%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 01:08:12 PM UTC 2026
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 7 RR)
% Number of literals : 13 ( 0 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
p201(skc1),
file('LCL684+1.001.p',unknown),
[] ).
cnf(2,axiom,
p101(skc1),
file('LCL684+1.001.p',unknown),
[] ).
cnf(3,axiom,
r1(u,u),
file('LCL684+1.001.p',unknown),
[] ).
cnf(5,axiom,
( ~ p101(u)
| ~ p201(u)
| ~ r1(v,u)
| ~ r1(skc1,v) ),
file('LCL684+1.001.p',unknown),
[] ).
cnf(8,plain,
( ~ p101(u)
| ~ p201(u)
| ~ r1(skc1,u) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.0,5.2')] ).
cnf(9,plain,
( ~ p101(skc1)
| ~ p201(skc1) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.2')] ).
cnf(10,plain,
$false,
inference(ssi,[status(thm)],[9,2,1]),
[iquote('0:SSi:9.1,9.0,2.0,1.0,2.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n028.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 16:35:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 6 clauses.
% 0.20/0.52 SPASS allocated 97600 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.52 0:00:00.06 for the input.
% 0.20/0.52 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.00 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.00 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 2, length 7 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : main reflexivity
% 0.20/0.52
%------------------------------------------------------------------------------