) ),
inference(mrr,[status(thm)],[1607,970]),
[iquote('0:MRR:1607.2,970.2')] ).
cnf(2292,plain,
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,1608]),
[iquote('0:Res:5.1,1608.1')] ).
cnf(2298,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(ssi,[status(thm)],[2292,41]),
[iquote('0:SSi:2292.0,41.0')] ).
cnf(2384,plain,
~ defined(additive_identity),
inference(res,[status(thm),theory(equality)],[51,2298]),
[iquote('0:Res:51.1,2298.0')] ).
cnf(2385,plain,
$false,
inference(ssi,[status(thm)],[2384,16]),
[iquote('0:SSi:2384.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD010-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 15:08:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.87/1.03
% 0.87/1.03 SPASS V 3.9
% 0.87/1.03 SPASS beiseite: Proof found.
% 0.87/1.03 % SZS status Theorem
% 0.87/1.03 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.87/1.03 SPASS derived 1750 clauses, backtracked 9 clauses, performed 1 splits and kept 1229 clauses.
% 0.87/1.03 SPASS allocated 77699 KBytes.
% 0.87/1.03 SPASS spent 0:00:00.67 on the problem.
% 0.87/1.03 0:00:00.03 for the input.
% 0.87/1.03 0:00:00.00 for the FLOTTER CNF translation.
% 0.87/1.03 0:00:00.02 for inferences.
% 0.87/1.03 0:00:00.02 for the backtracking.
% 0.87/1.03 0:00:00.57 for the reduction.
% 0.87/1.03
% 0.87/1.03
% 0.87/1.03 Here is a proof with depth 4, length 27 :
% 0.87/1.03 % SZS output start Refutation
% See solution above
% 0.87/1.03 Formulae used in the proof : not_sum_1 not_sum_2 existence_of_identity_addition existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1 distributivity_2 well_definedness_of_additive_identity well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse
% 0.87/1.03
%------------------------------------------------------------------------------