%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-3 : 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 : n020.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 0.13s 5.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 101 ( 81 unt; 0 def)
% Number of atoms : 123 ( 64 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 119 ( 23 sgn 13 !; 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(id_divide_a_is_b,axiom,
divide(identity,a) = b,
file('theBenchmark.p',id_divide_a_is_b) ).
cnf(c_10,plain,
divide(identity,a) = b,
inference(clausify,[status(thm)],[id_divide_a_is_b]) ).
cnf(c_11,plain,
b = divide(identity,a),
inference(copy,[status(thm)],[c_10]) ).
fof(id_divide_b_is_c,axiom,
divide(identity,b) = c,
file('theBenchmark.p',id_divide_b_is_c) ).
cnf(c_12,plain,
divide(identity,b) = c,
inference(clausify,[status(thm)],[id_divide_b_is_c]) ).
cnf(c_13,plain,
divide(identity,divide(identity,a)) = c,
inference(paramod,[status(thm)],[c_11,c_12]) ).
fof(id_divide_c_is_d,axiom,
divide(identity,c) = d,
file('theBenchmark.p',id_divide_c_is_d) ).
cnf(c_14,plain,
divide(identity,c) = d,
inference(clausify,[status(thm)],[id_divide_c_is_d]) ).
cnf(c_15,plain,
d = divide(identity,c),
inference(copy,[status(thm)],[c_14]) ).
fof(prove_b_equals_d,axiom,
b != d,
file('theBenchmark.p',prove_b_equals_d) ).
cnf(c_16,plain,
b != d,
inference(clausify,[status(thm)],[prove_b_equals_d]) ).
cnf(c_384,plain,
divide(identity,a) != d,
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_17,plain,
divide(identity,a) != divide(identity,c),
inference(paramod,[status(thm)],[c_15,c_384]) ).
cnf(c_18,plain,
divide(divide(A,B),A) = zero,
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_19,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_20,plain,
divide(zero,A) = zero,
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_21,plain,
divide(A,identity) = zero,
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_22,plain,
less_equal(divide(c,divide(A,divide(identity,a))),divide(divide(identity,A),divide(identity,a))),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_25,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)),
inference(paramod,[status(thm)],[c_18,c_4]) ).
cnf(c_385,plain,
less_equal(divide(divide(divide(A,B),C),divide(A,C)),divide(zero,C)),
inference(paramod,[status(thm)],[c_18,c_4]) ).
cnf(c_26,plain,
less_equal(divide(divide(divide(A,B),C),divide(A,C)),zero),
inference(paramod,[status(thm)],[c_20,c_385]) ).
cnf(c_27,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramod,[status(thm)],[c_18,c_4]) ).
cnf(c_28,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(paramod,[status(thm)],[c_20,c_4]) ).
cnf(c_386,plain,
less_equal(divide(divide(A,B),divide(identity,B)),divide(zero,B)),
inference(paramod,[status(thm)],[c_21,c_4]) ).
cnf(c_29,plain,
less_equal(divide(divide(A,B),divide(identity,B)),zero),
inference(paramod,[status(thm)],[c_20,c_386]) ).
cnf(c_31,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramod,[status(thm)],[c_18,c_27]) ).
cnf(c_387,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_388,plain,
zero = divide(divide(A,A),zero),
inference(resolve,[status(thm)],[c_387,c_31]) ).
cnf(c_32,plain,
divide(divide(A,A),zero) = zero,
inference(copy,[status(thm)],[c_388]) ).
cnf(c_33,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_2,c_32]) ).
cnf(c_389,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_390,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_389,c_33]) ).
cnf(c_36,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_390]) ).
cnf(c_391,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_392,plain,
zero = divide(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_391,c_29]) ).
cnf(c_55,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(copy,[status(thm)],[c_392]) ).
cnf(c_56,plain,
less_equal(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_2,c_55]) ).
cnf(c_60,plain,
divide(divide(A,divide(identity,a)),c) = zero,
inference(paramod,[status(thm)],[c_13,c_55]) ).
cnf(c_64,plain,
less_equal(divide(A,divide(identity,a)),c),
inference(paramod,[status(thm)],[c_13,c_56]) ).
cnf(c_68,plain,
less_equal(divide(c,divide(a,divide(identity,a))),zero),
inference(paramod,[status(thm)],[c_36,c_22]) ).
cnf(c_71,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramod,[status(thm)],[c_36,c_28]) ).
cnf(c_79,plain,
divide(divide(divide(A,c),divide(divide(identity,a),c)),zero) = zero,
inference(paramod,[status(thm)],[c_60,c_19]) ).
cnf(c_393,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_394,plain,
zero = divide(c,divide(a,divide(identity,a))),
inference(resolve,[status(thm)],[c_393,c_68]) ).
cnf(c_80,plain,
divide(c,divide(a,divide(identity,a))) = zero,
inference(copy,[status(thm)],[c_394]) ).
cnf(c_395,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_396,plain,
zero = divide(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_395,c_71]) ).
cnf(c_81,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(copy,[status(thm)],[c_396]) ).
cnf(c_83,plain,
less_equal(c,divide(a,divide(identity,a))),
inference(resolve,[status(thm)],[c_2,c_80]) ).
