%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:32:00 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn 19 !; 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(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(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(x_divde_zero_is_x,axiom,
! [VAR_0] : quotient(VAR_0,zero,VAR_0),
file('theBenchmark.p',x_divde_zero_is_x) ).
cnf(c_13,plain,
quotient(A,zero,A),
inference(clausify,[status(thm)],[x_divde_zero_is_x]) ).
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(xLEy,axiom,
less_equal(x,y),
file('theBenchmark.p',xLEy) ).
cnf(c_16,plain,
less_equal(x,y),
inference(clausify,[status(thm)],[xLEy]) ).
fof(zQy,axiom,
quotient(z,y,zQy),
file('theBenchmark.p',zQy) ).
cnf(c_17,plain,
quotient(z,y,zQy),
inference(clausify,[status(thm)],[zQy]) ).
fof(zQx,axiom,
quotient(z,x,zQx),
file('theBenchmark.p',zQx) ).
cnf(c_18,plain,
quotient(z,x,zQx),
inference(clausify,[status(thm)],[zQx]) ).
fof(prove_zQyLEzQx,axiom,
~ less_equal(zQy,zQx),
file('theBenchmark.p',prove_zQyLEzQx) ).
cnf(c_19,plain,
~ less_equal(zQy,zQx),
inference(clausify,[status(thm)],[prove_zQyLEzQx]) ).
cnf(c_21,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_35,plain,
quotient(x,y,zero),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_170,plain,
( less_equal(D,E)
| ~ quotient(zQx,A,E)
| ~ quotient(C,B,D)
| ~ quotient(z,A,C)
| ~ quotient(x,A,B) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_171,plain,
( less_equal(B,C)
| ~ quotient(zQx,y,C)
| ~ quotient(A,zero,B)
| ~ quotient(z,y,A) ),
inference(resolve,[status(thm)],[c_170,c_35]) ).
cnf(c_172,plain,
( less_equal(A,B)
| ~ quotient(zQx,y,B)
| ~ quotient(zQy,zero,A) ),
inference(resolve,[status(thm)],[c_171,c_17]) ).
cnf(c_173,plain,
( less_equal(zQy,A)
| ~ quotient(zQx,y,A) ),
inference(resolve,[status(thm)],[c_172,c_13]) ).
cnf(c_141,plain,
less_equal(zQy,divide(zQx,y)),
inference(resolve,[status(thm)],[c_173,c_8]) ).
cnf(c_174,plain,
( less_equal(A,B)
| ~ less_equal(A,divide(B,C)) ),
inference(resolve,[status(thm)],[c_14,c_21]) ).
cnf(c_168,plain,
~ less_equal(zQy,divide(zQx,A)),
inference(resolve,[status(thm)],[c_174,c_19]) ).
cnf(c_169,plain,
$false,
inference(resolve,[status(thm)],[c_168,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:57:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1418315 was started by sandbox on n008,
% 0.09/0.36 % Fri Sep 25 15:57:54 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.09/0.44 % Length of proof is 15.
% 0.09/0.44 % Level of proof is 3.
% 0.09/0.44 % Maximum clause weight is 23.000.
% 0.09/0.44 % Given clauses 29.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------