TSTP Solution File: LCL396-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL396-1 : 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 14:36:40 EDT 2022
% Result : Unsatisfiable 4.16s 4.34s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of clauses : 65 ( 40 unt; 0 nHn; 65 RR)
% Number of literals : 93 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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('LCL396-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL396-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL396-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL396-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(x__dfg)),y__dfg),implies__dfg(x__dfg,y__dfg))),
file('LCL396-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[15,2]),
[iquote('0:SoR:15.0,2.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[15,4]),
[iquote('0:SoR:15.0,4.0')] ).
cnf(19,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),u),v))),
inference(sor,[status(thm)],[15,3]),
[iquote('0:SoR:15.0,3.0')] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(u,w)) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w),implies__dfg(implies__dfg(u,v),w))),
inference(sor,[status(thm)],[15,19]),
[iquote('0:SoR:15.0,19.0')] ).
cnf(23,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),v)) ),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(30,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
cnf(35,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(60,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[23,4]),
[iquote('0:SoR:23.0,4.0')] ).
cnf(61,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(u),u)),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[23,3]),
[iquote('0:SoR:23.0,3.0')] ).
cnf(65,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(not__dfg(u),v)) ),
inference(res,[status(thm),theory(equality)],[60,1]),
[iquote('0:Res:60.0,1.1')] ).
cnf(91,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w))
| is_a_theorem(implies__dfg(implies__dfg(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(110,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,18]),
[iquote('0:SoR:35.0,18.0')] ).
cnf(111,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,22]),
[iquote('0:SoR:35.0,22.0')] ).
cnf(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(u,implies__dfg(x,w))))),
inference(sor,[status(thm)],[35,17]),
[iquote('0:SoR:35.0,17.0')] ).
cnf(124,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[21,110]),
[iquote('0:SoR:21.0,110.0')] ).
cnf(127,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x),implies__dfg(v,x))),
inference(sor,[status(thm)],[15,124]),
[iquote('0:SoR:15.0,124.0')] ).
cnf(168,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x))
| is_a_theorem(implies__dfg(v,x)) ),
inference(res,[status(thm),theory(equality)],[127,1]),
[iquote('0:Res:127.0,1.1')] ).
cnf(173,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[111,1]),
[iquote('0:Res:111.0,1.1')] ).
cnf(229,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[168,111]),
[iquote('0:SoR:168.0,111.0')] ).
cnf(246,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[229,1]),
[iquote('0:Res:229.0,1.1')] ).
cnf(268,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[246,1]),
[iquote('0:Res:246.1,1.1')] ).
cnf(307,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(w,implies__dfg(v,implies__dfg(u,x)))) ),
inference(sor,[status(thm)],[268,110]),
[iquote('0:SoR:268.1,110.0')] ).
cnf(310,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(x,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[268,18]),
[iquote('0:SoR:268.1,18.0')] ).
cnf(473,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(x,v),implies__dfg(u,implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[113,1]),
[iquote('0:Res:113.0,1.1')] ).
cnf(1019,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(v),w)))),
inference(sor,[status(thm)],[307,30]),
[iquote('0:SoR:307.0,30.0')] ).
cnf(1025,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v))),w)),
inference(sor,[status(thm)],[65,1019]),
[iquote('0:SoR:65.0,1019.0')] ).
cnf(1254,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[310,61]),
[iquote('0:SoR:310.0,61.0')] ).
cnf(1298,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[310,3]),
[iquote('0:SoR:310.0,3.0')] ).
cnf(1308,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[15,1298]),
[iquote('0:SoR:15.0,1298.0')] ).
cnf(1370,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[65,1254]),
[iquote('0:SoR:65.0,1254.0')] ).
cnf(1473,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1308,1]),
[iquote('0:Res:1308.0,1.1')] ).
cnf(2207,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[173,1308]),
[iquote('0:SoR:173.0,1308.0')] ).
