TSTP Solution File: FLD015-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD015-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 0.13s 0.34s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 9 unt; 0 nHn; 22 RR)
% Number of literals : 41 ( 0 equ; 27 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 : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD015-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD015-3.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,additive_inverse(a),additive_inverse(b)),
file('FLD015-3.p',unknown),
[] ).
cnf(4,axiom,
~ sum__dfg(additive_identity,a,b),
file('FLD015-3.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('FLD015-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD015-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD015-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD015-3.p',unknown),
[] ).
cnf(18,axiom,
defined(additive_identity),
file('FLD015-3.p',unknown),
[] ).
cnf(34,plain,
( ~ sum__dfg(u,v,b)
| ~ sum__dfg(u,w,additive_identity)
| ~ sum__dfg(w,a,v) ),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.3,4.0')] ).
cnf(39,plain,
( ~ sum__dfg(additive_identity,u,v)
| ~ sum__dfg(additive_inverse(a),w,u)
| sum__dfg(additive_inverse(b),w,v) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.0')] ).
cnf(70,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(72,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(122,plain,
( ~ defined(b)
| ~ sum__dfg(b,u,additive_identity)
| ~ sum__dfg(u,a,additive_identity) ),
inference(res,[status(thm),theory(equality)],[70,34]),
[iquote('0:Res:70.1,34.0')] ).
cnf(124,plain,
( ~ sum__dfg(b,u,additive_identity)
| ~ sum__dfg(u,a,additive_identity) ),
inference(ssi,[status(thm)],[122,2]),
[iquote('0:SSi:122.0,2.0')] ).
cnf(131,plain,
( ~ defined(b)
| ~ sum__dfg(additive_inverse(b),a,additive_identity) ),
inference(res,[status(thm),theory(equality)],[72,124]),
[iquote('0:Res:72.1,124.0')] ).
cnf(133,plain,
~ sum__dfg(additive_inverse(b),a,additive_identity),
inference(ssi,[status(thm)],[131,2]),
[iquote('0:SSi:131.0,2.0')] ).
cnf(175,plain,
( ~ defined(a)
| ~ sum__dfg(additive_identity,additive_identity,u)
| sum__dfg(additive_inverse(b),a,u) ),
inference(res,[status(thm),theory(equality)],[8,39]),
[iquote('0:Res:8.1,39.1')] ).
cnf(181,plain,
( ~ sum__dfg(additive_identity,additive_identity,u)
| sum__dfg(additive_inverse(b),a,u) ),
inference(ssi,[status(thm)],[175,1]),
[iquote('0:SSi:175.0,1.0')] ).
cnf(187,plain,
~ sum__dfg(additive_identity,additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[181,133]),
[iquote('0:Res:181.1,133.0')] ).
cnf(195,plain,
~ defined(additive_identity),
inference(res,[status(thm),theory(equality)],[7,187]),
[iquote('0:Res:7.1,187.0')] ).
cnf(199,plain,
$false,
inference(ssi,[status(thm)],[195,18]),
[iquote('0:SSi:195.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : FLD015-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jun 6 14:52:19 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.13/0.34
% 0.13/0.34 SPASS V 3.9
% 0.13/0.34 SPASS beiseite: Proof found.
% 0.13/0.34 % SZS status Theorem
% 0.13/0.34 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 130 clauses.
% 0.13/0.34 SPASS allocated 75799 KBytes.
% 0.13/0.34 SPASS spent 0:00:00.06 on the problem.
% 0.13/0.34 0:00:00.02 for the input.
% 0.13/0.34 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.34 0:00:00.00 for inferences.
% 0.13/0.34 0:00:00.00 for the backtracking.
% 0.13/0.34 0:00:00.01 for the reduction.
% 0.13/0.34
% 0.13/0.34
% 0.13/0.34 Here is a proof with depth 5, length 22 :
% 0.13/0.34 % SZS output start Refutation
% See solution above
% 0.13/0.34 Formulae used in the proof : a_is_defined b_is_defined sum_3 not_sum_4 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_identity
% 0.13/0.34
%------------------------------------------------------------------------------