TSTP Solution File: TOP050-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 0.98s 1.16s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 35
% Syntax : Number of clauses : 209 ( 209 unt; 0 nHn; 209 RR)
% Number of literals : 209 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 35 con; 0-31 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,u),u),
file('TOP050-1.p',unknown),
[] ).
cnf(2,axiom,
equal(product(product(u,v),v),u),
file('TOP050-1.p',unknown),
[] ).
cnf(3,axiom,
equal(product(product(u,v),product(w,v)),product(product(u,w),v)),
file('TOP050-1.p',unknown),
[] ).
cnf(4,axiom,
equal(product(a1,a31),a2),
file('TOP050-1.p',unknown),
[] ).
cnf(5,axiom,
equal(product(a2,a25),a3),
file('TOP050-1.p',unknown),
[] ).
cnf(6,axiom,
equal(product(a3,a29),a4),
file('TOP050-1.p',unknown),
[] ).
cnf(7,axiom,
equal(product(a4,a11),a5),
file('TOP050-1.p',unknown),
[] ).
cnf(8,axiom,
equal(product(a5,a15),a6),
file('TOP050-1.p',unknown),
[] ).
cnf(9,axiom,
equal(product(a7,a19),a8),
file('TOP050-1.p',unknown),
[] ).
cnf(10,axiom,
equal(product(a8,a5),a9),
file('TOP050-1.p',unknown),
[] ).
cnf(11,axiom,
equal(product(a9,a17),a10),
file('TOP050-1.p',unknown),
[] ).
cnf(12,axiom,
equal(product(a10,a7),a11),
file('TOP050-1.p',unknown),
[] ).
cnf(13,axiom,
equal(product(a11,a5),a12),
file('TOP050-1.p',unknown),
[] ).
cnf(14,axiom,
equal(product(a12,a19),a13),
file('TOP050-1.p',unknown),
[] ).
cnf(15,axiom,
equal(product(a13,a7),a14),
file('TOP050-1.p',unknown),
[] ).
cnf(16,axiom,
equal(product(a14,a17),a15),
file('TOP050-1.p',unknown),
[] ).
cnf(17,axiom,
equal(product(a15,a5),a16),
file('TOP050-1.p',unknown),
[] ).
cnf(18,axiom,
equal(product(a16,a19),a17),
file('TOP050-1.p',unknown),
[] ).
cnf(19,axiom,
equal(product(a17,a9),a18),
file('TOP050-1.p',unknown),
[] ).
cnf(20,axiom,
equal(product(a18,a15),a19),
file('TOP050-1.p',unknown),
[] ).
cnf(21,axiom,
equal(product(a19,a11),a20),
file('TOP050-1.p',unknown),
[] ).
cnf(22,axiom,
equal(product(a20,a29),a21),
file('TOP050-1.p',unknown),
[] ).
cnf(23,axiom,
equal(product(a21,a25),a22),
file('TOP050-1.p',unknown),
[] ).
cnf(24,axiom,
equal(product(a22,a31),a23),
file('TOP050-1.p',unknown),
[] ).
cnf(25,axiom,
equal(product(a23,a21),a24),
file('TOP050-1.p',unknown),
[] ).
cnf(26,axiom,
equal(product(a24,a3),a25),
file('TOP050-1.p',unknown),
[] ).
cnf(27,axiom,
equal(product(a25,a23),a26),
file('TOP050-1.p',unknown),
[] ).
cnf(28,axiom,
equal(product(a26,a1),a27),
file('TOP050-1.p',unknown),
[] ).
cnf(29,axiom,
equal(product(a27,a21),a28),
file('TOP050-1.p',unknown),
[] ).
cnf(30,axiom,
equal(product(a28,a3),a29),
file('TOP050-1.p',unknown),
[] ).
cnf(31,axiom,
equal(product(a29,a1),a30),
file('TOP050-1.p',unknown),
[] ).
cnf(32,axiom,
equal(product(a30,a23),a31),
file('TOP050-1.p',unknown),
[] ).
cnf(33,axiom,
equal(product(a31,a3),a32),
file('TOP050-1.p',unknown),
[] ).
cnf(34,axiom,
equal(product(a32,a21),a1),
file('TOP050-1.p',unknown),
[] ).
cnf(35,axiom,
~ equal(tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28),tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27)),
file('TOP050-1.p',unknown),
[] ).
cnf(70,plain,
equal(product(a1,a21),a32),
inference(spr,[status(thm),theory(equality)],[34,2]),
[iquote('0:SpR:34.0,2.0')] ).
cnf(71,plain,
equal(product(a28,a21),a27),
inference(spr,[status(thm),theory(equality)],[29,2]),
[iquote('0:SpR:29.0,2.0')] ).
cnf(73,plain,
equal(product(a32,a3),a31),
inference(spr,[status(thm),theory(equality)],[33,2]),
[iquote('0:SpR:33.0,2.0')] ).
