TSTP Solution File: LCL239-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:35:48 EDT 2022
% Result : Unsatisfiable 1.07s 1.25s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 21 unt; 0 nHn; 31 RR)
% Number of literals : 44 ( 0 equ; 14 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(not__dfg(and__dfg(p,not__dfg(p)))),
file('LCL239-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL239-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL239-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL239-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL239-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL239-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL239-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL239-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL239-3.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(18,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(19,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,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
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(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[38,19]),
[iquote('0:SoR:38.0,19.0')] ).
cnf(42,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[38,18]),
[iquote('0:SoR:38.0,18.0')] ).
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,
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(54,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,50]),
[iquote('0:Rew:7.0,50.0')] ).
cnf(88,plain,
( ~ theorem(implies__dfg(u,not__dfg(v)))
| ~ theorem(or__dfg(and__dfg(u,v),w))
| theorem(w) ),
inference(spl,[status(thm),theory(equality)],[20,9]),
[iquote('0:SpL:20.0,9.1')] ).
cnf(108,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[39,8]),
[iquote('0:SoR:39.0,8.1')] ).
cnf(114,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[38,54]),
[iquote('0:SoR:38.0,54.0')] ).
cnf(131,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[108,3]),
[iquote('0:SoR:108.0,3.0')] ).
cnf(156,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[42,131]),
[iquote('0:SoR:42.0,131.0')] ).
cnf(367,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[114,156]),
[iquote('0:SoR:114.0,156.0')] ).
cnf(369,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[44,367]),
[iquote('0:SoR:44.0,367.0')] ).
cnf(374,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[39,369]),
[iquote('0:SoR:39.0,369.0')] ).
cnf(381,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,374]),
[iquote('0:SpR:7.0,374.0')] ).
cnf(609,plain,
( ~ theorem(or__dfg(and__dfg(u,not__dfg(u)),v))
| theorem(v) ),
inference(sor,[status(thm)],[88,381]),
[iquote('0:SoR:88.0,381.0')] ).
cnf(3733,plain,
theorem(not__dfg(and__dfg(u,not__dfg(u)))),
inference(res,[status(thm),theory(equality)],[374,609]),
[iquote('0:Res:374.0,609.0')] ).
cnf(3743,plain,
$false,
inference(unc,[status(thm)],[3733,1]),
[iquote('0:UnC:3733.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 20:31:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.07/1.25
% 1.07/1.25 SPASS V 3.9
% 1.07/1.25 SPASS beiseite: Proof found.
% 1.07/1.25 % SZS status Theorem
% 1.07/1.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.25 SPASS derived 3160 clauses, backtracked 0 clauses, performed 0 splits and kept 1480 clauses.
% 1.07/1.25 SPASS allocated 82423 KBytes.
% 1.07/1.25 SPASS spent 0:00:00.87 on the problem.
% 1.07/1.25 0:00:00.04 for the input.
% 1.07/1.25 0:00:00.00 for the FLOTTER CNF translation.
% 1.07/1.25 0:00:00.06 for inferences.
% 1.07/1.25 0:00:00.00 for the backtracking.
% 1.07/1.25 0:00:00.74 for the reduction.
% 1.07/1.25
% 1.07/1.25
% 1.07/1.25 Here is a proof with depth 11, length 31 :
% 1.07/1.25 % SZS output start Refutation
% See solution above
% 1.07/1.25 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
% 1.07/1.25
%------------------------------------------------------------------------------