TSTP Solution File: ALG138+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14 18:02:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 38
% Syntax : Number of clauses : 91 ( 59 unt; 28 nHn; 91 RR)
% Number of literals : 155 ( 0 equ; 50 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e1,e0),
file('ALG138+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG138+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG138+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e2,e1),
file('ALG138+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e2),
file('ALG138+1.p',unknown),
[] ).
cnf(7,axiom,
equal(op(e0,e0),e0),
file('ALG138+1.p',unknown),
[] ).
cnf(8,axiom,
equal(op(e1,e1),e1),
file('ALG138+1.p',unknown),
[] ).
cnf(9,axiom,
equal(op(e2,e2),e2),
file('ALG138+1.p',unknown),
[] ).
cnf(10,axiom,
equal(op(e3,e3),e3),
file('ALG138+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(op(e1,e0),op(e0,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(op(e3,e0),op(e0,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(op(e3,e0),op(e1,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(op(e1,e1),op(e0,e1)),
file('ALG138+1.p',unknown),
[] ).
cnf(21,axiom,
~ equal(op(e3,e1),op(e1,e1)),
file('ALG138+1.p',unknown),
[] ).
cnf(26,axiom,
~ equal(op(e2,e2),op(e1,e2)),
file('ALG138+1.p',unknown),
[] ).
cnf(28,axiom,
~ equal(op(e3,e2),op(e2,e2)),
file('ALG138+1.p',unknown),
[] ).
cnf(41,axiom,
~ equal(op(e1,e1),op(e1,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(42,axiom,
~ equal(op(e1,e2),op(e1,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(43,axiom,
~ equal(op(e1,e3),op(e1,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(44,axiom,
~ equal(op(e1,e2),op(e1,e1)),
file('ALG138+1.p',unknown),
[] ).
cnf(48,axiom,
~ equal(op(e2,e2),op(e2,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(52,axiom,
~ equal(op(e2,e3),op(e2,e2)),
file('ALG138+1.p',unknown),
[] ).
cnf(53,axiom,
~ equal(op(e3,e1),op(e3,e0)),
file('ALG138+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG138+1.p',unknown),
[] ).
cnf(57,axiom,
~ equal(op(e3,e3),op(e3,e1)),
file('ALG138+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(op(e3,e3),op(e3,e2)),
file('ALG138+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ equal(op(e3,e2),e0)
| ~ equal(op(op(e3,e2),e2),e1) ),
file('ALG138+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ equal(op(e3,e2),e1)
| ~ equal(op(op(e3,e2),e2),e0) ),
file('ALG138+1.p',unknown),
[] ).
cnf(85,axiom,
( equal(op(e0,e3),e2)
| equal(op(e1,e3),e2)
| equal(op(e2,e3),e2)
| equal(op(e3,e3),e2) ),
file('ALG138+1.p',unknown),
[] ).
cnf(86,axiom,
( equal(op(e3,e0),e2)
| equal(op(e3,e1),e2)
| equal(op(e3,e2),e2)
| equal(op(e3,e3),e2) ),
file('ALG138+1.p',unknown),
[] ).
cnf(90,axiom,
( equal(op(e3,e0),e0)
| equal(op(e3,e1),e0)
| equal(op(e3,e2),e0)
| equal(op(e3,e3),e0) ),
file('ALG138+1.p',unknown),
[] ).
cnf(102,axiom,
( equal(op(e1,e0),e2)
| equal(op(e1,e1),e2)
| equal(op(e1,e2),e2)
| equal(op(e1,e3),e2) ),
file('ALG138+1.p',unknown),
[] ).
cnf(109,axiom,
( equal(op(e0,e0),e2)
| equal(op(e1,e0),e2)
| equal(op(e2,e0),e2)
| equal(op(e3,e0),e2) ),
file('ALG138+1.p',unknown),
[] ).
cnf(112,axiom,
( equal(op(e0,e0),e1)
| equal(op(e0,e1),e1)
| equal(op(e0,e2),e1)
| equal(op(e0,e3),e1) ),
file('ALG138+1.p',unknown),
[] ).
