TSTP Solution File: LCL401-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL401-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 14:36:41 EDT 2022
% Result : Unsatisfiable 9.89s 10.06s
% Output : Refutation 10.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of clauses : 72 ( 48 unt; 0 nHn; 72 RR)
% Number of literals : 99 ( 0 equ; 28 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 : 8 ( 8 usr; 6 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('LCL401-1.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('LCL401-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL401-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL401-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(not__dfg(implies__dfg(x__dfg,y__dfg)),not__dfg(y__dfg))),
file('LCL401-1.p',unknown),
[] ).
cnf(13,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(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
cnf(19,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)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),u),v))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w))),
inference(sor,[status(thm)],[13,18]),
[iquote('0:SoR:13.0,18.0')] ).
cnf(22,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(23,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)],[13,20]),
[iquote('0:SoR:13.0,20.0')] ).
cnf(24,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)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
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)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(53,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[24,4]),
[iquote('0:SoR:24.0,4.0')] ).
cnf(58,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)],[24,3]),
[iquote('0:SoR:24.0,3.0')] ).
cnf(76,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w)) ),
inference(res,[status(thm),theory(equality)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(88,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)],[23,1]),
[iquote('0:Res:23.0,1.1')] ).
cnf(113,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(114,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)],[33,23]),
[iquote('0:SoR:33.0,23.0')] ).
cnf(119,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[22,113]),
[iquote('0:SoR:22.0,113.0')] ).
cnf(122,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)],[113,1]),
[iquote('0:Res:113.0,1.1')] ).
cnf(126,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)],[13,119]),
[iquote('0:SoR:13.0,119.0')] ).
cnf(164,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)],[126,1]),
[iquote('0:Res:126.0,1.1')] ).
cnf(199,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)],[114,1]),
[iquote('0:Res:114.0,1.1')] ).
cnf(237,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[164,114]),
[iquote('0:SoR:164.0,114.0')] ).
cnf(253,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[237,1]),
[iquote('0:Res:237.0,1.1')] ).
cnf(269,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)],[253,1]),
[iquote('0:Res:253.1,1.1')] ).
cnf(315,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)],[269,18]),
[iquote('0:SoR:269.1,18.0')] ).
cnf(371,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[76,53]),
[iquote('0:SoR:76.0,53.0')] ).
cnf(385,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),v),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[76,58]),
[iquote('0:SoR:76.0,58.0')] ).
cnf(387,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),u)),
inference(sor,[status(thm)],[76,3]),
[iquote('0:SoR:76.0,3.0')] ).
cnf(399,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u),u)),
inference(sor,[status(thm)],[76,387]),
[iquote('0:SoR:76.0,387.0')] ).
cnf(492,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[371,1]),
[iquote('0:Res:371.0,1.1')] ).
cnf(501,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[399,1]),
[iquote('0:Res:399.0,1.1')] ).
cnf(1296,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[315,58]),
[iquote('0:SoR:315.0,58.0')] ).
cnf(1298,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[315,3]),
[iquote('0:SoR:315.0,3.0')] ).
cnf(1313,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1298]),
[iquote('0:SoR:13.0,1298.0')] ).
cnf(1371,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[492,1296]),
[iquote('0:SoR:492.0,1296.0')] ).
cnf(1382,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1296]),
[iquote('0:SoR:13.0,1296.0')] ).
cnf(1473,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(2093,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(not__dfg(implies__dfg(not__dfg(u),u)))),u)),
inference(sor,[status(thm)],[33,385]),
[iquote('0:SoR:33.0,385.0')] ).
cnf(2301,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(w,implies__dfg(u,v)))),
inference(sor,[status(thm)],[33,1382]),
[iquote('0:SoR:33.0,1382.0')] ).
cnf(2507,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[199,1313]),
[iquote('0:SoR:199.0,1313.0')] ).
cnf(2508,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)],[199,253]),
[iquote('0:SoR:199.0,253.1')] ).
cnf(2544,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1473,2507]),
[iquote('0:SoR:1473.0,2507.0')] ).
cnf(2553,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[501,2544]),
[iquote('0:SoR:501.0,2544.0')] ).
cnf(2590,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2553,1]),
[iquote('0:Res:2553.0,1.1')] ).
cnf(3587,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[164,2301]),
[iquote('0:SoR:164.0,2301.0')] ).
