%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN006-5 : 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 : n018.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 07:31:59 AM UTC 2026
% Result : Unsatisfiable 1.02s 0.62s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 33 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 14 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_zero_is_x,axiom,
! [VAR_0] : divide(VAR_0,zero) = VAR_0,
file('theBenchmark.p',x_divide_zero_is_x) ).
cnf(c_6,plain,
divide(A,zero) = A,
inference(clausify,[status(thm)],[x_divide_zero_is_x]) ).
fof(a_divide_b_divide_d_is_zero,axiom,
divide(divide(a,b),d) = zero,
file('theBenchmark.p',a_divide_b_divide_d_is_zero) ).
cnf(c_7,plain,
divide(divide(a,b),d) = zero,
inference(clausify,[status(thm)],[a_divide_b_divide_d_is_zero]) ).
cnf(c_8,plain,
zero = divide(divide(a,b),d),
inference(copy,[status(thm)],[c_7]) ).
fof(prove_property_of_divide1,axiom,
divide(divide(a,d),b) != zero,
file('theBenchmark.p',prove_property_of_divide1) ).
cnf(c_9,plain,
divide(divide(a,d),b) != zero,
inference(clausify,[status(thm)],[prove_property_of_divide1]) ).
cnf(c_10,plain,
divide(divide(a,d),b) != divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_11,plain,
divide(A,divide(divide(a,b),d)) = A,
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_267,plain,
( A = B
| divide(B,A) != zero
| divide(A,B) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_268,plain,
( A = B
| divide(B,A) != divide(divide(a,b),d)
| divide(A,B) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_8,c_267]) ).
cnf(c_269,plain,
( A = B
| divide(B,A) != divide(divide(a,b),d)
| divide(divide(a,b),d) != divide(A,B) ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_13,plain,
( A = B
| divide(divide(a,b),d) != divide(B,A)
| divide(divide(a,b),d) != divide(A,B) ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,plain,
divide(divide(divide(a,b),d),A) = zero,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_14,plain,
divide(divide(divide(a,b),d),A) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_8,c_270]) ).
cnf(c_15,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_271,plain,
divide(divide(A,B),A) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_16,plain,
divide(divide(a,b),d) = divide(divide(A,B),A),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_272,plain,
divide(divide(a,b),d) = divide(divide(divide(a,b),d),A),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_273,plain,
( divide(divide(a,b),d) = A
| divide(divide(a,b),d) != divide(A,divide(divide(a,b),d)) ),
inference(resolve,[status(thm)],[c_13,c_272]) ).
cnf(c_274,plain,
divide(divide(a,b),d) = divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_275,plain,
divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)),
inference(resolve,[status(thm)],[c_273,c_274]) ).
cnf(c_25,plain,
divide(divide(a,d),divide(b,d)) = divide(divide(a,b),d),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_276,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| divide(divide(a,b),d) != divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C)))
| divide(divide(a,b),d) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_277,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(divide(a,b),d)
| divide(divide(a,b),d) != divide(divide(a,b),d) ),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_31,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(divide(a,b),d) ),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_37,plain,
divide(A,divide(divide(B,C),B)) = A,
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_278,plain,
divide(divide(divide(divide(A,B),C),divide(A,C)),divide(divide(divide(a,b),d),C)) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_279,plain,
divide(divide(divide(divide(A,B),C),divide(A,C)),divide(divide(a,b),d)) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_14,c_278]) ).
cnf(c_46,plain,
divide(divide(divide(A,B),C),divide(A,C)) = divide(divide(a,b),d),
inference(paramod,[status(thm)],[c_11,c_279]) ).
cnf(c_280,plain,
( divide(divide(A,B),divide(divide(B,C),B)) = divide(divide(A,divide(B,C)),B)
| divide(divide(divide(A,divide(B,C)),B),divide(divide(A,B),divide(divide(a,b),d))) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_16,c_31]) ).
cnf(c_281,plain,
( divide(divide(A,B),divide(divide(B,C),B)) = divide(divide(A,divide(B,C)),B)
| divide(divide(divide(A,divide(B,C)),B),divide(A,B)) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_11,c_280]) ).
cnf(c_282,plain,
( divide(divide(A,B),divide(divide(B,C),B)) = divide(divide(A,divide(B,C)),B)
| divide(divide(a,b),d) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_46,c_281]) ).
cnf(c_283,plain,
( divide(A,B) = divide(divide(A,divide(B,C)),B)
| divide(divide(a,b),d) != divide(divide(a,b),d) ),
inference(paramod,[status(thm)],[c_37,c_282]) ).
cnf(c_284,plain,
( divide(divide(A,divide(B,C)),B) = divide(A,B)
| divide(divide(a,b),d) != divide(divide(a,b),d) ),
inference(copy,[status(thm)],[c_283]) ).
cnf(c_211,plain,
divide(divide(A,divide(B,C)),B) = divide(A,B),
inference(copy,[status(thm)],[c_284]) ).
cnf(c_285,plain,
divide(divide(divide(a,b),d),b) = divide(divide(a,d),b),
inference(paramod,[status(thm)],[c_25,c_211]) ).
cnf(c_286,plain,
divide(divide(a,b),d) = divide(divide(a,d),b),
inference(paramod,[status(thm)],[c_14,c_285]) ).
cnf(c_265,plain,
divide(divide(a,d),b) = divide(divide(a,b),d),
inference(copy,[status(thm)],[c_286]) ).
cnf(c_266,plain,
$false,
inference(resolve,[status(thm)],[c_265,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN006-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 15:58:50 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 2368379 was started by sandbox2 on n018,
% 0.17/0.43 % Fri Sep 25 15:58:50 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).
% 1.02/0.62
% 1.02/0.62 % SZS status Unsatisfiable for theBenchmark
% 1.02/0.62
% 1.02/0.62 % Proof 1 at 0.11 (+ 0.07) seconds.
% 1.02/0.62 % Length of proof is 21.
% 1.02/0.62 % Level of proof is 6.
% 1.02/0.62 % Maximum clause weight is 32.000.
% 1.02/0.62 % Given clauses 64.
% 1.02/0.62
% 1.02/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------