%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:07:28 PM UTC 2026
% Result : Unsatisfiable 1.05s 1.33s
% Output : Refutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 37 ( 5 unt; 0 nHn; 37 RR)
% Number of literals : 100 ( 0 equ; 64 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 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('LCL416-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(u,v),equivalent(w,v)),w))),
file('LCL416-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(a,a)),
file('LCL416-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),w)) ),
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(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(w) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.1')] ).
cnf(9,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(v,w))) ),
inference(sor,[status(thm)],[8,2]),
[iquote('0:SoR:8.1,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| is_a_theorem(v) ),
inference(sor,[status(thm)],[8,9]),
[iquote('0:SoR:8.1,9.1')] ).
cnf(11,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.1,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(w,equivalent(v,w))) ),
inference(sor,[status(thm)],[11,9]),
[iquote('0:SoR:11.1,9.1')] ).
cnf(17,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(x,w)),x))) ),
inference(sor,[status(thm)],[11,2]),
[iquote('0:SoR:11.1,2.0')] ).
cnf(18,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(x,equivalent(equivalent(v,w),x))) ),
inference(sor,[status(thm)],[15,9]),
[iquote('0:SoR:15.0,9.1')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(equivalent(equivalent(equivalent(u,w),equivalent(x,w)),x),v))) ),
inference(sor,[status(thm)],[15,2]),
[iquote('0:SoR:15.0,2.0')] ).
cnf(28,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(equivalent(v,equivalent(u,w)),x),equivalent(w,x))) ),
inference(sor,[status(thm)],[8,17]),
[iquote('0:SoR:8.1,17.1')] ).
cnf(32,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),equivalent(x,w)),x),u)) ),
inference(sor,[status(thm)],[10,20]),
[iquote('0:SoR:10.0,20.1')] ).
cnf(44,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(w,equivalent(equivalent(x,equivalent(v,x)),w))) ),
inference(sor,[status(thm)],[18,9]),
[iquote('0:SoR:18.0,9.1')] ).
cnf(93,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[8,28]),
[iquote('0:SoR:8.1,28.2')] ).
cnf(102,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| ~ is_a_theorem(v)
| ~ is_a_theorem(u)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[93,9]),
[iquote('0:SoR:93.0,9.1')] ).
cnf(113,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(equivalent(w,v))
| ~ is_a_theorem(w)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[102,7]),
[iquote('0:SoR:102.0,7.1')] ).
cnf(151,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),w))
| ~ is_a_theorem(u)
| ~ is_a_theorem(x)
| is_a_theorem(equivalent(y,equivalent(x,y))) ),
inference(sor,[status(thm)],[15,32]),
[iquote('0:SoR:15.0,32.2')] ).
cnf(164,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(v,w))) ),
inference(ssi,[status(thm)],[151,7]),
[iquote('0:SSi:151.0,7.1')] ).
cnf(179,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(u,v))) ),
inference(ems,[status(thm)],[164,2]),
[iquote('0:EmS:164.0,2.0')] ).
cnf(194,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(v,u)) ),
inference(sor,[status(thm)],[10,179]),
[iquote('0:SoR:10.0,179.1')] ).
cnf(228,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(w)
| ~ is_a_theorem(w)
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[113,194]),
[iquote('0:SoR:113.1,194.2')] ).
cnf(240,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(w)
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(obv,[status(thm),theory(equality)],[228]),
[iquote('0:Obv:228.1')] ).
cnf(241,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(con,[status(thm)],[240]),
[iquote('0:Con:240.1')] ).
cnf(272,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),w))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[241,2]),
[iquote('0:SoR:241.0,2.0')] ).
cnf(291,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| ~ is_a_theorem(w)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[272,194]),
[iquote('0:SoR:272.0,194.2')] ).
cnf(442,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(equivalent(x,equivalent(v,x)),w))) ),
inference(sor,[status(thm)],[44,194]),
[iquote('0:SoR:44.0,194.2')] ).
cnf(453,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(w,equivalent(equivalent(x,equivalent(v,x)),w))) ),
inference(obv,[status(thm),theory(equality)],[442]),
[iquote('0:Obv:442.0')] ).
cnf(454,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(equivalent(w,equivalent(u,w)),v))) ),
inference(con,[status(thm)],[453]),
[iquote('0:Con:453.0')] ).
cnf(463,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(w,equivalent(v,w)),u)) ),
inference(sor,[status(thm)],[10,454]),
[iquote('0:SoR:10.0,454.1')] ).
cnf(542,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(v,w)))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[291,2]),
[iquote('0:SoR:291.0,2.0')] ).
cnf(721,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,equivalent(u,equivalent(w,v))))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[542,463]),
[iquote('0:SoR:542.0,463.2')] ).
cnf(1066,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),v)))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[721,2]),
[iquote('0:SoR:721.1,2.0')] ).
cnf(1076,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),u),v)),
inference(sor,[status(thm)],[1066,2]),
[iquote('0:SoR:1066.0,2.0')] ).
cnf(1125,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[272,1076]),
[iquote('0:SoR:272.0,1076.0')] ).
cnf(1147,plain,
$false,
inference(unc,[status(thm)],[1125,3]),
[iquote('0:UnC:1125.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n027.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 12:14:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 1.05/1.33
% 1.05/1.33 SPASS V 3.9
% 1.05/1.33 SPASS beiseite: Proof found.
% 1.05/1.33 % SZS status Theorem
% 1.05/1.33 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/1.33 SPASS derived 1006 clauses, backtracked 0 clauses, performed 0 splits and kept 536 clauses.
% 1.05/1.33 SPASS allocated 77194 KBytes.
% 1.05/1.33 SPASS spent 0:00:00.94 on the problem.
% 1.05/1.33 0:00:00.06 for the input.
% 1.05/1.33 0:00:00.00 for the FLOTTER CNF translation.
% 1.05/1.33 0:00:00.04 for inferences.
% 1.05/1.33 0:00:00.00 for the backtracking.
% 1.05/1.33 0:00:00.80 for the reduction.
% 1.05/1.33
% 1.05/1.33
% 1.05/1.33 Here is a proof with depth 18, length 37 :
% 1.05/1.33 % SZS output start Refutation
% See solution above
% 1.05/1.33 Formulae used in the proof : condensed_detachment xcb prove_reflexivity
% 1.05/1.33
%------------------------------------------------------------------------------