%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD013-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 10 unt; 0 nHn; 21 RR)
% Number of literals : 40 ( 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 : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
defined(u__dfg),
file('FLD013-4.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,a,b),
file('FLD013-4.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(additive_identity,c,d),
file('FLD013-4.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(a,c,u__dfg),
file('FLD013-4.p',unknown),
[] ).
cnf(9,axiom,
~ sum__dfg(d,b,u__dfg),
file('FLD013-4.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD013-4.p',unknown),
[] ).
cnf(11,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD013-4.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD013-4.p',unknown),
[] ).
cnf(14,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD013-4.p',unknown),
[] ).
cnf(51,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(c,w,u)
| sum__dfg(d,w,v) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.0,11.0')] ).
cnf(62,plain,
( ~ sum__dfg(b,u,v)
| ~ sum__dfg(a,u,w)
| sum__dfg(additive_identity,w,v) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.0')] ).
cnf(63,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(a,w,u)
| sum__dfg(b,w,v) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.0,11.0')] ).
cnf(111,plain,
( ~ defined(u)
| ~ sum__dfg(a,v,u)
| sum__dfg(b,v,u) ),
inference(res,[status(thm),theory(equality)],[12,63]),
[iquote('0:Res:12.1,63.0')] ).
cnf(133,plain,
( ~ defined(u__dfg)
| sum__dfg(b,c,u__dfg) ),
inference(res,[status(thm),theory(equality)],[8,111]),
[iquote('0:Res:8.0,111.1')] ).
cnf(140,plain,
sum__dfg(b,c,u__dfg),
inference(ssi,[status(thm)],[133,5]),
[iquote('0:SSi:133.0,5.0')] ).
cnf(164,plain,
sum__dfg(c,b,u__dfg),
inference(res,[status(thm),theory(equality)],[140,14]),
[iquote('0:Res:140.0,14.0')] ).
cnf(353,plain,
( ~ sum__dfg(a,c,u)
| sum__dfg(additive_identity,u,u__dfg) ),
inference(res,[status(thm),theory(equality)],[140,62]),
[iquote('0:Res:140.0,62.0')] ).
cnf(391,plain,
sum__dfg(additive_identity,u__dfg,u__dfg),
inference(res,[status(thm),theory(equality)],[8,353]),
[iquote('0:Res:8.0,353.0')] ).
cnf(418,plain,
( ~ sum__dfg(c,u,u__dfg)
| sum__dfg(d,u,u__dfg) ),
inference(res,[status(thm),theory(equality)],[391,51]),
[iquote('0:Res:391.0,51.0')] ).
cnf(622,plain,
sum__dfg(d,b,u__dfg),
inference(res,[status(thm),theory(equality)],[164,418]),
[iquote('0:Res:164.0,418.0')] ).
cnf(623,plain,
$false,
inference(mrr,[status(thm)],[622,9]),
[iquote('0:MRR:622.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD013-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 6 19:35:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.52
% 0.18/0.52 SPASS V 3.9
% 0.18/0.52 SPASS beiseite: Proof found.
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52 SPASS derived 504 clauses, backtracked 0 clauses, performed 1 splits and kept 444 clauses.
% 0.18/0.52 SPASS allocated 76182 KBytes.
% 0.18/0.52 SPASS spent 0:00:00.18 on the problem.
% 0.18/0.52 0:00:00.04 for the input.
% 0.18/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.52 0:00:00.01 for inferences.
% 0.18/0.52 0:00:00.00 for the backtracking.
% 0.18/0.52 0:00:00.11 for the reduction.
% 0.18/0.52
% 0.18/0.52
% 0.18/0.52 Here is a proof with depth 7, length 21 :
% 0.18/0.52 % SZS output start Refutation
% See solution above
% 0.18/0.52 Formulae used in the proof : u_is_defined sum_6 sum_7 sum_8 not_sum_9 associativity_addition_1 associativity_addition_2 existence_of_identity_addition commutativity_addition
% 0.18/0.52
%------------------------------------------------------------------------------