TSTP Solution File: LCL199-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL199-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:35:22 EDT 2022
% Result : Unsatisfiable 258.57s 258.82s
% Output : Refutation 258.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 66 ( 44 unt; 0 nHn; 66 RR)
% Number of literals : 91 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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)),not__dfg(p))),
file('LCL199-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL199-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL199-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL199-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL199-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL199-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL199-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL199-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL199-3.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(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(19,plain,
axiom(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,15]),
[iquote('0:SpR:7.0,15.0')] ).
cnf(22,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,15]),
[iquote('0:SoR:18.0,15.0')] ).
cnf(24,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[18,16]),
[iquote('0:SoR:18.0,16.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,4]),
[iquote('0:SoR:18.0,4.0')] ).
cnf(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(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(44,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(46,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,44]),
[iquote('0:Rew:7.0,44.0')] ).
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(61,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(71,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[24,8]),
[iquote('0:SoR:24.0,8.1')] ).
cnf(72,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[18,46]),
[iquote('0:SoR:18.0,46.0')] ).
cnf(83,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[71,4]),
[iquote('0:SoR:71.0,4.0')] ).
cnf(84,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[71,3]),
[iquote('0:SoR:71.0,3.0')] ).
cnf(93,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[22,84]),
[iquote('0:SoR:22.0,84.0')] ).
cnf(122,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[22,83]),
[iquote('0:SoR:22.0,83.0')] ).
cnf(160,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[52,93]),
[iquote('0:SoR:52.0,93.0')] ).
cnf(162,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,160]),
[iquote('0:SoR:27.0,160.0')] ).
cnf(166,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[24,162]),
[iquote('0:SoR:24.0,162.0')] ).
cnf(167,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[52,162]),
[iquote('0:SoR:52.0,162.0')] ).
cnf(171,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,166]),
[iquote('0:SpR:7.0,166.0')] ).
cnf(173,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[43,171]),
[iquote('0:SoR:43.0,171.0')] ).
cnf(180,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[61,26]),
[iquote('0:SoR:61.0,26.1')] ).
cnf(200,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[72,122]),
[iquote('0:SoR:72.0,122.0')] ).
cnf(207,plain,
theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[72,171]),
[iquote('0:SoR:72.0,171.0')] ).
cnf(210,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[72,8]),
[iquote('0:SoR:72.0,8.1')] ).
cnf(229,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[25,167]),
[iquote('0:SoR:25.0,167.0')] ).
cnf(231,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,167]),
[iquote('0:SpR:7.0,167.0')] ).
cnf(233,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,231]),
[iquote('0:Rew:7.0,231.0')] ).
cnf(354,plain,
theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
inference(sor,[status(thm)],[180,93]),
[iquote('0:SoR:180.0,93.0')] ).
cnf(399,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[233,9]),
[iquote('0:Res:233.0,9.1')] ).
cnf(437,plain,
theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
inference(sor,[status(thm)],[52,354]),
[iquote('0:SoR:52.0,354.0')] ).
cnf(598,plain,
theorem(implies__dfg(implies__dfg(u,implies__dfg(v,not__dfg(w))),implies__dfg(u,implies__dfg(w,not__dfg(v))))),
inference(sor,[status(thm)],[210,19]),
[iquote('0:SoR:210.0,19.0')] ).
cnf(813,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[399,9]),
[iquote('0:Res:399.1,9.1')] ).
cnf(1371,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[173,9]),
[iquote('0:Res:173.0,9.1')] ).
cnf(1487,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,not__dfg(w))))
| theorem(implies__dfg(u,implies__dfg(w,not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[598,9]),
[iquote('0:Res:598.0,9.1')] ).
cnf(3833,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
inference(sor,[status(thm)],[1371,437]),
[iquote('0:SoR:1371.0,437.0')] ).
cnf(3891,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1371,229]),
[iquote('0:SoR:1371.0,229.0')] ).
cnf(4534,plain,
theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(v),not__dfg(u)))),
inference(sor,[status(thm)],[1487,207]),
[iquote('0:SoR:1487.0,207.0')] ).
cnf(5583,plain,
theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
inference(sor,[status(thm)],[27,3833]),
[iquote('0:SoR:27.0,3833.0')] ).
cnf(5801,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[22,3891]),
[iquote('0:SoR:22.0,3891.0')] ).
cnf(5804,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[813,5801]),
[iquote('0:SoR:813.1,5801.0')] ).
cnf(6876,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(not__dfg(v),not__dfg(u))) ),
inference(sor,[status(thm)],[813,4534]),
[iquote('0:SoR:813.1,4534.0')] ).
cnf(8102,plain,
theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
inference(sor,[status(thm)],[5804,5583]),
[iquote('0:SoR:5804.0,5583.0')] ).
cnf(8119,plain,
theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
inference(rew,[status(thm),theory(equality)],[7,8102]),
[iquote('0:Rew:7.0,8102.0')] ).
cnf(15022,plain,
( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
| theorem(w) ),
inference(sor,[status(thm)],[813,8119]),
[iquote('0:SoR:813.1,8119.0')] ).
cnf(85317,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[15022,200]),
[iquote('0:SoR:15022.0,200.0')] ).
cnf(85840,plain,
theorem(implies__dfg(not__dfg(or__dfg(u,v)),not__dfg(u))),
inference(sor,[status(thm)],[6876,85317]),
[iquote('0:SoR:6876.0,85317.0')] ).
cnf(85868,plain,
$false,
inference(unc,[status(thm)],[85840,1]),
[iquote('0:UnC:85840.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL199-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 15:20:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 258.57/258.82
% 258.57/258.82 SPASS V 3.9
% 258.57/258.82 SPASS beiseite: Proof found.
% 258.57/258.82 % SZS status Theorem
% 258.57/258.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 258.57/258.82 SPASS derived 78633 clauses, backtracked 0 clauses, performed 0 splits and kept 31265 clauses.
% 258.57/258.82 SPASS allocated 172391 KBytes.
% 258.57/258.82 SPASS spent 0:4:15.85 on the problem.
% 258.57/258.82 0:00:00.04 for the input.
% 258.57/258.82 0:00:00.00 for the FLOTTER CNF translation.
% 258.57/258.82 0:00:06.86 for inferences.
% 258.57/258.82 0:00:00.00 for the backtracking.
% 258.57/258.82 0:04:06.56 for the reduction.
% 258.57/258.82
% 258.57/258.82
% 258.57/258.82 Here is a proof with depth 18, length 66 :
% 258.57/258.82 % SZS output start Refutation
% See solution above
% 258.57/258.82 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
% 258.57/258.82
%------------------------------------------------------------------------------