TSTP Solution File: LCL539+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:37:34 EDT 2022
% Result : Theorem 1.45s 1.66s
% Output : Refutation 1.45s
% 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('LCL539+1.p',unknown),
[] ).
cnf(6,axiom,
op_strict_equiv,
file('LCL539+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL539+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL539+1.p',unknown),
[] ).
cnf(16,axiom,
and_2,
file('LCL539+1.p',unknown),
[] ).
cnf(23,axiom,
equivalence_3,
file('LCL539+1.p',unknown),
[] ).
cnf(24,axiom,
substitution_of_equivalents,
file('LCL539+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL539+1.p',unknown),
[] ).
cnf(31,axiom,
~ substitution_strict_equiv,
file('LCL539+1.p',unknown),
[] ).
cnf(41,axiom,
is_a_theorem(strict_equiv(skc154,skc155)),
file('LCL539+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skc155,skc154)
| substitution_strict_equiv ),
file('LCL539+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL539+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL539+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL539+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL539+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL539+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL539+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ op_strict_equiv
| equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)) ),
file('LCL539+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equivalence_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))) ),
file('LCL539+1.p',unknown),
[] ).
cnf(148,plain,
~ equal(skc155,skc154),
inference(mrr,[status(thm)],[45,31]),
[iquote('0:MRR:45.1,31.0')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(mrr,[status(thm)],[55,16]),
[iquote('0:MRR:55.0,16.0')] ).
cnf(156,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[53,15]),
[iquote('0:MRR:53.0,15.0')] ).
cnf(161,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[107,4]),
[iquote('0:MRR:107.0,4.0')] ).
cnf(165,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[94,24]),
[iquote('0:MRR:94.0,24.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
cnf(178,plain,
equal(and__dfg(strict_implies(u,v),strict_implies(v,u)),strict_equiv(u,v)),
inference(mrr,[status(thm)],[125,6]),
[iquote('0:MRR:125.0,6.0')] ).
cnf(182,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,u),equiv__dfg(u,v)))),
inference(mrr,[status(thm)],[128,23]),
[iquote('0:MRR:128.0,23.0')] ).
cnf(191,plain,
~ is_a_theorem(equiv__dfg(skc154,skc155)),
inference(res,[status(thm),theory(equality)],[165,148]),
[iquote('0:Res:165.1,148.0')] ).
cnf(217,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[161,149]),
[iquote('0:SpR:161.0,149.0')] ).
cnf(407,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[217,177]),
[iquote('0:Res:217.0,177.1')] ).
cnf(435,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(v,u))),
inference(spr,[status(thm),theory(equality)],[178,155]),
[iquote('0:SpR:178.0,155.0')] ).
cnf(436,plain,
is_a_theorem(implies__dfg(strict_equiv(u,v),strict_implies(u,v))),
inference(spr,[status(thm),theory(equality)],[178,156]),
[iquote('0:SpR:178.0,156.0')] ).
cnf(566,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(v,u)) ),
inference(res,[status(thm),theory(equality)],[435,177]),
[iquote('0:Res:435.0,177.1')] ).
cnf(568,plain,
( ~ is_a_theorem(strict_equiv(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(res,[status(thm),theory(equality)],[436,177]),
[iquote('0:Res:436.0,177.1')] ).
cnf(572,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)],[182,177]),
[iquote('0:Res:182.0,177.1')] ).
cnf(823,plain,
is_a_theorem(strict_implies(skc155,skc154)),
inference(sor,[status(thm)],[566,41]),
[iquote('0:SoR:566.0,41.0')] ).
cnf(824,plain,
is_a_theorem(implies__dfg(skc155,skc154)),
inference(sor,[status(thm)],[407,823]),
[iquote('0:SoR:407.0,823.0')] ).
cnf(833,plain,
is_a_theorem(strict_implies(skc154,skc155)),
inference(sor,[status(thm)],[568,41]),
[iquote('0:SoR:568.0,41.0')] ).
cnf(834,plain,
is_a_theorem(implies__dfg(skc154,skc155)),
inference(sor,[status(thm)],[407,833]),
[iquote('0:SoR:407.0,833.0')] ).
cnf(4325,plain,
is_a_theorem(implies__dfg(implies__dfg(skc155,skc154),equiv__dfg(skc154,skc155))),
inference(sor,[status(thm)],[572,834]),
[iquote('0:SoR:572.0,834.0')] ).
cnf(5636,plain,
( ~ is_a_theorem(implies__dfg(skc155,skc154))
| is_a_theorem(equiv__dfg(skc154,skc155)) ),
inference(res,[status(thm),theory(equality)],[4325,177]),
[iquote('0:Res:4325.0,177.1')] ).
cnf(5637,plain,
is_a_theorem(equiv__dfg(skc154,skc155)),
inference(ssi,[status(thm)],[5636,824]),
[iquote('0:SSi:5636.0,824.0')] ).
cnf(5638,plain,
$false,
inference(mrr,[status(thm)],[5637,191]),
[iquote('0:MRR:5637.0,191.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 00:31:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.45/1.66
% 1.45/1.66 SPASS V 3.9
% 1.45/1.66 SPASS beiseite: Proof found.
% 1.45/1.66 % SZS status Theorem
% 1.45/1.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/1.66 SPASS derived 4246 clauses, backtracked 0 clauses, performed 1 splits and kept 2548 clauses.
% 1.45/1.66 SPASS allocated 105666 KBytes.
% 1.45/1.66 SPASS spent 0:00:01.24 on the problem.
% 1.45/1.66 0:00:00.04 for the input.
% 1.45/1.66 0:00:00.06 for the FLOTTER CNF translation.
% 1.45/1.66 0:00:00.08 for inferences.
% 1.45/1.66 0:00:00.01 for the backtracking.
% 1.45/1.66 0:00:01.00 for the reduction.
% 1.45/1.66
% 1.45/1.66
% 1.45/1.66 Here is a proof with depth 6, length 44 :
% 1.45/1.66 % SZS output start Refutation
% See solution above
% 1.45/1.66 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 km4b_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
% 1.45/1.66
%------------------------------------------------------------------------------