%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:07:39 PM UTC 2026
% Result : Theorem 0.31s 0.58s
% Output : Refutation 0.31s
% 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
% 0.00/0.03 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 02:52:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.31/0.58
% 0.31/0.58 SPASS V 3.9
% 0.31/0.58 SPASS beiseite: Proof found.
% 0.31/0.58 % SZS status Theorem
% 0.31/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.58 SPASS derived 218 clauses, backtracked 0 clauses, performed 0 splits and kept 198 clauses.
% 0.31/0.58 SPASS allocated 98110 KBytes.
% 0.31/0.58 SPASS spent 0:00:00.20 on the problem.
% 0.31/0.58 0:00:00.06 for the input.
% 0.31/0.58 0:00:00.06 for the FLOTTER CNF translation.
% 0.31/0.58 0:00:00.01 for inferences.
% 0.31/0.58 0:00:00.00 for the backtracking.
% 0.31/0.58 0:00:00.03 for the reduction.
% 0.31/0.58
% 0.31/0.58
% 0.31/0.58 Here is a proof with depth 2, length 26 :
% 0.31/0.58 % SZS output start Refutation
% See solution above
% 0.31/0.58 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
% 0.31/0.58
%------------------------------------------------------------------------------