cnf(74,plain,
equal(product(a29,a3),a28),
inference(spr,[status(thm),theory(equality)],[30,2]),
[iquote('0:SpR:30.0,2.0')] ).
cnf(75,plain,
equal(product(a25,a3),a24),
inference(spr,[status(thm),theory(equality)],[26,2]),
[iquote('0:SpR:26.0,2.0')] ).
cnf(76,plain,
equal(product(a31,a23),a30),
inference(spr,[status(thm),theory(equality)],[32,2]),
[iquote('0:SpR:32.0,2.0')] ).
cnf(78,plain,
equal(product(a30,a1),a29),
inference(spr,[status(thm),theory(equality)],[31,2]),
[iquote('0:SpR:31.0,2.0')] ).
cnf(79,plain,
equal(product(a27,a1),a26),
inference(spr,[status(thm),theory(equality)],[28,2]),
[iquote('0:SpR:28.0,2.0')] ).
cnf(80,plain,
equal(product(a23,a31),a22),
inference(spr,[status(thm),theory(equality)],[24,2]),
[iquote('0:SpR:24.0,2.0')] ).
cnf(81,plain,
equal(product(a2,a31),a1),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(82,plain,
equal(product(a22,a25),a21),
inference(spr,[status(thm),theory(equality)],[23,2]),
[iquote('0:SpR:23.0,2.0')] ).
cnf(83,plain,
equal(product(a3,a25),a2),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(84,plain,
equal(product(a21,a29),a20),
inference(spr,[status(thm),theory(equality)],[22,2]),
[iquote('0:SpR:22.0,2.0')] ).
cnf(86,plain,
equal(product(a20,a11),a19),
inference(spr,[status(thm),theory(equality)],[21,2]),
[iquote('0:SpR:21.0,2.0')] ).
cnf(87,plain,
equal(product(a5,a11),a4),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(88,plain,
equal(product(a19,a15),a18),
inference(spr,[status(thm),theory(equality)],[20,2]),
[iquote('0:SpR:20.0,2.0')] ).
cnf(93,plain,
equal(product(a8,a19),a7),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(94,plain,
equal(product(a16,a5),a15),
inference(spr,[status(thm),theory(equality)],[17,2]),
[iquote('0:SpR:17.0,2.0')] ).
cnf(95,plain,
equal(product(a12,a5),a11),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(97,plain,
equal(product(a15,a17),a14),
inference(spr,[status(thm),theory(equality)],[16,2]),
[iquote('0:SpR:16.0,2.0')] ).
cnf(98,plain,
equal(product(a10,a17),a9),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(99,plain,
equal(product(a14,a7),a13),
inference(spr,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpR:15.0,2.0')] ).
cnf(100,plain,
equal(product(a11,a7),a10),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(111,plain,
equal(product(product(u,a23),a21),product(product(u,a21),a24)),
inference(spr,[status(thm),theory(equality)],[25,3]),
[iquote('0:SpR:25.0,3.0')] ).
cnf(112,plain,
equal(product(product(u,a21),a32),product(product(u,a1),a21)),
inference(spr,[status(thm),theory(equality)],[70,3]),
[iquote('0:SpR:70.0,3.0')] ).
cnf(115,plain,
equal(product(product(u,a24),a3),product(product(u,a3),a25)),
inference(spr,[status(thm),theory(equality)],[26,3]),
[iquote('0:SpR:26.0,3.0')] ).
cnf(116,plain,
equal(product(product(u,a30),a23),product(product(u,a23),a31)),
inference(spr,[status(thm),theory(equality)],[32,3]),
[iquote('0:SpR:32.0,3.0')] ).
cnf(121,plain,
equal(product(product(u,a31),a2),product(product(u,a1),a31)),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(122,plain,
equal(product(product(u,a21),a25),product(product(u,a25),a22)),
inference(spr,[status(thm),theory(equality)],[23,3]),
[iquote('0:SpR:23.0,3.0')] ).
cnf(148,plain,
equal(product(product(a28,u),a3),product(a29,product(u,a3))),
inference(spr,[status(thm),theory(equality)],[30,3]),
[iquote('0:SpR:30.0,3.0')] ).
cnf(220,plain,
equal(product(product(u,a23),a31),product(product(u,a31),a22)),
inference(spr,[status(thm),theory(equality)],[80,3]),
[iquote('0:SpR:80.0,3.0')] ).
cnf(221,plain,
equal(product(product(u,a30),a23),product(product(u,a31),a22)),
inference(rew,[status(thm),theory(equality)],[220,116]),
[iquote('0:Rew:220.0,116.0')] ).
cnf(233,plain,
equal(product(product(u,a3),a25),product(product(u,a25),a2)),
inference(spr,[status(thm),theory(equality)],[83,3]),
[iquote('0:SpR:83.0,3.0')] ).
cnf(234,plain,
equal(product(product(u,a24),a3),product(product(u,a25),a2)),
inference(rew,[status(thm),theory(equality)],[233,115]),
[iquote('0:Rew:233.0,115.0')] ).
