TSTP Solution File: LAT037-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% 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 06:48:43 EDT 2022
% Result : Unsatisfiable 1.18s 1.36s
% Output : Refutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 46 ( 32 unt; 0 nHn; 46 RR)
% Number of literals : 62 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(join(meet(u,v),meet(u,w)),meet(u,join(v,w))),
file('LAT037-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,n0),u),
file('LAT037-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,n1),u),
file('LAT037-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,n1),n1),
file('LAT037-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(meet(u,v),u)
| equal(join(u,meet(w,v)),meet(v,join(u,w))) ),
file('LAT037-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(xx,yy),n1),
file('LAT037-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(xx,zz),n1),
file('LAT037-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(xx,yy),n0),
file('LAT037-1.p',unknown),
[] ).
cnf(11,axiom,
equal(meet(xx,zz),n0),
file('LAT037-1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(zz,yy),
file('LAT037-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,u),u),
file('LAT037-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,join(u,v)),u),
file('LAT037-1.p',unknown),
[] ).
cnf(17,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT037-1.p',unknown),
[] ).
cnf(18,axiom,
equal(join(u,v),join(v,u)),
file('LAT037-1.p',unknown),
[] ).
cnf(20,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT037-1.p',unknown),
[] ).
cnf(49,plain,
equal(join(n1,u),n1),
inference(spr,[status(thm),theory(equality)],[18,6]),
[iquote('0:SpR:18.0,6.0')] ).
cnf(50,plain,
equal(join(n0,u),u),
inference(spr,[status(thm),theory(equality)],[18,4]),
[iquote('0:SpR:18.0,4.0')] ).
cnf(52,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[18,15]),
[iquote('0:SpR:18.0,15.0')] ).
cnf(62,plain,
equal(meet(n1,u),u),
inference(spr,[status(thm),theory(equality)],[17,5]),
[iquote('0:SpR:17.0,5.0')] ).
cnf(114,plain,
equal(join(xx,join(zz,u)),join(n1,u)),
inference(spr,[status(thm),theory(equality)],[9,20]),
[iquote('0:SpR:9.0,20.0')] ).
cnf(115,plain,
equal(join(xx,join(yy,u)),join(n1,u)),
inference(spr,[status(thm),theory(equality)],[8,20]),
[iquote('0:SpR:8.0,20.0')] ).
cnf(126,plain,
equal(join(xx,join(zz,u)),n1),
inference(rew,[status(thm),theory(equality)],[49,114]),
[iquote('0:Rew:49.0,114.0')] ).
cnf(127,plain,
equal(join(xx,join(yy,u)),n1),
inference(rew,[status(thm),theory(equality)],[49,115]),
[iquote('0:Rew:49.0,115.0')] ).
cnf(274,plain,
equal(join(meet(u,v),meet(w,u)),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[17,2]),
[iquote('0:SpR:17.0,2.0')] ).
cnf(280,plain,
equal(join(n0,meet(xx,u)),meet(xx,join(zz,u))),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(281,plain,
equal(join(n0,meet(xx,u)),meet(xx,join(yy,u))),
inference(spr,[status(thm),theory(equality)],[10,2]),
[iquote('0:SpR:10.0,2.0')] ).
cnf(303,plain,
equal(meet(xx,join(zz,u)),meet(xx,u)),
inference(rew,[status(thm),theory(equality)],[50,280]),
[iquote('0:Rew:50.0,280.0')] ).
cnf(304,plain,
equal(meet(xx,join(yy,u)),meet(xx,u)),
inference(rew,[status(thm),theory(equality)],[50,281]),
[iquote('0:Rew:50.0,281.0')] ).
cnf(689,plain,
( ~ equal(meet(u,yy),u)
| equal(meet(yy,join(u,xx)),join(u,n0)) ),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.1')] ).
cnf(698,plain,
( ~ equal(meet(u,v),u)
| equal(meet(v,join(u,v)),join(u,v)) ),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.1')] ).
cnf(714,plain,
( ~ equal(meet(u,yy),u)
| equal(meet(yy,join(u,xx)),u) ),
inference(rew,[status(thm),theory(equality)],[4,689]),
[iquote('0:Rew:4.0,689.1')] ).
cnf(716,plain,
( ~ equal(meet(u,v),u)
| equal(join(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[52,698]),
[iquote('0:Rew:52.0,698.1')] ).
cnf(6072,plain,
( ~ equal(meet(xx,join(zz,u)),xx)
| equal(join(zz,u),n1) ),
inference(spr,[status(thm),theory(equality)],[716,126]),
[iquote('0:SpR:716.1,126.0')] ).
