%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL207-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 01:07:02 PM UTC 2026
% Result : Unsatisfiable 0.37s 0.65s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 21 RR)
% Number of literals : 32 ( 0 equ; 12 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(not__dfg(p),q))),or__dfg(not__dfg(q),p))),
file('LCL207-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL207-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL207-1.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('LCL207-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL207-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL207-1.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('LCL207-1.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(293,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(556,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(u))),
inference(res,[status(thm),theory(equality)],[50,293]),
[iquote('0:Res:50.0,293.0')] ).
cnf(585,plain,
theorem(or__dfg(not__dfg(u),or__dfg(u,v))),
inference(sor,[status(thm)],[23,556]),
[iquote('0:SoR:23.0,556.0')] ).
cnf(588,plain,
theorem(or__dfg(u,or__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[39,585]),
[iquote('0:SoR:39.0,585.0')] ).
cnf(599,plain,
theorem(or__dfg(or__dfg(not__dfg(not__dfg(or__dfg(u,v))),w),not__dfg(v))),
inference(res,[status(thm),theory(equality)],[588,293]),
[iquote('0:Res:588.0,293.0')] ).
cnf(806,plain,
theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(not__dfg(or__dfg(v,u))),w))),
inference(sor,[status(thm)],[23,599]),
[iquote('0:SoR:23.0,599.0')] ).
cnf(836,plain,
theorem(or__dfg(not__dfg(not__dfg(or__dfg(u,v))),or__dfg(not__dfg(v),w))),
inference(sor,[status(thm)],[39,806]),
[iquote('0:SoR:39.0,806.0')] ).
cnf(842,plain,
$false,
inference(unc,[status(thm)],[836,1]),
[iquote('0:UnC:836.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL207-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 16:48:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.37/0.65
% 0.37/0.65 SPASS V 3.9
% 0.37/0.65 SPASS beiseite: Proof found.
% 0.37/0.65 % SZS status Theorem
% 0.37/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.65 SPASS derived 823 clauses, backtracked 0 clauses, performed 0 splits and kept 512 clauses.
% 0.37/0.65 SPASS allocated 76906 KBytes.
% 0.37/0.65 SPASS spent 0:00:00.26 on the problem.
% 0.37/0.65 0:00:00.06 for the input.
% 0.37/0.65 0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.65 0:00:00.03 for inferences.
% 0.37/0.65 0:00:00.00 for the backtracking.
% 0.37/0.65 0:00:00.12 for the reduction.
% 0.37/0.65
% 0.37/0.65
% 0.37/0.65 Here is a proof with depth 10, length 21 :
% 0.37/0.65 % SZS output start Refutation
% See solution above
% 0.37/0.66 Formulae used in the proof : prove_this axiom_1_3 axiom_1_4 axiom_1_5 rule_1 rule_2 rule_3
% 0.37/0.66
%------------------------------------------------------------------------------