%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 01:07:50 PM UTC 2026
% Result : Theorem 0.22s 0.56s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 5 unt; 9 nHn; 16 RR)
% Number of literals : 47 ( 0 equ; 24 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
r1(skc2,skc7),
file('LCL638+1.001.p',unknown),
[] ).
cnf(4,axiom,
~ p1(skc7),
file('LCL638+1.001.p',unknown),
[] ).
cnf(5,axiom,
~ p1(skf10(u)),
file('LCL638+1.001.p',unknown),
[] ).
cnf(6,axiom,
~ p1(skf6(u)),
file('LCL638+1.001.p',unknown),
[] ).
cnf(7,axiom,
( ~ r1(skc7,u)
| p1(u) ),
file('LCL638+1.001.p',unknown),
[] ).
cnf(8,axiom,
( ~ r1(skc2,u)
| r1(u,skf11(u)) ),
file('LCL638+1.001.p',unknown),
[] ).
cnf(10,axiom,
( ~ r1(u,v)
| ~ r1(skc2,u)
| p1(u)
| r1(v,skf6(v)) ),
file('LCL638+1.001.p',unknown),
[] ).
cnf(14,axiom,
( ~ r1(u,v)
| ~ r1(w,u)
| ~ r1(skc2,w)
| p1(v)
| r1(w,skf10(w)) ),
file('LCL638+1.001.p',unknown),
[] ).
cnf(30,plain,
( ~ r1(skc2,u)
| ~ r1(skc2,u)
| p1(u)
| r1(skf11(u),skf6(skf11(u))) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.1,10.0')] ).
cnf(32,plain,
( ~ r1(skc2,u)
| p1(u)
| r1(skf11(u),skf6(skf11(u))) ),
inference(obv,[status(thm),theory(equality)],[30]),
[iquote('0:Obv:30.0')] ).
cnf(69,plain,
( ~ r1(skc2,u)
| ~ r1(v,skf11(u))
| ~ r1(skc2,v)
| p1(u)
| p1(skf6(skf11(u)))
| r1(v,skf10(v)) ),
inference(res,[status(thm),theory(equality)],[32,14]),
[iquote('0:Res:32.2,14.0')] ).
cnf(72,plain,
( ~ r1(skc2,u)
| ~ r1(v,skf11(u))
| ~ r1(skc2,v)
| p1(u)
| r1(v,skf10(v)) ),
inference(mrr,[status(thm)],[69,6]),
[iquote('0:MRR:69.4,6.0')] ).
cnf(159,plain,
( ~ r1(skc2,u)
| ~ r1(skc2,u)
| ~ r1(skc2,u)
| p1(u)
| r1(u,skf10(u)) ),
inference(res,[status(thm),theory(equality)],[8,72]),
[iquote('0:Res:8.1,72.1')] ).
cnf(160,plain,
( ~ r1(skc2,u)
| p1(u)
| r1(u,skf10(u)) ),
inference(obv,[status(thm),theory(equality)],[159]),
[iquote('0:Obv:159.1')] ).
cnf(169,plain,
( ~ r1(skc2,skc7)
| p1(skc7)
| p1(skf10(skc7)) ),
inference(res,[status(thm),theory(equality)],[160,7]),
[iquote('0:Res:160.2,7.0')] ).
cnf(179,plain,
$false,
inference(mrr,[status(thm)],[169,2,4,5]),
[iquote('0:MRR:169.0,169.1,169.2,2.0,4.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 19:37:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.22/0.56
% 0.22/0.56 SPASS V 3.9
% 0.22/0.56 SPASS beiseite: Proof found.
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.56 SPASS derived 121 clauses, backtracked 0 clauses, performed 2 splits and kept 98 clauses.
% 0.22/0.56 SPASS allocated 97831 KBytes.
% 0.22/0.56 SPASS spent 0:00:00.18 on the problem.
% 0.22/0.56 0:00:00.06 for the input.
% 0.22/0.56 0:00:00.06 for the FLOTTER CNF translation.
% 0.22/0.56 0:00:00.00 for inferences.
% 0.22/0.56 0:00:00.00 for the backtracking.
% 0.22/0.56 0:00:00.01 for the reduction.
% 0.22/0.56
% 0.22/0.56
% 0.22/0.56 Here is a proof with depth 4, length 16 :
% 0.22/0.56 % SZS output start Refutation
% See solution above
% 0.22/0.56 Formulae used in the proof : main
% 0.22/0.56
%------------------------------------------------------------------------------