%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:07:23 PM UTC 2026
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 6 unt; 3 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ord(nil),
file('SWX200+1.p',unknown),
[] ).
cnf(6,axiom,
~ leqNat(s(u),z__dfg),
file('SWX200+1.p',unknown),
[] ).
cnf(7,axiom,
equal(merge(nil,u),u),
file('SWX200+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ord(u)
| ord(merge(u,v))
| ord(v) ),
file('SWX200+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ ord(cons(u,cons(v,w)))
| leqNat(u,v) ),
file('SWX200+1.p',unknown),
[] ).
cnf(20,plain,
( ord(merge(nil,u))
| ord(u) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(22,plain,
( ord(u)
| ord(u) ),
inference(rew,[status(thm),theory(equality)],[7,20]),
[iquote('0:Rew:7.0,20.0')] ).
cnf(23,plain,
ord(u),
inference(obv,[status(thm),theory(equality)],[22]),
[iquote('0:Obv:22.0')] ).
cnf(24,plain,
leqNat(u,v),
inference(mrr,[status(thm)],[15,23]),
[iquote('0:MRR:15.0,23.0')] ).
cnf(25,plain,
$false,
inference(unc,[status(thm)],[24,6]),
[iquote('0:UnC:24.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n002.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 11:15:01 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.18/0.43 SPASS allocated 97642 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 1, length 10 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : axiom_013 axiom_007 axiom_009 goal_016 axiom_015
% 0.18/0.43
%------------------------------------------------------------------------------