cnf(116,axiom,
( equal(op(e3,e2),e0)
| equal(op(e3,e2),e1)
| equal(op(e3,e2),e2)
| equal(op(e3,e2),e3) ),
file('ALG138+1.p',unknown),
[] ).
cnf(117,axiom,
( equal(op(e3,e1),e0)
| equal(op(e3,e1),e1)
| equal(op(e3,e1),e2)
| equal(op(e3,e1),e3) ),
file('ALG138+1.p',unknown),
[] ).
cnf(124,axiom,
( equal(op(e1,e2),e0)
| equal(op(e1,e2),e1)
| equal(op(e1,e2),e2)
| equal(op(e1,e2),e3) ),
file('ALG138+1.p',unknown),
[] ).
cnf(126,axiom,
( equal(op(e1,e0),e0)
| equal(op(e1,e0),e1)
| equal(op(e1,e0),e2)
| equal(op(e1,e0),e3) ),
file('ALG138+1.p',unknown),
[] ).
cnf(131,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[10,58]),
[iquote('0:Rew:10.0,58.0')] ).
cnf(132,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[10,57]),
[iquote('0:Rew:10.0,57.0')] ).
cnf(134,plain,
~ equal(op(e2,e3),e2),
inference(rew,[status(thm),theory(equality)],[9,52]),
[iquote('0:Rew:9.0,52.0')] ).
cnf(136,plain,
~ equal(op(e2,e0),e2),
inference(rew,[status(thm),theory(equality)],[9,48]),
[iquote('0:Rew:9.0,48.0')] ).
cnf(138,plain,
~ equal(op(e1,e2),e1),
inference(rew,[status(thm),theory(equality)],[8,44]),
[iquote('0:Rew:8.0,44.0')] ).
cnf(139,plain,
~ equal(op(e1,e0),e1),
inference(rew,[status(thm),theory(equality)],[8,41]),
[iquote('0:Rew:8.0,41.0')] ).
cnf(146,plain,
~ equal(op(e3,e2),e2),
inference(rew,[status(thm),theory(equality)],[9,28]),
[iquote('0:Rew:9.0,28.0')] ).
cnf(147,plain,
~ equal(op(e1,e2),e2),
inference(rew,[status(thm),theory(equality)],[9,26]),
[iquote('0:Rew:9.0,26.0')] ).
cnf(149,plain,
~ equal(op(e3,e1),e1),
inference(rew,[status(thm),theory(equality)],[8,21]),
[iquote('0:Rew:8.0,21.0')] ).
cnf(151,plain,
~ equal(op(e0,e1),e1),
inference(rew,[status(thm),theory(equality)],[8,17]),
[iquote('0:Rew:8.0,17.0')] ).
cnf(152,plain,
~ equal(op(e3,e0),e0),
inference(rew,[status(thm),theory(equality)],[7,13]),
[iquote('0:Rew:7.0,13.0')] ).
cnf(154,plain,
~ equal(op(e1,e0),e0),
inference(rew,[status(thm),theory(equality)],[7,11]),
[iquote('0:Rew:7.0,11.0')] ).
cnf(155,plain,
( equal(op(e0,e3),e2)
| equal(op(e1,e3),e2)
| equal(op(e2,e3),e2)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[10,85]),
[iquote('0:Rew:10.0,85.3')] ).
cnf(156,plain,
( equal(op(e1,e3),e2)
| equal(op(e0,e3),e2) ),
inference(mrr,[status(thm)],[155,134,6]),
[iquote('0:MRR:155.2,155.3,134.0,6.0')] ).
cnf(157,plain,
( equal(op(e3,e0),e2)
| equal(op(e3,e1),e2)
| equal(op(e3,e2),e2)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[10,86]),
[iquote('0:Rew:10.0,86.3')] ).
cnf(158,plain,
( equal(op(e3,e1),e2)
| equal(op(e3,e0),e2) ),
inference(mrr,[status(thm)],[157,146,6]),
[iquote('0:MRR:157.2,157.3,146.0,6.0')] ).