cnf(332,plain,
equal(product(product(a25,a21),a24),product(a26,a21)),
inference(spr,[status(thm),theory(equality)],[27,111]),
[iquote('0:SpR:27.0,111.0')] ).
cnf(403,plain,
equal(product(product(a27,a1),a21),product(a28,a32)),
inference(spr,[status(thm),theory(equality)],[29,112]),
[iquote('0:SpR:29.0,112.0')] ).
cnf(415,plain,
equal(product(a28,a32),product(a26,a21)),
inference(rew,[status(thm),theory(equality)],[79,403]),
[iquote('0:Rew:79.0,403.0')] ).
cnf(1295,plain,
equal(product(product(a26,a21),a3),product(a29,product(a32,a3))),
inference(spr,[status(thm),theory(equality)],[415,148]),
[iquote('0:SpR:415.0,148.0')] ).
cnf(1305,plain,
equal(product(product(a26,a21),a3),product(a29,a31)),
inference(rew,[status(thm),theory(equality)],[73,1295]),
[iquote('0:Rew:73.0,1295.0')] ).
cnf(2124,plain,
equal(product(product(a30,a31),a22),product(a30,a23)),
inference(spr,[status(thm),theory(equality)],[1,221]),
[iquote('0:SpR:1.0,221.0')] ).
cnf(2131,plain,
equal(product(product(a30,a31),a22),a31),
inference(rew,[status(thm),theory(equality)],[32,2124]),
[iquote('0:Rew:32.0,2124.0')] ).
cnf(2135,plain,
equal(product(a30,a31),product(a31,a22)),
inference(spr,[status(thm),theory(equality)],[2131,2]),
[iquote('0:SpR:2131.0,2.0')] ).
cnf(2177,plain,
equal(product(product(product(a25,a21),a25),a2),product(product(a26,a21),a3)),
inference(spr,[status(thm),theory(equality)],[332,234]),
[iquote('0:SpR:332.0,234.0')] ).
cnf(2185,plain,
equal(product(product(a25,a22),a2),product(a29,a31)),
inference(rew,[status(thm),theory(equality)],[1,2177,122,1305]),
[iquote('0:Rew:1.0,2177.0,122.0,2177.0,1305.0,2177.0')] ).
cnf(3407,plain,
equal(product(product(a29,a31),a2),product(a25,a22)),
inference(spr,[status(thm),theory(equality)],[2185,2]),
[iquote('0:SpR:2185.0,2.0')] ).
cnf(3413,plain,
equal(product(a25,a22),product(a31,a22)),
inference(rew,[status(thm),theory(equality)],[2135,3407,31,121]),
[iquote('0:Rew:2135.0,3407.0,31.0,3407.0,121.0,3407.0')] ).
cnf(3423,plain,
equal(product(product(a31,a22),a22),a25),
inference(spr,[status(thm),theory(equality)],[3413,2]),
[iquote('0:SpR:3413.0,2.0')] ).
cnf(3431,plain,
equal(a25,a31),
inference(rew,[status(thm),theory(equality)],[2,3423]),
[iquote('0:Rew:2.0,3423.0')] ).
cnf(3432,plain,
equal(product(a31,a23),a26),
inference(rew,[status(thm),theory(equality)],[3431,27]),
[iquote('0:Rew:3431.0,27.0')] ).
cnf(3434,plain,
equal(product(a21,a31),a22),
inference(rew,[status(thm),theory(equality)],[3431,23]),
[iquote('0:Rew:3431.0,23.0')] ).
cnf(3435,plain,
equal(product(a2,a31),a3),
inference(rew,[status(thm),theory(equality)],[3431,5]),
[iquote('0:Rew:3431.0,5.0')] ).
cnf(3436,plain,
~ equal(tuple(a2,a31,a32,a3,a31,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28),tuple(a1,a30,a31,a2,a24,a31,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27)),
inference(rew,[status(thm),theory(equality)],[3431,35]),
[iquote('0:Rew:3431.0,35.0')] ).
cnf(3437,plain,
equal(product(a31,a3),a24),
inference(rew,[status(thm),theory(equality)],[3431,75]),
[iquote('0:Rew:3431.0,75.0')] ).
cnf(3439,plain,
equal(product(a22,a31),a21),
inference(rew,[status(thm),theory(equality)],[3431,82]),
[iquote('0:Rew:3431.0,82.0')] ).
cnf(3638,plain,
equal(a30,a26),
inference(rew,[status(thm),theory(equality)],[76,3432]),
[iquote('0:Rew:76.0,3432.0')] ).
cnf(3639,plain,
equal(product(a26,a23),a31),
inference(rew,[status(thm),theory(equality)],[3638,32]),
[iquote('0:Rew:3638.0,32.0')] ).
cnf(3640,plain,
equal(product(a29,a1),a26),
inference(rew,[status(thm),theory(equality)],[3638,31]),
[iquote('0:Rew:3638.0,31.0')] ).
