TSTP Solution File: LCL069-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL069-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:34:23 EDT 2022
% Result : Unsatisfiable 1.28s 1.46s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of clauses : 68 ( 45 unt; 0 nHn; 68 RR)
% Number of literals : 92 ( 0 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL069-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
file('LCL069-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(not__dfg(u),w))),
file('LCL069-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(w,v),implies__dfg(implies__dfg(u,w),v)))),
file('LCL069-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(not__dfg(a),b))),
file('LCL069-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(12,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),v))
| is_a_theorem(implies__dfg(implies__dfg(w,v),implies__dfg(implies__dfg(u,w),v))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(16,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[11,2]),
[iquote('0:SoR:11.0,2.0')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[11,16]),
[iquote('0:SoR:11.0,16.0')] ).
cnf(24,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[12,16]),
[iquote('0:SoR:12.0,16.0')] ).
cnf(26,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[12,3]),
[iquote('0:SoR:12.0,3.0')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(v,w))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,u))))),
inference(sor,[status(thm)],[11,17]),
[iquote('0:SoR:11.0,17.0')] ).
cnf(34,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(implies__dfg(x,v),u),implies__dfg(v,w)))),
inference(sor,[status(thm)],[13,27]),
[iquote('0:SoR:13.0,27.0')] ).
cnf(35,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(w,u),implies__dfg(v,implies__dfg(w,x))))),
inference(sor,[status(thm)],[13,24]),
[iquote('0:SoR:13.0,24.0')] ).
cnf(36,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,not__dfg(x)))),implies__dfg(implies__dfg(x,u),implies__dfg(v,implies__dfg(w,not__dfg(x)))))),
inference(sor,[status(thm)],[13,17]),
[iquote('0:SoR:13.0,17.0')] ).
cnf(37,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,not__dfg(w))),implies__dfg(implies__dfg(w,u),implies__dfg(v,not__dfg(w))))),
inference(sor,[status(thm)],[13,16]),
[iquote('0:SoR:13.0,16.0')] ).
cnf(72,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(w))))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(v,not__dfg(w)))) ),
inference(res,[status(thm),theory(equality)],[37,1]),
[iquote('0:Res:37.0,1.1')] ).
cnf(81,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(x,v),u),implies__dfg(v,w))) ),
inference(res,[status(thm),theory(equality)],[34,1]),
[iquote('0:Res:34.0,1.1')] ).
cnf(103,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(implies__dfg(v,w))),implies__dfg(not__dfg(v),not__dfg(u)))),
inference(sor,[status(thm)],[72,26]),
[iquote('0:SoR:72.0,26.0')] ).
cnf(106,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(implies__dfg(v,w))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[72,27]),
[iquote('0:SoR:72.0,27.0')] ).
cnf(107,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),implies__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[72,16]),
[iquote('0:SoR:72.0,16.0')] ).
cnf(109,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),not__dfg(u))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[72,2]),
[iquote('0:SoR:72.0,2.0')] ).
cnf(115,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,not__dfg(implies__dfg(v,w)))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[72,106]),
[iquote('0:SoR:72.0,106.0')] ).
cnf(134,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),not__dfg(w)),implies__dfg(v,implies__dfg(w,x)))),
inference(sor,[status(thm)],[81,24]),
[iquote('0:SoR:81.0,24.0')] ).
cnf(162,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(v,w))))
| is_a_theorem(implies__dfg(not__dfg(v),not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[103,1]),
[iquote('0:Res:103.0,1.1')] ).
cnf(177,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),not__dfg(w)))
| is_a_theorem(implies__dfg(v,implies__dfg(w,x))) ),
inference(res,[status(thm),theory(equality)],[134,1]),
[iquote('0:Res:134.0,1.1')] ).
cnf(207,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(v,implies__dfg(w,x)))) ),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.1')] ).
cnf(263,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,not__dfg(x)))))
| is_a_theorem(implies__dfg(implies__dfg(x,u),implies__dfg(v,implies__dfg(w,not__dfg(x))))) ),
inference(res,[status(thm),theory(equality)],[36,1]),
[iquote('0:Res:36.0,1.1')] ).
cnf(270,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),not__dfg(u))))
| is_a_theorem(implies__dfg(w,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[109,1]),
[iquote('0:Res:109.0,1.1')] ).
cnf(277,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,not__dfg(implies__dfg(v,w)))))
| is_a_theorem(implies__dfg(w,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[115,1]),
[iquote('0:Res:115.0,1.1')] ).
cnf(962,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(implies__dfg(v,implies__dfg(w,u)))))),
inference(sor,[status(thm)],[270,27]),
[iquote('0:SoR:270.0,27.0')] ).
cnf(1131,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(implies__dfg(v,u),not__dfg(implies__dfg(v,u)))))),
inference(sor,[status(thm)],[277,107]),
[iquote('0:SoR:277.0,107.0')] ).
cnf(1220,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(u,implies__dfg(x,v))))),
inference(sor,[status(thm)],[207,29]),
[iquote('0:SoR:207.0,29.0')] ).
cnf(1222,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(w,implies__dfg(u,v)))),
inference(sor,[status(thm)],[207,16]),
[iquote('0:SoR:207.0,16.0')] ).
cnf(1287,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),not__dfg(v))),
inference(sor,[status(thm)],[162,1131]),
[iquote('0:SoR:162.0,1131.0')] ).
cnf(1402,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(u,implies__dfg(x,v)))) ),
inference(res,[status(thm),theory(equality)],[1220,1]),
[iquote('0:Res:1220.0,1.1')] ).
cnf(1413,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(w,implies__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[1222,1]),
[iquote('0:Res:1222.0,1.1')] ).
