%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 01:06:39 PM UTC 2026
% Result : Unsatisfiable 2.90s 3.16s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of clauses : 50 ( 30 unt; 0 nHn; 50 RR)
% Number of literals : 72 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 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('LCL047-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL047-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL047-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL047-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(b,a))),
file('LCL047-1.p',unknown),
[] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),u),v))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(19,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w),implies__dfg(implies__dfg(u,v),w))),
inference(sor,[status(thm)],[13,17]),
[iquote('0:SoR:13.0,17.0')] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),v)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w))),
inference(sor,[status(thm)],[13,19]),
[iquote('0:SoR:13.0,19.0')] ).
cnf(23,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(u,w)) ),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(u),u)),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
cnf(32,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[21,4]),
[iquote('0:SoR:21.0,4.0')] ).
cnf(38,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(56,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w))
| is_a_theorem(implies__dfg(implies__dfg(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(79,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(92,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[38,19]),
[iquote('0:SoR:38.0,19.0')] ).
cnf(94,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[38,20]),
[iquote('0:SoR:38.0,20.0')] ).
cnf(103,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[23,92]),
[iquote('0:SoR:23.0,92.0')] ).
cnf(106,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x),implies__dfg(v,x))),
inference(sor,[status(thm)],[13,103]),
[iquote('0:SoR:13.0,103.0')] ).
cnf(158,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x))
| is_a_theorem(implies__dfg(v,x)) ),
inference(res,[status(thm),theory(equality)],[106,1]),
[iquote('0:Res:106.0,1.1')] ).
cnf(172,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[94,1]),
[iquote('0:Res:94.0,1.1')] ).
cnf(240,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[158,94]),
[iquote('0:SoR:158.0,94.0')] ).
cnf(258,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[240,1]),
[iquote('0:Res:240.0,1.1')] ).
cnf(274,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[258,1]),
[iquote('0:Res:258.1,1.1')] ).
cnf(284,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[56,258]),
[iquote('0:SoR:56.0,258.1')] ).
cnf(340,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(x,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[274,19]),
[iquote('0:SoR:274.1,19.0')] ).
cnf(380,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),u)),
inference(sor,[status(thm)],[79,3]),
[iquote('0:SoR:79.0,3.0')] ).
cnf(396,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[79,32]),
[iquote('0:SoR:79.0,32.0')] ).
cnf(428,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u),u)),
inference(sor,[status(thm)],[79,380]),
[iquote('0:SoR:79.0,380.0')] ).
cnf(501,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[396,1]),
[iquote('0:Res:396.0,1.1')] ).
cnf(525,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[428,1]),
[iquote('0:Res:428.0,1.1')] ).
cnf(1341,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[340,27]),
[iquote('0:SoR:340.0,27.0')] ).
cnf(1342,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[340,3]),
[iquote('0:SoR:340.0,3.0')] ).
cnf(1410,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[284,1342]),
[iquote('0:SoR:284.0,1342.0')] ).
cnf(1479,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[501,1341]),
[iquote('0:SoR:501.0,1341.0')] ).
cnf(1599,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1410,1]),
[iquote('0:Res:1410.0,1.1')] ).
cnf(2348,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[172,1410]),
[iquote('0:SoR:172.0,1410.0')] ).
cnf(2356,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(u,v),w))) ),
inference(sor,[status(thm)],[172,258]),
[iquote('0:SoR:172.0,258.1')] ).
cnf(2383,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1599,2348]),
[iquote('0:SoR:1599.0,2348.0')] ).
cnf(2392,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[525,2383]),
[iquote('0:SoR:525.0,2383.0')] ).
cnf(2430,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2392,1]),
[iquote('0:Res:2392.0,1.1')] ).
cnf(4151,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2430,2356]),
[iquote('0:SoR:2430.0,2356.1')] ).
cnf(4182,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[56,4151]),
[iquote('0:SoR:56.0,4151.1')] ).
cnf(4561,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[4182,1479]),
[iquote('0:SoR:4182.0,1479.0')] ).
cnf(4717,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[38,4561]),
[iquote('0:SoR:38.0,4561.0')] ).
cnf(4921,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(sor,[status(thm)],[158,4717]),
[iquote('0:SoR:158.0,4717.0')] ).
cnf(4924,plain,
$false,
inference(unc,[status(thm)],[4921,5]),
[iquote('0:UnC:4921.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 22:05:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 2.90/3.16
% 2.90/3.16 SPASS V 3.9
% 2.90/3.16 SPASS beiseite: Proof found.
% 2.90/3.16 % SZS status Theorem
% 2.90/3.16 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/3.16 SPASS derived 4870 clauses, backtracked 0 clauses, performed 0 splits and kept 1893 clauses.
% 2.90/3.16 SPASS allocated 82793 KBytes.
% 2.90/3.16 SPASS spent 0:00:02.69 on the problem.
% 2.90/3.16 0:00:00.06 for the input.
% 2.90/3.16 0:00:00.00 for the FLOTTER CNF translation.
% 2.90/3.16 0:00:00.21 for inferences.
% 2.90/3.16 0:00:00.00 for the backtracking.
% 2.90/3.16 0:00:02.36 for the reduction.
% 2.90/3.16
% 2.90/3.16
% 2.90/3.16 Here is a proof with depth 22, length 50 :
% 2.90/3.16 % SZS output start Refutation
% See solution above
% 2.90/3.16 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_18
% 2.90/3.16
%------------------------------------------------------------------------------