%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL064-2 : 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 01:06:41 PM UTC 2026
% Result : Unsatisfiable 3.35s 3.67s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 31 ( 15 unt; 0 nHn; 31 RR)
% Number of literals : 50 ( 0 equ; 20 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(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL064-2.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL064-2.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
file('LCL064-2.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(a,b),implies__dfg(implies__dfg(b,c),implies__dfg(a,c)))),
file('LCL064-2.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(12,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)),implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w)))),
inference(sor,[status(thm)],[12,3]),
[iquote('0:SoR:12.0,3.0')] ).
cnf(16,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[12,9]),
[iquote('0:SoR:12.0,9.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(19,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(23,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(24,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[12,23]),
[iquote('0:SoR:12.0,23.0')] ).
cnf(27,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[24,1]),
[iquote('0:Res:24.0,1.1')] ).
cnf(30,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x))))),
inference(sor,[status(thm)],[16,3]),
[iquote('0:SoR:16.0,3.0')] ).
cnf(33,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[16,2]),
[iquote('0:SoR:16.0,2.0')] ).
cnf(35,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,x)),implies__dfg(v,w))),implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,x)),implies__dfg(v,x))))),
inference(sor,[status(thm)],[16,15]),
[iquote('0:SoR:16.0,15.0')] ).
cnf(36,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)))
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.0,1.1')] ).
cnf(39,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[33,1]),
[iquote('0:Res:33.0,1.1')] ).
cnf(49,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
inference(sor,[status(thm)],[39,9]),
[iquote('0:SoR:39.0,9.1')] ).
cnf(51,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[39,2]),
[iquote('0:SoR:39.0,2.0')] ).
cnf(82,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
| is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x)))) ),
inference(res,[status(thm),theory(equality)],[30,1]),
[iquote('0:Res:30.0,1.1')] ).
cnf(116,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(u,w)),implies__dfg(v,w))) ),
inference(sor,[status(thm)],[36,49]),
[iquote('0:SoR:36.0,49.1')] ).
cnf(147,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,x)),implies__dfg(v,w))))
| is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,x)),implies__dfg(v,x)))) ),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.1')] ).
cnf(204,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[27,9]),
[iquote('0:SoR:27.0,9.1')] ).
cnf(216,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[204,1]),
[iquote('0:Res:204.1,1.1')] ).
cnf(410,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(sor,[status(thm)],[82,2]),
[iquote('0:SoR:82.0,2.0')] ).
cnf(661,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(u,w)),implies__dfg(v,w)))),
inference(sor,[status(thm)],[147,51]),
[iquote('0:SoR:147.0,51.0')] ).
cnf(1606,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(u,w)) ),
inference(sor,[status(thm)],[216,116]),
[iquote('0:SoR:216.1,116.1')] ).
cnf(4318,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[1606,661]),
[iquote('0:SoR:1606.0,661.0')] ).
cnf(5188,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[4318,410]),
[iquote('0:SoR:4318.0,410.0')] ).
cnf(5288,plain,
$false,
inference(unc,[status(thm)],[5188,4]),
[iquote('0:UnC:5188.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL064-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n017.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 22:21:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.35/3.67
% 3.35/3.67 SPASS V 3.9
% 3.35/3.67 SPASS beiseite: Proof found.
% 3.35/3.67 % SZS status Theorem
% 3.35/3.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.35/3.67 SPASS derived 5209 clauses, backtracked 0 clauses, performed 0 splits and kept 1675 clauses.
% 3.35/3.67 SPASS allocated 81721 KBytes.
% 3.35/3.67 SPASS spent 0:00:03.21 on the problem.
% 3.35/3.67 0:00:00.06 for the input.
% 3.35/3.67 0:00:00.00 for the FLOTTER CNF translation.
% 3.35/3.67 0:00:00.19 for inferences.
% 3.35/3.67 0:00:00.00 for the backtracking.
% 3.35/3.67 0:00:02.90 for the reduction.
% 3.35/3.67
% 3.35/3.67
% 3.35/3.67 Here is a proof with depth 11, length 31 :
% 3.35/3.67 % SZS output start Refutation
% See solution above
% 3.35/3.67 Formulae used in the proof : condensed_detachment cn_18 cn_35 prove_cn_1
% 3.35/3.67
%------------------------------------------------------------------------------