TSTP Solution File: SYO038-1.003.003 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 19:51:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of clauses : 28 ( 24 unt; 0 nHn; 28 RR)
% Number of literals : 32 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(u,one),s(one)),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(2,axiom,
equal(s(s(f(one,u))),f(one,s(u))),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(3,axiom,
equal(f(u,f(s(u),v)),f(s(u),s(v))),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(4,axiom,
d(one),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(5,axiom,
( ~ d(u)
| d(s(u)) ),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(6,axiom,
~ d(f(s(s(one)),s(s(one)))),
file('SYO038-1.003.003.p',unknown),
[] ).
cnf(8,plain,
( ~ d(s(f(one,u)))
| d(f(one,s(u))) ),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.1')] ).
cnf(10,plain,
equal(f(one,s(one)),s(s(s(one)))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(12,plain,
equal(s(s(s(s(s(one))))),f(one,s(s(one)))),
inference(spr,[status(thm),theory(equality)],[10,2]),
[iquote('0:SpR:10.0,2.0')] ).
cnf(13,plain,
( ~ d(f(one,u))
| d(f(one,s(u))) ),
inference(sor,[status(thm)],[8,5]),
[iquote('0:SoR:8.0,5.1')] ).
cnf(14,plain,
( ~ d(s(s(s(s(one)))))
| d(f(one,s(s(one)))) ),
inference(spr,[status(thm),theory(equality)],[12,5]),
[iquote('0:SpR:12.0,5.1')] ).
cnf(16,plain,
d(f(one,s(s(one)))),
inference(ssi,[status(thm)],[14,5,4]),
[iquote('0:SSi:14.0,5.0,5.1,5.1,5.1,4.1')] ).
cnf(22,plain,
equal(f(s(u),s(one)),f(u,s(one))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(23,plain,
d(f(one,s(s(s(one))))),
inference(sor,[status(thm)],[13,16]),
[iquote('0:SoR:13.0,16.0')] ).
cnf(24,plain,
d(f(one,s(s(s(s(one)))))),
inference(sor,[status(thm)],[13,23]),
[iquote('0:SoR:13.0,23.0')] ).
cnf(25,plain,
d(f(one,s(s(s(s(s(one))))))),
inference(sor,[status(thm)],[13,24]),
[iquote('0:SoR:13.0,24.0')] ).
cnf(26,plain,
d(f(one,f(one,s(s(one))))),
inference(rew,[status(thm),theory(equality)],[12,25]),
[iquote('0:Rew:12.0,25.0')] ).
cnf(27,plain,
d(f(one,s(f(one,s(s(one)))))),
inference(sor,[status(thm)],[13,26]),
[iquote('0:SoR:13.0,26.0')] ).
cnf(29,plain,
equal(f(u,f(u,s(one))),f(s(u),s(s(one)))),
inference(spr,[status(thm),theory(equality)],[22,3]),
[iquote('0:SpR:22.0,3.0')] ).
cnf(36,plain,
d(f(one,s(s(f(one,s(s(one))))))),
inference(sor,[status(thm)],[13,27]),
[iquote('0:SoR:13.0,27.0')] ).
cnf(37,plain,
d(f(one,f(one,s(s(s(one)))))),
inference(rew,[status(thm),theory(equality)],[2,36]),
[iquote('0:Rew:2.0,36.0')] ).
cnf(113,plain,
equal(f(u,f(u,f(u,s(one)))),f(s(u),s(s(s(one))))),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(116,plain,
equal(f(s(u),f(u,s(one))),f(s(s(u)),s(s(one)))),
inference(spr,[status(thm),theory(equality)],[22,29]),
[iquote('0:SpR:22.0,29.0')] ).
cnf(117,plain,
~ d(f(s(one),f(one,s(one)))),
inference(rew,[status(thm),theory(equality)],[116,6]),
[iquote('0:Rew:116.0,6.0')] ).
cnf(118,plain,
~ d(f(s(one),s(s(s(one))))),
inference(rew,[status(thm),theory(equality)],[10,117]),
[iquote('0:Rew:10.0,117.0')] ).
cnf(419,plain,
equal(f(one,f(one,s(s(s(one))))),f(s(one),s(s(s(one))))),
inference(spr,[status(thm),theory(equality)],[10,113]),
[iquote('0:SpR:10.0,113.0')] ).
cnf(422,plain,
d(f(s(one),s(s(s(one))))),
inference(rew,[status(thm),theory(equality)],[419,37]),
[iquote('0:Rew:419.0,37.0')] ).
cnf(429,plain,
$false,
inference(mrr,[status(thm)],[422,118]),
[iquote('0:MRR:422.0,118.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.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 : Sat Jul 9 14:16:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 269 clauses, backtracked 0 clauses, performed 0 splits and kept 142 clauses.
% 0.19/0.49 SPASS allocated 76781 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.06 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 8, length 28 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : ax1 ax2 ax3 ax4 ax5 conj
% 0.19/0.49
%------------------------------------------------------------------------------