%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN011-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:32:04 AM UTC 2026
% Result : Unsatisfiable 1.10s 0.61s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 49 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 33 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 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 : 164 ( 15 sgn 20 !; 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(x_divide_zero_is_x,axiom,
! [VAR_0] : divide(VAR_0,zero) = VAR_0,
file('theBenchmark.p',x_divide_zero_is_x) ).
cnf(c_7,plain,
divide(A,zero) = A,
inference(clausify,[status(thm)],[x_divide_zero_is_x]) ).
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_8,plain,
( divide(A,C) = zero
| divide(B,C) != zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[transitivity_of_divide_to_zero]) ).
fof(property_of_divide1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(divide(VAR_0,VAR_2),VAR_1) = zero
| divide(divide(VAR_0,VAR_1),VAR_2) != zero ),
file('theBenchmark.p',property_of_divide1) ).
cnf(c_9,plain,
( divide(divide(A,C),B) = zero
| divide(divide(A,B),C) != zero ),
inference(clausify,[status(thm)],[property_of_divide1]) ).
fof(property_of_divide2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divide(divide(VAR_2,VAR_1),divide(VAR_2,VAR_0)) = zero
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',property_of_divide2) ).
cnf(c_10,plain,
( divide(divide(C,B),divide(C,A)) = zero
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[property_of_divide2]) ).
fof(one_inversion_equals_three,axiom,
! [VAR_0] : divide(identity,divide(identity,divide(identity,VAR_0))) = divide(identity,VAR_0),
file('theBenchmark.p',one_inversion_equals_three) ).
cnf(c_12,plain,
divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
inference(clausify,[status(thm)],[one_inversion_equals_three]) ).
fof(prove_this,axiom,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_this) ).
cnf(c_14,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_15,plain,
divide(divide(identity,b),divide(identity,divide(identity,a))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_505,plain,
divide(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)) = zero,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_16,plain,
divide(divide(A,B),divide(divide(A,divide(B,C)),B)) = zero,
inference(paramod,[status(thm)],[c_7,c_505]) ).
cnf(c_506,plain,
divide(divide(divide(divide(A,B),C),divide(A,C)),divide(zero,C)) = zero,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_507,plain,
divide(divide(divide(divide(A,B),C),divide(A,C)),zero) = zero,
inference(paramod,[status(thm)],[c_3,c_506]) ).
cnf(c_17,plain,
divide(divide(divide(A,B),C),divide(A,C)) = zero,
inference(paramod,[status(thm)],[c_7,c_507]) ).
cnf(c_508,plain,
divide(divide(divide(divide(divide(A,B),divide(C,B)),D),divide(divide(divide(A,C),B),D)),divide(zero,D)) = zero,
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_509,plain,
divide(divide(divide(divide(divide(A,B),divide(C,B)),D),divide(divide(divide(A,C),B),D)),zero) = zero,
inference(paramod,[status(thm)],[c_3,c_508]) ).
cnf(c_18,plain,
divide(divide(divide(divide(A,B),divide(C,B)),D),divide(divide(divide(A,C),B),D)) = zero,
inference(paramod,[status(thm)],[c_7,c_509]) ).
cnf(c_510,plain,
divide(divide(divide(divide(A,B),divide(divide(A,C),B)),divide(divide(C,B),divide(divide(A,C),B))),zero) = zero,
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_19,plain,
divide(divide(divide(A,B),divide(divide(A,C),B)),divide(divide(C,B),divide(divide(A,C),B))) = zero,
inference(paramod,[status(thm)],[c_7,c_510]) ).
cnf(c_20,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))) != zero ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_21,plain,
( divide(A,B) = A
| divide(A,divide(A,B)) != zero ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_511,plain,
( divide(divide(A,C),B) = zero
| divide(A,B) != zero ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_35,plain,
divide(divide(divide(A,B),C),A) = zero,
inference(resolve,[status(thm)],[c_511,c_1]) ).
cnf(c_37,plain,
divide(divide(A,divide(A,B)),B) = zero,
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_40,plain,
divide(divide(A,B),divide(A,divide(B,C))) = zero,
inference(resolve,[status(thm)],[c_10,c_1]) ).
cnf(c_512,plain,
( divide(divide(A,divide(B,C)),B) = divide(A,B)
| divide(divide(divide(A,divide(B,C)),B),divide(A,B)) != zero ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_513,plain,
( divide(divide(A,divide(B,C)),B) = divide(A,B)
| zero != zero ),
inference(paramod,[status(thm)],[c_17,c_512]) ).
cnf(c_60,plain,
divide(divide(A,divide(B,C)),B) = divide(A,B),
inference(copy,[status(thm)],[c_513]) ).
cnf(c_514,plain,
( divide(divide(A,C),B) = divide(A,B)
| divide(divide(A,B),divide(divide(A,C),B)) != zero ),
inference(resolve,[status(thm)],[c_4,c_17]) ).
cnf(c_515,plain,
divide(divide(divide(A,B),B),divide(divide(A,divide(A,B)),B)) = divide(divide(A,B),divide(divide(A,divide(A,B)),B)),
inference(resolve,[status(thm)],[c_514,c_19]) ).
cnf(c_516,plain,
divide(divide(divide(A,B),B),zero) = divide(divide(A,B),divide(divide(A,divide(A,B)),B)),
inference(paramod,[status(thm)],[c_37,c_515]) ).
