TSTP Solution File: LCL101-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL101-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:34:36 EDT 2022
% Result : Unsatisfiable 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 12 unt; 0 nHn; 18 RR)
% Number of literals : 25 ( 0 equ; 8 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 : 11 ( 11 usr; 10 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('LCL101-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),
file('LCL101-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),u))),
file('LCL101-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('LCL101-1.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x))
| is_a_theorem(x) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),u)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),equivalent(equivalent(equivalent(x,y),equivalent(x,z)),equivalent(y,z)))),
inference(sor,[status(thm)],[9,3]),
[iquote('0:SoR:9.0,3.0')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w))),
inference(sor,[status(thm)],[9,11]),
[iquote('0:SoR:9.0,11.0')] ).
cnf(16,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.0,1.1')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,v))),
inference(sor,[status(thm)],[16,11]),
[iquote('0:SoR:16.0,11.0')] ).
cnf(18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x))
| is_a_theorem(equivalent(equivalent(v,w),x)) ),
inference(sor,[status(thm)],[16,10]),
[iquote('0:SoR:16.0,10.1')] ).
cnf(22,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[16,17]),
[iquote('0:SoR:16.0,17.0')] ).
cnf(29,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v)))),
inference(sor,[status(thm)],[18,22]),
[iquote('0:SoR:18.0,22.0')] ).
cnf(30,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(equivalent(equivalent(w,x),equivalent(w,y)),equivalent(x,y)),equivalent(equivalent(z,u),equivalent(z,v))))),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(31,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x)))),
inference(sor,[status(thm)],[9,29]),
[iquote('0:SoR:9.0,29.0')] ).
cnf(49,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))))
| is_a_theorem(equivalent(u,equivalent(w,x))) ),
inference(res,[status(thm),theory(equality)],[31,1]),
[iquote('0:Res:31.0,1.1')] ).
cnf(109,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[49,30]),
[iquote('0:SoR:49.0,30.0')] ).
cnf(117,plain,
$false,
inference(unc,[status(thm)],[109,4]),
[iquote('0:UnC:109.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL101-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 2 23:42:45 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.44
% 0.22/0.44 SPASS V 3.9
% 0.22/0.44 SPASS beiseite: Proof found.
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.44 SPASS derived 108 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses.
% 0.22/0.44 SPASS allocated 75916 KBytes.
% 0.22/0.44 SPASS spent 0:00:00.07 on the problem.
% 0.22/0.44 0:00:00.03 for the input.
% 0.22/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.44 0:00:00.01 for inferences.
% 0.22/0.44 0:00:00.00 for the backtracking.
% 0.22/0.44 0:00:00.01 for the reduction.
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 Here is a proof with depth 10, length 18 :
% 0.22/0.44 % SZS output start Refutation
% See solution above
% 0.22/0.44 Formulae used in the proof : condensed_detachment lg_2 p_4 prove_p_1
% 0.22/0.44
%------------------------------------------------------------------------------