TSTP Solution File: LCL494+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL494+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:37:22 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of clauses : 41 ( 25 unt; 0 nHn; 41 RR)
% Number of literals : 60 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL494+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL494+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL494+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL494+1.p',unknown),
[] ).
cnf(6,axiom,
op_equiv,
file('LCL494+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL494+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL494+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL494+1.p',unknown),
[] ).
cnf(14,axiom,
~ equivalence_2,
file('LCL494+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ and_2
| is_a_theorem(implies__dfg(and__dfg(u,v),v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ is_a_theorem(implies__dfg(and__dfg(skc71,skc70),skc70))
| and_2 ),
file('LCL494+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL494+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ is_a_theorem(implies__dfg(equiv__dfg(skc84,skc83),implies__dfg(skc83,skc84)))
| equivalence_2 ),
file('LCL494+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL494+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL494+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL494+1.p',unknown),
[] ).
cnf(75,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,u))),
inference(mrr,[status(thm)],[36,9]),
[iquote('0:MRR:36.0,9.0')] ).
cnf(78,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,4.0')] ).
cnf(79,plain,
is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(mrr,[status(thm)],[49,10]),
[iquote('0:MRR:49.0,10.0')] ).
cnf(80,plain,
~ is_a_theorem(implies__dfg(equiv__dfg(skc84,skc83),implies__dfg(skc83,skc84))),
inference(mrr,[status(thm)],[48,14]),
[iquote('0:MRR:48.1,14.0')] ).
cnf(82,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[52,2]),
[iquote('0:MRR:52.0,2.0')] ).
cnf(83,plain,
( ~ op_and
| equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[78,59]),
[iquote('0:Rew:78.0,59.1')] ).
cnf(84,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(mrr,[status(thm)],[83,5]),
[iquote('0:MRR:83.0,5.0')] ).
cnf(85,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[82,58]),
[iquote('0:Rew:82.0,58.1')] ).
cnf(86,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[85,1]),
[iquote('0:MRR:85.0,1.0')] ).
cnf(94,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[53,7]),
[iquote('0:MRR:53.1,7.0')] ).
cnf(95,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[60,6]),
[iquote('0:MRR:60.0,6.0')] ).
cnf(115,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[78,75]),
[iquote('0:SpR:78.0,75.0')] ).
cnf(130,plain,
is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[86,115]),
[iquote('0:SpR:86.0,115.0')] ).
cnf(174,plain,
equal(or__dfg(implies__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[84,86]),
[iquote('0:SpR:84.0,86.0')] ).
cnf(261,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[79,94]),
[iquote('0:Res:79.0,94.1')] ).
cnf(293,plain,
( ~ and_2
| is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))) ),
inference(spr,[status(thm),theory(equality)],[95,24]),
[iquote('0:SpR:95.0,24.1')] ).
cnf(366,plain,
is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[261,130]),
[iquote('0:SoR:261.0,130.0')] ).
cnf(376,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),v)),
inference(rew,[status(thm),theory(equality)],[174,366]),
[iquote('0:Rew:174.0,366.0')] ).
cnf(377,plain,
and_2,
inference(mrr,[status(thm)],[25,376]),
[iquote('0:MRR:25.0,376.0')] ).
cnf(379,plain,
is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))),
inference(mrr,[status(thm)],[293,377]),
[iquote('0:MRR:293.0,377.0')] ).
cnf(380,plain,
$false,
inference(unc,[status(thm)],[379,80]),
[iquote('0:UnC:379.0,80.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL494+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 07:51:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 232 clauses, backtracked 0 clauses, performed 0 splits and kept 202 clauses.
% 0.20/0.49 SPASS allocated 98133 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.03 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 3, length 41 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and principia_op_implies_or principia_op_and principia_op_equiv principia_modus_ponens principia_r2 principia_r3 hilbert_equivalence_2 and_2 r2 equivalence_2 r3 op_implies_or op_implies_and modus_ponens op_or op_and op_equiv
% 0.20/0.50
%------------------------------------------------------------------------------