%------------------------------------------------------------------------------
% 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 : 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 : Mon Jul 18 20:01:31 EDT 2022
% Result : Theorem 32.44s 32.61s
% Output : Refutation 33.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 68 ( 58 unt; 0 nHn; 68 RR)
% Number of literals : 78 ( 0 equ; 20 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 : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL008+2.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL008+2.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL008+2.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL008+2.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL008+2.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL008+2.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL008+2.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL008+2.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL008+2.p',unknown),
[] ).
cnf(11,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
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(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL008+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(join(join(composition(skc6,join(skc7,skc8)),composition(skc6,skc7)),composition(skc6,skc8)),join(composition(skc6,skc7),composition(skc6,skc8)))
| ~ equal(join(join(composition(skc9,skc10),composition(skc9,skc11)),composition(skc9,join(skc10,skc11))),composition(skc9,join(skc10,skc11))) ),
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)],[5,12]),
[iquote('0:Rew:5.0,12.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,13]),
[iquote('0:Rew:6.0,13.0')] ).
cnf(17,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,join(skc7,skc8)),join(composition(skc6,skc7),composition(skc6,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[9,14]),
[iquote('0:Rew:9.0,14.1,9.0,14.0')] ).
cnf(28,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(29,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(33,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,76]),
[iquote('0:Rew:4.0,76.0')] ).
cnf(88,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(92,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.0')] ).
cnf(93,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,88]),
[iquote('0:Rew:5.0,88.0')] ).
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)],[6,92]),
[iquote('0:Rew:6.0,92.0')] ).
cnf(155,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(162,plain,
equal(join(join(u,v),w),join(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(170,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc8),join(composition(skc6,join(skc7,skc8)),composition(skc6,skc7))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
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)],[9,162]),
[iquote('0:Rew:9.0,162.0')] ).
cnf(178,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc8),join(composition(skc6,skc7),composition(skc6,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[5,170]),
[iquote('0:Rew:5.0,170.1')] ).
cnf(179,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc7),join(composition(skc6,join(skc7,skc8)),composition(skc6,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[155,178]),
[iquote('0:Rew:155.0,178.1')] ).
cnf(180,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc7),join(composition(skc6,skc8),composition(skc6,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[5,179]),
[iquote('0:Rew:5.0,179.1')] ).
cnf(219,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
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)],[8,11]),
[iquote('0:SpR:8.0,11.0')] ).
cnf(395,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,28]),
[iquote('0:SpR:1.0,28.0')] ).
cnf(398,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,395]),
[iquote('0:Rew:2.0,395.0')] ).
cnf(407,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[398,1]),
[iquote('0:SpR:398.0,1.0')] ).
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)],[424,6]),
[iquote('0:SpR:424.0,6.0')] ).
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)],[466,9]),
[iquote('0:SpR:466.0,9.0')] ).
cnf(610,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[29,7]),
[iquote('0:SpR:29.0,7.0')] ).
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)],[33,8]),
[iquote('0:SpR:33.0,8.0')] ).
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)],[174,5]),
[iquote('0:SpR:174.0,5.0')] ).
cnf(2155,plain,
equal(join(u,join(v,w)),join(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[9,2057]),
[iquote('0:Rew:9.0,2057.0')] ).
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)],[2,724]),
[iquote('0:SpR:2.0,724.0')] ).
cnf(12445,plain,
equal(join(join(u,join(v,w)),x),join(u,join(join(w,v),x))),
inference(spr,[status(thm),theory(equality)],[2155,9]),
[iquote('0:SpR:2155.0,9.0')] ).
cnf(12690,plain,
equal(join(u,join(v,join(w,x))),join(u,join(w,join(v,x)))),
inference(rew,[status(thm),theory(equality)],[9,12445]),
[iquote('0:Rew:9.0,12445.0,9.0,12445.0,9.0,12445.0')] ).
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)],[18128,9]),
[iquote('0:SpR:18128.0,9.0')] ).
cnf(18259,plain,
equal(join(u,join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[18128,174]),
[iquote('0:SpR:18128.0,174.0')] ).
cnf(78131,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[4907,2]),
[iquote('0:SpR:4907.0,2.0')] ).
cnf(78349,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[2,78131]),
[iquote('0:Rew:2.0,78131.0')] ).
cnf(78351,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc7),composition(skc6,join(skc8,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[78349,180]),
[iquote('0:Rew:78349.0,180.1')] ).
cnf(78615,plain,
( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(join(composition(skc6,skc7),composition(skc6,join(skc7,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
inference(rew,[status(thm),theory(equality)],[18259,78351]),
[iquote('0:Rew:18259.0,78351.1')] ).
cnf(78616,plain,
( ~ equal(composition(skc9,join(skc10,join(skc10,join(skc11,skc11)))),composition(skc9,join(skc10,skc11)))
| ~ equal(composition(skc6,join(skc7,join(skc7,skc8))),composition(skc6,join(skc7,skc8))) ),
inference(rew,[status(thm),theory(equality)],[78349,78615,12690]),
[iquote('0:Rew:78349.0,78615.1,78349.0,78615.1,12690.0,78615.0,78349.0,78615.0,78349.0,78615.0')] ).
cnf(78617,plain,
( ~ equal(composition(skc9,join(skc10,skc11)),composition(skc9,join(skc10,skc11)))
| ~ equal(composition(skc6,join(skc7,skc8)),composition(skc6,join(skc7,skc8))) ),
inference(rew,[status(thm),theory(equality)],[18248,78616,18128]),
[iquote('0:Rew:18248.0,78616.1,18128.0,78616.0,18248.0,78616.0')] ).
cnf(78618,plain,
$false,
inference(obv,[status(thm),theory(equality)],[78617]),
[iquote('0:Obv:78617.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL008+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 09:21:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 32.44/32.61
% 32.44/32.61 SPASS V 3.9
% 32.44/32.61 SPASS beiseite: Proof found.
% 32.44/32.61 % SZS status Theorem
% 32.44/32.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.44/32.61 SPASS derived 47419 clauses, backtracked 0 clauses, performed 0 splits and kept 5710 clauses.
% 32.44/32.61 SPASS allocated 148559 KBytes.
% 32.44/32.61 SPASS spent 0:0:32.20 on the problem.
% 32.44/32.61 0:00:00.04 for the input.
% 32.44/32.61 0:00:00.03 for the FLOTTER CNF translation.
% 32.44/32.61 0:00:00.31 for inferences.
% 32.44/32.61 0:00:00.00 for the backtracking.
% 32.44/32.61 0:0:31.76 for the reduction.
% 32.44/32.61
% 32.44/32.61
% 32.44/32.61 Here is a proof with depth 6, length 68 :
% 32.44/32.61 % SZS output start Refutation
% See solution above
% 33.73/33.91 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan goals
% 33.73/33.91
%------------------------------------------------------------------------------