%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 01:06:50 PM UTC 2026
% Result : Unsatisfiable 210.54s 210.94s
% Output : Refutation 210.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 42 ( 27 unt; 0 nHn; 42 RR)
% Number of literals : 59 ( 0 equ; 18 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 : 11 ( 11 usr; 10 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('LCL131-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(equivalent(v,w),equivalent(x,w)),equivalent(v,x))),u)),
file('LCL131-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('LCL131-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(v,w),equivalent(x,w)),equivalent(v,x))))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(u,w)),equivalent(equivalent(equivalent(x,y),equivalent(z,y)),equivalent(x,z)))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(u,w))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),x),equivalent(equivalent(u,w),x))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(12,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(equivalent(u,w)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(13,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(equivalent(u,x),equivalent(w,x)))),
inference(sor,[status(thm)],[12,8]),
[iquote('0:SoR:12.0,8.0')] ).
cnf(15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),w)),equivalent(u,x))),
inference(sor,[status(thm)],[7,11]),
[iquote('0:SoR:7.0,11.0')] ).
cnf(17,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),x))
| is_a_theorem(equivalent(equivalent(u,w),x)) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(18,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(u,v))),
inference(sor,[status(thm)],[12,13]),
[iquote('0:SoR:12.0,13.0')] ).
cnf(19,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,v)))
| is_a_theorem(equivalent(equivalent(u,x),equivalent(w,x))) ),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.1')] ).
cnf(20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),x),y),equivalent(equivalent(equivalent(u,w),x),y))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(23,plain,
is_a_theorem(equivalent(u,u)),
inference(sor,[status(thm)],[12,18]),
[iquote('0:SoR:12.0,18.0')] ).
cnf(28,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(v,w)))),
inference(sor,[status(thm)],[17,13]),
[iquote('0:SoR:17.0,13.0')] ).
cnf(32,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(x,w))),equivalent(u,equivalent(v,x)))),
inference(sor,[status(thm)],[17,2]),
[iquote('0:SoR:17.0,2.0')] ).
cnf(35,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,w),equivalent(v,w))) ),
inference(res,[status(thm),theory(equality)],[28,1]),
[iquote('0:Res:28.0,1.1')] ).
cnf(45,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(equivalent(equivalent(v,w),equivalent(x,w)),equivalent(v,x))),y),equivalent(u,y))),
inference(sor,[status(thm)],[35,2]),
[iquote('0:SoR:35.0,2.0')] ).
cnf(48,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(equivalent(u,equivalent(x,w)),equivalent(v,x)))),
inference(sor,[status(thm)],[17,32]),
[iquote('0:SoR:17.0,32.0')] ).
cnf(71,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,equivalent(w,w)),v))),
inference(sor,[status(thm)],[19,48]),
[iquote('0:SoR:19.0,48.0')] ).
cnf(99,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(u,equivalent(w,w)),v)) ),
inference(res,[status(thm),theory(equality)],[71,1]),
[iquote('0:Res:71.0,1.1')] ).
cnf(124,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,v)),u)),
inference(sor,[status(thm)],[99,23]),
[iquote('0:SoR:99.0,23.0')] ).
cnf(126,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,v)),w),equivalent(u,w))),
inference(sor,[status(thm)],[35,124]),
[iquote('0:SoR:35.0,124.0')] ).
cnf(132,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,v)))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[124,1]),
[iquote('0:Res:124.0,1.1')] ).
cnf(136,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(x,w)),equivalent(u,x))),
inference(sor,[status(thm)],[7,20]),
[iquote('0:SoR:7.0,20.0')] ).
cnf(154,plain,
is_a_theorem(equivalent(equivalent(u,u),equivalent(v,v))),
inference(sor,[status(thm)],[132,124]),
[iquote('0:SoR:132.0,124.0')] ).
cnf(158,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,u),v),equivalent(equivalent(w,w),v))),
inference(sor,[status(thm)],[35,154]),
[iquote('0:SoR:35.0,154.0')] ).
