TSTP Solution File: LCL259-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:35:58 EDT 2022
% Result : Unsatisfiable 234.26s 234.41s
% Output : Refutation 234.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of clauses : 69 ( 47 unt; 0 nHn; 69 RR)
% Number of literals : 94 ( 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(implies__dfg(implies__dfg(p,implies__dfg(p,q)),implies__dfg(p,q))),
file('LCL259-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL259-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL259-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL259-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL259-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL259-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL259-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL259-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL259-3.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(19,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(20,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[19,16]),
[iquote('0:SoR:19.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,15]),
[iquote('0:SoR:19.0,15.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,4]),
[iquote('0:SoR:19.0,4.0')] ).
cnf(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(36,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(37,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(40,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,36]),
[iquote('0:Rew:7.0,36.0')] ).
cnf(41,plain,
axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,37]),
[iquote('0:Rew:7.0,37.0')] ).
cnf(48,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[19,6]),
[iquote('0:SoR:19.0,6.0')] ).
cnf(49,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(51,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,49]),
[iquote('0:Rew:7.0,49.0')] ).
cnf(60,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,8]),
[iquote('0:SoR:20.0,8.1')] ).
cnf(71,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[60,4]),
[iquote('0:SoR:60.0,4.0')] ).
cnf(72,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[60,3]),
[iquote('0:SoR:60.0,3.0')] ).
cnf(73,plain,
theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
inference(sor,[status(thm)],[60,2]),
[iquote('0:SoR:60.0,2.0')] ).
cnf(76,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,40]),
[iquote('0:SoR:19.0,40.0')] ).
cnf(87,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,72]),
[iquote('0:SoR:23.0,72.0')] ).
cnf(94,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[19,41]),
[iquote('0:SoR:19.0,41.0')] ).
cnf(100,plain,
theorem(implies__dfg(or__dfg(u,u),u)),
inference(sor,[status(thm)],[23,73]),
[iquote('0:SoR:23.0,73.0')] ).
cnf(116,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[19,51]),
[iquote('0:SoR:19.0,51.0')] ).
cnf(119,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[23,71]),
[iquote('0:SoR:23.0,71.0')] ).
cnf(174,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[48,8]),
[iquote('0:SoR:48.0,8.1')] ).
cnf(190,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[76,87]),
[iquote('0:SoR:76.0,87.0')] ).
cnf(192,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,190]),
[iquote('0:SoR:27.0,190.0')] ).
cnf(196,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[20,192]),
[iquote('0:SoR:20.0,192.0')] ).
cnf(197,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[76,192]),
[iquote('0:SoR:76.0,192.0')] ).
cnf(201,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,196]),
[iquote('0:SpR:7.0,196.0')] ).
cnf(203,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[48,201]),
[iquote('0:SoR:48.0,201.0')] ).
cnf(210,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[94,26]),
[iquote('0:SoR:94.0,26.1')] ).
cnf(232,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[116,119]),
[iquote('0:SoR:116.0,119.0')] ).
cnf(238,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[116,100]),
[iquote('0:SoR:116.0,100.0')] ).
cnf(250,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[25,197]),
[iquote('0:SoR:25.0,197.0')] ).
cnf(252,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,197]),
[iquote('0:SpR:7.0,197.0')] ).
cnf(254,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,252]),
[iquote('0:Rew:7.0,252.0')] ).
cnf(289,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[254,9]),
[iquote('0:Res:254.0,9.1')] ).
cnf(431,plain,
theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
inference(sor,[status(thm)],[210,87]),
[iquote('0:SoR:210.0,87.0')] ).
cnf(465,plain,
theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
inference(sor,[status(thm)],[76,431]),
[iquote('0:SoR:76.0,431.0')] ).
cnf(574,plain,
theorem(implies__dfg(or__dfg(u,implies__dfg(v,w)),or__dfg(u,implies__dfg(implies__dfg(x,v),implies__dfg(x,w))))),
inference(sor,[status(thm)],[174,51]),
[iquote('0:SoR:174.0,51.0')] ).
cnf(690,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[289,9]),
[iquote('0:Res:289.1,9.1')] ).
cnf(1374,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[203,9]),
[iquote('0:Res:203.0,9.1')] ).
cnf(1524,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(or__dfg(u,implies__dfg(implies__dfg(x,v),implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[574,9]),
[iquote('0:Res:574.0,9.1')] ).
cnf(1945,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,v)))
| theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[690,238]),
[iquote('0:SoR:690.1,238.0')] ).
cnf(3844,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
inference(sor,[status(thm)],[1374,465]),
[iquote('0:SoR:1374.0,465.0')] ).
cnf(3902,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1374,250]),
[iquote('0:SoR:1374.0,250.0')] ).
cnf(4904,plain,
theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
inference(sor,[status(thm)],[27,3844]),
[iquote('0:SoR:27.0,3844.0')] ).
cnf(5112,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[23,3902]),
[iquote('0:SoR:23.0,3902.0')] ).
cnf(5115,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[690,5112]),
[iquote('0:SoR:690.1,5112.0')] ).
cnf(6737,plain,
theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
inference(sor,[status(thm)],[5115,4904]),
[iquote('0:SoR:5115.0,4904.0')] ).
cnf(6754,plain,
theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
inference(rew,[status(thm),theory(equality)],[7,6737]),
[iquote('0:Rew:7.0,6737.0')] ).
cnf(11950,plain,
( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
| theorem(w) ),
inference(sor,[status(thm)],[690,6754]),
[iquote('0:SoR:690.1,6754.0')] ).
cnf(64382,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[11950,232]),
[iquote('0:SoR:11950.0,232.0')] ).
cnf(64606,plain,
theorem(or__dfg(u,implies__dfg(u,v))),
inference(sor,[status(thm)],[76,64382]),
[iquote('0:SoR:76.0,64382.0')] ).
cnf(64637,plain,
theorem(or__dfg(u,implies__dfg(implies__dfg(v,u),implies__dfg(v,w)))),
inference(sor,[status(thm)],[1524,64606]),
[iquote('0:SoR:1524.0,64606.0')] ).
cnf(75365,plain,
theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[94,64637]),
[iquote('0:SoR:94.0,64637.0')] ).
cnf(80333,plain,
theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[1945,75365]),
[iquote('0:SoR:1945.0,75365.0')] ).
cnf(80342,plain,
$false,
inference(unc,[status(thm)],[80333,1]),
[iquote('0:UnC:80333.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jul 2 22:58:00 EDT 2022
% 0.15/0.35 % CPUTime :
% 234.26/234.41
% 234.26/234.41 SPASS V 3.9
% 234.26/234.41 SPASS beiseite: Proof found.
% 234.26/234.41 % SZS status Theorem
% 234.26/234.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 234.26/234.41 SPASS derived 74169 clauses, backtracked 0 clauses, performed 0 splits and kept 28278 clauses.
% 234.26/234.41 SPASS allocated 164594 KBytes.
% 234.26/234.41 SPASS spent 0:3:51.79 on the problem.
% 234.26/234.41 0:00:00.03 for the input.
% 234.26/234.41 0:00:00.00 for the FLOTTER CNF translation.
% 234.26/234.41 0:00:06.63 for inferences.
% 234.26/234.41 0:00:00.00 for the backtracking.
% 234.26/234.41 0:3:43.05 for the reduction.
% 234.26/234.41
% 234.26/234.41
% 234.26/234.41 Here is a proof with depth 21, length 69 :
% 234.26/234.41 % SZS output start Refutation
% See solution above
% 234.26/234.41 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
% 234.26/234.41
%------------------------------------------------------------------------------