TSTP Solution File: LCL208-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL208-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:35:27 EDT 2022
% Result : Unsatisfiable 1.89s 2.08s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 26 unt; 0 nHn; 38 RR)
% Number of literals : 52 ( 0 equ; 15 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(or__dfg(p,q),implies__dfg(not__dfg(p),q))),
file('LCL208-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL208-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL208-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL208-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL208-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL208-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL208-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL208-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL208-3.p',unknown),
[] ).
cnf(15,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(16,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(20,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(21,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,16]),
[iquote('0:SoR:20.0,16.0')] ).
cnf(24,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[20,15]),
[iquote('0:SoR:20.0,15.0')] ).
cnf(26,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[20,4]),
[iquote('0:SoR:20.0,4.0')] ).
cnf(28,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.0,2.0')] ).
cnf(30,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(34,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,30]),
[iquote('0:Rew:7.0,30.0')] ).
cnf(43,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[20,6]),
[iquote('0:SoR:20.0,6.0')] ).
cnf(51,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,34]),
[iquote('0:SoR:20.0,34.0')] ).
cnf(52,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,34]),
[iquote('0:SpR:7.0,34.0')] ).
cnf(54,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,52]),
[iquote('0:Rew:7.0,52.0')] ).
cnf(70,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[21,8]),
[iquote('0:SoR:21.0,8.1')] ).
cnf(86,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[70,3]),
[iquote('0:SoR:70.0,3.0')] ).
cnf(95,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,54]),
[iquote('0:SoR:20.0,54.0')] ).
cnf(97,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[24,86]),
[iquote('0:SoR:24.0,86.0')] ).
cnf(156,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[51,97]),
[iquote('0:SoR:51.0,97.0')] ).
cnf(159,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[28,156]),
[iquote('0:SoR:28.0,156.0')] ).
cnf(163,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,159]),
[iquote('0:SoR:21.0,159.0')] ).
cnf(164,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[51,159]),
[iquote('0:SoR:51.0,159.0')] ).
cnf(168,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,163]),
[iquote('0:SpR:7.0,163.0')] ).
cnf(170,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[43,168]),
[iquote('0:SoR:43.0,168.0')] ).
cnf(212,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[26,164]),
[iquote('0:SoR:26.0,164.0')] ).
cnf(1349,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[170,9]),
[iquote('0:Res:170.0,9.1')] ).
cnf(3883,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1349,212]),
[iquote('0:SoR:1349.0,212.0')] ).
cnf(5773,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[24,3883]),
[iquote('0:SoR:24.0,3883.0')] ).
cnf(5795,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[95,5773]),
[iquote('0:SoR:95.0,5773.0')] ).
cnf(5798,plain,
$false,
inference(unc,[status(thm)],[5795,1]),
[iquote('0:UnC:5795.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LCL208-3 : TPTP v8.1.0. Released v2.3.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.07/0.25 % Computer : n019.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 600
% 0.07/0.25 % DateTime : Sat Jul 2 16:17:53 EDT 2022
% 0.07/0.25 % CPUTime :
% 1.89/2.08
% 1.89/2.08 SPASS V 3.9
% 1.89/2.08 SPASS beiseite: Proof found.
% 1.89/2.08 % SZS status Theorem
% 1.89/2.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.89/2.08 SPASS derived 5452 clauses, backtracked 0 clauses, performed 0 splits and kept 2583 clauses.
% 1.89/2.08 SPASS allocated 82945 KBytes.
% 1.89/2.08 SPASS spent 0:00:01.77 on the problem.
% 1.89/2.08 0:00:00.02 for the input.
% 1.89/2.08 0:00:00.00 for the FLOTTER CNF translation.
% 1.89/2.08 0:00:00.23 for inferences.
% 1.89/2.08 0:00:00.00 for the backtracking.
% 1.89/2.08 0:00:01.46 for the reduction.
% 1.89/2.08
% 1.89/2.08
% 1.89/2.08 Here is a proof with depth 14, length 38 :
% 1.89/2.08 % SZS output start Refutation
% See solution above
% 1.89/2.08 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
% 1.89/2.08
%------------------------------------------------------------------------------