TSTP Solution File: LCL203-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 14:35:24 EDT 2022
% Result : Unsatisfiable 2.22s 2.40s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 55 ( 37 unt; 0 nHn; 55 RR)
% Number of literals : 76 ( 0 equ; 23 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(not__dfg(or__dfg(p,q)),or__dfg(not__dfg(p),not__dfg(q)))),
file('LCL203-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL203-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL203-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL203-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL203-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL203-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL203-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL203-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL203-3.p',unknown),
[] ).
cnf(10,plain,
~ theorem(implies__dfg(not__dfg(or__dfg(p,q)),implies__dfg(p,not__dfg(q)))),
inference(rew,[status(thm),theory(equality)],[7,1]),
[iquote('0:Rew:7.0,1.0')] ).
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(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)],[20,17]),
[iquote('0:SoR:20.0,17.0')] ).
cnf(24,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[20,16]),
[iquote('0:SoR:20.0,16.0')] ).
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(27,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[20,3]),
[iquote('0:SoR:20.0,3.0')] ).
cnf(28,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.0,2.0')] ).
cnf(36,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[20,5]),
[iquote('0:SoR:20.0,5.0')] ).
cnf(37,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(41,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,37]),
[iquote('0:Rew:7.0,37.0')] ).
cnf(49,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(61,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(72,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[61,4]),
[iquote('0:SoR:61.0,4.0')] ).
cnf(73,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[61,3]),
[iquote('0:SoR:61.0,3.0')] ).
cnf(77,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,41]),
[iquote('0:SoR:20.0,41.0')] ).
cnf(78,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)],[7,41]),
[iquote('0:SpR:7.0,41.0')] ).
cnf(80,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,78]),
[iquote('0:Rew:7.0,78.0')] ).
cnf(88,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[24,73]),
[iquote('0:SoR:24.0,73.0')] ).
cnf(120,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[24,72]),
[iquote('0:SoR:24.0,72.0')] ).
cnf(132,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,80]),
[iquote('0:SoR:20.0,80.0')] ).
cnf(145,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[36,27]),
[iquote('0:SoR:36.0,27.1')] ).
cnf(188,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[77,120]),
[iquote('0:SoR:77.0,120.0')] ).
cnf(191,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[77,88]),
[iquote('0:SoR:77.0,88.0')] ).
cnf(193,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[28,191]),
[iquote('0:SoR:28.0,191.0')] ).
cnf(197,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,193]),
[iquote('0:SoR:21.0,193.0')] ).
cnf(198,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[77,193]),
[iquote('0:SoR:77.0,193.0')] ).
cnf(202,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,197]),
[iquote('0:SpR:7.0,197.0')] ).
cnf(204,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[49,202]),
[iquote('0:SoR:49.0,202.0')] ).
cnf(263,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
inference(sor,[status(thm)],[26,188]),
[iquote('0:SoR:26.0,188.0')] ).
cnf(269,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,198]),
[iquote('0:SpR:7.0,198.0')] ).
cnf(271,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,269]),
[iquote('0:Rew:7.0,269.0')] ).
cnf(282,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[145,197]),
[iquote('0:SoR:145.0,197.0')] ).
cnf(290,plain,
theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[26,282]),
[iquote('0:SoR:26.0,282.0')] ).
cnf(299,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(spr,[status(thm),theory(equality)],[7,290]),
[iquote('0:SpR:7.0,290.0')] ).
cnf(319,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),or__dfg(w,v))),
inference(sor,[status(thm)],[145,299]),
[iquote('0:SoR:145.0,299.0')] ).
cnf(444,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[271,9]),
[iquote('0:Res:271.0,9.1')] ).
cnf(843,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[444,9]),
[iquote('0:Res:444.1,9.1')] ).
cnf(1386,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[204,9]),
[iquote('0:Res:204.0,9.1')] ).
cnf(3768,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
inference(sor,[status(thm)],[1386,263]),
[iquote('0:SoR:1386.0,263.0')] ).
cnf(4783,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[24,3768]),
[iquote('0:SoR:24.0,3768.0')] ).
cnf(4800,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
inference(sor,[status(thm)],[132,4783]),
[iquote('0:SoR:132.0,4783.0')] ).
cnf(4803,plain,
( ~ theorem(or__dfg(u,v))
| theorem(implies__dfg(not__dfg(v),u)) ),
inference(sor,[status(thm)],[843,4800]),
[iquote('0:SoR:843.1,4800.0')] ).
cnf(6183,plain,
theorem(implies__dfg(not__dfg(or__dfg(u,v)),implies__dfg(w,not__dfg(v)))),
inference(sor,[status(thm)],[4803,319]),
[iquote('0:SoR:4803.0,319.0')] ).
cnf(6396,plain,
$false,
inference(unc,[status(thm)],[6183,10]),
[iquote('0:UnC:6183.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 : Mon Jul 4 02:18:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.22/2.40
% 2.22/2.40 SPASS V 3.9
% 2.22/2.40 SPASS beiseite: Proof found.
% 2.22/2.40 % SZS status Theorem
% 2.22/2.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.22/2.40 SPASS derived 6055 clauses, backtracked 0 clauses, performed 0 splits and kept 2813 clauses.
% 2.22/2.40 SPASS allocated 83838 KBytes.
% 2.22/2.40 SPASS spent 0:00:02.01 on the problem.
% 2.22/2.40 0:00:00.04 for the input.
% 2.22/2.40 0:00:00.00 for the FLOTTER CNF translation.
% 2.22/2.40 0:00:00.24 for inferences.
% 2.22/2.40 0:00:00.00 for the backtracking.
% 2.22/2.40 0:00:01.67 for the reduction.
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Here is a proof with depth 16, length 55 :
% 2.22/2.40 % SZS output start Refutation
% See solution above
% 2.22/2.40 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
% 2.22/2.40
%------------------------------------------------------------------------------