%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN006-7 : 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 : n006.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 2.09s 0.75s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 29 unt; 0 def)
% Number of atoms : 91 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 87 ( 45 ~; 42 |; 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 : 73 ( 5 sgn 22 !; 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(zero_divide_anything_is_zero,axiom,
! [VAR_0] : quotient(zero,VAR_0,zero),
file('theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(c_11,plain,
quotient(zero,A,zero),
inference(clausify,[status(thm)],[zero_divide_anything_is_zero]) ).
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(xQy,axiom,
quotient(x,y,xQy),
file('theBenchmark.p',xQy) ).
cnf(c_14,plain,
quotient(x,y,xQy),
inference(clausify,[status(thm)],[xQy]) ).
fof(xQyLEz,axiom,
less_equal(xQy,z),
file('theBenchmark.p',xQyLEz) ).
cnf(c_15,plain,
less_equal(xQy,z),
inference(clausify,[status(thm)],[xQyLEz]) ).
fof(xQz,axiom,
quotient(x,z,xQz),
file('theBenchmark.p',xQz) ).
cnf(c_16,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_17,plain,
~ less_equal(xQz,y),
inference(clausify,[status(thm)],[prove_xQzLEy]) ).
cnf(c_41,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_62,plain,
quotient(xQy,z,zero),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_78,plain,
~ quotient(xQz,y,zero),
inference(resolve,[status(thm)],[c_2,c_17]) ).
cnf(c_161,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_14]) ).
cnf(c_162,plain,
( less_equal(C,D)
| ~ quotient(xQy,A,D)
| ~ quotient(B,divide(y,A),C)
| ~ quotient(x,A,B) ),
inference(resolve,[status(thm)],[c_161,c_8]) ).
cnf(c_163,plain,
( less_equal(A,B)
| ~ quotient(xQy,z,B)
| ~ quotient(xQz,divide(y,z),A) ),
inference(resolve,[status(thm)],[c_162,c_16]) ).
cnf(c_164,plain,
( less_equal(divide(xQz,divide(y,z)),A)
| ~ quotient(xQy,z,A) ),
inference(resolve,[status(thm)],[c_163,c_8]) ).
cnf(c_83,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolve,[status(thm)],[c_164,c_62]) ).
cnf(c_92,plain,
quotient(divide(A,B),A,zero),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_165,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_166,plain,
zero = divide(xQz,divide(y,z)),
inference(resolve,[status(thm)],[c_165,c_83]) ).
cnf(c_129,plain,
divide(xQz,divide(y,z)) = zero,
inference(copy,[status(thm)],[c_166]) ).
cnf(c_151,plain,
quotient(xQz,divide(y,z),zero),
inference(paramod,[status(thm)],[c_129,c_8]) ).
cnf(c_167,plain,
( less_equal(D,E)
| ~ quotient(zero,A,E)
| ~ quotient(C,B,D)
| ~ quotient(xQz,A,C)
| ~ quotient(divide(y,z),A,B) ),
inference(resolve,[status(thm)],[c_4,c_151]) ).
cnf(c_168,plain,
( less_equal(B,C)
| ~ quotient(zero,y,C)
| ~ quotient(A,zero,B)
| ~ quotient(xQz,y,A) ),
inference(resolve,[status(thm)],[c_167,c_92]) ).
cnf(c_169,plain,
( less_equal(A,B)
| ~ quotient(zero,y,B)
| ~ quotient(divide(xQz,y),zero,A) ),
inference(resolve,[status(thm)],[c_168,c_8]) ).
cnf(c_170,plain,
( less_equal(divide(xQz,y),A)
| ~ quotient(zero,y,A) ),
inference(resolve,[status(thm)],[c_169,c_13]) ).
cnf(c_157,plain,
less_equal(divide(xQz,y),zero),
inference(resolve,[status(thm)],[c_170,c_11]) ).
cnf(c_171,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_172,plain,
zero = divide(xQz,y),
inference(resolve,[status(thm)],[c_171,c_157]) ).
cnf(c_159,plain,
divide(xQz,y) = zero,
inference(copy,[status(thm)],[c_172]) ).
cnf(c_173,plain,
quotient(xQz,y,zero),
inference(paramod,[status(thm)],[c_159,c_8]) ).
cnf(c_160,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44 % Computer : n006.cluster.edu
% 0.14/0.44 % Model : x86_64 x86_64
% 0.14/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.44 % Memory : 8046.5625MB
% 0.14/0.44 % OS : Linux 6.8.0-71-generic
% 0.14/0.44 % CPULimit : 300
% 0.14/0.44 % WCLimit : 300
% 0.14/0.44 % DateTime : Fri Sep 25 15:56:42 UTC 2026
% 0.14/0.44 % CPUTime :
% 0.14/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.45 % Process 3292878 was started by sandbox2 on n006,
% 0.14/0.45 % Fri Sep 25 15:56:42 2026
% 0.14/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.45
% 0.14/0.45 % From the command line: assign(max_seconds, 300).
% 2.09/0.75
% 2.09/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.09/0.75
% 2.09/0.75 % Proof 1 at 0.18 (+ 0.09) seconds.
% 2.09/0.75 % Length of proof is 23.
% 2.09/0.75 % Level of proof is 7.
% 2.09/0.75 % Maximum clause weight is 28.000.
% 2.09/0.75 % Given clauses 95.
% 2.09/0.75
% 2.09/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------