%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL186-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 01:06:58 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 7 unt; 0 nHn; 13 RR)
% Number of literals : 21 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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(p)),or__dfg(not__dfg(p),q))),
file('LCL186-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL186-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL186-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL186-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL186-1.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('LCL186-1.p',unknown),
[] ).
cnf(11,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(p),q)))
| ~ axiom(or__dfg(not__dfg(not__dfg(p)),u)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.0')] ).
cnf(24,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(33,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[24,7]),
[iquote('0:SoR:24.0,7.1')] ).
cnf(43,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[33,4]),
[iquote('0:SoR:33.0,4.0')] ).
cnf(59,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
inference(sor,[status(thm)],[24,43]),
[iquote('0:SoR:24.0,43.0')] ).
cnf(109,plain,
~ axiom(or__dfg(not__dfg(not__dfg(p)),or__dfg(q,not__dfg(p)))),
inference(res,[status(thm),theory(equality)],[59,11]),
[iquote('0:Res:59.0,11.0')] ).
cnf(115,plain,
$false,
inference(mrr,[status(thm)],[109,3]),
[iquote('0:MRR:109.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n004.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 23:43:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.44
% 0.10/0.44 SPASS V 3.9
% 0.10/0.44 SPASS beiseite: Proof found.
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 SPASS derived 96 clauses, backtracked 0 clauses, performed 0 splits and kept 76 clauses.
% 0.10/0.44 SPASS allocated 75766 KBytes.
% 0.10/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.10/0.44 0:00:00.03 for the input.
% 0.10/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.10/0.44 0:00:00.00 for inferences.
% 0.10/0.44 0:00:00.00 for the backtracking.
% 0.10/0.44 0:00:00.00 for the reduction.
% 0.10/0.44
% 0.10/0.44
% 0.10/0.44 Here is a proof with depth 5, length 13 :
% 0.10/0.44 % SZS output start Refutation
% See solution above
% 0.10/0.44 Formulae used in the proof : prove_this axiom_1_3 axiom_1_4 rule_1 rule_2 rule_3
% 0.10/0.44
%------------------------------------------------------------------------------