TSTP Solution File: FLD007-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD007-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 02:28:14 EDT 2022
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 5 unt; 0 nHn; 16 RR)
% Number of literals : 31 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD007-3.p',unknown),
[] ).
cnf(2,axiom,
~ sum__dfg(additive_identity,additive_inverse(additive_inverse(a)),a),
file('FLD007-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD007-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD007-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD007-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD007-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD007-3.p',unknown),
[] ).
cnf(32,plain,
( ~ sum__dfg(u,v,a)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,additive_inverse(additive_inverse(a)),v) ),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.3,2.0')] ).
cnf(43,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.1,7.0')] ).
cnf(44,plain,
( ~ defined(u)
| sum__dfg(u,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.1,7.0')] ).
cnf(81,plain,
( ~ defined(additive_inverse(a))
| ~ sum__dfg(u,additive_identity,a)
| ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[44,32]),
[iquote('0:Res:44.1,32.2')] ).
cnf(84,plain,
( ~ sum__dfg(u,additive_identity,a)
| ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
inference(ssi,[status(thm)],[81,17,1]),
[iquote('0:SSi:81.0,17.0,1.1')] ).
cnf(100,plain,
( ~ defined(a)
| ~ sum__dfg(a,additive_identity,a) ),
inference(res,[status(thm),theory(equality)],[44,84]),
[iquote('0:Res:44.1,84.1')] ).
cnf(101,plain,
~ sum__dfg(a,additive_identity,a),
inference(ssi,[status(thm)],[100,1]),
[iquote('0:SSi:100.0,1.0')] ).
cnf(103,plain,
~ defined(a),
inference(res,[status(thm),theory(equality)],[43,101]),
[iquote('0:Res:43.1,101.0')] ).
cnf(104,plain,
$false,
inference(ssi,[status(thm)],[103,1]),
[iquote('0:SSi:103.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : FLD007-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 6 19:42:07 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.45
% 0.22/0.45 SPASS V 3.9
% 0.22/0.45 SPASS beiseite: Proof found.
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.45 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.22/0.45 SPASS allocated 75713 KBytes.
% 0.22/0.45 SPASS spent 0:00:00.07 on the problem.
% 0.22/0.45 0:00:00.04 for the input.
% 0.22/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45 0:00:00.00 for inferences.
% 0.22/0.45 0:00:00.00 for the backtracking.
% 0.22/0.45 0:00:00.01 for the reduction.
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 Here is a proof with depth 4, length 16 :
% 0.22/0.45 % SZS output start Refutation
% See solution above
% 0.22/0.45 Formulae used in the proof : a_is_defined not_sum_2 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse
% 0.22/0.45
%------------------------------------------------------------------------------