TSTP Solution File: LCL026-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL026-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 14:34:07 EDT 2022
% Result : Unsatisfiable 65.20s 65.39s
% Output : Refutation 66.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 67 ( 36 unt; 0 nHn; 67 RR)
% Number of literals : 103 ( 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 : 8 ( 8 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('LCL026-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL026-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),falsehood),u)),
file('LCL026-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
file('LCL026-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
file('LCL026-1.p',unknown),
[] ).
cnf(11,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
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,falsehood),falsehood))
| 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,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(19,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[13,11]),
[iquote('0:SoR:13.0,11.1')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)),implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w)))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),u),implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(24,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(30,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[24,2]),
[iquote('0:SoR:24.0,2.0')] ).
cnf(31,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[13,30]),
[iquote('0:SoR:13.0,30.0')] ).
cnf(35,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x))))),
inference(sor,[status(thm)],[19,4]),
[iquote('0:SoR:19.0,4.0')] ).
cnf(36,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),falsehood)),implies__dfg(u,v))),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(38,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(40,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,implies__dfg(v,implies__dfg(x,w))))),
inference(sor,[status(thm)],[19,38]),
[iquote('0:SoR:19.0,38.0')] ).
cnf(41,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[38,1]),
[iquote('0:Res:38.0,1.1')] ).
cnf(45,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
inference(sor,[status(thm)],[41,11]),
[iquote('0:SoR:41.0,11.1')] ).
cnf(52,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[41,2]),
[iquote('0:SoR:41.0,2.0')] ).
cnf(53,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,u)))),
inference(sor,[status(thm)],[13,52]),
[iquote('0:SoR:13.0,52.0')] ).
cnf(60,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),u))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v)) ),
inference(res,[status(thm),theory(equality)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(81,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)))
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(98,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,falsehood),falsehood))),implies__dfg(u,implies__dfg(v,w)))),
inference(sor,[status(thm)],[19,36]),
[iquote('0:SoR:19.0,36.0')] ).
cnf(99,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),falsehood)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[36,1]),
[iquote('0:Res:36.0,1.1')] ).
cnf(136,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
| is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x)))) ),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.1')] ).
cnf(152,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[31,1]),
[iquote('0:Res:31.0,1.1')] ).
cnf(155,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v)) ),
inference(sor,[status(thm)],[60,11]),
[iquote('0:SoR:60.0,11.1')] ).
cnf(178,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(u,w)),implies__dfg(v,w))) ),
inference(sor,[status(thm)],[81,45]),
[iquote('0:SoR:81.0,45.1')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,u),w)),implies__dfg(u,w))),
inference(sor,[status(thm)],[81,53]),
[iquote('0:SoR:81.0,53.0')] ).
cnf(289,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),u),u)),
inference(sor,[status(thm)],[99,31]),
[iquote('0:SoR:99.0,31.0')] ).
cnf(296,plain,
is_a_theorem(implies__dfg(falsehood,u)),
inference(sor,[status(thm)],[99,2]),
[iquote('0:SoR:99.0,2.0')] ).
cnf(301,plain,
is_a_theorem(implies__dfg(implies__dfg(falsehood,u),implies__dfg(falsehood,v))),
inference(sor,[status(thm)],[13,296]),
[iquote('0:SoR:13.0,296.0')] ).
cnf(305,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v))),
inference(sor,[status(thm)],[19,296]),
[iquote('0:SoR:19.0,296.0')] ).
cnf(308,plain,
is_a_theorem(implies__dfg(implies__dfg(falsehood,u),implies__dfg(v,implies__dfg(falsehood,w)))),
inference(sor,[status(thm)],[41,301]),
[iquote('0:SoR:41.0,301.0')] ).
cnf(323,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[19,289]),
[iquote('0:SoR:19.0,289.0')] ).
cnf(333,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,falsehood),falsehood)) ),
inference(sor,[status(thm)],[12,155]),
[iquote('0:SoR:12.0,155.1')] ).
cnf(334,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[155,1]),
[iquote('0:Res:155.1,1.1')] ).
cnf(337,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[41,305]),
[iquote('0:SoR:41.0,305.0')] ).
cnf(339,plain,
( ~ is_a_theorem(implies__dfg(u,falsehood))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[305,1]),
[iquote('0:Res:305.0,1.1')] ).
cnf(367,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,falsehood),v)) ),
inference(sor,[status(thm)],[339,333]),
[iquote('0:SoR:339.0,333.1')] ).
cnf(391,plain,
( ~ is_a_theorem(implies__dfg(falsehood,u))
| is_a_theorem(implies__dfg(v,implies__dfg(falsehood,w))) ),
inference(res,[status(thm),theory(equality)],[308,1]),
[iquote('0:Res:308.0,1.1')] ).
