TSTP Solution File: LAT394-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT394-2 : TPTP v8.1.0. Released v5.4.0.
% 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 : Sun Jul 17 06:51:53 EDT 2022
% Result : Unsatisfiable 3.28s 3.47s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(f(f(u,v),f(v,w)),x),f(v,f(f(v,f(f(u,u),u)),w))),v),
file('LAT394-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(f(x1__dfg,f(x1__dfg,x1__dfg)),f(x0__dfg,f(x0__dfg,x0__dfg))),
file('LAT394-2.p',unknown),
[] ).
cnf(3,plain,
equal(f(f(u,v),f(u,f(f(u,f(f(f(f(w,u),f(u,x)),f(f(w,u),f(u,x))),f(f(w,u),f(u,x)))),f(f(u,f(f(w,w),w)),x)))),u),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(7,plain,
equal(f(f(f(u,f(f(u,f(f(u,f(f(v,v),v)),w)),x)),y),f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),z),f(f(f(v,u),f(u,w)),z)),f(f(f(v,u),f(u,w)),z))),x))),f(u,f(f(u,f(f(v,v),v)),w))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(8,plain,
equal(f(u,f(f(u,v),f(f(f(u,v),f(f(f(w,u),f(w,u)),f(w,u))),x))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(23,plain,
equal(f(f(u,v),f(f(f(u,v),f(v,w)),v)),f(f(u,v),f(v,w))),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(48,plain,
equal(f(f(u,u),f(u,u)),u),
inference(spr,[status(thm),theory(equality)],[3,23]),
[iquote('0:SpR:3.0,23.0')] ).
cnf(62,plain,
equal(f(u,f(f(u,v),f(u,v))),f(u,v)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(106,plain,
equal(f(u,f(f(u,f(f(u,u),v)),f(u,u))),f(u,f(f(u,u),v))),
inference(spr,[status(thm),theory(equality)],[48,23]),
[iquote('0:SpR:48.0,23.0')] ).
cnf(113,plain,
equal(f(u,f(f(u,f(f(f(f(v,u),f(u,w)),f(f(v,u),f(u,w))),f(f(v,u),f(u,w)))),f(f(u,f(f(v,v),v)),w))),f(u,u)),
inference(spr,[status(thm),theory(equality)],[3,48]),
[iquote('0:SpR:3.0,48.0')] ).
cnf(116,plain,
equal(f(f(u,v),f(u,u)),u),
inference(rew,[status(thm),theory(equality)],[113,3]),
[iquote('0:Rew:113.0,3.0')] ).
cnf(128,plain,
equal(f(u,f(f(u,u),v)),f(u,u)),
inference(rew,[status(thm),theory(equality)],[116,106]),
[iquote('0:Rew:116.0,106.0')] ).
cnf(178,plain,
equal(f(f(u,u),f(u,v)),u),
inference(spr,[status(thm),theory(equality)],[116,128]),
[iquote('0:SpR:116.0,128.0')] ).
cnf(225,plain,
equal(f(f(f(u,v),f(u,v)),u),f(u,v)),
inference(spr,[status(thm),theory(equality)],[116,178]),
[iquote('0:SpR:116.0,178.0')] ).
cnf(459,plain,
equal(f(f(f(f(u,v),f(v,w)),x),f(v,v)),v),
inference(spr,[status(thm),theory(equality)],[1,62]),
[iquote('0:SpR:1.0,62.0')] ).
cnf(552,plain,
equal(f(f(u,v),f(v,v)),v),
inference(spr,[status(thm),theory(equality)],[116,459]),
[iquote('0:SpR:116.0,459.0')] ).
cnf(751,plain,
equal(f(u,f(f(v,u),f(v,u))),f(v,u)),
inference(spr,[status(thm),theory(equality)],[552,116]),
[iquote('0:SpR:552.0,116.0')] ).
cnf(754,plain,
equal(f(f(u,u),f(v,u)),u),
inference(spr,[status(thm),theory(equality)],[552,225]),
[iquote('0:SpR:552.0,225.0')] ).
cnf(758,plain,
equal(f(f(u,f(v,v)),v),f(v,v)),
inference(spr,[status(thm),theory(equality)],[552]),
[iquote('0:SpR:552.0,552.0')] ).
cnf(870,plain,
equal(f(f(u,f(f(u,f(f(v,v),v)),w)),f(u,f(f(u,f(f(v,v),v)),w))),u),
inference(spr,[status(thm),theory(equality)],[758,1]),
[iquote('0:SpR:758.0,1.0')] ).
cnf(1718,plain,
equal(f(f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),x),f(f(f(v,u),f(u,w)),x)),f(f(f(v,u),f(u,w)),x))),y)),f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),x),f(f(f(v,u),f(u,w)),x)),f(f(f(v,u),f(u,w)),x))),y))),f(u,f(f(u,f(f(v,v),v)),w))),f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),x),f(f(f(v,u),f(u,w)),x)),f(f(f(v,u),f(u,w)),x))),y))),
inference(spr,[status(thm),theory(equality)],[7,754]),
[iquote('0:SpR:7.0,754.0')] ).
