TSTP Solution File: LCL320-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL320-3 : TPTP v8.1.0. Released v2.3.0.
% 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 14:36:16 EDT 2022
% Result : Unsatisfiable 1.67s 1.88s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 42 ( 27 unt; 0 nHn; 42 RR)
% Number of literals : 59 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(implies__dfg(p,q),implies__dfg(not__dfg(p),q))),
file('LCL320-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL320-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL320-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL320-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL320-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL320-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL320-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL320-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL320-3.p',unknown),
[] ).
cnf(15,plain,
axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(16,plain,
axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(20,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(21,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,16]),
[iquote('0:SoR:20.0,16.0')] ).
cnf(24,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[20,15]),
[iquote('0:SoR:20.0,15.0')] ).
cnf(27,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[20,3]),
[iquote('0:SoR:20.0,3.0')] ).
cnf(28,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.0,2.0')] ).
cnf(29,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[20,5]),
[iquote('0:SoR:20.0,5.0')] ).
cnf(30,plain,
axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(31,plain,
axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(34,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,30]),
[iquote('0:Rew:7.0,30.0')] ).
cnf(35,plain,
axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,31]),
[iquote('0:Rew:7.0,31.0')] ).
cnf(44,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[20,6]),
[iquote('0:SoR:20.0,6.0')] ).
cnf(51,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,34]),
[iquote('0:SoR:20.0,34.0')] ).
cnf(64,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[20,35]),
[iquote('0:SoR:20.0,35.0')] ).
cnf(74,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[21,8]),
[iquote('0:SoR:21.0,8.1')] ).
cnf(89,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[74,3]),
[iquote('0:SoR:74.0,3.0')] ).
cnf(100,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[24,89]),
[iquote('0:SoR:24.0,89.0')] ).
cnf(107,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[29,27]),
[iquote('0:SoR:29.0,27.1')] ).
cnf(131,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[44,8]),
[iquote('0:SoR:44.0,8.1')] ).
cnf(151,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[51,100]),
[iquote('0:SoR:51.0,100.0')] ).
cnf(153,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[28,151]),
[iquote('0:SoR:28.0,151.0')] ).
cnf(157,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,153]),
[iquote('0:SoR:21.0,153.0')] ).
cnf(263,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[107,157]),
[iquote('0:SoR:107.0,157.0')] ).
cnf(528,plain,
theorem(implies__dfg(or__dfg(u,or__dfg(v,not__dfg(w))),or__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[131,15]),
[iquote('0:SoR:131.0,15.0')] ).
cnf(1534,plain,
( ~ theorem(or__dfg(u,or__dfg(v,not__dfg(w))))
| theorem(or__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[528,9]),
[iquote('0:Res:528.0,9.1')] ).
cnf(4349,plain,
theorem(or__dfg(u,implies__dfg(u,v))),
inference(sor,[status(thm)],[1534,263]),
[iquote('0:SoR:1534.0,263.0')] ).
cnf(4419,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[64,4349]),
[iquote('0:SoR:64.0,4349.0')] ).
cnf(4435,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(u))),
inference(sor,[status(thm)],[21,4419]),
[iquote('0:SoR:21.0,4419.0')] ).
cnf(4459,plain,
theorem(or__dfg(or__dfg(u,v),or__dfg(w,not__dfg(u)))),
inference(sor,[status(thm)],[107,4435]),
[iquote('0:SoR:107.0,4435.0')] ).
cnf(5466,plain,
theorem(or__dfg(or__dfg(u,v),implies__dfg(u,w))),
inference(sor,[status(thm)],[1534,4459]),
[iquote('0:SoR:1534.0,4459.0')] ).
cnf(5476,plain,
theorem(or__dfg(implies__dfg(u,v),implies__dfg(not__dfg(u),w))),
inference(spr,[status(thm),theory(equality)],[7,5466]),
[iquote('0:SpR:7.0,5466.0')] ).
cnf(5477,plain,
$false,
inference(unc,[status(thm)],[5476,1]),
[iquote('0:UnC:5476.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL320-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n008.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 11:28:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.67/1.88
% 1.67/1.88 SPASS V 3.9
% 1.67/1.88 SPASS beiseite: Proof found.
% 1.67/1.88 % SZS status Theorem
% 1.67/1.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.67/1.88 SPASS derived 5162 clauses, backtracked 0 clauses, performed 0 splits and kept 2412 clauses.
% 1.67/1.88 SPASS allocated 82266 KBytes.
% 1.67/1.88 SPASS spent 0:00:01.48 on the problem.
% 1.67/1.88 0:00:00.03 for the input.
% 1.67/1.88 0:00:00.00 for the FLOTTER CNF translation.
% 1.67/1.88 0:00:00.19 for inferences.
% 1.67/1.88 0:00:00.00 for the backtracking.
% 1.67/1.88 0:00:01.20 for the reduction.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Here is a proof with depth 15, length 42 :
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 1.67/1.88
%------------------------------------------------------------------------------