TSTP Solution File: LCL499+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:37:23 EDT 2022
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 17 unt; 0 nHn; 26 RR)
% Number of literals : 38 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 7 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_implies_or,
file('LCL499+1.p',unknown),
[] ).
cnf(5,axiom,
op_and,
file('LCL499+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL499+1.p',unknown),
[] ).
cnf(8,axiom,
r1,
file('LCL499+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL499+1.p',unknown),
[] ).
cnf(14,axiom,
~ kn1,
file('LCL499+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL499+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL499+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL499+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL499+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL499+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ op_and
| equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
file('LCL499+1.p',unknown),
[] ).
cnf(76,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(mrr,[status(thm)],[34,8]),
[iquote('0:MRR:34.0,8.0')] ).
cnf(77,plain,
~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87))),
inference(mrr,[status(thm)],[31,14]),
[iquote('0:MRR:31.1,14.0')] ).
cnf(79,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(80,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(83,plain,
( ~ op_and
| equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[79,59]),
[iquote('0:Rew:79.0,59.1')] ).
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(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(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[79,76]),
[iquote('0:SpR:79.0,76.0')] ).
cnf(171,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
inference(spr,[status(thm),theory(equality)],[84,79]),
[iquote('0:SpR:84.0,79.0')] ).
cnf(185,plain,
is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[171,113]),
[iquote('0:Rew:171.0,113.0')] ).
cnf(252,plain,
( ~ is_a_theorem(or__dfg(u,v))
| is_a_theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[80,94]),
[iquote('0:Res:80.0,94.1')] ).
cnf(345,plain,
is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
inference(sor,[status(thm)],[252,185]),
[iquote('0:SoR:252.0,185.0')] ).
cnf(354,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[79,345]),
[iquote('0:Rew:79.0,345.0')] ).
cnf(355,plain,
$false,
inference(unc,[status(thm)],[354,77]),
[iquote('0:UnC:354.0,77.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Sat Jul 2 21:47:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.49
% 0.18/0.49 SPASS V 3.9
% 0.18/0.49 SPASS beiseite: Proof found.
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 SPASS derived 218 clauses, backtracked 0 clauses, performed 0 splits and kept 198 clauses.
% 0.18/0.49 SPASS allocated 98110 KBytes.
% 0.18/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.49 0:00:00.04 for the input.
% 0.18/0.49 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.49 0:00:00.00 for inferences.
% 0.18/0.49 0:00:00.00 for the backtracking.
% 0.18/0.49 0:00:00.02 for the reduction.
% 0.18/0.49
% 0.18/0.49
% 0.18/0.49 Here is a proof with depth 2, length 26 :
% 0.18/0.49 % SZS output start Refutation
% See solution above
% 0.18/0.49 Formulae used in the proof : principia_op_implies_or principia_op_and principia_modus_ponens principia_r1 principia_r3 rosser_kn1 kn1 r1 r3 op_implies_or modus_ponens principia_r2 r2 op_and
% 0.18/0.49
%------------------------------------------------------------------------------