TSTP Solution File: LCL072-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL072-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 14:34:23 EDT 2022
% Result : Unsatisfiable 14.48s 14.65s
% Output : Refutation 14.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 68 ( 44 unt; 0 nHn; 68 RR)
% Number of literals : 93 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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('LCL072-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
file('LCL072-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(not__dfg(u),w))),
file('LCL072-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),implies__dfg(u,implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(v,x),w))))),
file('LCL072-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(not__dfg(a),b))),
file('LCL072-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(12,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),w)))
| is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(v,x),w)))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(14,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(w,implies__dfg(implies__dfg(x,v),implies__dfg(implies__dfg(u,x),v))))),
inference(sor,[status(thm)],[11,4]),
[iquote('0:SoR:11.0,4.0')] ).
cnf(16,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[11,2]),
[iquote('0:SoR:11.0,2.0')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[11,16]),
[iquote('0:SoR:11.0,16.0')] ).
cnf(26,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[12,3]),
[iquote('0:SoR:12.0,3.0')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(v,w))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,u))))),
inference(sor,[status(thm)],[11,17]),
[iquote('0:SoR:11.0,17.0')] ).
cnf(39,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(u,x),w)))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(40,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,not__dfg(v)),w),implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(v,x),w)))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(47,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(implies__dfg(w,x),implies__dfg(implies__dfg(u,w),x)))),
inference(sor,[status(thm)],[13,26]),
[iquote('0:SoR:13.0,26.0')] ).
cnf(64,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(u,x),w))) ),
inference(res,[status(thm),theory(equality)],[39,1]),
[iquote('0:Res:39.0,1.1')] ).
cnf(77,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(implies__dfg(u,w),x))))),
inference(sor,[status(thm)],[12,14]),
[iquote('0:SoR:12.0,14.0')] ).
cnf(84,plain,
( ~ is_a_theorem(not__dfg(implies__dfg(u,v)))
| is_a_theorem(implies__dfg(implies__dfg(w,x),implies__dfg(implies__dfg(u,w),x))) ),
inference(res,[status(thm),theory(equality)],[47,1]),
[iquote('0:Res:47.0,1.1')] ).
cnf(89,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),w))
| is_a_theorem(implies__dfg(implies__dfg(x,w),implies__dfg(implies__dfg(v,x),w))) ),
inference(res,[status(thm),theory(equality)],[40,1]),
[iquote('0:Res:40.0,1.1')] ).
cnf(96,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(implies__dfg(u,w),x))),implies__dfg(implies__dfg(y,v),implies__dfg(implies__dfg(w,x),implies__dfg(implies__dfg(u,w),x)))))),
inference(sor,[status(thm)],[13,77]),
[iquote('0:SoR:13.0,77.0')] ).
cnf(111,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(x,v),w))),implies__dfg(implies__dfg(implies__dfg(y,not__dfg(x)),u),implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(x,v),w))))),
inference(sor,[status(thm)],[64,40]),
[iquote('0:SoR:64.0,40.0')] ).
cnf(117,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(w,u),implies__dfg(v,implies__dfg(w,x))))),
inference(sor,[status(thm)],[64,16]),
[iquote('0:SoR:64.0,16.0')] ).
cnf(118,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(x,v),w))),implies__dfg(implies__dfg(implies__dfg(x,y),u),implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(x,v),w))))),
inference(sor,[status(thm)],[64,39]),
[iquote('0:SoR:64.0,39.0')] ).
cnf(143,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,not__dfg(w))),implies__dfg(implies__dfg(w,u),implies__dfg(v,not__dfg(w))))),
inference(sor,[status(thm)],[89,2]),
[iquote('0:SoR:89.0,2.0')] ).
cnf(147,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(w))))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(v,not__dfg(w)))) ),
inference(res,[status(thm),theory(equality)],[143,1]),
[iquote('0:Res:143.0,1.1')] ).
cnf(151,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(implies__dfg(v,w))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[147,27]),
[iquote('0:SoR:147.0,27.0')] ).
