TSTP Solution File: FLD014-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD014-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 1.81s 1.98s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 14 unt; 0 nHn; 38 RR)
% Number of literals : 76 ( 0 equ; 43 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 : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD014-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD014-3.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,a,b),
file('FLD014-3.p',unknown),
[] ).
cnf(4,axiom,
~ sum__dfg(additive_identity,additive_inverse(a),additive_inverse(b)),
file('FLD014-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD014-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD014-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD014-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD014-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD014-3.p',unknown),
[] ).
cnf(18,axiom,
defined(additive_identity),
file('FLD014-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD014-3.p',unknown),
[] ).
cnf(34,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(a,w,u)
| sum__dfg(b,w,v) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.0')] ).
cnf(35,plain,
sum__dfg(a,additive_identity,b),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(46,plain,
( ~ sum__dfg(u,v,additive_identity)
| ~ sum__dfg(u,w,additive_inverse(b))
| ~ sum__dfg(v,additive_inverse(a),w) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.3,4.0')] ).
cnf(73,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[7,9]),
[iquote('0:Res:7.1,9.0')] ).
cnf(74,plain,
( ~ defined(u)
| sum__dfg(u,additive_inverse(u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.0')] ).
cnf(126,plain,
( ~ defined(u)
| ~ sum__dfg(a,v,u)
| sum__dfg(b,v,u) ),
inference(res,[status(thm),theory(equality)],[7,34]),
[iquote('0:Res:7.1,34.0')] ).
cnf(166,plain,
( ~ defined(a)
| ~ defined(a)
| sum__dfg(b,additive_identity,a) ),
inference(res,[status(thm),theory(equality)],[73,126]),
[iquote('0:Res:73.1,126.1')] ).
cnf(168,plain,
( ~ defined(a)
| ~ defined(additive_identity)
| sum__dfg(b,additive_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[74,126]),
[iquote('0:Res:74.1,126.1')] ).
cnf(169,plain,
( ~ defined(a)
| sum__dfg(b,additive_identity,a) ),
inference(obv,[status(thm),theory(equality)],[166]),
[iquote('0:Obv:166.0')] ).
cnf(170,plain,
sum__dfg(b,additive_identity,a),
inference(ssi,[status(thm)],[169,1]),
[iquote('0:SSi:169.0,1.0')] ).
cnf(171,plain,
sum__dfg(b,additive_inverse(a),additive_identity),
inference(ssi,[status(thm)],[168,18,1]),
[iquote('0:SSi:168.1,168.0,18.0,1.0')] ).
cnf(188,plain,
( ~ defined(u)
| ~ sum__dfg(v,u,w)
| ~ sum__dfg(x,v,additive_identity)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.1,5.0')] ).
cnf(202,plain,
sum__dfg(additive_inverse(a),b,additive_identity),
inference(res,[status(thm),theory(equality)],[171,9]),
[iquote('0:Res:171.0,9.0')] ).
cnf(642,plain,
( ~ defined(additive_inverse(b))
| ~ sum__dfg(additive_inverse(b),u,additive_identity)
| ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[73,46]),
[iquote('0:Res:73.1,46.1')] ).
cnf(644,plain,
( ~ sum__dfg(additive_inverse(b),u,additive_identity)
| ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
inference(ssi,[status(thm)],[642,19,2]),
[iquote('0:SSi:642.0,19.0,2.1')] ).
cnf(895,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[35,188]),
[iquote('0:Res:35.0,188.1')] ).
cnf(935,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(u,b,additive_identity)
| sum__dfg(u,a,additive_identity) ),
inference(res,[status(thm),theory(equality)],[170,188]),
[iquote('0:Res:170.0,188.1')] ).
cnf(957,plain,
( ~ sum__dfg(u,a,additive_identity)
| sum__dfg(u,b,additive_identity) ),
inference(ssi,[status(thm)],[895,18]),
[iquote('0:SSi:895.0,18.0')] ).
cnf(960,plain,
( ~ sum__dfg(u,b,additive_identity)
| sum__dfg(u,a,additive_identity) ),
inference(ssi,[status(thm)],[935,18]),
[iquote('0:SSi:935.0,18.0')] ).
cnf(1217,plain,
( ~ sum__dfg(u,b,additive_identity)
| sum__dfg(a,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[960,9]),
[iquote('0:Res:960.1,9.0')] ).
cnf(1998,plain,
( ~ defined(b)
| sum__dfg(a,additive_inverse(b),additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,1217]),
[iquote('0:Res:8.1,1217.0')] ).
cnf(1999,plain,
sum__dfg(a,additive_inverse(a),additive_identity),
inference(res,[status(thm),theory(equality)],[202,1217]),
[iquote('0:Res:202.0,1217.0')] ).
cnf(2002,plain,
sum__dfg(a,additive_inverse(b),additive_identity),
inference(ssi,[status(thm)],[1998,2]),
[iquote('0:SSi:1998.0,2.0')] ).
cnf(2025,plain,
sum__dfg(additive_inverse(b),a,additive_identity),
inference(res,[status(thm),theory(equality)],[2002,9]),
[iquote('0:Res:2002.0,9.0')] ).
cnf(2109,plain,
sum__dfg(additive_inverse(b),b,additive_identity),
inference(res,[status(thm),theory(equality)],[2025,957]),
[iquote('0:Res:2025.0,957.0')] ).
cnf(5321,plain,
( ~ sum__dfg(additive_inverse(b),b,additive_identity)
| ~ sum__dfg(a,additive_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[960,644]),
[iquote('0:Res:960.1,644.0')] ).
cnf(5328,plain,
$false,
inference(mrr,[status(thm)],[5321,2109,1999]),
[iquote('0:MRR:5321.0,5321.1,2109.0,1999.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD014-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 18:54:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/1.98
% 1.81/1.98 SPASS V 3.9
% 1.81/1.98 SPASS beiseite: Proof found.
% 1.81/1.98 % SZS status Theorem
% 1.81/1.98 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.81/1.98 SPASS derived 4036 clauses, backtracked 13 clauses, performed 5 splits and kept 2885 clauses.
% 1.81/1.98 SPASS allocated 79700 KBytes.
% 1.81/1.98 SPASS spent 0:00:01.61 on the problem.
% 1.81/1.98 0:00:00.04 for the input.
% 1.81/1.98 0:00:00.00 for the FLOTTER CNF translation.
% 1.81/1.98 0:00:00.04 for inferences.
% 1.81/1.98 0:00:00.01 for the backtracking.
% 1.81/1.98 0:00:01.49 for the reduction.
% 1.81/1.98
% 1.81/1.98
% 1.81/1.98 Here is a proof with depth 8, length 38 :
% 1.81/1.98 % SZS output start Refutation
% See solution above
% 1.81/1.98 Formulae used in the proof : a_is_defined b_is_defined sum_3 not_sum_4 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_identity well_definedness_of_additive_inverse
% 1.81/1.98
%------------------------------------------------------------------------------