%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 0.07s 0.61s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 26 ( 19 unt; 0 nHn; 26 RR)
% Number of literals : 34 ( 0 equ; 9 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('LCL023-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,v),equivalent(u,w)))),
file('LCL023-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
file('LCL023-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,v),equivalent(u,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(equivalent(v,w),equivalent(x,v))),equivalent(equivalent(x,w),u))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(10,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(x,v))))
| is_a_theorem(equivalent(equivalent(x,w),u)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(equivalent(x,v),equivalent(w,x))))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
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(13,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(v,w),u))),
inference(sor,[status(thm)],[7,12]),
[iquote('0:SoR:7.0,12.0')] ).
cnf(17,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(w,v)))),
inference(sor,[status(thm)],[10,13]),
[iquote('0:SoR:10.0,13.0')] ).
cnf(20,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(v,v))),
inference(sor,[status(thm)],[10,17]),
[iquote('0:SoR:10.0,17.0')] ).
cnf(25,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,v)),equivalent(equivalent(w,w),u))),
inference(sor,[status(thm)],[7,20]),
[iquote('0:SoR:7.0,20.0')] ).
cnf(27,plain,
( ~ is_a_theorem(equivalent(u,u))
| is_a_theorem(equivalent(v,v)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(28,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[27,20]),
[iquote('0:SoR:27.0,20.0')] ).
cnf(31,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(v,u))),
inference(sor,[status(thm)],[7,28]),
[iquote('0:SoR:7.0,28.0')] ).
cnf(36,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(res,[status(thm),theory(equality)],[31,1]),
[iquote('0:Res:31.0,1.1')] ).
cnf(38,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(w,u),v))),
inference(sor,[status(thm)],[10,11]),
[iquote('0:SoR:10.0,11.0')] ).
cnf(51,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,v)))
| is_a_theorem(equivalent(equivalent(w,w),u)) ),
inference(res,[status(thm),theory(equality)],[25,1]),
[iquote('0:Res:25.0,1.1')] ).
cnf(58,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(v,equivalent(u,w)),w))),
inference(sor,[status(thm)],[10,38]),
[iquote('0:SoR:10.0,38.0')] ).
cnf(111,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),w),equivalent(v,u))),
inference(sor,[status(thm)],[36,58]),
[iquote('0:SoR:36.0,58.0')] ).
cnf(272,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(equivalent(v,equivalent(v,w)),w))),
inference(sor,[status(thm)],[51,111]),
[iquote('0:SoR:51.0,111.0')] ).
cnf(330,plain,
( ~ is_a_theorem(equivalent(u,u))
| is_a_theorem(equivalent(equivalent(v,equivalent(v,w)),w)) ),
inference(res,[status(thm),theory(equality)],[272,1]),
[iquote('0:Res:272.0,1.1')] ).
cnf(331,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(u,v)),v)),
inference(ssi,[status(thm)],[330,28]),
[iquote('0:SSi:330.0,28.0')] ).
cnf(335,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,equivalent(w,v)),u))),
inference(sor,[status(thm)],[7,331]),
[iquote('0:SoR:7.0,331.0')] ).
cnf(1221,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(u,v),w))),
inference(sor,[status(thm)],[10,335]),
[iquote('0:SoR:10.0,335.0')] ).
cnf(1229,plain,
$false,
inference(unc,[status(thm)],[1221,3]),
[iquote('0:UnC:1221.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 5 18:41:42 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.07/0.61
% 0.07/0.61 SPASS V 3.9
% 0.07/0.61 SPASS beiseite: Proof found.
% 0.07/0.61 % SZS status Theorem
% 0.07/0.61 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.61 SPASS derived 1218 clauses, backtracked 0 clauses, performed 0 splits and kept 671 clauses.
% 0.07/0.61 SPASS allocated 77630 KBytes.
% 0.07/0.61 SPASS spent 0:00:00.29 on the problem.
% 0.07/0.61 0:00:00.03 for the input.
% 0.07/0.61 0:00:00.00 for the FLOTTER CNF translation.
% 0.07/0.61 0:00:00.02 for inferences.
% 0.07/0.61 0:00:00.00 for the backtracking.
% 0.07/0.61 0:00:00.22 for the reduction.
% 0.07/0.61
% 0.07/0.61
% 0.07/0.61 Here is a proof with depth 16, length 26 :
% 0.07/0.61 % SZS output start Refutation
% See solution above
% 0.07/0.61 Formulae used in the proof : condensed_detachment yql prove_ec_2
% 0.07/0.61
%------------------------------------------------------------------------------