%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN012-1 : 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 : n020.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 07:32:04 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 66 ( 8 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 67 ( 35 ~; 32 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 7 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(prove_X_less_than_or_equal_to_X,axiom,
~ less_equal(x,x),
file('theBenchmark.p',prove_X_less_than_or_equal_to_X) ).
cnf(c_10,plain,
~ less_equal(x,x),
inference(clausify,[status(thm)],[prove_X_less_than_or_equal_to_X]) ).
cnf(c_14,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_16,plain,
~ quotient(x,x,zero),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_21,plain,
quotient(divide(A,B),A,zero),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_40,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_41,plain,
( less_equal(D,F)
| ~ quotient(divide(A,divide(B,E)),B,F)
| ~ quotient(C,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_40,c_21]) ).
cnf(c_42,plain,
( less_equal(C,E)
| ~ quotient(divide(A,divide(B,D)),B,E)
| ~ quotient(divide(A,B),zero,C) ),
inference(resolve,[status(thm)],[c_41,c_8]) ).
cnf(c_43,plain,
( less_equal(divide(divide(A,B),zero),D)
| ~ quotient(divide(A,divide(B,C)),B,D) ),
inference(resolve,[status(thm)],[c_42,c_8]) ).
cnf(c_24,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(resolve,[status(thm)],[c_43,c_21]) ).
cnf(c_44,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_45,plain,
zero = divide(divide(A,A),zero),
inference(resolve,[status(thm)],[c_44,c_24]) ).
cnf(c_29,plain,
divide(divide(A,A),zero) = zero,
inference(copy,[status(thm)],[c_45]) ).
cnf(c_30,plain,
quotient(divide(A,A),zero,zero),
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_36,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_2,c_30]) ).
cnf(c_46,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_47,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_46,c_36]) ).
cnf(c_37,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_47]) ).
cnf(c_38,plain,
quotient(A,A,zero),
inference(paramod,[status(thm)],[c_37,c_8]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 15:59:20 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3307065 was started by sandbox2 on n020,
% 0.17/0.43 % Fri Sep 25 15:59:20 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.49 % Length of proof is 18.
% 0.17/0.49 % Level of proof is 9.
% 0.17/0.49 % Maximum clause weight is 23.000.
% 0.17/0.49 % Given clauses 26.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------