%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 01:06:36 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.35s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 4 unt; 0 nHn; 8 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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('LCL013-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(u,w)),equivalent(w,v)))),
file('LCL013-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file('LCL013-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(u,w)),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,equivalent(u,w)))
| is_a_theorem(equivalent(w,v)) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.1')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(equivalent(w,u),v)) ),
inference(sor,[status(thm)],[8,2]),
[iquote('0:SoR:8.1,2.0')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(v,equivalent(w,u)))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(13,plain,
$false,
inference(unc,[status(thm)],[12,3]),
[iquote('0:UnC:12.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 4 14:00:28 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.08/0.35
% 0.08/0.35 SPASS V 3.9
% 0.08/0.35 SPASS beiseite: Proof found.
% 0.08/0.35 % SZS status Theorem
% 0.08/0.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.08/0.35 SPASS allocated 75600 KBytes.
% 0.08/0.35 SPASS spent 0:00:00.05 on the problem.
% 0.08/0.35 0:00:00.03 for the input.
% 0.08/0.35 0:00:00.00 for the FLOTTER CNF translation.
% 0.08/0.35 0:00:00.00 for inferences.
% 0.08/0.35 0:00:00.00 for the backtracking.
% 0.08/0.35 0:00:00.00 for the reduction.
% 0.08/0.35
% 0.08/0.35
% 0.08/0.35 Here is a proof with depth 4, length 8 :
% 0.08/0.35 % SZS output start Refutation
% See solution above
% 0.08/0.35 Formulae used in the proof : condensed_detachment xgf prove_um
% 0.08/0.35
%------------------------------------------------------------------------------