%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Sun Sep 27 07:28:07 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(associativity_of_lub,axiom,
! [VAR_0,VAR_1,VAR_2] : least_upper_bound(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(least_upper_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_lub) ).
cnf(c_8,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_lub]) ).
cnf(c_9,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(ax_lub1a_1,axiom,
least_upper_bound(a,c) = c,
file('theBenchmark.p',ax_lub1a_1) ).
cnf(c_22,plain,
least_upper_bound(a,c) = c,
inference(clausify,[status(thm)],[ax_lub1a_1]) ).
cnf(c_23,plain,
least_upper_bound(c,a) = c,
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(ax_lub1a_2,axiom,
least_upper_bound(b,c) = c,
file('theBenchmark.p',ax_lub1a_2) ).
cnf(c_24,plain,
least_upper_bound(b,c) = c,
inference(clausify,[status(thm)],[ax_lub1a_2]) ).
cnf(c_25,plain,
least_upper_bound(c,b) = c,
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_ax_lub1a,axiom,
least_upper_bound(least_upper_bound(a,b),c) != c,
file('theBenchmark.p',prove_ax_lub1a) ).
cnf(c_26,plain,
least_upper_bound(least_upper_bound(a,b),c) != c,
inference(clausify,[status(thm)],[prove_ax_lub1a]) ).
cnf(c_27,plain,
least_upper_bound(c,least_upper_bound(a,b)) != c,
inference(paramod,[status(thm)],[c_5,c_26]) ).
cnf(c_70,plain,
least_upper_bound(c,A) = least_upper_bound(c,least_upper_bound(a,A)),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_67,plain,
least_upper_bound(c,least_upper_bound(a,A)) = least_upper_bound(c,A),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
least_upper_bound(c,b) != c,
inference(paramod,[status(thm)],[c_67,c_27]) ).
cnf(c_72,plain,
c != c,
inference(paramod,[status(thm)],[c_25,c_71]) ).
cnf(c_69,plain,
$false,
inference(copy,[status(thm)],[c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 14:32:33 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3131253 was started by sandbox2 on n020,
% 0.07/0.35 % Fri Sep 25 14:32:33 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.39
% 0.07/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.39
% 0.07/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.07/0.39 % Length of proof is 11.
% 0.07/0.39 % Level of proof is 3.
% 0.07/0.39 % Maximum clause weight is 11.000.
% 0.07/0.39 % Given clauses 16.
% 0.07/0.39
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------