TSTP Solution File: LAT027-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT027-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 06:48:39 EDT 2022
% Result : Unsatisfiable 198.50s 198.72s
% Output : Refutation 198.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 64 RR)
% Number of literals : 64 ( 0 equ; 5 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(meet(u,join(v,join(u,w))),u),
file('LAT027-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(join(join(a,b),c),join(a,join(b,c))),
file('LAT027-1.p',unknown),
[] ).
cnf(3,axiom,
equal(meet(u,u),u),
file('LAT027-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,u),u),
file('LAT027-1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT027-1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('LAT027-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(meet(join(u,v),join(w,v)),v),v),
file('LAT027-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(join(meet(u,v),meet(w,v)),v),v),
file('LAT027-1.p',unknown),
[] ).
cnf(9,plain,
equal(join(u,join(meet(v,u),meet(w,u))),u),
inference(rew,[status(thm),theory(equality)],[6,8]),
[iquote('0:Rew:6.0,8.0')] ).
cnf(10,plain,
equal(meet(u,meet(join(v,u),join(w,u))),u),
inference(rew,[status(thm),theory(equality)],[5,7]),
[iquote('0:Rew:5.0,7.0')] ).
cnf(11,plain,
~ equal(join(c,join(a,b)),join(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[6,2]),
[iquote('0:Rew:6.0,2.0')] ).
cnf(27,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(28,plain,
equal(meet(u,join(v,join(w,u))),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(30,plain,
equal(meet(u,join(u,v)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(31,plain,
equal(meet(u,join(join(u,v),w)),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(50,plain,
equal(meet(u,join(join(v,u),w)),u),
inference(spr,[status(thm),theory(equality)],[6,28]),
[iquote('0:SpR:6.0,28.0')] ).
cnf(76,plain,
equal(join(join(u,v),join(meet(w,join(u,v)),v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[27,9]),
[iquote('0:SpR:27.0,9.0')] ).
cnf(82,plain,
equal(join(join(u,join(v,w)),join(v,meet(x,join(u,join(v,w))))),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(87,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(95,plain,
equal(join(join(u,v),join(v,meet(w,join(u,v)))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[6,76]),
[iquote('0:Rew:6.0,76.0')] ).
cnf(109,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[5,87]),
[iquote('0:SpR:5.0,87.0')] ).
cnf(111,plain,
equal(join(join(u,join(v,w)),v),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[1,87]),
[iquote('0:SpR:1.0,87.0')] ).
cnf(115,plain,
equal(join(join(join(u,v),w),u),join(join(u,v),w)),
inference(spr,[status(thm),theory(equality)],[31,87]),
[iquote('0:SpR:31.0,87.0')] ).
cnf(119,plain,
equal(join(u,join(v,join(u,w))),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[6,111]),
[iquote('0:Rew:6.0,111.0')] ).
cnf(121,plain,
equal(join(u,join(join(u,v),w)),join(join(u,v),w)),
inference(rew,[status(thm),theory(equality)],[6,115]),
[iquote('0:Rew:6.0,115.0')] ).
cnf(123,plain,
equal(meet(meet(u,v),join(w,u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[109,28]),
[iquote('0:SpR:109.0,28.0')] ).
cnf(153,plain,
equal(meet(meet(u,v),join(v,w)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[87,50]),
[iquote('0:SpR:87.0,50.0')] ).
cnf(189,plain,
equal(join(meet(join(u,v),join(w,v)),join(meet(x,meet(join(u,v),join(w,v))),v)),meet(join(u,v),join(w,v))),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.0,9.0')] ).
cnf(193,plain,
equal(meet(u,meet(join(v,u),join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(217,plain,
equal(join(meet(join(u,v),join(w,v)),join(v,meet(x,meet(join(u,v),join(w,v))))),meet(join(u,v),join(w,v))),
inference(rew,[status(thm),theory(equality)],[6,189]),
[iquote('0:Rew:6.0,189.0')] ).
cnf(468,plain,
equal(join(join(u,v),meet(v,w)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[123,87]),
[iquote('0:SpR:123.0,87.0')] ).