cnf(3642,plain,
equal(product(a26,a1),a29),
inference(rew,[status(thm),theory(equality)],[3638,78]),
[iquote('0:Rew:3638.0,78.0')] ).
cnf(3730,plain,
equal(a3,a1),
inference(rew,[status(thm),theory(equality)],[81,3435]),
[iquote('0:Rew:81.0,3435.0')] ).
cnf(3731,plain,
equal(product(a31,a1),a32),
inference(rew,[status(thm),theory(equality)],[3730,33]),
[iquote('0:Rew:3730.0,33.0')] ).
cnf(3733,plain,
equal(product(a1,a29),a4),
inference(rew,[status(thm),theory(equality)],[3730,6]),
[iquote('0:Rew:3730.0,6.0')] ).
cnf(3734,plain,
equal(product(a32,a1),a31),
inference(rew,[status(thm),theory(equality)],[3730,73]),
[iquote('0:Rew:3730.0,73.0')] ).
cnf(3735,plain,
equal(product(a29,a1),a28),
inference(rew,[status(thm),theory(equality)],[3730,74]),
[iquote('0:Rew:3730.0,74.0')] ).
cnf(3828,plain,
equal(product(a31,a1),a24),
inference(rew,[status(thm),theory(equality)],[3730,3437]),
[iquote('0:Rew:3730.0,3437.0')] ).
cnf(3831,plain,
equal(a23,a21),
inference(rew,[status(thm),theory(equality)],[24,3439]),
[iquote('0:Rew:24.0,3439.0')] ).
cnf(3832,plain,
equal(product(a21,a21),a24),
inference(rew,[status(thm),theory(equality)],[3831,25]),
[iquote('0:Rew:3831.0,25.0')] ).
cnf(3875,plain,
equal(product(a26,a21),a31),
inference(rew,[status(thm),theory(equality)],[3831,3639]),
[iquote('0:Rew:3831.0,3639.0')] ).
cnf(3889,plain,
equal(a27,a29),
inference(rew,[status(thm),theory(equality)],[28,3642]),
[iquote('0:Rew:28.0,3642.0')] ).
cnf(3892,plain,
equal(product(a28,a21),a29),
inference(rew,[status(thm),theory(equality)],[3889,71]),
[iquote('0:Rew:3889.0,71.0')] ).
cnf(3893,plain,
equal(product(a29,a1),a26),
inference(rew,[status(thm),theory(equality)],[3889,79]),
[iquote('0:Rew:3889.0,79.0')] ).
cnf(3920,plain,
equal(a32,a24),
inference(rew,[status(thm),theory(equality)],[3828,3731]),
[iquote('0:Rew:3828.0,3731.0')] ).
cnf(3921,plain,
equal(product(a24,a21),a1),
inference(rew,[status(thm),theory(equality)],[3920,34]),
[iquote('0:Rew:3920.0,34.0')] ).
cnf(3948,plain,
equal(product(a24,a1),a31),
inference(rew,[status(thm),theory(equality)],[3920,3734]),
[iquote('0:Rew:3920.0,3734.0')] ).
cnf(3949,plain,
equal(a28,a26),
inference(rew,[status(thm),theory(equality)],[3640,3735]),
[iquote('0:Rew:3640.0,3735.0')] ).
cnf(3956,plain,
equal(a24,a21),
inference(rew,[status(thm),theory(equality)],[1,3832]),
[iquote('0:Rew:1.0,3832.0')] ).
cnf(3957,plain,
equal(product(a31,a1),a21),
inference(rew,[status(thm),theory(equality)],[3956,3828]),
[iquote('0:Rew:3956.0,3828.0')] ).
cnf(3958,plain,
equal(a32,a21),
inference(rew,[status(thm),theory(equality)],[3956,3920]),
[iquote('0:Rew:3956.0,3920.0')] ).
cnf(3959,plain,
equal(product(a21,a1),a31),
inference(rew,[status(thm),theory(equality)],[3956,3948]),
[iquote('0:Rew:3956.0,3948.0')] ).
cnf(3964,plain,
equal(a29,a31),
inference(rew,[status(thm),theory(equality)],[3875,3892,3949]),
[iquote('0:Rew:3875.0,3892.0,3949.0,3892.0')] ).
cnf(3966,plain,
equal(product(a21,a31),a20),
inference(rew,[status(thm),theory(equality)],[3964,84]),
[iquote('0:Rew:3964.0,84.0')] ).
cnf(3997,plain,
equal(a27,a31),
inference(rew,[status(thm),theory(equality)],[3964,3889]),
[iquote('0:Rew:3964.0,3889.0')] ).
cnf(3998,plain,
equal(product(a1,a31),a4),
inference(rew,[status(thm),theory(equality)],[3964,3733]),
[iquote('0:Rew:3964.0,3733.0')] ).
