TSTP Solution File: LCL380-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL380-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:36:34 EDT 2022
% Result : Unsatisfiable 3.18s 3.39s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of clauses : 61 ( 38 unt; 0 nHn; 61 RR)
% Number of literals : 87 ( 0 equ; 27 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('LCL380-1.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('LCL380-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL380-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL380-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(x__dfg,y__dfg),implies__dfg(not__dfg(not__dfg(x__dfg)),y__dfg))),
file('LCL380-1.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(20,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)],[15,18]),
[iquote('0:SoR:15.0,18.0')] ).
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(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(77,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)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
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(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(123,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)],[108,1]),
[iquote('0:Res:108.0,1.1')] ).
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(231,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)],[231,1]),
[iquote('0:Res:231.0,1.1')] ).
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(312,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(339,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)],[77,59]),
[iquote('0:SoR:77.0,59.0')] ).
cnf(1257,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[312,59]),
[iquote('0:SoR:312.0,59.0')] ).
cnf(1301,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[312,3]),
[iquote('0:SoR:312.0,3.0')] ).
cnf(1311,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[15,1301]),
[iquote('0:SoR:15.0,1301.0')] ).
cnf(1373,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[63,1257]),
[iquote('0:SoR:63.0,1257.0')] ).
cnf(1378,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)],[15,1257]),
[iquote('0:SoR:15.0,1257.0')] ).
cnf(1486,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1311,1]),
[iquote('0:Res:1311.0,1.1')] ).
cnf(2175,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)],[33,339]),
[iquote('0:SoR:33.0,339.0')] ).
cnf(2221,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)],[33,1378]),
[iquote('0:SoR:33.0,1378.0')] ).
cnf(2273,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[170,1311]),
[iquote('0:SoR:170.0,1311.0')] ).
cnf(2279,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(2331,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1486,2273]),
[iquote('0:SoR:1486.0,2273.0')] ).
cnf(2338,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[11,2331]),
[iquote('0:SoR:11.0,2331.0')] ).
cnf(2368,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2338,1]),
[iquote('0:Res:2338.0,1.1')] ).
cnf(3666,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[165,2221]),
[iquote('0:SoR:165.0,2221.0')] ).
cnf(3675,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[170,3666]),
[iquote('0:SoR:170.0,3666.0')] ).
cnf(3728,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[3675,1]),
[iquote('0:Res:3675.0,1.1')] ).
cnf(4125,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),u)),
inference(sor,[status(thm)],[3728,2175]),
[iquote('0:SoR:3728.0,2175.0')] ).
cnf(4244,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)],[123,4125]),
[iquote('0:SoR:123.0,4125.0')] ).
cnf(5556,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2368,2279]),
[iquote('0:SoR:2368.0,2279.1')] ).
cnf(5583,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[89,5556]),
[iquote('0:SoR:89.0,5556.1')] ).
cnf(5591,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[5556,1]),
[iquote('0:Res:5556.1,1.1')] ).
cnf(6225,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[5583,1373]),
[iquote('0:SoR:5583.0,1373.0')] ).
cnf(6431,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[33,6225]),
[iquote('0:SoR:33.0,6225.0')] ).
cnf(7096,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[5591,6431]),
[iquote('0:SoR:5591.1,6431.0')] ).
cnf(8566,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u))))),
inference(sor,[status(thm)],[7096,4244]),
[iquote('0:SoR:7096.0,4244.0')] ).
cnf(8591,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)),implies__dfg(u,v))),
inference(sor,[status(thm)],[123,8566]),
[iquote('0:SoR:123.0,8566.0')] ).
cnf(8762,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[21,8591]),
[iquote('0:SoR:21.0,8591.0')] ).
cnf(8768,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(not__dfg(u)),v))),
inference(sor,[status(thm)],[170,8762]),
[iquote('0:SoR:170.0,8762.0')] ).
cnf(8781,plain,
$false,
inference(unc,[status(thm)],[8768,5]),
[iquote('0:UnC:8768.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL380-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 02:12:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.18/3.39
% 3.18/3.39 SPASS V 3.9
% 3.18/3.39 SPASS beiseite: Proof found.
% 3.18/3.39 % SZS status Theorem
% 3.18/3.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.18/3.39 SPASS derived 8713 clauses, backtracked 0 clauses, performed 0 splits and kept 3266 clauses.
% 3.18/3.39 SPASS allocated 87110 KBytes.
% 3.18/3.39 SPASS spent 0:00:02.96 on the problem.
% 3.18/3.39 0:00:00.03 for the input.
% 3.18/3.39 0:00:00.00 for the FLOTTER CNF translation.
% 3.18/3.39 0:00:00.18 for inferences.
% 3.18/3.39 0:00:00.00 for the backtracking.
% 3.18/3.39 0:00:02.70 for the reduction.
% 3.18/3.39
% 3.18/3.39
% 3.18/3.39 Here is a proof with depth 26, length 61 :
% 3.18/3.39 % SZS output start Refutation
% See solution above
% 3.18/3.39 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_41
% 3.18/3.39
%------------------------------------------------------------------------------