TSTP Solution File: LAT008-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 06:48:33 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(u,join(u,v)),u),
file('LAT008-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(meet(u,v),meet(w,v)),meet(v,join(w,u))),
file('LAT008-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(a,meet(a,b)),a),
file('LAT008-1.p',unknown),
[] ).
cnf(5,plain,
equal(meet(meet(u,v),meet(v,join(w,u))),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(7,plain,
equal(meet(join(u,v),join(u,w)),join(meet(w,join(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(14,plain,
equal(meet(meet(u,v),v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(26,plain,
equal(meet(u,join(meet(v,u),w)),join(meet(w,u),meet(v,u))),
inference(spr,[status(thm),theory(equality)],[14,2]),
[iquote('0:SpR:14.0,2.0')] ).
cnf(27,plain,
equal(meet(u,join(v,meet(w,u))),join(meet(w,u),meet(v,u))),
inference(spr,[status(thm),theory(equality)],[14,2]),
[iquote('0:SpR:14.0,2.0')] ).
cnf(34,plain,
equal(meet(u,join(meet(v,u),w)),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[2,26]),
[iquote('0:Rew:2.0,26.0')] ).
cnf(35,plain,
equal(meet(u,join(v,meet(w,u))),meet(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[2,27]),
[iquote('0:Rew:2.0,27.0')] ).
cnf(48,plain,
equal(meet(u,meet(u,join(v,w))),meet(u,join(w,meet(v,u)))),
inference(spr,[status(thm),theory(equality)],[2,34]),
[iquote('0:SpR:2.0,34.0')] ).
cnf(49,plain,
equal(meet(u,meet(u,join(v,w))),meet(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[35,48]),
[iquote('0:Rew:35.0,48.0')] ).
cnf(80,plain,
equal(meet(u,join(v,u)),meet(u,u)),
inference(spr,[status(thm),theory(equality)],[1,49]),
[iquote('0:SpR:1.0,49.0')] ).
cnf(108,plain,
equal(meet(u,u),u),
inference(spr,[status(thm),theory(equality)],[80,1]),
[iquote('0:SpR:80.0,1.0')] ).
cnf(121,plain,
equal(meet(u,join(v,u)),u),
inference(rew,[status(thm),theory(equality)],[108,80]),
[iquote('0:Rew:108.0,80.0')] ).
cnf(138,plain,
equal(join(meet(u,join(v,u)),v),join(v,u)),
inference(spr,[status(thm),theory(equality)],[108,7]),
[iquote('0:SpR:108.0,7.0')] ).
cnf(142,plain,
equal(meet(u,join(u,v)),join(meet(v,u),u)),
inference(spr,[status(thm),theory(equality)],[108,2]),
[iquote('0:SpR:108.0,2.0')] ).
cnf(150,plain,
equal(join(u,v),join(v,u)),
inference(rew,[status(thm),theory(equality)],[121,138]),
[iquote('0:Rew:121.0,138.0')] ).
cnf(167,plain,
equal(join(meet(u,v),v),v),
inference(rew,[status(thm),theory(equality)],[1,142]),
[iquote('0:Rew:1.0,142.0')] ).
cnf(168,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[150,167]),
[iquote('0:Rew:150.0,167.0')] ).
cnf(267,plain,
equal(join(u,u),u),
inference(spr,[status(thm),theory(equality)],[108,168]),
[iquote('0:SpR:108.0,168.0')] ).
cnf(283,plain,
equal(meet(u,join(v,v)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[267,2]),
[iquote('0:SpR:267.0,2.0')] ).
cnf(292,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[267,283]),
[iquote('0:Rew:267.0,283.0')] ).
cnf(320,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[292,168]),
[iquote('0:SpR:292.0,168.0')] ).
cnf(336,plain,
$false,
inference(unc,[status(thm)],[320,3]),
[iquote('0:UnC:320.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 30 06:25:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 251 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.19/0.45 SPASS allocated 63532 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.03 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 10, length 25 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : absorption distribution prove_absorbtion_dual
% 0.19/0.45
%------------------------------------------------------------------------------