%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 07:07:21 PM UTC 2026
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 11 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
~ equal(cons(u,v),nil),
file('SWX186+1.p',unknown),
[] ).
cnf(7,axiom,
equal(drop(s(u),nil),nil),
file('SWX186+1.p',unknown),
[] ).
cnf(8,axiom,
equal(drop(s(u),cons(v,w)),drop(u,w)),
file('SWX186+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(drop(u,v),drop(u,w))
| equal(v,w) ),
file('SWX186+1.p',unknown),
[] ).
cnf(24,plain,
( ~ equal(drop(s(u),v),nil)
| equal(nil,v) ),
inference(spl,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpL:7.0,9.0')] ).
cnf(32,plain,
( ~ equal(drop(u,v),nil)
| equal(cons(w,v),nil) ),
inference(spl,[status(thm),theory(equality)],[8,24]),
[iquote('0:SpL:8.0,24.0')] ).
cnf(33,plain,
~ equal(drop(u,v),nil),
inference(mrr,[status(thm)],[32,6]),
[iquote('0:MRR:32.1,6.0')] ).
cnf(34,plain,
$false,
inference(unc,[status(thm)],[33,7]),
[iquote('0:UnC:33.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n016.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
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 09:38:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.18/0.42 SPASS allocated 85101 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 2, length 8 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : axiom_003 axiom_006 axiom_007 goal_009
% 0.18/0.42
%------------------------------------------------------------------------------