cnf(597,plain,
equal(meet(u,meet(join(u,v),join(u,w))),u),
inference(spr,[status(thm),theory(equality)],[6,193]),
[iquote('0:SpR:6.0,193.0')] ).
cnf(972,plain,
equal(join(join(u,join(v,w)),join(v,u)),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[30,82]),
[iquote('0:SpR:30.0,82.0')] ).
cnf(1003,plain,
equal(join(join(u,v),join(v,join(u,w))),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[6,972]),
[iquote('0:Rew:6.0,972.0')] ).
cnf(2200,plain,
equal(join(meet(u,v),join(w,u)),join(w,u)),
inference(spr,[status(thm),theory(equality)],[468,6]),
[iquote('0:SpR:468.0,6.0')] ).
cnf(2449,plain,
equal(join(meet(join(u,v),join(u,v)),join(v,u)),meet(join(u,v),join(u,v))),
inference(spr,[status(thm),theory(equality)],[597,217]),
[iquote('0:SpR:597.0,217.0')] ).
cnf(2541,plain,
equal(join(join(u,v),join(v,u)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2449]),
[iquote('0:Rew:3.0,2449.0')] ).
cnf(4411,plain,
equal(meet(u,meet(join(join(u,v),w),join(u,x))),u),
inference(spr,[status(thm),theory(equality)],[121,597]),
[iquote('0:SpR:121.0,597.0')] ).
cnf(5270,plain,
equal(join(join(u,v),join(v,meet(w,u))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[153,95]),
[iquote('0:SpR:153.0,95.0')] ).
cnf(5745,plain,
equal(meet(join(u,v),join(join(v,u),w)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[2541,50]),
[iquote('0:SpR:2541.0,50.0')] ).
cnf(5758,plain,
equal(join(meet(join(u,v),w),join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[2541,2200]),
[iquote('0:SpR:2541.0,2200.0')] ).
cnf(5899,plain,
equal(join(join(u,v),meet(join(v,u),w)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[6,5758]),
[iquote('0:Rew:6.0,5758.0')] ).
cnf(11955,plain,
equal(meet(join(u,v),join(v,join(u,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[1003,30]),
[iquote('0:SpR:1003.0,30.0')] ).
cnf(12040,plain,
equal(join(join(u,v),join(v,join(w,u))),join(v,join(w,u))),
inference(spr,[status(thm),theory(equality)],[6,1003]),
[iquote('0:SpR:6.0,1003.0')] ).
cnf(50536,plain,
equal(join(meet(join(join(u,v),w),join(u,w)),join(w,u)),meet(join(join(u,v),w),join(u,w))),
inference(spr,[status(thm),theory(equality)],[4411,217]),
[iquote('0:SpR:4411.0,217.0')] ).
cnf(50969,plain,
equal(join(join(u,v),meet(join(v,u),join(join(v,w),u))),meet(join(v,u),join(join(v,w),u))),
inference(rew,[status(thm),theory(equality)],[6,50536,5]),
[iquote('0:Rew:6.0,50536.0,5.0,50536.0')] ).
cnf(50970,plain,
equal(meet(join(u,v),join(join(u,w),v)),join(v,u)),
inference(rew,[status(thm),theory(equality)],[5899,50969]),
[iquote('0:Rew:5899.0,50969.0')] ).
cnf(70112,plain,
equal(meet(join(u,v),join(u,join(v,w))),join(u,v)),
inference(spr,[status(thm),theory(equality)],[1003,5745]),
[iquote('0:SpR:1003.0,5745.0')] ).
cnf(95806,plain,
equal(join(join(u,join(v,w)),join(join(v,w),join(v,u))),join(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[11955,95]),
[iquote('0:SpR:11955.0,95.0')] ).
cnf(96263,plain,
equal(join(join(u,v),join(u,w)),join(w,join(u,v))),
inference(rew,[status(thm),theory(equality)],[12040,95806]),
[iquote('0:Rew:12040.0,95806.0')] ).
