%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN007-5 : 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 : n013.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 0.77s 0.58s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 31 unt; 0 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 48 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 93 ( 19 sgn 12 !; 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(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(transitivity_of_divide_to_zero,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(VAR_0,VAR_2) = zero
| divide(VAR_1,VAR_2) != zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',transitivity_of_divide_to_zero) ).
cnf(c_6,plain,
( divide(A,C) = zero
| divide(B,C) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[transitivity_of_divide_to_zero]) ).
fof(a_divide_b_is_zero,axiom,
divide(a,b) = zero,
file('theBenchmark.p',a_divide_b_is_zero) ).
cnf(c_7,plain,
divide(a,b) = zero,
inference(clausify,[status(thm)],[a_divide_b_is_zero]) ).
cnf(c_8,plain,
zero = divide(a,b),
inference(copy,[status(thm)],[c_7]) ).
fof(prove_property_of_divide2,axiom,
divide(divide(c,b),divide(c,a)) != zero,
file('theBenchmark.p',prove_property_of_divide2) ).
cnf(c_9,plain,
divide(divide(c,b),divide(c,a)) != zero,
inference(clausify,[status(thm)],[prove_property_of_divide2]) ).
cnf(c_10,plain,
divide(divide(c,b),divide(c,a)) != divide(a,b),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_265,plain,
( divide(A,C) = zero
| divide(B,C) != zero
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_266,plain,
( divide(A,C) = zero
| divide(B,C) != divide(a,b)
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_8,c_265]) ).
cnf(c_267,plain,
( divide(A,C) = divide(a,b)
| divide(B,C) != divide(a,b)
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_8,c_266]) ).
cnf(c_268,plain,
( divide(A,C) = divide(a,b)
| divide(B,C) != divide(a,b)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_269,plain,
( divide(A,C) = divide(a,b)
| divide(a,b) != divide(B,C)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_11,plain,
( divide(a,b) = divide(A,C)
| divide(a,b) != divide(B,C)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,plain,
divide(A,identity) = divide(a,b),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_12,plain,
divide(a,b) = divide(A,identity),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_272,plain,
( A = B
| divide(B,A) != divide(a,b)
| divide(A,B) != divide(a,b) ),
inference(paramod,[status(thm)],[c_8,c_271]) ).
cnf(c_273,plain,
( A = B
| divide(B,A) != divide(a,b)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_13,plain,
( A = B
| divide(a,b) != divide(B,A)
| divide(a,b) != divide(A,B) ),
inference(copy,[status(thm)],[c_273]) ).
cnf(c_274,plain,
divide(divide(a,b),A) = zero,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_14,plain,
divide(divide(a,b),A) = divide(a,b),
inference(paramod,[status(thm)],[c_8,c_274]) ).
cnf(c_15,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(a,b),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_16,plain,
divide(divide(A,B),A) = divide(a,b),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_32,plain,
divide(divide(A,identity),B) = divide(a,b),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_37,plain,
divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b)) = divide(a,b),
inference(paramod,[status(thm)],[c_12,c_15]) ).
cnf(c_275,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| divide(a,b) != divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C)))
| divide(a,b) != divide(a,b) ),
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_276,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) != divide(a,b)
| divide(a,b) != divide(a,b) ),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_40,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) != divide(a,b) ),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_277,plain,
divide(a,b) = divide(divide(A,B),A),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_278,plain,
( divide(a,b) = divide(A,B)
| divide(a,b) != divide(A,divide(B,C)) ),
inference(resolve,[status(thm)],[c_11,c_277]) ).
cnf(c_279,plain,
divide(a,b) != divide(divide(c,b),divide(c,a)),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_280,plain,
divide(a,b) != divide(divide(c,b),divide(divide(c,a),A)),
inference(resolve,[status(thm)],[c_278,c_279]) ).
cnf(c_47,plain,
divide(divide(c,b),divide(divide(c,a),A)) != divide(a,b),
inference(copy,[status(thm)],[c_280]) ).
cnf(c_281,plain,
( divide(divide(divide(A,b),divide(divide(A,a),b)),divide(divide(B,identity),divide(divide(A,a),b))) = divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b))
| divide(divide(a,b),divide(divide(divide(A,b),divide(divide(A,a),b)),divide(divide(B,identity),divide(divide(A,a),b)))) != divide(a,b) ),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_282,plain,
( divide(divide(divide(A,b),divide(divide(A,a),b)),divide(divide(B,identity),divide(divide(A,a),b))) = divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b))
| divide(divide(a,b),divide(divide(divide(A,b),divide(divide(A,a),b)),divide(a,b))) != divide(a,b) ),
inference(paramod,[status(thm)],[c_32,c_281]) ).
cnf(c_283,plain,
( divide(divide(divide(A,b),divide(divide(A,a),b)),divide(divide(B,identity),divide(divide(A,a),b))) = divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b))
| divide(a,b) != divide(a,b) ),
inference(paramod,[status(thm)],[c_14,c_282]) ).
cnf(c_284,plain,
( divide(divide(divide(A,b),divide(divide(A,a),b)),divide(a,b)) = divide(divide(divide(A,b),divide(B,identity)),divide(divide(A,a),b))
| divide(a,b) != divide(a,b) ),
inference(paramod,[status(thm)],[c_32,c_283]) ).
cnf(c_285,plain,
( divide(divide(divide(A,b),divide(divide(A,a),b)),divide(a,b)) = divide(a,b)
| divide(a,b) != divide(a,b) ),
inference(paramod,[status(thm)],[c_37,c_284]) ).
cnf(c_232,plain,
divide(divide(divide(A,b),divide(divide(A,a),b)),divide(a,b)) = divide(a,b),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_286,plain,
divide(a,b) = divide(divide(a,b),A),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_287,plain,
( A = divide(a,b)
| divide(a,b) != divide(A,divide(a,b)) ),
inference(resolve,[status(thm)],[c_13,c_286]) ).
cnf(c_288,plain,
divide(a,b) != divide(divide(divide(c,b),divide(divide(c,a),A)),divide(a,b)),
inference(resolve,[status(thm)],[c_287,c_47]) ).
cnf(c_263,plain,
divide(divide(divide(c,b),divide(divide(c,a),A)),divide(a,b)) != divide(a,b),
inference(copy,[status(thm)],[c_288]) ).
cnf(c_264,plain,
$false,
inference(resolve,[status(thm)],[c_263,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN007-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 15:56:21 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 783962 was started by sandbox2 on n013,
% 0.18/0.44 % Fri Sep 25 15:56:21 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.77/0.58
% 0.77/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.77/0.58
% 0.77/0.58 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.77/0.58 % Length of proof is 23.
% 0.77/0.58 % Level of proof is 5.
% 0.77/0.58 % Maximum clause weight is 90.000.
% 0.77/0.58 % Given clauses 66.
% 0.77/0.58
% 0.77/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------