TSTP Solution File: TOP049-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% 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 : Thu Jul 21 21:35:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 78 RR)
% Number of literals : 78 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-9 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,u),u),
file('TOP049-1.p',unknown),
[] ).
cnf(2,axiom,
equal(product(product(u,v),v),u),
file('TOP049-1.p',unknown),
[] ).
cnf(3,axiom,
equal(product(product(u,v),product(w,v)),product(product(u,w),v)),
file('TOP049-1.p',unknown),
[] ).
cnf(4,axiom,
equal(product(a9,a7),a1),
file('TOP049-1.p',unknown),
[] ).
cnf(5,axiom,
equal(product(a1,a2),a3),
file('TOP049-1.p',unknown),
[] ).
cnf(6,axiom,
equal(product(a3,a4),a2),
file('TOP049-1.p',unknown),
[] ).
cnf(7,axiom,
equal(product(a2,a10),a5),
file('TOP049-1.p',unknown),
[] ).
cnf(8,axiom,
equal(product(a5,a4),a6),
file('TOP049-1.p',unknown),
[] ).
cnf(9,axiom,
equal(product(a6,a1),a7),
file('TOP049-1.p',unknown),
[] ).
cnf(10,axiom,
equal(product(a7,a4),a8),
file('TOP049-1.p',unknown),
[] ).
cnf(11,axiom,
equal(product(a8,a9),a10),
file('TOP049-1.p',unknown),
[] ).
cnf(12,axiom,
equal(product(a10,a3),a4),
file('TOP049-1.p',unknown),
[] ).
cnf(13,axiom,
equal(product(a4,a8),a9),
file('TOP049-1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5)),
file('TOP049-1.p',unknown),
[] ).
cnf(29,plain,
equal(product(a4,a3),a10),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(30,plain,
equal(product(a10,a9),a8),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(31,plain,
equal(product(a8,a4),a7),
inference(spr,[status(thm),theory(equality)],[10,2]),
[iquote('0:SpR:10.0,2.0')] ).
cnf(33,plain,
equal(product(a2,a4),a3),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(35,plain,
equal(product(a5,a10),a2),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(36,plain,
equal(product(a3,a2),a1),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(48,plain,
equal(product(product(u,a8),a9),product(product(u,a4),a8)),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(49,plain,
equal(product(product(u,a10),a3),product(product(u,a3),a4)),
inference(spr,[status(thm),theory(equality)],[12,3]),
[iquote('0:SpR:12.0,3.0')] ).
cnf(50,plain,
equal(product(product(u,a4),a3),product(product(u,a3),a10)),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(51,plain,
equal(product(product(u,a8),a9),product(product(u,a9),a10)),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(52,plain,
equal(product(product(u,a4),a8),product(product(u,a7),a4)),
inference(spr,[status(thm),theory(equality)],[10,3]),
[iquote('0:SpR:10.0,3.0')] ).
cnf(77,plain,
equal(product(product(u,a4),a8),product(product(u,a9),a10)),
inference(rew,[status(thm),theory(equality)],[48,51]),
[iquote('0:Rew:48.0,51.0')] ).
cnf(79,plain,
equal(product(product(u,a7),a4),product(product(u,a9),a10)),
inference(rew,[status(thm),theory(equality)],[77,52]),
[iquote('0:Rew:77.0,52.0')] ).
cnf(96,plain,
equal(product(product(a2,u),a4),product(a3,product(u,a4))),
inference(spr,[status(thm),theory(equality)],[33,3]),
[iquote('0:SpR:33.0,3.0')] ).
cnf(121,plain,
equal(product(product(a2,a3),a4),product(a5,a3)),
inference(spr,[status(thm),theory(equality)],[7,49]),
[iquote('0:SpR:7.0,49.0')] ).
cnf(122,plain,
equal(product(product(a5,a3),a4),product(a2,a3)),
inference(spr,[status(thm),theory(equality)],[35,49]),
[iquote('0:SpR:35.0,49.0')] ).
cnf(125,plain,
equal(product(a3,product(a3,a4)),product(a5,a3)),
inference(rew,[status(thm),theory(equality)],[96,121]),
[iquote('0:Rew:96.0,121.0')] ).
cnf(126,plain,
equal(product(a5,a3),a1),
inference(rew,[status(thm),theory(equality)],[36,125,6]),
[iquote('0:Rew:36.0,125.0,6.0,125.0')] ).
cnf(127,plain,
equal(product(a2,a3),product(a1,a4)),
inference(rew,[status(thm),theory(equality)],[126,122]),
[iquote('0:Rew:126.0,122.0')] ).
