%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL066-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.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 01:06:42 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.61s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 19 unt; 0 nHn; 30 RR)
% Number of literals : 42 ( 0 equ; 13 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 : 7 ( 7 usr; 5 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('LCL066-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL066-1.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('LCL066-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL066-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(not__dfg(a),b))),
file('LCL066-1.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(12,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
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(18,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(19,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(21,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(23,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(28,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[23,2]),
[iquote('0:SoR:23.0,2.0')] ).
cnf(36,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)],[18,4]),
[iquote('0:SoR:18.0,4.0')] ).
cnf(37,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(40,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| 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(48,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(u,u)))),
inference(sor,[status(thm)],[40,21]),
[iquote('0:SoR:40.0,21.0')] ).
cnf(69,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(u,u))) ),
inference(res,[status(thm),theory(equality)],[48,1]),
[iquote('0:Res:48.0,1.1')] ).
cnf(81,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)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(87,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[69,28]),
[iquote('0:SoR:69.0,28.0')] ).
cnf(113,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)],[36,1]),
[iquote('0:Res:36.0,1.1')] ).
cnf(195,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[81,87]),
[iquote('0:SoR:81.0,87.0')] ).
cnf(202,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[195,1]),
[iquote('0:Res:195.0,1.1')] ).
cnf(450,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[113,2]),
[iquote('0:SoR:113.0,2.0')] ).
cnf(452,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,u))),
inference(sor,[status(thm)],[113,450]),
[iquote('0:SoR:113.0,450.0')] ).
cnf(459,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[202,452]),
[iquote('0:SoR:202.0,452.0')] ).
cnf(470,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[12,459]),
[iquote('0:SoR:12.0,459.0')] ).
cnf(477,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,not__dfg(not__dfg(u))))),
inference(sor,[status(thm)],[40,470]),
[iquote('0:SoR:40.0,470.0')] ).
cnf(593,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[113,477]),
[iquote('0:SoR:113.0,477.0')] ).
cnf(601,plain,
$false,
inference(unc,[status(thm)],[593,5]),
[iquote('0:UnC:593.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL066-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 21:04:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.32/0.61
% 0.32/0.61 SPASS V 3.9
% 0.32/0.61 SPASS beiseite: Proof found.
% 0.32/0.61 % SZS status Theorem
% 0.32/0.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.61 SPASS derived 584 clauses, backtracked 0 clauses, performed 0 splits and kept 326 clauses.
% 0.32/0.61 SPASS allocated 76660 KBytes.
% 0.32/0.61 SPASS spent 0:00:00.23 on the problem.
% 0.32/0.61 0:00:00.06 for the input.
% 0.32/0.61 0:00:00.00 for the FLOTTER CNF translation.
% 0.32/0.61 0:00:00.02 for inferences.
% 0.32/0.61 0:00:00.00 for the backtracking.
% 0.32/0.61 0:00:00.10 for the reduction.
% 0.32/0.61
% 0.32/0.61
% 0.32/0.61 Here is a proof with depth 13, length 30 :
% 0.32/0.61 % SZS output start Refutation
% See solution above
% 0.32/0.61 Formulae used in the proof : condensed_detachment cn_18 cn_35 cn_49 prove_cn_3
% 0.32/0.61
%------------------------------------------------------------------------------