%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 0.16s 6.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 21 RR)
% Number of literals : 30 ( 0 equ; 10 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 : 8 ( 8 usr; 7 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('LCL010-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(w,v)))),
file('LCL010-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))),
file('LCL010-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(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(equivalent(equivalent(equivalent(u,v),w),equivalent(w,equivalent(equivalent(u,x),equivalent(x,v))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(w,equivalent(equivalent(u,x),equivalent(x,v)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(v,w)),equivalent(equivalent(u,x),equivalent(x,w)))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(v,w)))
| is_a_theorem(equivalent(equivalent(u,x),equivalent(x,w))) ),
inference(res,[status(thm),theory(equality)],[12,1]),
[iquote('0:Res:12.0,1.1')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,u),v),equivalent(v,equivalent(w,w)))),
inference(sor,[status(thm)],[15,12]),
[iquote('0:SoR:15.0,12.0')] ).
cnf(22,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),v))
| is_a_theorem(equivalent(v,equivalent(w,w))) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(34,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,u),equivalent(v,v)),equivalent(w,w))),
inference(sor,[status(thm)],[22,17]),
[iquote('0:SoR:22.0,17.0')] ).
cnf(44,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(v,v))),
inference(sor,[status(thm)],[22,34]),
[iquote('0:SoR:22.0,34.0')] ).
cnf(45,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),equivalent(v,v)))
| is_a_theorem(equivalent(w,w)) ),
inference(res,[status(thm),theory(equality)],[34,1]),
[iquote('0:Res:34.0,1.1')] ).
cnf(46,plain,
is_a_theorem(equivalent(u,u)),
inference(mrr,[status(thm)],[45,44]),
[iquote('0:MRR:45.0,44.0')] ).
cnf(52,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
inference(sor,[status(thm)],[7,46]),
[iquote('0:SoR:7.0,46.0')] ).
cnf(62,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(w,equivalent(v,u)))),
inference(sor,[status(thm)],[7,52]),
[iquote('0:SoR:7.0,52.0')] ).
cnf(66,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[52,1]),
[iquote('0:Res:52.0,1.1')] ).
cnf(77,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(v,w)),equivalent(u,w))),
inference(sor,[status(thm)],[66,2]),
[iquote('0:SoR:66.0,2.0')] ).
cnf(118,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(w,equivalent(v,u))) ),
inference(res,[status(thm),theory(equality)],[62,1]),
[iquote('0:Res:62.0,1.1')] ).
cnf(3939,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(u,w)))),
inference(sor,[status(thm)],[118,77]),
[iquote('0:SoR:118.0,77.0')] ).
cnf(4077,plain,
$false,
inference(unc,[status(thm)],[3939,3]),
[iquote('0:UnC:3939.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n013.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 : Sat Sep 5 12:39:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.16/6.20
% 0.16/6.20 SPASS V 3.9
% 0.16/6.20 SPASS beiseite: Proof found.
% 0.16/6.20 % SZS status Theorem
% 0.16/6.20 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/6.20 SPASS derived 4065 clauses, backtracked 0 clauses, performed 0 splits and kept 2145 clauses.
% 0.16/6.20 SPASS allocated 82318 KBytes.
% 0.16/6.20 SPASS spent 0:00:05.70 on the problem.
% 0.16/6.20 0:00:00.06 for the input.
% 0.16/6.20 0:00:00.00 for the FLOTTER CNF translation.
% 0.16/6.20 0:00:00.23 for inferences.
% 0.16/6.20 0:00:00.00 for the backtracking.
% 0.16/6.20 0:00:05.34 for the reduction.
% 0.16/6.20
% 0.16/6.20
% 0.16/6.20 Here is a proof with depth 13, length 21 :
% 0.16/6.20 % SZS output start Refutation
% See solution above
% 0.16/6.20 Formulae used in the proof : condensed_detachment yqf prove_yql
% 0.16/6.20
%------------------------------------------------------------------------------