%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN004-3 : 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 07:31:57 AM UTC 2026
% Result : Unsatisfiable 0.09s 10.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 25 unt; 0 def)
% Number of atoms : 49 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 20 ~; 13 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn 12 !; 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(prove_x_divide_zero_is_x,axiom,
divide(a,zero) != a,
file('theBenchmark.p',prove_x_divide_zero_is_x) ).
cnf(c_8,plain,
divide(a,zero) != a,
inference(clausify,[status(thm)],[prove_x_divide_zero_is_x]) ).
cnf(c_9,plain,
divide(divide(A,B),A) = zero,
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
divide(zero,A) = zero,
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_43,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_12,plain,
~ less_equal(a,divide(a,zero)),
inference(resolve,[status(thm)],[c_43,c_8]) ).
cnf(c_15,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_16,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_17,plain,
divide(a,divide(a,zero)) != zero,
inference(resolve,[status(thm)],[c_2,c_12]) ).
cnf(c_44,plain,
( A = zero
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_18,plain,
~ less_equal(divide(a,divide(a,zero)),zero),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_19,plain,
divide(divide(a,divide(a,zero)),zero) != zero,
inference(resolve,[status(thm)],[c_2,c_18]) ).
cnf(c_45,plain,
( A = zero
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_20,plain,
~ less_equal(divide(divide(a,divide(a,zero)),zero),zero),
inference(resolve,[status(thm)],[c_45,c_19]) ).
cnf(c_23,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_46,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_47,plain,
zero = divide(divide(A,A),zero),
inference(resolve,[status(thm)],[c_46,c_23]) ).
cnf(c_24,plain,
divide(divide(A,A),zero) = zero,
inference(copy,[status(thm)],[c_47]) ).
cnf(c_25,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_2,c_24]) ).
cnf(c_48,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_49,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_48,c_25]) ).
cnf(c_28,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_49]) ).
cnf(c_41,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramod,[status(thm)],[c_28,c_16]) ).
cnf(c_42,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.54 % Computer : n017.cluster.edu
% 0.09/10.54 % Model : x86_64 x86_64
% 0.09/10.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.54 % Memory : 8046.5625MB
% 0.09/10.54 % OS : Linux 6.8.0-71-generic
% 0.09/10.54 % CPULimit : 300
% 0.09/10.54 % WCLimit : 300
% 0.09/10.54 % DateTime : Fri Sep 25 15:51:27 UTC 2026
% 0.09/10.54 % CPUTime :
% 0.09/10.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.55 % Process 2693379 was started by sandbox on n017,
% 0.09/10.55 % Fri Sep 25 15:51:28 2026
% 0.09/10.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.55
% 0.09/10.55 % From the command line: assign(max_seconds, 300).
% 0.09/10.56
% 0.09/10.56 % SZS status Unsatisfiable for theBenchmark
% 0.09/10.56
% 0.09/10.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/10.56 % Length of proof is 22.
% 0.09/10.56 % Level of proof is 8.
% 0.09/10.56 % Maximum clause weight is 25.000.
% 0.09/10.56 % Given clauses 30.
% 0.09/10.56
% 0.09/10.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------