TSTP Solution File: FLD016-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD016-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 02:28:18 EDT 2022
% Result : Unsatisfiable 0.21s 0.58s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 8 unt; 0 nHn; 17 RR)
% Number of literals : 33 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD016-3.p',unknown),
[] ).
cnf(4,axiom,
defined(v__dfg),
file('FLD016-3.p',unknown),
[] ).
cnf(5,axiom,
sum__dfg(a,u__dfg,b),
file('FLD016-3.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(a,v__dfg,b),
file('FLD016-3.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,u__dfg,v__dfg),
file('FLD016-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD016-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD016-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD016-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD016-3.p',unknown),
[] ).
cnf(41,plain,
( ~ sum__dfg(u,v__dfg,v)
| ~ sum__dfg(w,a,u)
| sum__dfg(w,b,v) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.1')] ).
cnf(61,plain,
( ~ sum__dfg(u,v,v__dfg)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,u__dfg,v) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.3,7.0')] ).
cnf(70,plain,
( ~ sum__dfg(u,b,v__dfg)
| ~ sum__dfg(u,a,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,61]),
[iquote('0:Res:5.0,61.1')] ).
cnf(618,plain,
( ~ defined(v__dfg)
| ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,b,v__dfg) ),
inference(res,[status(thm),theory(equality)],[10,41]),
[iquote('0:Res:10.1,41.0')] ).
cnf(636,plain,
( ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,b,v__dfg) ),
inference(ssi,[status(thm)],[618,4]),
[iquote('0:SSi:618.0,4.0')] ).
cnf(637,plain,
~ sum__dfg(u,a,additive_identity),
inference(mrr,[status(thm)],[636,70]),
[iquote('0:MRR:636.1,70.0')] ).
cnf(645,plain,
~ defined(a),
inference(res,[status(thm),theory(equality)],[11,637]),
[iquote('0:Res:11.1,637.0')] ).
cnf(647,plain,
$false,
inference(ssi,[status(thm)],[645,1]),
[iquote('0:SSi:645.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD016-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 6 20:18:46 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.58
% 0.21/0.58 SPASS V 3.9
% 0.21/0.58 SPASS beiseite: Proof found.
% 0.21/0.58 % SZS status Theorem
% 0.21/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.58 SPASS derived 538 clauses, backtracked 13 clauses, performed 2 splits and kept 491 clauses.
% 0.21/0.58 SPASS allocated 76181 KBytes.
% 0.21/0.58 SPASS spent 0:00:00.21 on the problem.
% 0.21/0.58 0:00:00.04 for the input.
% 0.21/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.58 0:00:00.01 for inferences.
% 0.21/0.58 0:00:00.00 for the backtracking.
% 0.21/0.58 0:00:00.14 for the reduction.
% 0.21/0.58
% 0.21/0.58
% 0.21/0.58 Here is a proof with depth 3, length 17 :
% 0.21/0.58 % SZS output start Refutation
% See solution above
% 0.21/0.58 Formulae used in the proof : a_is_defined v_is_defined sum_5 sum_6 not_sum_7 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition
% 0.21/0.58
%------------------------------------------------------------------------------