TSTP Solution File: LCL083-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL083-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:34:28 EDT 2022
% Result : Unsatisfiable 1.73s 1.97s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 62 ( 32 unt; 0 nHn; 62 RR)
% Number of literals : 98 ( 0 equ; 37 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 : 11 ( 11 usr; 10 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('LCL083-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(w,u),implies__dfg(x,u)))),
file('LCL083-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
file('LCL083-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(x,u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),implies__dfg(y,implies__dfg(v,x)))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(y,v))),implies__dfg(z,implies__dfg(implies__dfg(x,v),implies__dfg(y,v))))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(v,x))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w))))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w)))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(u,v)))),
inference(ems,[status(thm)],[14,11]),
[iquote('0:EmS:14.0,11.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,u)),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,v),implies__dfg(implies__dfg(w,v),implies__dfg(v,v))))),
inference(sor,[status(thm)],[10,9]),
[iquote('0:SoR:10.0,9.0')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(x,w))),implies__dfg(y,implies__dfg(w,z))),implies__dfg(x1,implies__dfg(y,implies__dfg(w,z))))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(22,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(y,v))))
| is_a_theorem(implies__dfg(z,implies__dfg(implies__dfg(x,v),implies__dfg(y,v)))) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(36,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,v),implies__dfg(implies__dfg(w,v),implies__dfg(v,v)))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(37,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)))),implies__dfg(x2,implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)))))),
inference(sor,[status(thm)],[7,21]),
[iquote('0:SoR:7.0,21.0')] ).
cnf(40,plain,
is_a_theorem(implies__dfg(implies__dfg(u,u),implies__dfg(implies__dfg(v,u),implies__dfg(u,u)))),
inference(ems,[status(thm)],[36,18]),
[iquote('0:EmS:36.0,18.0')] ).
cnf(48,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,v)),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[7,40]),
[iquote('0:SoR:7.0,40.0')] ).
cnf(61,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,w)))),
inference(sor,[status(thm)],[22,48]),
[iquote('0:SoR:22.0,48.0')] ).
cnf(66,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v)))),
inference(sor,[status(thm)],[22,2]),
[iquote('0:SoR:22.0,2.0')] ).
cnf(73,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,w))) ),
inference(res,[status(thm),theory(equality)],[61,1]),
[iquote('0:Res:61.0,1.1')] ).
cnf(74,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,v))),
inference(ems,[status(thm)],[73,18]),
[iquote('0:EmS:73.0,18.0')] ).
cnf(83,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[7,74]),
[iquote('0:SoR:7.0,74.0')] ).
cnf(86,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[74,1]),
[iquote('0:Res:74.0,1.1')] ).
cnf(88,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,v))),
inference(sor,[status(thm)],[86,18]),
[iquote('0:SoR:86.0,18.0')] ).
cnf(98,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u)),x),implies__dfg(y,x))),
inference(sor,[status(thm)],[7,66]),
[iquote('0:SoR:7.0,66.0')] ).
cnf(104,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(sor,[status(thm)],[7,88]),
[iquote('0:SoR:7.0,88.0')] ).
cnf(109,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[10,83]),
[iquote('0:SoR:10.0,83.0')] ).
cnf(114,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[83,1]),
[iquote('0:Res:83.0,1.1')] ).
cnf(120,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[109,1]),
[iquote('0:Res:109.0,1.1')] ).
cnf(121,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[120,88]),
[iquote('0:EmS:120.0,88.0')] ).
cnf(139,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[121,1]),
[iquote('0:Res:121.0,1.1')] ).
cnf(141,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[7,139]),
[iquote('0:SoR:7.0,139.1')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w)))),
inference(sor,[status(thm)],[7,104]),
[iquote('0:SoR:7.0,104.0')] ).
cnf(160,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[114,88]),
[iquote('0:SoR:114.0,88.0')] ).
cnf(176,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[160,1]),
[iquote('0:Res:160.0,1.1')] ).
cnf(178,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[176,37]),
[iquote('0:EmS:176.0,37.0')] ).
cnf(198,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u)),x))
| is_a_theorem(implies__dfg(y,x)) ),
inference(res,[status(thm),theory(equality)],[98,1]),
[iquote('0:Res:98.0,1.1')] ).
cnf(208,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
inference(sor,[status(thm)],[114,141]),
[iquote('0:SoR:114.0,141.1')] ).
cnf(212,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),implies__dfg(x,w))) ),
inference(sor,[status(thm)],[7,208]),
[iquote('0:SoR:7.0,208.1')] ).
cnf(343,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(implies__dfg(v,u),w))
| is_a_theorem(implies__dfg(x,w)) ),
inference(res,[status(thm),theory(equality)],[212,1]),
[iquote('0:Res:212.1,1.1')] ).
