%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL076-1 : 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 01:06:42 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.58s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 28 ( 17 unt; 0 nHn; 28 RR)
% Number of literals : 40 ( 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 : 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('LCL076-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL076-1.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('LCL076-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL076-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(a,not__dfg(not__dfg(a)))),
file('LCL076-1.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(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(38,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(51,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)],[51,1]),
[iquote('0:Res:51.0,1.1')] ).
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(89,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)],[38,1]),
[iquote('0:Res:38.0,1.1')] ).
cnf(199,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[83,89]),
[iquote('0:SoR:83.0,89.0')] ).
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(455,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(457,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,u))),
inference(sor,[status(thm)],[116,455]),
[iquote('0:SoR:116.0,455.0')] ).
cnf(463,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[207,457]),
[iquote('0:SoR:207.0,457.0')] ).
cnf(472,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[12,463]),
[iquote('0:SoR:12.0,463.0')] ).
cnf(481,plain,
$false,
inference(unc,[status(thm)],[472,5]),
[iquote('0:UnC:472.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL076-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n017.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 : Sat Sep 5 13:28:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.32/0.58
% 0.32/0.58 SPASS V 3.9
% 0.32/0.58 SPASS beiseite: Proof found.
% 0.32/0.58 % SZS status Theorem
% 0.32/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.58 SPASS derived 466 clauses, backtracked 0 clauses, performed 0 splits and kept 260 clauses.
% 0.32/0.58 SPASS allocated 76428 KBytes.
% 0.32/0.58 SPASS spent 0:00:00.19 on the problem.
% 0.32/0.58 0:00:00.06 for the input.
% 0.32/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.32/0.58 0:00:00.02 for inferences.
% 0.32/0.58 0:00:00.00 for the backtracking.
% 0.32/0.58 0:00:00.07 for the reduction.
% 0.32/0.58
% 0.32/0.58
% 0.32/0.58 Here is a proof with depth 11, length 28 :
% 0.32/0.58 % SZS output start Refutation
% See solution above
% 0.32/0.58 Formulae used in the proof : condensed_detachment cn_18 cn_35 cn_49 prove_cn_40
% 0.32/0.58
%------------------------------------------------------------------------------