TSTP Solution File: LCL381-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL381-1 : 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 14:36:34 EDT 2022
% Result : Unsatisfiable 4.00s 4.18s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 64 ( 39 unt; 0 nHn; 64 RR)
% Number of literals : 92 ( 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 : 9 ( 9 usr; 7 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('LCL381-1.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('LCL381-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL381-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL381-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(x__dfg)),y__dfg),z__dfg),implies__dfg(implies__dfg(x__dfg,y__dfg),z__dfg))),
file('LCL381-1.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(13,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)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
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)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
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)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
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)],[13,19]),
[iquote('0:SoR:13.0,19.0')] ).
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(115,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(u,w),x),implies__dfg(implies__dfg(v,w),x)))),
inference(sor,[status(thm)],[35,2]),
[iquote('0:SoR:35.0,2.0')] ).
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)],[13,124]),
[iquote('0:SoR:13.0,124.0')] ).
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(230,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(253,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[230,1]),
[iquote('0:Res:230.0,1.1')] ).
cnf(269,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)],[253,1]),
[iquote('0:Res:253.1,1.1')] ).
cnf(309,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)],[269,110]),
[iquote('0:SoR:269.1,110.0')] ).
cnf(312,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)],[269,18]),
[iquote('0:SoR:269.1,18.0')] ).
cnf(451,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(496,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,w),x),implies__dfg(implies__dfg(v,w),x))) ),
inference(res,[status(thm),theory(equality)],[115,1]),
[iquote('0:Res:115.0,1.1')] ).
cnf(1023,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(v),w)))),
inference(sor,[status(thm)],[309,30]),
[iquote('0:SoR:309.0,30.0')] ).
cnf(1029,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v))),w)),
inference(sor,[status(thm)],[65,1023]),
[iquote('0:SoR:65.0,1023.0')] ).
cnf(1258,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[312,61]),
[iquote('0:SoR:312.0,61.0')] ).
cnf(1302,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[312,3]),
[iquote('0:SoR:312.0,3.0')] ).
cnf(1312,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1302]),
[iquote('0:SoR:13.0,1302.0')] ).
cnf(1374,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[65,1258]),
[iquote('0:SoR:65.0,1258.0')] ).
cnf(1487,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1312,1]),
[iquote('0:Res:1312.0,1.1')] ).
cnf(2263,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[173,1312]),
[iquote('0:SoR:173.0,1312.0')] ).
cnf(2269,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)],[173,253]),
[iquote('0:SoR:173.0,253.1')] ).
cnf(2321,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1487,2263]),
[iquote('0:SoR:1487.0,2263.0')] ).
cnf(2328,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2321]),
[iquote('0:SoR:11.0,2321.0')] ).
cnf(2358,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2328,1]),
[iquote('0:Res:2328.0,1.1')] ).
cnf(3672,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2358,2269]),
[iquote('0:SoR:2358.0,2269.1')] ).
cnf(3713,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[91,3672]),
[iquote('0:SoR:91.0,3672.1')] ).
cnf(3721,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[3672,1]),
[iquote('0:Res:3672.1,1.1')] ).
cnf(4216,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[3713,1374]),
[iquote('0:SoR:3713.0,1374.0')] ).
cnf(4227,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w),w)),
inference(sor,[status(thm)],[3713,1029]),
[iquote('0:SoR:3713.0,1029.0')] ).
cnf(4513,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[35,4216]),
[iquote('0:SoR:35.0,4216.0')] ).
cnf(4525,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[3721,4227]),
[iquote('0:SoR:3721.1,4227.0')] ).
cnf(4704,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[3721,4513]),
[iquote('0:SoR:3721.1,4513.0')] ).
cnf(4713,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,u),u))),
inference(sor,[status(thm)],[35,4513]),
[iquote('0:SoR:35.0,4513.0')] ).
cnf(4714,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[168,4513]),
[iquote('0:SoR:168.0,4513.0')] ).
cnf(4732,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[13,4714]),
[iquote('0:SoR:13.0,4714.0')] ).
cnf(4848,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[3721,4732]),
[iquote('0:SoR:3721.1,4732.0')] ).
cnf(5106,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[4848,4713]),
[iquote('0:SoR:4848.0,4713.0')] ).
cnf(5279,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[451,5106]),
[iquote('0:SoR:451.0,5106.0')] ).
cnf(10711,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[4525,5279]),
[iquote('0:SoR:4525.0,5279.0')] ).
cnf(10713,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[4704,10711]),
[iquote('0:SoR:4704.0,10711.0')] ).
cnf(10761,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),w),implies__dfg(implies__dfg(u,v),w))),
inference(sor,[status(thm)],[496,10713]),
[iquote('0:SoR:496.0,10713.0')] ).
cnf(10776,plain,
$false,
inference(unc,[status(thm)],[10761,5]),
[iquote('0:UnC:10761.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL381-1 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.12 % 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 : Sun Jul 3 14:26:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.00/4.18
% 4.00/4.18 SPASS V 3.9
% 4.00/4.18 SPASS beiseite: Proof found.
% 4.00/4.18 % SZS status Theorem
% 4.00/4.18 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.00/4.18 SPASS derived 10699 clauses, backtracked 0 clauses, performed 0 splits and kept 3909 clauses.
% 4.00/4.18 SPASS allocated 89128 KBytes.
% 4.00/4.18 SPASS spent 0:00:03.84 on the problem.
% 4.00/4.18 0:00:00.03 for the input.
% 4.00/4.18 0:00:00.00 for the FLOTTER CNF translation.
% 4.00/4.18 0:00:00.21 for inferences.
% 4.00/4.18 0:00:00.00 for the backtracking.
% 4.00/4.18 0:00:03.55 for the reduction.
% 4.00/4.18
% 4.00/4.18
% 4.00/4.18 Here is a proof with depth 29, length 64 :
% 4.00/4.18 % SZS output start Refutation
% See solution above
% 4.00/4.18 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_42
% 4.08/4.28
%------------------------------------------------------------------------------