%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL190-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 01:06:59 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 0 equ; 7 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(q,r))),or__dfg(p,or__dfg(r,q)))),
file('LCL190-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL190-1.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('LCL190-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL190-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL190-1.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(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(50,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(54,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(114,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[50,54]),
[iquote('0:SoR:50.0,54.0')] ).
cnf(124,plain,
$false,
inference(unc,[status(thm)],[114,1]),
[iquote('0:UnC:114.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL190-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 02:05:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 105 clauses, backtracked 0 clauses, performed 0 splits and kept 78 clauses.
% 0.22/0.49 SPASS allocated 75790 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.11 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.01 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 5, length 12 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : prove_this axiom_1_4 axiom_1_6 rule_1 rule_2
% 0.22/0.49
%------------------------------------------------------------------------------