%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL196-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 01:07:00 PM UTC 2026
% Result : Unsatisfiable 131.35s 131.62s
% Output : Refutation 131.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 46 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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(p,or__dfg(p,q))),or__dfg(p,q))),
file('LCL196-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL196-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL196-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL196-1.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('LCL196-1.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('LCL196-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL196-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL196-1.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('LCL196-1.p',unknown),
[] ).
cnf(12,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(p,q)))
| ~ axiom(or__dfg(not__dfg(or__dfg(p,or__dfg(p,q))),u)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.0')] ).
cnf(21,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.1')] ).
cnf(22,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.1')] ).
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(48,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(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(80,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[39,22]),
[iquote('0:SoR:39.0,22.1')] ).
cnf(140,plain,
~ theorem(or__dfg(not__dfg(or__dfg(or__dfg(p,q),p)),or__dfg(p,q))),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.1')] ).
cnf(326,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(605,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(u))),
inference(res,[status(thm),theory(equality)],[50,326]),
[iquote('0:Res:50.0,326.0')] ).
cnf(637,plain,
theorem(or__dfg(not__dfg(u),or__dfg(u,v))),
inference(sor,[status(thm)],[23,605]),
[iquote('0:SoR:23.0,605.0')] ).
cnf(641,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(u,or__dfg(v,w)))),
inference(sor,[status(thm)],[48,637]),
[iquote('0:SoR:48.0,637.0')] ).
cnf(2707,plain,
theorem(or__dfg(u,or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,w)))),
inference(sor,[status(thm)],[39,641]),
[iquote('0:SoR:39.0,641.0')] ).
cnf(4040,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,w)),u)),
inference(sor,[status(thm)],[23,2707]),
[iquote('0:SoR:23.0,2707.0')] ).
cnf(5147,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,w)),or__dfg(x,u))),
inference(sor,[status(thm)],[80,4040]),
[iquote('0:SoR:80.0,4040.0')] ).
cnf(32886,plain,
theorem(or__dfg(not__dfg(or__dfg(or__dfg(u,v),u)),or__dfg(u,v))),
inference(sor,[status(thm)],[21,5147]),
[iquote('0:SoR:21.0,5147.0')] ).
cnf(32893,plain,
$false,
inference(unc,[status(thm)],[32886,140]),
[iquote('0:UnC:32886.0,140.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL196-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 04:09:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 131.35/131.62
% 131.35/131.62 SPASS V 3.9
% 131.35/131.62 SPASS beiseite: Proof found.
% 131.35/131.62 % SZS status Theorem
% 131.35/131.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.35/131.62 SPASS derived 32863 clauses, backtracked 0 clauses, performed 0 splits and kept 18854 clauses.
% 131.35/131.62 SPASS allocated 127900 KBytes.
% 131.35/131.62 SPASS spent 0:02:07.82 on the problem.
% 131.35/131.62 0:00:00.06 for the input.
% 131.35/131.62 0:00:00.00 for the FLOTTER CNF translation.
% 131.35/131.62 0:00:02.20 for inferences.
% 131.35/131.62 0:00:00.00 for the backtracking.
% 131.35/131.62 0:02:04.52 for the reduction.
% 131.35/131.62
% 131.35/131.62
% 131.35/131.62 Here is a proof with depth 11, length 30 :
% 131.35/131.62 % SZS output start Refutation
% See solution above
% 131.35/131.62 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 131.35/131.62
%------------------------------------------------------------------------------