%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL044-1 : 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 01:06:39 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.96s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 41 ( 24 unt; 0 nHn; 41 RR)
% Number of literals : 61 ( 0 equ; 21 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 : 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('LCL044-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL044-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL044-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
file('LCL044-1.p',unknown),
[] ).
cnf(5,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
file('LCL044-1.p',unknown),
[] ).
cnf(6,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),v),v))),
file('LCL044-1.p',unknown),
[] ).
cnf(7,axiom,
~ is_a_theorem(implies__dfg(a,not__dfg(not__dfg(a)))),
file('LCL044-1.p',unknown),
[] ).
cnf(15,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(16,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(not__dfg(u),v)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(17,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),v)) ),
inference(res,[status(thm),theory(equality)],[6,1]),
[iquote('0:Res:6.0,1.1')] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(22,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),v)) ),
inference(sor,[status(thm)],[17,16]),
[iquote('0:SoR:17.0,16.1')] ).
cnf(27,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),implies__dfg(v,u)),implies__dfg(v,u))),
inference(sor,[status(thm)],[17,3]),
[iquote('0:SoR:17.0,3.0')] ).
cnf(29,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.1,1.1')] ).
cnf(31,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(v,u)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[27,1]),
[iquote('0:Res:27.0,1.1')] ).
cnf(37,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.0,1.1')] ).
cnf(52,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
inference(sor,[status(thm)],[21,15]),
[iquote('0:SoR:21.0,15.1')] ).
cnf(56,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[21,6]),
[iquote('0:SoR:21.0,6.0')] ).
cnf(57,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[21,2]),
[iquote('0:SoR:21.0,2.0')] ).
cnf(58,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
cnf(61,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(sor,[status(thm)],[29,58]),
[iquote('0:SoR:29.1,58.0')] ).
cnf(73,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[61,57]),
[iquote('0:EmS:61.0,57.0')] ).
cnf(81,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(sor,[status(thm)],[21,73]),
[iquote('0:SoR:21.0,73.0')] ).
cnf(90,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(u,implies__dfg(v,w)))),
inference(sor,[status(thm)],[37,57]),
[iquote('0:SoR:37.0,57.0')] ).
cnf(96,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(not__dfg(v),w)))),
inference(sor,[status(thm)],[37,2]),
[iquote('0:SoR:37.0,2.0')] ).
cnf(113,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[81,1]),
[iquote('0:Res:81.0,1.1')] ).
cnf(125,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[113,1]),
[iquote('0:Res:113.1,1.1')] ).
cnf(235,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),v))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[125,56]),
[iquote('0:SoR:125.1,56.0')] ).
cnf(276,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),w))) ),
inference(sor,[status(thm)],[125,96]),
[iquote('0:SoR:125.1,96.0')] ).
cnf(618,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[31,2]),
[iquote('0:SoR:31.0,2.0')] ).
cnf(621,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,u))),
inference(sor,[status(thm)],[52,618]),
[iquote('0:SoR:52.0,618.0')] ).
cnf(634,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(v)),v))),
inference(sor,[status(thm)],[21,621]),
[iquote('0:SoR:21.0,621.0')] ).
cnf(1475,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[235,57]),
[iquote('0:SoR:235.0,57.0')] ).
cnf(1526,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[125,1475]),
[iquote('0:SoR:125.1,1475.0')] ).
cnf(1757,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(v)),v)),w))),
inference(sor,[status(thm)],[276,634]),
[iquote('0:SoR:276.0,634.0')] ).
cnf(2799,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),u)),v)),
inference(sor,[status(thm)],[1526,1757]),
[iquote('0:SoR:1526.0,1757.0')] ).
cnf(2831,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),u),v),v)),
inference(sor,[status(thm)],[235,2799]),
[iquote('0:SoR:235.0,2799.0')] ).
cnf(2879,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[125,2831]),
[iquote('0:SoR:125.1,2831.0')] ).
cnf(4087,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(not__dfg(u))),implies__dfg(u,v))),
inference(sor,[status(thm)],[2879,90]),
[iquote('0:SoR:2879.0,90.0')] ).
cnf(4172,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[31,4087]),
[iquote('0:SoR:31.0,4087.0')] ).
cnf(4176,plain,
$false,
inference(unc,[status(thm)],[4172,7]),
[iquote('0:UnC:4172.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL044-1 : 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 : Sat Sep 5 05:17:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 1.66/1.96
% 1.66/1.96 SPASS V 3.9
% 1.66/1.96 SPASS beiseite: Proof found.
% 1.66/1.96 % SZS status Theorem
% 1.66/1.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.66/1.96 SPASS derived 4113 clauses, backtracked 0 clauses, performed 0 splits and kept 1561 clauses.
% 1.66/1.96 SPASS allocated 80422 KBytes.
% 1.66/1.96 SPASS spent 0:00:01.53 on the problem.
% 1.66/1.96 0:00:00.06 for the input.
% 1.66/1.96 0:00:00.00 for the FLOTTER CNF translation.
% 1.66/1.96 0:00:00.17 for inferences.
% 1.66/1.96 0:00:00.00 for the backtracking.
% 1.66/1.96 0:00:01.22 for the reduction.
% 1.66/1.96
% 1.66/1.96
% 1.66/1.96 Here is a proof with depth 16, length 41 :
% 1.66/1.96 % SZS output start Refutation
% See solution above
% 1.66/1.96 Formulae used in the proof : condensed_detachment cn_3 cn_18 cn_21 cn_22 cn_54 prove_cn_40
% 1.66/1.96
%------------------------------------------------------------------------------