%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 01:06:55 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.50s
% Output : Refutation 0.23s
% 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 : 3 ( 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(q,implies__dfg(p,q))),
file('LCL170-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL170-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL170-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL170-3.p',unknown),
[] ).
cnf(10,plain,
~ axiom(implies__dfg(q,implies__dfg(p,q))),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.0')] ).
cnf(14,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(16,plain,
$false,
inference(unc,[status(thm)],[14,10]),
[iquote('0:UnC:14.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 22:55:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.23/0.50
% 0.23/0.50 SPASS V 3.9
% 0.23/0.50 SPASS beiseite: Proof found.
% 0.23/0.50 % SZS status Theorem
% 0.23/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.50 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.23/0.50 SPASS allocated 75602 KBytes.
% 0.23/0.50 SPASS spent 0:00:00.09 on the problem.
% 0.23/0.50 0:00:00.05 for the input.
% 0.23/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.50 0:00:00.00 for inferences.
% 0.23/0.50 0:00:00.00 for the backtracking.
% 0.23/0.50 0:00:00.00 for the reduction.
% 0.23/0.50
% 0.23/0.50
% 0.23/0.50 Here is a proof with depth 1, length 7 :
% 0.23/0.50 % SZS output start Refutation
% See solution above
% 0.23/0.50 Formulae used in the proof : prove_this axiom_1_3 implies_definition rule_1
% 0.23/0.50
%------------------------------------------------------------------------------