%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL230-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 01:07:07 PM UTC 2026
% Result : Unsatisfiable 13.87s 14.13s
% Output : Refutation 13.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 42 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(not__dfg(or__dfg(not__dfg(or__dfg(p,q)),or__dfg(p,r))),or__dfg(p,or__dfg(not__dfg(q),r)))),
file('LCL230-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL230-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL230-1.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('LCL230-1.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('LCL230-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL230-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL230-1.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('LCL230-1.p',unknown),
[] ).
cnf(12,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(p,or__dfg(not__dfg(q),r))))
| ~ axiom(or__dfg(not__dfg(or__dfg(not__dfg(or__dfg(p,q)),or__dfg(p,r))),u)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.0')] ).
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(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(32,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(39,plain,
( ~ theorem(or__dfg(not__dfg(u),v))
| theorem(or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.1')] ).
cnf(41,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
inference(sor,[status(thm)],[23,32]),
[iquote('0:SoR:23.0,32.0')] ).
cnf(43,plain,
theorem(or__dfg(u,or__dfg(not__dfg(or__dfg(v,u)),v))),
inference(sor,[status(thm)],[30,41]),
[iquote('0:SoR:30.0,41.0')] ).
cnf(50,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(88,plain,
( ~ axiom(or__dfg(not__dfg(u),v))
| ~ theorem(or__dfg(not__dfg(v),w))
| theorem(or__dfg(not__dfg(or__dfg(x,u)),or__dfg(x,w))) ),
inference(sor,[status(thm)],[39,9]),
[iquote('0:SoR:39.0,9.2')] ).
cnf(140,plain,
~ theorem(or__dfg(not__dfg(or__dfg(p,or__dfg(not__dfg(or__dfg(p,q)),r))),or__dfg(p,or__dfg(not__dfg(q),r)))),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.0,12.1')] ).
cnf(277,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(v))) ),
inference(res,[status(thm),theory(equality)],[3,50]),
[iquote('0:Res:3.0,50.0')] ).
cnf(448,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(not__dfg(or__dfg(x,or__dfg(v,u))),or__dfg(x,w))) ),
inference(res,[status(thm),theory(equality)],[4,88]),
[iquote('0:Res:4.0,88.0')] ).
cnf(678,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,not__dfg(or__dfg(v,w)))),u),not__dfg(w))),
inference(res,[status(thm),theory(equality)],[43,277]),
[iquote('0:Res:43.0,277.0')] ).
cnf(1688,plain,
~ theorem(or__dfg(not__dfg(or__dfg(r,not__dfg(or__dfg(p,q)))),or__dfg(not__dfg(q),r))),
inference(res,[status(thm),theory(equality)],[448,140]),
[iquote('0:Res:448.1,140.0')] ).
cnf(7622,plain,
theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(or__dfg(v,not__dfg(or__dfg(w,u)))),v))),
inference(sor,[status(thm)],[23,678]),
[iquote('0:SoR:23.0,678.0')] ).
cnf(11385,plain,
theorem(or__dfg(not__dfg(or__dfg(u,not__dfg(or__dfg(v,w)))),or__dfg(not__dfg(w),u))),
inference(sor,[status(thm)],[30,7622]),
[iquote('0:SoR:30.0,7622.0')] ).
cnf(11410,plain,
$false,
inference(unc,[status(thm)],[11385,1688]),
[iquote('0:UnC:11385.0,1688.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL230-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n028.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 14:43:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 13.87/14.13
% 13.87/14.13 SPASS V 3.9
% 13.87/14.13 SPASS beiseite: Proof found.
% 13.87/14.13 % SZS status Theorem
% 13.87/14.13 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.87/14.13 SPASS derived 11388 clauses, backtracked 0 clauses, performed 0 splits and kept 6418 clauses.
% 13.87/14.13 SPASS allocated 93447 KBytes.
% 13.87/14.13 SPASS spent 0:0:13.35 on the problem.
% 13.87/14.13 0:00:00.06 for the input.
% 13.87/14.13 0:00:00.00 for the FLOTTER CNF translation.
% 13.87/14.13 0:00:00.56 for inferences.
% 13.87/14.13 0:00:00.00 for the backtracking.
% 13.87/14.13 0:0:12.46 for the reduction.
% 13.87/14.13
% 13.87/14.13
% 13.87/14.13 Here is a proof with depth 8, length 26 :
% 13.87/14.13 % SZS output start Refutation
% See solution above
% 13.87/14.13 Formulae used in the proof : prove_this axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 13.87/14.13
%------------------------------------------------------------------------------