%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:32:03 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 25 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 23 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_smaller_than_numerator,axiom,
! [VAR_0,VAR_1] : divide(divide(VAR_0,VAR_1),VAR_0) = zero,
file('theBenchmark.p',quotient_smaller_than_numerator) ).
cnf(c_1,plain,
divide(divide(A,B),A) = zero,
inference(clausify,[status(thm)],[quotient_smaller_than_numerator]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1)),divide(divide(VAR_0,VAR_2),VAR_1)) = zero,
file('theBenchmark.p',quotient_property) ).
cnf(c_2,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : divide(zero,VAR_0) = zero,
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_3,plain,
divide(zero,A) = zero,
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(divide_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| divide(VAR_1,VAR_0) != zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',divide_and_equal) ).
cnf(c_4,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[divide_and_equal]) ).
fof(transitivity_of_divide_to_zero,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(VAR_0,VAR_2) = zero
| divide(VAR_1,VAR_2) != zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',transitivity_of_divide_to_zero) ).
cnf(c_6,plain,
( divide(A,C) = zero
| divide(B,C) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[transitivity_of_divide_to_zero]) ).
fof(property_of_divide1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(divide(VAR_0,VAR_2),VAR_1) = zero
| divide(divide(VAR_0,VAR_1),VAR_2) != zero ),
file('theBenchmark.p',property_of_divide1) ).
cnf(c_7,plain,
( divide(divide(A,C),B) = zero
| divide(divide(A,B),C) != zero ),
inference(clausify,[status(thm)],[property_of_divide1]) ).
fof(prove_this,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(c_9,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_10,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_393,plain,
( divide(divide(divide(A,C),divide(B,C)),D) = zero
| divide(divide(divide(A,B),C),D) != zero ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_20,plain,
divide(divide(divide(A,B),divide(C,B)),divide(A,C)) = zero,
inference(resolve,[status(thm)],[c_393,c_1]) ).
cnf(c_24,plain,
divide(divide(A,A),B) = zero,
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_394,plain,
( divide(A,B) = A
| divide(A,divide(A,B)) != zero ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_28,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero,
inference(resolve,[status(thm)],[c_394,c_10]) ).
cnf(c_395,plain,
( zero = A
| divide(A,zero) != zero ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_396,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_395,c_24]) ).
cnf(c_50,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_396]) ).
cnf(c_397,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) != zero ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_398,plain,
divide(divide(A,divide(A,B)),divide(B,divide(A,B))) = divide(divide(A,B),divide(A,B)),
inference(resolve,[status(thm)],[c_397,c_24]) ).
cnf(c_51,plain,
divide(divide(A,divide(A,B)),divide(B,divide(A,B))) = zero,
inference(paramod,[status(thm)],[c_50,c_398]) ).
cnf(c_52,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(resolve,[status(thm)],[c_7,c_50]) ).
cnf(c_399,plain,
( zero = A
| divide(A,zero) != zero ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_400,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_399,c_52]) ).
cnf(c_104,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_400]) ).
cnf(c_401,plain,
( divide(A,B) = A
| divide(A,divide(A,B)) != zero ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_128,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_401,c_104]) ).
cnf(c_402,plain,
divide(divide(divide(A,B),zero),divide(A,divide(C,divide(C,B)))) = zero,
inference(paramod,[status(thm)],[c_52,c_20]) ).
cnf(c_301,plain,
divide(divide(A,B),divide(A,divide(C,divide(C,B)))) = zero,
inference(paramod,[status(thm)],[c_128,c_402]) ).
cnf(c_403,plain,
( divide(A,divide(C,divide(B,C))) = zero
| divide(A,divide(B,divide(B,C))) != zero ),
inference(resolve,[status(thm)],[c_6,c_51]) ).
cnf(c_404,plain,
divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero,
inference(resolve,[status(thm)],[c_403,c_28]) ).
cnf(c_405,plain,
zero != zero,
inference(paramod,[status(thm)],[c_301,c_404]) ).
cnf(c_392,plain,
$false,
inference(copy,[status(thm)],[c_405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 15:58:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3305841 was started by sandbox on n020,
% 0.11/0.37 % Fri Sep 25 15:58:48 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.43
% 0.11/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.43
% 0.11/0.43 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.11/0.43 % Length of proof is 18.
% 0.11/0.43 % Level of proof is 7.
% 0.11/0.43 % Maximum clause weight is 50.000.
% 0.11/0.43 % Given clauses 50.
% 0.11/0.43
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------