%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 01:07:04 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 6 unt; 0 nHn; 10 RR)
% Number of literals : 16 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(not__dfg(p),implies__dfg(q,implies__dfg(implies__dfg(p,q),q)))),
file('LCL212-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL212-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL212-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL212-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL212-3.p',unknown),
[] ).
cnf(13,plain,
axiom(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(19,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(24,plain,
( ~ theorem(u)
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,13]),
[iquote('0:SoR:19.0,13.0')] ).
cnf(31,plain,
~ theorem(implies__dfg(q,implies__dfg(implies__dfg(p,q),q))),
inference(res,[status(thm),theory(equality)],[24,1]),
[iquote('0:Res:24.1,1.0')] ).
cnf(32,plain,
$false,
inference(ssi,[status(thm)],[31,8,13]),
[iquote('0:SSi:31.0,8.0,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n013.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 20:15:20 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.42
% 0.13/0.42 SPASS V 3.9
% 0.13/0.42 SPASS beiseite: Proof found.
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42 SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 25 clauses.
% 0.13/0.42 SPASS allocated 75640 KBytes.
% 0.13/0.42 SPASS spent 0:00:00.05 on the problem.
% 0.13/0.42 0:00:00.03 for the input.
% 0.13/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.42 0:00:00.00 for inferences.
% 0.13/0.42 0:00:00.00 for the backtracking.
% 0.13/0.42 0:00:00.00 for the reduction.
% 0.13/0.42
% 0.13/0.42
% 0.13/0.42 Here is a proof with depth 3, length 10 :
% 0.13/0.42 % SZS output start Refutation
% See solution above
% 0.13/0.42 Formulae used in the proof : prove_this axiom_1_3 implies_definition rule_1 rule_2
% 0.13/0.42
%------------------------------------------------------------------------------