%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL106-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 01:06:47 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.51s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 6 unt; 0 nHn; 15 RR)
% Number of literals : 28 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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('LCL106-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),u)))),
file('LCL106-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w))),
file('LCL106-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
file('LCL106-1.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,w),equivalent(equivalent(w,v),u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(12,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,w))
| is_a_theorem(equivalent(equivalent(w,v),u)) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.1,1.1')] ).
cnf(13,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(w,x),v),equivalent(x,w)),u)) ),
inference(sor,[status(thm)],[12,10]),
[iquote('0:SoR:12.1,10.1')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),equivalent(equivalent(w,v),x)),x),u)) ),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.1,2.0')] ).
cnf(16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,u),w)),x))
| is_a_theorem(equivalent(w,x)) ),
inference(sor,[status(thm)],[9,14]),
[iquote('0:SoR:9.0,14.1')] ).
cnf(22,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(equivalent(v,w),u),x))
| is_a_theorem(equivalent(equivalent(w,v),x)) ),
inference(sor,[status(thm)],[9,13]),
[iquote('0:SoR:9.0,13.2')] ).
cnf(82,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,u),equivalent(w,v))) ),
inference(sor,[status(thm)],[22,3]),
[iquote('0:SoR:22.1,3.0')] ).
cnf(93,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(v,x))),equivalent(u,equivalent(w,x)))),
inference(sor,[status(thm)],[82,3]),
[iquote('0:SoR:82.0,3.0')] ).
cnf(156,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v)))),
inference(sor,[status(thm)],[16,93]),
[iquote('0:SoR:16.0,93.0')] ).
cnf(160,plain,
$false,
inference(unc,[status(thm)],[156,4]),
[iquote('0:UnC:156.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL106-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 13:30:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.25/0.51
% 0.25/0.51 SPASS V 3.9
% 0.25/0.51 SPASS beiseite: Proof found.
% 0.25/0.51 % SZS status Theorem
% 0.25/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.51 SPASS derived 151 clauses, backtracked 0 clauses, performed 0 splits and kept 95 clauses.
% 0.25/0.51 SPASS allocated 75991 KBytes.
% 0.25/0.51 SPASS spent 0:00:00.13 on the problem.
% 0.25/0.51 0:00:00.06 for the input.
% 0.25/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.25/0.51 0:00:00.01 for inferences.
% 0.25/0.51 0:00:00.00 for the backtracking.
% 0.25/0.51 0:00:00.02 for the reduction.
% 0.25/0.51
% 0.25/0.51
% 0.25/0.51 Here is a proof with depth 7, length 15 :
% 0.25/0.51 % SZS output start Refutation
% See solution above
% 0.25/0.51 Formulae used in the proof : condensed_detachment q_1 q_4 prove_q_2
% 0.25/0.51
%------------------------------------------------------------------------------