%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL178-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 01:06:56 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 17 RR)
% Number of literals : 24 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 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,
~ theorem(or__dfg(not__dfg(p),not__dfg(not__dfg(p)))),
file('LCL178-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL178-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL178-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL178-1.p',unknown),
[] ).
cnf(5,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(v,or__dfg(u,w)))),
file('LCL178-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL178-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL178-1.p',unknown),
[] ).
cnf(22,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.1')] ).
cnf(24,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.1')] ).
cnf(28,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.1')] ).
cnf(31,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[24,7]),
[iquote('0:SoR:24.0,7.1')] ).
cnf(40,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[31,3]),
[iquote('0:SoR:31.0,3.0')] ).
cnf(42,plain,
theorem(or__dfg(not__dfg(u),or__dfg(v,u))),
inference(sor,[status(thm)],[24,40]),
[iquote('0:SoR:24.0,40.0')] ).
cnf(63,plain,
theorem(or__dfg(u,or__dfg(not__dfg(v),v))),
inference(sor,[status(thm)],[28,42]),
[iquote('0:SoR:28.0,42.0')] ).
cnf(67,plain,
theorem(or__dfg(not__dfg(u),u)),
inference(sor,[status(thm)],[22,63]),
[iquote('0:SoR:22.0,63.0')] ).
cnf(71,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[24,67]),
[iquote('0:SoR:24.0,67.0')] ).
cnf(74,plain,
$false,
inference(unc,[status(thm)],[71,1]),
[iquote('0:UnC:71.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL178-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n020.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 15:22:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.48
% 0.14/0.48 SPASS V 3.9
% 0.14/0.48 SPASS beiseite: Proof found.
% 0.14/0.48 % SZS status Theorem
% 0.14/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.48 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.14/0.48 SPASS allocated 75702 KBytes.
% 0.14/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.14/0.48 0:00:00.06 for the input.
% 0.14/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.48 0:00:00.00 for inferences.
% 0.14/0.48 0:00:00.00 for the backtracking.
% 0.14/0.48 0:00:00.00 for the reduction.
% 0.14/0.48
% 0.14/0.48
% 0.14/0.48 Here is a proof with depth 7, length 17 :
% 0.14/0.48 % SZS output start Refutation
% See solution above
% 0.14/0.48 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 rule_1 rule_2
% 0.14/0.48
%------------------------------------------------------------------------------