TSTP Solution File: LCL323-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL323-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 14:36:17 EDT 2022
% Result : Unsatisfiable 194.84s 195.03s
% Output : Refutation 194.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of clauses : 67 ( 45 unt; 0 nHn; 67 RR)
% Number of literals : 92 ( 0 equ; 26 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; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(implies__dfg(p,q),implies__dfg(q,r))),
file('LCL323-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL323-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL323-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL323-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL323-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL323-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL323-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL323-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL323-3.p',unknown),
[] ).
cnf(13,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(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(18,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)],[18,16]),
[iquote('0:SoR:18.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,15]),
[iquote('0:SoR:18.0,15.0')] ).
cnf(24,plain,
( ~ theorem(u)
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,13]),
[iquote('0:SoR:18.0,13.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,4]),
[iquote('0:SoR:18.0,4.0')] ).
cnf(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
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(43,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[18,6]),
[iquote('0:SoR:18.0,6.0')] ).
cnf(44,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(46,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,44]),
[iquote('0:Rew:7.0,44.0')] ).
cnf(52,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[18,34]),
[iquote('0:SoR:18.0,34.0')] ).
cnf(65,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[18,35]),
[iquote('0:SoR:18.0,35.0')] ).
cnf(72,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[18,46]),
[iquote('0:SoR:18.0,46.0')] ).
cnf(75,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(or__dfg(v,u)))),
inference(sor,[status(thm)],[75,4]),
[iquote('0:SoR:75.0,4.0')] ).
cnf(90,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[75,3]),
[iquote('0:SoR:75.0,3.0')] ).
cnf(99,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,90]),
[iquote('0:SoR:23.0,90.0')] ).
cnf(128,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[23,89]),
[iquote('0:SoR:23.0,89.0')] ).
cnf(165,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,implies__dfg(w,v))) ),
inference(sor,[status(thm)],[52,24]),
[iquote('0:SoR:52.0,24.1')] ).
cnf(166,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[52,99]),
[iquote('0:SoR:52.0,99.0')] ).
cnf(168,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,166]),
[iquote('0:SoR:27.0,166.0')] ).
cnf(172,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,168]),
[iquote('0:SoR:21.0,168.0')] ).
cnf(173,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[52,168]),
[iquote('0:SoR:52.0,168.0')] ).
cnf(177,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,172]),
[iquote('0:SpR:7.0,172.0')] ).
cnf(179,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[43,177]),
[iquote('0:SoR:43.0,177.0')] ).
cnf(186,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[65,26]),
[iquote('0:SoR:65.0,26.1')] ).
cnf(204,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[72,128]),
[iquote('0:SoR:72.0,128.0')] ).
cnf(220,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[25,173]),
[iquote('0:SoR:25.0,173.0')] ).
cnf(222,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,173]),
[iquote('0:SpR:7.0,173.0')] ).
cnf(224,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,222]),
[iquote('0:Rew:7.0,222.0')] ).
cnf(249,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[224,9]),
[iquote('0:Res:224.0,9.1')] ).
cnf(372,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),implies__dfg(w,u))),
inference(sor,[status(thm)],[165,220]),
[iquote('0:SoR:165.0,220.0')] ).
cnf(412,plain,
theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
inference(sor,[status(thm)],[186,99]),
[iquote('0:SoR:186.0,99.0')] ).
cnf(446,plain,
theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
inference(sor,[status(thm)],[52,412]),
[iquote('0:SoR:52.0,412.0')] ).
cnf(643,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[249,9]),
[iquote('0:Res:249.1,9.1')] ).
cnf(1355,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[179,9]),
[iquote('0:Res:179.0,9.1')] ).
cnf(2085,plain,
theorem(or__dfg(implies__dfg(u,v),implies__dfg(or__dfg(v,w),w))),
inference(sor,[status(thm)],[25,372]),
[iquote('0:SoR:25.0,372.0')] ).
cnf(2884,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(implies__dfg(w,u),v))),
inference(sor,[status(thm)],[65,2085]),
[iquote('0:SoR:65.0,2085.0')] ).
cnf(3412,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(implies__dfg(w,u),v)) ),
inference(sor,[status(thm)],[643,2884]),
[iquote('0:SoR:643.1,2884.0')] ).
cnf(3772,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
inference(sor,[status(thm)],[1355,446]),
[iquote('0:SoR:1355.0,446.0')] ).
cnf(3833,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1355,220]),
[iquote('0:SoR:1355.0,220.0')] ).
cnf(5531,plain,
theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
inference(sor,[status(thm)],[27,3772]),
[iquote('0:SoR:27.0,3772.0')] ).
cnf(5746,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[23,3833]),
[iquote('0:SoR:23.0,3833.0')] ).
cnf(5749,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[643,5746]),
[iquote('0:SoR:643.1,5746.0')] ).
cnf(7022,plain,
theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
inference(sor,[status(thm)],[5749,5531]),
[iquote('0:SoR:5749.0,5531.0')] ).
cnf(7038,plain,
theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
inference(rew,[status(thm),theory(equality)],[7,7022]),
[iquote('0:Rew:7.0,7022.0')] ).
cnf(14389,plain,
( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
| theorem(w) ),
inference(sor,[status(thm)],[643,7038]),
[iquote('0:SoR:643.1,7038.0')] ).
cnf(83267,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[14389,204]),
[iquote('0:SoR:14389.0,204.0')] ).
cnf(83691,plain,
theorem(or__dfg(u,implies__dfg(u,v))),
inference(sor,[status(thm)],[52,83267]),
[iquote('0:SoR:52.0,83267.0')] ).
cnf(83713,plain,
theorem(or__dfg(implies__dfg(u,v),implies__dfg(v,w))),
inference(sor,[status(thm)],[3412,83691]),
[iquote('0:SoR:3412.0,83691.0')] ).
cnf(83731,plain,
$false,
inference(unc,[status(thm)],[83713,1]),
[iquote('0:UnC:83713.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL323-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jul 2 22:39:37 EDT 2022
% 0.12/0.32 % CPUTime :
% 194.84/195.03
% 194.84/195.03 SPASS V 3.9
% 194.84/195.03 SPASS beiseite: Proof found.
% 194.84/195.03 % SZS status Theorem
% 194.84/195.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 194.84/195.03 SPASS derived 76581 clauses, backtracked 0 clauses, performed 0 splits and kept 30171 clauses.
% 194.84/195.03 SPASS allocated 168968 KBytes.
% 194.84/195.03 SPASS spent 0:3:12.34 on the problem.
% 194.84/195.03 0:00:00.04 for the input.
% 194.84/195.03 0:00:00.00 for the FLOTTER CNF translation.
% 194.84/195.03 0:00:05.15 for inferences.
% 194.84/195.03 0:00:00.00 for the backtracking.
% 194.84/195.03 0:03:05.51 for the reduction.
% 194.84/195.03
% 194.84/195.03
% 194.84/195.03 Here is a proof with depth 19, length 67 :
% 194.84/195.03 % SZS output start Refutation
% See solution above
% 194.84/195.03 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
% 194.84/195.03
%------------------------------------------------------------------------------