TSTP Solution File: LCL531+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 14:37:32 EDT 2022
% Result : Theorem 0.75s 0.90s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 27 ( 14 unt; 0 nHn; 27 RR)
% Number of literals : 44 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL531+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL531+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL531+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL531+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL531+1.p',unknown),
[] ).
cnf(30,axiom,
~ axiom_m4,
file('LCL531+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL531+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(implies__dfg(skc126,and__dfg(skc126,skc126)))
| kn1 ),
file('LCL531+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL531+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ is_a_theorem(strict_implies(skc177,and__dfg(skc177,skc177)))
| axiom_m4 ),
file('LCL531+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL531+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL531+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL531+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL531+1.p',unknown),
[] ).
cnf(148,plain,
~ is_a_theorem(strict_implies(skc177,and__dfg(skc177,skc177))),
inference(mrr,[status(thm)],[74,30]),
[iquote('0:MRR:74.1,30.0')] ).
cnf(149,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[68,26]),
[iquote('0:MRR:68.1,26.0')] ).
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(162,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[94,17]),
[iquote('0:MRR:94.0,17.0')] ).
cnf(172,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[111,13]),
[iquote('0:MRR:111.0,13.0')] ).
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(219,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[159,149]),
[iquote('0:SpR:159.0,149.1')] ).
cnf(296,plain,
( ~ kn1
| is_a_theorem(strict_implies(u,and__dfg(u,u))) ),
inference(sor,[status(thm)],[219,60]),
[iquote('0:SoR:219.0,60.1')] ).
cnf(312,plain,
~ kn1,
inference(res,[status(thm),theory(equality)],[296,148]),
[iquote('0:Res:296.1,148.0')] ).
cnf(313,plain,
~ is_a_theorem(implies__dfg(skc126,and__dfg(skc126,skc126))),
inference(mrr,[status(thm)],[61,312]),
[iquote('0:MRR:61.1,312.0')] ).
cnf(456,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[172,175]),
[iquote('0:Res:172.0,175.1')] ).
cnf(2257,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[456,162]),
[iquote('0:SoR:456.0,162.0')] ).
cnf(2260,plain,
$false,
inference(unc,[status(thm)],[2257,313]),
[iquote('0:UnC:2257.0,313.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 18:21:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.75/0.90
% 0.75/0.90 SPASS V 3.9
% 0.75/0.90 SPASS beiseite: Proof found.
% 0.75/0.90 % SZS status Theorem
% 0.75/0.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.90 SPASS derived 1627 clauses, backtracked 0 clauses, performed 2 splits and kept 1102 clauses.
% 0.75/0.90 SPASS allocated 100811 KBytes.
% 0.75/0.90 SPASS spent 0:00:00.52 on the problem.
% 0.75/0.90 0:00:00.04 for the input.
% 0.75/0.90 0:00:00.06 for the FLOTTER CNF translation.
% 0.75/0.90 0:00:00.04 for inferences.
% 0.75/0.90 0:00:00.00 for the backtracking.
% 0.75/0.90 0:00:00.34 for the reduction.
% 0.75/0.90
% 0.75/0.90
% 0.75/0.90 Here is a proof with depth 3, length 27 :
% 0.75/0.90 % SZS output start Refutation
% See solution above
% 0.75/0.90 Formulae used in the proof : s1_0_op_strict_implies hilbert_modus_ponens hilbert_implies_2 hilbert_and_3 km5_necessitation s1_0_axiom_m4 kn1 necessitation km5_axiom_M axiom_M axiom_m4 and_3 op_strict_implies modus_ponens implies_2
% 0.75/0.90
%------------------------------------------------------------------------------