TSTP Solution File: LCL405-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL405-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:36:43 EDT 2022
% Result : Unsatisfiable 7.05s 7.31s
% Output : Refutation 7.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 66 ( 42 unt; 0 nHn; 66 RR)
% Number of literals : 93 ( 0 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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('LCL405-1.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('LCL405-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL405-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL405-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(not__dfg(implies__dfg(implies__dfg(x__dfg,x__dfg),not__dfg(implies__dfg(y__dfg,y__dfg))))),
file('LCL405-1.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(16,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(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w))),
inference(sor,[status(thm)],[15,18]),
[iquote('0:SoR:15.0,18.0')] ).
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(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)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
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(79,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
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(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(125,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[110,1]),
[iquote('0:Res:110.0,1.1')] ).
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(305,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(361,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),v),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[79,61]),
[iquote('0:SoR:79.0,61.0')] ).
cnf(1242,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[305,61]),
[iquote('0:SoR:305.0,61.0')] ).
cnf(1286,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[305,3]),
[iquote('0:SoR:305.0,3.0')] ).
cnf(1296,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[15,1286]),
[iquote('0:SoR:15.0,1286.0')] ).
cnf(1358,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[65,1242]),
[iquote('0:SoR:65.0,1242.0')] ).
cnf(1363,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[15,1242]),
[iquote('0:SoR:15.0,1242.0')] ).
cnf(1469,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1296,1]),
[iquote('0:Res:1296.0,1.1')] ).
cnf(2116,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(w,implies__dfg(u,v)))),
inference(sor,[status(thm)],[35,1363]),
[iquote('0:SoR:35.0,1363.0')] ).
cnf(2139,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(not__dfg(implies__dfg(not__dfg(u),u)))),u)),
inference(sor,[status(thm)],[35,361]),
[iquote('0:SoR:35.0,361.0')] ).
cnf(2225,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[173,1296]),
[iquote('0:SoR:173.0,1296.0')] ).
cnf(2231,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(2303,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),not__dfg(u)),w))),
inference(sor,[status(thm)],[21,2225]),
[iquote('0:SoR:21.0,2225.0')] ).
cnf(2309,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1469,2225]),
[iquote('0:SoR:1469.0,2225.0')] ).
cnf(2316,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2309]),
[iquote('0:SoR:11.0,2309.0')] ).
cnf(2346,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2316,1]),
[iquote('0:Res:2316.0,1.1')] ).
cnf(2599,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),not__dfg(implies__dfg(v,v))),w)),
inference(sor,[status(thm)],[2346,2303]),
[iquote('0:SoR:2346.0,2303.0')] ).
cnf(3590,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[168,2116]),
[iquote('0:SoR:168.0,2116.0')] ).
cnf(3599,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[173,3590]),
[iquote('0:SoR:173.0,3590.0')] ).
cnf(3635,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[3599,1]),
[iquote('0:Res:3599.0,1.1')] ).
cnf(3870,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),u)),
inference(sor,[status(thm)],[3635,2139]),
[iquote('0:SoR:3635.0,2139.0')] ).
cnf(4163,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)))),v))),
inference(sor,[status(thm)],[125,3870]),
[iquote('0:SoR:125.0,3870.0')] ).
cnf(5488,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2346,2231]),
[iquote('0:SoR:2346.0,2231.1')] ).
cnf(5515,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[91,5488]),
[iquote('0:SoR:91.0,5488.1')] ).
cnf(5523,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[5488,1]),
[iquote('0:Res:5488.1,1.1')] ).
cnf(6148,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[5515,1358]),
[iquote('0:SoR:5515.0,1358.0')] ).
cnf(6357,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[35,6148]),
[iquote('0:SoR:35.0,6148.0')] ).
cnf(7016,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[5523,6357]),
[iquote('0:SoR:5523.1,6357.0')] ).
cnf(8482,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u))))),
inference(sor,[status(thm)],[7016,4163]),
[iquote('0:SoR:7016.0,4163.0')] ).
cnf(8507,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)),implies__dfg(u,v))),
inference(sor,[status(thm)],[125,8482]),
[iquote('0:SoR:125.0,8482.0')] ).
cnf(8660,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[21,8507]),
[iquote('0:SoR:21.0,8507.0')] ).
cnf(8684,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(not__dfg(u)),v))),
inference(sor,[status(thm)],[173,8660]),
[iquote('0:SoR:173.0,8660.0')] ).
cnf(9691,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(sor,[status(thm)],[7016,8684]),
[iquote('0:SoR:7016.0,8684.0')] ).
cnf(9724,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(u)))
| is_a_theorem(not__dfg(u)) ),
inference(sor,[status(thm)],[5523,9691]),
[iquote('0:SoR:5523.1,9691.0')] ).
cnf(9831,plain,
is_a_theorem(not__dfg(implies__dfg(implies__dfg(u,u),not__dfg(implies__dfg(v,v))))),
inference(sor,[status(thm)],[9724,2599]),
[iquote('0:SoR:9724.0,2599.0')] ).
cnf(9874,plain,
$false,
inference(unc,[status(thm)],[9831,5]),
[iquote('0:UnC:9831.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LCL405-1 : TPTP v8.1.0. Released v2.3.0.
% 0.00/0.08 % Command : run_spass %d %s
% 0.07/0.26 % Computer : n029.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jul 4 17:15:56 EDT 2022
% 0.07/0.26 % CPUTime :
% 7.05/7.31
% 7.05/7.31 SPASS V 3.9
% 7.05/7.31 SPASS beiseite: Proof found.
% 7.05/7.31 % SZS status Theorem
% 7.05/7.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.05/7.31 SPASS derived 9801 clauses, backtracked 0 clauses, performed 0 splits and kept 3689 clauses.
% 7.05/7.31 SPASS allocated 88278 KBytes.
% 7.05/7.31 SPASS spent 0:00:07.03 on the problem.
% 7.05/7.31 0:00:00.03 for the input.
% 7.05/7.31 0:00:00.00 for the FLOTTER CNF translation.
% 7.05/7.31 0:00:00.35 for inferences.
% 7.05/7.31 0:00:00.00 for the backtracking.
% 7.05/7.31 0:00:06.58 for the reduction.
% 7.05/7.31
% 7.05/7.31
% 7.05/7.31 Here is a proof with depth 29, length 66 :
% 7.05/7.31 % SZS output start Refutation
% See solution above
% 7.31/7.48 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_71
% 7.31/7.48
%------------------------------------------------------------------------------