cnf(97011,plain,
equal(meet(join(u,join(v,meet(w,u))),join(u,v)),join(join(v,meet(w,u)),u)),
inference(spr,[status(thm),theory(equality)],[5270,50970]),
[iquote('0:SpR:5270.0,50970.0')] ).
cnf(97349,plain,
equal(meet(join(u,v),join(u,join(v,meet(w,u)))),join(u,join(v,meet(w,u)))),
inference(rew,[status(thm),theory(equality)],[5,97011,6]),
[iquote('0:Rew:5.0,97011.0,6.0,97011.0')] ).
cnf(97350,plain,
equal(join(u,join(v,meet(w,u))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[70112,97349]),
[iquote('0:Rew:70112.0,97349.0')] ).
cnf(101028,plain,
equal(join(u,join(meet(v,u),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[6,97350]),
[iquote('0:SpR:6.0,97350.0')] ).
cnf(103659,plain,
equal(join(join(u,v),join(v,w)),join(join(u,v),w)),
inference(spr,[status(thm),theory(equality)],[27,101028]),
[iquote('0:SpR:27.0,101028.0')] ).
cnf(103851,plain,
equal(join(join(u,v),join(u,w)),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[103659,1003]),
[iquote('0:Rew:103659.0,1003.0')] ).
cnf(103893,plain,
equal(join(join(u,v),join(w,u)),join(v,join(w,u))),
inference(rew,[status(thm),theory(equality)],[103659,12040]),
[iquote('0:Rew:103659.0,12040.0')] ).
cnf(103899,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(rew,[status(thm),theory(equality)],[96263,103851]),
[iquote('0:Rew:96263.0,103851.0')] ).
cnf(103906,plain,
~ equal(join(b,join(a,c)),join(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[103899,11]),
[iquote('0:Rew:103899.0,11.0')] ).
cnf(104069,plain,
equal(join(u,join(v,join(u,w))),join(w,join(v,u))),
inference(rew,[status(thm),theory(equality)],[103899,103893]),
[iquote('0:Rew:103899.0,103893.0')] ).
cnf(104070,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(rew,[status(thm),theory(equality)],[119,104069]),
[iquote('0:Rew:119.0,104069.0')] ).
cnf(104077,plain,
~ equal(join(a,join(c,b)),join(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[104070,103906]),
[iquote('0:Rew:104070.0,103906.0')] ).
cnf(104195,plain,
~ equal(join(a,join(b,c)),join(a,join(b,c))),
inference(rew,[status(thm),theory(equality)],[6,104077]),
[iquote('0:Rew:6.0,104077.0')] ).
cnf(104196,plain,
$false,
inference(obv,[status(thm),theory(equality)],[104195]),
[iquote('0:Obv:104195.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT027-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.11 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Wed Jun 29 03:57:13 EDT 2022
% 0.10/0.31 % CPUTime :
% 198.50/198.72
% 198.50/198.72 SPASS V 3.9
% 198.50/198.72 SPASS beiseite: Proof found.
% 198.50/198.72 % SZS status Theorem
% 198.50/198.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 198.50/198.72 SPASS derived 85651 clauses, backtracked 0 clauses, performed 0 splits and kept 14817 clauses.
% 198.50/198.72 SPASS allocated 159196 KBytes.
% 198.50/198.72 SPASS spent 0:3:16.95 on the problem.
% 198.50/198.72 0:00:00.03 for the input.
% 198.50/198.72 0:00:00.00 for the FLOTTER CNF translation.
% 198.50/198.72 0:00:00.56 for inferences.
% 198.50/198.72 0:00:00.00 for the backtracking.
% 198.50/198.72 0:3:16.29 for the reduction.
% 198.50/198.72
% 198.50/198.72
% 198.50/198.72 Here is a proof with depth 7, length 64 :
% 198.50/198.72 % SZS output start Refutation
% See solution above
% 198.50/198.72 Formulae used in the proof : absorption prove_associativity_of_join idempotence_of_meet idempotence_of_join commutativity_of_meet commutativity_of_join wal_1 wal_2
% 198.50/198.72
%------------------------------------------------------------------------------