%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN010-3 : 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 : n016.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 07:32:02 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 56 unt; 0 def)
% Number of atoms : 90 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 21 sgn 13 !; 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(identity_is_largest,axiom,
! [VAR_0] : less_equal(VAR_0,identity),
file('theBenchmark.p',identity_is_largest) ).
cnf(c_7,plain,
less_equal(A,identity),
inference(clausify,[status(thm)],[identity_is_largest]) ).
fof(prove_property_of_inversion,axiom,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('theBenchmark.p',prove_property_of_inversion) ).
cnf(c_8,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(clausify,[status(thm)],[prove_property_of_inversion]) ).
cnf(c_9,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(copy,[status(thm)],[c_8]) ).
cnf(c_10,plain,
divide(divide(A,B),A) = zero,
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
divide(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) = zero,
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
divide(zero,A) = zero,
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_13,plain,
divide(A,identity) = zero,
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_210,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_14,plain,
~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(resolve,[status(thm)],[c_210,c_9]) ).
cnf(c_15,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,divide(B,C)),B)),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_211,plain,
less_equal(divide(divide(divide(A,B),C),divide(A,C)),divide(zero,C)),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_16,plain,
less_equal(divide(divide(divide(A,B),C),divide(A,C)),zero),
inference(paramod,[status(thm)],[c_12,c_211]) ).
cnf(c_17,plain,
less_equal(divide(divide(A,A),divide(B,A)),zero),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_22,plain,
less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)),
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_212,plain,
less_equal(divide(divide(A,B),divide(identity,B)),divide(zero,B)),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_23,plain,
less_equal(divide(divide(A,B),divide(identity,B)),zero),
inference(paramod,[status(thm)],[c_12,c_212]) ).
cnf(c_25,plain,
less_equal(divide(divide(A,A),zero),zero),
inference(paramod,[status(thm)],[c_10,c_17]) ).
cnf(c_213,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_214,plain,
zero = divide(divide(A,A),zero),
inference(resolve,[status(thm)],[c_213,c_25]) ).
cnf(c_26,plain,
divide(divide(A,A),zero) = zero,
inference(copy,[status(thm)],[c_214]) ).
cnf(c_27,plain,
less_equal(divide(A,A),zero),
inference(resolve,[status(thm)],[c_2,c_26]) ).
cnf(c_215,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_216,plain,
zero = divide(A,A),
inference(resolve,[status(thm)],[c_215,c_27]) ).
cnf(c_30,plain,
divide(A,A) = zero,
inference(copy,[status(thm)],[c_216]) ).
cnf(c_217,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_218,plain,
zero = divide(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_217,c_23]) ).
cnf(c_50,plain,
divide(divide(A,B),divide(identity,B)) = zero,
inference(copy,[status(thm)],[c_218]) ).
cnf(c_51,plain,
less_equal(divide(A,B),divide(identity,B)),
inference(resolve,[status(thm)],[c_2,c_50]) ).
cnf(c_58,plain,
less_equal(divide(divide(A,divide(A,zero)),zero),zero),
inference(paramod,[status(thm)],[c_30,c_22]) ).
cnf(c_219,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_220,plain,
zero = divide(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_219,c_58]) ).
cnf(c_66,plain,
divide(divide(A,divide(A,zero)),zero) = zero,
inference(copy,[status(thm)],[c_220]) ).
cnf(c_68,plain,
less_equal(divide(A,divide(A,zero)),zero),
inference(resolve,[status(thm)],[c_2,c_66]) ).
cnf(c_221,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_222,plain,
zero = divide(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_221,c_68]) ).
cnf(c_73,plain,
divide(A,divide(A,zero)) = zero,
inference(copy,[status(thm)],[c_222]) ).
cnf(c_74,plain,
less_equal(A,divide(A,zero)),
inference(resolve,[status(thm)],[c_2,c_73]) ).
cnf(c_80,plain,
divide(divide(divide(A,divide(divide(A,B),zero)),divide(B,divide(divide(A,B),zero))),zero) = zero,
inference(paramod,[status(thm)],[c_73,c_11]) ).
cnf(c_223,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_224,plain,
zero = divide(divide(divide(A,B),C),divide(A,C)),
inference(resolve,[status(thm)],[c_223,c_16]) ).
cnf(c_83,plain,
divide(divide(divide(A,B),C),divide(A,C)) = zero,
inference(copy,[status(thm)],[c_224]) ).
cnf(c_225,plain,
( divide(A,B) = A
| ~ less_equal(A,divide(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_89,plain,
divide(A,zero) = A,
inference(resolve,[status(thm)],[c_225,c_74]) ).
cnf(c_226,plain,
divide(divide(divide(A,divide(A,B)),divide(B,divide(divide(A,B),zero))),zero) = zero,
inference(paramod,[status(thm)],[c_89,c_80]) ).
cnf(c_227,plain,
divide(divide(divide(A,divide(A,B)),divide(B,divide(A,B))),zero) = zero,
inference(paramod,[status(thm)],[c_89,c_226]) ).
cnf(c_92,plain,
divide(divide(A,divide(A,B)),divide(B,divide(A,B))) = zero,
inference(paramod,[status(thm)],[c_89,c_227]) ).
cnf(c_106,plain,
less_equal(divide(A,B),divide(divide(A,divide(B,C)),B)),
inference(paramod,[status(thm)],[c_89,c_15]) ).
cnf(c_119,plain,
less_equal(divide(divide(A,B),C),divide(A,C)),
inference(resolve,[status(thm)],[c_2,c_83]) ).
cnf(c_228,plain,
( divide(divide(A,C),B) = divide(A,B)
| ~ less_equal(divide(A,B),divide(divide(A,C),B)) ),
inference(resolve,[status(thm)],[c_6,c_119]) ).
cnf(c_130,plain,
divide(divide(A,divide(B,C)),B) = divide(A,B),
inference(resolve,[status(thm)],[c_228,c_106]) ).
cnf(c_131,plain,
less_equal(divide(A,B),divide(A,divide(B,C))),
inference(paramod,[status(thm)],[c_130,c_3]) ).
cnf(c_154,plain,
less_equal(divide(A,divide(A,B)),divide(B,divide(A,B))),
inference(resolve,[status(thm)],[c_2,c_92]) ).
cnf(c_229,plain,
( divide(B,A) = divide(identity,A)
| ~ less_equal(divide(identity,A),divide(B,A)) ),
inference(resolve,[status(thm)],[c_6,c_51]) ).
cnf(c_230,plain,
divide(A,divide(identity,A)) = divide(identity,divide(identity,A)),
inference(resolve,[status(thm)],[c_229,c_154]) ).
cnf(c_167,plain,
divide(identity,divide(identity,A)) = divide(A,divide(identity,A)),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_171,plain,
~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),
inference(paramod,[status(thm)],[c_167,c_14]) ).
cnf(c_208,plain,
less_equal(divide(A,B),divide(A,divide(identity,divide(identity,B)))),
inference(paramod,[status(thm)],[c_167,c_131]) ).
cnf(c_209,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 16:02:29 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 2810811 was started by sandbox2 on n016,
% 0.08/0.35 % Fri Sep 25 16:02:29 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.47
% 0.13/0.47 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.13/0.47 % Length of proof is 43.
% 0.13/0.47 % Level of proof is 17.
% 0.13/0.47 % Maximum clause weight is 63.000.
% 0.13/0.47 % Given clauses 62.
% 0.13/0.47
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------