%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN006-2 : 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 : n013.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 07:31:59 AM UTC 2026
% Result : Unsatisfiable 5.28s 1.23s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 21 unt; 0 def)
% Number of atoms : 75 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 39 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 5 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal,axiom,
! [VAR_0,VAR_1] :
( quotient(VAR_0,VAR_1,zero)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal) ).
cnf(c_1,plain,
( quotient(A,B,zero)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal]) ).
fof(less_equal_quotient,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| ~ quotient(VAR_0,VAR_1,zero) ),
file('theBenchmark.p',less_equal_quotient) ).
cnf(c_2,plain,
( less_equal(A,B)
| ~ quotient(A,B,zero) ),
inference(clausify,[status(thm)],[less_equal_quotient]) ).
fof(divisor_existence,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less_equal(VAR_2,VAR_0)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',divisor_existence) ).
cnf(c_3,plain,
( less_equal(C,A)
| ~ quotient(A,B,C) ),
inference(clausify,[status(thm)],[divisor_existence]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( less_equal(VAR_6,VAR_7)
| ~ quotient(VAR_2,VAR_3,VAR_7)
| ~ quotient(VAR_5,VAR_4,VAR_6)
| ~ quotient(VAR_0,VAR_3,VAR_5)
| ~ quotient(VAR_1,VAR_3,VAR_4)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
( less_equal(V6,V7)
| ~ quotient(C,D,V7)
| ~ quotient(F,E,V6)
| ~ quotient(A,D,F)
| ~ quotient(B,D,E)
| ~ quotient(A,B,C) ),
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(closure,axiom,
! [VAR_0,VAR_1] : quotient(VAR_0,VAR_1,divide(VAR_0,VAR_1)),
file('theBenchmark.p',closure) ).
cnf(c_8,plain,
quotient(A,B,divide(A,B)),
inference(clausify,[status(thm)],[closure]) ).
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_14,plain,
( less_equal(A,C)
| ~ less_equal(B,C)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less_equal]) ).
fof(xQy,axiom,
quotient(x,y,xQy),
file('theBenchmark.p',xQy) ).
cnf(c_15,plain,
quotient(x,y,xQy),
inference(clausify,[status(thm)],[xQy]) ).
fof(xQyLEz,axiom,
less_equal(xQy,z),
file('theBenchmark.p',xQyLEz) ).
cnf(c_16,plain,
less_equal(xQy,z),
inference(clausify,[status(thm)],[xQyLEz]) ).
fof(xQz,axiom,
quotient(x,z,xQz),
file('theBenchmark.p',xQz) ).
cnf(c_17,plain,
quotient(x,z,xQz),
inference(clausify,[status(thm)],[xQz]) ).
fof(prove_xQzLEy,axiom,
~ less_equal(xQz,y),
file('theBenchmark.p',prove_xQzLEy) ).
cnf(c_18,plain,
~ less_equal(xQz,y),
inference(clausify,[status(thm)],[prove_xQzLEy]) ).
cnf(c_20,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_41,plain,
quotient(xQy,z,zero),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_696,plain,
( less_equal(D,E)
| ~ quotient(xQy,A,E)
| ~ quotient(C,B,D)
| ~ quotient(x,A,C)
| ~ quotient(y,A,B) ),
inference(resolve,[status(thm)],[c_4,c_15]) ).
cnf(c_697,plain,
( less_equal(C,D)
| ~ quotient(xQy,A,D)
| ~ quotient(B,divide(y,A),C)
| ~ quotient(x,A,B) ),
inference(resolve,[status(thm)],[c_696,c_8]) ).
cnf(c_698,plain,
( less_equal(A,B)
| ~ quotient(xQy,z,B)
| ~ quotient(xQz,divide(y,z),A) ),
inference(resolve,[status(thm)],[c_697,c_17]) ).
cnf(c_699,plain,
( less_equal(divide(xQz,divide(y,z)),A)
| ~ quotient(xQy,z,A) ),
inference(resolve,[status(thm)],[c_698,c_8]) ).
cnf(c_105,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolve,[status(thm)],[c_699,c_41]) ).
cnf(c_700,plain,
( less_equal(A,B)
| ~ less_equal(A,divide(B,C)) ),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_132,plain,
~ less_equal(xQz,divide(y,A)),
inference(resolve,[status(thm)],[c_700,c_18]) ).
cnf(c_701,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_702,plain,
zero = divide(xQz,divide(y,z)),
inference(resolve,[status(thm)],[c_701,c_105]) ).
cnf(c_423,plain,
divide(xQz,divide(y,z)) = zero,
inference(copy,[status(thm)],[c_702]) ).
cnf(c_687,plain,
quotient(xQz,divide(y,z),zero),
inference(paramod,[status(thm)],[c_423,c_8]) ).
cnf(c_694,plain,
less_equal(xQz,divide(y,z)),
inference(resolve,[status(thm)],[c_2,c_687]) ).
cnf(c_695,plain,
$false,
inference(resolve,[status(thm)],[c_694,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % 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 15:56:06 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 783539 was started by sandbox2 on n013,
% 0.15/0.43 % Fri Sep 25 15:56:06 2026
% 0.15/0.43 % 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).
% 5.28/1.23
% 5.28/1.23 % SZS status Unsatisfiable for theBenchmark
% 5.28/1.23
% 5.28/1.23 % Proof 1 at 0.55 (+ 0.24) seconds.
% 5.28/1.23 % Length of proof is 20.
% 5.28/1.23 % Level of proof is 6.
% 5.28/1.23 % Maximum clause weight is 23.000.
% 5.28/1.23 % Given clauses 143.
% 5.28/1.23
% 5.28/1.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------