%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 01:06:35 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.48s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL007-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
file('LCL007-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(u,equivalent(v,w)))),
file('LCL007-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
file('LCL007-1.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(u,v),w))),
inference(sor,[status(thm)],[9,3]),
[iquote('0:SoR:9.0,3.0')] ).
cnf(13,plain,
$false,
inference(unc,[status(thm)],[11,4]),
[iquote('0:UnC:11.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 17:54:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.24/0.48
% 0.24/0.48 SPASS V 3.9
% 0.24/0.48 SPASS beiseite: Proof found.
% 0.24/0.48 % SZS status Theorem
% 0.24/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.48 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 7 clauses.
% 0.24/0.48 SPASS allocated 75596 KBytes.
% 0.24/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.24/0.48 0:00:00.06 for the input.
% 0.24/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.48 0:00:00.00 for inferences.
% 0.24/0.48 0:00:00.00 for the backtracking.
% 0.24/0.48 0:00:00.00 for the reduction.
% 0.24/0.48
% 0.24/0.48
% 0.24/0.48 Here is a proof with depth 2, length 7 :
% 0.24/0.48 % SZS output start Refutation
% See solution above
% 0.24/0.48 Formulae used in the proof : condensed_detachment ec_4 ec_5 prove_ec_2
% 0.24/0.48
%------------------------------------------------------------------------------