%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 0.56s 0.83s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 17 RR)
% Number of literals : 25 ( 0 equ; 9 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('LCL077-2.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL077-2.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('LCL077-2.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL077-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ is_a_theorem(implies__dfg(u,v))
| ~ is_a_theorem(implies__dfg(w,u))
| is_a_theorem(implies__dfg(w,v)) ),
file('LCL077-2.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(not__dfg(not__dfg(a)),a)),
file('LCL077-2.p',unknown),
[] ).
cnf(17,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)],[4,5]),
[iquote('0:Res:4.0,5.0')] ).
cnf(24,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(33,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(40,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),implies__dfg(v,u))),
inference(res,[status(thm),theory(equality)],[33,17]),
[iquote('0:Res:33.0,17.0')] ).
cnf(50,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),implies__dfg(not__dfg(not__dfg(u)),u))),
inference(sor,[status(thm)],[24,40]),
[iquote('0:SoR:24.0,40.0')] ).
cnf(54,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[24,2]),
[iquote('0:SoR:24.0,2.0')] ).
cnf(57,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[54,1]),
[iquote('0:Res:54.0,1.1')] ).
cnf(72,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[57,2]),
[iquote('0:SoR:57.0,2.0')] ).
cnf(640,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),v))
| is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)) ),
inference(res,[status(thm),theory(equality)],[50,1]),
[iquote('0:Res:50.0,1.1')] ).
cnf(1183,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[640,72]),
[iquote('0:SoR:640.0,72.0')] ).
cnf(1213,plain,
$false,
inference(unc,[status(thm)],[1183,6]),
[iquote('0:UnC:1183.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n028.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 05:44:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.56/0.83
% 0.56/0.83 SPASS V 3.9
% 0.56/0.83 SPASS beiseite: Proof found.
% 0.56/0.83 % SZS status Theorem
% 0.56/0.83 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.83 SPASS derived 1181 clauses, backtracked 0 clauses, performed 0 splits and kept 698 clauses.
% 0.56/0.83 SPASS allocated 77051 KBytes.
% 0.56/0.83 SPASS spent 0:00:00.44 on the problem.
% 0.56/0.83 0:00:00.06 for the input.
% 0.56/0.83 0:00:00.00 for the FLOTTER CNF translation.
% 0.56/0.83 0:00:00.03 for inferences.
% 0.56/0.83 0:00:00.00 for the backtracking.
% 0.56/0.83 0:00:00.30 for the reduction.
% 0.56/0.83
% 0.56/0.83
% 0.56/0.83 Here is a proof with depth 6, length 17 :
% 0.56/0.83 % SZS output start Refutation
% See solution above
% 0.56/0.83 Formulae used in the proof : condensed_detachment cn_18 cn_35 cn_49 transitivity prove_cn_39
% 0.56/0.83
%------------------------------------------------------------------------------