cnf(2085,plain,
equal(f(u,f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),x),f(f(f(v,u),f(u,w)),x)),f(f(f(v,u),f(u,w)),x))),y))),f(u,f(f(u,f(f(v,v),v)),w))),
inference(spr,[status(thm),theory(equality)],[116,7]),
[iquote('0:SpR:116.0,7.0')] ).
cnf(2268,plain,
equal(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(u,f(f(u,f(f(v,v),v)),w)),f(f(f(f(f(v,u),f(u,w)),x),f(f(f(v,u),f(u,w)),x)),f(f(f(v,u),f(u,w)),x))),y)),u),
inference(rew,[status(thm),theory(equality)],[870,1718]),
[iquote('0:Rew:870.0,1718.0,870.0,1718.0')] ).
cnf(2282,plain,
equal(f(u,f(f(u,f(f(v,v),v)),w)),f(u,u)),
inference(rew,[status(thm),theory(equality)],[2268,2085]),
[iquote('0:Rew:2268.0,2085.0')] ).
cnf(3135,plain,
equal(f(u,u),f(u,f(f(v,v),v))),
inference(spr,[status(thm),theory(equality)],[2282,62]),
[iquote('0:SpR:2282.0,62.0')] ).
cnf(3239,plain,
equal(f(f(u,v),f(u,f(f(w,w),w))),u),
inference(spr,[status(thm),theory(equality)],[3135,116]),
[iquote('0:SpR:3135.0,116.0')] ).
cnf(3259,plain,
equal(f(f(u,u),f(f(v,v),v)),u),
inference(spr,[status(thm),theory(equality)],[3135,116]),
[iquote('0:SpR:3135.0,116.0')] ).
cnf(3369,plain,
equal(f(u,u),f(u,f(v,f(v,v)))),
inference(spr,[status(thm),theory(equality)],[116,3135]),
[iquote('0:SpR:116.0,3135.0')] ).
cnf(3384,plain,
equal(f(f(f(u,u),u),f(v,v)),v),
inference(spr,[status(thm),theory(equality)],[3259,751]),
[iquote('0:SpR:3259.0,751.0')] ).
cnf(3436,plain,
equal(f(f(u,u),f(v,f(v,v))),u),
inference(spr,[status(thm),theory(equality)],[116,3259]),
[iquote('0:SpR:116.0,3259.0')] ).
cnf(3542,plain,
equal(f(f(u,f(u,u)),f(f(v,v),f(v,v))),f(v,v)),
inference(spr,[status(thm),theory(equality)],[3369,751]),
[iquote('0:SpR:3369.0,751.0')] ).
cnf(3604,plain,
equal(f(f(u,f(u,u)),v),f(v,v)),
inference(rew,[status(thm),theory(equality)],[552,3542]),
[iquote('0:Rew:552.0,3542.0')] ).
cnf(4775,plain,
equal(f(f(f(u,f(u,u)),v),f(f(f(w,w),w),f(f(w,w),w))),f(u,f(u,u))),
inference(spr,[status(thm),theory(equality)],[3604,3239]),
[iquote('0:SpR:3604.0,3239.0')] ).
cnf(4789,plain,
equal(f(u,f(f(f(v,v),v),f(f(w,w),w))),f(f(v,v),v)),
inference(spr,[status(thm),theory(equality)],[3384,3239]),
[iquote('0:SpR:3384.0,3239.0')] ).
cnf(4812,plain,
equal(f(f(u,u),u),f(v,f(v,v))),
inference(rew,[status(thm),theory(equality)],[4789,4775]),
[iquote('0:Rew:4789.0,4775.0')] ).
cnf(4851,plain,
equal(f(u,f(u,u)),f(v,f(v,v))),
inference(spr,[status(thm),theory(equality)],[4812,3436]),
[iquote('0:SpR:4812.0,3436.0')] ).
cnf(4941,plain,
$false,
inference(unc,[status(thm)],[4851,2]),
[iquote('0:UnC:4851.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT394-2 : TPTP v8.1.0. Released v5.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 29 20:15:08 EDT 2022
% 0.20/0.34 % CPUTime :
% 3.28/3.47
% 3.28/3.47 SPASS V 3.9
% 3.28/3.47 SPASS beiseite: Proof found.
% 3.28/3.47 % SZS status Theorem
% 3.28/3.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.28/3.47 SPASS derived 4152 clauses, backtracked 0 clauses, performed 0 splits and kept 901 clauses.
% 3.28/3.47 SPASS allocated 82938 KBytes.
% 3.28/3.47 SPASS spent 0:00:03.04 on the problem.
% 3.28/3.47 0:00:00.03 for the input.
% 3.28/3.47 0:00:00.00 for the FLOTTER CNF translation.
% 3.28/3.47 0:00:00.06 for inferences.
% 3.28/3.47 0:00:00.00 for the backtracking.
% 3.28/3.47 0:00:02.92 for the reduction.
% 3.28/3.47
% 3.28/3.47
% 3.28/3.47 Here is a proof with depth 8, length 37 :
% 3.28/3.47 % SZS output start Refutation
% See solution above
% 3.28/3.48 Formulae used in the proof : sos goals
% 3.28/3.48
%------------------------------------------------------------------------------