TSTP Solution File: LCL248-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL248-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:35:53 EDT 2022
% Result : Unsatisfiable 7.66s 7.83s
% Output : Refutation 7.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of clauses : 46 ( 30 unt; 0 nHn; 46 RR)
% Number of literals : 64 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(and__dfg(p,q),implies__dfg(p,q))),
file('LCL248-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL248-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL248-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL248-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL248-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL248-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL248-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL248-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL248-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL248-3.p',unknown),
[] ).
cnf(11,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(15,plain,
axiom(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(17,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(18,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(38,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(39,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[38,17]),
[iquote('0:SoR:38.0,17.0')] ).
cnf(40,plain,
( ~ theorem(u)
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[38,15]),
[iquote('0:SoR:38.0,15.0')] ).
cnf(41,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[38,18]),
[iquote('0:SoR:38.0,18.0')] ).
cnf(43,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[38,3]),
[iquote('0:SoR:38.0,3.0')] ).
cnf(44,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[38,2]),
[iquote('0:SoR:38.0,2.0')] ).
cnf(50,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[38,5]),
[iquote('0:SoR:38.0,5.0')] ).
cnf(51,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(55,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,51]),
[iquote('0:Rew:7.0,51.0')] ).
cnf(62,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[38,6]),
[iquote('0:SoR:38.0,6.0')] ).
cnf(102,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[38,55]),
[iquote('0:SoR:38.0,55.0')] ).
cnf(104,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,55]),
[iquote('0:SpR:7.0,55.0')] ).
cnf(107,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,104]),
[iquote('0:Rew:7.0,104.0')] ).
cnf(126,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[41,8]),
[iquote('0:SoR:41.0,8.1')] ).
cnf(151,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[126,3]),
[iquote('0:SoR:126.0,3.0')] ).
cnf(172,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[39,151]),
[iquote('0:SoR:39.0,151.0')] ).
cnf(273,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[38,107]),
[iquote('0:SoR:38.0,107.0')] ).
cnf(314,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[50,43]),
[iquote('0:SoR:50.0,43.1')] ).
cnf(385,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[102,172]),
[iquote('0:SoR:102.0,172.0')] ).
cnf(387,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[44,385]),
[iquote('0:SoR:44.0,385.0')] ).
cnf(392,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[41,387]),
[iquote('0:SoR:41.0,387.0')] ).
cnf(399,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,392]),
[iquote('0:SpR:7.0,392.0')] ).
cnf(401,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[62,399]),
[iquote('0:SoR:62.0,399.0')] ).
cnf(712,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[401,9]),
[iquote('0:Res:401.0,9.1')] ).
cnf(1107,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[314,392]),
[iquote('0:SoR:314.0,392.0')] ).
cnf(1131,plain,
theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,1107]),
[iquote('0:SpR:7.0,1107.0')] ).
cnf(1407,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(sor,[status(thm)],[273,40]),
[iquote('0:SoR:273.0,40.1')] ).
cnf(13322,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,not__dfg(u)))))),
inference(sor,[status(thm)],[712,1131]),
[iquote('0:SoR:712.0,1131.0')] ).
cnf(13369,plain,
theorem(or__dfg(u,not__dfg(and__dfg(v,u)))),
inference(rew,[status(thm),theory(equality)],[11,13322]),
[iquote('0:Rew:11.0,13322.0')] ).
cnf(13430,plain,
theorem(implies__dfg(and__dfg(u,v),v)),
inference(sor,[status(thm)],[39,13369]),
[iquote('0:SoR:39.0,13369.0')] ).
cnf(14338,plain,
theorem(implies__dfg(and__dfg(u,v),implies__dfg(w,v))),
inference(sor,[status(thm)],[1407,13430]),
[iquote('0:SoR:1407.0,13430.0')] ).
cnf(14352,plain,
$false,
inference(unc,[status(thm)],[14338,1]),
[iquote('0:UnC:14338.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : LCL248-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 4 01:07:01 EDT 2022
% 0.15/0.36 % CPUTime :
% 7.66/7.83
% 7.66/7.83 SPASS V 3.9
% 7.66/7.83 SPASS beiseite: Proof found.
% 7.66/7.83 % SZS status Theorem
% 7.66/7.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.66/7.83 SPASS derived 11479 clauses, backtracked 0 clauses, performed 0 splits and kept 4195 clauses.
% 7.66/7.83 SPASS allocated 103359 KBytes.
% 7.66/7.83 SPASS spent 0:00:07.28 on the problem.
% 7.66/7.83 0:00:00.04 for the input.
% 7.66/7.83 0:00:00.00 for the FLOTTER CNF translation.
% 7.66/7.83 0:00:00.30 for inferences.
% 7.66/7.83 0:00:00.00 for the backtracking.
% 7.66/7.83 0:00:06.86 for the reduction.
% 7.66/7.83
% 7.66/7.83
% 7.66/7.83 Here is a proof with depth 14, length 46 :
% 7.66/7.83 % SZS output start Refutation
% See solution above
% 7.66/7.84 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 and_defn
% 7.66/7.84
%------------------------------------------------------------------------------