%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HEN008-1 : 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 : n002.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 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 20 unt; 0 def)
% Number of atoms : 62 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quotient_less_equal,axiom,
! [VAR_0,VAR_1] :
( quotient(VAR_0,VAR_1,zero)
| ~ less_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',quotient_less_equal) ).
cnf(c_1,plain,
( quotient(A,B,zero)
| ~ less_equal(A,B) ),
inference(clausify,[status(thm)],[quotient_less_equal]) ).
fof(less_equal_quotient,axiom,
! [VAR_0,VAR_1] :
( less_equal(VAR_0,VAR_1)
| ~ quotient(VAR_0,VAR_1,zero) ),
file('theBenchmark.p',less_equal_quotient) ).
cnf(c_2,plain,
( less_equal(A,B)
| ~ quotient(A,B,zero) ),
inference(clausify,[status(thm)],[less_equal_quotient]) ).
fof(quotient_property,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( less_equal(VAR_6,VAR_7)
| ~ quotient(VAR_2,VAR_3,VAR_7)
| ~ quotient(VAR_5,VAR_4,VAR_6)
| ~ quotient(VAR_0,VAR_3,VAR_5)
| ~ quotient(VAR_1,VAR_3,VAR_4)
| ~ quotient(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',quotient_property) ).
cnf(c_4,plain,
( less_equal(V6,V7)
| ~ quotient(C,D,V7)
| ~ quotient(F,E,V6)
| ~ quotient(A,D,F)
| ~ quotient(B,D,E)
| ~ quotient(A,B,C) ),
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(closure,axiom,
! [VAR_0,VAR_1] : quotient(VAR_0,VAR_1,divide(VAR_0,VAR_1)),
file('theBenchmark.p',closure) ).
cnf(c_8,plain,
quotient(A,B,divide(A,B)),
inference(clausify,[status(thm)],[closure]) ).
fof(aLEb,axiom,
less_equal(a,b),
file('theBenchmark.p',aLEb) ).
cnf(c_10,plain,
less_equal(a,b),
inference(clausify,[status(thm)],[aLEb]) ).
fof(aQc,axiom,
quotient(a,c,aQc),
file('theBenchmark.p',aQc) ).
cnf(c_11,plain,
quotient(a,c,aQc),
inference(clausify,[status(thm)],[aQc]) ).
fof(bQc,axiom,
quotient(b,c,bQc),
file('theBenchmark.p',bQc) ).
cnf(c_12,plain,
quotient(b,c,bQc),
inference(clausify,[status(thm)],[bQc]) ).
fof(prove_aQcLEbQc,axiom,
~ less_equal(aQc,bQc),
file('theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_13,plain,
~ less_equal(aQc,bQc),
inference(clausify,[status(thm)],[prove_aQcLEbQc]) ).
cnf(c_14,plain,
quotient(zero,A,zero),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_18,plain,
quotient(a,b,zero),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_36,plain,
~ quotient(aQc,bQc,zero),
inference(resolve,[status(thm)],[c_2,c_13]) ).
cnf(c_72,plain,
( less_equal(D,E)
| ~ quotient(zero,A,E)
| ~ quotient(C,B,D)
| ~ quotient(a,A,C)
| ~ quotient(b,A,B) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_73,plain,
( less_equal(B,C)
| ~ quotient(zero,c,C)
| ~ quotient(A,bQc,B)
| ~ quotient(a,c,A) ),
inference(resolve,[status(thm)],[c_72,c_12]) ).
cnf(c_74,plain,
( less_equal(A,B)
| ~ quotient(zero,c,B)
| ~ quotient(aQc,bQc,A) ),
inference(resolve,[status(thm)],[c_73,c_11]) ).
cnf(c_75,plain,
( less_equal(divide(aQc,bQc),A)
| ~ quotient(zero,c,A) ),
inference(resolve,[status(thm)],[c_74,c_8]) ).
cnf(c_50,plain,
less_equal(divide(aQc,bQc),zero),
inference(resolve,[status(thm)],[c_75,c_14]) ).
cnf(c_76,plain,
( zero = A
| ~ less_equal(A,zero) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_77,plain,
zero = divide(aQc,bQc),
inference(resolve,[status(thm)],[c_76,c_50]) ).
cnf(c_66,plain,
divide(aQc,bQc) = zero,
inference(copy,[status(thm)],[c_77]) ).
cnf(c_70,plain,
quotient(aQc,bQc,zero),
inference(paramod,[status(thm)],[c_66,c_8]) ).
cnf(c_71,plain,
$false,
inference(resolve,[status(thm)],[c_70,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:59:50 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3704742 was started by sandbox2 on n002,
% 0.16/0.43 % Fri Sep 25 15:59:50 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.47 % Length of proof is 17.
% 0.16/0.47 % Level of proof is 5.
% 0.16/0.47 % Maximum clause weight is 28.000.
% 0.16/0.47 % Given clauses 38.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------