%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 34 ( 3 sgn 11 !; 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(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(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(property_of_divide2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(divide(VAR_2,VAR_1),divide(VAR_2,VAR_0)) = zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',property_of_divide2) ).
cnf(c_8,plain,
( divide(divide(C,B),divide(C,A)) = zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[property_of_divide2]) ).
fof(prove_this,axiom,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(c_9,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_10,plain,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_34,plain,
divide(divide(A,A),B) = zero,
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_92,plain,
( zero = A
| divide(A,zero) != zero ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_93,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_92,c_34]) ).
cnf(c_51,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_93]) ).
cnf(c_53,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(resolve,[status(thm)],[c_7,c_51]) ).
cnf(c_82,plain,
divide(divide(A,B),divide(A,divide(C,divide(C,B)))) = zero,
inference(resolve,[status(thm)],[c_8,c_53]) ).
cnf(c_94,plain,
( A = divide(B,divide(B,A))
| divide(A,divide(B,divide(B,A))) != zero ),
inference(resolve,[status(thm)],[c_4,c_53]) ).
cnf(c_95,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_96,plain,
divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero,
inference(resolve,[status(thm)],[c_94,c_95]) ).
cnf(c_97,plain,
zero != zero,
inference(paramod,[status(thm)],[c_82,c_96]) ).
cnf(c_91,plain,
$false,
inference(copy,[status(thm)],[c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 15:57:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 616458 was started by sandbox2 on n014,
% 0.10/0.35 % Fri Sep 25 15:57:32 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.38 % Length of proof is 12.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 14.000.
% 0.13/0.38 % Given clauses 18.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------