TSTP Solution File: LCL294-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL294-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:36:09 EDT 2022
% Result : Unsatisfiable 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 25 unt; 0 nHn; 37 RR)
% Number of literals : 51 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(equivalent(implies__dfg(p,q),or__dfg(not__dfg(p),q))),
file('LCL294-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL294-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL294-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL294-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL294-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL294-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL294-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL294-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL294-3.p',unknown),
[] ).
cnf(11,axiom,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equivalent(u,v)),
file('LCL294-3.p',unknown),
[] ).
cnf(12,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(13,plain,
~ theorem(equivalent(implies__dfg(p,q),implies__dfg(p,q))),
inference(rew,[status(thm),theory(equality)],[7,1]),
[iquote('0:Rew:7.0,1.0')] ).
cnf(16,plain,
axiom(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(19,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(20,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(22,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(26,plain,
axiom(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[22,16]),
[iquote('0:Rew:22.0,16.0')] ).
cnf(40,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(41,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[40,19]),
[iquote('0:SoR:40.0,19.0')] ).
cnf(43,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[40,20]),
[iquote('0:SoR:40.0,20.0')] ).
cnf(44,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[40,4]),
[iquote('0:SoR:40.0,4.0')] ).
cnf(46,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[40,2]),
[iquote('0:SoR:40.0,2.0')] ).
cnf(55,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[44,8]),
[iquote('0:SoR:44.0,8.1')] ).
cnf(61,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(65,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,61]),
[iquote('0:Rew:7.0,61.0')] ).
cnf(72,plain,
theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[55,26]),
[iquote('0:SoR:55.0,26.0')] ).
cnf(73,plain,
theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[7,72]),
[iquote('0:Rew:7.0,72.0')] ).
cnf(76,plain,
( ~ theorem(u)
| theorem(and__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[73,9]),
[iquote('0:Res:73.0,9.1')] ).
cnf(82,plain,
( ~ theorem(implies__dfg(u,u))
| theorem(equivalent(u,u)) ),
inference(spr,[status(thm),theory(equality)],[11,76]),
[iquote('0:SpR:11.0,76.1')] ).
cnf(125,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[40,65]),
[iquote('0:SoR:40.0,65.0')] ).
cnf(160,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[43,8]),
[iquote('0:SoR:43.0,8.1')] ).
cnf(200,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[160,3]),
[iquote('0:SoR:160.0,3.0')] ).
cnf(231,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[41,200]),
[iquote('0:SoR:41.0,200.0')] ).
cnf(446,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[125,231]),
[iquote('0:SoR:125.0,231.0')] ).
cnf(448,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[46,446]),
[iquote('0:SoR:46.0,446.0')] ).
cnf(452,plain,
theorem(equivalent(u,u)),
inference(mrr,[status(thm)],[82,448]),
[iquote('0:MRR:82.0,448.0')] ).
cnf(453,plain,
$false,
inference(unc,[status(thm)],[452,13]),
[iquote('0:UnC:452.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL294-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 00:49:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 324 clauses, backtracked 0 clauses, performed 0 splits and kept 173 clauses.
% 0.18/0.45 SPASS allocated 76287 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.45 0:00:00.04 for the input.
% 0.18/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.01 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.03 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 7, length 37 :
% 0.18/0.45 % SZS output start Refutation
% See solution above
% 0.18/0.45 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 implies_definition rule_1 rule_2 and_defn equivalent_defn
% 0.18/0.45
%------------------------------------------------------------------------------