TSTP Solution File: FLD019-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD019-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 02:28:19 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 6 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 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 : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD019-3.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(additive_identity,additive_inverse(a),additive_identity),
file('FLD019-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD019-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD019-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD019-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD019-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD019-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD019-3.p',unknown),
[] ).
cnf(35,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,a,v) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.3,3.0')] ).
cnf(42,plain,
( ~ sum__dfg(u,v,additive_inverse(a))
| ~ sum__dfg(additive_identity,u,w)
| sum__dfg(w,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.2')] ).
cnf(51,plain,
( ~ sum__dfg(additive_inverse(a),u,additive_inverse(a))
| sum__dfg(additive_identity,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,42]),
[iquote('0:Res:2.0,42.0')] ).
cnf(61,plain,
( ~ sum__dfg(additive_identity,u,additive_identity)
| ~ sum__dfg(additive_inverse(a),a,u) ),
inference(res,[status(thm),theory(equality)],[2,35]),
[iquote('0:Res:2.0,35.0')] ).
cnf(80,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.1,8.0')] ).
cnf(90,plain,
( ~ defined(additive_inverse(a))
| sum__dfg(additive_identity,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[80,51]),
[iquote('0:Res:80.1,51.0')] ).
cnf(91,plain,
sum__dfg(additive_identity,additive_identity,additive_identity),
inference(ssi,[status(thm)],[90,18,1]),
[iquote('0:SSi:90.0,18.0,1.1')] ).
cnf(93,plain,
( ~ defined(a)
| ~ sum__dfg(additive_identity,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,61]),
[iquote('0:Res:7.1,61.1')] ).
cnf(94,plain,
~ sum__dfg(additive_identity,additive_identity,additive_identity),
inference(ssi,[status(thm)],[93,1]),
[iquote('0:SSi:93.0,1.0')] ).
cnf(95,plain,
$false,
inference(mrr,[status(thm)],[94,91]),
[iquote('0:MRR:94.0,91.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD019-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 6 21:53:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 52 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses.
% 0.21/0.43 SPASS allocated 75678 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.43 0:00:00.04 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.00 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 3, length 18 :
% 0.21/0.43 % SZS output start Refutation
% See solution above
% 0.21/0.43 Formulae used in the proof : a_is_defined sum_2 not_sum_3 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse
% 0.21/0.43
%------------------------------------------------------------------------------