%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 25 unt; 0 def)
% Number of atoms : 45 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 47 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(x_divide_x_is_zero,axiom,
! [VAR_0] : divide(VAR_0,VAR_0) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(c_10,plain,
divide(A,A) = zero,
inference(clausify,[status(thm)],[x_divide_x_is_zero]) ).
fof(property_of_divide1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(divide(VAR_0,VAR_2),VAR_1)
| ~ less_equal(divide(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',property_of_divide1) ).
cnf(c_13,plain,
( less_equal(divide(A,C),B)
| ~ less_equal(divide(A,B),C) ),
inference(clausify,[status(thm)],[property_of_divide1]) ).
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_property_of_inversion,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_property_of_inversion) ).
cnf(c_17,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_property_of_inversion]) ).
cnf(c_18,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_23,plain,
less_equal(A,A),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_24,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,B),B)),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_215,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_45,plain,
~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(resolve,[status(thm)],[c_215,c_18]) ).
cnf(c_62,plain,
less_equal(divide(A,divide(A,B)),B),
inference(resolve,[status(thm)],[c_13,c_23]) ).
cnf(c_216,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_217,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_216,c_62]) ).
cnf(c_149,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_217]) ).
cnf(c_173,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_149]) ).
cnf(c_218,plain,
less_equal(divide(divide(identity,A),zero),divide(divide(identity,divide(identity,divide(identity,A))),divide(identity,divide(identity,A)))),
inference(paramod,[status(thm)],[c_16,c_24]) ).
cnf(c_188,plain,
less_equal(divide(divide(identity,A),zero),divide(divide(identity,A),divide(identity,divide(identity,A)))),
inference(paramod,[status(thm)],[c_16,c_218]) ).
cnf(c_219,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_212,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_219,c_173]) ).
cnf(c_213,plain,
less_equal(divide(identity,A),divide(divide(identity,A),divide(identity,divide(identity,A)))),
inference(paramod,[status(thm)],[c_212,c_188]) ).
cnf(c_214,plain,
$false,
inference(resolve,[status(thm)],[c_213,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 15:57:43 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2422608 was started by sandbox2 on n011,
% 0.17/0.43 % Fri Sep 25 15:57:43 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 20.
% 0.17/0.50 % Level of proof is 7.
% 0.17/0.50 % Maximum clause weight is 15.000.
% 0.17/0.50 % Given clauses 50.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------