%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 01:07:58 PM UTC 2026
% Result : Theorem 0.24s 0.54s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 54 ( 0 equ; 31 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
r1(skc9,skc10),
file('LCL654+1.001.p',unknown),
[] ).
cnf(2,axiom,
r1(skc8,skc9),
file('LCL654+1.001.p',unknown),
[] ).
cnf(3,axiom,
r1(skc4,skc8),
file('LCL654+1.001.p',unknown),
[] ).
cnf(4,axiom,
~ p1(skc10),
file('LCL654+1.001.p',unknown),
[] ).
cnf(5,axiom,
r1(u,u),
file('LCL654+1.001.p',unknown),
[] ).
cnf(6,axiom,
r1(u,skf9(u)),
file('LCL654+1.001.p',unknown),
[] ).
cnf(7,axiom,
r1(u,skf7(u)),
file('LCL654+1.001.p',unknown),
[] ).
cnf(8,axiom,
r1(u,skf6(u)),
file('LCL654+1.001.p',unknown),
[] ).
cnf(10,axiom,
( ~ r1(skc8,u)
| p1(u) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(13,axiom,
( ~ p1(skf7(u))
| ~ r1(v,u)
| ~ r1(skc4,v)
| skP0(v) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(14,axiom,
( ~ skP0(u)
| ~ r1(u,v)
| ~ r1(skf9(v),w)
| p1(w) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(15,axiom,
( ~ p1(skf6(u))
| ~ r1(v,w)
| ~ r1(v,u)
| ~ r1(x,v)
| ~ r1(skc4,x)
| p1(w) ),
file('LCL654+1.001.p',unknown),
[] ).
cnf(22,plain,
p1(skc8),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(25,plain,
p1(skf7(skc8)),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.0,10.0')] ).
cnf(42,plain,
( ~ r1(u,skc8)
| ~ r1(skc4,u)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[25,13]),
[iquote('0:Res:25.0,13.0')] ).
cnf(44,plain,
( ~ r1(skc4,skc8)
| skP0(skc8) ),
inference(res,[status(thm),theory(equality)],[5,42]),
[iquote('0:Res:5.0,42.0')] ).
cnf(46,plain,
skP0(skc8),
inference(mrr,[status(thm)],[44,3]),
[iquote('0:MRR:44.0,3.0')] ).
cnf(49,plain,
( ~ skP0(u)
| ~ r1(u,v)
| p1(skf6(skf9(v))) ),
inference(res,[status(thm),theory(equality)],[8,14]),
[iquote('0:Res:8.0,14.2')] ).
cnf(76,plain,
( ~ skP0(skc8)
| p1(skf6(skf9(skc9))) ),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.1')] ).
cnf(85,plain,
p1(skf6(skf9(skc9))),
inference(ssi,[status(thm)],[76,22,46]),
[iquote('0:SSi:76.0,22.0,46.0')] ).
cnf(87,plain,
( ~ r1(u,v)
| ~ r1(u,skf9(skc9))
| ~ r1(w,u)
| ~ r1(skc4,w)
| p1(v) ),
inference(res,[status(thm),theory(equality)],[85,15]),
[iquote('0:Res:85.0,15.0')] ).
cnf(218,plain,
( ~ r1(skc9,u)
| ~ r1(v,skc9)
| ~ r1(skc4,v)
| p1(u) ),
inference(res,[status(thm),theory(equality)],[6,87]),
[iquote('0:Res:6.0,87.1')] ).
cnf(219,plain,
( ~ r1(u,skc9)
| ~ r1(skc4,u)
| p1(skc10) ),
inference(res,[status(thm),theory(equality)],[1,218]),
[iquote('0:Res:1.0,218.0')] ).
cnf(226,plain,
( ~ r1(u,skc9)
| ~ r1(skc4,u) ),
inference(mrr,[status(thm)],[219,4]),
[iquote('0:MRR:219.2,4.0')] ).
cnf(227,plain,
~ r1(skc4,skc8),
inference(res,[status(thm),theory(equality)],[2,226]),
[iquote('0:Res:2.0,226.0')] ).
cnf(229,plain,
$false,
inference(mrr,[status(thm)],[227,3]),
[iquote('0:MRR:227.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 00:39:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.24/0.54
% 0.24/0.54 SPASS V 3.9
% 0.24/0.54 SPASS beiseite: Proof found.
% 0.24/0.54 % SZS status Theorem
% 0.24/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.54 SPASS derived 172 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.24/0.54 SPASS allocated 97791 KBytes.
% 0.24/0.54 SPASS spent 0:00:00.16 on the problem.
% 0.24/0.54 0:00:00.06 for the input.
% 0.24/0.54 0:00:00.05 for the FLOTTER CNF translation.
% 0.24/0.54 0:00:00.01 for inferences.
% 0.24/0.54 0:00:00.00 for the backtracking.
% 0.24/0.54 0:00:00.02 for the reduction.
% 0.24/0.54
% 0.24/0.54
% 0.24/0.54 Here is a proof with depth 6, length 26 :
% 0.24/0.54 % SZS output start Refutation
% See solution above
% 0.24/0.54 Formulae used in the proof : main reflexivity
% 0.24/0.54
%------------------------------------------------------------------------------