TSTP Solution File: LCL006-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:34:01 EDT 2022
% Result : Unsatisfiable 11.09s 11.35s
% Output : Refutation 11.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 29 RR)
% Number of literals : 41 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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('LCL006-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
file('LCL006-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(u,equivalent(v,w)))),
file('LCL006-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('LCL006-1.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(u,v),w))),
inference(sor,[status(thm)],[9,3]),
[iquote('0:SoR:9.0,3.0')] ).
cnf(12,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(u,equivalent(v,w))) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(14,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(equivalent(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(15,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(w,equivalent(u,equivalent(v,w))))),
inference(sor,[status(thm)],[12,3]),
[iquote('0:SoR:12.0,3.0')] ).
cnf(17,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(v,u)))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(v,u))) ),
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,equivalent(w,u))),equivalent(v,w))),
inference(sor,[status(thm)],[9,15]),
[iquote('0:SoR:9.0,15.0')] ).
cnf(26,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(w,equivalent(u,equivalent(v,w)))) ),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.0,1.1')] ).
cnf(34,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,u),v)) ),
inference(sor,[status(thm)],[9,20]),
[iquote('0:SoR:9.0,20.1')] ).
cnf(94,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,u)),equivalent(v,w)))),
inference(sor,[status(thm)],[12,25]),
[iquote('0:SoR:12.0,25.0')] ).
cnf(96,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,equivalent(w,u))))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[25,1]),
[iquote('0:Res:25.0,1.1')] ).
cnf(100,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,u))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[34,1]),
[iquote('0:Res:34.1,1.1')] ).
cnf(233,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),u)))),
inference(sor,[status(thm)],[26,2]),
[iquote('0:SoR:26.0,2.0')] ).
cnf(378,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(equivalent(w,equivalent(x,equivalent(u,v))),equivalent(w,x))))),
inference(sor,[status(thm)],[12,94]),
[iquote('0:SoR:12.0,94.0')] ).
cnf(594,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(w,v),u))),
inference(sor,[status(thm)],[14,233]),
[iquote('0:SoR:14.0,233.0')] ).
cnf(1442,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(w,equivalent(v,u))) ),
inference(sor,[status(thm)],[100,594]),
[iquote('0:SoR:100.1,594.0')] ).
cnf(3214,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(w,equivalent(equivalent(v,w),u))))),
inference(sor,[status(thm)],[96,378]),
[iquote('0:SoR:96.0,378.0')] ).
cnf(5007,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,equivalent(equivalent(u,v),w))),w)),
inference(sor,[status(thm)],[9,3214]),
[iquote('0:SoR:9.0,3214.0')] ).
cnf(6216,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(equivalent(u,v),w)),w))),
inference(sor,[status(thm)],[12,5007]),
[iquote('0:SoR:12.0,5007.0')] ).
cnf(6897,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,u),equivalent(w,v))),w)),
inference(sor,[status(thm)],[96,6216]),
[iquote('0:SoR:96.0,6216.0')] ).
cnf(7395,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(equivalent(w,v),equivalent(u,w))))),
inference(sor,[status(thm)],[9,6897]),
[iquote('0:SoR:9.0,6897.0')] ).
cnf(7992,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(u,w)))),
inference(sor,[status(thm)],[14,7395]),
[iquote('0:SoR:14.0,7395.0')] ).
cnf(11614,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,u)),equivalent(v,w))),
inference(sor,[status(thm)],[1442,7992]),
[iquote('0:SoR:1442.0,7992.0')] ).
cnf(11655,plain,
$false,
inference(unc,[status(thm)],[11614,4]),
[iquote('0:UnC:11614.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 22:16:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 11.09/11.35
% 11.09/11.35 SPASS V 3.9
% 11.09/11.35 SPASS beiseite: Proof found.
% 11.09/11.35 % SZS status Theorem
% 11.09/11.35 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.09/11.35 SPASS derived 11641 clauses, backtracked 0 clauses, performed 0 splits and kept 5604 clauses.
% 11.09/11.35 SPASS allocated 88927 KBytes.
% 11.09/11.35 SPASS spent 0:0:10.84 on the problem.
% 11.09/11.35 0:00:00.03 for the input.
% 11.09/11.35 0:00:00.00 for the FLOTTER CNF translation.
% 11.09/11.35 0:00:00.42 for inferences.
% 11.09/11.35 0:00:00.00 for the backtracking.
% 11.09/11.35 0:0:10.29 for the reduction.
% 11.09/11.35
% 11.09/11.35
% 11.09/11.35 Here is a proof with depth 12, length 29 :
% 11.09/11.35 % SZS output start Refutation
% See solution above
% 11.09/11.35 Formulae used in the proof : condensed_detachment ec_4 ec_5 prove_ec_1
% 11.09/11.35
%------------------------------------------------------------------------------