%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN006-1 : 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 : 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 07:31:59 AM UTC 2026
% Result : Unsatisfiable 0.86s 0.49s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 30 unt; 0 def)
% Number of atoms : 94 ( 11 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 89 ( 46 ~; 43 |; 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 : 71 ( 5 sgn 20 !; 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(xQy,axiom,
quotient(x,y,xQy),
file('theBenchmark.p',xQy) ).
cnf(c_10,plain,
quotient(x,y,xQy),
inference(clausify,[status(thm)],[xQy]) ).
fof(xQyLEz,axiom,
less_equal(xQy,z),
file('theBenchmark.p',xQyLEz) ).
cnf(c_11,plain,
less_equal(xQy,z),
inference(clausify,[status(thm)],[xQyLEz]) ).
fof(xQz,axiom,
quotient(x,z,xQz),
file('theBenchmark.p',xQz) ).
cnf(c_12,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_13,plain,
~ less_equal(xQz,y),
inference(clausify,[status(thm)],[prove_xQzLEy]) ).
cnf(c_14,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_25,plain,
quotient(xQy,z,zero),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_36,plain,
~ quotient(xQz,y,zero),
inference(resolve,[status(thm)],[c_2,c_13]) ).
cnf(c_154,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_10]) ).
cnf(c_155,plain,
( less_equal(C,D)
| ~ quotient(xQy,A,D)
| ~ quotient(B,divide(y,A),C)
| ~ quotient(x,A,B) ),
inference(resolve,[status(thm)],[c_154,c_8]) ).
cnf(c_156,plain,
( less_equal(A,B)
| ~ quotient(xQy,z,B)
| ~ quotient(xQz,divide(y,z),A) ),
inference(resolve,[status(thm)],[c_155,c_12]) ).
cnf(c_157,plain,
( less_equal(divide(xQz,divide(y,z)),A)
| ~ quotient(xQy,z,A) ),
inference(resolve,[status(thm)],[c_156,c_8]) ).
cnf(c_48,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolve,[status(thm)],[c_157,c_25]) ).
cnf(c_64,plain,
quotient(divide(A,B),A,zero),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_158,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_159,plain,
zero = divide(xQz,divide(y,z)),
inference(resolve,[status(thm)],[c_158,c_48]) ).
cnf(c_85,plain,
divide(xQz,divide(y,z)) = zero,
inference(copy,[status(thm)],[c_159]) ).
cnf(c_105,plain,
quotient(xQz,divide(y,z),zero),
inference(paramod,[status(thm)],[c_85,c_8]) ).
cnf(c_160,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_105]) ).
cnf(c_161,plain,
( less_equal(B,C)
| ~ quotient(zero,y,C)
| ~ quotient(A,zero,B)
| ~ quotient(xQz,y,A) ),
inference(resolve,[status(thm)],[c_160,c_64]) ).
cnf(c_162,plain,
( less_equal(A,B)
| ~ quotient(zero,y,B)
| ~ quotient(divide(xQz,y),zero,A) ),
inference(resolve,[status(thm)],[c_161,c_8]) ).
cnf(c_163,plain,
( less_equal(divide(divide(xQz,y),zero),A)
| ~ quotient(zero,y,A) ),
inference(resolve,[status(thm)],[c_162,c_8]) ).
cnf(c_110,plain,
less_equal(divide(divide(xQz,y),zero),zero),
inference(resolve,[status(thm)],[c_163,c_14]) ).
cnf(c_164,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_165,plain,
zero = divide(divide(xQz,y),zero),
inference(resolve,[status(thm)],[c_164,c_110]) ).
cnf(c_141,plain,
divide(divide(xQz,y),zero) = zero,
inference(copy,[status(thm)],[c_165]) ).
cnf(c_143,plain,
quotient(divide(xQz,y),zero,zero),
inference(paramod,[status(thm)],[c_141,c_8]) ).
cnf(c_148,plain,
less_equal(divide(xQz,y),zero),
inference(resolve,[status(thm)],[c_2,c_143]) ).
cnf(c_166,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_167,plain,
zero = divide(xQz,y),
inference(resolve,[status(thm)],[c_166,c_148]) ).
cnf(c_149,plain,
divide(xQz,y) = zero,
inference(copy,[status(thm)],[c_167]) ).
cnf(c_152,plain,
quotient(xQz,y,zero),
inference(paramod,[status(thm)],[c_149,c_8]) ).
cnf(c_153,plain,
$false,
inference(resolve,[status(thm)],[c_152,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:56:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2419388 was started by sandbox on n011,
% 0.08/0.36 % Fri Sep 25 15:56:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.86/0.49
% 0.86/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.86/0.49
% 0.86/0.49 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.86/0.49 % Length of proof is 26.
% 0.86/0.49 % Level of proof is 11.
% 0.86/0.49 % Maximum clause weight is 23.000.
% 0.86/0.49 % Given clauses 75.
% 0.86/0.49
% 0.86/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------