cnf(691,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),implies__dfg(x,w)))) ),
inference(sor,[status(thm)],[343,2]),
[iquote('0:SoR:343.1,2.0')] ).
cnf(700,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(y,x))) ),
inference(sor,[status(thm)],[7,691]),
[iquote('0:SoR:7.0,691.1')] ).
cnf(754,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,v)),implies__dfg(y,implies__dfg(x,v)))),
inference(sor,[status(thm)],[7,149]),
[iquote('0:SoR:7.0,149.0')] ).
cnf(2482,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,v)))
| is_a_theorem(implies__dfg(y,implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[754,1]),
[iquote('0:Res:754.0,1.1')] ).
cnf(3565,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(y,x)) ),
inference(res,[status(thm),theory(equality)],[700,1]),
[iquote('0:Res:700.1,1.1')] ).
cnf(5159,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),x),w),implies__dfg(v,w)))),
inference(sor,[status(thm)],[2482,2]),
[iquote('0:SoR:2482.0,2.0')] ).
cnf(5213,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),x),w),implies__dfg(v,w))) ),
inference(res,[status(thm),theory(equality)],[5159,1]),
[iquote('0:Res:5159.0,1.1')] ).
cnf(5214,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),w),v),implies__dfg(u,v))),
inference(ems,[status(thm)],[5213,178]),
[iquote('0:EmS:5213.0,178.0')] ).
cnf(5321,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(u,v),w)),implies__dfg(x,implies__dfg(implies__dfg(u,v),w)))),
inference(sor,[status(thm)],[7,5214]),
[iquote('0:SoR:7.0,5214.0')] ).
cnf(10464,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),w)))),
inference(sor,[status(thm)],[198,5321]),
[iquote('0:SoR:198.0,5321.0')] ).
cnf(10469,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(implies__dfg(u,x),x)))) ),
inference(sor,[status(thm)],[3565,5321]),
[iquote('0:SoR:3565.1,5321.0')] ).
cnf(10577,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),w))) ),
inference(res,[status(thm),theory(equality)],[10464,1]),
[iquote('0:Res:10464.0,1.1')] ).
cnf(10765,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(w,implies__dfg(implies__dfg(u,x),x))) ),
inference(res,[status(thm),theory(equality)],[10469,1]),
[iquote('0:Res:10469.1,1.1')] ).
cnf(10766,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),w))) ),
inference(con,[status(thm)],[10765]),
[iquote('0:Con:10765.1')] ).
cnf(10846,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(implies__dfg(u,w),w)) ),
inference(res,[status(thm),theory(equality)],[10766,1]),
[iquote('0:Res:10766.1,1.1')] ).
cnf(10847,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(con,[status(thm)],[10846]),
[iquote('0:Con:10846.1')] ).
cnf(10916,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[10847,1]),
[iquote('0:Res:10847.1,1.1')] ).
cnf(11183,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),v))),
inference(ems,[status(thm)],[10577,178]),
[iquote('0:EmS:10577.0,178.0')] ).
cnf(11519,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),v)) ),
inference(sor,[status(thm)],[10916,11183]),
[iquote('0:SoR:10916.1,11183.0')] ).
cnf(11558,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
inference(ems,[status(thm)],[11519,178]),
[iquote('0:EmS:11519.0,178.0')] ).
cnf(11718,plain,
$false,
inference(unc,[status(thm)],[11558,3]),
[iquote('0:UnC:11558.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL083-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 18:59:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.97
% 1.73/1.97 SPASS V 3.9
% 1.73/1.97 SPASS beiseite: Proof found.
% 1.73/1.97 % SZS status Theorem
% 1.73/1.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.73/1.97 SPASS derived 11492 clauses, backtracked 0 clauses, performed 0 splits and kept 1084 clauses.
% 1.73/1.97 SPASS allocated 85666 KBytes.
% 1.73/1.97 SPASS spent 0:00:01.63 on the problem.
% 1.73/1.97 0:00:00.04 for the input.
% 1.73/1.97 0:00:00.00 for the FLOTTER CNF translation.
% 1.73/1.97 0:00:00.24 for inferences.
% 1.73/1.97 0:00:00.00 for the backtracking.
% 1.73/1.97 0:00:01.31 for the reduction.
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Here is a proof with depth 30, length 62 :
% 1.73/1.97 % SZS output start Refutation
% See solution above
% 1.81/2.06 Formulae used in the proof : condensed_detachment ic_JLukasiewicz prove_ic_3
% 1.81/2.06
%------------------------------------------------------------------------------