cnf(133,plain,
equal(product(a1,a3),a5),
inference(spr,[status(thm),theory(equality)],[126,2]),
[iquote('0:SpR:126.0,2.0')] ).
cnf(156,plain,
equal(product(product(a2,a3),a10),product(a3,a3)),
inference(spr,[status(thm),theory(equality)],[33,50]),
[iquote('0:SpR:33.0,50.0')] ).
cnf(163,plain,
equal(product(product(a1,a4),a10),a3),
inference(rew,[status(thm),theory(equality)],[127,156,1]),
[iquote('0:Rew:127.0,156.0,1.0,156.0')] ).
cnf(177,plain,
equal(product(product(a4,a9),a10),product(a4,a8)),
inference(spr,[status(thm),theory(equality)],[1,77]),
[iquote('0:SpR:1.0,77.0')] ).
cnf(183,plain,
equal(product(product(a4,a9),a10),a9),
inference(rew,[status(thm),theory(equality)],[13,177]),
[iquote('0:Rew:13.0,177.0')] ).
cnf(209,plain,
equal(product(product(a9,a9),a10),product(a1,a4)),
inference(spr,[status(thm),theory(equality)],[4,79]),
[iquote('0:SpR:4.0,79.0')] ).
cnf(213,plain,
equal(product(a9,a10),product(a1,a4)),
inference(rew,[status(thm),theory(equality)],[1,209]),
[iquote('0:Rew:1.0,209.0')] ).
cnf(233,plain,
equal(product(a4,a9),product(a9,a10)),
inference(spr,[status(thm),theory(equality)],[183,2]),
[iquote('0:SpR:183.0,2.0')] ).
cnf(237,plain,
equal(product(a4,a9),product(a1,a4)),
inference(rew,[status(thm),theory(equality)],[213,233]),
[iquote('0:Rew:213.0,233.0')] ).
cnf(238,plain,
equal(product(product(a1,a4),a10),a9),
inference(rew,[status(thm),theory(equality)],[237,183]),
[iquote('0:Rew:237.0,183.0')] ).
cnf(239,plain,
equal(a3,a9),
inference(rew,[status(thm),theory(equality)],[163,238]),
[iquote('0:Rew:163.0,238.0')] ).
cnf(240,plain,
equal(product(a10,a9),a4),
inference(rew,[status(thm),theory(equality)],[239,12]),
[iquote('0:Rew:239.0,12.0')] ).
cnf(241,plain,
equal(product(a9,a4),a2),
inference(rew,[status(thm),theory(equality)],[239,6]),
[iquote('0:Rew:239.0,6.0')] ).
cnf(243,plain,
equal(product(a4,a9),a10),
inference(rew,[status(thm),theory(equality)],[239,29]),
[iquote('0:Rew:239.0,29.0')] ).
cnf(245,plain,
~ equal(tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),tuple(a1,a9,a8,a6,a7,a2,a9,a4,a5)),
inference(rew,[status(thm),theory(equality)],[239,14]),
[iquote('0:Rew:239.0,14.0')] ).
cnf(248,plain,
equal(product(a5,a9),a1),
inference(rew,[status(thm),theory(equality)],[239,126]),
[iquote('0:Rew:239.0,126.0')] ).
cnf(249,plain,
equal(product(a1,a9),a5),
inference(rew,[status(thm),theory(equality)],[239,133]),
[iquote('0:Rew:239.0,133.0')] ).
cnf(287,plain,
equal(a8,a4),
inference(rew,[status(thm),theory(equality)],[30,240]),
[iquote('0:Rew:30.0,240.0')] ).
cnf(288,plain,
equal(product(a4,a4),a9),
inference(rew,[status(thm),theory(equality)],[287,13]),
[iquote('0:Rew:287.0,13.0')] ).
cnf(289,plain,
equal(product(a4,a9),a10),
inference(rew,[status(thm),theory(equality)],[287,11]),
[iquote('0:Rew:287.0,11.0')] ).
cnf(293,plain,
equal(product(a4,a4),a7),
inference(rew,[status(thm),theory(equality)],[287,31]),
[iquote('0:Rew:287.0,31.0')] ).
cnf(322,plain,
equal(product(a1,a4),a10),
inference(rew,[status(thm),theory(equality)],[237,243]),
[iquote('0:Rew:237.0,243.0')] ).
cnf(325,plain,
equal(a4,a9),
inference(rew,[status(thm),theory(equality)],[1,288]),
[iquote('0:Rew:1.0,288.0')] ).
