%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN008-4 : 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 : n009.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 07:32:01 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 38 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 30 ( 2 sgn 11 !; 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_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(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(a_LE_b,axiom,
less_equal(a,b),
file('theBenchmark.p',a_LE_b) ).
cnf(c_15,plain,
less_equal(a,b),
inference(clausify,[status(thm)],[a_LE_b]) ).
fof(prove_a_divide_c_LE_b_divide_c,axiom,
~ less_equal(divide(a,c),divide(b,c)),
file('theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
cnf(c_16,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(clausify,[status(thm)],[prove_a_divide_c_LE_b_divide_c]) ).
cnf(c_20,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| ~ less_equal(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_50,plain,
divide(a,b) = zero,
inference(resolve,[status(thm)],[c_15,c_1]) ).
cnf(c_57,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(resolve,[status(thm)],[c_2,c_16]) ).
cnf(c_118,plain,
( divide(divide(a,A),divide(b,A)) = divide(divide(a,b),A)
| ~ less_equal(divide(zero,A),divide(divide(a,A),divide(b,A))) ),
inference(paramod,[status(thm)],[c_50,c_20]) ).
cnf(c_119,plain,
( divide(divide(a,A),divide(b,A)) = divide(divide(a,b),A)
| ~ less_equal(zero,divide(divide(a,A),divide(b,A))) ),
inference(paramod,[status(thm)],[c_9,c_118]) ).
cnf(c_120,plain,
( divide(divide(a,A),divide(b,A)) = divide(zero,A)
| ~ less_equal(zero,divide(divide(a,A),divide(b,A))) ),
inference(paramod,[status(thm)],[c_50,c_119]) ).
cnf(c_121,plain,
( divide(divide(a,A),divide(b,A)) = zero
| ~ less_equal(zero,divide(divide(a,A),divide(b,A))) ),
inference(paramod,[status(thm)],[c_9,c_120]) ).
cnf(c_116,plain,
divide(divide(a,A),divide(b,A)) = zero,
inference(resolve,[status(thm)],[c_5,c_121]) ).
cnf(c_117,plain,
$false,
inference(resolve,[status(thm)],[c_116,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:57:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1983905 was started by sandbox on n009,
% 0.08/0.36 % Fri Sep 25 15:57:29 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 13.
% 0.08/0.39 % Level of proof is 3.
% 0.08/0.39 % Maximum clause weight is 71.000.
% 0.08/0.39 % Given clauses 39.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------