cnf(1560,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(w,implies__dfg(v,not__dfg(u))))),
inference(sor,[status(thm)],[263,24]),
[iquote('0:SoR:263.0,24.0')] ).
cnf(1601,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(w,implies__dfg(v,not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[1560,1]),
[iquote('0:Res:1560.0,1.1')] ).
cnf(1611,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(implies__dfg(v,implies__dfg(w,x))),not__dfg(x)))),
inference(sor,[status(thm)],[1601,962]),
[iquote('0:SoR:1601.0,962.0')] ).
cnf(1662,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(not__dfg(implies__dfg(v,implies__dfg(w,x))),not__dfg(x))) ),
inference(res,[status(thm),theory(equality)],[1611,1]),
[iquote('0:Res:1611.0,1.1')] ).
cnf(1713,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,implies__dfg(v,w))),not__dfg(w))),
inference(ems,[status(thm)],[1662,1287]),
[iquote('0:EmS:1662.0,1287.0')] ).
cnf(2507,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,not__dfg(v)),not__dfg(v)))),
inference(sor,[status(thm)],[1413,107]),
[iquote('0:SoR:1413.0,107.0')] ).
cnf(2514,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[1413,16]),
[iquote('0:SoR:1413.0,16.0')] ).
cnf(2554,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[2514,1]),
[iquote('0:Res:2514.0,1.1')] ).
cnf(2559,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[2554,1713]),
[iquote('0:EmS:2554.0,1713.0')] ).
cnf(2735,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[1601,2559]),
[iquote('0:SoR:1601.0,2559.0')] ).
cnf(2771,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[2735,1]),
[iquote('0:Res:2735.0,1.1')] ).
cnf(2810,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(ems,[status(thm)],[2771,1713]),
[iquote('0:EmS:2771.0,1713.0')] ).
cnf(2977,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,not__dfg(not__dfg(v)))))),
inference(sor,[status(thm)],[1402,2810]),
[iquote('0:SoR:1402.0,2810.0')] ).
cnf(3125,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,not__dfg(v)),not__dfg(v))) ),
inference(res,[status(thm),theory(equality)],[2507,1]),
[iquote('0:Res:2507.0,1.1')] ).
cnf(3177,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,not__dfg(not__dfg(v))))) ),
inference(res,[status(thm),theory(equality)],[2977,1]),
[iquote('0:Res:2977.0,1.1')] ).
cnf(3308,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(ems,[status(thm)],[3125,1713]),
[iquote('0:EmS:3125.0,1713.0')] ).
cnf(3507,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(u)))
| is_a_theorem(not__dfg(u)) ),
inference(res,[status(thm),theory(equality)],[3308,1]),
[iquote('0:Res:3308.0,1.1')] ).
cnf(3668,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(not__dfg(u))))),
inference(ems,[status(thm)],[3177,1713]),
[iquote('0:EmS:3177.0,1713.0')] ).
cnf(3863,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(v,not__dfg(not__dfg(u))))),
inference(sor,[status(thm)],[72,3668]),
[iquote('0:SoR:72.0,3668.0')] ).
cnf(3928,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[1413,3863]),
[iquote('0:SoR:1413.0,3863.0')] ).
cnf(3935,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(v,not__dfg(not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[3863,1]),
[iquote('0:Res:3863.0,1.1')] ).
cnf(3963,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(v),v),not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[3928,1]),
[iquote('0:Res:3928.0,1.1')] ).
cnf(4143,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(implies__dfg(v,v))))),
inference(sor,[status(thm)],[3935,2514]),
[iquote('0:SoR:3935.0,2514.0')] ).
cnf(4225,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v))))))),
inference(sor,[status(thm)],[3935,4143]),
[iquote('0:SoR:3935.0,4143.0')] ).
cnf(4399,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v))))))))),
inference(sor,[status(thm)],[3935,4225]),
[iquote('0:SoR:3935.0,4225.0')] ).
cnf(5646,plain,
is_a_theorem(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(u,u)))))))),
inference(sor,[status(thm)],[3507,4399]),
[iquote('0:SoR:3507.0,4399.0')] ).
cnf(5757,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u)))),
inference(ems,[status(thm)],[3963,5646]),
[iquote('0:EmS:3963.0,5646.0')] ).
cnf(6050,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[177,5757]),
[iquote('0:SoR:177.0,5757.0')] ).
cnf(6054,plain,
$false,
inference(unc,[status(thm)],[6050,5]),
[iquote('0:UnC:6050.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL069-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 2 23:28:03 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.28/1.46
% 1.28/1.46 SPASS V 3.9
% 1.28/1.46 SPASS beiseite: Proof found.
% 1.28/1.46 % SZS status Theorem
% 1.28/1.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.28/1.46 SPASS derived 6028 clauses, backtracked 0 clauses, performed 0 splits and kept 1907 clauses.
% 1.28/1.46 SPASS allocated 83933 KBytes.
% 1.28/1.46 SPASS spent 0:00:01.13 on the problem.
% 1.28/1.46 0:00:00.04 for the input.
% 1.28/1.46 0:00:00.00 for the FLOTTER CNF translation.
% 1.28/1.46 0:00:00.12 for inferences.
% 1.28/1.46 0:00:00.00 for the backtracking.
% 1.28/1.46 0:00:00.93 for the reduction.
% 1.28/1.46
% 1.28/1.46
% 1.28/1.46 Here is a proof with depth 25, length 68 :
% 1.28/1.46 % SZS output start Refutation
% See solution above
% 1.28/1.50 Formulae used in the proof : condensed_detachment cn_19 cn_37 cn_59 prove_cn_3
% 1.28/1.50
%------------------------------------------------------------------------------