cnf(4002,plain,
equal(product(a31,a1),a26),
inference(rew,[status(thm),theory(equality)],[3964,3893]),
[iquote('0:Rew:3964.0,3893.0')] ).
cnf(4003,plain,
equal(product(a21,a21),a1),
inference(rew,[status(thm),theory(equality)],[3956,3921]),
[iquote('0:Rew:3956.0,3921.0')] ).
cnf(4004,plain,
equal(a21,a1),
inference(rew,[status(thm),theory(equality)],[1,4003]),
[iquote('0:Rew:1.0,4003.0')] ).
cnf(4006,plain,
equal(product(a1,a31),a22),
inference(rew,[status(thm),theory(equality)],[4004,3434]),
[iquote('0:Rew:4004.0,3434.0')] ).
cnf(4007,plain,
equal(a23,a1),
inference(rew,[status(thm),theory(equality)],[4004,3831]),
[iquote('0:Rew:4004.0,3831.0')] ).
cnf(4010,plain,
equal(a24,a1),
inference(rew,[status(thm),theory(equality)],[4004,3956]),
[iquote('0:Rew:4004.0,3956.0')] ).
cnf(4011,plain,
equal(a32,a1),
inference(rew,[status(thm),theory(equality)],[4004,3958]),
[iquote('0:Rew:4004.0,3958.0')] ).
cnf(4015,plain,
equal(a26,a1),
inference(rew,[status(thm),theory(equality)],[4002,3957,4004]),
[iquote('0:Rew:4002.0,3957.0,4004.0,3957.0')] ).
cnf(4016,plain,
equal(a30,a1),
inference(rew,[status(thm),theory(equality)],[4015,3638]),
[iquote('0:Rew:4015.0,3638.0')] ).
cnf(4017,plain,
equal(a28,a1),
inference(rew,[status(thm),theory(equality)],[4015,3949]),
[iquote('0:Rew:4015.0,3949.0')] ).
cnf(4020,plain,
equal(product(a1,a1),a31),
inference(rew,[status(thm),theory(equality)],[4004,3959]),
[iquote('0:Rew:4004.0,3959.0')] ).
cnf(4021,plain,
equal(a31,a1),
inference(rew,[status(thm),theory(equality)],[1,4020]),
[iquote('0:Rew:1.0,4020.0')] ).
cnf(4022,plain,
equal(product(a1,a1),a2),
inference(rew,[status(thm),theory(equality)],[4021,4]),
[iquote('0:Rew:4021.0,4.0')] ).
cnf(4037,plain,
equal(a29,a1),
inference(rew,[status(thm),theory(equality)],[4021,3964]),
[iquote('0:Rew:4021.0,3964.0')] ).
cnf(4038,plain,
equal(a27,a1),
inference(rew,[status(thm),theory(equality)],[4021,3997]),
[iquote('0:Rew:4021.0,3997.0')] ).
cnf(4040,plain,
equal(product(a1,a1),a20),
inference(rew,[status(thm),theory(equality)],[4004,3966,4021]),
[iquote('0:Rew:4004.0,3966.0,4021.0,3966.0')] ).
cnf(4041,plain,
equal(a20,a1),
inference(rew,[status(thm),theory(equality)],[1,4040]),
[iquote('0:Rew:1.0,4040.0')] ).
cnf(4043,plain,
equal(product(a1,a11),a19),
inference(rew,[status(thm),theory(equality)],[4041,86]),
[iquote('0:Rew:4041.0,86.0')] ).
cnf(4097,plain,
equal(product(a1,a1),a4),
inference(rew,[status(thm),theory(equality)],[4021,3998]),
[iquote('0:Rew:4021.0,3998.0')] ).
cnf(4098,plain,
equal(a4,a1),
inference(rew,[status(thm),theory(equality)],[1,4097]),
[iquote('0:Rew:1.0,4097.0')] ).
cnf(4099,plain,
equal(product(a1,a11),a5),
inference(rew,[status(thm),theory(equality)],[4098,7]),
[iquote('0:Rew:4098.0,7.0')] ).
cnf(4100,plain,
equal(product(a5,a11),a1),
inference(rew,[status(thm),theory(equality)],[4098,87]),
[iquote('0:Rew:4098.0,87.0')] ).
cnf(4221,plain,
equal(product(a1,a1),a22),
inference(rew,[status(thm),theory(equality)],[4021,4006]),
[iquote('0:Rew:4021.0,4006.0')] ).
cnf(4222,plain,
equal(a22,a1),
inference(rew,[status(thm),theory(equality)],[1,4221]),
[iquote('0:Rew:1.0,4221.0')] ).
cnf(4228,plain,
equal(a2,a1),
inference(rew,[status(thm),theory(equality)],[1,4022]),
[iquote('0:Rew:1.0,4022.0')] ).
cnf(4230,plain,
equal(a19,a5),
inference(rew,[status(thm),theory(equality)],[4043,4099]),
[iquote('0:Rew:4043.0,4099.0')] ).
