TSTP Solution File: LCL089-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL089-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:34:31 EDT 2022
% Result : Unsatisfiable 0.57s 0.73s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of clauses : 63 ( 35 unt; 0 nHn; 63 RR)
% Number of literals : 95 ( 0 equ; 33 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 : 12 ( 12 usr; 11 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('LCL089-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)),implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u))))),
file('LCL089-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(a,b),implies__dfg(implies__dfg(b,c),implies__dfg(a,c)))),
file('LCL089-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u)))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,implies__dfg(w,x)),y),implies__dfg(implies__dfg(implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)),implies__dfg(w,x)),y)))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,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(ems,[status(thm)],[10,8]),
[iquote('0:EmS:10.0,8.0')] ).
cnf(14,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)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(16,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w))))),
inference(sor,[status(thm)],[14,11]),
[iquote('0:SoR:14.0,11.0')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w))))),
inference(sor,[status(thm)],[14,2]),
[iquote('0:SoR:14.0,2.0')] ).
cnf(20,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)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1)))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(26,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(u,v)))),
inference(ems,[status(thm)],[20,17]),
[iquote('0:EmS:20.0,17.0')] ).
cnf(33,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[7,27]),
[iquote('0:SoR:7.0,27.0')] ).
cnf(52,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[33,1]),
[iquote('0:Res:33.0,1.1')] ).
cnf(53,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(ems,[status(thm)],[26,27]),
[iquote('0:EmS:26.0,27.0')] ).
cnf(63,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[53,1]),
[iquote('0:Res:53.0,1.1')] ).
cnf(67,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)],[63,1]),
[iquote('0:Res:63.1,1.1')] ).
cnf(71,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1))) ),
inference(res,[status(thm),theory(equality)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(83,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(v,u))),
inference(ems,[status(thm)],[52,27]),
[iquote('0:EmS:52.0,27.0')] ).
cnf(97,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[14,83]),
[iquote('0:SoR:14.0,83.0')] ).
cnf(101,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,97]),
[iquote('0:SoR:7.0,97.0')] ).
cnf(103,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[97,1]),
[iquote('0:Res:97.0,1.1')] ).
cnf(107,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[103,83]),
[iquote('0:EmS:103.0,83.0')] ).
cnf(119,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v)))),
inference(sor,[status(thm)],[7,107]),
[iquote('0:SoR:7.0,107.0')] ).
cnf(157,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),y),z),implies__dfg(implies__dfg(implies__dfg(x1,implies__dfg(v,x)),y),z))),
inference(ems,[status(thm)],[71,2]),
[iquote('0:EmS:71.0,2.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x))) ),
inference(res,[status(thm),theory(equality)],[101,1]),
[iquote('0:Res:101.0,1.1')] ).
cnf(180,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[119,1]),
[iquote('0:Res:119.0,1.1')] ).
cnf(273,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(ems,[status(thm)],[175,107]),
[iquote('0:EmS:175.0,107.0')] ).
cnf(293,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(x,implies__dfg(v,w))) ),
inference(sor,[status(thm)],[67,273]),
[iquote('0:SoR:67.1,273.0')] ).
cnf(299,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[273,1]),
[iquote('0:Res:273.0,1.1')] ).
cnf(345,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(implies__dfg(v,x),implies__dfg(u,x))))),
inference(sor,[status(thm)],[299,2]),
[iquote('0:SoR:299.0,2.0')] ).
cnf(374,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(ems,[status(thm)],[180,157]),
[iquote('0:EmS:180.0,157.0')] ).
cnf(403,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w))))),
inference(sor,[status(thm)],[7,374]),
[iquote('0:SoR:7.0,374.0')] ).
cnf(407,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,u)) ),
inference(res,[status(thm),theory(equality)],[374,1]),
[iquote('0:Res:374.0,1.1')] ).
cnf(408,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[407,374]),
[iquote('0:SoR:407.0,374.0')] ).
cnf(444,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[408,1]),
[iquote('0:Res:408.0,1.1')] ).
cnf(445,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[444,374]),
[iquote('0:EmS:444.0,374.0')] ).
