%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 01:07:59 PM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 18 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
p100(skc1),
file('LCL656+1.001.p',unknown),
[] ).
cnf(2,axiom,
~ p101(skc1),
file('LCL656+1.001.p',unknown),
[] ).
cnf(3,axiom,
r1(u,u),
file('LCL656+1.001.p',unknown),
[] ).
cnf(5,axiom,
r1(u,skf2(u)),
file('LCL656+1.001.p',unknown),
[] ).
cnf(6,axiom,
( ~ r1(skc1,u)
| p2(u) ),
file('LCL656+1.001.p',unknown),
[] ).
cnf(12,axiom,
( ~ p100(u)
| ~ p2(skf2(u))
| ~ r1(skc1,u)
| p101(u) ),
file('LCL656+1.001.p',unknown),
[] ).
cnf(35,plain,
p2(skc1),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.0')] ).
cnf(36,plain,
p2(skf2(skc1)),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.0,6.0')] ).
cnf(65,plain,
( ~ p100(skc1)
| ~ r1(skc1,skc1)
| p101(skc1) ),
inference(res,[status(thm),theory(equality)],[36,12]),
[iquote('0:Res:36.0,12.1')] ).
cnf(66,plain,
( ~ r1(skc1,skc1)
| p101(skc1) ),
inference(ssi,[status(thm)],[65,1,35]),
[iquote('0:SSi:65.0,1.0,35.0')] ).
cnf(67,plain,
$false,
inference(mrr,[status(thm)],[66,3,2]),
[iquote('0:MRR:66.0,66.1,3.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 02:15:42 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.22/0.51
% 0.22/0.51 SPASS V 3.9
% 0.22/0.51 SPASS beiseite: Proof found.
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.22/0.51 SPASS allocated 97654 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.22/0.51 0:00:00.06 for the input.
% 0.22/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.00 for inferences.
% 0.22/0.51 0:00:00.00 for the backtracking.
% 0.22/0.51 0:00:00.00 for the reduction.
% 0.22/0.51
% 0.22/0.51
% 0.22/0.51 Here is a proof with depth 2, length 11 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : main reflexivity
% 0.22/0.51
%------------------------------------------------------------------------------