cnf(c_517,plain,
divide(divide(A,B),B) = divide(divide(A,B),divide(divide(A,divide(A,B)),B)),
inference(paramod,[status(thm)],[c_7,c_516]) ).
cnf(c_518,plain,
divide(divide(A,B),B) = divide(divide(A,B),zero),
inference(paramod,[status(thm)],[c_37,c_517]) ).
cnf(c_154,plain,
divide(divide(A,B),B) = divide(A,B),
inference(paramod,[status(thm)],[c_7,c_518]) ).
cnf(c_192,plain,
divide(divide(divide(A,B),C),divide(divide(divide(A,C),B),C)) = zero,
inference(paramod,[status(thm)],[c_60,c_18]) ).
cnf(c_193,plain,
divide(divide(divide(A,B),C),divide(A,divide(B,D))) = zero,
inference(paramod,[status(thm)],[c_60,c_35]) ).
cnf(c_519,plain,
( divide(divide(divide(A,B),B),divide(C,B)) = divide(divide(divide(A,B),C),B)
| divide(divide(divide(divide(A,B),C),B),divide(divide(A,B),divide(C,B))) != zero ),
inference(paramod,[status(thm)],[c_154,c_20]) ).
cnf(c_520,plain,
( divide(divide(divide(A,B),B),divide(C,B)) = divide(divide(divide(A,B),C),B)
| zero != zero ),
inference(paramod,[status(thm)],[c_193,c_519]) ).
cnf(c_521,plain,
( divide(divide(A,B),divide(C,B)) = divide(divide(divide(A,B),C),B)
| zero != zero ),
inference(paramod,[status(thm)],[c_154,c_520]) ).
cnf(c_522,plain,
( divide(divide(divide(A,B),C),B) = divide(divide(A,B),divide(C,B))
| zero != zero ),
inference(copy,[status(thm)],[c_521]) ).
cnf(c_205,plain,
divide(divide(divide(A,B),C),B) = divide(divide(A,B),divide(C,B)),
inference(copy,[status(thm)],[c_522]) ).
cnf(c_207,plain,
divide(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) = zero,
inference(paramod,[status(thm)],[c_205,c_192]) ).
cnf(c_523,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| zero != zero ),
inference(paramod,[status(thm)],[c_207,c_20]) ).
cnf(c_209,plain,
divide(divide(A,B),divide(C,B)) = divide(divide(A,C),B),
inference(copy,[status(thm)],[c_523]) ).
cnf(c_210,plain,
divide(divide(divide(A,B),C),B) = divide(divide(A,C),B),
inference(paramod,[status(thm)],[c_209,c_205]) ).
cnf(c_302,plain,
divide(divide(divide(A,B),C),divide(divide(A,C),B)) = zero,
inference(paramod,[status(thm)],[c_209,c_40]) ).
cnf(c_524,plain,
( divide(divide(divide(A,B),C),B) = divide(divide(A,B),C)
| divide(divide(divide(A,B),C),divide(divide(A,C),B)) != zero ),
inference(paramod,[status(thm)],[c_210,c_21]) ).
cnf(c_525,plain,
( divide(divide(divide(A,B),C),B) = divide(divide(A,B),C)
| zero != zero ),
inference(paramod,[status(thm)],[c_302,c_524]) ).
cnf(c_526,plain,
( divide(divide(A,C),B) = divide(divide(A,B),C)
| zero != zero ),
inference(paramod,[status(thm)],[c_210,c_525]) ).
cnf(c_443,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(copy,[status(thm)],[c_526]) ).
cnf(c_527,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),divide(identity,divide(identity,A))),
inference(paramod,[status(thm)],[c_12,c_443]) ).
cnf(c_503,plain,
divide(divide(identity,A),divide(identity,divide(identity,B))) = divide(divide(identity,B),A),
inference(copy,[status(thm)],[c_527]) ).
cnf(c_528,plain,
divide(divide(identity,divide(identity,divide(identity,a))),b) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(paramod,[status(thm)],[c_443,c_15]) ).
cnf(c_529,plain,
divide(divide(identity,a),b) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(paramod,[status(thm)],[c_12,c_528]) ).
cnf(c_530,plain,
divide(divide(identity,a),b) != divide(divide(identity,b),a),
inference(paramod,[status(thm)],[c_503,c_529]) ).
cnf(c_531,plain,
divide(divide(identity,a),b) != divide(divide(identity,a),b),
inference(paramod,[status(thm)],[c_443,c_530]) ).
cnf(c_504,plain,
$false,
inference(copy,[status(thm)],[c_531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN011-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 15:57:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3884423 was started by sandbox2 on n005,
% 0.08/0.35 % Fri Sep 25 15:57:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 1.10/0.61
% 1.10/0.61 % SZS status Unsatisfiable for theBenchmark
% 1.10/0.61
% 1.10/0.61 % Proof 1 at 0.16 (+ 0.07) seconds.
% 1.10/0.61 % Length of proof is 33.
% 1.10/0.61 % Level of proof is 10.
% 1.10/0.61 % Maximum clause weight is 88.000.
% 1.10/0.61 % Given clauses 91.
% 1.10/0.61
% 1.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------