TSTP Solution File: LCL056-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL056-1 : TPTP v8.1.0. Released v1.0.0.
% 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 14:34:18 EDT 2022
% Result : Unsatisfiable 3.59s 3.81s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of clauses : 58 ( 36 unt; 0 nHn; 58 RR)
% Number of literals : 83 ( 0 equ; 26 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 : 7 ( 7 usr; 5 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('LCL056-1.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('LCL056-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL056-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL056-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(not__dfg(not__dfg(a)),a)),
file('LCL056-1.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(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
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(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)],[13,17]),
[iquote('0:SoR:13.0,17.0')] ).
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)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
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)],[13,19]),
[iquote('0:SoR:13.0,19.0')] ).
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)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
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(57,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(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[33,17]),
[iquote('0:SoR:33.0,17.0')] ).
cnf(114,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(119,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[22,113]),
[iquote('0:SoR:22.0,113.0')] ).
cnf(122,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)],[113,1]),
[iquote('0:Res:113.0,1.1')] ).
cnf(126,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)],[13,119]),
[iquote('0:SoR:13.0,119.0')] ).
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)],[126,1]),
[iquote('0:Res:126.0,1.1')] ).
cnf(199,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)],[114,1]),
[iquote('0:Res:114.0,1.1')] ).
cnf(237,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[164,114]),
[iquote('0:SoR:164.0,114.0')] ).
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)],[237,1]),
[iquote('0:Res:237.0,1.1')] ).
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(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)],[269,17]),
[iquote('0:SoR:269.1,17.0')] ).
cnf(384,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)],[76,57]),
[iquote('0:SoR:76.0,57.0')] ).
cnf(1286,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[311,57]),
[iquote('0:SoR:311.0,57.0')] ).
cnf(1288,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(1317,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1288]),
[iquote('0:SoR:13.0,1288.0')] ).
cnf(1386,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)],[13,1286]),
[iquote('0:SoR:13.0,1286.0')] ).
cnf(1471,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1317,1]),
[iquote('0:Res:1317.0,1.1')] ).
cnf(2114,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)],[33,384]),
[iquote('0:SoR:33.0,384.0')] ).
cnf(2161,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)],[33,1386]),
[iquote('0:SoR:33.0,1386.0')] ).
cnf(2508,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[199,1317]),
[iquote('0:SoR:199.0,1317.0')] ).
cnf(2509,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)],[199,253]),
[iquote('0:SoR:199.0,253.1')] ).
cnf(2569,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1471,2508]),
[iquote('0:SoR:1471.0,2508.0')] ).
cnf(2581,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2569]),
[iquote('0:SoR:11.0,2569.0')] ).
cnf(2615,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2581,1]),
[iquote('0:Res:2581.0,1.1')] ).
cnf(3585,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[164,2161]),
[iquote('0:SoR:164.0,2161.0')] ).
cnf(3613,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[199,3585]),
[iquote('0:SoR:199.0,3585.0')] ).
cnf(3654,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[3613,1]),
[iquote('0:Res:3613.0,1.1')] ).
cnf(4151,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),u)),
inference(sor,[status(thm)],[3654,2114]),
[iquote('0:SoR:3654.0,2114.0')] ).
cnf(4165,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)],[122,4151]),
[iquote('0:SoR:122.0,4151.0')] ).
cnf(5481,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2615,2509]),
[iquote('0:SoR:2615.0,2509.1')] ).
cnf(5725,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[88,5481]),
[iquote('0:SoR:88.0,5481.1')] ).
cnf(5746,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[5481,1]),
[iquote('0:Res:5481.1,1.1')] ).
cnf(6189,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[5725,1286]),
[iquote('0:SoR:5725.0,1286.0')] ).
cnf(6395,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[33,6189]),
[iquote('0:SoR:33.0,6189.0')] ).
cnf(7064,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[5746,6395]),
[iquote('0:SoR:5746.1,6395.0')] ).
cnf(8689,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u))))),
inference(sor,[status(thm)],[7064,4165]),
[iquote('0:SoR:7064.0,4165.0')] ).
cnf(8857,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)),implies__dfg(u,v))),
inference(sor,[status(thm)],[122,8689]),
[iquote('0:SoR:122.0,8689.0')] ).
cnf(8979,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[22,8857]),
[iquote('0:SoR:22.0,8857.0')] ).
cnf(9017,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[7064,8979]),
[iquote('0:SoR:7064.0,8979.0')] ).
cnf(9032,plain,
$false,
inference(unc,[status(thm)],[9017,5]),
[iquote('0:UnC:9017.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 2 11:57:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.59/3.81
% 3.59/3.81 SPASS V 3.9
% 3.59/3.81 SPASS beiseite: Proof found.
% 3.59/3.81 % SZS status Theorem
% 3.59/3.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/3.81 SPASS derived 8964 clauses, backtracked 0 clauses, performed 0 splits and kept 3383 clauses.
% 3.59/3.81 SPASS allocated 87449 KBytes.
% 3.59/3.81 SPASS spent 0:00:03.35 on the problem.
% 3.59/3.81 0:00:00.03 for the input.
% 3.59/3.81 0:00:00.00 for the FLOTTER CNF translation.
% 3.59/3.81 0:00:00.19 for inferences.
% 3.59/3.81 0:00:00.00 for the backtracking.
% 3.59/3.81 0:00:03.07 for the reduction.
% 3.59/3.81
% 3.59/3.81
% 3.59/3.81 Here is a proof with depth 26, length 58 :
% 3.59/3.81 % SZS output start Refutation
% See solution above
% 3.59/3.81 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_39
% 3.59/3.81
%------------------------------------------------------------------------------