TSTP Solution File: FLD018-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD018-3 : 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 02:28:19 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% 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('FLD018-3.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(additive_identity,a,additive_identity),
file('FLD018-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,additive_inverse(a),additive_identity),
file('FLD018-3.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('FLD018-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD018-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD018-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD018-3.p',unknown),
[] ).
cnf(35,plain,
( ~ sum__dfg(u,v,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(47,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,additive_inverse(a),v) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.3,3.0')] ).
cnf(50,plain,
( ~ sum__dfg(a,u,a)
| sum__dfg(additive_identity,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2,35]),
[iquote('0:Res:2.0,35.0')] ).
cnf(58,plain,
( ~ sum__dfg(additive_identity,u,additive_identity)
| ~ sum__dfg(a,additive_inverse(a),u) ),
inference(res,[status(thm),theory(equality)],[2,47]),
[iquote('0:Res:2.0,47.0')] ).
cnf(75,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(77,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(78,plain,
( ~ defined(a)
| sum__dfg(additive_identity,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[75,50]),
[iquote('0:Res:75.1,50.0')] ).
cnf(80,plain,
sum__dfg(additive_identity,additive_identity,additive_identity),
inference(ssi,[status(thm)],[78,1]),
[iquote('0:SSi:78.0,1.0')] ).
cnf(88,plain,
( ~ defined(a)
| ~ sum__dfg(additive_identity,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[77,58]),
[iquote('0:Res:77.1,58.1')] ).
cnf(89,plain,
~ sum__dfg(additive_identity,additive_identity,additive_identity),
inference(ssi,[status(thm)],[88,1]),
[iquote('0:SSi:88.0,1.0')] ).
cnf(90,plain,
$false,
inference(mrr,[status(thm)],[89,80]),
[iquote('0:MRR:89.0,80.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % 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 23:03:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.19/0.42 SPASS allocated 75672 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 18 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 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
% 0.19/0.42
%------------------------------------------------------------------------------