%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL011-1 : 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 01:06:36 PM UTC 2026
% Result : Unsatisfiable 14.36s 14.63s
% Output : Refutation 14.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 40 ( 25 unt; 0 nHn; 40 RR)
% Number of literals : 58 ( 0 equ; 19 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('LCL011-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(v,w)))),
file('LCL011-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
file('LCL011-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,u),equivalent(v,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(equivalent(x,v),equivalent(w,x)),u))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(equivalent(equivalent(x,v),equivalent(w,x)),u)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(x,v))),equivalent(y,u)),equivalent(y,equivalent(w,x)))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(12,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(x,v),u)),equivalent(w,x))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(13,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(equivalent(y,w),v))),equivalent(equivalent(x,y),u))),
inference(sor,[status(thm)],[7,12]),
[iquote('0:SoR:7.0,12.0')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(x,v),u)))
| is_a_theorem(equivalent(w,x)) ),
inference(res,[status(thm),theory(equality)],[12,1]),
[iquote('0:Res:12.0,1.1')] ).
cnf(16,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(u,v)))),
inference(sor,[status(thm)],[15,8]),
[iquote('0:SoR:15.0,8.0')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,equivalent(v,w)),u))),
inference(sor,[status(thm)],[7,16]),
[iquote('0:SoR:7.0,16.0')] ).
cnf(18,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(w,v),u)),w)),
inference(sor,[status(thm)],[10,16]),
[iquote('0:SoR:10.0,16.0')] ).
cnf(19,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(u,v))) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(26,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(u,v)) ),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('0:Res:19.1,1.1')] ).
cnf(34,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,equivalent(v,w)),u)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(37,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),u)))
| is_a_theorem(w) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(38,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(equivalent(w,x),equivalent(y,w))),equivalent(z,v))),equivalent(equivalent(z,equivalent(x,y)),u))),
inference(sor,[status(thm)],[7,11]),
[iquote('0:SoR:7.0,11.0')] ).
cnf(39,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(w,x),u)),equivalent(equivalent(y,equivalent(equivalent(z,w),equivalent(x,z))),equivalent(v,y)))),
inference(sor,[status(thm)],[10,11]),
[iquote('0:SoR:10.0,11.0')] ).
cnf(82,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[37,8]),
[iquote('0:SoR:37.0,8.0')] ).
cnf(84,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,u)),v)),
inference(sor,[status(thm)],[34,82]),
[iquote('0:SoR:34.0,82.0')] ).
cnf(85,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
inference(sor,[status(thm)],[7,82]),
[iquote('0:SoR:7.0,82.0')] ).
cnf(91,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,equivalent(w,v))),equivalent(w,u))),
inference(sor,[status(thm)],[7,84]),
[iquote('0:SoR:7.0,84.0')] ).
cnf(94,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,u)))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[84,1]),
[iquote('0:Res:84.0,1.1')] ).
cnf(105,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[85,1]),
[iquote('0:Res:85.0,1.1')] ).
cnf(108,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[94,26]),
[iquote('0:SoR:94.0,26.2')] ).
cnf(211,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),v),u)),
inference(sor,[status(thm)],[15,91]),
[iquote('0:SoR:15.0,91.0')] ).
cnf(217,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(u,v),v))),
inference(sor,[status(thm)],[105,211]),
[iquote('0:SoR:105.0,211.0')] ).
cnf(228,plain,
is_a_theorem(equivalent(u,equivalent(v,equivalent(v,u)))),
inference(sor,[status(thm)],[15,217]),
[iquote('0:SoR:15.0,217.0')] ).
cnf(235,plain,
( ~ is_a_theorem(equivalent(u,equivalent(u,v)))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[108,228]),
[iquote('0:SoR:108.0,228.0')] ).
cnf(297,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,x)),equivalent(equivalent(y,w),v))))
| is_a_theorem(equivalent(equivalent(x,y),u)) ),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.1')] ).
cnf(413,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,v),u))),
inference(sor,[status(thm)],[235,39]),
[iquote('0:SoR:235.0,39.0')] ).
cnf(418,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[108,413]),
[iquote('0:SoR:108.0,413.0')] ).
cnf(476,plain,
is_a_theorem(equivalent(u,equivalent(u,equivalent(v,v)))),
inference(sor,[status(thm)],[418,228]),
[iquote('0:SoR:418.0,228.0')] ).
cnf(496,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(equivalent(w,x),equivalent(y,w))),equivalent(z,v))))
| is_a_theorem(equivalent(equivalent(z,equivalent(x,y)),u)) ),
inference(res,[status(thm),theory(equality)],[38,1]),
[iquote('0:Res:38.0,1.1')] ).
cnf(512,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(v,equivalent(w,w)),u))),
inference(sor,[status(thm)],[7,476]),
[iquote('0:SoR:7.0,476.0')] ).
cnf(2751,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(equivalent(v,u),w),w))),
inference(sor,[status(thm)],[297,512]),
[iquote('0:SoR:297.0,512.0')] ).
cnf(3971,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(v,w)),equivalent(u,w))),
inference(sor,[status(thm)],[496,2751]),
[iquote('0:SoR:496.0,2751.0')] ).
cnf(5777,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(w,v)))),
inference(sor,[status(thm)],[105,3971]),
[iquote('0:SoR:105.0,3971.0')] ).
cnf(5797,plain,
$false,
inference(unc,[status(thm)],[5777,3]),
[iquote('0:UnC:5777.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL011-1 : 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 14:26:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 14.36/14.63
% 14.36/14.63 SPASS V 3.9
% 14.36/14.63 SPASS beiseite: Proof found.
% 14.36/14.63 % SZS status Theorem
% 14.36/14.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.36/14.63 SPASS derived 5788 clauses, backtracked 0 clauses, performed 0 splits and kept 3450 clauses.
% 14.36/14.63 SPASS allocated 86477 KBytes.
% 14.36/14.63 SPASS spent 0:0:14.06 on the problem.
% 14.36/14.63 0:00:00.06 for the input.
% 14.36/14.63 0:00:00.00 for the FLOTTER CNF translation.
% 14.36/14.63 0:00:00.41 for inferences.
% 14.36/14.63 0:00:00.00 for the backtracking.
% 14.36/14.63 0:0:13.48 for the reduction.
% 14.36/14.63
% 14.36/14.63
% 14.36/14.63 Here is a proof with depth 22, length 40 :
% 14.36/14.63 % SZS output start Refutation
% See solution above
% 14.36/14.63 Formulae used in the proof : condensed_detachment yqj prove_yqf
% 14.36/14.63
%------------------------------------------------------------------------------