%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN011-4 : 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 : n019.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 07:32:04 AM UTC 2026
% Result : Unsatisfiable 2.19s 0.74s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 39 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(transitivity_of_less_equal,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_0,VAR_2)
| ~ less_equal(VAR_1,VAR_2)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less_equal) ).
cnf(c_12,plain,
( less_equal(A,C)
| ~ less_equal(B,C)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_equal]) ).
fof(property_of_divide2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(divide(VAR_2,VAR_1),divide(VAR_2,VAR_0))
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',property_of_divide2) ).
cnf(c_14,plain,
( less_equal(divide(C,B),divide(C,A))
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[property_of_divide2]) ).
fof(one_inversion_equals_three,axiom,
! [VAR_0] : divide(identity,divide(identity,divide(identity,VAR_0))) = divide(identity,VAR_0),
file('theBenchmark.p',one_inversion_equals_three) ).
cnf(c_16,plain,
divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
inference(clausify,[status(thm)],[one_inversion_equals_three]) ).
fof(prove_this,axiom,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(c_18,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_19,plain,
divide(divide(identity,b),divide(identity,divide(identity,a))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_36,plain,
less_equal(divide(A,B),divide(A,divide(B,C))),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_562,plain,
( less_equal(divide(A,B),D)
| ~ less_equal(divide(A,divide(B,C)),D) ),
inference(resolve,[status(thm)],[c_12,c_36]) ).
cnf(c_179,plain,
less_equal(divide(divide(A,B),C),divide(divide(A,C),B)),
inference(resolve,[status(thm)],[c_562,c_4]) ).
cnf(c_563,plain,
( divide(divide(A,C),B) = divide(divide(A,B),C)
| ~ less_equal(divide(divide(A,B),C),divide(divide(A,C),B)) ),
inference(resolve,[status(thm)],[c_6,c_179]) ).
cnf(c_382,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(resolve,[status(thm)],[c_563,c_179]) ).
cnf(c_564,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),divide(identity,divide(identity,A))),
inference(paramod,[status(thm)],[c_16,c_382]) ).
cnf(c_559,plain,
divide(divide(identity,A),divide(identity,divide(identity,B))) = divide(divide(identity,B),A),
inference(copy,[status(thm)],[c_564]) ).
cnf(c_565,plain,
divide(divide(identity,divide(identity,divide(identity,a))),b) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(paramod,[status(thm)],[c_382,c_19]) ).
cnf(c_566,plain,
divide(divide(identity,a),b) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(paramod,[status(thm)],[c_16,c_565]) ).
cnf(c_567,plain,
divide(divide(identity,a),b) != divide(divide(identity,b),a),
inference(paramod,[status(thm)],[c_559,c_566]) ).
cnf(c_568,plain,
divide(divide(identity,a),b) != divide(divide(identity,a),b),
inference(paramod,[status(thm)],[c_382,c_567]) ).
cnf(c_561,plain,
$false,
inference(copy,[status(thm)],[c_568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n019.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 15:58:19 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3172295 was started by sandbox2 on n019,
% 0.15/0.44 % Fri Sep 25 15:58:19 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 2.19/0.74
% 2.19/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.19/0.74
% 2.19/0.74 % Proof 1 at 0.11 (+ 0.06) seconds.
% 2.19/0.74 % Length of proof is 13.
% 2.19/0.74 % Level of proof is 5.
% 2.19/0.74 % Maximum clause weight is 51.000.
% 2.19/0.74 % Given clauses 58.
% 2.19/0.74
% 2.19/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------