%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN004-5 : 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 : n026.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 07:31:58 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_smaller_than_numerator,axiom,
! [VAR_0,VAR_1] : divide(divide(VAR_0,VAR_1),VAR_0) = zero,
file('theBenchmark.p',quotient_smaller_than_numerator) ).
cnf(c_1,plain,
divide(divide(A,B),A) = zero,
inference(clausify,[status(thm)],[quotient_smaller_than_numerator]) ).
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(x_divide_x_is_zero,axiom,
! [VAR_0] : divide(VAR_0,VAR_0) = zero,
file('theBenchmark.p',x_divide_x_is_zero) ).
cnf(c_6,plain,
divide(A,A) = zero,
inference(clausify,[status(thm)],[x_divide_x_is_zero]) ).
fof(prove_x_divide_zero_is_x,axiom,
divide(a,zero) != a,
file('theBenchmark.p',prove_x_divide_zero_is_x) ).
cnf(c_7,plain,
divide(a,zero) != a,
inference(clausify,[status(thm)],[prove_x_divide_zero_is_x]) ).
cnf(c_13,plain,
divide(divide(divide(A,B),zero),divide(divide(A,zero),B)) = zero,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_38,plain,
( divide(A,B) = A
| divide(A,divide(A,B)) != zero ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_17,plain,
divide(a,divide(a,zero)) != zero,
inference(resolve,[status(thm)],[c_38,c_7]) ).
cnf(c_39,plain,
( A = zero
| divide(A,zero) != zero ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_24,plain,
divide(divide(a,divide(a,zero)),zero) != zero,
inference(resolve,[status(thm)],[c_39,c_17]) ).
cnf(c_40,plain,
( A = zero
| divide(A,zero) != zero ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_25,plain,
divide(divide(divide(a,divide(a,zero)),zero),zero) != zero,
inference(resolve,[status(thm)],[c_40,c_24]) ).
cnf(c_36,plain,
divide(divide(divide(A,divide(A,zero)),zero),zero) = zero,
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.35 % Computer : n026.cluster.edu
% 0.06/0.35 % Model : x86_64 x86_64
% 0.06/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.35 % Memory : 8046.5625MB
% 0.06/0.35 % OS : Linux 6.8.0-71-generic
% 0.06/0.35 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Fri Sep 25 15:58:57 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.36 % Process 2956405 was started by sandbox on n026,
% 0.06/0.36 % Fri Sep 25 15:58:57 2026
% 0.06/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.36
% 0.06/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.41
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.41
% 0.12/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.41 % Length of proof is 12.
% 0.12/0.41 % Level of proof is 4.
% 0.12/0.41 % Maximum clause weight is 45.000.
% 0.12/0.41 % Given clauses 15.
% 0.12/0.41
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------