cnf(4231,plain,
equal(product(a18,a15),a5),
inference(rew,[status(thm),theory(equality)],[4230,20]),
[iquote('0:Rew:4230.0,20.0')] ).
cnf(4232,plain,
equal(product(a16,a5),a17),
inference(rew,[status(thm),theory(equality)],[4230,18]),
[iquote('0:Rew:4230.0,18.0')] ).
cnf(4233,plain,
equal(product(a12,a5),a13),
inference(rew,[status(thm),theory(equality)],[4230,14]),
[iquote('0:Rew:4230.0,14.0')] ).
cnf(4234,plain,
equal(product(a7,a5),a8),
inference(rew,[status(thm),theory(equality)],[4230,9]),
[iquote('0:Rew:4230.0,9.0')] ).
cnf(4235,plain,
equal(product(a5,a15),a18),
inference(rew,[status(thm),theory(equality)],[4230,88]),
[iquote('0:Rew:4230.0,88.0')] ).
cnf(4238,plain,
equal(product(a8,a5),a7),
inference(rew,[status(thm),theory(equality)],[4230,93]),
[iquote('0:Rew:4230.0,93.0')] ).
cnf(4364,plain,
equal(a17,a15),
inference(rew,[status(thm),theory(equality)],[94,4232]),
[iquote('0:Rew:94.0,4232.0')] ).
cnf(4365,plain,
equal(product(a15,a9),a18),
inference(rew,[status(thm),theory(equality)],[4364,19]),
[iquote('0:Rew:4364.0,19.0')] ).
cnf(4369,plain,
equal(product(a15,a15),a14),
inference(rew,[status(thm),theory(equality)],[4364,97]),
[iquote('0:Rew:4364.0,97.0')] ).
cnf(4370,plain,
equal(product(a10,a15),a9),
inference(rew,[status(thm),theory(equality)],[4364,98]),
[iquote('0:Rew:4364.0,98.0')] ).
cnf(4449,plain,
equal(a13,a11),
inference(rew,[status(thm),theory(equality)],[95,4233]),
[iquote('0:Rew:95.0,4233.0')] ).
cnf(4450,plain,
equal(product(a11,a7),a14),
inference(rew,[status(thm),theory(equality)],[4449,15]),
[iquote('0:Rew:4449.0,15.0')] ).
cnf(4451,plain,
equal(product(a14,a7),a11),
inference(rew,[status(thm),theory(equality)],[4449,99]),
[iquote('0:Rew:4449.0,99.0')] ).
cnf(4469,plain,
equal(a18,a6),
inference(rew,[status(thm),theory(equality)],[8,4235]),
[iquote('0:Rew:8.0,4235.0')] ).
cnf(4482,plain,
equal(product(a6,a15),a5),
inference(rew,[status(thm),theory(equality)],[4469,4231]),
[iquote('0:Rew:4469.0,4231.0')] ).
cnf(4485,plain,
equal(a9,a7),
inference(rew,[status(thm),theory(equality)],[10,4238]),
[iquote('0:Rew:10.0,4238.0')] ).
cnf(4501,plain,
equal(product(a15,a7),a6),
inference(rew,[status(thm),theory(equality)],[4485,4365,4469]),
[iquote('0:Rew:4485.0,4365.0,4469.0,4365.0')] ).
cnf(4504,plain,
equal(a14,a15),
inference(rew,[status(thm),theory(equality)],[1,4369]),
[iquote('0:Rew:1.0,4369.0')] ).
cnf(4506,plain,
equal(product(a10,a15),a7),
inference(rew,[status(thm),theory(equality)],[4485,4370]),
[iquote('0:Rew:4485.0,4370.0')] ).
cnf(4507,plain,
equal(a14,a10),
inference(rew,[status(thm),theory(equality)],[100,4450]),
[iquote('0:Rew:100.0,4450.0')] ).
cnf(4508,plain,
equal(a10,a15),
inference(rew,[status(thm),theory(equality)],[4504,4507]),
[iquote('0:Rew:4504.0,4507.0')] ).
cnf(4525,plain,
equal(product(a15,a15),a7),
inference(rew,[status(thm),theory(equality)],[4508,4506]),
[iquote('0:Rew:4508.0,4506.0')] ).
cnf(4526,plain,
equal(a6,a11),
inference(rew,[status(thm),theory(equality)],[4501,4451,4504]),
[iquote('0:Rew:4501.0,4451.0,4504.0,4451.0')] ).
cnf(4553,plain,
equal(a18,a11),
inference(rew,[status(thm),theory(equality)],[4526,4469]),
[iquote('0:Rew:4526.0,4469.0')] ).
cnf(4554,plain,
equal(product(a15,a7),a11),
inference(rew,[status(thm),theory(equality)],[4526,4501]),
[iquote('0:Rew:4526.0,4501.0')] ).
cnf(4556,plain,
equal(product(a11,a15),a5),
inference(rew,[status(thm),theory(equality)],[4526,4482]),
[iquote('0:Rew:4526.0,4482.0')] ).
