%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN007-3 : 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 : 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 07:32:00 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.59s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 84 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal1,axiom,
! [VAR_0,VAR_1] :
( divide(VAR_0,VAR_1) = zero
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal1) ).
cnf(c_1,plain,
( divide(A,B) = zero
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal1]) ).
fof(quotient_less_equal2,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| divide(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',quotient_less_equal2) ).
cnf(c_2,plain,
( less_equal(A,B)
| divide(A,B) != zero ),
inference(clausify,[status(thm)],[quotient_less_equal2]) ).
fof(quotient_smaller_than_numerator,axiom,
! [VAR_0,VAR_1] : less_equal(divide(VAR_0,VAR_1),VAR_0),
file('theBenchmark.p',quotient_smaller_than_numerator) ).
cnf(c_3,plain,
less_equal(divide(A,B),A),
inference(clausify,[status(thm)],[quotient_smaller_than_numerator]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2] : less_equal(divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1)),divide(divide(VAR_0,VAR_2),VAR_1)),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
inference(clausify,[status(thm)],[quotient_property]) ).
fof(zero_is_smallest,axiom,
! [VAR_0] : less_equal(zero,VAR_0),
file('theBenchmark.p',zero_is_smallest) ).
cnf(c_5,plain,
less_equal(zero,A),
inference(clausify,[status(thm)],[zero_is_smallest]) ).
fof(less_equal_and_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ less_equal(VAR_1,VAR_0)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',less_equal_and_equal) ).
cnf(c_6,plain,
( A = B
| ~ less_equal(B,A)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[less_equal_and_equal]) ).
fof(a_LE_b,axiom,
less_equal(a,b),
file('theBenchmark.p',a_LE_b) ).
cnf(c_8,plain,
less_equal(a,b),
inference(clausify,[status(thm)],[a_LE_b]) ).
fof(prove_c_divide_b_LE_c_divide_a,axiom,
~ less_equal(divide(c,b),divide(c,a)),
file('theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
cnf(c_9,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(clausify,[status(thm)],[prove_c_divide_b_LE_c_divide_a]) ).
cnf(c_10,plain,
divide(divide(A,B),A) = zero,
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_12,plain,
divide(zero,A) = zero,
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_14,plain,
( divide(divide(A,C),divide(B,C)) = divide(divide(A,B),C)
| ~ less_equal(divide(divide(A,B),C),divide(divide(A,C),divide(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_15,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_19,plain,
divide(a,b) = zero,
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_23,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_28,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_215,plain,
( divide(divide(A,B),A) = divide(A,B)
| ~ less_equal(divide(A,B),zero) ),
inference(paramod,[status(thm)],[c_10,c_15]) ).
cnf(c_216,plain,
( zero = divide(A,B)
| ~ less_equal(divide(A,B),zero) ),
inference(paramod,[status(thm)],[c_10,c_215]) ).
cnf(c_48,plain,
( divide(A,B) = zero
| ~ less_equal(divide(A,B),zero) ),
inference(copy,[status(thm)],[c_216]) ).
cnf(c_51,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramod,[status(thm)],[c_10,c_23]) ).
cnf(c_52,plain,
divide(divide(A,A),zero) = zero,
inference(resolve,[status(thm)],[c_51,c_48]) ).
cnf(c_53,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_52,c_2]) ).
cnf(c_217,plain,
( divide(divide(A,A),zero) = divide(A,A)
| ~ less_equal(divide(A,A),zero) ),
inference(paramod,[status(thm)],[c_52,c_15]) ).
cnf(c_218,plain,
( zero = divide(A,A)
| ~ less_equal(divide(A,A),zero) ),
inference(paramod,[status(thm)],[c_52,c_217]) ).
cnf(c_219,plain,
( divide(A,A) = zero
| ~ less_equal(divide(A,A),zero) ),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_58,plain,
divide(A,A) = zero,
inference(resolve,[status(thm)],[c_53,c_219]) ).
cnf(c_220,plain,
( divide(divide(divide(B,C),A),divide(B,A)) = divide(divide(divide(B,C),B),A)
| ~ less_equal(divide(zero,A),divide(divide(divide(B,C),A),divide(B,A))) ),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_221,plain,
( divide(divide(divide(B,C),A),divide(B,A)) = divide(divide(divide(B,C),B),A)
| ~ less_equal(zero,divide(divide(divide(B,C),A),divide(B,A))) ),
inference(paramod,[status(thm)],[c_12,c_220]) ).
