TSTP Solution File: REL046-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Mon Jul 18 20:02:28 EDT 2022
% Result : Unsatisfiable 1.28s 1.46s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 49 unt; 0 nHn; 51 RR)
% Number of literals : 53 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(sk1,meet(sk2,sk3)),meet(sk2,sk3)),
file('REL046-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(join(sk1,sk3),sk3)
| ~ equal(join(sk1,sk2),sk2) ),
file('REL046-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('REL046-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL046-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL046-1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL046-1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(u,one),u),
file('REL046-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL046-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL046-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL046-1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(u,complement(u)),top),
file('REL046-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,complement(u)),zero),
file('REL046-1.p',unknown),
[] ).
cnf(16,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3,13]),
[iquote('0:Rew:3.0,13.0')] ).
cnf(17,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(29,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(77,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.0,6.0')] ).
cnf(78,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(80,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[15,77]),
[iquote('0:Rew:15.0,77.0')] ).
cnf(81,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,78]),
[iquote('0:Rew:6.0,78.0')] ).
cnf(89,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[80,6]),
[iquote('0:SpR:80.0,6.0')] ).
cnf(103,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[14,17]),
[iquote('0:SpR:14.0,17.0')] ).
cnf(106,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(107,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[15,17]),
[iquote('0:SpR:15.0,17.0')] ).
cnf(108,plain,
equal(join(meet(u,v),complement(join(complement(v),u))),v),
inference(spr,[status(thm),theory(equality)],[81,17]),
[iquote('0:SpR:81.0,17.0')] ).
cnf(112,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[3,103,80]),
[iquote('0:Rew:3.0,103.0,80.0,103.0')] ).
cnf(113,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[3,106]),
[iquote('0:Rew:3.0,106.0')] ).
cnf(114,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,107]),
[iquote('0:Rew:6.0,107.0')] ).
cnf(128,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[89,6]),
[iquote('0:SpR:89.0,6.0')] ).
cnf(202,plain,
equal(join(sk1,join(meet(sk2,sk3),u)),join(meet(sk2,sk3),u)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(469,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[8,29]),
[iquote('0:SpR:8.0,29.0')] ).
cnf(472,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[10,469]),
[iquote('0:Rew:10.0,469.0')] ).
cnf(481,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[472,8]),
[iquote('0:SpR:472.0,8.0')] ).
cnf(487,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[472,16]),
[iquote('0:SpR:472.0,16.0')] ).
cnf(491,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[481,472]),
[iquote('0:Rew:481.0,472.0')] ).
cnf(498,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[491,487]),
[iquote('0:Rew:491.0,487.0')] ).
cnf(534,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[498,6]),
[iquote('0:SpR:498.0,6.0')] ).
cnf(540,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[80,498]),
[iquote('0:SpR:80.0,498.0')] ).
cnf(559,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[534,114]),
[iquote('0:Rew:534.0,114.0')] ).
cnf(659,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[540,4]),
[iquote('0:SpR:540.0,4.0')] ).
cnf(928,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[112,659]),
[iquote('0:SpR:112.0,659.0')] ).
cnf(935,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[928,559]),
[iquote('0:Rew:928.0,559.0')] ).
cnf(936,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[928,89]),
[iquote('0:Rew:928.0,89.0')] ).
cnf(950,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[928,128]),
[iquote('0:Rew:928.0,128.0')] ).
cnf(968,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[935,936]),
[iquote('0:Rew:935.0,936.0')] ).
cnf(1020,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[968,950]),
[iquote('0:Rew:968.0,950.0')] ).
cnf(1022,plain,
equal(join(meet(u,v),meet(v,complement(u))),v),
inference(rew,[status(thm),theory(equality)],[1020,108]),
[iquote('0:Rew:1020.0,108.0')] ).
cnf(2844,plain,
equal(join(sk1,sk2),sk2),
inference(spr,[status(thm),theory(equality)],[113,202]),
[iquote('0:SpR:113.0,202.0')] ).
cnf(2849,plain,
( ~ equal(join(sk1,sk3),sk3)
| ~ equal(sk2,sk2) ),
inference(rew,[status(thm),theory(equality)],[2844,2]),
[iquote('0:Rew:2844.0,2.1')] ).
cnf(2851,plain,
~ equal(join(sk1,sk3),sk3),
inference(obv,[status(thm),theory(equality)],[2849]),
[iquote('0:Obv:2849.1')] ).
cnf(8752,plain,
equal(join(sk1,sk3),sk3),
inference(spr,[status(thm),theory(equality)],[1022,202]),
[iquote('0:SpR:1022.0,202.0')] ).
cnf(8783,plain,
$false,
inference(mrr,[status(thm)],[8752,2851]),
[iquote('0:MRR:8752.0,2851.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 : Fri Jul 8 12:34:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.28/1.46
% 1.28/1.46 SPASS V 3.9
% 1.28/1.46 SPASS beiseite: Proof found.
% 1.28/1.46 % SZS status Theorem
% 1.28/1.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.28/1.46 SPASS derived 5432 clauses, backtracked 0 clauses, performed 0 splits and kept 1051 clauses.
% 1.28/1.46 SPASS allocated 71792 KBytes.
% 1.28/1.46 SPASS spent 0:00:01.05 on the problem.
% 1.28/1.46 0:00:00.03 for the input.
% 1.28/1.46 0:00:00.00 for the FLOTTER CNF translation.
% 1.28/1.46 0:00:00.05 for inferences.
% 1.28/1.46 0:00:00.00 for the backtracking.
% 1.28/1.46 0:00:00.94 for the reduction.
% 1.28/1.46
% 1.28/1.46
% 1.28/1.46 Here is a proof with depth 6, length 51 :
% 1.28/1.46 % SZS output start Refutation
% See solution above
% 1.28/1.46 Formulae used in the proof : goals_14 goals_15 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_identity_6 converse_idempotence_8 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 1.28/1.46
%------------------------------------------------------------------------------