TSTP Solution File: LAT237-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT237-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 06:49:42 EDT 2022
% Result : Unsatisfiable 1.21s 1.42s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 37 unt; 0 nHn; 41 RR)
% Number of literals : 47 ( 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(x,meet(w,join(u,v)))))),meet(u,join(v,meet(w,join(u,x))))),
file('LAT237-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(b,a),a),
file('LAT237-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(complement(b),complement(a)),complement(a)),
file('LAT237-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT237-1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(u,meet(u,v)),u),
file('LAT237-1.p',unknown),
[] ).
cnf(8,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT237-1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(u,v),join(v,u)),
file('LAT237-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT237-1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT237-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(u,complement(u)),one),
file('LAT237-1.p',unknown),
[] ).
cnf(13,axiom,
equal(meet(u,complement(u)),zero),
file('LAT237-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(u,v),one)
| ~ equal(meet(u,v),zero)
| equal(complement(u),v) ),
file('LAT237-1.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(37,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(50,plain,
equal(meet(zero,u),zero),
inference(spr,[status(thm),theory(equality)],[36,7]),
[iquote('0:SpR:36.0,7.0')] ).
cnf(68,plain,
equal(meet(one,u),u),
inference(spr,[status(thm),theory(equality)],[8,31]),
[iquote('0:SpR:8.0,31.0')] ).
cnf(69,plain,
equal(meet(u,zero),zero),
inference(spr,[status(thm),theory(equality)],[8,50]),
[iquote('0:SpR:8.0,50.0')] ).
cnf(85,plain,
equal(join(one,u),one),
inference(spr,[status(thm),theory(equality)],[68,7]),
[iquote('0:SpR:68.0,7.0')] ).
cnf(177,plain,
equal(join(u,join(complement(u),v)),join(one,v)),
inference(spr,[status(thm),theory(equality)],[12,11]),
[iquote('0:SpR:12.0,11.0')] ).
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(192,plain,
equal(join(u,join(complement(u),v)),one),
inference(rew,[status(thm),theory(equality)],[85,177]),
[iquote('0:Rew:85.0,177.0')] ).
cnf(212,plain,
equal(join(u,join(v,complement(u))),one),
inference(spr,[status(thm),theory(equality)],[9,192]),
[iquote('0:SpR:9.0,192.0')] ).
cnf(286,plain,
equal(meet(u,meet(join(u,v),w)),meet(u,w)),
inference(spr,[status(thm),theory(equality)],[6,10]),
[iquote('0:SpR:6.0,10.0')] ).
cnf(433,plain,
equal(meet(u,join(complement(u),meet(v,join(w,meet(v,one))))),meet(u,join(complement(u),meet(v,join(u,w))))),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(502,plain,
equal(meet(u,join(complement(u),meet(v,join(u,w)))),meet(u,join(complement(u),v))),
inference(rew,[status(thm),theory(equality)],[37,433,31]),
[iquote('0:Rew:37.0,433.0,31.0,433.0')] ).
cnf(2984,plain,
equal(meet(u,complement(join(u,v))),meet(u,zero)),
inference(spr,[status(thm),theory(equality)],[13,286]),
[iquote('0:SpR:13.0,286.0')] ).
cnf(3028,plain,
equal(meet(u,complement(join(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[69,2984]),
[iquote('0:Rew:69.0,2984.0')] ).
cnf(3546,plain,
equal(meet(u,complement(join(v,u))),zero),
inference(spr,[status(thm),theory(equality)],[9,3028]),
[iquote('0:SpR:9.0,3028.0')] ).
cnf(3663,plain,
equal(meet(join(a,u),complement(join(b,u))),zero),
inference(spr,[status(thm),theory(equality)],[183,3546]),
[iquote('0:SpR:183.0,3546.0')] ).
cnf(7564,plain,
equal(meet(join(a,meet(b,u)),complement(b)),zero),
inference(spr,[status(thm),theory(equality)],[7,3663]),
[iquote('0:SpR:7.0,3663.0')] ).
cnf(7652,plain,
equal(meet(complement(b),join(a,meet(b,u))),zero),
inference(rew,[status(thm),theory(equality)],[8,7564]),
[iquote('0:Rew:8.0,7564.0')] ).
cnf(8256,plain,
equal(meet(a,join(complement(a),complement(b))),meet(a,join(complement(a),zero))),
inference(spr,[status(thm),theory(equality)],[7652,502]),
[iquote('0:SpR:7652.0,502.0')] ).
cnf(8336,plain,
equal(meet(a,join(complement(b),complement(a))),zero),
inference(rew,[status(thm),theory(equality)],[9,8256,13,36]),
[iquote('0:Rew:9.0,8256.0,13.0,8256.0,36.0,8256.0,9.0,8256.0')] ).
cnf(8384,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| ~ equal(zero,zero)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(spl,[status(thm),theory(equality)],[8336,14]),
[iquote('0:SpL:8336.0,14.1')] ).
cnf(8415,plain,
( ~ equal(join(a,join(complement(b),complement(a))),one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(obv,[status(thm),theory(equality)],[8384]),
[iquote('0:Obv:8384.1')] ).
cnf(8416,plain,
( ~ equal(one,one)
| equal(join(complement(b),complement(a)),complement(a)) ),
inference(rew,[status(thm),theory(equality)],[212,8415]),
[iquote('0:Rew:212.0,8415.0')] ).
cnf(8417,plain,
equal(join(complement(b),complement(a)),complement(a)),
inference(obv,[status(thm),theory(equality)],[8416]),
[iquote('0:Obv:8416.0')] ).
cnf(8418,plain,
$false,
inference(mrr,[status(thm)],[8417,3]),
[iquote('0:MRR:8417.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT237-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.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 : Tue Jun 28 22:56:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.21/1.42
% 1.21/1.42 SPASS V 3.9
% 1.21/1.42 SPASS beiseite: Proof found.
% 1.21/1.42 % SZS status Theorem
% 1.21/1.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.42 SPASS derived 5787 clauses, backtracked 0 clauses, performed 0 splits and kept 734 clauses.
% 1.21/1.42 SPASS allocated 70010 KBytes.
% 1.21/1.42 SPASS spent 0:00:01.04 on the problem.
% 1.21/1.42 0:00:00.03 for the input.
% 1.21/1.42 0:00:00.00 for the FLOTTER CNF translation.
% 1.21/1.42 0:00:00.05 for inferences.
% 1.21/1.42 0:00:00.00 for the backtracking.
% 1.21/1.42 0:00:00.93 for the reduction.
% 1.21/1.42
% 1.21/1.42
% 1.21/1.42 Here is a proof with depth 7, length 41 :
% 1.21/1.42 % SZS output start Refutation
% See solution above
% 1.21/1.42 Formulae used in the proof : equation_H40 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
% 1.21/1.42
%------------------------------------------------------------------------------