%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN008-5 : 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 : n008.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 07:32:01 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.62s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 24 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 10 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1)),divide(divide(VAR_0,VAR_2),VAR_1)) = zero,
file('theBenchmark.p',quotient_property) ).
cnf(c_2,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : divide(zero,VAR_0) = zero,
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_3,plain,
divide(zero,A) = zero,
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(divide_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| divide(VAR_1,VAR_0) != zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',divide_and_equal) ).
cnf(c_4,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[divide_and_equal]) ).
fof(identity_is_largest,axiom,
! [VAR_0] : divide(VAR_0,identity) = zero,
file('theBenchmark.p',identity_is_largest) ).
cnf(c_5,plain,
divide(A,identity) = zero,
inference(clausify,[status(thm)],[identity_is_largest]) ).
fof(a_divide_b_is_zero,axiom,
divide(a,b) = zero,
file('theBenchmark.p',a_divide_b_is_zero) ).
cnf(c_6,plain,
divide(a,b) = zero,
inference(clausify,[status(thm)],[a_divide_b_is_zero]) ).
cnf(c_7,plain,
zero = divide(a,b),
inference(copy,[status(thm)],[c_6]) ).
fof(prove_property_of_divide3,axiom,
divide(divide(a,c),divide(b,c)) != zero,
file('theBenchmark.p',prove_property_of_divide3) ).
cnf(c_8,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(clausify,[status(thm)],[prove_property_of_divide3]) ).
cnf(c_9,plain,
divide(divide(a,c),divide(b,c)) != divide(a,b),
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_27,plain,
divide(A,identity) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_10,plain,
divide(a,b) = divide(A,identity),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_28,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_29,plain,
( A = B
| divide(B,A) != divide(a,b)
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_7,c_28]) ).
cnf(c_30,plain,
( A = B
| divide(B,A) != divide(a,b)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_11,plain,
( A = B
| divide(a,b) != divide(B,A)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_31,plain,
divide(divide(a,b),A) = zero,
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_12,plain,
divide(divide(a,b),A) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_31]) ).
cnf(c_13,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(a,b),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_32,plain,
divide(a,b) = divide(divide(a,b),A),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_33,plain,
( A = divide(a,b)
| divide(a,b) != divide(A,divide(a,b)) ),
inference(resolve,[status(thm)],[c_11,c_32]) ).
cnf(c_34,plain,
divide(a,b) != divide(divide(divide(a,c),divide(b,c)),divide(a,b)),
inference(resolve,[status(thm)],[c_33,c_9]) ).
cnf(c_21,plain,
divide(divide(divide(a,c),divide(b,c)),divide(a,b)) != divide(a,b),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_22,plain,
divide(divide(A,identity),B) = divide(a,b),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_35,plain,
divide(divide(divide(a,A),divide(b,A)),divide(divide(B,identity),A)) = divide(a,b),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_25,plain,
divide(divide(divide(a,A),divide(b,A)),divide(a,b)) = divide(a,b),
inference(paramod,[status(thm)],[c_22,c_35]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.59 % Computer : n008.cluster.edu
% 0.13/5.59 % Model : x86_64 x86_64
% 0.13/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.59 % Memory : 8046.5625MB
% 0.13/5.59 % OS : Linux 6.8.0-71-generic
% 0.13/5.59 % CPULimit : 300
% 0.13/5.59 % WCLimit : 300
% 0.13/5.59 % DateTime : Fri Sep 25 15:58:15 UTC 2026
% 0.15/5.60 % CPUTime :
% 0.15/5.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.60 % Process 1418767 was started by sandbox on n008,
% 0.15/5.60 % Fri Sep 25 15:58:15 2026
% 0.15/5.60 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.60
% 0.15/5.60 % From the command line: assign(max_seconds, 300).
% 0.15/5.62
% 0.15/5.62 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.62
% 0.15/5.62 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.62 % Length of proof is 16.
% 0.15/5.62 % Level of proof is 5.
% 0.15/5.62 % Maximum clause weight is 17.000.
% 0.15/5.62 % Given clauses 6.
% 0.15/5.62
% 0.15/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------