cnf(2213,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(u,v),w))) ),
inference(sor,[status(thm)],[173,246]),
[iquote('0:SoR:173.0,246.1')] ).
cnf(2265,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1473,2207]),
[iquote('0:SoR:1473.0,2207.0')] ).
cnf(2272,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2265]),
[iquote('0:SoR:11.0,2265.0')] ).
cnf(2302,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2272,1]),
[iquote('0:Res:2272.0,1.1')] ).
cnf(3599,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2302,2213]),
[iquote('0:SoR:2302.0,2213.1')] ).
cnf(3640,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[91,3599]),
[iquote('0:SoR:91.0,3599.1')] ).
cnf(3648,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[3599,1]),
[iquote('0:Res:3599.1,1.1')] ).
cnf(4137,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[3640,1370]),
[iquote('0:SoR:3640.0,1370.0')] ).
cnf(4147,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w),w)),
inference(sor,[status(thm)],[3640,1025]),
[iquote('0:SoR:3640.0,1025.0')] ).
cnf(4429,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[35,4137]),
[iquote('0:SoR:35.0,4137.0')] ).
cnf(4441,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[3648,4147]),
[iquote('0:SoR:3648.1,4147.0')] ).
cnf(4618,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[3648,4429]),
[iquote('0:SoR:3648.1,4429.0')] ).
cnf(4627,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,u),u))),
inference(sor,[status(thm)],[35,4429]),
[iquote('0:SoR:35.0,4429.0')] ).
cnf(4628,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[168,4429]),
[iquote('0:SoR:168.0,4429.0')] ).
cnf(4646,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[15,4628]),
[iquote('0:SoR:15.0,4628.0')] ).
cnf(4762,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[3648,4646]),
[iquote('0:SoR:3648.1,4646.0')] ).
cnf(4930,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),u)) ),
inference(sor,[status(thm)],[3648,4627]),
[iquote('0:SoR:3648.1,4627.0')] ).
cnf(5020,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[4762,4627]),
[iquote('0:SoR:4762.0,4627.0')] ).
cnf(5191,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[473,5020]),
[iquote('0:SoR:473.0,5020.0')] ).
cnf(10584,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[4441,5191]),
[iquote('0:SoR:4441.0,5191.0')] ).
cnf(10586,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[4618,10584]),
[iquote('0:SoR:4618.0,10584.0')] ).
cnf(10645,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(sor,[status(thm)],[4930,10586]),
[iquote('0:SoR:4930.0,10586.0')] ).
cnf(10720,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[21,10645]),
[iquote('0:SoR:21.0,10645.0')] ).
cnf(10739,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),implies__dfg(u,v))),
inference(sor,[status(thm)],[15,10720]),
[iquote('0:SoR:15.0,10720.0')] ).
cnf(10765,plain,
$false,
inference(unc,[status(thm)],[10739,5]),
[iquote('0:UnC:10739.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL396-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 18:40:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.16/4.34
% 4.16/4.34 SPASS V 3.9
% 4.16/4.34 SPASS beiseite: Proof found.
% 4.16/4.34 % SZS status Theorem
% 4.16/4.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.16/4.34 SPASS derived 10688 clauses, backtracked 0 clauses, performed 0 splits and kept 3949 clauses.
% 4.16/4.34 SPASS allocated 89059 KBytes.
% 4.16/4.34 SPASS spent 0:00:03.89 on the problem.
% 4.16/4.34 0:00:00.03 for the input.
% 4.16/4.34 0:00:00.00 for the FLOTTER CNF translation.
% 4.16/4.34 0:00:00.20 for inferences.
% 4.16/4.34 0:00:00.00 for the backtracking.
% 4.16/4.34 0:00:03.61 for the reduction.
% 4.16/4.34
% 4.16/4.34
% 4.16/4.34 Here is a proof with depth 31, length 65 :
% 4.16/4.34 % SZS output start Refutation
% See solution above
% 4.16/4.34 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_62
% 4.16/4.34
%------------------------------------------------------------------------------