TSTP Solution File: LAT028-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Sun Jul 17 06:48:40 EDT 2022
% Result : Unsatisfiable 0.84s 1.01s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet2(u,u),u),
file('LAT028-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet2(u,v),meet2(v,u)),
file('LAT028-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet2(meet2(join(u,v),join(w,v)),v),v),
file('LAT028-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(meet2(u,v),meet2(w,v)),v),v),
file('LAT028-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(meet(a,b),meet2(a,b)),
file('LAT028-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,u),u),
file('LAT028-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT028-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT028-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(join(u,v),join(w,v)),v),v),
file('LAT028-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(meet(u,v),meet(w,v)),v),v),
file('LAT028-1.p',unknown),
[] ).
cnf(12,plain,
equal(join(u,join(meet(v,u),meet(w,u))),u),
inference(rew,[status(thm),theory(equality)],[9,11]),
[iquote('0:Rew:9.0,11.0')] ).
cnf(13,plain,
equal(meet(u,meet(join(v,u),join(w,u))),u),
inference(rew,[status(thm),theory(equality)],[8,10]),
[iquote('0:Rew:8.0,10.0')] ).
cnf(14,plain,
equal(join(u,join(meet2(v,u),meet2(w,u))),u),
inference(rew,[status(thm),theory(equality)],[9,4]),
[iquote('0:Rew:9.0,4.0')] ).
cnf(15,plain,
equal(meet2(u,meet2(join(v,u),join(w,u))),u),
inference(rew,[status(thm),theory(equality)],[2,3]),
[iquote('0:Rew:2.0,3.0')] ).
cnf(39,plain,
equal(join(u,join(meet(v,u),meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[8,12]),
[iquote('0:SpR:8.0,12.0')] ).
cnf(44,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(139,plain,
equal(meet(join(meet2(u,v),meet2(w,v)),meet(join(x,join(meet2(u,v),meet2(w,v))),v)),join(meet2(u,v),meet2(w,v))),
inference(spr,[status(thm),theory(equality)],[14,13]),
[iquote('0:SpR:14.0,13.0')] ).
cnf(143,plain,
equal(join(u,join(meet2(v,u),meet2(u,w))),u),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(156,plain,
equal(meet(join(meet2(u,v),meet2(w,v)),meet(v,join(x,join(meet2(u,v),meet2(w,v))))),join(meet2(u,v),meet2(w,v))),
inference(rew,[status(thm),theory(equality)],[8,139]),
[iquote('0:Rew:8.0,139.0')] ).
cnf(235,plain,
equal(meet2(join(meet(u,v),meet(w,v)),meet2(v,join(x,join(meet(u,v),meet(w,v))))),join(meet(u,v),meet(w,v))),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.0,15.0')] ).
cnf(242,plain,
equal(meet2(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(270,plain,
equal(meet2(meet(u,v),v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[44,242]),
[iquote('0:SpR:44.0,242.0')] ).
cnf(275,plain,
equal(meet2(u,meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[2,270]),
[iquote('0:Rew:2.0,270.0')] ).
cnf(367,plain,
equal(join(u,join(meet(u,v),meet(u,w))),u),
inference(spr,[status(thm),theory(equality)],[8,39]),
[iquote('0:SpR:8.0,39.0')] ).
cnf(711,plain,
equal(join(u,join(meet2(u,v),meet2(u,w))),u),
inference(spr,[status(thm),theory(equality)],[2,143]),
[iquote('0:SpR:2.0,143.0')] ).
cnf(2432,plain,
equal(meet(join(meet2(u,v),meet2(u,v)),meet(v,u)),join(meet2(u,v),meet2(u,v))),
inference(spr,[status(thm),theory(equality)],[711,156]),
[iquote('0:SpR:711.0,156.0')] ).
cnf(2498,plain,
equal(meet(meet2(u,v),meet(v,u)),meet2(u,v)),
inference(rew,[status(thm),theory(equality)],[7,2432]),
[iquote('0:Rew:7.0,2432.0')] ).
cnf(3482,plain,
equal(meet2(join(meet(u,v),meet(u,v)),meet2(v,u)),join(meet(u,v),meet(u,v))),
inference(spr,[status(thm),theory(equality)],[367,235]),
[iquote('0:SpR:367.0,235.0')] ).
cnf(3530,plain,
equal(meet2(meet2(u,v),meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[2,3482,7]),
[iquote('0:Rew:2.0,3482.0,7.0,3482.0')] ).
cnf(4045,plain,
equal(meet2(meet(u,v),meet2(v,u)),meet2(v,u)),
inference(spr,[status(thm),theory(equality)],[2498,275]),
[iquote('0:SpR:2498.0,275.0')] ).
cnf(4116,plain,
equal(meet2(meet2(u,v),meet(v,u)),meet2(u,v)),
inference(rew,[status(thm),theory(equality)],[2,4045]),
[iquote('0:Rew:2.0,4045.0')] ).
cnf(4117,plain,
equal(meet(u,v),meet2(v,u)),
inference(rew,[status(thm),theory(equality)],[3530,4116]),
[iquote('0:Rew:3530.0,4116.0')] ).
cnf(4132,plain,
~ equal(meet2(b,a),meet2(a,b)),
inference(rew,[status(thm),theory(equality)],[4117,5]),
[iquote('0:Rew:4117.0,5.0')] ).
cnf(4469,plain,
~ equal(meet2(a,b),meet2(a,b)),
inference(rew,[status(thm),theory(equality)],[2,4132]),
[iquote('0:Rew:2.0,4132.0')] ).
cnf(4470,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4469]),
[iquote('0:Obv:4469.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 : Wed Jun 29 23:14:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.84/1.01
% 0.84/1.01 SPASS V 3.9
% 0.84/1.01 SPASS beiseite: Proof found.
% 0.84/1.01 % SZS status Theorem
% 0.84/1.01 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.01 SPASS derived 3031 clauses, backtracked 0 clauses, performed 0 splits and kept 441 clauses.
% 0.84/1.01 SPASS allocated 68368 KBytes.
% 0.84/1.01 SPASS spent 0:00:00.64 on the problem.
% 0.84/1.01 0:00:00.04 for the input.
% 0.84/1.01 0:00:00.00 for the FLOTTER CNF translation.
% 0.84/1.01 0:00:00.03 for inferences.
% 0.84/1.01 0:00:00.00 for the backtracking.
% 0.84/1.01 0:00:00.55 for the reduction.
% 0.84/1.01
% 0.84/1.01
% 0.84/1.01 Here is a proof with depth 4, length 35 :
% 0.84/1.01 % SZS output start Refutation
% See solution above
% 0.84/1.01 Formulae used in the proof : idempotence_of_meet2 commutativity_of_meet2 wal_1_2 wal_2_2 name__dfg idempotence_of_join commutativity_of_meet commutativity_of_join wal_1 wal_2
% 0.84/1.01
%------------------------------------------------------------------------------