%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP188-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:28:19 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 6 !; 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(idempotence_of_lub,axiom,
! [VAR_0] : least_upper_bound(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_lub) ).
cnf(c_10,plain,
least_upper_bound(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_lub]) ).
fof(prove_p38a,axiom,
least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
file('theBenchmark.p',prove_p38a) ).
cnf(c_25,plain,
least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b),
inference(clausify,[status(thm)],[prove_p38a]) ).
cnf(c_32,plain,
least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_30,plain,
least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(B,least_upper_bound(A,C)),
inference(paramod,[status(thm)],[c_9,c_32]) ).
cnf(c_33,plain,
least_upper_bound(a,least_upper_bound(b,b)) != least_upper_bound(a,b),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_34,plain,
least_upper_bound(a,b) != least_upper_bound(a,b),
inference(paramod,[status(thm)],[c_10,c_33]) ).
cnf(c_31,plain,
$false,
inference(copy,[status(thm)],[c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP188-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 25 14:36:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3397041 was started by sandbox on n004,
% 0.09/0.36 % Fri Sep 25 14:36:38 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 7.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 11.000.
% 0.09/0.38 % Given clauses 7.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------