TSTP Solution File: FLD005-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD005-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 02:28:13 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 4 unt; 0 nHn; 17 RR)
% Number of literals : 39 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD005-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD005-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(a,u,b),
file('FLD005-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD005-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD005-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD005-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD005-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD005-3.p',unknown),
[] ).
cnf(22,axiom,
( ~ defined(u)
| ~ defined(v)
| sum__dfg(v,u,add(v,u)) ),
file('FLD005-3.p',unknown),
[] ).
cnf(31,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,b)
| ~ sum__dfg(a,u,x) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.3,3.0')] ).
cnf(45,plain,
( ~ defined(u)
| sum__dfg(u,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,8]),
[iquote('0:Res:7.1,8.0')] ).
cnf(65,plain,
( ~ defined(u)
| ~ defined(v)
| ~ sum__dfg(w,u,b)
| ~ sum__dfg(a,v,w) ),
inference(res,[status(thm),theory(equality)],[22,31]),
[iquote('0:Res:22.2,31.0')] ).
cnf(162,plain,
( ~ defined(b)
| ~ defined(b)
| ~ defined(u)
| ~ sum__dfg(a,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[6,65]),
[iquote('0:Res:6.1,65.2')] ).
cnf(165,plain,
( ~ defined(b)
| ~ defined(u)
| ~ sum__dfg(a,u,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[162]),
[iquote('0:Obv:162.0')] ).
cnf(166,plain,
( ~ defined(u)
| ~ sum__dfg(a,u,additive_identity) ),
inference(ssi,[status(thm)],[165,2]),
[iquote('0:SSi:165.0,2.0')] ).
cnf(167,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[45,166]),
[iquote('0:Res:45.1,166.1')] ).
cnf(169,plain,
$false,
inference(ssi,[status(thm)],[167,18,1]),
[iquote('0:SSi:167.1,167.0,18.0,1.0,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD005-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 6 11:21:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 109 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.45 SPASS allocated 75767 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 4, length 17 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 associativity_addition_1 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse totality_of_addition
% 0.20/0.45
%------------------------------------------------------------------------------