%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP156-1 : 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 : n019.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 07:28:09 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
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(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(ax_mono1c_1,axiom,
least_upper_bound(a,b) = b,
file('theBenchmark.p',ax_mono1c_1) ).
cnf(c_22,plain,
least_upper_bound(a,b) = b,
inference(clausify,[status(thm)],[ax_mono1c_1]) ).
cnf(c_23,plain,
least_upper_bound(b,a) = b,
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(prove_ax_mono1c,axiom,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
file('theBenchmark.p',prove_ax_mono1c) ).
cnf(c_24,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c),
inference(clausify,[status(thm)],[prove_ax_mono1c]) ).
cnf(c_93,plain,
greatest_lower_bound(multiply(b,c),multiply(a,c)) != multiply(a,c),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_25,plain,
multiply(greatest_lower_bound(b,a),c) != multiply(a,c),
inference(paramod,[status(thm)],[c_21,c_93]) ).
cnf(c_41,plain,
greatest_lower_bound(A,least_upper_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_94,plain,
greatest_lower_bound(a,b) = a,
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_91,plain,
greatest_lower_bound(b,a) = a,
inference(paramod,[status(thm)],[c_4,c_94]) ).
cnf(c_95,plain,
multiply(a,c) != multiply(a,c),
inference(paramod,[status(thm)],[c_91,c_25]) ).
cnf(c_92,plain,
$false,
inference(copy,[status(thm)],[c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP156-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:32:18 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2968973 was started by sandbox2 on n019,
% 0.11/0.36 % Fri Sep 25 14:32:18 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.39 % Length of proof is 12.
% 0.15/0.39 % Level of proof is 3.
% 0.15/0.39 % Maximum clause weight is 13.000.
% 0.15/0.39 % Given clauses 22.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------