%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN004-2 : 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 : n001.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 07:31:57 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.43s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 23 unt; 0 def)
% Number of atoms : 69 ( 10 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 64 ( 33 ~; 31 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_divide_x_is_zero,axiom,
! [VAR_0] : quotient(VAR_0,VAR_0,zero),
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(c_12,plain,
quotient(A,A,zero),
inference(clausify,[status(thm)],[x_divide_x_is_zero]) ).
fof(prove_x_divde_zero_is_x,axiom,
~ quotient(x,zero,x),
file('theBenchmark.p',prove_x_divde_zero_is_x) ).
cnf(c_13,plain,
~ quotient(x,zero,x),
inference(clausify,[status(thm)],[prove_x_divde_zero_is_x]) ).
cnf(c_15,plain,
less_equal(divide(A,B),A),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_71,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_72,plain,
( less_equal(D,E)
| ~ quotient(divide(A,zero),B,E)
| ~ quotient(C,zero,D)
| ~ quotient(A,B,C) ),
inference(resolve,[status(thm)],[c_71,c_11]) ).
cnf(c_73,plain,
( less_equal(C,D)
| ~ quotient(divide(A,zero),B,D)
| ~ quotient(divide(A,B),zero,C) ),
inference(resolve,[status(thm)],[c_72,c_8]) ).
cnf(c_74,plain,
( less_equal(divide(divide(A,B),zero),C)
| ~ quotient(divide(A,zero),B,C) ),
inference(resolve,[status(thm)],[c_73,c_8]) ).
cnf(c_22,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(resolve,[status(thm)],[c_74,c_12]) ).
cnf(c_75,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_76,plain,
zero = divide(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_75,c_22]) ).
cnf(c_40,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(copy,[status(thm)],[c_76]) ).
cnf(c_44,plain,
quotient(divide(A,divide(A,zero)),zero,zero),
inference(paramod,[status(thm)],[c_40,c_8]) ).
cnf(c_47,plain,
less_equal(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_2,c_44]) ).
cnf(c_77,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_78,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_77,c_47]) ).
cnf(c_48,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_78]) ).
cnf(c_49,plain,
quotient(A,divide(A,zero),zero),
inference(paramod,[status(thm)],[c_48,c_8]) ).
cnf(c_61,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_49]) ).
cnf(c_79,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_15]) ).
cnf(c_63,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_79,c_61]) ).
cnf(c_69,plain,
quotient(A,zero,A),
inference(paramod,[status(thm)],[c_63,c_8]) ).
cnf(c_70,plain,
$false,
inference(resolve,[status(thm)],[c_69,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 16:01:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3759790 was started by sandbox on n001,
% 0.08/0.36 % Fri Sep 25 16:01:41 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).
% 0.08/0.43
% 0.08/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.43
% 0.08/0.43 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.08/0.43 % Length of proof is 20.
% 0.08/0.43 % Level of proof is 10.
% 0.08/0.43 % Maximum clause weight is 25.000.
% 0.08/0.43 % Given clauses 39.
% 0.08/0.43
% 0.08/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------