%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:06:55 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.51s
% Output : Refutation 0.24s
% 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(not__dfg(p),q)),or__dfg(not__dfg(or__dfg(not__dfg(q),r)),or__dfg(not__dfg(p),r)))),
file('LCL174-1.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('LCL174-1.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('LCL174-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL174-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL174-1.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(200,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(205,plain,
$false,
inference(unc,[status(thm)],[200,1]),
[iquote('0:UnC:200.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n027.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 5 02:44:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.24/0.51
% 0.24/0.51 SPASS V 3.9
% 0.24/0.51 SPASS beiseite: Proof found.
% 0.24/0.51 % SZS status Theorem
% 0.24/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.51 SPASS derived 186 clauses, backtracked 0 clauses, performed 0 splits and kept 137 clauses.
% 0.24/0.51 SPASS allocated 75918 KBytes.
% 0.24/0.51 SPASS spent 0:00:00.12 on the problem.
% 0.24/0.51 0:00:00.06 for the input.
% 0.24/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.51 0:00:00.01 for inferences.
% 0.24/0.51 0:00:00.00 for the backtracking.
% 0.24/0.51 0:00:00.01 for the reduction.
% 0.24/0.51
% 0.24/0.51
% 0.24/0.51 Here is a proof with depth 3, length 9 :
% 0.24/0.51 % SZS output start Refutation
% See solution above
% 0.24/0.51 Formulae used in the proof : prove_this axiom_1_5 axiom_1_6 rule_1 rule_2
% 0.24/0.51
%------------------------------------------------------------------------------