TSTP Solution File: LAT168-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT168-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 06:49:20 EDT 2022
% Result : Unsatisfiable 1.32s 1.51s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 41 RR)
% Number of literals : 41 ( 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(u,meet(join(u,v),meet(join(u,w),join(v,meet(u,w))))),meet(join(u,v),join(u,w))),
file('LAT168-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),meet(a,join(b,c))),
file('LAT168-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT168-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,join(u,v)),u),
file('LAT168-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,meet(u,v)),u),
file('LAT168-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT168-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(u,v),join(v,u)),
file('LAT168-1.p',unknown),
[] ).
cnf(9,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT168-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT168-1.p',unknown),
[] ).
cnf(20,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(28,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(46,plain,
equal(meet(meet(u,v),v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[28,20]),
[iquote('0:SpR:28.0,20.0')] ).
cnf(49,plain,
equal(join(join(u,v),u),join(u,v)),
inference(spr,[status(thm),theory(equality)],[5,28]),
[iquote('0:SpR:5.0,28.0')] ).
cnf(50,plain,
equal(join(join(u,v),v),join(u,v)),
inference(spr,[status(thm),theory(equality)],[20,28]),
[iquote('0:SpR:20.0,28.0')] ).
cnf(52,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,46]),
[iquote('0:Rew:7.0,46.0')] ).
cnf(53,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[8,49]),
[iquote('0:Rew:8.0,49.0')] ).
cnf(54,plain,
equal(join(u,join(v,u)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[8,50]),
[iquote('0:Rew:8.0,50.0')] ).
cnf(160,plain,
equal(meet(u,meet(v,w)),meet(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(169,plain,
equal(join(u,meet(v,meet(w,u))),u),
inference(spr,[status(thm),theory(equality)],[9,28]),
[iquote('0:SpR:9.0,28.0')] ).
cnf(174,plain,
equal(meet(u,meet(join(u,v),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(175,plain,
equal(meet(u,meet(join(v,u),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[20,9]),
[iquote('0:SpR:20.0,9.0')] ).
cnf(230,plain,
equal(join(join(u,v),meet(w,u)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[5,169]),
[iquote('0:SpR:5.0,169.0')] ).
cnf(247,plain,
equal(join(u,join(v,meet(w,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[10,230]),
[iquote('0:Rew:10.0,230.0')] ).
cnf(698,plain,
equal(join(u,meet(join(u,v),meet(join(u,w),join(v,meet(w,u))))),meet(join(u,v),join(u,w))),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(733,plain,
equal(join(u,meet(join(v,u),meet(join(u,w),join(join(v,u),meet(u,w))))),meet(join(v,u),join(u,w))),
inference(spr,[status(thm),theory(equality)],[54,1]),
[iquote('0:SpR:54.0,1.0')] ).
cnf(765,plain,
equal(join(u,meet(join(u,v),join(w,u))),meet(join(w,u),join(u,v))),
inference(rew,[status(thm),theory(equality)],[52,733,6,10]),
[iquote('0:Rew:52.0,733.0,6.0,733.0,10.0,733.0')] ).
cnf(925,plain,
equal(meet(u,meet(v,w)),meet(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[7,160]),
[iquote('0:SpR:7.0,160.0')] ).
cnf(1315,plain,
equal(join(u,meet(join(u,v),join(v,meet(u,join(u,v))))),meet(join(u,v),join(u,join(u,v)))),
inference(spr,[status(thm),theory(equality)],[175,1]),
[iquote('0:SpR:175.0,1.0')] ).
cnf(1388,plain,
equal(join(u,meet(join(u,v),join(v,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[5,1315,3,53]),
[iquote('0:Rew:5.0,1315.0,3.0,1315.0,53.0,1315.0')] ).
cnf(1389,plain,
equal(meet(join(u,v),join(v,u)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[765,1388]),
[iquote('0:Rew:765.0,1388.0')] ).
cnf(1649,plain,
equal(meet(join(u,meet(v,w)),meet(join(w,u),x)),meet(join(u,meet(v,w)),x)),
inference(spr,[status(thm),theory(equality)],[247,175]),
[iquote('0:SpR:247.0,175.0')] ).
cnf(1728,plain,
equal(meet(join(u,v),meet(w,join(v,meet(x,u)))),meet(join(v,meet(x,u)),w)),
inference(rew,[status(thm),theory(equality)],[160,1649]),
[iquote('0:Rew:160.0,1649.0')] ).
cnf(1729,plain,
equal(join(u,meet(join(v,meet(w,u)),join(u,w))),meet(join(u,v),join(u,w))),
inference(rew,[status(thm),theory(equality)],[1728,698]),
[iquote('0:Rew:1728.0,698.0')] ).
cnf(1734,plain,
equal(join(u,meet(join(u,v),join(w,meet(v,u)))),meet(join(u,w),join(u,v))),
inference(rew,[status(thm),theory(equality)],[7,1729]),
[iquote('0:Rew:7.0,1729.0')] ).
cnf(3110,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(join(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1389,9]),
[iquote('0:SpR:1389.0,9.0')] ).
cnf(3122,plain,
equal(meet(join(u,v),meet(join(v,u),w)),meet(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[1389,925]),
[iquote('0:SpR:1389.0,925.0')] ).
cnf(3218,plain,
equal(meet(join(u,v),w),meet(w,join(v,u))),
inference(rew,[status(thm),theory(equality)],[3110,3122]),
[iquote('0:Rew:3110.0,3122.0')] ).
cnf(5472,plain,
equal(join(u,meet(join(v,u),join(w,meet(v,u)))),meet(join(u,w),join(v,u))),
inference(spr,[status(thm),theory(equality)],[8,1734]),
[iquote('0:SpR:8.0,1734.0')] ).
cnf(5524,plain,
~ equal(meet(a,meet(join(b,c),join(a,b))),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[5472,2]),
[iquote('0:Rew:5472.0,2.0')] ).
cnf(5525,plain,
~ equal(meet(a,join(b,c)),meet(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[174,5524,8,3218]),
[iquote('0:Rew:174.0,5524.0,8.0,5524.0,3218.0,5524.0')] ).
cnf(5526,plain,
$false,
inference(obv,[status(thm),theory(equality)],[5525]),
[iquote('0:Obv:5525.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT168-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 29 15:33:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.32/1.51
% 1.32/1.51 SPASS V 3.9
% 1.32/1.51 SPASS beiseite: Proof found.
% 1.32/1.51 % SZS status Theorem
% 1.32/1.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.32/1.51 SPASS derived 3661 clauses, backtracked 0 clauses, performed 0 splits and kept 618 clauses.
% 1.32/1.51 SPASS allocated 68075 KBytes.
% 1.32/1.51 SPASS spent 0:00:01.12 on the problem.
% 1.32/1.51 0:00:00.04 for the input.
% 1.32/1.51 0:00:00.00 for the FLOTTER CNF translation.
% 1.32/1.51 0:00:00.03 for inferences.
% 1.32/1.51 0:00:00.00 for the backtracking.
% 1.32/1.51 0:00:01.02 for the reduction.
% 1.32/1.51
% 1.32/1.51
% 1.32/1.51 Here is a proof with depth 4, length 41 :
% 1.32/1.51 % SZS output start Refutation
% See solution above
% 1.32/1.51 Formulae used in the proof : equation_H18_dual prove_H58 idempotence_of_meet absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 1.32/1.51
%------------------------------------------------------------------------------