TSTP Solution File: LCL185-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL185-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:35:12 EDT 2022
% Result : Unsatisfiable 1.23s 1.40s
% Output : Refutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 23 unt; 0 nHn; 38 RR)
% Number of literals : 55 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(p,or__dfg(p,q))),
file('LCL185-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL185-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL185-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL185-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL185-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL185-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL185-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL185-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL185-3.p',unknown),
[] ).
cnf(16,plain,
axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(17,plain,
axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(18,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(22,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[18,17]),
[iquote('0:SoR:18.0,17.0')] ).
cnf(25,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(26,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,16]),
[iquote('0:SoR:18.0,16.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(30,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[18,5]),
[iquote('0:SoR:18.0,5.0')] ).
cnf(31,plain,
axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(32,plain,
axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(35,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,31]),
[iquote('0:Rew:7.0,31.0')] ).
cnf(36,plain,
axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,32]),
[iquote('0:Rew:7.0,32.0')] ).
cnf(43,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[18,6]),
[iquote('0:SoR:18.0,6.0')] ).
cnf(52,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[18,35]),
[iquote('0:SoR:18.0,35.0')] ).
cnf(64,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[18,36]),
[iquote('0:SoR:18.0,36.0')] ).
cnf(73,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[22,8]),
[iquote('0:SoR:22.0,8.1')] ).
cnf(86,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[73,3]),
[iquote('0:SoR:73.0,3.0')] ).
cnf(99,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[26,86]),
[iquote('0:SoR:26.0,86.0')] ).
cnf(106,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[30,25]),
[iquote('0:SoR:30.0,25.1')] ).
cnf(130,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[43,8]),
[iquote('0:SoR:43.0,8.1')] ).
cnf(149,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[52,99]),
[iquote('0:SoR:52.0,99.0')] ).
cnf(152,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,149]),
[iquote('0:SoR:27.0,149.0')] ).
cnf(156,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[22,152]),
[iquote('0:SoR:22.0,152.0')] ).
cnf(270,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[106,156]),
[iquote('0:SoR:106.0,156.0')] ).
cnf(538,plain,
theorem(implies__dfg(or__dfg(u,or__dfg(v,not__dfg(w))),or__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[130,16]),
[iquote('0:SoR:130.0,16.0')] ).
cnf(1540,plain,
( ~ theorem(or__dfg(u,or__dfg(v,not__dfg(w))))
| theorem(or__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[538,9]),
[iquote('0:Res:538.0,9.1')] ).
cnf(4398,plain,
theorem(or__dfg(u,implies__dfg(u,v))),
inference(sor,[status(thm)],[1540,270]),
[iquote('0:SoR:1540.0,270.0')] ).
cnf(4418,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[64,4398]),
[iquote('0:SoR:64.0,4398.0')] ).
cnf(4420,plain,
$false,
inference(unc,[status(thm)],[4418,1]),
[iquote('0:UnC:4418.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL185-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 3 20:35:25 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.23/1.40
% 1.23/1.40 SPASS V 3.9
% 1.23/1.40 SPASS beiseite: Proof found.
% 1.23/1.40 % SZS status Theorem
% 1.23/1.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.23/1.40 SPASS derived 4181 clauses, backtracked 0 clauses, performed 0 splits and kept 1906 clauses.
% 1.23/1.40 SPASS allocated 80974 KBytes.
% 1.23/1.40 SPASS spent 0:00:01.04 on the problem.
% 1.23/1.40 0:00:00.04 for the input.
% 1.23/1.40 0:00:00.00 for the FLOTTER CNF translation.
% 1.23/1.40 0:00:00.14 for inferences.
% 1.23/1.40 0:00:00.00 for the backtracking.
% 1.23/1.40 0:00:00.81 for the reduction.
% 1.23/1.40
% 1.23/1.40
% 1.23/1.40 Here is a proof with depth 11, length 38 :
% 1.23/1.40 % SZS output start Refutation
% See solution above
% 1.23/1.40 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 1.23/1.40
%------------------------------------------------------------------------------