cnf(538,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
inference(sor,[status(thm)],[293,408]),
[iquote('0:SoR:293.0,408.0')] ).
cnf(565,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w)))),
inference(sor,[status(thm)],[7,538]),
[iquote('0:SoR:7.0,538.0')] ).
cnf(611,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w))) ),
inference(res,[status(thm),theory(equality)],[565,1]),
[iquote('0:Res:565.0,1.1')] ).
cnf(679,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(ems,[status(thm)],[611,445]),
[iquote('0:EmS:611.0,445.0')] ).
cnf(1170,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w)))) ),
inference(res,[status(thm),theory(equality)],[403,1]),
[iquote('0:Res:403.0,1.1')] ).
cnf(2182,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(w,implies__dfg(u,v)))),
inference(ems,[status(thm)],[1170,445]),
[iquote('0:EmS:1170.0,445.0')] ).
cnf(2272,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)],[2182,1]),
[iquote('0:Res:2182.0,1.1')] ).
cnf(2274,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[2272,679]),
[iquote('0:SoR:2272.0,679.0')] ).
cnf(2280,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),v))),
inference(sor,[status(thm)],[2272,374]),
[iquote('0:SoR:2272.0,374.0')] ).
cnf(2284,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(v,w)))),
inference(sor,[status(thm)],[2272,2182]),
[iquote('0:SoR:2272.0,2182.0')] ).
cnf(2342,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),w))) ),
inference(sor,[status(thm)],[2272,63]),
[iquote('0:SoR:2272.0,63.1')] ).
cnf(2438,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),w)) ),
inference(res,[status(thm),theory(equality)],[2274,1]),
[iquote('0:Res:2274.0,1.1')] ).
cnf(2482,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)],[2342,1]),
[iquote('0:Res:2342.1,1.1')] ).
cnf(2483,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(con,[status(thm)],[2482]),
[iquote('0:Con:2482.1')] ).
cnf(2506,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2483,1]),
[iquote('0:Res:2483.1,1.1')] ).
cnf(2660,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(ems,[status(thm)],[2438,445]),
[iquote('0:EmS:2438.0,445.0')] ).
cnf(2743,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[2506,2660]),
[iquote('0:SoR:2506.1,2660.0')] ).
cnf(2782,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
inference(sor,[status(thm)],[2743,2280]),
[iquote('0:SoR:2743.0,2280.0')] ).
cnf(2862,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[2506,2782]),
[iquote('0:SoR:2506.1,2782.0')] ).
cnf(3227,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[2862,2284]),
[iquote('0:SoR:2862.0,2284.0')] ).
cnf(3242,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[2506,3227]),
[iquote('0:SoR:2506.1,3227.0')] ).
cnf(3269,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[3242,345]),
[iquote('0:SoR:3242.0,345.0')] ).
cnf(3336,plain,
$false,
inference(unc,[status(thm)],[3269,3]),
[iquote('0:UnC:3269.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL089-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 : Mon Jul 4 19:19:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.73
% 0.57/0.73 SPASS V 3.9
% 0.57/0.73 SPASS beiseite: Proof found.
% 0.57/0.73 % SZS status Theorem
% 0.57/0.73 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.73 SPASS derived 3280 clauses, backtracked 0 clauses, performed 0 splits and kept 507 clauses.
% 0.57/0.73 SPASS allocated 79488 KBytes.
% 0.57/0.73 SPASS spent 0:00:00.40 on the problem.
% 0.57/0.73 0:00:00.03 for the input.
% 0.57/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.57/0.73 0:00:00.08 for inferences.
% 0.57/0.73 0:00:00.00 for the backtracking.
% 0.57/0.73 0:00:00.26 for the reduction.
% 0.57/0.73
% 0.57/0.73
% 0.57/0.73 Here is a proof with depth 32, length 63 :
% 0.57/0.73 % SZS output start Refutation
% See solution above
% 0.57/0.76 Formulae used in the proof : condensed_detachment ic_JLukasiewicz_4 prove_ic_4
% 0.57/0.76
%------------------------------------------------------------------------------