TSTP Solution File: LCL009-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:34:02 EDT 2022
% Result : Unsatisfiable 0.56s 0.76s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 29 ( 21 unt; 0 nHn; 29 RR)
% Number of literals : 38 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL009-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(u,w)))),
file('LCL009-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('LCL009-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,v),equivalent(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(x,v))),equivalent(equivalent(x,w),u))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(x,v))))
| is_a_theorem(equivalent(equivalent(x,w),u)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(equivalent(x,v),equivalent(w,x))))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,v))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(13,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(v,w),u))),
inference(sor,[status(thm)],[7,12]),
[iquote('0:SoR:7.0,12.0')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(w,v)))),
inference(sor,[status(thm)],[10,13]),
[iquote('0:SoR:10.0,13.0')] ).
cnf(20,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(v,v))),
inference(sor,[status(thm)],[10,17]),
[iquote('0:SoR:10.0,17.0')] ).
cnf(21,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,w),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(25,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,v)),equivalent(equivalent(w,w),u))),
inference(sor,[status(thm)],[7,20]),
[iquote('0:SoR:7.0,20.0')] ).
cnf(27,plain,
( ~ is_a_theorem(equivalent(u,u))
| is_a_theorem(equivalent(v,v)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(28,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[27,20]),
[iquote('0:SoR:27.0,20.0')] ).
cnf(31,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
inference(sor,[status(thm)],[7,28]),
[iquote('0:SoR:7.0,28.0')] ).
cnf(36,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[31,1]),
[iquote('0:Res:31.0,1.1')] ).
cnf(38,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(w,u),v))),
inference(sor,[status(thm)],[10,11]),
[iquote('0:SoR:10.0,11.0')] ).
cnf(51,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,v)))
| is_a_theorem(equivalent(equivalent(w,w),u)) ),
inference(res,[status(thm),theory(equality)],[25,1]),
[iquote('0:Res:25.0,1.1')] ).
cnf(56,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(v,w),u))),
inference(sor,[status(thm)],[36,38]),
[iquote('0:SoR:36.0,38.0')] ).
cnf(108,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(equivalent(u,w),w),v))),
inference(sor,[status(thm)],[10,56]),
[iquote('0:SoR:10.0,56.0')] ).
cnf(167,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),v),w),equivalent(u,w))),
inference(sor,[status(thm)],[36,108]),
[iquote('0:SoR:36.0,108.0')] ).
cnf(268,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(equivalent(equivalent(v,w),w),v))),
inference(sor,[status(thm)],[51,167]),
[iquote('0:SoR:51.0,167.0')] ).
cnf(305,plain,
( ~ is_a_theorem(equivalent(u,u))
| is_a_theorem(equivalent(equivalent(equivalent(v,w),w),v)) ),
inference(res,[status(thm),theory(equality)],[268,1]),
[iquote('0:Res:268.0,1.1')] ).
cnf(306,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),v),u)),
inference(ssi,[status(thm)],[305,28]),
[iquote('0:SSi:305.0,28.0')] ).
cnf(317,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(u,v),v))),
inference(sor,[status(thm)],[36,306]),
[iquote('0:SoR:36.0,306.0')] ).
cnf(323,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,equivalent(equivalent(u,w),w)))),
inference(sor,[status(thm)],[21,317]),
[iquote('0:SoR:21.0,317.0')] ).
cnf(1200,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(u,equivalent(v,w)))),
inference(sor,[status(thm)],[10,323]),
[iquote('0:SoR:10.0,323.0')] ).
cnf(1208,plain,
$false,
inference(unc,[status(thm)],[1200,3]),
[iquote('0:UnC:1200.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.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
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 13:00:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.56/0.76
% 0.56/0.76 SPASS V 3.9
% 0.56/0.76 SPASS beiseite: Proof found.
% 0.56/0.76 % SZS status Theorem
% 0.56/0.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.76 SPASS derived 1197 clauses, backtracked 0 clauses, performed 0 splits and kept 669 clauses.
% 0.56/0.76 SPASS allocated 77632 KBytes.
% 0.56/0.76 SPASS spent 0:00:00.40 on the problem.
% 0.56/0.76 0:00:00.04 for the input.
% 0.56/0.76 0:00:00.00 for the FLOTTER CNF translation.
% 0.56/0.76 0:00:00.03 for inferences.
% 0.56/0.76 0:00:00.00 for the backtracking.
% 0.56/0.76 0:00:00.31 for the reduction.
% 0.56/0.76
% 0.56/0.76
% 0.56/0.76 Here is a proof with depth 19, length 29 :
% 0.56/0.76 % SZS output start Refutation
% See solution above
% 0.56/0.76 Formulae used in the proof : condensed_detachment yql prove_ec_5
% 0.56/0.76
%------------------------------------------------------------------------------