cnf(c_222,plain,
( divide(divide(divide(B,C),A),divide(B,A)) = divide(zero,A)
| ~ less_equal(zero,divide(divide(divide(B,C),A),divide(B,A))) ),
inference(paramod,[status(thm)],[c_10,c_221]) ).
cnf(c_223,plain,
( divide(divide(divide(B,C),A),divide(B,A)) = zero
| ~ less_equal(zero,divide(divide(divide(B,C),A),divide(B,A))) ),
inference(paramod,[status(thm)],[c_12,c_222]) ).
cnf(c_59,plain,
divide(divide(divide(A,B),C),divide(A,C)) = zero,
inference(resolve,[status(thm)],[c_5,c_223]) ).
cnf(c_224,plain,
( divide(divide(A,b),divide(a,b)) = divide(divide(A,a),b)
| ~ less_equal(divide(divide(A,a),b),divide(divide(A,b),zero)) ),
inference(paramod,[status(thm)],[c_19,c_14]) ).
cnf(c_64,plain,
( divide(divide(A,b),zero) = divide(divide(A,a),b)
| ~ less_equal(divide(divide(A,a),b),divide(divide(A,b),zero)) ),
inference(paramod,[status(thm)],[c_19,c_224]) ).
cnf(c_100,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramod,[status(thm)],[c_58,c_28]) ).
cnf(c_109,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(resolve,[status(thm)],[c_100,c_48]) ).
cnf(c_140,plain,
less_equal(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_109,c_2]) ).
cnf(c_225,plain,
( divide(divide(A,divide(A,zero)),zero) = divide(A,divide(A,zero))
| ~ less_equal(divide(A,divide(A,zero)),zero) ),
inference(paramod,[status(thm)],[c_109,c_15]) ).
cnf(c_226,plain,
( zero = divide(A,divide(A,zero))
| ~ less_equal(divide(A,divide(A,zero)),zero) ),
inference(paramod,[status(thm)],[c_109,c_225]) ).
cnf(c_227,plain,
( divide(A,divide(A,zero)) = zero
| ~ less_equal(divide(A,divide(A,zero)),zero) ),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_145,plain,
divide(A,divide(A,zero)) = zero,
inference(resolve,[status(thm)],[c_140,c_227]) ).
cnf(c_146,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_145,c_2]) ).
cnf(c_163,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_146,c_15]) ).
cnf(c_228,plain,
( divide(divide(A,b),zero) = divide(divide(A,a),b)
| ~ less_equal(divide(divide(A,a),b),divide(A,b)) ),
inference(paramod,[status(thm)],[c_163,c_64]) ).
cnf(c_229,plain,
( divide(A,b) = divide(divide(A,a),b)
| ~ less_equal(divide(divide(A,a),b),divide(A,b)) ),
inference(paramod,[status(thm)],[c_163,c_228]) ).
cnf(c_180,plain,
( divide(divide(A,a),b) = divide(A,b)
| ~ less_equal(divide(divide(A,a),b),divide(A,b)) ),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_187,plain,
less_equal(divide(divide(A,B),C),divide(A,C)),
inference(resolve,[status(thm)],[c_59,c_2]) ).
cnf(c_201,plain,
divide(divide(A,a),b) = divide(A,b),
inference(resolve,[status(thm)],[c_187,c_180]) ).
cnf(c_213,plain,
less_equal(divide(A,b),divide(A,a)),
inference(paramod,[status(thm)],[c_201,c_3]) ).
cnf(c_214,plain,
$false,
inference(resolve,[status(thm)],[c_213,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n018.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Fri Sep 25 15:59:06 UTC 2026
% 0.08/0.55 % CPUTime :
% 0.08/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.55 % Process 2369145 was started by sandbox on n018,
% 0.08/0.55 % Fri Sep 25 15:59:06 2026
% 0.08/0.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.55
% 0.08/0.55 % From the command line: assign(max_seconds, 300).
% 0.12/0.59
% 0.12/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.59
% 0.12/0.59 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.59 % Length of proof is 33.
% 0.12/0.59 % Level of proof is 16.
% 0.12/0.59 % Maximum clause weight is 71.000.
% 0.12/0.59 % Given clauses 69.
% 0.12/0.59
% 0.12/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------