%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-4 : 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 : n026.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 07:32:02 AM UTC 2026
% Result : Unsatisfiable 0.24s 5.51s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 31 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal2,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',quotient_less_equal2) ).
cnf(c_2,plain,
( less_equal(A,B)
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[quotient_less_equal2]) ).
fof(less_equal_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ less_equal(VAR_1,VAR_0)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',less_equal_and_equal) ).
cnf(c_6,plain,
( A = B
| ~ less_equal(B,A)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[less_equal_and_equal]) ).
fof(x_divide_x_is_zero,axiom,
! [VAR_0] : divide(VAR_0,VAR_0) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(c_10,plain,
divide(A,A) = zero,
inference(clausify,[status(thm)],[x_divide_x_is_zero]) ).
fof(property_of_divide1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(divide(VAR_0,VAR_2),VAR_1)
| ~ less_equal(divide(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',property_of_divide1) ).
cnf(c_13,plain,
( less_equal(divide(A,C),B)
| ~ less_equal(divide(A,B),C) ),
inference(clausify,[status(thm)],[property_of_divide1]) ).
fof(property_of_divide2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(divide(VAR_2,VAR_1),divide(VAR_2,VAR_0))
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',property_of_divide2) ).
cnf(c_14,plain,
( less_equal(divide(C,B),divide(C,A))
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[property_of_divide2]) ).
fof(prove_this,axiom,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(c_16,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_17,plain,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_22,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_42,plain,
less_equal(divide(A,divide(A,B)),B),
inference(resolve,[status(thm)],[c_13,c_22]) ).
cnf(c_83,plain,
less_equal(divide(A,B),divide(A,divide(C,divide(C,B)))),
inference(resolve,[status(thm)],[c_14,c_42]) ).
cnf(c_97,plain,
( A = divide(B,divide(B,A))
| ~ less_equal(A,divide(B,divide(B,A))) ),
inference(resolve,[status(thm)],[c_6,c_42]) ).
cnf(c_98,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_95,plain,
~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),
inference(resolve,[status(thm)],[c_97,c_98]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_95,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.47 % Computer : n026.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Fri Sep 25 16:00:15 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.47 % Process 2959574 was started by sandbox2 on n026,
% 0.19/5.47 % Fri Sep 25 16:00:15 2026
% 0.19/5.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.48
% 0.19/5.48 % From the command line: assign(max_seconds, 300).
% 0.24/5.51
% 0.24/5.51 % SZS status Unsatisfiable for theBenchmark
% 0.24/5.51
% 0.24/5.51 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.24/5.51 % Length of proof is 12.
% 0.24/5.51 % Level of proof is 4.
% 0.24/5.51 % Maximum clause weight is 11.000.
% 0.24/5.51 % Given clauses 25.
% 0.24/5.51
% 0.24/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------