cnf(187,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(x,w)))
| is_a_theorem(equivalent(u,x)) ),
inference(res,[status(thm),theory(equality)],[136,1]),
[iquote('0:Res:136.0,1.1')] ).
cnf(196,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(v,v)),w))
| is_a_theorem(equivalent(u,w)) ),
inference(res,[status(thm),theory(equality)],[126,1]),
[iquote('0:Res:126.0,1.1')] ).
cnf(207,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,w),equivalent(v,u)))),
inference(sor,[status(thm)],[17,158]),
[iquote('0:SoR:17.0,158.0')] ).
cnf(487,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(u,equivalent(v,w)),equivalent(w,v)))),
inference(sor,[status(thm)],[196,48]),
[iquote('0:SoR:196.0,48.0')] ).
cnf(495,plain,
is_a_theorem(equivalent(u,equivalent(equivalent(v,v),equivalent(equivalent(w,w),u)))),
inference(sor,[status(thm)],[196,207]),
[iquote('0:SoR:196.0,207.0')] ).
cnf(582,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,v),equivalent(equivalent(w,w),u))) ),
inference(res,[status(thm),theory(equality)],[495,1]),
[iquote('0:Res:495.0,1.1')] ).
cnf(1225,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,v))
| is_a_theorem(equivalent(equivalent(w,w),u)) ),
inference(res,[status(thm),theory(equality)],[582,1]),
[iquote('0:Res:582.1,1.1')] ).
cnf(1226,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,v),u)) ),
inference(ssi,[status(thm)],[1225,23]),
[iquote('0:SSi:1225.1,23.0')] ).
cnf(1242,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(sor,[status(thm)],[187,1226]),
[iquote('0:SoR:187.0,1226.1')] ).
cnf(1259,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(w,v)),u)),
inference(sor,[status(thm)],[1242,487]),
[iquote('0:SoR:1242.0,487.0')] ).
cnf(1380,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(equivalent(v,w),equivalent(x,w)),equivalent(v,x))),y))
| is_a_theorem(equivalent(u,y)) ),
inference(res,[status(thm),theory(equality)],[45,1]),
[iquote('0:Res:45.0,1.1')] ).
cnf(27815,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))),u)),
inference(sor,[status(thm)],[1380,1259]),
[iquote('0:SoR:1380.0,1259.0')] ).
cnf(40807,plain,
is_a_theorem(equivalent(u,equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(v,x),equivalent(w,x)))))),
inference(sor,[status(thm)],[1242,27815]),
[iquote('0:SoR:1242.0,27815.0')] ).
cnf(40883,plain,
$false,
inference(unc,[status(thm)],[40807,3]),
[iquote('0:UnC:40807.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 05:36:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 210.54/210.94
% 210.54/210.94 SPASS V 3.9
% 210.54/210.94 SPASS beiseite: Proof found.
% 210.54/210.94 % SZS status Theorem
% 210.54/210.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 210.54/210.94 SPASS derived 40562 clauses, backtracked 0 clauses, performed 0 splits and kept 16346 clauses.
% 210.54/210.94 SPASS allocated 122089 KBytes.
% 210.54/210.94 SPASS spent 0:3:28.80 on the problem.
% 210.54/210.94 0:00:00.06 for the input.
% 210.54/210.94 0:00:00.00 for the FLOTTER CNF translation.
% 210.54/210.94 0:00:01.85 for inferences.
% 210.54/210.94 0:00:00.00 for the backtracking.
% 210.54/210.94 0:3:26.62 for the reduction.
% 210.54/210.94
% 210.54/210.94
% 210.54/210.94 Here is a proof with depth 21, length 42 :
% 210.54/210.94 % SZS output start Refutation
% See solution above
% 210.54/210.94 Formulae used in the proof : condensed_detachment s_6 prove_lg_2
% 210.54/210.94
%------------------------------------------------------------------------------