%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL065-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 0.55s 0.81s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 17 unt; 0 nHn; 27 RR)
% Number of literals : 38 ( 0 equ; 12 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 : 6 ( 6 usr; 4 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('LCL065-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL065-1.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('LCL065-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL065-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(a),a),a)),
file('LCL065-1.p',unknown),
[] ).
cnf(11,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(13,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(17,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)],[13,11]),
[iquote('0:SoR:13.0,11.1')] ).
cnf(18,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)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(22,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[22,2]),
[iquote('0:SoR:22.0,2.0')] ).
cnf(37,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),not__dfg(w))),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[17,4]),
[iquote('0:SoR:17.0,4.0')] ).
cnf(39,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[17,2]),
[iquote('0:SoR:17.0,2.0')] ).
cnf(42,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[39,1]),
[iquote('0:Res:39.0,1.1')] ).
cnf(50,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(u,u)))),
inference(sor,[status(thm)],[42,20]),
[iquote('0:SoR:42.0,20.0')] ).
cnf(71,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(u,u))) ),
inference(res,[status(thm),theory(equality)],[50,1]),
[iquote('0:Res:50.0,1.1')] ).
cnf(83,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)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(101,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[71,27]),
[iquote('0:SoR:71.0,27.0')] ).
cnf(116,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),not__dfg(w))))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[37,1]),
[iquote('0:Res:37.0,1.1')] ).
cnf(199,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[83,101]),
[iquote('0:SoR:83.0,101.0')] ).
cnf(207,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[199,1]),
[iquote('0:Res:199.0,1.1')] ).
cnf(447,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[116,2]),
[iquote('0:SoR:116.0,2.0')] ).
cnf(448,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[13,447]),
[iquote('0:SoR:13.0,447.0')] ).
cnf(1007,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(v,u))),
inference(sor,[status(thm)],[116,448]),
[iquote('0:SoR:116.0,448.0')] ).
cnf(1074,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
inference(sor,[status(thm)],[207,1007]),
[iquote('0:SoR:207.0,1007.0')] ).
cnf(1083,plain,
$false,
inference(unc,[status(thm)],[1074,5]),
[iquote('0:UnC:1074.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL065-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n031.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
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Fri Sep 4 23:28:54 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.55/0.81
% 0.55/0.81 SPASS V 3.9
% 0.55/0.81 SPASS beiseite: Proof found.
% 0.55/0.81 % SZS status Theorem
% 0.55/0.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.81 SPASS derived 1065 clauses, backtracked 0 clauses, performed 0 splits and kept 604 clauses.
% 0.55/0.81 SPASS allocated 77525 KBytes.
% 0.55/0.81 SPASS spent 0:00:00.41 on the problem.
% 0.55/0.81 0:00:00.06 for the input.
% 0.55/0.81 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.81 0:00:00.04 for inferences.
% 0.55/0.81 0:00:00.00 for the backtracking.
% 0.55/0.81 0:00:00.26 for the reduction.
% 0.55/0.81
% 0.55/0.81
% 0.55/0.81 Here is a proof with depth 10, length 27 :
% 0.55/0.81 % SZS output start Refutation
% See solution above
% 0.55/0.81 Formulae used in the proof : condensed_detachment cn_18 cn_35 cn_49 prove_cn_2
% 0.55/0.81
%------------------------------------------------------------------------------