cnf(152,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),implies__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[147,16]),
[iquote('0:SoR:147.0,16.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),not__dfg(u))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[147,2]),
[iquote('0:SoR:147.0,2.0')] ).
cnf(166,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,not__dfg(implies__dfg(v,w)))),implies__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[147,151]),
[iquote('0:SoR:147.0,151.0')] ).
cnf(218,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),not__dfg(u))))
| is_a_theorem(implies__dfg(w,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[154,1]),
[iquote('0:Res:154.0,1.1')] ).
cnf(224,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,not__dfg(implies__dfg(v,w)))))
| is_a_theorem(implies__dfg(w,not__dfg(u))) ),
inference(res,[status(thm),theory(equality)],[166,1]),
[iquote('0:Res:166.0,1.1')] ).
cnf(309,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(v,implies__dfg(w,x)))) ),
inference(res,[status(thm),theory(equality)],[117,1]),
[iquote('0:Res:117.0,1.1')] ).
cnf(367,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(implies__dfg(v,u),not__dfg(implies__dfg(v,u)))))),
inference(sor,[status(thm)],[224,152]),
[iquote('0:SoR:224.0,152.0')] ).
cnf(401,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(implies__dfg(implies__dfg(v,u),not__dfg(implies__dfg(v,u))))) ),
inference(res,[status(thm),theory(equality)],[367,1]),
[iquote('0:Res:367.0,1.1')] ).
cnf(407,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(implies__dfg(implies__dfg(v,w),u),implies__dfg(implies__dfg(x,y),implies__dfg(implies__dfg(v,x),y))))),
inference(sor,[status(thm)],[12,118]),
[iquote('0:SoR:12.0,118.0')] ).
cnf(442,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(implies__dfg(implies__dfg(v,not__dfg(w)),u),implies__dfg(implies__dfg(x,y),implies__dfg(implies__dfg(w,x),y))))),
inference(sor,[status(thm)],[12,111]),
[iquote('0:SoR:12.0,111.0')] ).
cnf(456,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(implies__dfg(x,u),v),w))) ),
inference(sor,[status(thm)],[84,401]),
[iquote('0:SoR:84.0,401.1')] ).
cnf(545,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(not__dfg(v),implies__dfg(implies__dfg(implies__dfg(w,u),v),x))) ),
inference(sor,[status(thm)],[12,456]),
[iquote('0:SoR:12.0,456.1')] ).
cnf(550,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,not__dfg(not__dfg(v)))) ),
inference(sor,[status(thm)],[218,545]),
[iquote('0:SoR:218.0,545.1')] ).
cnf(560,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(ems,[status(thm)],[550,96]),
[iquote('0:EmS:550.0,96.0')] ).
cnf(1327,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(u,implies__dfg(x,v))))),
inference(sor,[status(thm)],[309,29]),
[iquote('0:SoR:309.0,29.0')] ).
cnf(1329,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(w,implies__dfg(u,v)))),
inference(sor,[status(thm)],[309,16]),
[iquote('0:SoR:309.0,16.0')] ).
cnf(1366,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(u,implies__dfg(x,v)))) ),
inference(res,[status(thm),theory(equality)],[1327,1]),
[iquote('0:Res:1327.0,1.1')] ).
cnf(1375,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(w,implies__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[1329,1]),
[iquote('0:Res:1329.0,1.1')] ).
cnf(1466,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,not__dfg(not__dfg(v)))))),
inference(sor,[status(thm)],[1366,560]),
[iquote('0:SoR:1366.0,560.0')] ).
cnf(1552,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,not__dfg(not__dfg(v))))) ),
inference(res,[status(thm),theory(equality)],[1466,1]),
[iquote('0:Res:1466.0,1.1')] ).
cnf(1579,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(not__dfg(u))))),
inference(ems,[status(thm)],[1552,407]),
[iquote('0:EmS:1552.0,407.0')] ).
