%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN007-1 : 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 : n014.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 2.48s 0.75s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 36 unt; 0 def)
% Number of atoms : 116 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 111 ( 57 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 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 : 86 ( 4 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(xLEy,axiom,
less_equal(x,y),
file('theBenchmark.p',xLEy) ).
cnf(c_10,plain,
less_equal(x,y),
inference(clausify,[status(thm)],[xLEy]) ).
fof(zQy,axiom,
quotient(z,y,zQy),
file('theBenchmark.p',zQy) ).
cnf(c_11,plain,
quotient(z,y,zQy),
inference(clausify,[status(thm)],[zQy]) ).
fof(zQx,axiom,
quotient(z,x,zQx),
file('theBenchmark.p',zQx) ).
cnf(c_12,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_13,plain,
~ less_equal(zQy,zQx),
inference(clausify,[status(thm)],[prove_zQyLEzQx]) ).
cnf(c_14,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_18,plain,
quotient(x,y,zero),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_34,plain,
less_equal(zQx,z),
inference(resolve,[status(thm)],[c_3,c_12]) ).
cnf(c_35,plain,
~ quotient(zQx,A,zQy),
inference(resolve,[status(thm)],[c_3,c_13]) ).
cnf(c_47,plain,
quotient(zQx,z,zero),
inference(resolve,[status(thm)],[c_1,c_34]) ).
cnf(c_821,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_12]) ).
cnf(c_822,plain,
( less_equal(B,C)
| ~ quotient(zQx,y,C)
| ~ quotient(A,zero,B)
| ~ quotient(z,y,A) ),
inference(resolve,[status(thm)],[c_821,c_18]) ).
cnf(c_823,plain,
( less_equal(A,B)
| ~ quotient(zQx,y,B)
| ~ quotient(zQy,zero,A) ),
inference(resolve,[status(thm)],[c_822,c_11]) ).
cnf(c_824,plain,
( less_equal(divide(zQy,zero),A)
| ~ quotient(zQx,y,A) ),
inference(resolve,[status(thm)],[c_823,c_8]) ).
cnf(c_49,plain,
less_equal(divide(zQy,zero),divide(zQx,y)),
inference(resolve,[status(thm)],[c_824,c_8]) ).
cnf(c_825,plain,
( less_equal(D,E)
| ~ quotient(zero,A,E)
| ~ quotient(C,B,D)
| ~ quotient(zQx,A,C)
| ~ quotient(z,A,B) ),
inference(resolve,[status(thm)],[c_4,c_47]) ).
cnf(c_826,plain,
( less_equal(B,C)
| ~ quotient(zero,y,C)
| ~ quotient(A,zQy,B)
| ~ quotient(zQx,y,A) ),
inference(resolve,[status(thm)],[c_825,c_11]) ).
cnf(c_827,plain,
( less_equal(A,B)
| ~ quotient(zero,y,B)
| ~ quotient(divide(zQx,y),zQy,A) ),
inference(resolve,[status(thm)],[c_826,c_8]) ).
cnf(c_828,plain,
( less_equal(divide(divide(zQx,y),zQy),A)
| ~ quotient(zero,y,A) ),
inference(resolve,[status(thm)],[c_827,c_8]) ).
cnf(c_62,plain,
less_equal(divide(divide(zQx,y),zQy),zero),
inference(resolve,[status(thm)],[c_828,c_14]) ).
cnf(c_85,plain,
quotient(divide(zQy,zero),divide(zQx,y),zero),
inference(resolve,[status(thm)],[c_1,c_49]) ).
cnf(c_829,plain,
( less_equal(F,V6)
| ~ quotient(divide(D,A),B,V6)
| ~ quotient(E,C,F)
| ~ quotient(D,B,E)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_830,plain,
( less_equal(D,E)
| ~ quotient(divide(A,zero),B,E)
| ~ quotient(C,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_829,c_14]) ).
cnf(c_831,plain,
( less_equal(C,D)
| ~ quotient(divide(A,zero),B,D)
| ~ quotient(divide(A,B),zero,C) ),
inference(resolve,[status(thm)],[c_830,c_8]) ).
cnf(c_832,plain,
( less_equal(divide(divide(A,B),zero),C)
| ~ quotient(divide(A,zero),B,C) ),
inference(resolve,[status(thm)],[c_831,c_8]) ).
cnf(c_87,plain,
less_equal(divide(divide(zQy,divide(zQx,y)),zero),zero),
inference(resolve,[status(thm)],[c_832,c_85]) ).
cnf(c_833,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_834,plain,
zero = divide(divide(zQx,y),zQy),
inference(resolve,[status(thm)],[c_833,c_62]) ).
cnf(c_98,plain,
divide(divide(zQx,y),zQy) = zero,
inference(copy,[status(thm)],[c_834]) ).
cnf(c_127,plain,
quotient(divide(zQx,y),zQy,zero),
inference(paramod,[status(thm)],[c_98,c_8]) ).
cnf(c_133,plain,
less_equal(divide(zQx,y),zQy),
inference(resolve,[status(thm)],[c_2,c_127]) ).
cnf(c_835,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_836,plain,
zero = divide(divide(zQy,divide(zQx,y)),zero),
inference(resolve,[status(thm)],[c_835,c_87]) ).
cnf(c_352,plain,
divide(divide(zQy,divide(zQx,y)),zero) = zero,
inference(copy,[status(thm)],[c_836]) ).
cnf(c_788,plain,
quotient(divide(zQy,divide(zQx,y)),zero,zero),
inference(paramod,[status(thm)],[c_352,c_8]) ).
cnf(c_801,plain,
less_equal(divide(zQy,divide(zQx,y)),zero),
inference(resolve,[status(thm)],[c_2,c_788]) ).
cnf(c_837,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_838,plain,
zero = divide(zQy,divide(zQx,y)),
inference(resolve,[status(thm)],[c_837,c_801]) ).
cnf(c_802,plain,
divide(zQy,divide(zQx,y)) = zero,
inference(copy,[status(thm)],[c_838]) ).
cnf(c_803,plain,
quotient(zQy,divide(zQx,y),zero),
inference(paramod,[status(thm)],[c_802,c_8]) ).
cnf(c_817,plain,
less_equal(zQy,divide(zQx,y)),
inference(resolve,[status(thm)],[c_2,c_803]) ).
cnf(c_839,plain,
( divide(zQx,y) = zQy
| ~ less_equal(zQy,divide(zQx,y)) ),
inference(resolve,[status(thm)],[c_6,c_133]) ).
cnf(c_818,plain,
divide(zQx,y) = zQy,
inference(resolve,[status(thm)],[c_839,c_817]) ).
cnf(c_819,plain,
quotient(zQx,y,zQy),
inference(paramod,[status(thm)],[c_818,c_8]) ).
cnf(c_820,plain,
$false,
inference(resolve,[status(thm)],[c_819,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 15:56:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 614720 was started by sandbox2 on n014,
% 0.08/0.35 % Fri Sep 25 15:56:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 2.48/0.75
% 2.48/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.48/0.75
% 2.48/0.75 % Proof 1 at 0.29 (+ 0.08) seconds.
% 2.48/0.75 % Length of proof is 32.
% 2.48/0.75 % Level of proof is 13.
% 2.48/0.75 % Maximum clause weight is 39.000.
% 2.48/0.75 % Given clauses 211.
% 2.48/0.75
% 2.48/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------