cnf(4557,plain,
equal(a7,a15),
inference(rew,[status(thm),theory(equality)],[1,4525]),
[iquote('0:Rew:1.0,4525.0')] ).
cnf(4558,plain,
equal(product(a15,a5),a8),
inference(rew,[status(thm),theory(equality)],[4557,4234]),
[iquote('0:Rew:4557.0,4234.0')] ).
cnf(4559,plain,
equal(a9,a15),
inference(rew,[status(thm),theory(equality)],[4557,4485]),
[iquote('0:Rew:4557.0,4485.0')] ).
cnf(4564,plain,
equal(product(a15,a15),a11),
inference(rew,[status(thm),theory(equality)],[4557,4554]),
[iquote('0:Rew:4557.0,4554.0')] ).
cnf(4565,plain,
equal(a15,a11),
inference(rew,[status(thm),theory(equality)],[1,4564]),
[iquote('0:Rew:1.0,4564.0')] ).
cnf(4566,plain,
equal(product(a11,a5),a16),
inference(rew,[status(thm),theory(equality)],[4565,17]),
[iquote('0:Rew:4565.0,17.0')] ).
cnf(4583,plain,
equal(a17,a11),
inference(rew,[status(thm),theory(equality)],[4565,4364]),
[iquote('0:Rew:4565.0,4364.0')] ).
cnf(4584,plain,
equal(a14,a11),
inference(rew,[status(thm),theory(equality)],[4565,4504]),
[iquote('0:Rew:4565.0,4504.0')] ).
cnf(4585,plain,
equal(a10,a11),
inference(rew,[status(thm),theory(equality)],[4565,4508]),
[iquote('0:Rew:4565.0,4508.0')] ).
cnf(4586,plain,
equal(product(a11,a11),a5),
inference(rew,[status(thm),theory(equality)],[4565,4556]),
[iquote('0:Rew:4565.0,4556.0')] ).
cnf(4587,plain,
equal(a7,a11),
inference(rew,[status(thm),theory(equality)],[4565,4557]),
[iquote('0:Rew:4565.0,4557.0')] ).
cnf(4588,plain,
equal(a9,a11),
inference(rew,[status(thm),theory(equality)],[4565,4559]),
[iquote('0:Rew:4565.0,4559.0')] ).
cnf(4591,plain,
equal(product(a11,a5),a8),
inference(rew,[status(thm),theory(equality)],[4565,4558]),
[iquote('0:Rew:4565.0,4558.0')] ).
cnf(4592,plain,
equal(a12,a8),
inference(rew,[status(thm),theory(equality)],[13,4591]),
[iquote('0:Rew:13.0,4591.0')] ).
cnf(4593,plain,
equal(product(a11,a5),a8),
inference(rew,[status(thm),theory(equality)],[4592,13]),
[iquote('0:Rew:4592.0,13.0')] ).
cnf(4603,plain,
equal(a5,a11),
inference(rew,[status(thm),theory(equality)],[1,4586]),
[iquote('0:Rew:1.0,4586.0')] ).
cnf(4604,plain,
equal(a19,a11),
inference(rew,[status(thm),theory(equality)],[4603,4230]),
[iquote('0:Rew:4603.0,4230.0')] ).
cnf(4605,plain,
equal(product(a11,a11),a1),
inference(rew,[status(thm),theory(equality)],[4603,4100]),
[iquote('0:Rew:4603.0,4100.0')] ).
cnf(4608,plain,
equal(product(a11,a11),a16),
inference(rew,[status(thm),theory(equality)],[4603,4566]),
[iquote('0:Rew:4603.0,4566.0')] ).
cnf(4611,plain,
equal(product(a11,a11),a8),
inference(rew,[status(thm),theory(equality)],[4603,4593]),
[iquote('0:Rew:4603.0,4593.0')] ).
cnf(4612,plain,
equal(a8,a11),
inference(rew,[status(thm),theory(equality)],[1,4611]),
[iquote('0:Rew:1.0,4611.0')] ).
cnf(4613,plain,
equal(a12,a11),
inference(rew,[status(thm),theory(equality)],[4612,4592]),
[iquote('0:Rew:4612.0,4592.0')] ).
cnf(4615,plain,
equal(a11,a1),
inference(rew,[status(thm),theory(equality)],[1,4605]),
[iquote('0:Rew:1.0,4605.0')] ).
cnf(4616,plain,
equal(a13,a1),
inference(rew,[status(thm),theory(equality)],[4615,4449]),
[iquote('0:Rew:4615.0,4449.0')] ).
cnf(4617,plain,
equal(a6,a1),
inference(rew,[status(thm),theory(equality)],[4615,4526]),
[iquote('0:Rew:4615.0,4526.0')] ).
cnf(4618,plain,
equal(a18,a1),
inference(rew,[status(thm),theory(equality)],[4615,4553]),
[iquote('0:Rew:4615.0,4553.0')] ).
