TSTP Solution File: LCL526+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:37:30 EDT 2022
% Result : Theorem 1.07s 1.28s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of clauses : 44 ( 28 unt; 0 nHn; 44 RR)
% Number of literals : 64 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL526+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL526+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL526+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL526+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL526+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL526+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL526+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL526+1.p',unknown),
[] ).
cnf(30,axiom,
~ substitution_strict_equiv,
file('LCL526+1.p',unknown),
[] ).
cnf(40,axiom,
is_a_theorem(strict_equiv(skc154,skc155)),
file('LCL526+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL526+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL526+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL526+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL526+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL526+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL526+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL526+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL526+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL526+1.p',unknown),
[] ).
cnf(147,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[44,30]),
[iquote('0:MRR:44.1,30.0')] ).
cnf(148,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[46,28]),
[iquote('0:MRR:46.0,28.0')] ).
cnf(153,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[54,16]),
[iquote('0:MRR:54.0,16.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[52,15]),
[iquote('0:MRR:52.0,15.0')] ).
cnf(159,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[106,4]),
[iquote('0:MRR:106.0,4.0')] ).
cnf(163,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[93,24]),
[iquote('0:MRR:93.0,24.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[108,10]),
[iquote('0:MRR:108.1,10.0')] ).
cnf(176,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[124,6]),
[iquote('0:MRR:124.0,6.0')] ).
cnf(180,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[127,23]),
[iquote('0:MRR:127.0,23.0')] ).
cnf(189,plain,
~ is_a_theorem(equiv__dfg(skc154,skc155)),
inference(res,[status(thm),theory(equality)],[163,147]),
[iquote('0:Res:163.1,147.0')] ).
cnf(217,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[159,148]),
[iquote('0:SpR:159.0,148.0')] ).
cnf(418,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[217,175]),
[iquote('0:Res:217.0,175.1')] ).
cnf(444,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[176,153]),
[iquote('0:SpR:176.0,153.0')] ).
cnf(445,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[176,154]),
[iquote('0:SpR:176.0,154.0')] ).
cnf(546,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[444,175]),
[iquote('0:Res:444.0,175.1')] ).
cnf(575,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[445,175]),
[iquote('0:Res:445.0,175.1')] ).
cnf(581,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[180,175]),
[iquote('0:Res:180.0,175.1')] ).
cnf(834,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[546,40]),
[iquote('0:SoR:546.0,40.0')] ).
cnf(835,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[418,834]),
[iquote('0:SoR:418.0,834.0')] ).
cnf(843,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[575,40]),
[iquote('0:SoR:575.0,40.0')] ).
cnf(844,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[418,843]),
[iquote('0:SoR:418.0,843.0')] ).
cnf(4407,plain,
is_a_theorem(implies__dfg(implies__dfg(skc155,skc154),equiv__dfg(skc154,skc155))),
inference(sor,[status(thm)],[581,844]),
[iquote('0:SoR:581.0,844.0')] ).
cnf(4507,plain,
( ~ is_a_theorem(implies__dfg(skc155,skc154))
| is_a_theorem(equiv__dfg(skc154,skc155)) ),
inference(res,[status(thm),theory(equality)],[4407,175]),
[iquote('0:Res:4407.0,175.1')] ).
cnf(4508,plain,
is_a_theorem(equiv__dfg(skc154,skc155)),
inference(ssi,[status(thm)],[4507,835]),
[iquote('0:SSi:4507.0,835.0')] ).
cnf(4509,plain,
$false,
inference(mrr,[status(thm)],[4508,189]),
[iquote('0:MRR:4508.0,189.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 21:50:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.07/1.28
% 1.07/1.28 SPASS V 3.9
% 1.07/1.28 SPASS beiseite: Proof found.
% 1.07/1.28 % SZS status Theorem
% 1.07/1.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.28 SPASS derived 3343 clauses, backtracked 0 clauses, performed 1 splits and kept 2150 clauses.
% 1.07/1.28 SPASS allocated 103789 KBytes.
% 1.07/1.28 SPASS spent 0:00:00.89 on the problem.
% 1.07/1.28 0:00:00.04 for the input.
% 1.07/1.28 0:00:00.06 for the FLOTTER CNF translation.
% 1.07/1.28 0:00:00.06 for inferences.
% 1.07/1.28 0:00:00.01 for the backtracking.
% 1.07/1.28 0:00:00.68 for the reduction.
% 1.07/1.28
% 1.07/1.28
% 1.07/1.28 Here is a proof with depth 6, length 44 :
% 1.07/1.28 % SZS output start Refutation
% See solution above
% 1.07/1.28 Formulae used in the proof : s1_0_op_strict_implies s1_0_op_strict_equiv hilbert_modus_ponens hilbert_and_1 hilbert_and_2 hilbert_equivalence_3 substitution_of_equivalents km5_axiom_M s1_0_substitution_strict_equiv substitution_strict_equiv axiom_M and_1 and_2 op_strict_implies modus_ponens hilbert_and_3 and_3 op_strict_equiv equivalence_3
% 1.07/1.28
%------------------------------------------------------------------------------