%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL169-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 01:06:54 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(implies__dfg(p,not__dfg(p)),not__dfg(p))),
file('LCL169-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL169-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL169-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL169-3.p',unknown),
[] ).
cnf(10,plain,
~ axiom(implies__dfg(implies__dfg(p,not__dfg(p)),not__dfg(p))),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.0')] ).
cnf(12,plain,
axiom(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(15,plain,
$false,
inference(unc,[status(thm)],[12,10]),
[iquote('0:UnC:12.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL169-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n028.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 01:45:59 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.22/0.47
% 0.22/0.47 SPASS V 3.9
% 0.22/0.47 SPASS beiseite: Proof found.
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.47 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.22/0.47 SPASS allocated 75600 KBytes.
% 0.22/0.47 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.47 0:00:00.06 for the input.
% 0.22/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.47 0:00:00.00 for inferences.
% 0.22/0.47 0:00:00.00 for the backtracking.
% 0.22/0.47 0:00:00.00 for the reduction.
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 Here is a proof with depth 1, length 7 :
% 0.22/0.47 % SZS output start Refutation
% See solution above
% 0.22/0.47 Formulae used in the proof : prove_this axiom_1_2 implies_definition rule_1
% 0.22/0.47
%------------------------------------------------------------------------------