cnf(c_397,plain,
( divide(A,divide(identity,a)) = c
| ~ less_equal(c,divide(A,divide(identity,a))) ),
inference(resolve,[status(thm)],[c_6,c_64]) ).
cnf(c_89,plain,
divide(a,divide(identity,a)) = c,
inference(resolve,[status(thm)],[c_397,c_83]) ).
cnf(c_100,plain,
less_equal(divide(divide(A,a),zero),divide(divide(A,c),a)),
inference(paramod,[status(thm)],[c_89,c_25]) ).
cnf(c_398,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_399,plain,
zero = divide(divide(divide(A,B),C),divide(A,C)),
inference(resolve,[status(thm)],[c_398,c_26]) ).
cnf(c_117,plain,
divide(divide(divide(A,B),C),divide(A,C)) = zero,
inference(copy,[status(thm)],[c_399]) ).
cnf(c_122,plain,
less_equal(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_2,c_81]) ).
cnf(c_400,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_401,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_400,c_122]) ).
cnf(c_127,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_401]) ).
cnf(c_128,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_127]) ).
cnf(c_129,plain,
less_equal(divide(divide(A,divide(B,zero)),zero),divide(divide(A,B),divide(B,zero))),
inference(paramod,[status(thm)],[c_127,c_4]) ).
cnf(c_402,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_144,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_402,c_128]) ).
cnf(c_403,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,B),divide(B,zero))),
inference(paramod,[status(thm)],[c_144,c_129]) ).
cnf(c_404,plain,
less_equal(divide(A,B),divide(divide(A,B),divide(B,zero))),
inference(paramod,[status(thm)],[c_144,c_403]) ).
cnf(c_148,plain,
less_equal(divide(A,B),divide(divide(A,B),B)),
inference(paramod,[status(thm)],[c_144,c_404]) ).
cnf(c_160,plain,
less_equal(divide(A,a),divide(divide(A,c),a)),
inference(paramod,[status(thm)],[c_144,c_100]) ).
cnf(c_164,plain,
divide(divide(A,c),divide(divide(identity,a),c)) = zero,
inference(paramod,[status(thm)],[c_144,c_79]) ).
cnf(c_405,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_199,plain,
divide(divide(A,B),B) = divide(A,B),
inference(resolve,[status(thm)],[c_405,c_148]) ).
cnf(c_406,plain,
( divide(B,A) = divide(identity,A)
| ~ less_equal(divide(identity,A),divide(B,A)) ),
inference(resolve,[status(thm)],[c_6,c_56]) ).
cnf(c_200,plain,
divide(divide(identity,c),a) = divide(identity,a),
inference(resolve,[status(thm)],[c_406,c_160]) ).
cnf(c_214,plain,
less_equal(divide(identity,a),divide(identity,c)),
inference(paramod,[status(thm)],[c_200,c_3]) ).
cnf(c_407,plain,
( divide(identity,c) = divide(identity,a)
| ~ less_equal(divide(identity,c),divide(identity,a)) ),
inference(resolve,[status(thm)],[c_6,c_214]) ).
cnf(c_408,plain,
divide(identity,c) != divide(identity,a),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_220,plain,
~ less_equal(divide(identity,c),divide(identity,a)),
inference(resolve,[status(thm)],[c_407,c_408]) ).
cnf(c_228,plain,
divide(divide(identity,c),divide(identity,a)) != zero,
inference(resolve,[status(thm)],[c_2,c_220]) ).
cnf(c_334,plain,
less_equal(divide(divide(A,B),C),divide(A,C)),
inference(resolve,[status(thm)],[c_2,c_117]) ).
cnf(c_409,plain,
( divide(A,a) = divide(divide(A,c),a)
| ~ less_equal(divide(divide(A,c),a),divide(A,a)) ),
inference(resolve,[status(thm)],[c_6,c_160]) ).
cnf(c_410,plain,
divide(A,a) = divide(divide(A,c),a),
inference(resolve,[status(thm)],[c_409,c_334]) ).
cnf(c_360,plain,
divide(divide(A,c),a) = divide(A,a),
inference(copy,[status(thm)],[c_410]) ).
cnf(c_365,plain,
less_equal(divide(A,a),divide(A,c)),
inference(paramod,[status(thm)],[c_360,c_3]) ).
cnf(c_379,plain,
less_equal(divide(A,a),divide(divide(A,a),c)),
inference(paramod,[status(thm)],[c_199,c_365]) ).
cnf(c_411,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_381,plain,
divide(divide(A,a),c) = divide(A,a),
inference(resolve,[status(thm)],[c_411,c_379]) ).
cnf(c_382,plain,
divide(divide(A,c),divide(identity,a)) = zero,
inference(paramod,[status(thm)],[c_381,c_164]) ).
cnf(c_383,plain,
$false,
inference(resolve,[status(thm)],[c_382,c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n020.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Fri Sep 25 15:58:24 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.36 % Process 3303987 was started by sandbox2 on n020,
% 0.10/5.36 % Fri Sep 25 15:58:24 2026
% 0.10/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 0.13/5.43
% 0.13/5.43 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.43
% 0.13/5.43 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.13/5.43 % Length of proof is 62.
% 0.13/5.43 % Level of proof is 19.
% 0.13/5.43 % Maximum clause weight is 46.000.
% 0.13/5.43 % Given clauses 103.
% 0.13/5.43
% 0.13/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------