TSTP Solution File: LCL378-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL378-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:36:33 EDT 2022
% Result : Unsatisfiable 4.07s 4.26s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of clauses : 64 ( 40 unt; 0 nHn; 64 RR)
% Number of literals : 91 ( 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('LCL378-1.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('LCL378-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL378-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL378-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(not__dfg(x__dfg),implies__dfg(x__dfg,y__dfg))),
file('LCL378-1.p',unknown),
[] ).
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(18,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(19,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(20,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(implies__dfg(u,v),w),implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w))),
inference(sor,[status(thm)],[13,19]),
[iquote('0:SoR:13.0,19.0')] ).
cnf(22,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)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(23,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)],[13,20]),
[iquote('0:SoR:13.0,20.0')] ).
cnf(24,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)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(31,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[22,3]),
[iquote('0:SoR:22.0,3.0')] ).
cnf(33,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)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(56,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[24,4]),
[iquote('0:SoR:24.0,4.0')] ).
cnf(58,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)],[24,3]),
[iquote('0:SoR:24.0,3.0')] ).
cnf(76,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)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(88,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)],[23,1]),
[iquote('0:Res:23.0,1.1')] ).
cnf(108,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[33,19]),
[iquote('0:SoR:33.0,19.0')] ).
cnf(109,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)],[33,23]),
[iquote('0:SoR:33.0,23.0')] ).
cnf(111,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)],[33,18]),
[iquote('0:SoR:33.0,18.0')] ).
cnf(121,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[22,108]),
[iquote('0:SoR:22.0,108.0')] ).
cnf(124,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)],[13,121]),
[iquote('0:SoR:13.0,121.0')] ).
cnf(164,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)],[124,1]),
[iquote('0:Res:124.0,1.1')] ).
cnf(169,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)],[109,1]),
[iquote('0:Res:109.0,1.1')] ).
cnf(230,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[164,109]),
[iquote('0:SoR:164.0,109.0')] ).
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(306,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)],[269,108]),
[iquote('0:SoR:269.1,108.0')] ).
cnf(311,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)],[269,19]),
[iquote('0:SoR:269.1,19.0')] ).
cnf(364,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[76,56]),
[iquote('0:SoR:76.0,56.0')] ).
cnf(386,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),u)),
inference(sor,[status(thm)],[76,3]),
[iquote('0:SoR:76.0,3.0')] ).
cnf(400,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u),u)),
inference(sor,[status(thm)],[76,386]),
[iquote('0:SoR:76.0,386.0')] ).
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)],[111,1]),
[iquote('0:Res:111.0,1.1')] ).
cnf(492,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[364,1]),
[iquote('0:Res:364.0,1.1')] ).
cnf(518,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[400,1]),
[iquote('0:Res:400.0,1.1')] ).
cnf(1016,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(v),w)))),
inference(sor,[status(thm)],[306,31]),
[iquote('0:SoR:306.0,31.0')] ).
cnf(1022,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v))),w)),
inference(sor,[status(thm)],[492,1016]),
[iquote('0:SoR:492.0,1016.0')] ).
cnf(1297,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[311,58]),
[iquote('0:SoR:311.0,58.0')] ).
cnf(1298,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[311,3]),
[iquote('0:SoR:311.0,3.0')] ).
cnf(1312,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1298]),
[iquote('0:SoR:13.0,1298.0')] ).
cnf(1367,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[492,1297]),
[iquote('0:SoR:492.0,1297.0')] ).
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)],[1312,1]),
[iquote('0:Res:1312.0,1.1')] ).
cnf(2214,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[169,1312]),
[iquote('0:SoR:169.0,1312.0')] ).
cnf(2221,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)],[169,253]),
[iquote('0:SoR:169.0,253.1')] ).
cnf(2258,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1473,2214]),
[iquote('0:SoR:1473.0,2214.0')] ).
cnf(2267,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[518,2258]),
[iquote('0:SoR:518.0,2258.0')] ).
cnf(2302,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2267,1]),
[iquote('0:Res:2267.0,1.1')] ).
cnf(3591,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2302,2221]),
[iquote('0:SoR:2302.0,2221.1')] ).
cnf(3638,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[88,3591]),
[iquote('0:SoR:88.0,3591.1')] ).
cnf(3648,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[3591,1]),
[iquote('0:Res:3591.1,1.1')] ).
cnf(4146,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w),w)),
inference(sor,[status(thm)],[3638,1022]),
[iquote('0:SoR:3638.0,1022.0')] ).
cnf(4148,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[3638,1367]),
[iquote('0:SoR:3638.0,1367.0')] ).
cnf(4419,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[3648,4146]),
[iquote('0:SoR:3648.1,4146.0')] ).
cnf(4453,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[33,4148]),
[iquote('0:SoR:33.0,4148.0')] ).
cnf(4657,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,u),u))),
inference(sor,[status(thm)],[33,4453]),
[iquote('0:SoR:33.0,4453.0')] ).
cnf(4658,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[164,4453]),
[iquote('0:SoR:164.0,4453.0')] ).
cnf(4670,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[13,4658]),
[iquote('0:SoR:13.0,4658.0')] ).
cnf(4806,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[3648,4670]),
[iquote('0:SoR:3648.1,4670.0')] ).
cnf(5057,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[4806,4657]),
[iquote('0:SoR:4806.0,4657.0')] ).
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)],[473,5057]),
[iquote('0:SoR:473.0,5057.0')] ).
cnf(10582,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[4419,5191]),
[iquote('0:SoR:4419.0,5191.0')] ).
cnf(10587,plain,
$false,
inference(unc,[status(thm)],[10582,5]),
[iquote('0:UnC:10582.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL378-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 2 11:22:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.07/4.26
% 4.07/4.26 SPASS V 3.9
% 4.07/4.26 SPASS beiseite: Proof found.
% 4.07/4.26 % SZS status Theorem
% 4.07/4.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.07/4.26 SPASS derived 10510 clauses, backtracked 0 clauses, performed 0 splits and kept 3837 clauses.
% 4.07/4.26 SPASS allocated 88808 KBytes.
% 4.07/4.26 SPASS spent 0:00:03.90 on the problem.
% 4.07/4.26 0:00:00.04 for the input.
% 4.07/4.26 0:00:00.00 for the FLOTTER CNF translation.
% 4.07/4.26 0:00:00.21 for inferences.
% 4.07/4.26 0:00:00.00 for the backtracking.
% 4.07/4.26 0:00:03.60 for the reduction.
% 4.07/4.26
% 4.07/4.26
% 4.07/4.26 Here is a proof with depth 27, length 64 :
% 4.07/4.26 % SZS output start Refutation
% See solution above
% 4.07/4.26 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_36
% 4.18/4.36
%------------------------------------------------------------------------------