TSTP Solution File: LCL055-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL055-1 : 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 4.49s 4.68s
% Output : Refutation 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of clauses : 60 ( 37 unt; 0 nHn; 60 RR)
% Number of literals : 86 ( 0 equ; 27 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('LCL055-1.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('LCL055-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL055-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL055-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),c),implies__dfg(not__dfg(a),c))),
file('LCL055-1.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(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)],[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(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(31,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
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)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(58,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(59,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(63,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)],[58,1]),
[iquote('0:Res:58.0,1.1')] ).
cnf(89,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(108,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[33,18]),
[iquote('0:SoR:33.0,18.0')] ).
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)],[33,22]),
[iquote('0:SoR:33.0,22.0')] ).
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)],[33,17]),
[iquote('0:SoR:33.0,17.0')] ).
cnf(122,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[21,108]),
[iquote('0:SoR:21.0,108.0')] ).
cnf(125,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)],[15,122]),
[iquote('0:SoR:15.0,122.0')] ).
cnf(165,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)],[125,1]),
[iquote('0:Res:125.0,1.1')] ).
cnf(170,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)],[165,109]),
[iquote('0:SoR:165.0,109.0')] ).
cnf(254,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(270,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)],[254,1]),
[iquote('0:Res:254.1,1.1')] ).
cnf(308,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)],[270,108]),
[iquote('0:SoR:270.1,108.0')] ).
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)],[270,18]),
[iquote('0:SoR:270.1,18.0')] ).
cnf(452,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(1024,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(v),w)))),
inference(sor,[status(thm)],[308,31]),
[iquote('0:SoR:308.0,31.0')] ).
cnf(1030,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v))),w)),
inference(sor,[status(thm)],[63,1024]),
[iquote('0:SoR:63.0,1024.0')] ).
cnf(1259,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[311,59]),
[iquote('0:SoR:311.0,59.0')] ).
cnf(1303,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(1313,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[15,1303]),
[iquote('0:SoR:15.0,1303.0')] ).
cnf(1375,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[63,1259]),
[iquote('0:SoR:63.0,1259.0')] ).
cnf(1488,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1313,1]),
[iquote('0:Res:1313.0,1.1')] ).
cnf(2270,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)],[170,254]),
[iquote('0:SoR:170.0,254.1')] ).
cnf(2281,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[170,1313]),
[iquote('0:SoR:170.0,1313.0')] ).
cnf(2322,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1488,2281]),
[iquote('0:SoR:1488.0,2281.0')] ).
cnf(2329,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2322]),
[iquote('0:SoR:11.0,2322.0')] ).
cnf(2359,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2329,1]),
[iquote('0:Res:2329.0,1.1')] ).
cnf(3673,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2359,2270]),
[iquote('0:SoR:2359.0,2270.1')] ).
cnf(3714,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[89,3673]),
[iquote('0:SoR:89.0,3673.1')] ).
cnf(3722,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[3673,1]),
[iquote('0:Res:3673.1,1.1')] ).
cnf(4217,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[3714,1375]),
[iquote('0:SoR:3714.0,1375.0')] ).
cnf(4228,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w),w)),
inference(sor,[status(thm)],[3714,1030]),
[iquote('0:SoR:3714.0,1030.0')] ).
cnf(4514,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[33,4217]),
[iquote('0:SoR:33.0,4217.0')] ).
cnf(4526,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(u),v)),w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[3722,4228]),
[iquote('0:SoR:3722.1,4228.0')] ).
cnf(4714,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,u),u))),
inference(sor,[status(thm)],[33,4514]),
[iquote('0:SoR:33.0,4514.0')] ).
cnf(4715,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[165,4514]),
[iquote('0:SoR:165.0,4514.0')] ).
cnf(4733,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[15,4715]),
[iquote('0:SoR:15.0,4715.0')] ).
cnf(4849,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[3722,4733]),
[iquote('0:SoR:3722.1,4733.0')] ).
cnf(5107,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[4849,4714]),
[iquote('0:SoR:4849.0,4714.0')] ).
cnf(5280,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[452,5107]),
[iquote('0:SoR:452.0,5107.0')] ).
cnf(10712,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[4526,5280]),
[iquote('0:SoR:4526.0,5280.0')] ).
cnf(10728,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[15,10712]),
[iquote('0:SoR:15.0,10712.0')] ).
cnf(10732,plain,
$false,
inference(unc,[status(thm)],[10728,5]),
[iquote('0:UnC:10728.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % 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 : Sun Jul 3 13:18:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.49/4.68
% 4.49/4.68 SPASS V 3.9
% 4.49/4.68 SPASS beiseite: Proof found.
% 4.49/4.68 % SZS status Theorem
% 4.49/4.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.49/4.68 SPASS derived 10655 clauses, backtracked 0 clauses, performed 0 splits and kept 3882 clauses.
% 4.49/4.68 SPASS allocated 88973 KBytes.
% 4.49/4.68 SPASS spent 0:00:04.20 on the problem.
% 4.49/4.68 0:00:00.03 for the input.
% 4.49/4.68 0:00:00.00 for the FLOTTER CNF translation.
% 4.49/4.68 0:00:00.22 for inferences.
% 4.49/4.68 0:00:00.00 for the backtracking.
% 4.49/4.68 0:00:03.89 for the reduction.
% 4.49/4.68
% 4.49/4.68
% 4.49/4.68 Here is a proof with depth 28, length 60 :
% 4.49/4.68 % SZS output start Refutation
% See solution above
% 4.49/4.68 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_37
% 4.49/4.68
%------------------------------------------------------------------------------