cnf(165,plain,
( equal(op(e3,e0),e0)
| equal(op(e3,e1),e0)
| equal(op(e3,e2),e0)
| equal(e3,e0) ),
inference(rew,[status(thm),theory(equality)],[10,90]),
[iquote('0:Rew:10.0,90.3')] ).
cnf(166,plain,
( equal(op(e3,e2),e0)
| equal(op(e3,e1),e0) ),
inference(mrr,[status(thm)],[165,152,3]),
[iquote('0:MRR:165.0,165.3,152.0,3.0')] ).
cnf(185,plain,
( equal(op(e1,e0),e2)
| equal(e2,e1)
| equal(op(e1,e2),e2)
| equal(op(e1,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[8,102]),
[iquote('0:Rew:8.0,102.1')] ).
cnf(186,plain,
( equal(op(e1,e3),e2)
| equal(op(e1,e0),e2) ),
inference(mrr,[status(thm)],[185,4,147]),
[iquote('0:MRR:185.1,185.2,4.0,147.0')] ).
cnf(195,plain,
( equal(e2,e0)
| equal(op(e1,e0),e2)
| equal(op(e2,e0),e2)
| equal(op(e3,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[7,109]),
[iquote('0:Rew:7.0,109.0')] ).
cnf(196,plain,
( equal(op(e3,e0),e2)
| equal(op(e1,e0),e2) ),
inference(mrr,[status(thm)],[195,2,136]),
[iquote('0:MRR:195.0,195.2,2.0,136.0')] ).
cnf(201,plain,
( equal(e1,e0)
| equal(op(e0,e1),e1)
| equal(op(e0,e2),e1)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[7,112]),
[iquote('0:Rew:7.0,112.0')] ).
cnf(202,plain,
( equal(op(e0,e3),e1)
| equal(op(e0,e2),e1) ),
inference(mrr,[status(thm)],[201,1,151]),
[iquote('0:MRR:201.0,201.1,1.0,151.0')] ).
cnf(203,plain,
( equal(op(e3,e2),e1)
| equal(op(e3,e2),e0) ),
inference(mrr,[status(thm)],[116,146,131]),
[iquote('0:MRR:116.2,116.3,146.0,131.0')] ).
cnf(204,plain,
( equal(op(e3,e1),e2)
| equal(op(e3,e1),e0) ),
inference(mrr,[status(thm)],[117,149,132]),
[iquote('0:MRR:117.1,117.3,149.0,132.0')] ).
cnf(210,plain,
( equal(op(e1,e2),e3)
| equal(op(e1,e2),e0) ),
inference(mrr,[status(thm)],[124,138,147]),
[iquote('0:MRR:124.1,124.2,138.0,147.0')] ).
cnf(211,plain,
( equal(op(e1,e0),e3)
| equal(op(e1,e0),e2) ),
inference(mrr,[status(thm)],[126,154,139]),
[iquote('0:MRR:126.0,126.1,154.0,139.0')] ).
cnf(215,plain,
equal(op(e1,e3),e2),
inference(spt,[spt(split,[position(s1)])],[156]),
[iquote('1:Spt:156.0')] ).
cnf(223,plain,
~ equal(op(e1,e0),e2),
inference(rew,[status(thm),theory(equality)],[215,43]),
[iquote('1:Rew:215.0,43.0')] ).
cnf(226,plain,
equal(op(e3,e0),e2),
inference(mrr,[status(thm)],[196,223]),
[iquote('1:MRR:196.1,223.0')] ).
cnf(227,plain,
equal(op(e1,e0),e3),
inference(mrr,[status(thm)],[211,223]),
[iquote('1:MRR:211.1,223.0')] ).
cnf(235,plain,
~ equal(op(e3,e1),e2),
inference(rew,[status(thm),theory(equality)],[226,53]),
[iquote('1:Rew:226.0,53.0')] ).
