TSTP Solution File: FLD013-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD013-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 02:28:17 EDT 2022
% Result : Unsatisfiable 0.46s 0.63s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 44 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
defined(u__dfg),
file('FLD013-5.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(additive_identity,a,b),
file('FLD013-5.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(additive_identity,c,d),
file('FLD013-5.p',unknown),
[] ).
cnf(9,axiom,
sum__dfg(a,c,u__dfg),
file('FLD013-5.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(d,b,v__dfg),
file('FLD013-5.p',unknown),
[] ).
cnf(11,axiom,
~ sum__dfg(additive_identity,u__dfg,v__dfg),
file('FLD013-5.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD013-5.p',unknown),
[] ).
cnf(13,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD013-5.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD013-5.p',unknown),
[] ).
cnf(16,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD013-5.p',unknown),
[] ).
cnf(54,plain,
sum__dfg(c,a,u__dfg),
inference(res,[status(thm),theory(equality)],[9,16]),
[iquote('0:Res:9.0,16.0')] ).
cnf(64,plain,
( ~ sum__dfg(d,u,v)
| ~ sum__dfg(c,u,w)
| sum__dfg(additive_identity,w,v) ),
inference(res,[status(thm),theory(equality)],[8,12]),
[iquote('0:Res:8.0,12.0')] ).
cnf(65,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(c,w,u)
| sum__dfg(d,w,v) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.0,13.0')] ).
cnf(70,plain,
( ~ sum__dfg(u,d,v)
| ~ sum__dfg(u,additive_identity,w)
| sum__dfg(w,c,v) ),
inference(res,[status(thm),theory(equality)],[8,13]),
[iquote('0:Res:8.0,13.1')] ).
cnf(92,plain,
sum__dfg(a,additive_identity,b),
inference(res,[status(thm),theory(equality)],[7,16]),
[iquote('0:Res:7.0,16.0')] ).
cnf(110,plain,
( ~ defined(u)
| ~ sum__dfg(c,v,u)
| sum__dfg(d,v,u) ),
inference(res,[status(thm),theory(equality)],[14,65]),
[iquote('0:Res:14.1,65.0')] ).
cnf(139,plain,
( ~ defined(u__dfg)
| sum__dfg(d,a,u__dfg) ),
inference(res,[status(thm),theory(equality)],[54,110]),
[iquote('0:Res:54.0,110.1')] ).
cnf(145,plain,
sum__dfg(d,a,u__dfg),
inference(ssi,[status(thm)],[139,5]),
[iquote('0:SSi:139.0,5.0')] ).
cnf(152,plain,
sum__dfg(a,d,u__dfg),
inference(res,[status(thm),theory(equality)],[145,16]),
[iquote('0:Res:145.0,16.0')] ).
cnf(365,plain,
( ~ sum__dfg(c,b,u)
| sum__dfg(additive_identity,u,v__dfg) ),
inference(res,[status(thm),theory(equality)],[10,64]),
[iquote('0:Res:10.0,64.0')] ).
cnf(611,plain,
( ~ sum__dfg(a,additive_identity,u)
| sum__dfg(u,c,u__dfg) ),
inference(res,[status(thm),theory(equality)],[152,70]),
[iquote('0:Res:152.0,70.0')] ).
cnf(1061,plain,
sum__dfg(b,c,u__dfg),
inference(res,[status(thm),theory(equality)],[92,611]),
[iquote('0:Res:92.0,611.0')] ).
cnf(1075,plain,
sum__dfg(c,b,u__dfg),
inference(res,[status(thm),theory(equality)],[1061,16]),
[iquote('0:Res:1061.0,16.0')] ).
cnf(1077,plain,
sum__dfg(additive_identity,u__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[1075,365]),
[iquote('0:Res:1075.0,365.0')] ).
cnf(1084,plain,
$false,
inference(mrr,[status(thm)],[1077,11]),
[iquote('0:MRR:1077.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD013-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 23:37:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.63
% 0.46/0.63 SPASS V 3.9
% 0.46/0.63 SPASS beiseite: Proof found.
% 0.46/0.63 % SZS status Theorem
% 0.46/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.63 SPASS derived 906 clauses, backtracked 0 clauses, performed 2 splits and kept 776 clauses.
% 0.46/0.63 SPASS allocated 76527 KBytes.
% 0.46/0.63 SPASS spent 0:00:00.28 on the problem.
% 0.46/0.63 0:00:00.04 for the input.
% 0.46/0.63 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.63 0:00:00.01 for inferences.
% 0.46/0.63 0:00:00.00 for the backtracking.
% 0.46/0.63 0:00:00.21 for the reduction.
% 0.46/0.63
% 0.46/0.63
% 0.46/0.63 Here is a proof with depth 8, length 25 :
% 0.46/0.63 % SZS output start Refutation
% See solution above
% 0.46/0.63 Formulae used in the proof : u_is_defined sum_7 sum_8 sum_9 sum_10 not_sum_11 associativity_addition_1 associativity_addition_2 existence_of_identity_addition commutativity_addition
% 0.46/0.63
%------------------------------------------------------------------------------