cnf(4619,plain,
equal(a15,a1),
inference(rew,[status(thm),theory(equality)],[4615,4565]),
[iquote('0:Rew:4615.0,4565.0')] ).
cnf(4620,plain,
equal(a17,a1),
inference(rew,[status(thm),theory(equality)],[4615,4583]),
[iquote('0:Rew:4615.0,4583.0')] ).
cnf(4621,plain,
equal(a14,a1),
inference(rew,[status(thm),theory(equality)],[4615,4584]),
[iquote('0:Rew:4615.0,4584.0')] ).
cnf(4622,plain,
equal(a10,a1),
inference(rew,[status(thm),theory(equality)],[4615,4585]),
[iquote('0:Rew:4615.0,4585.0')] ).
cnf(4623,plain,
equal(a7,a1),
inference(rew,[status(thm),theory(equality)],[4615,4587]),
[iquote('0:Rew:4615.0,4587.0')] ).
cnf(4624,plain,
equal(a9,a1),
inference(rew,[status(thm),theory(equality)],[4615,4588]),
[iquote('0:Rew:4615.0,4588.0')] ).
cnf(4625,plain,
equal(a5,a1),
inference(rew,[status(thm),theory(equality)],[4615,4603]),
[iquote('0:Rew:4615.0,4603.0')] ).
cnf(4626,plain,
equal(a19,a1),
inference(rew,[status(thm),theory(equality)],[4615,4604]),
[iquote('0:Rew:4615.0,4604.0')] ).
cnf(4627,plain,
equal(a8,a1),
inference(rew,[status(thm),theory(equality)],[4615,4612]),
[iquote('0:Rew:4615.0,4612.0')] ).
cnf(4628,plain,
equal(a12,a1),
inference(rew,[status(thm),theory(equality)],[4615,4613]),
[iquote('0:Rew:4615.0,4613.0')] ).
cnf(4631,plain,
equal(a16,a11),
inference(rew,[status(thm),theory(equality)],[1,4608]),
[iquote('0:Rew:1.0,4608.0')] ).
cnf(4632,plain,
equal(a16,a1),
inference(rew,[status(thm),theory(equality)],[4615,4631]),
[iquote('0:Rew:4615.0,4631.0')] ).
cnf(6231,plain,
~ equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1,a1)),
inference(rew,[status(thm),theory(equality)],[4011,3436,4016,4228,4010,4021,3730,4017,4037,4098,4622,4615,4625,4621,4619,4617,4623,4618,4626,4627,4624,4632,4620,4628,4616,4041,4004,4222,4007,4015,4038]),
[iquote('0:Rew:4011.0,3436.0,4016.0,3436.0,4228.0,3436.0,4010.0,3436.0,4021.0,3436.0,3730.0,3436.0,4017.0,3436.0,4037.0,3436.0,4098.0,3436.0,4622.0,3436.0,4615.0,3436.0,4625.0,3436.0,4621.0,3436.0,4619.0,3436.0,4617.0,3436.0,4623.0,3436.0,4618.0,3436.0,4626.0,3436.0,4627.0,3436.0,4624.0,3436.0,4632.0,3436.0,4620.0,3436.0,4628.0,3436.0,4616.0,3436.0,4041.0,3436.0,4004.0,3436.0,4222.0,3436.0,4007.0,3436.0,4015.0,3436.0,4038.0,3436.0')] ).
cnf(6232,plain,
$false,
inference(obv,[status(thm),theory(equality)],[6231]),
[iquote('0:Obv:6231.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 : Sun May 29 03:46:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.98/1.16
% 0.98/1.16 SPASS V 3.9
% 0.98/1.16 SPASS beiseite: Proof found.
% 0.98/1.16 % SZS status Theorem
% 0.98/1.16 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.98/1.16 SPASS derived 3424 clauses, backtracked 0 clauses, performed 0 splits and kept 1296 clauses.
% 0.98/1.16 SPASS allocated 68620 KBytes.
% 0.98/1.16 SPASS spent 0:00:00.81 on the problem.
% 0.98/1.16 0:00:00.04 for the input.
% 0.98/1.16 0:00:00.00 for the FLOTTER CNF translation.
% 0.98/1.16 0:00:00.03 for inferences.
% 0.98/1.16 0:00:00.00 for the backtracking.
% 0.98/1.16 0:00:00.71 for the reduction.
% 0.98/1.16
% 0.98/1.16
% 0.98/1.16 Here is a proof with depth 5, length 209 :
% 0.98/1.16 % SZS output start Refutation
% See solution above
% 1.01/1.20 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 knot_12 knot_13 knot_14 knot_15 knot_16 knot_17 knot_18 knot_19 knot_20 knot_21 knot_22 knot_23 knot_24 knot_25 knot_26 knot_27 knot_28 knot_29 knot_30 knot_31 knot_32 goal
% 1.01/1.20
%------------------------------------------------------------------------------