%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:32:00 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 9 !; 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(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(transitivity_of_less_equal,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_0,VAR_2)
| ~ less_equal(VAR_1,VAR_2)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less_equal) ).
cnf(c_12,plain,
( less_equal(A,C)
| ~ less_equal(B,C)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_equal]) ).
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(a_LE_b,axiom,
less_equal(a,b),
file('theBenchmark.p',a_LE_b) ).
cnf(c_14,plain,
less_equal(a,b),
inference(clausify,[status(thm)],[a_LE_b]) ).
fof(prove_c_divide_b_LE_c_divide_a,axiom,
~ less_equal(divide(c,b),divide(c,a)),
file('theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
cnf(c_15,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(clausify,[status(thm)],[prove_c_divide_b_LE_c_divide_a]) ).
cnf(c_20,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_34,plain,
~ less_equal(divide(c,divide(c,a)),b),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_50,plain,
less_equal(divide(A,divide(A,B)),B),
inference(resolve,[status(thm)],[c_13,c_20]) ).
cnf(c_107,plain,
( less_equal(divide(C,divide(C,A)),B)
| ~ less_equal(A,B) ),
inference(resolve,[status(thm)],[c_12,c_50]) ).
cnf(c_105,plain,
less_equal(divide(A,divide(A,a)),b),
inference(resolve,[status(thm)],[c_107,c_14]) ).
cnf(c_106,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n017.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:52:17 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2695078 was started by sandbox on n017,
% 0.16/0.44 % Fri Sep 25 15:52:17 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/0.47 % Length of proof is 11.
% 0.16/0.47 % Level of proof is 4.
% 0.16/0.47 % Maximum clause weight is 10.000.
% 0.16/0.47 % Given clauses 31.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------