TSTP Solution File: LCL022-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% 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 14:34:05 EDT 2022
% Result : Unsatisfiable 0.17s 0.44s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 19 ( 13 unt; 0 nHn; 19 RR)
% Number of literals : 26 ( 0 equ; 8 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('LCL022-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(u,w)))),
file('LCL022-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('LCL022-1.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(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(39,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,w),equivalent(equivalent(x,v),equivalent(w,x)))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(141,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(v,w)))),
inference(sor,[status(thm)],[39,28]),
[iquote('0:SoR:39.0,28.0')] ).
cnf(203,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,u)),equivalent(v,w))),
inference(sor,[status(thm)],[36,141]),
[iquote('0:SoR:36.0,141.0')] ).
cnf(208,plain,
$false,
inference(unc,[status(thm)],[203,3]),
[iquote('0:UnC:203.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 4 15:40:09 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.44
% 0.17/0.44 SPASS V 3.9
% 0.17/0.44 SPASS beiseite: Proof found.
% 0.17/0.44 % SZS status Theorem
% 0.17/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 SPASS derived 201 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.17/0.44 SPASS allocated 76093 KBytes.
% 0.17/0.44 SPASS spent 0:00:00.11 on the problem.
% 0.17/0.44 0:00:00.04 for the input.
% 0.17/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.44 0:00:00.01 for inferences.
% 0.17/0.44 0:00:00.00 for the backtracking.
% 0.17/0.44 0:00:00.04 for the reduction.
% 0.17/0.44
% 0.17/0.44
% 0.17/0.44 Here is a proof with depth 12, length 19 :
% 0.17/0.44 % SZS output start Refutation
% See solution above
% 0.17/0.44 Formulae used in the proof : condensed_detachment yql prove_ec_1
% 0.17/0.44
%------------------------------------------------------------------------------