%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT052-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 : Tue Sep 8 06:19:56 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.49s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 4 unt; 2 nHn; 8 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ dissimilar(u,v,w)
| is_aligned(u,w)
| is_aligned(u,v) ),
file('MGT052-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ is_aligned(u,v)
| ~ is_aligned(u,w)
| ~ dissimilar(u,w,v) ),
file('MGT052-1.p',unknown),
[] ).
cnf(8,axiom,
dissimilar(sk1,sk2,sk2),
file('MGT052-1.p',unknown),
[] ).
cnf(20,plain,
( ~ is_aligned(sk1,sk2)
| ~ is_aligned(sk1,sk2) ),
inference(res,[status(thm),theory(equality)],[8,3]),
[iquote('0:Res:8.0,3.0')] ).
cnf(21,plain,
( is_aligned(sk1,sk2)
| is_aligned(sk1,sk2) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.0,2.0')] ).
cnf(23,plain,
is_aligned(sk1,sk2),
inference(obv,[status(thm),theory(equality)],[21]),
[iquote('0:Obv:21.0')] ).
cnf(24,plain,
~ is_aligned(sk1,sk2),
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('0:Obv:20.0')] ).
cnf(25,plain,
$false,
inference(mrr,[status(thm)],[24,23]),
[iquote('0:MRR:24.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT052-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n010.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 7 13:22:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.24/0.49
% 0.24/0.49 SPASS V 3.9
% 0.24/0.49 SPASS beiseite: Proof found.
% 0.24/0.49 % SZS status Theorem
% 0.24/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.49 SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.24/0.49 SPASS allocated 75593 KBytes.
% 0.24/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.24/0.49 0:00:00.06 for the input.
% 0.24/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.49 0:00:00.00 for inferences.
% 0.24/0.49 0:00:00.00 for the backtracking.
% 0.24/0.49 0:00:00.00 for the reduction.
% 0.24/0.49
% 0.24/0.49
% 0.24/0.49 Here is a proof with depth 1, length 8 :
% 0.24/0.49 % SZS output start Refutation
% See solution above
% 0.24/0.49 Formulae used in the proof : definition_2_30 definition_2_31 background_assumption_1_36
% 0.24/0.49
%------------------------------------------------------------------------------