%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL226-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 01:07:06 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.36s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 14 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(not__dfg(or__dfg(q,r)),or__dfg(not__dfg(or__dfg(not__dfg(r),s)),or__dfg(q,s)))),
file('LCL226-1.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('LCL226-1.p',unknown),
[] ).
cnf(6,axiom,
axiom(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v)))),
file('LCL226-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL226-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL226-1.p',unknown),
[] ).
cnf(30,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(48,plain,
( ~ axiom(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[30,7]),
[iquote('0:SoR:30.0,7.1')] ).
cnf(198,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(or__dfg(not__dfg(v),w)),or__dfg(u,w)))),
inference(sor,[status(thm)],[48,6]),
[iquote('0:SoR:48.0,6.0')] ).
cnf(203,plain,
$false,
inference(unc,[status(thm)],[198,1]),
[iquote('0:UnC:198.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL226-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 4 18:32:27 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.08/0.36
% 0.08/0.36 SPASS V 3.9
% 0.08/0.36 SPASS beiseite: Proof found.
% 0.08/0.36 % SZS status Theorem
% 0.08/0.36 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 SPASS derived 184 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.08/0.36 SPASS allocated 75903 KBytes.
% 0.08/0.36 SPASS spent 0:00:00.06 on the problem.
% 0.08/0.36 0:00:00.03 for the input.
% 0.08/0.36 0:00:00.00 for the FLOTTER CNF translation.
% 0.08/0.36 0:00:00.00 for inferences.
% 0.08/0.36 0:00:00.00 for the backtracking.
% 0.08/0.36 0:00:00.01 for the reduction.
% 0.08/0.36
% 0.08/0.36
% 0.08/0.36 Here is a proof with depth 3, length 9 :
% 0.08/0.36 % SZS output start Refutation
% See solution above
% 0.08/0.36 Formulae used in the proof : prove_this axiom_1_5 axiom_1_6 rule_1 rule_2
% 0.08/0.36
%------------------------------------------------------------------------------