TSTP Solution File: LAT235-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT235-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 06:49:41 EDT 2022
% Result : Unsatisfiable 4.39s 4.61s
% Output : Refutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 34 unt; 0 nHn; 38 RR)
% Number of literals : 44 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(u,join(v,meet(w,join(v,meet(x,join(v,w)))))),meet(u,join(v,meet(w,x)))),
file('LAT235-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(b,a),a),
file('LAT235-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(complement(b),complement(a)),complement(a)),
file('LAT235-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT235-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,meet(u,v)),u),
file('LAT235-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT235-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT235-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT235-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT235-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(u,complement(u)),one),
file('LAT235-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,complement(u)),zero),
file('LAT235-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(u,v),one)
| ~ equal(meet(u,v),zero)
| equal(complement(u),v) ),
file('LAT235-1.p',unknown),
[] ).
cnf(22,plain,
equal(join(b,a),b),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(24,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(31,plain,
equal(meet(u,one),u),
inference(spr,[status(thm),theory(equality)],[12,6]),
[iquote('0:SpR:12.0,6.0')] ).
cnf(36,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[9,24]),
[iquote('0:SpR:9.0,24.0')] ).
cnf(50,plain,
equal(meet(zero,u),zero),
inference(spr,[status(thm),theory(equality)],[36,7]),
[iquote('0:SpR:36.0,7.0')] ).
cnf(66,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(68,plain,
equal(meet(one,u),u),
inference(spr,[status(thm),theory(equality)],[8,31]),
[iquote('0:SpR:8.0,31.0')] ).
cnf(85,plain,
equal(join(one,u),one),
inference(spr,[status(thm),theory(equality)],[68,7]),
[iquote('0:SpR:68.0,7.0')] ).
cnf(100,plain,
equal(join(u,one),one),
inference(spr,[status(thm),theory(equality)],[85,9]),
[iquote('0:SpR:85.0,9.0')] ).
cnf(183,plain,
equal(join(b,join(a,u)),join(b,u)),
inference(spr,[status(thm),theory(equality)],[22,11]),
[iquote('0:SpR:22.0,11.0')] ).
cnf(245,plain,
equal(join(b,complement(a)),join(b,one)),
inference(spr,[status(thm),theory(equality)],[12,183]),
[iquote('0:SpR:12.0,183.0')] ).
cnf(255,plain,
equal(join(b,complement(a)),one),
inference(rew,[status(thm),theory(equality)],[100,245]),
[iquote('0:Rew:100.0,245.0')] ).
cnf(284,plain,
equal(meet(u,meet(complement(u),v)),meet(zero,v)),
inference(spr,[status(thm),theory(equality)],[13,10]),
[iquote('0:SpR:13.0,10.0')] ).
cnf(299,plain,
equal(meet(u,meet(complement(u),v)),zero),
inference(rew,[status(thm),theory(equality)],[50,284]),
[iquote('0:Rew:50.0,284.0')] ).
cnf(453,plain,
equal(meet(u,join(v,meet(complement(v),join(v,meet(w,one))))),meet(u,join(v,meet(complement(v),w)))),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(527,plain,
equal(meet(u,join(v,meet(complement(v),join(v,w)))),meet(u,join(v,meet(complement(v),w)))),
inference(rew,[status(thm),theory(equality)],[31,453]),
[iquote('0:Rew:31.0,453.0')] ).
cnf(5607,plain,
equal(meet(u,join(b,meet(complement(b),complement(a)))),meet(u,join(b,meet(complement(b),one)))),
inference(spr,[status(thm),theory(equality)],[255,527]),
[iquote('0:SpR:255.0,527.0')] ).
cnf(5662,plain,
equal(meet(u,join(b,meet(complement(b),complement(a)))),u),
inference(rew,[status(thm),theory(equality)],[31,5607,12,68,8]),
[iquote('0:Rew:31.0,5607.0,12.0,5607.0,68.0,5607.0,8.0,5607.0')] ).
cnf(20125,plain,
equal(join(b,meet(complement(b),complement(a))),one),
inference(spr,[status(thm),theory(equality)],[5662,68]),
[iquote('0:SpR:5662.0,68.0')] ).
cnf(20677,plain,
( ~ equal(one,one)
| ~ equal(meet(b,meet(complement(b),complement(a))),zero)
| equal(meet(complement(b),complement(a)),complement(b)) ),
inference(spl,[status(thm),theory(equality)],[20125,14]),
[iquote('0:SpL:20125.0,14.0')] ).
cnf(20720,plain,
( ~ equal(meet(b,meet(complement(b),complement(a))),zero)
| equal(meet(complement(b),complement(a)),complement(b)) ),
inference(obv,[status(thm),theory(equality)],[20677]),
[iquote('0:Obv:20677.0')] ).
cnf(20721,plain,
( ~ equal(zero,zero)
| equal(meet(complement(b),complement(a)),complement(b)) ),
inference(rew,[status(thm),theory(equality)],[299,20720]),
[iquote('0:Rew:299.0,20720.0')] ).
cnf(20722,plain,
equal(meet(complement(b),complement(a)),complement(b)),
inference(obv,[status(thm),theory(equality)],[20721]),
[iquote('0:Obv:20721.0')] ).
cnf(20747,plain,
equal(join(complement(a),complement(b)),complement(a)),
inference(spr,[status(thm),theory(equality)],[20722,66]),
[iquote('0:SpR:20722.0,66.0')] ).
cnf(20778,plain,
equal(join(complement(b),complement(a)),complement(a)),
inference(rew,[status(thm),theory(equality)],[9,20747]),
[iquote('0:Rew:9.0,20747.0')] ).
cnf(20779,plain,
$false,
inference(mrr,[status(thm)],[20778,3]),
[iquote('0:MRR:20778.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT235-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 11:19:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.39/4.61
% 4.39/4.61 SPASS V 3.9
% 4.39/4.61 SPASS beiseite: Proof found.
% 4.39/4.61 % SZS status Theorem
% 4.39/4.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/4.61 SPASS derived 13551 clauses, backtracked 0 clauses, performed 0 splits and kept 1276 clauses.
% 4.39/4.61 SPASS allocated 80559 KBytes.
% 4.39/4.61 SPASS spent 0:00:04.14 on the problem.
% 4.39/4.61 0:00:00.04 for the input.
% 4.39/4.61 0:00:00.00 for the FLOTTER CNF translation.
% 4.39/4.61 0:00:00.09 for inferences.
% 4.39/4.61 0:00:00.00 for the backtracking.
% 4.39/4.61 0:00:03.99 for the reduction.
% 4.39/4.61
% 4.39/4.61
% 4.39/4.61 Here is a proof with depth 7, length 38 :
% 4.39/4.61 % SZS output start Refutation
% See solution above
% 4.39/4.61 Formulae used in the proof : equation_H34 prove_distributivity_hypothesis prove_distributivity absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join complement_join complement_meet meet_join_complement
% 4.39/4.61
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