%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL008-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 20:01:31 EDT 2022
% Result : Unsatisfiable 37.05s 37.30s
% Output : Refutation 37.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 67 ( 60 unt; 0 nHn; 67 RR)
% Number of literals : 74 ( 0 equ; 17 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) ),
file('REL008-2.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL008-2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL008-2.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL008-2.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL008-2.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL008-2.p',unknown),
[] ).
cnf(8,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL008-2.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL008-2.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL008-2.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL008-2.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL008-2.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL008-2.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL008-2.p',unknown),
[] ).
cnf(15,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(17,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.1,3.0,1.0')] ).
cnf(28,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(29,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(33,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[13,5]),
[iquote('0:SpR:13.0,5.0')] ).
cnf(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,76]),
[iquote('0:Rew:14.0,76.0')] ).
cnf(88,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[13,16]),
[iquote('0:SpR:13.0,16.0')] ).
cnf(92,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[14,16]),
[iquote('0:SpR:14.0,16.0')] ).
cnf(93,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,88]),
[iquote('0:Rew:2.0,88.0')] ).
cnf(94,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[79,93]),
[iquote('0:Rew:79.0,93.0')] ).
cnf(96,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,92]),
[iquote('0:Rew:5.0,92.0')] ).
cnf(155,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(162,plain,
equal(join(join(u,v),w),join(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(170,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk3),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[155,17]),
[iquote('0:Rew:155.0,17.1')] ).
cnf(174,plain,
equal(join(u,join(v,w)),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[3,162]),
[iquote('0:Rew:3.0,162.0')] ).
cnf(178,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[2,170]),
[iquote('0:Rew:2.0,170.1')] ).
cnf(179,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk3))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[155,178]),
[iquote('0:Rew:155.0,178.1')] ).
cnf(180,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[2,179]),
[iquote('0:Rew:2.0,179.1')] ).
cnf(219,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[9,15]),
[iquote('0:SpR:9.0,15.0')] ).
cnf(265,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(395,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(398,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,395]),
[iquote('0:Rew:9.0,395.0')] ).
cnf(407,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[398,7]),
[iquote('0:SpR:398.0,7.0')] ).
cnf(413,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[398,15]),
[iquote('0:SpR:398.0,15.0')] ).
cnf(417,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[407,398]),
[iquote('0:Rew:407.0,398.0')] ).
cnf(424,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[417,413]),
[iquote('0:Rew:417.0,413.0')] ).
cnf(460,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[424,5]),
[iquote('0:SpR:424.0,5.0')] ).
cnf(466,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[79,424]),
[iquote('0:SpR:79.0,424.0')] ).
cnf(484,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[460,96]),
[iquote('0:Rew:460.0,96.0')] ).
cnf(540,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[466,3]),
[iquote('0:SpR:466.0,3.0')] ).
cnf(610,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[29,10]),
[iquote('0:SpR:29.0,10.0')] ).
cnf(631,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[610,265]),
[iquote('0:Rew:610.0,265.0')] ).
cnf(688,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[33,11]),
[iquote('0:SpR:33.0,11.0')] ).
cnf(724,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[688,631]),
[iquote('0:Rew:688.0,631.0')] ).
cnf(736,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[94,540]),
[iquote('0:SpR:94.0,540.0')] ).
cnf(742,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[736,484]),
[iquote('0:Rew:736.0,484.0')] ).
cnf(2057,plain,
equal(join(join(u,v),w),join(u,join(w,v))),
inference(spr,[status(thm),theory(equality)],[174,2]),
[iquote('0:SpR:174.0,2.0')] ).
cnf(2155,plain,
equal(join(u,join(v,w)),join(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[3,2057]),
[iquote('0:Rew:3.0,2057.0')] ).
cnf(2560,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[742,219]),
[iquote('0:SpR:742.0,219.0')] ).
cnf(4907,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[9,724]),
[iquote('0:SpR:9.0,724.0')] ).
cnf(12445,plain,
equal(join(join(u,join(v,w)),x),join(u,join(join(w,v),x))),
inference(spr,[status(thm),theory(equality)],[2155,3]),
[iquote('0:SpR:2155.0,3.0')] ).
cnf(12690,plain,
equal(join(u,join(v,join(w,x))),join(u,join(w,join(v,x)))),
inference(rew,[status(thm),theory(equality)],[3,12445]),
[iquote('0:Rew:3.0,12445.0,3.0,12445.0,3.0,12445.0')] ).
cnf(18118,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[417,2560]),
[iquote('0:SpR:417.0,2560.0')] ).
cnf(18128,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[742,18118,417,407]),
[iquote('0:Rew:742.0,18118.0,417.0,18118.0,407.0,18118.0')] ).
cnf(18248,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[18128,3]),
[iquote('0:SpR:18128.0,3.0')] ).
cnf(78131,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[4907,9]),
[iquote('0:SpR:4907.0,9.0')] ).
cnf(78349,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[9,78131]),
[iquote('0:Rew:9.0,78131.0')] ).
cnf(78351,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))) ),
inference(rew,[status(thm),theory(equality)],[78349,180]),
[iquote('0:Rew:78349.0,180.1')] ).
cnf(78615,plain,
~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))),
inference(obv,[status(thm),theory(equality)],[78351]),
[iquote('0:Obv:78351.0')] ).
cnf(78616,plain,
~ equal(composition(sk1,join(sk2,join(sk2,join(sk3,sk3)))),composition(sk1,join(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[12690,78615,78349]),
[iquote('0:Rew:12690.0,78615.0,78349.0,78615.0,78349.0,78615.0')] ).
cnf(78617,plain,
~ equal(composition(sk1,join(sk2,sk3)),composition(sk1,join(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[18248,78616,18128]),
[iquote('0:Rew:18248.0,78616.0,18128.0,78616.0')] ).
cnf(78618,plain,
$false,
inference(obv,[status(thm),theory(equality)],[78617]),
[iquote('0:Obv:78617.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL008-2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 08:11:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 37.05/37.30
% 37.05/37.30 SPASS V 3.9
% 37.05/37.30 SPASS beiseite: Proof found.
% 37.05/37.30 % SZS status Theorem
% 37.05/37.30 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.05/37.30 SPASS derived 47419 clauses, backtracked 0 clauses, performed 0 splits and kept 5710 clauses.
% 37.05/37.30 SPASS allocated 126564 KBytes.
% 37.05/37.30 SPASS spent 0:0:36.87 on the problem.
% 37.05/37.30 0:00:00.04 for the input.
% 37.05/37.30 0:00:00.00 for the FLOTTER CNF translation.
% 37.05/37.30 0:00:00.36 for inferences.
% 37.05/37.30 0:00:00.00 for the backtracking.
% 37.05/37.30 0:0:36.40 for the reduction.
% 37.05/37.30
% 37.05/37.30
% 37.05/37.30 Here is a proof with depth 6, length 67 :
% 37.05/37.30 % SZS output start Refutation
% See solution above
% 37.05/37.30 Formulae used in the proof : goals_14 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_identity_6 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 38.54/38.72
%------------------------------------------------------------------------------