TSTP Solution File: LCL118-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL118-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:34:46 EDT 2022
% Result : Unsatisfiable 1.08s 1.24s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of clauses : 41 ( 22 unt; 0 nHn; 41 RR)
% Number of literals : 63 ( 0 equ; 23 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(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL118-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(w,equivalent(v,u)))),
file('LCL118-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
file('LCL118-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(w,equivalent(v,u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(w,equivalent(v,equivalent(u,w))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(w,equivalent(v,equivalent(u,w)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,equivalent(x,v))),equivalent(equivalent(x,w),u)))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(12,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(equivalent(x,equivalent(w,v)),u)))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,equivalent(v,equivalent(u,x))),w))),
inference(sor,[status(thm)],[7,11]),
[iquote('0:SoR:7.0,11.0')] ).
cnf(15,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(w,equivalent(x,v))),equivalent(equivalent(x,w),u))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),x),equivalent(equivalent(w,equivalent(v,u)),x))),
inference(sor,[status(thm)],[7,12]),
[iquote('0:SoR:7.0,12.0')] ).
cnf(21,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(equivalent(x,equivalent(v,equivalent(u,x))),w)) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.0,1.1')] ).
cnf(24,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),x))
| is_a_theorem(equivalent(equivalent(w,equivalent(v,u)),x)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(27,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,equivalent(w,equivalent(x,v))))
| is_a_theorem(equivalent(equivalent(x,w),u)) ),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.1,1.1')] ).
cnf(38,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(x,u))),equivalent(w,equivalent(v,x)))),
inference(sor,[status(thm)],[21,2]),
[iquote('0:SoR:21.0,2.0')] ).
cnf(48,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(w,equivalent(x,equivalent(equivalent(u,w),equivalent(v,x)))))),
inference(sor,[status(thm)],[7,38]),
[iquote('0:SoR:7.0,38.0')] ).
cnf(71,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(v,w)))),
inference(sor,[status(thm)],[24,2]),
[iquote('0:SoR:24.0,2.0')] ).
cnf(78,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(w,equivalent(w,equivalent(u,v))))),
inference(sor,[status(thm)],[7,71]),
[iquote('0:SoR:7.0,71.0')] ).
cnf(85,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(x,equivalent(x,equivalent(w,equivalent(v,u)))))),
inference(sor,[status(thm)],[24,78]),
[iquote('0:SoR:24.0,78.0')] ).
cnf(86,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(w,equivalent(w,equivalent(u,v)))) ),
inference(res,[status(thm),theory(equality)],[78,1]),
[iquote('0:Res:78.0,1.1')] ).
cnf(171,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,v),u)) ),
inference(sor,[status(thm)],[27,85]),
[iquote('0:SoR:27.1,85.0')] ).
cnf(188,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(v,equivalent(equivalent(w,w),u)))) ),
inference(sor,[status(thm)],[86,171]),
[iquote('0:SoR:86.0,171.1')] ).
cnf(191,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,equivalent(u,equivalent(w,w)))) ),
inference(sor,[status(thm)],[7,171]),
[iquote('0:SoR:7.0,171.1')] ).
cnf(205,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(v,v),u),equivalent(w,w))) ),
inference(sor,[status(thm)],[7,188]),
[iquote('0:SoR:7.0,188.1')] ).
cnf(304,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,v),u))
| is_a_theorem(equivalent(w,w)) ),
inference(res,[status(thm),theory(equality)],[205,1]),
[iquote('0:Res:205.1,1.1')] ).
cnf(305,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,v)) ),
inference(ssi,[status(thm)],[304,171]),
[iquote('0:SSi:304.1,171.1')] ).
cnf(320,plain,
is_a_theorem(equivalent(u,u)),
inference(ems,[status(thm)],[305,85]),
[iquote('0:EmS:305.0,85.0')] ).
cnf(352,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(v,u)))),
inference(sor,[status(thm)],[10,320]),
[iquote('0:SoR:10.0,320.0')] ).
cnf(355,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,equivalent(w,u))),equivalent(w,v))),
inference(sor,[status(thm)],[21,320]),
[iquote('0:SoR:21.0,320.0')] ).
cnf(367,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(u,v)),equivalent(v,equivalent(w,w)))),
inference(sor,[status(thm)],[191,352]),
[iquote('0:SoR:191.0,352.0')] ).
cnf(430,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(u,w))),
inference(sor,[status(thm)],[24,355]),
[iquote('0:SoR:24.0,355.0')] ).
cnf(431,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,equivalent(w,u))))
| is_a_theorem(equivalent(w,v)) ),
inference(res,[status(thm),theory(equality)],[355,1]),
[iquote('0:Res:355.0,1.1')] ).
cnf(532,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(equivalent(u,w)) ),
inference(res,[status(thm),theory(equality)],[430,1]),
[iquote('0:Res:430.0,1.1')] ).
cnf(699,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(u,v)),v)),
inference(sor,[status(thm)],[431,367]),
[iquote('0:SoR:431.0,367.0')] ).
cnf(749,plain,
( ~ is_a_theorem(equivalent(u,equivalent(u,v)))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[699,1]),
[iquote('0:Res:699.0,1.1')] ).
cnf(768,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[749,171]),
[iquote('0:SoR:749.0,171.1')] ).
cnf(952,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(equivalent(w,u),equivalent(w,v))))),
inference(sor,[status(thm)],[768,48]),
[iquote('0:SoR:768.0,48.0')] ).
cnf(1360,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(w,v))),
inference(sor,[status(thm)],[7,952]),
[iquote('0:SoR:7.0,952.0')] ).
cnf(2062,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(sor,[status(thm)],[532,171]),
[iquote('0:SoR:532.0,171.1')] ).
cnf(2162,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(w,u)))),
inference(sor,[status(thm)],[2062,1360]),
[iquote('0:SoR:2062.0,1360.0')] ).
cnf(2258,plain,
$false,
inference(unc,[status(thm)],[2162,3]),
[iquote('0:UnC:2162.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL118-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 3 06:00:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 1.08/1.24
% 1.08/1.24 SPASS V 3.9
% 1.08/1.24 SPASS beiseite: Proof found.
% 1.08/1.24 % SZS status Theorem
% 1.08/1.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/1.24 SPASS derived 2229 clauses, backtracked 0 clauses, performed 0 splits and kept 1159 clauses.
% 1.08/1.24 SPASS allocated 79133 KBytes.
% 1.08/1.24 SPASS spent 0:00:00.85 on the problem.
% 1.08/1.24 0:00:00.03 for the input.
% 1.08/1.24 0:00:00.00 for the FLOTTER CNF translation.
% 1.08/1.24 0:00:00.06 for inferences.
% 1.08/1.24 0:00:00.00 for the backtracking.
% 1.08/1.24 0:00:00.73 for the reduction.
% 1.08/1.24
% 1.08/1.24
% 1.08/1.24 Here is a proof with depth 22, length 41 :
% 1.08/1.24 % SZS output start Refutation
% See solution above
% 1.08/1.24 Formulae used in the proof : condensed_detachment wo prove_yqm
% 1.08/1.24
%------------------------------------------------------------------------------