cnf(326,plain,
equal(product(a5,a9),a6),
inference(rew,[status(thm),theory(equality)],[325,8]),
[iquote('0:Rew:325.0,8.0')] ).
cnf(337,plain,
equal(a8,a9),
inference(rew,[status(thm),theory(equality)],[325,287]),
[iquote('0:Rew:325.0,287.0')] ).
cnf(338,plain,
equal(product(a9,a9),a2),
inference(rew,[status(thm),theory(equality)],[325,241]),
[iquote('0:Rew:325.0,241.0')] ).
cnf(339,plain,
equal(product(a1,a9),a10),
inference(rew,[status(thm),theory(equality)],[325,322]),
[iquote('0:Rew:325.0,322.0')] ).
cnf(341,plain,
equal(product(a9,a9),a10),
inference(rew,[status(thm),theory(equality)],[325,289]),
[iquote('0:Rew:325.0,289.0')] ).
cnf(342,plain,
equal(a10,a9),
inference(rew,[status(thm),theory(equality)],[1,341]),
[iquote('0:Rew:1.0,341.0')] ).
cnf(352,plain,
equal(a4,a7),
inference(rew,[status(thm),theory(equality)],[1,293]),
[iquote('0:Rew:1.0,293.0')] ).
cnf(353,plain,
equal(a7,a9),
inference(rew,[status(thm),theory(equality)],[325,352]),
[iquote('0:Rew:325.0,352.0')] ).
cnf(354,plain,
equal(product(a6,a1),a9),
inference(rew,[status(thm),theory(equality)],[353,9]),
[iquote('0:Rew:353.0,9.0')] ).
cnf(371,plain,
equal(a6,a1),
inference(rew,[status(thm),theory(equality)],[248,326]),
[iquote('0:Rew:248.0,326.0')] ).
cnf(373,plain,
equal(a2,a9),
inference(rew,[status(thm),theory(equality)],[1,338]),
[iquote('0:Rew:1.0,338.0')] ).
cnf(376,plain,
equal(a5,a9),
inference(rew,[status(thm),theory(equality)],[249,339,342]),
[iquote('0:Rew:249.0,339.0,342.0,339.0')] ).
cnf(382,plain,
equal(product(a1,a1),a9),
inference(rew,[status(thm),theory(equality)],[371,354]),
[iquote('0:Rew:371.0,354.0')] ).
cnf(383,plain,
equal(a9,a1),
inference(rew,[status(thm),theory(equality)],[1,382]),
[iquote('0:Rew:1.0,382.0')] ).
cnf(385,plain,
equal(a4,a1),
inference(rew,[status(thm),theory(equality)],[383,325]),
[iquote('0:Rew:383.0,325.0')] ).
cnf(386,plain,
equal(a8,a1),
inference(rew,[status(thm),theory(equality)],[383,337]),
[iquote('0:Rew:383.0,337.0')] ).
cnf(387,plain,
equal(a10,a1),
inference(rew,[status(thm),theory(equality)],[383,342]),
[iquote('0:Rew:383.0,342.0')] ).
cnf(388,plain,
equal(a7,a1),
inference(rew,[status(thm),theory(equality)],[383,353]),
[iquote('0:Rew:383.0,353.0')] ).
cnf(389,plain,
equal(a2,a1),
inference(rew,[status(thm),theory(equality)],[383,373]),
[iquote('0:Rew:383.0,373.0')] ).
cnf(390,plain,
equal(a5,a1),
inference(rew,[status(thm),theory(equality)],[383,376]),
[iquote('0:Rew:383.0,376.0')] ).
cnf(518,plain,
~ equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)),
inference(rew,[status(thm),theory(equality)],[387,245,386,371,388,389,383,385,390]),
[iquote('0:Rew:387.0,245.0,386.0,245.0,371.0,245.0,388.0,245.0,389.0,245.0,383.0,245.0,385.0,245.0,390.0,245.0')] ).
cnf(519,plain,
$false,
inference(obv,[status(thm),theory(equality)],[518]),
[iquote('0:Obv:518.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.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 : Sun May 29 08:01:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 312 clauses, backtracked 0 clauses, performed 0 splits and kept 151 clauses.
% 0.20/0.44 SPASS allocated 63492 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.03 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.03 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 3, length 78 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : involutory_quandle involutory_quandle_01 involutory_quandle_02 knot knot_03 knot_04 knot_05 knot_06 knot_07 knot_08 knot_09 knot_10 knot_11 goal
% 0.20/0.44
%------------------------------------------------------------------------------