cnf(3632,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[199,3587]),
[iquote('0:SoR:199.0,3587.0')] ).
cnf(3656,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[3632,1]),
[iquote('0:Res:3632.0,1.1')] ).
cnf(4153,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),u)),
inference(sor,[status(thm)],[3656,2093]),
[iquote('0:SoR:3656.0,2093.0')] ).
cnf(4167,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)))),v))),
inference(sor,[status(thm)],[122,4153]),
[iquote('0:SoR:122.0,4153.0')] ).
cnf(5702,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2590,2508]),
[iquote('0:SoR:2590.0,2508.1')] ).
cnf(5727,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[88,5702]),
[iquote('0:SoR:88.0,5702.1')] ).
cnf(5748,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[5702,1]),
[iquote('0:Res:5702.1,1.1')] ).
cnf(6184,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[5727,1371]),
[iquote('0:SoR:5727.0,1371.0')] ).
cnf(6373,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[33,6184]),
[iquote('0:SoR:33.0,6184.0')] ).
cnf(7038,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[5748,6373]),
[iquote('0:SoR:5748.1,6373.0')] ).
cnf(8439,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u))))),
inference(sor,[status(thm)],[7038,4167]),
[iquote('0:SoR:7038.0,4167.0')] ).
cnf(8560,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)),implies__dfg(u,v))),
inference(sor,[status(thm)],[122,8439]),
[iquote('0:SoR:122.0,8439.0')] ).
cnf(8678,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[22,8560]),
[iquote('0:SoR:22.0,8560.0')] ).
cnf(8696,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[7038,8678]),
[iquote('0:SoR:7038.0,8678.0')] ).
cnf(8697,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(not__dfg(u)),v))),
inference(sor,[status(thm)],[199,8678]),
[iquote('0:SoR:199.0,8678.0')] ).
cnf(8742,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(not__dfg(u))),v))),
inference(sor,[status(thm)],[122,8696]),
[iquote('0:SoR:122.0,8696.0')] ).
cnf(8777,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[7038,8742]),
[iquote('0:SoR:7038.0,8742.0')] ).
cnf(8797,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(implies__dfg(v,u))))),
inference(sor,[status(thm)],[3656,8777]),
[iquote('0:SoR:3656.0,8777.0')] ).
cnf(9717,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),v)) ),
inference(sor,[status(thm)],[5748,8697]),
[iquote('0:SoR:5748.1,8697.0')] ).
cnf(13750,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),not__dfg(not__dfg(implies__dfg(v,u))))),
inference(sor,[status(thm)],[9717,8797]),
[iquote('0:SoR:9717.0,8797.0')] ).
cnf(14213,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(not__dfg(not__dfg(v)),w))),
inference(sor,[status(thm)],[122,13750]),
[iquote('0:SoR:122.0,13750.0')] ).
cnf(18898,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(u,v)),not__dfg(v))),
inference(sor,[status(thm)],[7038,14213]),
[iquote('0:SoR:7038.0,14213.0')] ).
cnf(18926,plain,
$false,
inference(unc,[status(thm)],[18898,5]),
[iquote('0:UnC:18898.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL401-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 4 12:31:39 EDT 2022
% 0.11/0.33 % CPUTime :
% 9.89/10.06
% 9.89/10.06 SPASS V 3.9
% 9.89/10.06 SPASS beiseite: Proof found.
% 9.89/10.06 % SZS status Theorem
% 9.89/10.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.89/10.06 SPASS derived 18837 clauses, backtracked 0 clauses, performed 0 splits and kept 7563 clauses.
% 9.89/10.06 SPASS allocated 100465 KBytes.
% 9.89/10.06 SPASS spent 0:00:09.71 on the problem.
% 9.89/10.06 0:00:00.04 for the input.
% 9.89/10.06 0:00:00.00 for the FLOTTER CNF translation.
% 9.89/10.06 0:00:00.35 for inferences.
% 9.89/10.06 0:00:00.00 for the backtracking.
% 9.89/10.06 0:00:09.24 for the reduction.
% 9.89/10.06
% 9.89/10.06
% 9.89/10.06 Here is a proof with depth 32, length 72 :
% 9.89/10.06 % SZS output start Refutation
% See solution above
% 10.10/10.27 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_67
% 10.10/10.27
%------------------------------------------------------------------------------