%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 01:07:37 PM UTC 2026
% Result : Theorem 0.24s 0.62s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 12 unt; 0 nHn; 19 RR)
% Number of literals : 26 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL483+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL483+1.p',unknown),
[] ).
cnf(4,axiom,
op_implies_or,
file('LCL483+1.p',unknown),
[] ).
cnf(10,axiom,
r3,
file('LCL483+1.p',unknown),
[] ).
cnf(14,axiom,
~ modus_tollens,
file('LCL483+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ r3
| is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
file('LCL483+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL483+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL483+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(skc59),not__dfg(skc60)),implies__dfg(skc60,skc59)))
| modus_tollens ),
file('LCL483+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL483+1.p',unknown),
[] ).
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(81,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(84,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[81,58]),
[iquote('0:Rew:81.0,58.1')] ).
cnf(85,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[84,1]),
[iquote('0:MRR:84.0,1.0')] ).
cnf(91,plain,
( ~ is_a_theorem(implies__dfg(or__dfg(skc59,not__dfg(skc60)),implies__dfg(skc60,skc59)))
| modus_tollens ),
inference(rew,[status(thm),theory(equality)],[85,55]),
[iquote('0:Rew:85.0,55.0')] ).
cnf(92,plain,
~ is_a_theorem(implies__dfg(or__dfg(skc59,not__dfg(skc60)),implies__dfg(skc60,skc59))),
inference(mrr,[status(thm)],[91,14]),
[iquote('0:MRR:91.1,14.0')] ).
cnf(135,plain,
is_a_theorem(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[78,79]),
[iquote('0:SpR:78.0,79.0')] ).
cnf(137,plain,
$false,
inference(unc,[status(thm)],[135,92]),
[iquote('0:UnC:135.0,92.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.43 % Computer : n005.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Sat Sep 5 10:29:36 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.24/0.62
% 0.24/0.62 SPASS V 3.9
% 0.24/0.62 SPASS beiseite: Proof found.
% 0.24/0.62 % SZS status Theorem
% 0.24/0.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.62 SPASS derived 37 clauses, backtracked 0 clauses, performed 0 splits and kept 83 clauses.
% 0.24/0.62 SPASS allocated 97856 KBytes.
% 0.24/0.62 SPASS spent 0:00:00.17 on the problem.
% 0.24/0.62 0:00:00.06 for the input.
% 0.24/0.62 0:00:00.06 for the FLOTTER CNF translation.
% 0.24/0.62 0:00:00.00 for inferences.
% 0.24/0.62 0:00:00.00 for the backtracking.
% 0.24/0.62 0:00:00.01 for the reduction.
% 0.24/0.62
% 0.24/0.62
% 0.24/0.62 Here is a proof with depth 1, length 19 :
% 0.24/0.62 % SZS output start Refutation
% See solution above
% 0.24/0.62 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and principia_op_implies_or principia_r3 hilbert_modus_tollens r3 op_implies_or op_implies_and modus_tollens op_or
% 0.24/0.62
%------------------------------------------------------------------------------