cnf(6073,plain,
( ~ equal(meet(xx,join(yy,u)),xx)
| equal(join(yy,u),n1) ),
inference(spr,[status(thm),theory(equality)],[716,127]),
[iquote('0:SpR:716.1,127.0')] ).
cnf(6195,plain,
( ~ equal(meet(xx,u),xx)
| equal(join(zz,u),n1) ),
inference(rew,[status(thm),theory(equality)],[303,6072]),
[iquote('0:Rew:303.0,6072.0')] ).
cnf(6197,plain,
( ~ equal(meet(xx,u),xx)
| equal(join(yy,u),n1) ),
inference(rew,[status(thm),theory(equality)],[304,6073]),
[iquote('0:Rew:304.0,6073.0')] ).
cnf(8346,plain,
( ~ equal(meet(xx,xx),xx)
| ~ equal(meet(zz,yy),zz)
| equal(meet(yy,n1),zz) ),
inference(spr,[status(thm),theory(equality)],[6195,714]),
[iquote('0:SpR:6195.1,714.1')] ).
cnf(8367,plain,
( ~ equal(xx,xx)
| ~ equal(meet(yy,zz),zz)
| equal(zz,yy) ),
inference(rew,[status(thm),theory(equality)],[62,8346,17,13]),
[iquote('0:Rew:62.0,8346.2,17.0,8346.2,17.0,8346.1,13.0,8346.0')] ).
cnf(8368,plain,
( ~ equal(meet(yy,zz),zz)
| equal(zz,yy) ),
inference(obv,[status(thm),theory(equality)],[8367]),
[iquote('0:Obv:8367.0')] ).
cnf(8369,plain,
~ equal(meet(yy,zz),zz),
inference(mrr,[status(thm)],[8368,12]),
[iquote('0:MRR:8368.1,12.0')] ).
cnf(9209,plain,
equal(join(meet(zz,u),n0),meet(zz,join(u,xx))),
inference(spr,[status(thm),theory(equality)],[11,274]),
[iquote('0:SpR:11.0,274.0')] ).
cnf(9321,plain,
equal(meet(zz,join(u,xx)),meet(zz,u)),
inference(rew,[status(thm),theory(equality)],[50,9209,18]),
[iquote('0:Rew:50.0,9209.0,18.0,9209.0')] ).
cnf(9573,plain,
( ~ equal(meet(xx,xx),xx)
| equal(meet(zz,yy),meet(zz,n1)) ),
inference(spr,[status(thm),theory(equality)],[6197,9321]),
[iquote('0:SpR:6197.1,9321.0')] ).
cnf(9600,plain,
( ~ equal(xx,xx)
| equal(meet(yy,zz),zz) ),
inference(rew,[status(thm),theory(equality)],[17,9573,62,13]),
[iquote('0:Rew:17.0,9573.1,62.0,9573.1,17.0,9573.1,13.0,9573.0')] ).
cnf(9601,plain,
equal(meet(yy,zz),zz),
inference(obv,[status(thm),theory(equality)],[9600]),
[iquote('0:Obv:9600.0')] ).
cnf(9602,plain,
$false,
inference(mrr,[status(thm)],[9601,8369]),
[iquote('0:MRR:9601.0,8369.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 : Thu Jun 30 13:11:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.18/1.36
% 1.18/1.36 SPASS V 3.9
% 1.18/1.36 SPASS beiseite: Proof found.
% 1.18/1.36 % SZS status Theorem
% 1.18/1.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.18/1.36 SPASS derived 6368 clauses, backtracked 0 clauses, performed 0 splits and kept 827 clauses.
% 1.18/1.36 SPASS allocated 69253 KBytes.
% 1.18/1.36 SPASS spent 0:00:00.98 on the problem.
% 1.18/1.36 0:00:00.03 for the input.
% 1.18/1.36 0:00:00.00 for the FLOTTER CNF translation.
% 1.18/1.36 0:00:00.04 for inferences.
% 1.18/1.36 0:00:00.00 for the backtracking.
% 1.18/1.36 0:00:00.88 for the reduction.
% 1.18/1.36
% 1.18/1.36
% 1.18/1.36 Here is a proof with depth 3, length 46 :
% 1.18/1.36 % SZS output start Refutation
% See solution above
% 1.18/1.36 Formulae used in the proof : dist_meet x_join_0 x_meet_1 x_join_1 modular lhs1 lhs2 lhs3 lhs4 rhs idempotence_of_meet absorption1 commutativity_of_meet commutativity_of_join associativity_of_join
% 1.18/1.36
%------------------------------------------------------------------------------