TSTP Solution File: NUN134-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Mon Jul 18 16:38:52 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(a43_(u,v),a43_(v,u)),
file('NUN134-1.p',unknown),
[] ).
cnf(2,axiom,
equal(a43_(a43_(u,v),w),a43_(u,a43_(v,w))),
file('NUN134-1.p',unknown),
[] ).
cnf(3,axiom,
equal(times(u,v),times(v,u)),
file('NUN134-1.p',unknown),
[] ).
cnf(10,axiom,
equal(a43_(s(u),v),s(a43_(u,v))),
file('NUN134-1.p',unknown),
[] ).
cnf(11,axiom,
equal(times(s(u),v),a43_(v,times(u,v))),
file('NUN134-1.p',unknown),
[] ).
cnf(13,axiom,
equal(a43_(s(u),sum__dfg(u)),sum__dfg(s(u))),
file('NUN134-1.p',unknown),
[] ).
cnf(14,axiom,
equal(times(a,s(a)),a43_(sum__dfg(a),sum__dfg(a))),
file('NUN134-1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(times(s(a),s(s(a))),a43_(sum__dfg(s(a)),sum__dfg(s(a)))),
file('NUN134-1.p',unknown),
[] ).
cnf(16,plain,
equal(s(a43_(u,sum__dfg(u))),sum__dfg(s(u))),
inference(rew,[status(thm),theory(equality)],[10,13]),
[iquote('0:Rew:10.0,13.0')] ).
cnf(17,plain,
~ equal(s(s(a43_(a,times(a,s(s(a)))))),a43_(sum__dfg(s(a)),sum__dfg(s(a)))),
inference(rew,[status(thm),theory(equality)],[10,15,11]),
[iquote('0:Rew:10.0,15.0,10.0,15.0,11.0,15.0')] ).
cnf(64,plain,
equal(s(a43_(u,v)),a43_(v,s(u))),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(68,plain,
equal(s(a43_(a43_(u,sum__dfg(u)),v)),a43_(sum__dfg(s(u)),v)),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.0,10.0')] ).
cnf(70,plain,
equal(a43_(sum__dfg(s(u)),v),s(a43_(u,a43_(sum__dfg(u),v)))),
inference(rew,[status(thm),theory(equality)],[2,68]),
[iquote('0:Rew:2.0,68.0')] ).
cnf(71,plain,
~ equal(s(s(a43_(a,times(a,s(s(a)))))),s(a43_(a,a43_(sum__dfg(a),sum__dfg(s(a)))))),
inference(rew,[status(thm),theory(equality)],[70,17]),
[iquote('0:Rew:70.0,17.0')] ).
cnf(82,plain,
equal(a43_(u,s(v)),s(a43_(u,v))),
inference(spr,[status(thm),theory(equality)],[1,64]),
[iquote('0:SpR:1.0,64.0')] ).
cnf(86,plain,
equal(s(a43_(a43_(u,sum__dfg(u)),v)),a43_(v,sum__dfg(s(u)))),
inference(spr,[status(thm),theory(equality)],[16,64]),
[iquote('0:SpR:16.0,64.0')] ).
cnf(99,plain,
equal(s(a43_(u,a43_(sum__dfg(u),v))),a43_(v,sum__dfg(s(u)))),
inference(rew,[status(thm),theory(equality)],[2,86]),
[iquote('0:Rew:2.0,86.0')] ).
cnf(100,plain,
~ equal(s(s(a43_(a,times(a,s(s(a)))))),s(a43_(a,s(a43_(a,a43_(sum__dfg(a),sum__dfg(a))))))),
inference(rew,[status(thm),theory(equality)],[99,71]),
[iquote('0:Rew:99.0,71.0')] ).
cnf(101,plain,
~ equal(s(s(a43_(a,times(a,s(s(a)))))),s(s(a43_(a,a43_(a,a43_(sum__dfg(a),sum__dfg(a))))))),
inference(rew,[status(thm),theory(equality)],[82,100]),
[iquote('0:Rew:82.0,100.0')] ).
cnf(149,plain,
equal(a43_(u,times(v,u)),times(u,s(v))),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(157,plain,
equal(a43_(a,times(a,a)),a43_(sum__dfg(a),sum__dfg(a))),
inference(rew,[status(thm),theory(equality)],[149,14]),
[iquote('0:Rew:149.0,14.0')] ).
cnf(244,plain,
equal(times(u,s(v)),a43_(u,times(u,v))),
inference(spr,[status(thm),theory(equality)],[3,149]),
[iquote('0:SpR:3.0,149.0')] ).
cnf(263,plain,
~ equal(s(s(a43_(a,a43_(a,times(a,s(a)))))),s(s(a43_(a,a43_(a,a43_(sum__dfg(a),sum__dfg(a))))))),
inference(rew,[status(thm),theory(equality)],[244,101]),
[iquote('0:Rew:244.0,101.0')] ).
cnf(281,plain,
~ equal(s(s(a43_(a,a43_(a,a43_(a,times(a,a)))))),s(s(a43_(a,a43_(a,a43_(sum__dfg(a),sum__dfg(a))))))),
inference(rew,[status(thm),theory(equality)],[244,263]),
[iquote('0:Rew:244.0,263.0')] ).
cnf(282,plain,
~ equal(s(s(a43_(a,a43_(a,a43_(sum__dfg(a),sum__dfg(a)))))),s(s(a43_(a,a43_(a,a43_(sum__dfg(a),sum__dfg(a))))))),
inference(rew,[status(thm),theory(equality)],[157,281]),
[iquote('0:Rew:157.0,281.0')] ).
cnf(283,plain,
$false,
inference(obv,[status(thm),theory(equality)],[282]),
[iquote('0:Obv:282.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n020.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Thu Jun 2 04:32:08 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 172 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.18/0.41 SPASS allocated 63382 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 2, length 26 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : plus_comm plus_assoc times_comm plus_s times_s sum_s induction_hypothesis goal
% 0.18/0.41
%------------------------------------------------------------------------------