%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 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 07:32:02 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 46 unt; 0 def)
% Number of atoms : 76 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 7 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal1,axiom,
! [VAR_0,VAR_1] :
( divide(VAR_0,VAR_1) = zero
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal1) ).
cnf(c_1,plain,
( divide(A,B) = zero
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal1]) ).
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(quotient_smaller_than_numerator,axiom,
! [VAR_0,VAR_1] : less_equal(divide(VAR_0,VAR_1),VAR_0),
file('theBenchmark.p',quotient_smaller_than_numerator) ).
cnf(c_3,plain,
less_equal(divide(A,B),A),
inference(clausify,[status(thm)],[quotient_smaller_than_numerator]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2] : less_equal(divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1)),divide(divide(VAR_0,VAR_2),VAR_1)),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : less_equal(zero,VAR_0),
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_5,plain,
less_equal(zero,A),
inference(clausify,[status(thm)],[zero_is_smallest]) ).
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(identity_is_largest,axiom,
! [VAR_0] : less_equal(VAR_0,identity),
file('theBenchmark.p',identity_is_largest) ).
cnf(c_7,plain,
less_equal(A,identity),
inference(clausify,[status(thm)],[identity_is_largest]) ).
fof(zero_divide_anything_is_zero,axiom,
! [VAR_0] : divide(zero,VAR_0) = zero,
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(c_9,plain,
divide(zero,A) = zero,
inference(clausify,[status(thm)],[zero_divide_anything_is_zero]) ).
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_11,plain,
( less_equal(divide(A,C),B)
| ~ less_equal(divide(A,B),C) ),
inference(clausify,[status(thm)],[property_of_divide1]) ).
fof(property_of_divide3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(divide(VAR_0,VAR_2),divide(VAR_1,VAR_2))
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',property_of_divide3) ).
cnf(c_12,plain,
( less_equal(divide(A,C),divide(B,C))
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[property_of_divide3]) ).
fof(id_divide_a_is_b,axiom,
divide(identity,a) = b,
file('theBenchmark.p',id_divide_a_is_b) ).
cnf(c_15,plain,
divide(identity,a) = b,
inference(clausify,[status(thm)],[id_divide_a_is_b]) ).
cnf(c_16,plain,
b = divide(identity,a),
inference(copy,[status(thm)],[c_15]) ).
fof(id_divide_b_is_c,axiom,
divide(identity,b) = c,
file('theBenchmark.p',id_divide_b_is_c) ).
cnf(c_17,plain,
divide(identity,b) = c,
inference(clausify,[status(thm)],[id_divide_b_is_c]) ).
cnf(c_18,plain,
divide(identity,divide(identity,a)) = c,
inference(paramod,[status(thm)],[c_16,c_17]) ).
fof(id_divide_c_is_d,axiom,
divide(identity,c) = d,
file('theBenchmark.p',id_divide_c_is_d) ).
cnf(c_19,plain,
divide(identity,c) = d,
inference(clausify,[status(thm)],[id_divide_c_is_d]) ).
cnf(c_20,plain,
d = divide(identity,c),
inference(copy,[status(thm)],[c_19]) ).
fof(prove_b_equals_d,axiom,
b != d,
file('theBenchmark.p',prove_b_equals_d) ).
cnf(c_21,plain,
b != d,
inference(clausify,[status(thm)],[prove_b_equals_d]) ).
cnf(c_243,plain,
divide(identity,a) != d,
inference(paramod,[status(thm)],[c_16,c_21]) ).
cnf(c_22,plain,
divide(identity,a) != divide(identity,c),
inference(paramod,[status(thm)],[c_20,c_243]) ).
cnf(c_27,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_31,plain,
less_equal(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_42,plain,
less_equal(divide(A,divide(A,B)),B),
inference(resolve,[status(thm)],[c_11,c_27]) ).
cnf(c_44,plain,
less_equal(divide(A,divide(identity,B)),B),
inference(resolve,[status(thm)],[c_11,c_31]) ).
cnf(c_244,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_245,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_244,c_42]) ).
cnf(c_48,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_245]) ).
cnf(c_49,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(resolve,[status(thm)],[c_1,c_42]) ).
cnf(c_51,plain,
less_equal(c,a),
inference(paramod,[status(thm)],[c_18,c_42]) ).
cnf(c_54,plain,
divide(c,a) = zero,
inference(resolve,[status(thm)],[c_1,c_51]) ).
cnf(c_71,plain,
less_equal(divide(divide(A,a),zero),divide(divide(A,c),a)),
inference(paramod,[status(thm)],[c_54,c_4]) ).
cnf(c_82,plain,
less_equal(divide(A,c),divide(identity,a)),
inference(paramod,[status(thm)],[c_18,c_44]) ).
cnf(c_88,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_48]) ).
cnf(c_246,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_100,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_246,c_88]) ).
cnf(c_106,plain,
less_equal(divide(A,a),divide(divide(A,c),a)),
inference(paramod,[status(thm)],[c_100,c_71]) ).
cnf(c_247,plain,
( divide(identity,a) = divide(A,c)
| ~ less_equal(divide(identity,a),divide(A,c)) ),
inference(resolve,[status(thm)],[c_6,c_82]) ).
cnf(c_126,plain,
~ less_equal(divide(identity,a),divide(identity,c)),
inference(resolve,[status(thm)],[c_247,c_22]) ).
cnf(c_139,plain,
~ less_equal(divide(identity,divide(identity,c)),a),
inference(resolve,[status(thm)],[c_11,c_126]) ).
cnf(c_141,plain,
divide(divide(identity,divide(identity,c)),a) != zero,
inference(resolve,[status(thm)],[c_2,c_139]) ).
cnf(c_248,plain,
( A = zero
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_143,plain,
~ less_equal(divide(divide(identity,divide(identity,c)),a),zero),
inference(resolve,[status(thm)],[c_248,c_141]) ).
cnf(c_249,plain,
less_equal(divide(divide(A,divide(A,c)),a),divide(zero,a)),
inference(paramod,[status(thm)],[c_49,c_106]) ).
cnf(c_241,plain,
less_equal(divide(divide(A,divide(A,c)),a),zero),
inference(paramod,[status(thm)],[c_9,c_249]) ).
cnf(c_242,plain,
$false,
inference(resolve,[status(thm)],[c_241,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n019.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Fri Sep 25 15:58:03 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3171898 was started by sandbox2 on n019,
% 0.15/0.44 % Fri Sep 25 15:58:03 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 0.15/0.49
% 0.15/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.49
% 0.15/0.49 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.49 % Length of proof is 38.
% 0.15/0.49 % Level of proof is 8.
% 0.15/0.49 % Maximum clause weight is 13.000.
% 0.15/0.49 % Given clauses 64.
% 0.15/0.49
% 0.15/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------