TSTP Solution File: LCL076-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL076-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 14:34:25 EDT 2022
% Result : Unsatisfiable 0.45s 0.67s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 12 unt; 0 nHn; 19 RR)
% Number of literals : 28 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL076-3.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL076-3.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
file('LCL076-3.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL076-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ is_a_theorem(implies__dfg(u,v))
| ~ is_a_theorem(implies__dfg(w,u))
| is_a_theorem(implies__dfg(w,v)) ),
file('LCL076-3.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(a,not__dfg(not__dfg(a)))),
file('LCL076-3.p',unknown),
[] ).
cnf(15,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(17,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),not__dfg(w))))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.0,5.0')] ).
cnf(24,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(40,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(45,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,u))),
inference(res,[status(thm),theory(equality)],[40,17]),
[iquote('0:Res:40.0,17.0')] ).
cnf(65,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),implies__dfg(not__dfg(not__dfg(u)),u))),
inference(sor,[status(thm)],[24,45]),
[iquote('0:SoR:24.0,45.0')] ).
cnf(67,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[24,2]),
[iquote('0:SoR:24.0,2.0')] ).
cnf(72,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[67,1]),
[iquote('0:Res:67.0,1.1')] ).
cnf(90,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[72,2]),
[iquote('0:SoR:72.0,2.0')] ).
cnf(687,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),v))
| is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)) ),
inference(res,[status(thm),theory(equality)],[65,1]),
[iquote('0:Res:65.0,1.1')] ).
cnf(1157,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[687,90]),
[iquote('0:SoR:687.0,90.0')] ).
cnf(1209,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[15,1157]),
[iquote('0:SoR:15.0,1157.0')] ).
cnf(1229,plain,
$false,
inference(unc,[status(thm)],[1209,6]),
[iquote('0:UnC:1209.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL076-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 02:07:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.67
% 0.45/0.67 SPASS V 3.9
% 0.45/0.67 SPASS beiseite: Proof found.
% 0.45/0.67 % SZS status Theorem
% 0.45/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.67 SPASS derived 1200 clauses, backtracked 0 clauses, performed 0 splits and kept 695 clauses.
% 0.45/0.67 SPASS allocated 77065 KBytes.
% 0.45/0.67 SPASS spent 0:00:00.31 on the problem.
% 0.45/0.67 0:00:00.04 for the input.
% 0.45/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.67 0:00:00.02 for inferences.
% 0.45/0.67 0:00:00.00 for the backtracking.
% 0.45/0.67 0:00:00.23 for the reduction.
% 0.45/0.67
% 0.45/0.67
% 0.45/0.67 Here is a proof with depth 7, length 19 :
% 0.45/0.67 % SZS output start Refutation
% See solution above
% 0.45/0.67 Formulae used in the proof : condensed_detachment cn_18 cn_35 cn_49 transitivity prove_cn_40
% 0.45/0.67
%------------------------------------------------------------------------------