cnf(392,plain,
is_a_theorem(implies__dfg(u,implies__dfg(falsehood,v))),
inference(ssi,[status(thm)],[391,296]),
[iquote('0:SSi:391.0,296.0')] ).
cnf(395,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(falsehood,w)))),
inference(sor,[status(thm)],[41,392]),
[iquote('0:SoR:41.0,392.0')] ).
cnf(404,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[40,1]),
[iquote('0:Res:40.0,1.1')] ).
cnf(535,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,falsehood),falsehood))))
| is_a_theorem(implies__dfg(u,implies__dfg(v,w))) ),
inference(res,[status(thm),theory(equality)],[98,1]),
[iquote('0:Res:98.0,1.1')] ).
cnf(584,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(v,u),implies__dfg(v,w)))),
inference(sor,[status(thm)],[136,337]),
[iquote('0:SoR:136.0,337.0')] ).
cnf(624,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),implies__dfg(v,w)))),
inference(sor,[status(thm)],[136,395]),
[iquote('0:SoR:136.0,395.0')] ).
cnf(1009,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[323,1]),
[iquote('0:Res:323.0,1.1')] ).
cnf(1833,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[334,367]),
[iquote('0:SoR:334.1,367.1')] ).
cnf(3480,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(v,falsehood),u),v))),
inference(sor,[status(thm)],[535,584]),
[iquote('0:SoR:535.0,584.0')] ).
cnf(3951,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(v,falsehood),u),implies__dfg(w,v)))),
inference(sor,[status(thm)],[404,3480]),
[iquote('0:SoR:404.0,3480.0')] ).
cnf(10719,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),w)) ),
inference(sor,[status(thm)],[152,45]),
[iquote('0:SoR:152.0,45.1')] ).
cnf(10796,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v)),w),w)),
inference(sor,[status(thm)],[152,624]),
[iquote('0:SoR:152.0,624.0')] ).
cnf(10837,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| ~ is_a_theorem(v)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[1833,10719]),
[iquote('0:SoR:1833.1,10719.1')] ).
cnf(11222,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v)),w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[1833,10796]),
[iquote('0:SoR:1833.1,10796.0')] ).
cnf(11448,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[10837,180]),
[iquote('0:SoR:10837.0,180.0')] ).
cnf(11837,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[11448,31]),
[iquote('0:SoR:11448.0,31.0')] ).
cnf(11926,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(implies__dfg(v,w),w)))),
inference(sor,[status(thm)],[19,11837]),
[iquote('0:SoR:19.0,11837.0')] ).
cnf(15287,plain,
is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(u,v),w),w))),
inference(sor,[status(thm)],[11222,11926]),
[iquote('0:SoR:11222.0,11926.0')] ).
cnf(16692,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,falsehood),implies__dfg(u,v)),v)) ),
inference(sor,[status(thm)],[1009,178]),
[iquote('0:SoR:1009.0,178.1')] ).
cnf(16757,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,u)))
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[1833,16692]),
[iquote('0:SoR:1833.1,16692.1')] ).
cnf(51008,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,u)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[16757,3951]),
[iquote('0:SoR:16757.0,3951.0')] ).
cnf(51668,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
inference(sor,[status(thm)],[51008,15287]),
[iquote('0:SoR:51008.0,15287.0')] ).
cnf(51864,plain,
$false,
inference(unc,[status(thm)],[51668,5]),
[iquote('0:UnC:51668.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : LCL026-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.07 % Command : run_spass %d %s
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 600
% 0.07/0.25 % DateTime : Sun Jul 3 06:02:46 EDT 2022
% 0.07/0.25 % CPUTime :
% 65.20/65.39
% 65.20/65.39 SPASS V 3.9
% 65.20/65.39 SPASS beiseite: Proof found.
% 65.20/65.39 % SZS status Theorem
% 65.20/65.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.20/65.39 SPASS derived 51568 clauses, backtracked 0 clauses, performed 0 splits and kept 14401 clauses.
% 65.20/65.39 SPASS allocated 138229 KBytes.
% 65.20/65.39 SPASS spent 0:01:05.09 on the problem.
% 65.20/65.39 0:00:00.02 for the input.
% 65.20/65.39 0:00:00.00 for the FLOTTER CNF translation.
% 65.20/65.39 0:00:01.01 for inferences.
% 65.20/65.39 0:00:00.00 for the backtracking.
% 65.20/65.39 0:01:03.81 for the reduction.
% 65.20/65.39
% 65.20/65.39
% 65.20/65.39 Here is a proof with depth 15, length 67 :
% 65.20/65.39 % SZS output start Refutation
% See solution above
% 66.42/66.61 Formulae used in the proof : condensed_detachment c0_2 c0_5 c0_6 prove_c0_3
% 66.42/66.61
%------------------------------------------------------------------------------