cnf(1709,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(v,not__dfg(not__dfg(u))))),
inference(sor,[status(thm)],[147,1579]),
[iquote('0:SoR:147.0,1579.0')] ).
cnf(1730,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(v,not__dfg(not__dfg(u)))) ),
inference(res,[status(thm),theory(equality)],[1709,1]),
[iquote('0:Res:1709.0,1.1')] ).
cnf(1789,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(implies__dfg(v,v))))),
inference(sor,[status(thm)],[1730,27]),
[iquote('0:SoR:1730.0,27.0')] ).
cnf(1801,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v))))))),
inference(sor,[status(thm)],[1730,1789]),
[iquote('0:SoR:1730.0,1789.0')] ).
cnf(1802,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(implies__dfg(v,v)))) ),
inference(res,[status(thm),theory(equality)],[1789,1]),
[iquote('0:Res:1789.0,1.1')] ).
cnf(1815,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,u)))),
inference(ems,[status(thm)],[1802,442]),
[iquote('0:EmS:1802.0,442.0')] ).
cnf(2006,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v))))))))),
inference(sor,[status(thm)],[1730,1801]),
[iquote('0:SoR:1730.0,1801.0')] ).
cnf(2007,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v)))))) ),
inference(res,[status(thm),theory(equality)],[1801,1]),
[iquote('0:Res:1801.0,1.1')] ).
cnf(2279,plain,
is_a_theorem(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(u,u)))))),
inference(ems,[status(thm)],[2007,1815]),
[iquote('0:EmS:2007.0,1815.0')] ).
cnf(2635,plain,
( ~ is_a_theorem(u)
| is_a_theorem(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(v,v)))))))) ),
inference(res,[status(thm),theory(equality)],[2006,1]),
[iquote('0:Res:2006.0,1.1')] ).
cnf(3386,plain,
is_a_theorem(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(not__dfg(implies__dfg(u,u)))))))),
inference(ems,[status(thm)],[2635,2279]),
[iquote('0:EmS:2635.0,2279.0')] ).
cnf(22101,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[1375,16]),
[iquote('0:SoR:1375.0,16.0')] ).
cnf(22135,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[22101,1]),
[iquote('0:Res:22101.0,1.1')] ).
cnf(22137,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[22135,3386]),
[iquote('0:EmS:22135.0,3386.0')] ).
cnf(22644,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[12,22137]),
[iquote('0:SoR:12.0,22137.0')] ).
cnf(22685,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[309,22644]),
[iquote('0:SoR:309.0,22644.0')] ).
cnf(24769,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)],[22685,1]),
[iquote('0:Res:22685.0,1.1')] ).
cnf(31388,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[24769,22137]),
[iquote('0:SoR:24769.0,22137.0')] ).
cnf(31406,plain,
$false,
inference(unc,[status(thm)],[31388,5]),
[iquote('0:UnC:31388.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL072-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 09:41:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 14.48/14.65
% 14.48/14.65 SPASS V 3.9
% 14.48/14.65 SPASS beiseite: Proof found.
% 14.48/14.65 % SZS status Theorem
% 14.48/14.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.48/14.65 SPASS derived 31332 clauses, backtracked 0 clauses, performed 0 splits and kept 9472 clauses.
% 14.48/14.65 SPASS allocated 111934 KBytes.
% 14.48/14.65 SPASS spent 0:0:14.29 on the problem.
% 14.48/14.65 0:00:00.04 for the input.
% 14.48/14.65 0:00:00.00 for the FLOTTER CNF translation.
% 14.48/14.65 0:00:00.52 for inferences.
% 14.48/14.65 0:00:00.00 for the backtracking.
% 14.48/14.65 0:0:13.59 for the reduction.
% 14.48/14.65
% 14.48/14.65
% 14.48/14.65 Here is a proof with depth 29, length 68 :
% 14.48/14.65 % SZS output start Refutation
% See solution above
% 14.86/15.07 Formulae used in the proof : condensed_detachment cn_19 cn_37 cn_60 prove_cn_3
% 14.86/15.07
%------------------------------------------------------------------------------