cnf(241,plain,
~ equal(op(e1,e2),e3),
inference(rew,[status(thm),theory(equality)],[227,42]),
[iquote('1:Rew:227.0,42.0')] ).
cnf(262,plain,
equal(op(e3,e1),e0),
inference(mrr,[status(thm)],[204,235]),
[iquote('1:MRR:204.0,235.0')] ).
cnf(266,plain,
~ equal(op(e3,e2),e0),
inference(rew,[status(thm),theory(equality)],[262,56]),
[iquote('1:Rew:262.0,56.0')] ).
cnf(271,plain,
equal(op(e1,e2),e0),
inference(mrr,[status(thm)],[210,241]),
[iquote('1:MRR:210.0,241.0')] ).
cnf(308,plain,
equal(op(e3,e2),e1),
inference(mrr,[status(thm)],[203,266]),
[iquote('1:MRR:203.1,266.0')] ).
cnf(309,plain,
( ~ equal(e1,e1)
| ~ equal(op(op(e3,e2),e2),e0) ),
inference(rew,[status(thm),theory(equality)],[308,66]),
[iquote('1:Rew:308.0,66.0')] ).
cnf(355,plain,
~ equal(op(op(e3,e2),e2),e0),
inference(obv,[status(thm),theory(equality)],[309]),
[iquote('1:Obv:309.0')] ).
cnf(356,plain,
~ equal(e0,e0),
inference(rew,[status(thm),theory(equality)],[271,355,308]),
[iquote('1:Rew:271.0,355.0,308.0,355.0')] ).
cnf(357,plain,
$false,
inference(obv,[status(thm),theory(equality)],[356]),
[iquote('1:Obv:356.0')] ).
cnf(358,plain,
~ equal(op(e1,e3),e2),
inference(spt,[spt(split,[position(sa)])],[357,215]),
[iquote('1:Spt:357.0,156.0,215.0')] ).
cnf(359,plain,
equal(op(e0,e3),e2),
inference(spt,[spt(split,[position(s2)])],[156]),
[iquote('1:Spt:357.0,156.1')] ).
cnf(366,plain,
equal(op(e1,e0),e2),
inference(mrr,[status(thm)],[186,358]),
[iquote('1:MRR:186.0,358.0')] ).
cnf(370,plain,
~ equal(op(e3,e0),e2),
inference(rew,[status(thm),theory(equality)],[366,15]),
[iquote('1:Rew:366.0,15.0')] ).
cnf(379,plain,
equal(op(e3,e1),e2),
inference(mrr,[status(thm)],[158,370]),
[iquote('1:MRR:158.1,370.0')] ).
cnf(418,plain,
( equal(e2,e1)
| equal(op(e0,e2),e1) ),
inference(rew,[status(thm),theory(equality)],[359,202]),
[iquote('1:Rew:359.0,202.0')] ).
cnf(419,plain,
equal(op(e0,e2),e1),
inference(mrr,[status(thm)],[418,4]),
[iquote('1:MRR:418.0,4.0')] ).
cnf(424,plain,
( equal(op(e3,e2),e0)
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[379,166]),
[iquote('1:Rew:379.0,166.1')] ).
cnf(425,plain,
equal(op(e3,e2),e0),
inference(mrr,[status(thm)],[424,2]),
[iquote('1:MRR:424.1,2.0')] ).
cnf(478,plain,
( ~ equal(e0,e0)
| ~ equal(e1,e1) ),
inference(rew,[status(thm),theory(equality)],[419,60,425]),
[iquote('1:Rew:419.0,60.1,425.0,60.1,425.0,60.0')] ).
cnf(479,plain,
$false,
inference(obv,[status(thm),theory(equality)],[478]),
[iquote('1:Obv:478.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Wed Jun 8 11:41:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 143 clauses, backtracked 109 clauses, performed 1 splits and kept 224 clauses.
% 0.19/0.47 SPASS allocated 85413 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.01 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 1, length 91 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : ax4 ax5 ax3 ax7 ax13 ax2 ax1
% 0.19/0.47
%------------------------------------------------------------------------------