%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL217-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 01:07:05 PM UTC 2026
% Result : Unsatisfiable 29.66s 29.93s
% Output : Refutation 29.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 38 ( 0 equ; 15 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(p),not__dfg(q))),not__dfg(p)))),
file('LCL217-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL217-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL217-1.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('LCL217-1.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('LCL217-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL217-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL217-1.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('LCL217-1.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(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(34,plain,
theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
inference(sor,[status(thm)],[27,2]),
[iquote('0:SoR:27.0,2.0')] ).
cnf(36,plain,
theorem(or__dfg(not__dfg(or__dfg(u,u)),u)),
inference(sor,[status(thm)],[23,34]),
[iquote('0:SoR:23.0,34.0')] ).
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(60,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(94,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,v))),or__dfg(u,v))),
inference(sor,[status(thm)],[39,36]),
[iquote('0:SoR:39.0,36.0')] ).
cnf(280,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)],[4,60]),
[iquote('0:Res:4.0,60.0')] ).
cnf(282,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(u,w))),x))
| theorem(or__dfg(x,not__dfg(or__dfg(not__dfg(v),w)))) ),
inference(res,[status(thm),theory(equality)],[6,60]),
[iquote('0:Res:6.0,60.0')] ).
cnf(775,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)],[23,280]),
[iquote('0:SoR:23.0,280.1')] ).
cnf(1654,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,v)),u),not__dfg(or__dfg(not__dfg(v),u)))),
inference(res,[status(thm),theory(equality)],[94,282]),
[iquote('0:Res:94.0,282.0')] ).
cnf(9988,plain,
theorem(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(v,u)),v))),
inference(sor,[status(thm)],[23,1654]),
[iquote('0:SoR:23.0,1654.0')] ).
cnf(14164,plain,
theorem(or__dfg(not__dfg(or__dfg(u,not__dfg(v))),or__dfg(not__dfg(or__dfg(u,v)),u))),
inference(res,[status(thm),theory(equality)],[9988,775]),
[iquote('0:Res:9988.0,775.0')] ).
cnf(16407,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(or__dfg(u,not__dfg(v))),u))),
inference(sor,[status(thm)],[30,14164]),
[iquote('0:SoR:30.0,14164.0')] ).
cnf(16432,plain,
$false,
inference(unc,[status(thm)],[16407,1]),
[iquote('0:UnC:16407.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL217-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 03:32:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 29.66/29.93
% 29.66/29.93 SPASS V 3.9
% 29.66/29.93 SPASS beiseite: Proof found.
% 29.66/29.93 % SZS status Theorem
% 29.66/29.93 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.66/29.93 SPASS derived 16408 clauses, backtracked 0 clauses, performed 0 splits and kept 9548 clauses.
% 29.66/29.93 SPASS allocated 101172 KBytes.
% 29.66/29.93 SPASS spent 0:0:28.76 on the problem.
% 29.66/29.93 0:00:00.06 for the input.
% 29.66/29.93 0:00:00.00 for the FLOTTER CNF translation.
% 29.66/29.93 0:00:00.86 for inferences.
% 29.66/29.93 0:00:00.00 for the backtracking.
% 29.66/29.93 0:0:27.43 for the reduction.
% 29.66/29.93
% 29.66/29.93
% 29.66/29.93 Here is a proof with depth 9, length 24 :
% 29.66/29.93 % SZS output start Refutation
% See solution above
% 29.66/29.93 Formulae used in the proof : prove_this axiom_1_2 axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 29.66/29.93
%------------------------------------------------------------------------------