%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 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 01:06:46 PM UTC 2026
% Result : Unsatisfiable 6.88s 7.19s
% Output : Refutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 18 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 9 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('LCL096-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),
file('LCL096-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y)),
file('LCL096-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x)))),
file('LCL096-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
file('LCL096-1.p',unknown),
[] ).
cnf(14,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),w),x))
| is_a_theorem(equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(48,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z),equivalent(equivalent(equivalent(equivalent(v,w),x),y),z))),
inference(sor,[status(thm)],[14,3]),
[iquote('0:SoR:14.0,3.0')] ).
cnf(49,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),equivalent(equivalent(equivalent(v,w),x),y))),
inference(sor,[status(thm)],[14,2]),
[iquote('0:SoR:14.0,2.0')] ).
cnf(118,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y))
| is_a_theorem(equivalent(equivalent(equivalent(v,w),x),y)) ),
inference(res,[status(thm),theory(equality)],[49,1]),
[iquote('0:Res:49.0,1.1')] ).
cnf(168,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),y),z))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),x),y),z)) ),
inference(res,[status(thm),theory(equality)],[48,1]),
[iquote('0:Res:48.0,1.1')] ).
cnf(1804,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w))),y),y)),
inference(sor,[status(thm)],[168,3]),
[iquote('0:SoR:168.0,3.0')] ).
cnf(5266,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,v),u)),w),w)),
inference(sor,[status(thm)],[118,1804]),
[iquote('0:SoR:118.0,1804.0')] ).
cnf(5286,plain,
$false,
inference(unc,[status(thm)],[5266,5]),
[iquote('0:UnC:5266.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n028.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 15:24:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 6.88/7.19
% 6.88/7.19 SPASS V 3.9
% 6.88/7.19 SPASS beiseite: Proof found.
% 6.88/7.19 % SZS status Theorem
% 6.88/7.19 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/7.19 SPASS derived 5274 clauses, backtracked 0 clauses, performed 0 splits and kept 2357 clauses.
% 6.88/7.19 SPASS allocated 83813 KBytes.
% 6.88/7.19 SPASS spent 0:00:06.70 on the problem.
% 6.88/7.19 0:00:00.06 for the input.
% 6.88/7.19 0:00:00.00 for the FLOTTER CNF translation.
% 6.88/7.19 0:00:00.27 for inferences.
% 6.88/7.19 0:00:00.00 for the backtracking.
% 6.88/7.19 0:00:06.27 for the reduction.
% 6.88/7.19
% 6.88/7.19
% 6.88/7.19 Here is a proof with depth 5, length 13 :
% 6.88/7.19 % SZS output start Refutation
% See solution above
% 6.88/7.19 Formulae used in the proof : condensed_detachment lg_2 lg_3 lg_4 prove_lg_1
% 6.88/7.19
%------------------------------------------------------------------------------