%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL097-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n001.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 0.31s 0.62s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 13 RR)
% Number of literals : 17 ( 0 equ; 5 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 : 13 ( 13 usr; 12 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('LCL097-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w)),x),x)),
file('LCL097-1.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('LCL097-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('LCL097-1.p',unknown),
[] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y))
| is_a_theorem(y) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[10,3]),
[iquote('0:SoR:10.0,3.0')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,v))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x))),
inference(sor,[status(thm)],[10,12]),
[iquote('0:SoR:10.0,12.0')] ).
cnf(21,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(equivalent(equivalent(w,x),equivalent(w,y)),u),equivalent(equivalent(x,y),v)))),
inference(sor,[status(thm)],[10,11]),
[iquote('0:SoR:10.0,11.0')] ).
cnf(36,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x))
| is_a_theorem(equivalent(equivalent(v,w),x)) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.0,1.1')] ).
cnf(59,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(x,y),equivalent(x,z)),x1)),equivalent(equivalent(v,w),equivalent(equivalent(y,z),x1)))),
inference(sor,[status(thm)],[10,21]),
[iquote('0:SoR:10.0,21.0')] ).
cnf(759,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x)))),
inference(sor,[status(thm)],[36,59]),
[iquote('0:SoR:36.0,59.0')] ).
cnf(765,plain,
$false,
inference(unc,[status(thm)],[759,4]),
[iquote('0:UnC:759.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL097-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 5 18:52:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.31/0.62
% 0.31/0.62 SPASS V 3.9
% 0.31/0.62 SPASS beiseite: Proof found.
% 0.31/0.62 % SZS status Theorem
% 0.31/0.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.62 SPASS derived 756 clauses, backtracked 0 clauses, performed 0 splits and kept 538 clauses.
% 0.31/0.62 SPASS allocated 77503 KBytes.
% 0.31/0.62 SPASS spent 0:00:00.23 on the problem.
% 0.31/0.62 0:00:00.03 for the input.
% 0.31/0.62 0:00:00.00 for the FLOTTER CNF translation.
% 0.31/0.62 0:00:00.02 for inferences.
% 0.31/0.62 0:00:00.00 for the backtracking.
% 0.31/0.62 0:00:00.15 for the reduction.
% 0.31/0.62
% 0.31/0.62
% 0.31/0.62 Here is a proof with depth 5, length 13 :
% 0.31/0.62 % SZS output start Refutation
% See solution above
% 0.31/0.62 Formulae used in the proof : condensed_detachment lg_2 lg_3 prove_lg_4
% 0.31/0.62
%------------------------------------------------------------------------------