%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL201-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 01:07:01 PM UTC 2026
% Result : Unsatisfiable 12.66s 12.94s
% Output : Refutation 12.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 14 unt; 0 nHn; 24 RR)
% Number of literals : 37 ( 0 equ; 14 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(not__dfg(not__dfg(or__dfg(p,q))),or__dfg(not__dfg(p),q))),
file('LCL201-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL201-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL201-1.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('LCL201-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL201-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL201-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(or__dfg(not__dfg(u),v))
| ~ axiom(or__dfg(not__dfg(w),u))
| theorem(or__dfg(not__dfg(w),v)) ),
file('LCL201-1.p',unknown),
[] ).
cnf(23,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(27,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[23,7]),
[iquote('0:SoR:23.0,7.1')] ).
cnf(39,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(41,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[27,4]),
[iquote('0:SoR:27.0,4.0')] ).
cnf(50,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
inference(sor,[status(thm)],[23,41]),
[iquote('0:SoR:23.0,41.0')] ).
cnf(53,plain,
( ~ axiom(or__dfg(not__dfg(u),v))
| ~ theorem(or__dfg(not__dfg(v),w))
| theorem(or__dfg(w,not__dfg(u))) ),
inference(sor,[status(thm)],[23,9]),
[iquote('0:SoR:23.0,9.2')] ).
cnf(276,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(v))) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.0')] ).
cnf(277,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(or__dfg(v,u)))) ),
inference(res,[status(thm),theory(equality)],[4,53]),
[iquote('0:Res:4.0,53.0')] ).
cnf(584,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(u))),
inference(res,[status(thm),theory(equality)],[50,276]),
[iquote('0:Res:50.0,276.0')] ).
cnf(616,plain,
theorem(or__dfg(not__dfg(u),or__dfg(u,v))),
inference(sor,[status(thm)],[23,584]),
[iquote('0:SoR:23.0,584.0')] ).
cnf(619,plain,
theorem(or__dfg(u,or__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[39,616]),
[iquote('0:SoR:39.0,616.0')] ).
cnf(762,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(not__dfg(or__dfg(v,u)),w)) ),
inference(sor,[status(thm)],[23,277]),
[iquote('0:SoR:23.0,277.1')] ).
cnf(4504,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(not__dfg(or__dfg(v,u))),w))),
inference(res,[status(thm),theory(equality)],[619,762]),
[iquote('0:Res:619.0,762.0')] ).
cnf(10497,plain,
theorem(or__dfg(or__dfg(not__dfg(not__dfg(or__dfg(u,v))),w),not__dfg(u))),
inference(res,[status(thm),theory(equality)],[4504,276]),
[iquote('0:Res:4504.0,276.0')] ).
cnf(10506,plain,
theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(not__dfg(or__dfg(u,v))),w))),
inference(sor,[status(thm)],[23,10497]),
[iquote('0:SoR:23.0,10497.0')] ).
cnf(10511,plain,
theorem(or__dfg(not__dfg(not__dfg(or__dfg(u,v))),or__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[39,10506]),
[iquote('0:SoR:39.0,10506.0')] ).
cnf(10537,plain,
$false,
inference(unc,[status(thm)],[10511,1]),
[iquote('0:UnC:10511.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL201-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 02:56:38 UTC 2026
% 0.07/0.35 % CPUTime :
% 12.66/12.94
% 12.66/12.94 SPASS V 3.9
% 12.66/12.94 SPASS beiseite: Proof found.
% 12.66/12.94 % SZS status Theorem
% 12.66/12.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.66/12.94 SPASS derived 10515 clauses, backtracked 0 clauses, performed 0 splits and kept 5966 clauses.
% 12.66/12.94 SPASS allocated 92059 KBytes.
% 12.66/12.94 SPASS spent 0:0:12.21 on the problem.
% 12.66/12.94 0:00:00.06 for the input.
% 12.66/12.94 0:00:00.00 for the FLOTTER CNF translation.
% 12.66/12.94 0:00:00.51 for inferences.
% 12.66/12.94 0:00:00.00 for the backtracking.
% 12.66/12.94 0:0:11.40 for the reduction.
% 12.66/12.94
% 12.66/12.94
% 12.66/12.94 Here is a proof with depth 11, length 24 :
% 12.66/12.94 % SZS output start Refutation
% See solution above
% 12.66/12.94 Formulae used in the proof : prove_this axiom_1_3 axiom_1_4 axiom_1_5 rule_1 rule_2 rule_3
% 12.66/12.94
%------------------------------------------------------------------------------